Файловый менеджер - Редактировать - /var/www/html/mediawiki-1.43.1/extensions/Math/tests/phpunit/unit/WikiTexVC/data/reference.json
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[ { "input": "e^{i \\pi} + 1 = 0\\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>", "skipped": false }, { "input": "e^{i \\pi} + 1 = 0\\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>", "skipped": false }, { "input": "\\definecolor{red}{RGB}{255,0,0}\\pagecolor{red}e^{i \\pi} + 1 = 0\\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>", "skipped": false }, { "input": "\\sqrt{\\pi}", "params": { "alt": "Square root of pi" }, "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mi>π<\/mi><\/msqrt><\/mrow><\/math>" }, { "input": "\\sqrt{\\pi}", "params": { "alt": "square root of pi" }, "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mi>π<\/mi><\/msqrt><\/mrow><\/math>" }, { "input": "\\pi", "params": { "title": "pi" }, "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>π<\/mi><\/math>" }, { "input": "\\pi", "params": { "title": "pi" }, "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>π<\/mi><\/math>" }, { "input": "\\text{abc}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>abc<\/mtext><\/mrow><\/math>" }, { "input": "\\alpha\\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>α<\/mi><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": " f(x) = x^2\\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\sqrt{2}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/math>" }, { "input": "\\sqrt{1-e^2}\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><mo stretchy=\"false\">−<\/mo><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/msqrt><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\sqrt{1-z^3}\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><mo stretchy=\"false\">−<\/mo><msup><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/msqrt><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "x", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>" }, { "input": "\\dot{a}, \\ddot{a}, \\acute{a}, \\grave{a} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>\u02d9<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>\u00a8<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo data-mjx-pseudoscript=\"true\">\u00b4<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo data-mjx-pseudoscript=\"true\">`<\/mo><\/mover><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\check{a}, \\breve{a}, \\tilde{a}, \\bar{a} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>\u02c7<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>\u02d8<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>~<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>\u00af<\/mo><\/mover><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\hat{a}, \\widehat{a}, \\vec{a} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>^<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo stretchy=\"true\">^<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>\u2192<\/mo><\/mover><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\exp_a b = a^b, \\exp b = e^b, 10^m \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>exp<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><\/msub><mi>b<\/mi><mo stretchy=\"false\">=<\/mo><msup><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/msup><mo>,<\/mo><mi>exp<\/mi><mo>⁡<\/mo><mi>b<\/mi><mo stretchy=\"false\">=<\/mo><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/msup><mo>,<\/mo><mn>1<\/mn><msup><mn>0<\/mn><mrow data-mjx-texclass=\"ORD\"><mi>m<\/mi><\/mrow><\/msup><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\ln c, \\lg d = \\log e, \\log_{10} f \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>ln<\/mi><mo>⁡<\/mo><mi>c<\/mi><mo>,<\/mo><mi>lg<\/mi><mo>⁡<\/mo><mi>d<\/mi><mo stretchy=\"false\">=<\/mo><mi>log<\/mi><mo>⁡<\/mo><mi>e<\/mi><mo>,<\/mo><msub><mi>log<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><mn>0<\/mn><\/mrow><\/mrow><\/msub><mi>f<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>", "skipped": false }, { "input": "\\sin a, \\cos b, \\tan c, \\cot d, \\sec e, \\csc f\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sin<\/mi><mo>⁡<\/mo><mi>a<\/mi><mo>,<\/mo><mi>cos<\/mi><mo>⁡<\/mo><mi>b<\/mi><mo>,<\/mo><mi>tan<\/mi><mo>⁡<\/mo><mi>c<\/mi><mo>,<\/mo><mi>cot<\/mi><mo>⁡<\/mo><mi>d<\/mi><mo>,<\/mo><mi>sec<\/mi><mo>⁡<\/mo><mi>e<\/mi><mo>,<\/mo><mi>csc<\/mi><mo>⁡<\/mo><mi>f<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\arcsin h, \\arccos i, \\arctan j \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>arcsin<\/mi><mo>⁡<\/mo><mi>h<\/mi><mo>,<\/mo><mi>arccos<\/mi><mo>⁡<\/mo><mi>i<\/mi><mo>,<\/mo><mi>arctan<\/mi><mo>⁡<\/mo><mi>j<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\sinh k, \\cosh l, \\tanh m, \\coth n \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sinh<\/mi><mo>⁡<\/mo><mi>k<\/mi><mo>,<\/mo><mi>cosh<\/mi><mo>⁡<\/mo><mi>l<\/mi><mo>,<\/mo><mi>tanh<\/mi><mo>⁡<\/mo><mi>m<\/mi><mo>,<\/mo><mi>coth<\/mi><mo>⁡<\/mo><mi>n<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\operatorname{sh}\\,k, \\operatorname{ch}\\,l, \\operatorname{th}\\,m, \\operatorname{coth}\\,n \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sh<\/mi><mo>⁡<\/mo><mspace width=\"0.167em\"><\/mspace><mi>k<\/mi><mo>,<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">ch<\/mi><mo>⁡<\/mo><mspace width=\"0.167em\"><\/mspace><mi>l<\/mi><mo>,<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">th<\/mi><mo>⁡<\/mo><mspace width=\"0.167em\"><\/mspace><mi>m<\/mi><mo>,<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">coth<\/mi><mo>⁡<\/mo><mspace width=\"0.167em\"><\/mspace><mi>n<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\operatorname{argsh}\\,o, \\operatorname{argch}\\,p, \\operatorname{argth}\\,q \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">argsh<\/mi><mo>⁡<\/mo><mspace width=\"0.167em\"><\/mspace><mi>o<\/mi><mo>,<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">argch<\/mi><mo>⁡<\/mo><mspace width=\"0.167em\"><\/mspace><mi>p<\/mi><mo>,<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">argth<\/mi><mo>⁡<\/mo><mspace width=\"0.167em\"><\/mspace><mi>q<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\sgn r, \\left\\vert s \\right\\vert \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sgn<\/mi><mo>⁡<\/mo><mi>r<\/mi><mo>,<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">|<\/mo><mi>s<\/mi><mo data-mjx-texclass=\"CLOSE\">|<\/mo><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\min(x,y), \\max(x,y) \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>min<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo>,<\/mo><mi>max<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\min x, \\max y, \\inf s, \\sup t \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>min<\/mi><mo>⁡<\/mo><mi>x<\/mi><mo>,<\/mo><mi>max<\/mi><mo>⁡<\/mo><mi>y<\/mi><mo>,<\/mo><mi>inf<\/mi><mo>⁡<\/mo><mi>s<\/mi><mo>,<\/mo><mi>sup<\/mi><mo>⁡<\/mo><mi>t<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\lim u, \\liminf v, \\limsup w \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>lim<\/mi><mo>⁡<\/mo><mi>u<\/mi><mo>,<\/mo><mi>lim inf<\/mi><mo>⁡<\/mo><mi>v<\/mi><mo>,<\/mo><mi>lim sup<\/mi><mo>⁡<\/mo><mi>w<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\dim p, \\deg q, \\det m, \\ker\\phi \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>dim<\/mi><mo>⁡<\/mo><mi>p<\/mi><mo>,<\/mo><mi>deg<\/mi><mo>⁡<\/mo><mi>q<\/mi><mo>,<\/mo><mi>det<\/mi><mo>⁡<\/mo><mi>m<\/mi><mo>,<\/mo><mi>ker<\/mi><mo>⁡<\/mo><mi>ϕ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Pr j, \\hom l, \\lVert z \\rVert, \\arg z \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>Pr<\/mi><mo>⁡<\/mo><mi>j<\/mi><mo>,<\/mo><mi>hom<\/mi><mo>⁡<\/mo><mi>l<\/mi><mo>,<\/mo><mo stretchy=\"false\">‖<\/mo><mi>z<\/mi><mo stretchy=\"false\">‖<\/mo><mo>,<\/mo><mi>arg<\/mi><mo>⁡<\/mo><mi>z<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "dt, \\operatorname{d}\\!t, \\partial t, \\nabla\\psi\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>d<\/mi><mi>t<\/mi><mo>,<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">d<\/mi><mo>⁡<\/mo><mspace width=\"-0.167em\"><\/mspace><mi>t<\/mi><mo>,<\/mo><mi>∂<\/mi><mi>t<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">∇<\/mi><mi>ψ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "dy\/dx, \\operatorname{d}\\!y\/\\operatorname{d}\\!x, {dy \\over dx}, {\\operatorname{d}\\!y\\over\\operatorname{d}\\!x}, {\\partial^2\\over\\partial x_1\\partial x_2}y \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>d<\/mi><mi>y<\/mi><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mi>d<\/mi><mi>x<\/mi><mo>,<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">d<\/mi><mo>⁡<\/mo><mspace width=\"-0.167em\"><\/mspace><mi>y<\/mi><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">d<\/mi><mo>⁡<\/mo><mspace width=\"-0.167em\"><\/mspace><mi>x<\/mi><mo>,<\/mo><mfrac><mrow><mi>d<\/mi><mi>y<\/mi><\/mrow><mrow><mi>d<\/mi><mi>x<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mfrac><mrow><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">d<\/mi><mo>⁡<\/mo><mspace width=\"-0.167em\"><\/mspace><mi>y<\/mi><\/mrow><mrow><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">d<\/mi><mo>⁡<\/mo><mspace width=\"-0.167em\"><\/mspace><mi>x<\/mi><\/mrow><\/mfrac><mo>,<\/mo><mfrac><mrow><msup><mi>∂<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>∂<\/mi><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><mi>∂<\/mi><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><mi>y<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>", "skipped": false, "comment": "skipped too long and malformatted output" }, { "input": "\\prime, \\backprime, f^\\prime, f', f'', f^{(3)} \\!, \\dot y, \\ddot y", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi alternate=\"1\">′<\/mi><mo>,<\/mo><mi variantform=\"True\">‵<\/mi><mo>,<\/mo><msup><mi>f<\/mi><mrow data-mjx-texclass=\"ORD\"><mi alternate=\"1\">′<\/mi><\/mrow><\/msup><mo>,<\/mo><msup><mi>f<\/mi><mo>′<\/mo><\/msup><mo>,<\/mo><msup><mi>f<\/mi><mo>″<\/mo><\/msup><mo>,<\/mo><msup><mi>f<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/mrow><\/msup><mspace width=\"-0.167em\"><\/mspace><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>y<\/mi><mo>\u02d9<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>y<\/mi><mo>\u00a8<\/mo><\/mover><\/mrow><\/mrow><\/math>", "skipped": false, "comment": "f' and f' not recognized by texVC as uq" }, { "input": "\\infty, \\aleph, \\complement, \\backepsilon, \\eth, \\Finv, \\hbar \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">∞<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">ℵ<\/mi><mo>,<\/mo><mi>∁<\/mi><mo>,<\/mo><mo stretchy=\"false\">∍<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">ð<\/mi><mo>,<\/mo><mi>Ⅎ<\/mi><mo>,<\/mo><mi alternate=\"1\">ℏ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Im, \\imath, \\jmath, \\Bbbk, \\ell, \\mho, \\wp, \\Re, \\circledS \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">ℑ<\/mi><mo>,<\/mo><mi>ı<\/mi><mo>,<\/mo><mi>ȷ<\/mi><mo>,<\/mo><mi mathvariant=\"double-struck\">k<\/mi><mo>,<\/mo><mi>ℓ<\/mi><mo>,<\/mo><mi>℧<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">℘<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">ℜ<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">Ⓢ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "s_k \\equiv 0 \\pmod{m} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>s<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><\/mrow><\/msub><mo stretchy=\"false\">≡<\/mo><mn>0<\/mn><mrow data-mjx-texclass=\"ORD\"><mspace width=\"0.444em\"><\/mspace><mo stretchy=\"false\">(<\/mo><mi>mod<\/mi><mspace width=\"0.333em\"><\/mspace><mi>m<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "a\\,\\bmod\\,b \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mspace width=\"0.167em\"><\/mspace><mrow data-mjx-texclass=\"ORD\"><mo lspace=\"0.27777777777778em\" rspace=\"0.27777777777778em\">mod<\/mo><mrow data-mjx-texclass=\"ORD\"><mspace width=\"0.167em\"><\/mspace><\/mrow><mrow data-mjx-texclass=\"ORD\"><mspace width=\"0.167em\"\/><\/mrow><\/mrow><mi>b<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>", "skipped": false, "comemnt": "implement macros later tbd" }, { "input": "\\gcd(m, n), \\operatorname{lcm}(m, n)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>gcd<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>m<\/mi><mo>,<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><mo>,<\/mo><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">lcm<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>m<\/mi><mo>,<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><\/math>" }, { "input": "\\mid, \\nmid, \\shortmid, \\nshortmid \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∣<\/mo><mo>,<\/mo><mo stretchy=\"false\">∤<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">∣<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">∤<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>", "skipped": false, "comment": "These are ams mappings, import AmsMappings.js for parsing these" }, { "input": "\\sqrt[3]{x^3+y^3 \\over 2} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mroot><mfrac><mrow><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><msup><mi>y<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><\/mrow><\/mfrac><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/mroot><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\surd, \\sqrt{2}, \\sqrt[n]{}, \\sqrt[3]{x^3+y^3 \\over 2} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">√<\/mo><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mroot><mrow data-mjx-texclass=\"ORD\"\/><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/mroot><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mroot><mfrac><mrow><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><msup><mi>y<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><\/mrow><mrow><mn>2<\/mn><\/mrow><\/mfrac><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/mroot><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>", "skipped": false, "comment": "skipping this testcase because mathjax output seems to be flawed with mrow element here, previous testcase is enough for validation of infix\/over" }, { "input": "+, -, \\pm, \\mp, \\dotplus \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">+<\/mo><mo>,<\/mo><mo stretchy=\"false\">−<\/mo><mo>,<\/mo><mo stretchy=\"false\">±<\/mo><mo>,<\/mo><mo stretchy=\"false\">∓<\/mo><mo>,<\/mo><mo stretchy=\"false\">∔<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\times, \\div, \\divideontimes, \/, \\backslash \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">×<\/mo><mo>,<\/mo><mo stretchy=\"false\">÷<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋇<\/mo><mo>,<\/mo><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">∖<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\cdot, * \\ast, \\star, \\circ, \\bullet \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⋅<\/mo><mo>,<\/mo><mo stretchy=\"false\">*<\/mo><mo stretchy=\"false\">∗<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋆<\/mo><mo>,<\/mo><mo stretchy=\"false\">∘<\/mo><mo>,<\/mo><mo stretchy=\"false\">∙<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boxplus, \\boxminus, \\boxtimes, \\boxdot \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊞<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊟<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊠<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊡<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\oplus, \\ominus, \\otimes, \\oslash, \\odot\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊕<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊖<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊗<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊘<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊙<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\circleddash, \\circledcirc, \\circledast \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊝<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊚<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊛<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\bigoplus, \\bigotimes, \\bigodot \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⨁<\/mo><mo>,<\/mo><mo stretchy=\"false\">⨂<\/mo><mo>,<\/mo><mo stretchy=\"false\">⨀<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\{ \\}, \\O \\empty \\emptyset, \\varnothing \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo fence=\"false\" stretchy=\"false\">{<\/mo><mo fence=\"false\" stretchy=\"false\">}<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">∅<\/mi><mi mathvariant=\"normal\">∅<\/mi><mi mathvariant=\"normal\">∅<\/mi><mo>,<\/mo><mi variantform=\"True\">∅<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\in, \\notin \\not\\in, \\ni, \\not\\ni \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∈<\/mo><mo>,<\/mo><mo stretchy=\"false\">∉<\/mo><mo stretchy=\"false\">∉<\/mo><mo>,<\/mo><mo stretchy=\"false\">∋<\/mo><mo>,<\/mo><mo stretchy=\"false\">∌<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\cap, \\Cap, \\sqcap, \\bigcap \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∩<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋒<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊓<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋂<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\cup, \\Cup, \\sqcup, \\bigcup, \\bigsqcup, \\uplus, \\biguplus \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∪<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋓<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊔<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋃<\/mo><mo>,<\/mo><mo stretchy=\"false\">⨆<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊎<\/mo><mo>,<\/mo><mo stretchy=\"false\">⨄<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\setminus, \\smallsetminus, \\times \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∖<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"True\">∖<\/mo><mo>,<\/mo><mo stretchy=\"false\">×<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\subset, \\Subset, \\sqsubset \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊂<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋐<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊏<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\supset, \\Supset, \\sqsupset \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊃<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋑<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊐<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\subseteq, \\nsubseteq, \\subsetneq, \\varsubsetneq, \\sqsubseteq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊆<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊈<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊊<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⊊<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊑<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\supseteq, \\nsupseteq, \\supsetneq, \\varsupsetneq, \\sqsupseteq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊇<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊉<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊋<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⊋<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊒<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\subseteqq, \\nsubseteqq, \\subsetneqq, \\varsubsetneqq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⫅<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⊈<\/mo><mo>,<\/mo><mo stretchy=\"false\">⫋<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⫋<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\supseteqq, \\nsupseteqq, \\supsetneqq, \\varsupsetneqq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⫆<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⊉<\/mo><mo>,<\/mo><mo stretchy=\"false\">⫌<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⫌<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "=, \\ne, \\neq, \\equiv, \\not\\equiv \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">=<\/mo><mo>,<\/mo><mo stretchy=\"false\">≠<\/mo><mo>,<\/mo><mo stretchy=\"false\">≠<\/mo><mo>,<\/mo><mo stretchy=\"false\">≡<\/mo><mo>,<\/mo><mo stretchy=\"false\">≢<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\doteq, \\doteqdot, \\overset{\\underset{\\mathrm{def}}{}}{=}, := \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≐<\/mo><mo>,<\/mo><mo stretchy=\"false\">≑<\/mo><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mover><mrow><mo stretchy=\"false\">=<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">f<\/mi><\/mrow><\/mrow><\/mrow><\/mover><\/mrow><mo>,<\/mo><mo stretchy=\"false\">:<\/mo><mo stretchy=\"false\">=<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\sim, \\nsim, \\backsim, \\thicksim, \\simeq, \\backsimeq, \\eqsim, \\cong, \\ncong \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∼<\/mo><mo>,<\/mo><mo stretchy=\"false\">≁<\/mo><mo>,<\/mo><mo stretchy=\"false\">∽<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"True\">∼<\/mo><mo>,<\/mo><mo stretchy=\"false\">≃<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋍<\/mo><mo>,<\/mo><mo stretchy=\"false\">≂<\/mo><mo>,<\/mo><mo stretchy=\"false\">≅<\/mo><mo>,<\/mo><mo stretchy=\"false\">≆<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\approx, \\thickapprox, \\approxeq, \\asymp, \\propto, \\varpropto \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≈<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"True\">≈<\/mo><mo>,<\/mo><mo stretchy=\"false\">≊<\/mo><mo>,<\/mo><mo stretchy=\"false\">≍<\/mo><mo>,<\/mo><mo stretchy=\"false\">∝<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">∝<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "<, \\nless, \\ll, \\not\\ll, \\lll, \\not\\lll, \\lessdot \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo><<\/mo><mo>,<\/mo><mo stretchy=\"false\">≮<\/mo><mo>,<\/mo><mo stretchy=\"false\">≪<\/mo><mo>,<\/mo><mo stretchy=\"false\">≪̸<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋘<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋘̸<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋖<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": ">, \\ngtr, \\gg, \\not\\gg, \\ggg, \\not\\ggg, \\gtrdot \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>><\/mo><mo>,<\/mo><mo stretchy=\"false\">≯<\/mo><mo>,<\/mo><mo stretchy=\"false\">≫<\/mo><mo>,<\/mo><mo stretchy=\"false\">≫̸<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋙<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋙̸<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋗<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\le \\leq, \\lneq, \\leqq, \\nleqq, \\lneqq, \\lvertneqq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≤<\/mo><mo stretchy=\"false\">≤<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪇<\/mo><mo>,<\/mo><mo stretchy=\"false\">≦<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">≰<\/mo><mo>,<\/mo><mo stretchy=\"false\">≨<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">≨<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\ge \\geq, \\gneq, \\geqq, \\ngeqq, \\gneqq, \\gvertneqq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≥<\/mo><mo stretchy=\"false\">≥<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪈<\/mo><mo>,<\/mo><mo stretchy=\"false\">≧<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">≱<\/mo><mo>,<\/mo><mo stretchy=\"false\">≩<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">≩<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\lessgtr \\lesseqgtr \\lesseqqgtr \\gtrless \\gtreqless \\gtreqqless \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≶<\/mo><mo stretchy=\"false\">⋚<\/mo><mo stretchy=\"false\">⪋<\/mo><mo stretchy=\"false\">≷<\/mo><mo stretchy=\"false\">⋛<\/mo><mo stretchy=\"false\">⪌<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\leqslant, \\nleqslant, \\eqslantless \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⩽<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⪇<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪕<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\geqslant, \\ngeqslant, \\eqslantgtr \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⩾<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⪈<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪖<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\lesssim, \\lnsim, \\lessapprox, \\lnapprox \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≲<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋦<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪅<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪉<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": " \\gtrsim, \\gnsim, \\gtrapprox, \\gnapprox \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≳<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋧<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪆<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪊<\/mo><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\prec, \\nprec, \\preceq, \\npreceq, \\precneqq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≺<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊀<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪯<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⋠<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪵<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\succ, \\nsucc, \\succeq, \\nsucceq, \\succneqq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≻<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊁<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪰<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⋡<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪶<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\preccurlyeq, \\curlyeqprec \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≼<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋞<\/mo><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\succcurlyeq, \\curlyeqsucc \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≽<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋟<\/mo><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\precsim, \\precnsim, \\precapprox, \\precnapprox \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≾<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋨<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪷<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪹<\/mo><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\succsim, \\succnsim, \\succapprox, \\succnapprox \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≿<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋩<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪸<\/mo><mo>,<\/mo><mo stretchy=\"false\">⪺<\/mo><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\parallel, \\nparallel, \\shortparallel, \\nshortparallel \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∥<\/mo><mo>,<\/mo><mo stretchy=\"false\">∦<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">∥<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">∦<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\perp, \\angle, \\sphericalangle, \\measuredangle, 45^\\circ \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊥<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">∠<\/mi><mo>,<\/mo><mi>∢<\/mi><mo>,<\/mo><mi>∡<\/mi><mo>,<\/mo><mn>4<\/mn><msup><mn>5<\/mn><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">∘<\/mo><\/mrow><\/msup><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Box, \\blacksquare, \\diamond, \\Diamond \\lozenge, \\blacklozenge, \\bigstar \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>◻<\/mi><mo>,<\/mo><mi>◼<\/mi><mo>,<\/mo><mo stretchy=\"false\">⋄<\/mo><mo>,<\/mo><mi>◊<\/mi><mi>◊<\/mi><mo>,<\/mo><mi>⧫<\/mi><mo>,<\/mo><mi>★<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\bigcirc, \\triangle \\bigtriangleup, \\bigtriangledown \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">◯<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">△<\/mi><mo stretchy=\"false\">△<\/mo><mo>,<\/mo><mo stretchy=\"false\">▽<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\vartriangle, \\triangledown\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\" variantform=\"1\">△<\/mo><mo>,<\/mo><mi variantform=\"True\">▽<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\blacktriangle, \\blacktriangledown, \\blacktriangleleft, \\blacktriangleright \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>▴<\/mi><mo>,<\/mo><mi>▾<\/mi><mo>,<\/mo><mo stretchy=\"false\">◂<\/mo><mo>,<\/mo><mo stretchy=\"false\">▸<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\forall, \\exists, \\nexists \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">∀<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">∃<\/mi><mo>,<\/mo><mi>∄<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\therefore, \\because, \\And \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∴<\/mo><mo>,<\/mo><mo stretchy=\"false\">∵<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">&<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\or \\lor \\vee, \\curlyvee, \\bigvee \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∨<\/mo><mo stretchy=\"false\">∨<\/mo><mo stretchy=\"false\">∨<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋎<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋁<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\and \\land \\wedge, \\curlywedge, \\bigwedge \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∧<\/mo><mo stretchy=\"false\">∧<\/mo><mo stretchy=\"false\">∧<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋏<\/mo><mo>,<\/mo><mo stretchy=\"false\">⋀<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\bar{q}, \\bar{abc}, \\overline{q}, \\overline{abc}, \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>q<\/mi><mo>\u00af<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>b<\/mi><mi>c<\/mi><\/mrow><mo>\u00af<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mover><mi>q<\/mi><mo>‾<\/mo><\/mover><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mover><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>b<\/mi><mi>c<\/mi><\/mrow><mo>‾<\/mo><\/mover><\/mrow><mo>,<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\lnot \\neg, \\not\\operatorname{R}, \\bot, \\top \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">¬<\/mi><mi mathvariant=\"normal\">¬<\/mi><mo>,<\/mo><mrow data-mjx-texclass=\"REL\"><mpadded width=\"0\"><mtext>⧸<\/mtext><\/mpadded><\/mrow><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">R<\/mi><mo>⁡<\/mo><mo>,<\/mo><mi mathvariant=\"normal\">⊥<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">⊤<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\vdash \\dashv, \\vDash, \\Vdash, \\models \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊢<\/mo><mo stretchy=\"false\">⊣<\/mo><mo>,<\/mo><mo stretchy=\"false\" variantform=\"1\">⊨<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊩<\/mo><mo>,<\/mo><mo stretchy=\"false\">⊨<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Vvdash \\nvdash \\nVdash \\nvDash \\nVDash \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊪<\/mo><mo stretchy=\"false\">⊬<\/mo><mo stretchy=\"false\">⊮<\/mo><mo stretchy=\"false\">⊭<\/mo><mo stretchy=\"false\">⊯<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\ulcorner \\urcorner \\llcorner \\lrcorner \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⌜<\/mo><mo stretchy=\"false\">⌝<\/mo><mo stretchy=\"false\">⌞<\/mo><mo stretchy=\"false\">⌟<\/mo><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\Rrightarrow, \\Lleftarrow \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⇛<\/mo><mo>,<\/mo><mo stretchy=\"false\">⇚<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Rightarrow, \\nRightarrow, \\Longrightarrow \\implies\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⇒<\/mo><mo>,<\/mo><mo stretchy=\"false\">⇏<\/mo><mo>,<\/mo><mo stretchy=\"false\">⟹<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"0.278em\"\/><\/mstyle><mo>⟹<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"0.278em\"\/><\/mstyle><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Leftarrow, \\nLeftarrow, \\Longleftarrow \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⇐<\/mo><mo>,<\/mo><mo stretchy=\"false\">⇍<\/mo><mo>,<\/mo><mo stretchy=\"false\">⟸<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Leftrightarrow, \\nLeftrightarrow, \\Longleftrightarrow \\iff \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⇔<\/mo><mo>,<\/mo><mo stretchy=\"false\">⇎<\/mo><mo>,<\/mo><mo stretchy=\"false\">⟺<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"0.278em\"\/><\/mstyle><mo>⟺<\/mo><mstyle scriptlevel=\"0\"><mspace width=\"0.278em\"\/><\/mstyle><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Uparrow, \\Downarrow, \\Updownarrow \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⇑<\/mo><mo>,<\/mo><mo stretchy=\"false\">⇓<\/mo><mo>,<\/mo><mo stretchy=\"false\">⇕<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\rightarrow \\to, \\nrightarrow, \\longrightarrow\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">→<\/mo><mo stretchy=\"false\" accent=\"false\">→<\/mo><mo>,<\/mo><mo stretchy=\"false\">↛<\/mo><mo>,<\/mo><mo stretchy=\"false\">⟶<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\leftarrow \\gets, \\nleftarrow, \\longleftarrow\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">←<\/mo><mo stretchy=\"false\">←<\/mo><mo>,<\/mo><mo stretchy=\"false\">↚<\/mo><mo>,<\/mo><mo stretchy=\"false\">⟵<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\leftrightarrow, \\nleftrightarrow, \\longleftrightarrow \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">↔<\/mo><mo>,<\/mo><mo stretchy=\"false\">↮<\/mo><mo>,<\/mo><mo stretchy=\"false\">⟷<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\uparrow, \\downarrow, \\updownarrow \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">↑<\/mo><mo>,<\/mo><mo stretchy=\"false\">↓<\/mo><mo>,<\/mo><mo stretchy=\"false\">↕<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\nearrow, \\swarrow, \\nwarrow, \\searrow \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">↗<\/mo><mo>,<\/mo><mo stretchy=\"false\">↙<\/mo><mo>,<\/mo><mo stretchy=\"false\">↖<\/mo><mo>,<\/mo><mo stretchy=\"false\">↘<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mapsto, \\longmapsto \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">↦<\/mo><mo>,<\/mo><mo stretchy=\"false\">⟼<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\rightharpoonup \\rightharpoondown \\leftharpoonup \\leftharpoondown \\upharpoonleft \\upharpoonright \\downharpoonleft \\downharpoonright \\rightleftharpoons \\leftrightharpoons \\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⇀<\/mo><mo stretchy=\"false\">⇁<\/mo><mo stretchy=\"false\">↼<\/mo><mo stretchy=\"false\">↽<\/mo><mo stretchy=\"false\">↿<\/mo><mo stretchy=\"false\">↾<\/mo><mo stretchy=\"false\">⇃<\/mo><mo stretchy=\"false\">⇂<\/mo><mo stretchy=\"false\">⇌<\/mo><mo stretchy=\"false\">⇋<\/mo><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\curvearrowleft \\circlearrowleft \\Lsh \\upuparrows \\rightrightarrows \\rightleftarrows \\rightarrowtail \\looparrowright \\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">↶<\/mo><mo stretchy=\"false\">↺<\/mo><mo stretchy=\"false\">↰<\/mo><mo stretchy=\"false\">⇈<\/mo><mo stretchy=\"false\">⇉<\/mo><mo stretchy=\"false\">⇄<\/mo><mo stretchy=\"false\">↣<\/mo><mo stretchy=\"false\">↬<\/mo><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\curvearrowright \\circlearrowright \\Rsh \\downdownarrows \\leftleftarrows \\leftrightarrows \\leftarrowtail \\looparrowleft \\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">↷<\/mo><mo stretchy=\"false\">↻<\/mo><mo stretchy=\"false\">↱<\/mo><mo stretchy=\"false\">⇊<\/mo><mo stretchy=\"false\">⇇<\/mo><mo stretchy=\"false\">⇆<\/mo><mo stretchy=\"false\">↢<\/mo><mo stretchy=\"false\">↫<\/mo><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\hookrightarrow \\hookleftarrow \\multimap \\leftrightsquigarrow \\rightsquigarrow \\twoheadrightarrow \\twoheadleftarrow \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">↪<\/mo><mo stretchy=\"false\">↩<\/mo><mo stretchy=\"false\">⊸<\/mo><mo stretchy=\"false\">↭<\/mo><mo stretchy=\"false\">⇝<\/mo><mo stretchy=\"false\">↠<\/mo><mo stretchy=\"false\">↞<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\amalg \\P \\S \\% \\dagger \\ddagger \\ldots \\cdots \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⨿<\/mo><mo>¶<\/mo><mi mathvariant=\"normal\">§<\/mi><mi mathvariant=\"normal\">%<\/mi><mo stretchy=\"false\">†<\/mo><mo stretchy=\"false\">‡<\/mo><mo stretchy=\"false\">…<\/mo><mo stretchy=\"false\">⋯<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\smile \\frown \\wr \\triangleleft \\triangleright\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⌣<\/mo><mo stretchy=\"false\">⌢<\/mo><mo stretchy=\"false\">≀<\/mo><mo stretchy=\"false\">◃<\/mo><mo stretchy=\"false\">▹<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\diamondsuit, \\heartsuit, \\clubsuit, \\spadesuit, \\Game, \\flat, \\natural, \\sharp \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">♢<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">♡<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">♣<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">♠<\/mi><mo>,<\/mo><mi>⅁<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">♭<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">♮<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">♯<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\diagup \\diagdown \\centerdot \\ltimes \\rtimes \\leftthreetimes \\rightthreetimes \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>╱<\/mi><mi>╲<\/mi><mo stretchy=\"false\" variantform=\"True\">⋅<\/mo><mo stretchy=\"false\">⋉<\/mo><mo stretchy=\"false\">⋊<\/mo><mo stretchy=\"false\">⋋<\/mo><mo stretchy=\"false\">⋌<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\eqcirc \\circeq \\triangleq \\bumpeq \\Bumpeq \\doteqdot \\risingdotseq \\fallingdotseq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">≖<\/mo><mo stretchy=\"false\">≗<\/mo><mo stretchy=\"false\">≜<\/mo><mo stretchy=\"false\">≏<\/mo><mo stretchy=\"false\">≎<\/mo><mo stretchy=\"false\">≑<\/mo><mo stretchy=\"false\">≓<\/mo><mo stretchy=\"false\">≒<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\intercal \\barwedge \\veebar \\doublebarwedge \\between \\pitchfork \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊺<\/mo><mo stretchy=\"false\">⊼<\/mo><mo stretchy=\"false\">⊻<\/mo><mo stretchy=\"false\">⩞<\/mo><mo stretchy=\"false\">≬<\/mo><mo stretchy=\"false\">⋔<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\vartriangleleft \\ntriangleleft \\vartriangleright \\ntriangleright \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊲<\/mo><mo stretchy=\"false\">⋪<\/mo><mo stretchy=\"false\">⊳<\/mo><mo stretchy=\"false\">⋫<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\trianglelefteq \\ntrianglelefteq \\trianglerighteq \\ntrianglerighteq \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">⊴<\/mo><mo stretchy=\"false\">⋬<\/mo><mo stretchy=\"false\">⊵<\/mo><mo stretchy=\"false\">⋭<\/mo><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "a^2", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/math>" }, { "input": "a_2", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msub><\/math>" }, { "input": "10^{30} a^{2+2}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><msup><mn>0<\/mn><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><mn>0<\/mn><\/mrow><\/mrow><\/msup><msup><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "a_{i,j} b_{f'}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo>,<\/mo><mi>j<\/mi><\/mrow><\/mrow><\/msub><msub><mi>b<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msup><mi>f<\/mi><mo>′<\/mo><\/msup><\/mrow><\/mrow><\/msub><\/math>" }, { "input": "x_2^3", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msubsup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msubsup><\/math>" }, { "input": "{x_2}^3 \\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msub><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "10^{10^{8}}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><msup><mn>0<\/mn><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><msup><mn>0<\/mn><mrow data-mjx-texclass=\"ORD\"><mn>8<\/mn><\/mrow><\/msup><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "\\sideset{_1^2}{_3^4}\\prod_a^b", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"OP\"><munderover><mstyle displaystyle=\"true\"><mmultiscripts><mo largeop=\"true\" movablelimits=\"false\" symmetric=\"true\">∏<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><\/mrow><mprescripts\/><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mmultiscripts><\/mstyle><mrow><mi>a<\/mi><\/mrow><mrow><mi>b<\/mi><\/mrow><\/munderover><\/mrow><\/math>" }, { "input": "{}_1^2\\!\\Omega_3^4", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msubsup><mrow data-mjx-texclass=\"ORD\"\/><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msubsup><mspace width=\"-0.167em\"><\/mspace><msubsup><mi mathvariant=\"normal\">Ω<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><\/mrow><\/msubsup><\/math>" }, { "input": "\\overset{\\alpha}{\\omega}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow><mi>ω<\/mi><\/mrow><mi>α<\/mi><\/mover><\/mrow><\/math>" }, { "input": "\\underset{\\alpha}{\\omega}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><munder><mi>ω<\/mi><mi>α<\/mi><\/munder><\/mrow><\/math>" }, { "input": "\\overset{\\alpha}{\\underset{\\gamma}{\\omega}}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow><mrow data-mjx-texclass=\"ORD\"><munder><mi>ω<\/mi><mi>γ<\/mi><\/munder><\/mrow><\/mrow><mi>α<\/mi><\/mover><\/mrow><\/math>" }, { "input": "\\stackrel{\\alpha}{\\omega}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"REL\"><mover><mrow data-mjx-texclass=\"OP\"><mi>ω<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>α<\/mi><\/mrow><\/mover><\/mrow><\/mrow><\/math>" }, { "input": "x', y'', f', f''", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mo>′<\/mo><\/msup><mo>,<\/mo><msup><mi>y<\/mi><mo>″<\/mo><\/msup><mo>,<\/mo><msup><mi>f<\/mi><mo>′<\/mo><\/msup><mo>,<\/mo><msup><mi>f<\/mi><mo>″<\/mo><\/msup><\/math>" }, { "input": "x^\\prime, y^{\\prime\\prime}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi alternate=\"1\">′<\/mi><\/mrow><\/msup><mo>,<\/mo><msup><mi>y<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi alternate=\"1\">′<\/mi><mi alternate=\"1\">′<\/mi><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "\\dot{x}, \\ddot{x}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>x<\/mi><mo>\u02d9<\/mo><\/mover><\/mrow><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>x<\/mi><mo>\u00a8<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": " \\hat a \\ \\bar b \\ \\vec c", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>a<\/mi><mo>^<\/mo><\/mover><\/mrow><\/mrow><mtext> <\/mtext><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>b<\/mi><mo>\u00af<\/mo><\/mover><\/mrow><\/mrow><mtext> <\/mtext><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>c<\/mi><mo>\u2192<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": " \\overrightarrow{a b} \\ \\overleftarrow{c d} \\ \\widehat{d e f}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>b<\/mi><\/mrow><mo>→<\/mo><\/mover><\/mrow><mtext> <\/mtext><mrow data-mjx-texclass=\"ORD\"><mover><mrow data-mjx-texclass=\"ORD\"><mi>c<\/mi><mi>d<\/mi><\/mrow><mo>←<\/mo><\/mover><\/mrow><mtext> <\/mtext><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow data-mjx-texclass=\"ORD\"><mi>d<\/mi><mi>e<\/mi><mi>f<\/mi><\/mrow><mo stretchy=\"true\">^<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": " \\overline{g h i} \\ \\underline{j k l}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow data-mjx-texclass=\"ORD\"><mi>g<\/mi><mi>h<\/mi><mi>i<\/mi><\/mrow><mo>‾<\/mo><\/mover><\/mrow><mtext> <\/mtext><mrow data-mjx-texclass=\"ORD\"><munder><mrow data-mjx-texclass=\"ORD\"><mi>j<\/mi><mi>k<\/mi><mi>l<\/mi><\/mrow><mo>_<\/mo><\/munder><\/mrow><\/math>" }, { "input": "\\overset{\\frown} {AB}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow><mrow data-mjx-texclass=\"ORD\"><mi>A<\/mi><mi>B<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">⌢<\/mo><\/mover><\/mrow><\/math>" }, { "input": " A \\xleftarrow{n+\\mu-1} B \\xrightarrow[T]{n\\pm i-1} C", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mover><mstyle scriptlevel=\"0\"><mo data-mjx-texclass=\"REL\">\u2190<\/mo><\/mstyle><mpadded height=\"-.2em\" lspace=\"0.556em\" voffset=\"-.2em\" width=\"+0.833em\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">+<\/mo><mi>μ<\/mi><mo stretchy=\"false\">−<\/mo><mn>1<\/mn><\/mrow><mspace depth=\".25em\"><\/mspace><\/mpadded><\/mover><mi>B<\/mi><mrow data-mjx-texclass=\"ORD\"><munderover><mstyle scriptlevel=\"0\"><mo data-mjx-texclass=\"REL\">\u2192<\/mo><\/mstyle><mpadded height=\"-.2em\" lspace=\"0.278em\" voffset=\"-.2em\" width=\"+0.833em\"><mrow data-mjx-texclass=\"ORD\"><mi>T<\/mi><\/mrow><mspace depth=\".25em\"><\/mspace><\/mpadded><mpadded height=\"-.2em\" lspace=\"0.278em\" voffset=\"-.2em\" width=\"+0.833em\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">±<\/mo><mi>i<\/mi><mo stretchy=\"false\">−<\/mo><mn>1<\/mn><\/mrow><\/mpadded><\/munderover><\/mrow><mi>C<\/mi><\/math>" }, { "input": "\\overbrace{ 1+2+\\cdots+100 }^{5050}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mover><mrow data-mjx-texclass=\"OP\"><mover><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><mo stretchy=\"false\">+<\/mo><mo stretchy=\"false\">⋯<\/mo><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>0<\/mn><mn>0<\/mn><\/mrow><mo>⏞<\/mo><\/mover><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>5<\/mn><mn>0<\/mn><mn>5<\/mn><mn>0<\/mn><\/mrow><\/mrow><\/mover><\/math>" }, { "input": "\\underbrace{ a+b+\\cdots+z }_{26}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mrow data-mjx-texclass=\"OP\"><munder><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mo stretchy=\"false\">+<\/mo><mi>b<\/mi><mo stretchy=\"false\">+<\/mo><mo stretchy=\"false\">⋯<\/mo><mo stretchy=\"false\">+<\/mo><mi>z<\/mi><\/mrow><mo>⏟<\/mo><\/munder><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><mn>6<\/mn><\/mrow><\/mrow><\/munder><\/math>" }, { "input": "\\sum_{k=1}^N k^2", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/munderover><\/mstyle><msup><mi>k<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/math>" }, { "input": "\\textstyle \\sum_{k=1}^N k^2", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><msubsup><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/msubsup><msup><mi>k<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mstyle><\/math>" }, { "input": "\\frac{\\sum_{k=1}^N k^2}{a}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/munderover><\/mstyle><msup><mi>k<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\frac{\\displaystyle \\sum_{k=1}^N k^2}{a}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/munderover><\/mstyle><msup><mi>k<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mstyle><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\frac{\\sum\\limits^{^N}_{k=1} k^2}{a}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><munderover><mo form=\"prefix\" stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><msup><mi\/><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/msup><\/mrow><\/munderover><msup><mi>k<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\prod_{i=1}^N x_i", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∏<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/munderover><\/mstyle><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\textstyle \\prod_{i=1}^N x_i", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><msubsup><mo stretchy=\"false\">∏<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/msubsup><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><\/mrow><\/msub><\/mstyle><\/math>" }, { "input": "\\coprod_{i=1}^N x_i", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∐<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/munderover><\/mstyle><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\textstyle \\coprod_{i=1}^N x_i", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><msubsup><mo stretchy=\"false\">∐<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/msubsup><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><\/mrow><\/msub><\/mstyle><\/math>" }, { "input": "\\lim_{n \\to \\infty}x_n", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mi form=\"prefix\">lim<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\" accent=\"false\">→<\/mo><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/mrow><\/munder><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\textstyle \\lim_{n \\to \\infty}x_n", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><munder><mi form=\"prefix\" movablelimits=\"true\">lim<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\" accent=\"false\">→<\/mo><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/mrow><\/munder><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><\/mstyle><\/math>" }, { "input": "\\int\\limits_{1}^{3}\\frac{e^3\/x}{x^2}\\, dx", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munderover><mo form=\"prefix\" stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/munderover><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mi>x<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mrow><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><\/math>" }, { "input": "\\int_{1}^{3}\\frac{e^3\/x}{x^2}\\, dx", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/munderover><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mi>x<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mrow><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><\/math>" }, { "input": "\\textstyle \\int\\limits_{-N}^{N} e^x\\, dx", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><munderover><mo form=\"prefix\" movablelimits=\"true\" stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mi>N<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/munderover><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><\/mstyle><\/math>" }, { "input": "\\textstyle \\int_{-N}^{N} e^x\\, dx", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><msubsup><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mi>N<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/msubsup><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><\/mstyle><\/math>" }, { "input": "\\iint\\limits_D \\, dx\\,dy", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mo form=\"prefix\" stretchy=\"false\">∬<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>D<\/mi><\/mrow><\/munder><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><\/math>" }, { "input": "\\iiint\\limits_E \\, dx\\,dy\\,dz", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mo form=\"prefix\" stretchy=\"false\">∭<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>E<\/mi><\/mrow><\/munder><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>z<\/mi><\/math>" }, { "input": "\\iiiint\\limits_F \\, dx\\,dy\\,dz\\,dt", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mo form=\"prefix\" stretchy=\"false\">⨌<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>F<\/mi><\/mrow><\/munder><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>z<\/mi><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>t<\/mi><\/math>" }, { "input": "\\int_{(x,y)\\in C} x^3\\, dx + 4y^2\\, dy", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">∈<\/mo><mi>C<\/mi><\/mrow><\/mrow><\/munder><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mn>4<\/mn><msup><mi>y<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><\/math>" }, { "input": "\\oint_{(x,y)\\in C} x^3\\, dx + 4y^2\\, dy", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mstyle displaystyle=\"true\"><mo>∮<\/mo><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>,<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">∈<\/mo><mi>C<\/mi><\/mrow><\/mrow><\/msub><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mn>4<\/mn><msup><mi>y<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><\/math>", "skipped": false }, { "input": "\\bigcap_{i=_1}^n E_i", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">⋂<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><msub><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/munderover><\/mstyle><msub><mi>E<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\bigcup_{i=_1}^n E_i", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">⋃<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><msub><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/munderover><\/mstyle><msub><mi>E<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\frac{2}{4}=0.5", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><\/mrow><\/mfrac><\/mrow><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mo stretchy=\"false\">.<\/mo><mn>5<\/mn><\/math>" }, { "input": "\\tfrac{2}{4} = 0.5", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mo stretchy=\"false\">.<\/mo><mn>5<\/mn><\/math>" }, { "input": "\\dfrac{2}{4} = 0.5 \\qquad \\dfrac{2}{c + \\dfrac{2}{d + \\dfrac{2}{4}}} = a", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mo stretchy=\"false\">.<\/mo><mn>5<\/mn><mspace width=\"2em\"><\/mspace><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>c<\/mi><mo stretchy=\"false\">+<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>d<\/mi><mo stretchy=\"false\">+<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">=<\/mo><mi>a<\/mi><\/math>" }, { "input": "\\cfrac{2}{c + \\cfrac{2}{d + \\cfrac{2}{4}}} = a", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mstyle><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>c<\/mi><mo stretchy=\"false\">+<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mstyle><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>d<\/mi><mo stretchy=\"false\">+<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mstyle><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><\/mrow><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><\/mrow><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><mo stretchy=\"false\">=<\/mo><mi>a<\/mi><\/math>" }, { "input": "\\cfrac{x}{1 + \\cfrac{\\cancel{y}}{\\cancel{y}}} = \\cfrac{x}{2}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/mstyle><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><mo stretchy=\"false\">+<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><menclose notation=\"updiagonalstrike\" class=\"menclose\"><mi>y<\/mi><mrow class=\"menclose-updiagonalstrike\"\/><\/menclose><\/mrow><\/mstyle><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><menclose notation=\"updiagonalstrike\" class=\"menclose\"><mi>y<\/mi><mrow class=\"menclose-updiagonalstrike\"\/><\/menclose><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><\/mrow><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/mstyle><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mpadded depth=\"3pt\" height=\"8.6pt\" width=\"0\"><\/mpadded><\/mrow><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\binom{n}{k}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"OPEN\"><mo minsize=\"2.047em\">(<\/mo><\/mrow><mfrac linethickness=\"0\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><\/mrow><\/mfrac><mrow data-mjx-texclass=\"CLOSE\"><mo minsize=\"2.047em\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "\\tbinom{n}{k}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"OPEN\"><mo minsize=\"1.2em\">(<\/mo><\/mrow><mfrac linethickness=\"0\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><\/mrow><\/mfrac><mrow data-mjx-texclass=\"CLOSE\"><mo minsize=\"1.2em\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "\\dbinom{n}{k}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"OPEN\"><mo minsize=\"2.047em\">(<\/mo><\/mrow><mfrac linethickness=\"0\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>k<\/mi><\/mrow><\/mfrac><mrow data-mjx-texclass=\"CLOSE\"><mo minsize=\"2.047em\">)<\/mo><\/mrow><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "\\begin{matrix} x & y \\\\ z & v\n\\end{matrix}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\"><\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\"><mtr><mtd><mi>x<\/mi><\/mtd><mtd><mi>y<\/mi><\/mtd><\/mtr><mtr><mtd><mi>z<\/mi><\/mtd><mtd><mi>v<\/mi><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\\begin{vmatrix} x & y \\\\ z & v\n\\end{vmatrix}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">|<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\"><mtr><mtd><mi>x<\/mi><\/mtd><mtd><mi>y<\/mi><\/mtd><\/mtr><mtr><mtd><mi>z<\/mi><\/mtd><mtd><mi>v<\/mi><\/mtd><\/mtr><\/mtable><mo fence=\"true\" stretchy=\"true\" symmetric=\"true\" data-mjx-texclass=\"CLOSE\">|<\/mo><\/mrow><\/math>" }, { "input": "\\begin{Vmatrix} x & y \\\\ z & v\n\\end{Vmatrix}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">‖<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\"><mtr><mtd><mi>x<\/mi><\/mtd><mtd><mi>y<\/mi><\/mtd><\/mtr><mtr><mtd><mi>z<\/mi><\/mtd><mtd><mi>v<\/mi><\/mtd><\/mtr><\/mtable><mo fence=\"true\" stretchy=\"true\" symmetric=\"true\" data-mjx-texclass=\"CLOSE\">‖<\/mo><\/mrow><\/math>" }, { "input": "\\begin{bmatrix} 0 & \\cdots & 0 \\\\ \\vdots\n& \\ddots & \\vdots \\\\ 0 & \\cdots &\n0\\end{bmatrix} ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\"><mtr><mtd><mn>0<\/mn><\/mtd><mtd><mo stretchy=\"false\">⋯<\/mo><\/mtd><mtd><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">⋮<\/mo><\/mtd><mtd><mo stretchy=\"false\">⋱<\/mo><\/mtd><mtd><mo stretchy=\"false\">⋮<\/mo><\/mtd><\/mtr><mtr><mtd><mn>0<\/mn><\/mtd><mtd><mo stretchy=\"false\">⋯<\/mo><\/mtd><mtd><mn>0<\/mn><\/mtd><\/mtr><\/mtable><mo fence=\"true\" stretchy=\"true\" symmetric=\"true\" data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math>" }, { "input": "\\begin{Bmatrix} x & y \\\\ z & v\n\\end{Bmatrix}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">{<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\"><mtr><mtd><mi>x<\/mi><\/mtd><mtd><mi>y<\/mi><\/mtd><\/mtr><mtr><mtd><mi>z<\/mi><\/mtd><mtd><mi>v<\/mi><\/mtd><\/mtr><\/mtable><mo fence=\"true\" stretchy=\"true\" symmetric=\"true\" data-mjx-texclass=\"CLOSE\">}<\/mo><\/mrow><\/math>" }, { "input": "\\begin{pmatrix} x & y \\\\ z & v\n\\end{pmatrix}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\"><mtr><mtd><mi>x<\/mi><\/mtd><mtd><mi>y<\/mi><\/mtd><\/mtr><mtr><mtd><mi>z<\/mi><\/mtd><mtd><mi>v<\/mi><\/mtd><\/mtr><\/mtable><mo fence=\"true\" stretchy=\"true\" symmetric=\"true\" data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math>" }, { "input": "\n\\bigl( \\begin{smallmatrix}\na&b\\\\ c&d\n\\end{smallmatrix} \\bigr)\n", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo maxsize=\"1.2em\" minsize=\"1.2em\" data-mjx-texclass=\"OPEN\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\"><\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\"><mtr><mtd><mi>a<\/mi><\/mtd><mtd><mi>b<\/mi><\/mtd><\/mtr><mtr><mtd><mi>c<\/mi><\/mtd><mtd><mi>d<\/mi><\/mtd><\/mtr><\/mtable><\/mrow><mo maxsize=\"1.2em\" minsize=\"1.2em\" data-mjx-texclass=\"CLOSE\">)<\/mo><\/math>" }, { "input": "f(n) =\n\\begin{cases}\nn\/2, & \\text{if }n\\text{ is even} \\\\\n3n+1, & \\text{if }n\\text{ is odd}\n\\end{cases} ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">{<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\" columnalign=\"left left\"><mtr><mtd><mi>n<\/mi><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mn>2<\/mn><mo>,<\/mo><\/mtd><mtd><mrow data-mjx-texclass=\"ORD\"><mtext>if <\/mtext><\/mrow><mi>n<\/mi><mrow data-mjx-texclass=\"ORD\"><mtext> is even<\/mtext><\/mrow><\/mtd><\/mtr><mtr><mtd><mn>3<\/mn><mi>n<\/mi><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo>,<\/mo><\/mtd><mtd><mrow data-mjx-texclass=\"ORD\"><mtext>if <\/mtext><\/mrow><mi>n<\/mi><mrow data-mjx-texclass=\"ORD\"><mtext> is odd<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\n\\begin{align}\nf(x) & = (a+b)^2 \\\\\n& = a^2+2ab+b^2 \\\\\n\\end{align}\n", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\" rowspacing=\"3pt\"><mtr><mtd><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo stretchy=\"false\">+<\/mo><mi>b<\/mi><msup><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><msup><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><mi>a<\/mi><mi>b<\/mi><mo stretchy=\"false\">+<\/mo><msup><mi>b<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mtd><\/mtr><mtr><mtd><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\n\\begin{alignat}{2}\nf(x) & = (a-b)^2 \\\\\n& = a^2-2ab+b^2 \\\\\n\\end{alignat}\n", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\" rowspacing=\"3pt\"><mtr><mtd><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo stretchy=\"false\">−<\/mo><mi>b<\/mi><msup><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mtd><\/mtr><mtr><mtd><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><msup><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">−<\/mo><mn>2<\/mn><mi>a<\/mi><mi>b<\/mi><mo stretchy=\"false\">+<\/mo><msup><mi>b<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mtd><\/mtr><mtr><mtd><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\\begin{array}{lcl}\nz & = & a \\\\\nf(x,y,z) & = & x + y + z\n\\end{array}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnspacing=\"1em\" rowspacing=\"4pt\" columnalign=\"left center left \"><mtr><mtd><mi>z<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><\/mtd><mtd><mi>a<\/mi><\/mtd><\/mtr><mtr><mtd><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>,<\/mo><mi>y<\/mi><mo>,<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><\/mtd><mtd><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mi>y<\/mi><mo stretchy=\"false\">+<\/mo><mi>z<\/mi><\/mtd><\/mtr><\/mtable><\/math>" }, { "input": "\\begin{array}{lcr}\nz & = & a \\\\\nf(x,y,z) & = & x + y + z\n\\end{array}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnspacing=\"1em\" rowspacing=\"4pt\" columnalign=\"left center right \"><mtr><mtd><mi>z<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><\/mtd><mtd><mi>a<\/mi><\/mtd><\/mtr><mtr><mtd><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>,<\/mo><mi>y<\/mi><mo>,<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><\/mtd><mtd><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mi>y<\/mi><mo stretchy=\"false\">+<\/mo><mi>z<\/mi><\/mtd><\/mtr><\/mtable><\/math>" }, { "input": "f(x) \\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "= \\sum_{n=0}^\\infty a_n x^n ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><\/math>" }, { "input": "= a_0+a_1x+a_2x^2+\\cdots", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">=<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><mo stretchy=\"false\">+<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msub><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mo stretchy=\"false\">⋯<\/mo><\/math>" }, { "input": "f(x) \\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "= \\sum_{n=0}^\\infty a_n x^n ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><\/math>" }, { "input": "= a_0 +a_1x+a_2x^2+\\cdots", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">=<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><mo stretchy=\"false\">+<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msub><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mo stretchy=\"false\">⋯<\/mo><\/math>" }, { "input": "\\begin{cases} 3x + 5y + z \\\\ 7x - 2y + 4z \\\\ -6x + 3y + 2z \\end{cases}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">{<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\" columnalign=\"left left\"><mtr><mtd><mn>3<\/mn><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mn>5<\/mn><mi>y<\/mi><mo stretchy=\"false\">+<\/mo><mi>z<\/mi><\/mtd><\/mtr><mtr><mtd><mn>7<\/mn><mi>x<\/mi><mo stretchy=\"false\">−<\/mo><mn>2<\/mn><mi>y<\/mi><mo stretchy=\"false\">+<\/mo><mn>4<\/mn><mi>z<\/mi><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">−<\/mo><mn>6<\/mn><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mn>3<\/mn><mi>y<\/mi><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><mi>z<\/mi><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\n\\begin{array}{|c|c||c|} a & b & S \\\\\n\\hline\n0&0&1\\\\\n0&1&1\\\\\n1&0&1\\\\\n1&1&0\\\\\n\\end{array}\n", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnspacing=\"1em\" rowspacing=\"4pt\" columnalign=\"center center center \"><mtr><mtd class=\"mwe-math-matrix-bottom mwe-math-matrix-left mwe-math-matrix-right\"><mi>a<\/mi><\/mtd><mtd class=\"mwe-math-matrix-bottom mwe-math-matrix-left mwe-math-matrix-right\"><mi>b<\/mi><\/mtd><mtd class=\"mwe-math-matrix-bottom mwe-math-matrix-left mwe-math-matrix-right\"><mi>S<\/mi><\/mtd><\/mtr><mtr><mtd class=\"mwe-math-matrix-top mwe-math-matrix-left mwe-math-matrix-right\"><mn>0<\/mn><\/mtd><mtd class=\"mwe-math-matrix-top mwe-math-matrix-left mwe-math-matrix-right\"><mn>0<\/mn><\/mtd><mtd class=\"mwe-math-matrix-top mwe-math-matrix-left mwe-math-matrix-right\"><mn>1<\/mn><\/mtd><\/mtr><mtr><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>0<\/mn><\/mtd><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>1<\/mn><\/mtd><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>1<\/mn><\/mtd><\/mtr><mtr><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>1<\/mn><\/mtd><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>0<\/mn><\/mtd><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>1<\/mn><\/mtd><\/mtr><mtr><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>1<\/mn><\/mtd><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>1<\/mn><\/mtd><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd class=\"mwe-math-matrix-left mwe-math-matrix-right\"><\/mtd><\/mtr><\/mtable><\/math>" }, { "input": "( \\frac{1}{2} )", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mfrac><\/mrow><mo stretchy=\"false\">)<\/mo><\/math>" }, { "input": "\\left ( \\frac{1}{2} \\right )", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math>" }, { "input": "\\left ( \\frac{a}{b} \\right )", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math>" }, { "input": "\\left [ \\frac{a}{b} \\right ] \\quad \\left \\lbrack \\frac{a}{b} \\right \\rbrack", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math>" }, { "input": "\\left \\{ \\frac{a}{b} \\right \\} \\quad \\left \\lbrace \\frac{a}{b} \\right \\rbrace", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">{<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">}<\/mo><\/mrow><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">{<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">}<\/mo><\/mrow><\/math>" }, { "input": "\\left \\langle \\frac{a}{b} \\right \\rangle", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">⟨<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">⟩<\/mo><\/mrow><\/math>" }, { "input": "\\left | \\frac{a}{b} \\right \\vert \\quad \\left \\Vert \\frac{c}{d} \\right \\|", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">|<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">|<\/mo><\/mrow><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">‖<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>c<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>d<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">‖<\/mo><\/mrow><\/math>" }, { "input": "\\left \\lfloor \\frac{a}{b} \\right \\rfloor \\quad \\left \\lceil \\frac{c}{d} \\right \\rceil", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">⌊<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">⌋<\/mo><\/mrow><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">⌈<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>c<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>d<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">⌉<\/mo><\/mrow><\/math>" }, { "input": "\\left \/ \\frac{a}{b} \\right \\backslash", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">\/<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">\\<\/mo><\/mrow><\/math>" }, { "input": "\\left \\uparrow \\frac{a}{b} \\right \\downarrow \\quad \\left \\Uparrow \\frac{a}{b} \\right \\Downarrow \\quad \\left \\updownarrow \\frac{a}{b} \\right \\Updownarrow", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">↑<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">↓<\/mo><\/mrow><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">⇑<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">⇓<\/mo><\/mrow><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">↕<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">⇕<\/mo><\/mrow><\/math>" }, { "input": "\\left [ 0,1 \\right )", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mn>0<\/mn><mo>,<\/mo><mn>1<\/mn><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math>" }, { "input": "\\left \\langle \\psi \\right |", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">⟨<\/mo><mi>ψ<\/mi><mo data-mjx-texclass=\"CLOSE\">|<\/mo><\/mrow><\/math>" }, { "input": "\\left . \\frac{A}{B} \\right \\} \\to X", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\"><\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>A<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>B<\/mi><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">}<\/mo><\/mrow><mo stretchy=\"false\" accent=\"false\">→<\/mo><mi>X<\/mi><\/math>" }, { "input": "\\big( \\Big( \\bigg( \\Bigg( \\dots \\Bigg] \\bigg] \\Big] \\big]", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo maxsize=\"1.2em\" minsize=\"1.2em\">(<\/mo><mo maxsize=\"1.623em\" minsize=\"1.623em\">(<\/mo><mo maxsize=\"2.047em\" minsize=\"2.047em\">(<\/mo><mo maxsize=\"2.470em\" minsize=\"2.470em\">(<\/mo><mo>…<\/mo><mo maxsize=\"2.470em\" minsize=\"2.470em\">]<\/mo><mo maxsize=\"2.047em\" minsize=\"2.047em\">]<\/mo><mo maxsize=\"1.623em\" minsize=\"1.623em\">]<\/mo><mo maxsize=\"1.2em\" minsize=\"1.2em\">]<\/mo><\/math>" }, { "input": "\\big\\{ \\Big\\{ \\bigg\\{ \\Bigg\\{ \\dots \\Bigg\\rangle \\bigg\\rangle \\Big\\rangle \\big\\rangle", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo maxsize=\"1.2em\" minsize=\"1.2em\">{<\/mo><mo maxsize=\"1.623em\" minsize=\"1.623em\">{<\/mo><mo maxsize=\"2.047em\" minsize=\"2.047em\">{<\/mo><mo maxsize=\"2.470em\" minsize=\"2.470em\">{<\/mo><mo>…<\/mo><mo maxsize=\"2.470em\" minsize=\"2.470em\">⟩<\/mo><mo maxsize=\"2.047em\" minsize=\"2.047em\">⟩<\/mo><mo maxsize=\"1.623em\" minsize=\"1.623em\">⟩<\/mo><mo maxsize=\"1.2em\" minsize=\"1.2em\">⟩<\/mo><\/math>" }, { "input": "\\big\\| \\Big\\| \\bigg\\| \\Bigg\\| \\dots \\Bigg| \\bigg| \\Big| \\big|", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\" symmetric=\"true\">‖<\/mo><mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\" symmetric=\"true\">‖<\/mo><mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\" symmetric=\"true\">‖<\/mo><mo maxsize=\"2.470em\" minsize=\"2.470em\" stretchy=\"true\" symmetric=\"true\">‖<\/mo><mo>…<\/mo><mo maxsize=\"2.470em\" minsize=\"2.470em\" stretchy=\"true\" symmetric=\"true\">|<\/mo><mo maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\" symmetric=\"true\">|<\/mo><mo maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\" symmetric=\"true\">|<\/mo><mo maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\" symmetric=\"true\">|<\/mo><\/math>" }, { "input": "\\big\\lfloor \\Big\\lfloor \\bigg\\lfloor \\Bigg\\lfloor \\dots \\Bigg\\rceil \\bigg\\rceil \\Big\\rceil \\big\\rceil", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo maxsize=\"1.2em\" minsize=\"1.2em\">⌊<\/mo><mo maxsize=\"1.623em\" minsize=\"1.623em\">⌊<\/mo><mo maxsize=\"2.047em\" minsize=\"2.047em\">⌊<\/mo><mo maxsize=\"2.470em\" minsize=\"2.470em\">⌊<\/mo><mo>…<\/mo><mo maxsize=\"2.470em\" minsize=\"2.470em\">⌉<\/mo><mo maxsize=\"2.047em\" minsize=\"2.047em\">⌉<\/mo><mo maxsize=\"1.623em\" minsize=\"1.623em\">⌉<\/mo><mo maxsize=\"1.2em\" minsize=\"1.2em\">⌉<\/mo><\/math>" }, { "input": "\\big\\uparrow \\Big\\uparrow \\bigg\\uparrow \\Bigg\\uparrow \\dots \\Bigg\\Downarrow \\bigg\\Downarrow \\Big\\Downarrow \\big\\Downarrow", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo fence=\"true\" maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\" symmetric=\"true\">↑<\/mo><mo fence=\"true\" maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\" symmetric=\"true\">↑<\/mo><mo fence=\"true\" maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\" symmetric=\"true\">↑<\/mo><mo fence=\"true\" maxsize=\"2.470em\" minsize=\"2.470em\" stretchy=\"true\" symmetric=\"true\">↑<\/mo><mo>…<\/mo><mo fence=\"true\" maxsize=\"2.470em\" minsize=\"2.470em\" stretchy=\"true\" symmetric=\"true\">⇓<\/mo><mo fence=\"true\" maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\" symmetric=\"true\">⇓<\/mo><mo fence=\"true\" maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\" symmetric=\"true\">⇓<\/mo><mo fence=\"true\" maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\" symmetric=\"true\">⇓<\/mo><\/math>" }, { "input": "\\big\\updownarrow \\Big\\updownarrow \\bigg\\updownarrow \\Bigg\\updownarrow \\dots \\Bigg\\Updownarrow \\bigg\\Updownarrow \\Big\\Updownarrow \\big\\Updownarrow", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo fence=\"true\" maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\" symmetric=\"true\">↕<\/mo><mo fence=\"true\" maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\" symmetric=\"true\">↕<\/mo><mo fence=\"true\" maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\" symmetric=\"true\">↕<\/mo><mo fence=\"true\" maxsize=\"2.470em\" minsize=\"2.470em\" stretchy=\"true\" symmetric=\"true\">↕<\/mo><mo>…<\/mo><mo fence=\"true\" maxsize=\"2.470em\" minsize=\"2.470em\" stretchy=\"true\" symmetric=\"true\">⇕<\/mo><mo fence=\"true\" maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\" symmetric=\"true\">⇕<\/mo><mo fence=\"true\" maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\" symmetric=\"true\">⇕<\/mo><mo fence=\"true\" maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\" symmetric=\"true\">⇕<\/mo><\/math>" }, { "input": "\\big \/ \\Big \/ \\bigg \/ \\Bigg \/ \\dots \\Bigg\\backslash \\bigg\\backslash \\Big\\backslash \\big\\backslash", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo fence=\"true\" maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\" symmetric=\"true\">\/<\/mo><mo fence=\"true\" maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\" symmetric=\"true\">\/<\/mo><mo fence=\"true\" maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\" symmetric=\"true\">\/<\/mo><mo fence=\"true\" maxsize=\"2.470em\" minsize=\"2.470em\" stretchy=\"true\" symmetric=\"true\">\/<\/mo><mo>…<\/mo><mo fence=\"true\" maxsize=\"2.470em\" minsize=\"2.470em\" stretchy=\"true\" symmetric=\"true\">\\<\/mo><mo fence=\"true\" maxsize=\"2.047em\" minsize=\"2.047em\" stretchy=\"true\" symmetric=\"true\">\\<\/mo><mo fence=\"true\" maxsize=\"1.623em\" minsize=\"1.623em\" stretchy=\"true\" symmetric=\"true\">\\<\/mo><mo fence=\"true\" maxsize=\"1.2em\" minsize=\"1.2em\" stretchy=\"true\" symmetric=\"true\">\\<\/mo><\/math>" }, { "input": "x^2 + y^2 + z^2 = 1 \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><msup><mi>y<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><msup><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\Alpha \\Beta \\Gamma \\Delta \\Epsilon \\Zeta \\Eta \\Theta \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">A<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">B<\/mi><\/mrow><mi mathvariant=\"normal\">Γ<\/mi><mi mathvariant=\"normal\">Δ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">E<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Z<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">H<\/mi><\/mrow><mi mathvariant=\"normal\">Θ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Iota \\Kappa \\Lambda \\Mu \\Nu \\Xi \\Pi \\Rho \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">I<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">K<\/mi><\/mrow><mi mathvariant=\"normal\">Λ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">M<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">N<\/mi><\/mrow><mi mathvariant=\"normal\">Ξ<\/mi><mi mathvariant=\"normal\">Π<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">P<\/mi><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\Sigma \\Tau \\Upsilon \\Phi \\Chi \\Psi \\Omega \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">Σ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">T<\/mi><\/mrow><mi mathvariant=\"normal\">Υ<\/mi><mi mathvariant=\"normal\">Φ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">X<\/mi><\/mrow><mi mathvariant=\"normal\">Ψ<\/mi><mi mathvariant=\"normal\">Ω<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\alpha \\beta \\gamma \\delta \\epsilon \\zeta \\eta \\theta \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>α<\/mi><mi>β<\/mi><mi>γ<\/mi><mi>δ<\/mi><mi>ϵ<\/mi><mi>ζ<\/mi><mi>η<\/mi><mi>θ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\iota \\kappa \\lambda \\mu \\nu \\xi \\pi \\rho \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>ι<\/mi><mi>κ<\/mi><mi>λ<\/mi><mi>μ<\/mi><mi>ν<\/mi><mi>ξ<\/mi><mi>π<\/mi><mi>ρ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\sigma \\tau \\upsilon \\phi \\chi \\psi \\omega \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>σ<\/mi><mi>τ<\/mi><mi>υ<\/mi><mi>ϕ<\/mi><mi>χ<\/mi><mi>ψ<\/mi><mi>ω<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\varepsilon \\digamma \\varkappa \\varpi \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>ε<\/mi><mi>ϝ<\/mi><mi>ϰ<\/mi><mi>ϖ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\varrho \\varsigma \\vartheta \\varphi \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>ϱ<\/mi><mi>ς<\/mi><mi>ϑ<\/mi><mi>φ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\aleph \\beth \\gimel \\daleth \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">ℵ<\/mi><mi>ℶ<\/mi><mi>ℷ<\/mi><mi>ℸ<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbb{ABCDEFGHI} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"double-struck\">𝔸<\/mi><mi mathvariant=\"double-struck\">𝔹<\/mi><mi mathvariant=\"double-struck\">ℂ<\/mi><mi mathvariant=\"double-struck\">𝔻<\/mi><mi mathvariant=\"double-struck\">𝔼<\/mi><mi mathvariant=\"double-struck\">𝔽<\/mi><mi mathvariant=\"double-struck\">𝔾<\/mi><mi mathvariant=\"double-struck\">ℍ<\/mi><mi mathvariant=\"double-struck\">𝕀<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbb{JKLMNOPQR} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"double-struck\">𝕁<\/mi><mi mathvariant=\"double-struck\">𝕂<\/mi><mi mathvariant=\"double-struck\">𝕃<\/mi><mi mathvariant=\"double-struck\">𝕄<\/mi><mi mathvariant=\"double-struck\">ℕ<\/mi><mi mathvariant=\"double-struck\">𝕆<\/mi><mi mathvariant=\"double-struck\">ℙ<\/mi><mi mathvariant=\"double-struck\">ℚ<\/mi><mi mathvariant=\"double-struck\">ℝ<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbb{STUVWXYZ} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"double-struck\">𝕊<\/mi><mi mathvariant=\"double-struck\">𝕋<\/mi><mi mathvariant=\"double-struck\">𝕌<\/mi><mi mathvariant=\"double-struck\">𝕍<\/mi><mi mathvariant=\"double-struck\">𝕎<\/mi><mi mathvariant=\"double-struck\">𝕏<\/mi><mi mathvariant=\"double-struck\">𝕐<\/mi><mi mathvariant=\"double-struck\">ℤ<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbf{ABCDEFGHI} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐀<\/mi><mi mathvariant=\"bold\">𝐁<\/mi><mi mathvariant=\"bold\">𝐂<\/mi><mi mathvariant=\"bold\">𝐃<\/mi><mi mathvariant=\"bold\">𝐄<\/mi><mi mathvariant=\"bold\">𝐅<\/mi><mi mathvariant=\"bold\">𝐆<\/mi><mi mathvariant=\"bold\">𝐇<\/mi><mi mathvariant=\"bold\">𝐈<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbf{JKLMNOPQR} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐉<\/mi><mi mathvariant=\"bold\">𝐊<\/mi><mi mathvariant=\"bold\">𝐋<\/mi><mi mathvariant=\"bold\">𝐌<\/mi><mi mathvariant=\"bold\">𝐍<\/mi><mi mathvariant=\"bold\">𝐎<\/mi><mi mathvariant=\"bold\">𝐏<\/mi><mi mathvariant=\"bold\">𝐐<\/mi><mi mathvariant=\"bold\">𝐑<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbf{STUVWXYZ} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐒<\/mi><mi mathvariant=\"bold\">𝐓<\/mi><mi mathvariant=\"bold\">𝐔<\/mi><mi mathvariant=\"bold\">𝐕<\/mi><mi mathvariant=\"bold\">𝐖<\/mi><mi mathvariant=\"bold\">𝐗<\/mi><mi mathvariant=\"bold\">𝐘<\/mi><mi mathvariant=\"bold\">𝐙<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbf{abcdefghijklm} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐚<\/mi><mi mathvariant=\"bold\">𝐛<\/mi><mi mathvariant=\"bold\">𝐜<\/mi><mi mathvariant=\"bold\">𝐝<\/mi><mi mathvariant=\"bold\">𝐞<\/mi><mi mathvariant=\"bold\">𝐟<\/mi><mi mathvariant=\"bold\">𝐠<\/mi><mi mathvariant=\"bold\">𝐡<\/mi><mi mathvariant=\"bold\">𝐢<\/mi><mi mathvariant=\"bold\">𝐣<\/mi><mi mathvariant=\"bold\">𝐤<\/mi><mi mathvariant=\"bold\">𝐥<\/mi><mi mathvariant=\"bold\">𝐦<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbf{nopqrstuvwxyz} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐧<\/mi><mi mathvariant=\"bold\">𝐨<\/mi><mi mathvariant=\"bold\">𝐩<\/mi><mi mathvariant=\"bold\">𝐪<\/mi><mi mathvariant=\"bold\">𝐫<\/mi><mi mathvariant=\"bold\">𝐬<\/mi><mi mathvariant=\"bold\">𝐭<\/mi><mi mathvariant=\"bold\">𝐮<\/mi><mi mathvariant=\"bold\">𝐯<\/mi><mi mathvariant=\"bold\">𝐰<\/mi><mi mathvariant=\"bold\">𝐱<\/mi><mi mathvariant=\"bold\">𝐲<\/mi><mi mathvariant=\"bold\">𝐳<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathbf{0123456789} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn mathvariant=\"bold\">𝟎<\/mn><mn mathvariant=\"bold\">𝟏<\/mn><mn mathvariant=\"bold\">𝟐<\/mn><mn mathvariant=\"bold\">𝟑<\/mn><mn mathvariant=\"bold\">𝟒<\/mn><mn mathvariant=\"bold\">𝟓<\/mn><mn mathvariant=\"bold\">𝟔<\/mn><mn mathvariant=\"bold\">𝟕<\/mn><mn mathvariant=\"bold\">𝟖<\/mn><mn mathvariant=\"bold\">𝟗<\/mn><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\Alpha\\Beta\\Gamma\\Delta\\Epsilon\\Zeta\\Eta\\Theta} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">A<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">B<\/mi><\/mrow><mi mathvariant=\"normal\">Γ<\/mi><mi mathvariant=\"normal\">Δ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">E<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Z<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">H<\/mi><\/mrow><mi mathvariant=\"normal\">Θ<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\Iota\\Kappa\\Lambda\\Mu\\Nu\\Xi\\Pi\\Rho} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">I<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">K<\/mi><\/mrow><mi mathvariant=\"normal\">Λ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">M<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">N<\/mi><\/mrow><mi mathvariant=\"normal\">Ξ<\/mi><mi mathvariant=\"normal\">Π<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">P<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\Sigma\\Tau\\Upsilon\\Phi\\Chi\\Psi\\Omega} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Σ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">T<\/mi><\/mrow><mi mathvariant=\"normal\">Υ<\/mi><mi mathvariant=\"normal\">Φ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">X<\/mi><\/mrow><mi mathvariant=\"normal\">Ψ<\/mi><mi mathvariant=\"normal\">Ω<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\alpha\\beta\\gamma\\delta\\epsilon\\zeta\\eta\\theta} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">α<\/mi><mi mathvariant=\"bold-italic\">β<\/mi><mi mathvariant=\"bold-italic\">γ<\/mi><mi mathvariant=\"bold-italic\">δ<\/mi><mi mathvariant=\"bold-italic\">ϵ<\/mi><mi mathvariant=\"bold-italic\">ζ<\/mi><mi mathvariant=\"bold-italic\">η<\/mi><mi mathvariant=\"bold-italic\">θ<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\iota\\kappa\\lambda\\mu\\nu\\xi\\pi\\rho} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">ι<\/mi><mi mathvariant=\"bold-italic\">κ<\/mi><mi mathvariant=\"bold-italic\">λ<\/mi><mi mathvariant=\"bold-italic\">μ<\/mi><mi mathvariant=\"bold-italic\">ν<\/mi><mi mathvariant=\"bold-italic\">ξ<\/mi><mi mathvariant=\"bold-italic\">π<\/mi><mi mathvariant=\"bold-italic\">ρ<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\sigma\\tau\\upsilon\\phi\\chi\\psi\\omega} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">σ<\/mi><mi mathvariant=\"bold-italic\">τ<\/mi><mi mathvariant=\"bold-italic\">υ<\/mi><mi mathvariant=\"bold-italic\">ϕ<\/mi><mi mathvariant=\"bold-italic\">χ<\/mi><mi mathvariant=\"bold-italic\">ψ<\/mi><mi mathvariant=\"bold-italic\">ω<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\varepsilon\\digamma\\varkappa\\varpi} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">ε<\/mi><mi mathvariant=\"bold-italic\">ϝ<\/mi><mi mathvariant=\"bold-italic\">ϰ<\/mi><mi mathvariant=\"bold-italic\">ϖ<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\varrho\\varsigma\\vartheta\\varphi} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">ϱ<\/mi><mi mathvariant=\"bold-italic\">ς<\/mi><mi mathvariant=\"bold-italic\">ϑ<\/mi><mi mathvariant=\"bold-italic\">φ<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathit{0123456789} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn mathvariant=\"-tex-mathit\">0<\/mn><mn mathvariant=\"-tex-mathit\">1<\/mn><mn mathvariant=\"-tex-mathit\">2<\/mn><mn mathvariant=\"-tex-mathit\">3<\/mn><mn mathvariant=\"-tex-mathit\">4<\/mn><mn mathvariant=\"-tex-mathit\">5<\/mn><mn mathvariant=\"-tex-mathit\">6<\/mn><mn mathvariant=\"-tex-mathit\">7<\/mn><mn mathvariant=\"-tex-mathit\">8<\/mn><mn mathvariant=\"-tex-mathit\">9<\/mn><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathit{\\Alpha\\Beta\\Gamma\\Delta\\Epsilon\\Zeta\\Eta\\Theta} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">A<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">B<\/mi><\/mrow><mi mathvariant=\"normal\">Γ<\/mi><mi mathvariant=\"normal\">Δ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">E<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Z<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">H<\/mi><\/mrow><mi mathvariant=\"normal\">Θ<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathit{\\Iota\\Kappa\\Lambda\\Mu\\Nu\\Xi\\Pi\\Rho} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">I<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">K<\/mi><\/mrow><mi mathvariant=\"normal\">Λ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">M<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">N<\/mi><\/mrow><mi mathvariant=\"normal\">Ξ<\/mi><mi mathvariant=\"normal\">Π<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">P<\/mi><\/mrow><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathit{\\Sigma\\Tau\\Upsilon\\Phi\\Chi\\Psi\\Omega} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Σ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">T<\/mi><\/mrow><mi mathvariant=\"normal\">Υ<\/mi><mi mathvariant=\"normal\">Φ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">X<\/mi><\/mrow><mi mathvariant=\"normal\">Ψ<\/mi><mi mathvariant=\"normal\">Ω<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathrm{ABCDEFGHI} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">A<\/mi><mi mathvariant=\"normal\">B<\/mi><mi mathvariant=\"normal\">C<\/mi><mi mathvariant=\"normal\">D<\/mi><mi mathvariant=\"normal\">E<\/mi><mi mathvariant=\"normal\">F<\/mi><mi mathvariant=\"normal\">G<\/mi><mi mathvariant=\"normal\">H<\/mi><mi mathvariant=\"normal\">I<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathrm{JKLMNOPQR} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">J<\/mi><mi mathvariant=\"normal\">K<\/mi><mi mathvariant=\"normal\">L<\/mi><mi mathvariant=\"normal\">M<\/mi><mi mathvariant=\"normal\">N<\/mi><mi mathvariant=\"normal\">O<\/mi><mi mathvariant=\"normal\">P<\/mi><mi mathvariant=\"normal\">Q<\/mi><mi mathvariant=\"normal\">R<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathrm{STUVWXYZ} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">S<\/mi><mi mathvariant=\"normal\">T<\/mi><mi mathvariant=\"normal\">U<\/mi><mi mathvariant=\"normal\">V<\/mi><mi mathvariant=\"normal\">W<\/mi><mi mathvariant=\"normal\">X<\/mi><mi mathvariant=\"normal\">Y<\/mi><mi mathvariant=\"normal\">Z<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathrm{abcdefghijklm} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">a<\/mi><mi mathvariant=\"normal\">b<\/mi><mi mathvariant=\"normal\">c<\/mi><mi mathvariant=\"normal\">d<\/mi><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">f<\/mi><mi mathvariant=\"normal\">g<\/mi><mi mathvariant=\"normal\">h<\/mi><mi mathvariant=\"normal\">i<\/mi><mi mathvariant=\"normal\">j<\/mi><mi mathvariant=\"normal\">k<\/mi><mi mathvariant=\"normal\">l<\/mi><mi mathvariant=\"normal\">m<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathrm{nopqrstuvwxyz} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">n<\/mi><mi mathvariant=\"normal\">o<\/mi><mi mathvariant=\"normal\">p<\/mi><mi mathvariant=\"normal\">q<\/mi><mi mathvariant=\"normal\">r<\/mi><mi mathvariant=\"normal\">s<\/mi><mi mathvariant=\"normal\">t<\/mi><mi mathvariant=\"normal\">u<\/mi><mi mathvariant=\"normal\">v<\/mi><mi mathvariant=\"normal\">w<\/mi><mi mathvariant=\"normal\">x<\/mi><mi mathvariant=\"normal\">y<\/mi><mi mathvariant=\"normal\">z<\/mi><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathrm{0123456789} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn mathvariant=\"normal\">0<\/mn><mn mathvariant=\"normal\">1<\/mn><mn mathvariant=\"normal\">2<\/mn><mn mathvariant=\"normal\">3<\/mn><mn mathvariant=\"normal\">4<\/mn><mn mathvariant=\"normal\">5<\/mn><mn mathvariant=\"normal\">6<\/mn><mn mathvariant=\"normal\">7<\/mn><mn mathvariant=\"normal\">8<\/mn><mn mathvariant=\"normal\">9<\/mn><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{ABCDEFGHI} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">A<\/mi><mi mathvariant=\"sans-serif\">B<\/mi><mi mathvariant=\"sans-serif\">C<\/mi><mi mathvariant=\"sans-serif\">D<\/mi><mi mathvariant=\"sans-serif\">E<\/mi><mi mathvariant=\"sans-serif\">F<\/mi><mi mathvariant=\"sans-serif\">G<\/mi><mi mathvariant=\"sans-serif\">H<\/mi><mi mathvariant=\"sans-serif\">I<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{JKLMNOPQR} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">J<\/mi><mi mathvariant=\"sans-serif\">K<\/mi><mi mathvariant=\"sans-serif\">L<\/mi><mi mathvariant=\"sans-serif\">M<\/mi><mi mathvariant=\"sans-serif\">N<\/mi><mi mathvariant=\"sans-serif\">O<\/mi><mi mathvariant=\"sans-serif\">P<\/mi><mi mathvariant=\"sans-serif\">Q<\/mi><mi mathvariant=\"sans-serif\">R<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{STUVWXYZ} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">S<\/mi><mi mathvariant=\"sans-serif\">T<\/mi><mi mathvariant=\"sans-serif\">U<\/mi><mi mathvariant=\"sans-serif\">V<\/mi><mi mathvariant=\"sans-serif\">W<\/mi><mi mathvariant=\"sans-serif\">X<\/mi><mi mathvariant=\"sans-serif\">Y<\/mi><mi mathvariant=\"sans-serif\">Z<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{abcdefghijklm} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">a<\/mi><mi mathvariant=\"sans-serif\">b<\/mi><mi mathvariant=\"sans-serif\">c<\/mi><mi mathvariant=\"sans-serif\">d<\/mi><mi mathvariant=\"sans-serif\">e<\/mi><mi mathvariant=\"sans-serif\">f<\/mi><mi mathvariant=\"sans-serif\">g<\/mi><mi mathvariant=\"sans-serif\">h<\/mi><mi mathvariant=\"sans-serif\">i<\/mi><mi mathvariant=\"sans-serif\">j<\/mi><mi mathvariant=\"sans-serif\">k<\/mi><mi mathvariant=\"sans-serif\">l<\/mi><mi mathvariant=\"sans-serif\">m<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{nopqrstuvwxyz} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">n<\/mi><mi mathvariant=\"sans-serif\">o<\/mi><mi mathvariant=\"sans-serif\">p<\/mi><mi mathvariant=\"sans-serif\">q<\/mi><mi mathvariant=\"sans-serif\">r<\/mi><mi mathvariant=\"sans-serif\">s<\/mi><mi mathvariant=\"sans-serif\">t<\/mi><mi mathvariant=\"sans-serif\">u<\/mi><mi mathvariant=\"sans-serif\">v<\/mi><mi mathvariant=\"sans-serif\">w<\/mi><mi mathvariant=\"sans-serif\">x<\/mi><mi mathvariant=\"sans-serif\">y<\/mi><mi mathvariant=\"sans-serif\">z<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{0123456789} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn mathvariant=\"sans-serif\">0<\/mn><mn mathvariant=\"sans-serif\">1<\/mn><mn mathvariant=\"sans-serif\">2<\/mn><mn mathvariant=\"sans-serif\">3<\/mn><mn mathvariant=\"sans-serif\">4<\/mn><mn mathvariant=\"sans-serif\">5<\/mn><mn mathvariant=\"sans-serif\">6<\/mn><mn mathvariant=\"sans-serif\">7<\/mn><mn mathvariant=\"sans-serif\">8<\/mn><mn mathvariant=\"sans-serif\">9<\/mn><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{\\Alpha \\Beta \\Gamma \\Delta \\Epsilon \\Zeta \\Eta \\Theta} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">A<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">B<\/mi><\/mrow><mi mathvariant=\"normal\">Γ<\/mi><mi mathvariant=\"normal\">Δ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">E<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Z<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">H<\/mi><\/mrow><mi mathvariant=\"normal\">Θ<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{\\Iota \\Kappa \\Lambda \\Mu \\Nu \\Xi \\Pi \\Rho} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">I<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">K<\/mi><\/mrow><mi mathvariant=\"normal\">Λ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">M<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">N<\/mi><\/mrow><mi mathvariant=\"normal\">Ξ<\/mi><mi mathvariant=\"normal\">Π<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">P<\/mi><\/mrow><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathsf{\\Sigma \\Tau \\Upsilon \\Phi \\Chi \\Psi \\Omega}\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Σ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">T<\/mi><\/mrow><mi mathvariant=\"normal\">Υ<\/mi><mi mathvariant=\"normal\">Φ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">X<\/mi><\/mrow><mi mathvariant=\"normal\">Ψ<\/mi><mi mathvariant=\"normal\">Ω<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathcal{ABCDEFGHI} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"-tex-calligraphic\">𝒜<\/mi><mi mathvariant=\"-tex-calligraphic\">ℬ<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒞<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒟<\/mi><mi mathvariant=\"-tex-calligraphic\">ℰ<\/mi><mi mathvariant=\"-tex-calligraphic\">ℱ<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒢<\/mi><mi mathvariant=\"-tex-calligraphic\">ℋ<\/mi><mi mathvariant=\"-tex-calligraphic\">ℐ<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathcal{JKLMNOPQR} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"-tex-calligraphic\">𝒥<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒦<\/mi><mi mathvariant=\"-tex-calligraphic\">ℒ<\/mi><mi mathvariant=\"-tex-calligraphic\">ℳ<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒩<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒪<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒫<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒬<\/mi><mi mathvariant=\"-tex-calligraphic\">ℛ<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathcal{STUVWXYZ} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"-tex-calligraphic\">𝒮<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒯<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒰<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒱<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒲<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒳<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒴<\/mi><mi mathvariant=\"-tex-calligraphic\">𝒵<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathfrak{ABCDEFGHI} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"fraktur\">𝔄<\/mi><mi mathvariant=\"fraktur\">𝔅<\/mi><mi mathvariant=\"fraktur\">ℭ<\/mi><mi mathvariant=\"fraktur\">𝔇<\/mi><mi mathvariant=\"fraktur\">𝔈<\/mi><mi mathvariant=\"fraktur\">𝔉<\/mi><mi mathvariant=\"fraktur\">𝔊<\/mi><mi mathvariant=\"fraktur\">ℌ<\/mi><mi mathvariant=\"fraktur\">ℑ<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathfrak{JKLMNOPQR} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"fraktur\">𝔍<\/mi><mi mathvariant=\"fraktur\">𝔎<\/mi><mi mathvariant=\"fraktur\">𝔏<\/mi><mi mathvariant=\"fraktur\">𝔐<\/mi><mi mathvariant=\"fraktur\">𝔑<\/mi><mi mathvariant=\"fraktur\">𝔒<\/mi><mi mathvariant=\"fraktur\">𝔓<\/mi><mi mathvariant=\"fraktur\">𝔔<\/mi><mi mathvariant=\"fraktur\">ℜ<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathfrak{STUVWXYZ} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"fraktur\">𝔖<\/mi><mi mathvariant=\"fraktur\">𝔗<\/mi><mi mathvariant=\"fraktur\">𝔘<\/mi><mi mathvariant=\"fraktur\">𝔙<\/mi><mi mathvariant=\"fraktur\">𝔚<\/mi><mi mathvariant=\"fraktur\">𝔛<\/mi><mi mathvariant=\"fraktur\">𝔜<\/mi><mi mathvariant=\"fraktur\">ℤ<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathfrak{abcdefghijklm} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"fraktur\">𝔞<\/mi><mi mathvariant=\"fraktur\">𝔟<\/mi><mi mathvariant=\"fraktur\">𝔠<\/mi><mi mathvariant=\"fraktur\">𝔡<\/mi><mi mathvariant=\"fraktur\">𝔢<\/mi><mi mathvariant=\"fraktur\">𝔣<\/mi><mi mathvariant=\"fraktur\">𝔤<\/mi><mi mathvariant=\"fraktur\">𝔥<\/mi><mi mathvariant=\"fraktur\">𝔦<\/mi><mi mathvariant=\"fraktur\">𝔧<\/mi><mi mathvariant=\"fraktur\">𝔨<\/mi><mi mathvariant=\"fraktur\">𝔩<\/mi><mi mathvariant=\"fraktur\">𝔪<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathfrak{nopqrstuvwxyz} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"fraktur\">𝔫<\/mi><mi mathvariant=\"fraktur\">𝔬<\/mi><mi mathvariant=\"fraktur\">𝔭<\/mi><mi mathvariant=\"fraktur\">𝔮<\/mi><mi mathvariant=\"fraktur\">𝔯<\/mi><mi mathvariant=\"fraktur\">𝔰<\/mi><mi mathvariant=\"fraktur\">𝔱<\/mi><mi mathvariant=\"fraktur\">𝔲<\/mi><mi mathvariant=\"fraktur\">𝔳<\/mi><mi mathvariant=\"fraktur\">𝔴<\/mi><mi mathvariant=\"fraktur\">𝔵<\/mi><mi mathvariant=\"fraktur\">𝔶<\/mi><mi mathvariant=\"fraktur\">𝔷<\/mi><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\mathfrak{0123456789} \\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn mathvariant=\"fraktur\">0<\/mn><mn mathvariant=\"fraktur\">1<\/mn><mn mathvariant=\"fraktur\">2<\/mn><mn mathvariant=\"fraktur\">3<\/mn><mn mathvariant=\"fraktur\">4<\/mn><mn mathvariant=\"fraktur\">5<\/mn><mn mathvariant=\"fraktur\">6<\/mn><mn mathvariant=\"fraktur\">7<\/mn><mn mathvariant=\"fraktur\">8<\/mn><mn mathvariant=\"fraktur\">9<\/mn><\/mrow><\/mrow><\/mrow><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "x y z", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mi>y<\/mi><mi>z<\/mi><\/math>" }, { "input": "\\text{x y z}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>x y z<\/mtext><\/mrow><\/math>" }, { "input": "\\text{if} n \\text{is even}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>if<\/mtext><\/mrow><mi>n<\/mi><mrow data-mjx-texclass=\"ORD\"><mtext>is even<\/mtext><\/mrow><\/math>" }, { "input": "\\text{if }n\\text{ is even}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>if <\/mtext><\/mrow><mi>n<\/mi><mrow data-mjx-texclass=\"ORD\"><mtext> is even<\/mtext><\/mrow><\/math>" }, { "input": "\\text{if}~n\\ \\text{is even}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>if<\/mtext><\/mrow><mspace width=\"0.5em\"\/><mi>n<\/mi><mtext> <\/mtext><mrow data-mjx-texclass=\"ORD\"><mtext>is even<\/mtext><\/mrow><\/math>" }, { "input": "{\\color{Blue}x^2}+{\\color{YellowOrange}2x}-{\\color{OliveGreen}1}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle mathcolor=\"#2D2F92\"><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mstyle><\/mrow><mo stretchy=\"false\">+<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle mathcolor=\"#FAA21A\"><mn>2<\/mn><\/mstyle><mstyle mathcolor=\"#FAA21A\"><mi>x<\/mi><\/mstyle><\/mrow><mo stretchy=\"false\">−<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle mathcolor=\"#3C8031\"><mn>1<\/mn><\/mstyle><\/mrow><\/math>" }, { "input": "x_{1,2}=\\frac{-b\\pm\\sqrt{\\color{Red}b^2-4ac}}{2a}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><\/mrow><\/mrow><\/msub><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mi>b<\/mi><mo stretchy=\"false\">±<\/mo><mrow data-mjx-texclass=\"ORD\"><msqrt><mrow data-mjx-texclass=\"ORD\"><mstyle mathcolor=\"#ED1B23\"><msup><mi>b<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mstyle><mstyle mathcolor=\"#ED1B23\"><mo stretchy=\"false\">−<\/mo><\/mstyle><mstyle mathcolor=\"#ED1B23\"><mn>4<\/mn><\/mstyle><mstyle mathcolor=\"#ED1B23\"><mi>a<\/mi><\/mstyle><mstyle mathcolor=\"#ED1B23\"><mi>c<\/mi><\/mstyle><\/mrow><\/msqrt><\/mrow><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><mi>a<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "e^{i \\pi} + 1 = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "\\definecolor{orange}{RGB}{255,165,0}\\pagecolor{orange}e^{i \\pi} + 1 = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "e^{i \\pi} + 1 = 0\\,\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mspace width=\"0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "\\definecolor{orange}{RGB}{255,165,0}\\pagecolor{orange}e^{i \\pi} + 1 = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "e^{i \\pi} + 1 = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "\\definecolor{orange}{RGB}{255,165,0}\\pagecolor{orange}e^{i \\pi} + 1 = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mi>π<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "\\color{Apricot}\\text{Apricot}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#FBB982\"><mrow data-mjx-texclass=\"ORD\"><mtext>Apricot<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Aquamarine}\\text{Aquamarine}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00B5BE\"><mrow data-mjx-texclass=\"ORD\"><mtext>Aquamarine<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Bittersweet}\\text{Bittersweet}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#C04F17\"><mrow data-mjx-texclass=\"ORD\"><mtext>Bittersweet<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Black}\\text{Black}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#221E1F\"><mrow data-mjx-texclass=\"ORD\"><mtext>Black<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Blue}\\text{Blue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#2D2F92\"><mrow data-mjx-texclass=\"ORD\"><mtext>Blue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{BlueGreen}\\text{BlueGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00B3B8\"><mrow data-mjx-texclass=\"ORD\"><mtext>BlueGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{BlueViolet}\\text{BlueViolet}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#473992\"><mrow data-mjx-texclass=\"ORD\"><mtext>BlueViolet<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{BrickRed}\\text{BrickRed}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#B6321C\"><mrow data-mjx-texclass=\"ORD\"><mtext>BrickRed<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Brown}\\text{Brown}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#792500\"><mrow data-mjx-texclass=\"ORD\"><mtext>Brown<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{BurntOrange}\\text{BurntOrange}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#F7921D\"><mrow data-mjx-texclass=\"ORD\"><mtext>BurntOrange<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{CadetBlue}\\text{CadetBlue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#74729A\"><mrow data-mjx-texclass=\"ORD\"><mtext>CadetBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{CarnationPink}\\text{CarnationPink}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#F282B4\"><mrow data-mjx-texclass=\"ORD\"><mtext>CarnationPink<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Cerulean}\\text{Cerulean}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00A2E3\"><mrow data-mjx-texclass=\"ORD\"><mtext>Cerulean<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{CornflowerBlue}\\text{CornflowerBlue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#41B0E4\"><mrow data-mjx-texclass=\"ORD\"><mtext>CornflowerBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Cyan}\\text{Cyan}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00AEEF\"><mrow data-mjx-texclass=\"ORD\"><mtext>Cyan<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Dandelion}\\text{Dandelion}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#FDBC42\"><mrow data-mjx-texclass=\"ORD\"><mtext>Dandelion<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{DarkOrchid}\\text{DarkOrchid}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#A4538A\"><mrow data-mjx-texclass=\"ORD\"><mtext>DarkOrchid<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Emerald}\\text{Emerald}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00A99D\"><mrow data-mjx-texclass=\"ORD\"><mtext>Emerald<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{ForestGreen}\\text{ForestGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#009B55\"><mrow data-mjx-texclass=\"ORD\"><mtext>ForestGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Fuchsia}\\text{Fuchsia}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#8C368C\"><mrow data-mjx-texclass=\"ORD\"><mtext>Fuchsia<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Goldenrod}\\text{Goldenrod}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#FFDF42\"><mrow data-mjx-texclass=\"ORD\"><mtext>Goldenrod<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Gray}\\text{Gray}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#949698\"><mrow data-mjx-texclass=\"ORD\"><mtext>Gray<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Green}\\text{Green}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00A64F\"><mrow data-mjx-texclass=\"ORD\"><mtext>Green<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{GreenYellow}\\text{GreenYellow}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#DFE674\"><mrow data-mjx-texclass=\"ORD\"><mtext>GreenYellow<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{JungleGreen}\\text{JungleGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00A99A\"><mrow data-mjx-texclass=\"ORD\"><mtext>JungleGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Lavender}\\text{Lavender}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#F49EC4\"><mrow data-mjx-texclass=\"ORD\"><mtext>Lavender<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{LimeGreen}\\text{LimeGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#8DC73E\"><mrow data-mjx-texclass=\"ORD\"><mtext>LimeGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Magenta}\\text{Magenta}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#EC008C\"><mrow data-mjx-texclass=\"ORD\"><mtext>Magenta<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Mahogany}\\text{Mahogany}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#A9341F\"><mrow data-mjx-texclass=\"ORD\"><mtext>Mahogany<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Maroon}\\text{Maroon}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#AF3235\"><mrow data-mjx-texclass=\"ORD\"><mtext>Maroon<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Melon}\\text{Melon}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#F89E7B\"><mrow data-mjx-texclass=\"ORD\"><mtext>Melon<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{MidnightBlue}\\text{MidnightBlue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#006795\"><mrow data-mjx-texclass=\"ORD\"><mtext>MidnightBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Mulberry}\\text{Mulberry}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#A93C93\"><mrow data-mjx-texclass=\"ORD\"><mtext>Mulberry<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{NavyBlue}\\text{NavyBlue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#006EB8\"><mrow data-mjx-texclass=\"ORD\"><mtext>NavyBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{OliveGreen}\\text{OliveGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#3C8031\"><mrow data-mjx-texclass=\"ORD\"><mtext>OliveGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Orange}\\text{Orange}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#F58137\"><mrow data-mjx-texclass=\"ORD\"><mtext>Orange<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{OrangeRed}\\text{OrangeRed}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#ED135A\"><mrow data-mjx-texclass=\"ORD\"><mtext>OrangeRed<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Orchid}\\text{Orchid}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#AF72B0\"><mrow data-mjx-texclass=\"ORD\"><mtext>Orchid<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Peach}\\text{Peach}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#F7965A\"><mrow data-mjx-texclass=\"ORD\"><mtext>Peach<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Periwinkle}\\text{Periwinkle}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#7977B8\"><mrow data-mjx-texclass=\"ORD\"><mtext>Periwinkle<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{PineGreen}\\text{PineGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#008B72\"><mrow data-mjx-texclass=\"ORD\"><mtext>PineGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Plum}\\text{Plum}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#92268F\"><mrow data-mjx-texclass=\"ORD\"><mtext>Plum<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{ProcessBlue}\\text{ProcessBlue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00B0F0\"><mrow data-mjx-texclass=\"ORD\"><mtext>ProcessBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Purple}\\text{Purple}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#99479B\"><mrow data-mjx-texclass=\"ORD\"><mtext>Purple<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RawSienna}\\text{RawSienna}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#974006\"><mrow data-mjx-texclass=\"ORD\"><mtext>RawSienna<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Red}\\text{Red}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#ED1B23\"><mrow data-mjx-texclass=\"ORD\"><mtext>Red<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RedOrange}\\text{RedOrange}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#F26035\"><mrow data-mjx-texclass=\"ORD\"><mtext>RedOrange<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RedViolet}\\text{RedViolet}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#A1246B\"><mrow data-mjx-texclass=\"ORD\"><mtext>RedViolet<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Rhodamine}\\text{Rhodamine}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#EF559F\"><mrow data-mjx-texclass=\"ORD\"><mtext>Rhodamine<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RoyalBlue}\\text{RoyalBlue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#0071BC\"><mrow data-mjx-texclass=\"ORD\"><mtext>RoyalBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RoyalPurple}\\text{RoyalPurple}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#613F99\"><mrow data-mjx-texclass=\"ORD\"><mtext>RoyalPurple<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RubineRed}\\text{RubineRed}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#ED017D\"><mrow data-mjx-texclass=\"ORD\"><mtext>RubineRed<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Salmon}\\text{Salmon}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#F69289\"><mrow data-mjx-texclass=\"ORD\"><mtext>Salmon<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{SeaGreen}\\text{SeaGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#3FBC9D\"><mrow data-mjx-texclass=\"ORD\"><mtext>SeaGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Sepia}\\text{Sepia}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#671800\"><mrow data-mjx-texclass=\"ORD\"><mtext>Sepia<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{SkyBlue}\\text{SkyBlue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#46C5DD\"><mrow data-mjx-texclass=\"ORD\"><mtext>SkyBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{SpringGreen}\\text{SpringGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#C6DC67\"><mrow data-mjx-texclass=\"ORD\"><mtext>SpringGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Tan}\\text{Tan}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#DA9D76\"><mrow data-mjx-texclass=\"ORD\"><mtext>Tan<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{TealBlue}\\text{TealBlue}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00AEB3\"><mrow data-mjx-texclass=\"ORD\"><mtext>TealBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Thistle}\\text{Thistle}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#D883B7\"><mrow data-mjx-texclass=\"ORD\"><mtext>Thistle<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Turquoise}\\text{Turquoise}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#00B4CE\"><mrow data-mjx-texclass=\"ORD\"><mtext>Turquoise<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Violet}\\text{Violet}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#58429B\"><mrow data-mjx-texclass=\"ORD\"><mtext>Violet<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{VioletRed}\\text{VioletRed}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#EF58A0\"><mrow data-mjx-texclass=\"ORD\"><mtext>VioletRed<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\pagecolor{Black}\\color{White}\\text{White}", "params": { "style": "background: black" }, "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#FFFFFF\"><mrow data-mjx-texclass=\"ORD\"><mtext>White<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{WildStrawberry}\\text{WildStrawberry}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#EE2967\"><mrow data-mjx-texclass=\"ORD\"><mtext>WildStrawberry<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\pagecolor{Black}\\color{Yellow}\\text{Yellow}", "params": { "style": "background: black" }, "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#FFF200\"><mrow data-mjx-texclass=\"ORD\"><mtext>Yellow<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{YellowGreen}\\text{YellowGreen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#98CC70\"><mrow data-mjx-texclass=\"ORD\"><mtext>YellowGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{YellowOrange}\\text{YellowOrange}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle mathcolor=\"#FAA21A\"><mrow data-mjx-texclass=\"ORD\"><mtext>YellowOrange<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "a \\qquad b", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mspace width=\"2em\"><\/mspace><mi>b<\/mi><\/math>" }, { "input": "a \\quad b", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mspace width=\"1em\"><\/mspace><mi>b<\/mi><\/math>" }, { "input": "a\\ b", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mtext> <\/mtext><mi>b<\/mi><\/math>" }, { "input": "a \\mbox{ } b", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mtext> <\/mtext><\/mrow><mi>b<\/mi><\/math>" }, { "input": "a\\;b", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mspace width=\"0.278em\"><\/mspace><mi>b<\/mi><\/math>" }, { "input": "a\\,b", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mspace width=\"0.167em\"><\/mspace><mi>b<\/mi><\/math>" }, { "input": "ab", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mi>b<\/mi><\/math>" }, { "input": "\\mathit{ab}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"-tex-mathit\">a<\/mi><mi mathvariant=\"-tex-mathit\">b<\/mi><\/mrow><\/mrow><\/mrow><\/math>" }, { "input": "a\\!b", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><mspace width=\"-0.167em\"><\/mspace><mi>b<\/mi><\/math>" }, { "input": "0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\\cdots", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>0<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><mo stretchy=\"false\">+<\/mo><mn>3<\/mn><mo stretchy=\"false\">+<\/mo><mn>4<\/mn><mo stretchy=\"false\">+<\/mo><mn>5<\/mn><mo stretchy=\"false\">+<\/mo><mn>6<\/mn><mo stretchy=\"false\">+<\/mo><mn>7<\/mn><mo stretchy=\"false\">+<\/mo><mn>8<\/mn><mo stretchy=\"false\">+<\/mo><mn>9<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>0<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>1<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>2<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>3<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>4<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>5<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>6<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>7<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>8<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>9<\/mn><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><mn>0<\/mn><mo stretchy=\"false\">+<\/mo><mo stretchy=\"false\">⋯<\/mo><\/math>" }, { "input": "{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\\cdots}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><mo stretchy=\"false\">+<\/mo><mn>3<\/mn><mo stretchy=\"false\">+<\/mo><mn>4<\/mn><mo stretchy=\"false\">+<\/mo><mn>5<\/mn><mo stretchy=\"false\">+<\/mo><mn>6<\/mn><mo stretchy=\"false\">+<\/mo><mn>7<\/mn><mo stretchy=\"false\">+<\/mo><mn>8<\/mn><mo stretchy=\"false\">+<\/mo><mn>9<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>0<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>1<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>2<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>3<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>4<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>5<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>6<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>7<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>8<\/mn><mo stretchy=\"false\">+<\/mo><mn>1<\/mn><mn>9<\/mn><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><mn>0<\/mn><mo stretchy=\"false\">+<\/mo><mo stretchy=\"false\">⋯<\/mo><\/mrow><\/math>" }, { "input": "\\int_{-N}^{N} e^x\\, dx", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mi>N<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>N<\/mi><\/mrow><\/munderover><\/mstyle><msup><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>x<\/mi><\/math>" }, { "input": "\\sum_{i=0}^\\infty 2^{-i}", "params": { "display": "inline" }, "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><msup><mn>2<\/mn><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mi>i<\/mi><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "\\text{geometric series:}\\quad \\begin{align} \\sum_{i=0}^\\infty 2^{-i}=2 \\end{align}", "params": { "display": "block" }, "output": "<math class=\"mwe-math-element\" display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>geometric series:<\/mtext><\/mrow><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"ORD\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\" rowspacing=\"3pt\"><mtr><mtd><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><msup><mn>2<\/mn><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mi>i<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">=<\/mo><mn>2<\/mn><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\\sum_{i=0}^\\infty 2^{-i}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><msup><mn>2<\/mn><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mi>i<\/mi><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "\\text{geometric series:}\\quad \\sum_{i=0}^\\infty 2^{-i}=2 ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>geometric series:<\/mtext><\/mrow><mspace width=\"1em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><msup><mn>2<\/mn><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mi>i<\/mi><\/mrow><\/mrow><\/msup><mo stretchy=\"false\">=<\/mo><mn>2<\/mn><\/math>" }, { "input": "\\iint", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∬<\/mo><\/math>" }, { "input": "\\oint", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\"><mo>∮<\/mo><\/mstyle><\/math>", "skipped": false }, { "input": "\\iint\\limits_{S}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\subset\\!\\supset \\mathbf D \\cdot \\mathrm{d}\\mathbf A", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mo form=\"prefix\" stretchy=\"false\">∬<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>S<\/mi><\/mrow><\/munder><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mo stretchy=\"false\">⊂<\/mo><mspace width=\"-0.167em\"><\/mspace><mo stretchy=\"false\">⊃<\/mo><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐃<\/mi><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐀<\/mi><\/mrow><\/math>" }, { "input": "\\int\\!\\!\\!\\!\\int_{\\partial V}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\;\\;\\;\\bigcirc\\,\\,\\mathbf D\\cdot\\mathrm{d}\\mathbf A", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∫<\/mo><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><munder><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>V<\/mi><\/mrow><\/mrow><\/munder><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mo stretchy=\"false\">◯<\/mo><mspace width=\"0.167em\"><\/mspace><mspace width=\"0.167em\"><\/mspace><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐃<\/mi><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐀<\/mi><\/mrow><\/math>" }, { "input": "\\int\\!\\!\\!\\!\\!\\int\\!\\!\\!\\!\\!\\int_{\\partial V}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\;\\;\\;\\subset\\!\\supset \\mathbf D\\cdot\\mathrm{d}\\mathbf A", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∫<\/mo><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mo stretchy=\"false\">∫<\/mo><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><munder><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>V<\/mi><\/mrow><\/mrow><\/munder><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mo stretchy=\"false\">⊂<\/mo><mspace width=\"-0.167em\"><\/mspace><mo stretchy=\"false\">⊃<\/mo><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐃<\/mi><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐀<\/mi><\/mrow><\/math>" }, { "input": "\\int\\!\\!\\!\\!\\!\\int\\!\\!\\!\\!\\!\\int_{\\partial V}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\;\\;\\;\\bigcirc\\,\\,\\mathbf D\\;\\cdot\\mathrm{d}\\mathbf A", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">∫<\/mo><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mo stretchy=\"false\">∫<\/mo><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><munder><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>V<\/mi><\/mrow><\/mrow><\/munder><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mspace width=\"0.278em\"><\/mspace><mo stretchy=\"false\">◯<\/mo><mspace width=\"0.167em\"><\/mspace><mspace width=\"0.167em\"><\/mspace><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐃<\/mi><\/mrow><mspace width=\"0.278em\"><\/mspace><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐀<\/mi><\/mrow><\/math>" }, { "input": "{\\scriptstyle S}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"1\"><mi>S<\/mi><\/mstyle><\/mrow><\/math>" }, { "input": "( \\nabla \\times \\bold{F} ) \\cdot {\\rm d}\\bold{S} = \\oint_{\\partial S} \\bold{F} \\cdot {\\rm d}\\boldsymbol{\\ell} ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"normal\">∇<\/mi><mo stretchy=\"false\">×<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐅<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐒<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">=<\/mo><msub><mstyle displaystyle=\"true\"><mo>∮<\/mo><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>S<\/mi><\/mrow><\/mrow><\/msub><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐅<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">ℓ<\/mi><\/mrow><\/math>", "skipped": false }, { "input": "{\\scriptstyle S}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"1\"><mi>S<\/mi><\/mstyle><\/mrow><\/math>" }, { "input": "( \\nabla \\times \\bold{F} ) \\cdot {\\rm d}\\bold{S} = \\oint_{\\partial S} \\bold{F} \\cdot {\\rm d}\\boldsymbol{\\ell} ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">(<\/mo><mi mathvariant=\"normal\">∇<\/mi><mo stretchy=\"false\">×<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐅<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐒<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">=<\/mo><msub><mstyle displaystyle=\"true\"><mo>∮<\/mo><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>S<\/mi><\/mrow><\/mrow><\/msub><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐅<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">ℓ<\/mi><\/mrow><\/math>", "skipped": false }, { "input": "\\oint_C \\bold{B} \\cdot {\\rm d} \\boldsymbol{\\ell} = \\mu_0 ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mstyle displaystyle=\"true\"><mo>∮<\/mo><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mi>C<\/mi><\/mrow><\/msub><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐁<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">ℓ<\/mi><\/mrow><mo stretchy=\"false\">=<\/mo><msub><mi>μ<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><\/math>", "skipped": false }, { "input": "{\\scriptstyle S}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"1\"><mi>S<\/mi><\/mstyle><\/mrow><\/math>" }, { "input": "\\left ( \\bold{J} + \\epsilon_0\\frac{\\partial \\bold{E}}{\\partial t} \\right ) \\cdot {\\rm d}\\bold{S}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐉<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">+<\/mo><msub><mi>ϵ<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐄<\/mi><\/mrow><\/mrow><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>t<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐒<\/mi><\/mrow><\/mrow><\/math>" }, { "input": "\\oint_{\\partial S} \\bold{B} \\cdot {\\rm d} \\boldsymbol{\\ell} = \\mu_0 ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mstyle displaystyle=\"true\"><mo>∮<\/mo><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>S<\/mi><\/mrow><\/mrow><\/msub><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐁<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold-italic\">ℓ<\/mi><\/mrow><mo stretchy=\"false\">=<\/mo><msub><mi>μ<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><\/math>" }, { "input": "{\\scriptstyle S}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"1\"><mi>S<\/mi><\/mstyle><\/mrow><\/math>" }, { "input": "\\left ( \\bold{J} + \\epsilon_0\\frac{\\partial \\bold{E}}{\\partial t} \\right ) \\cdot {\\rm d}\\bold{S}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐉<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">+<\/mo><msub><mi>ϵ<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐄<\/mi><\/mrow><\/mrow><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>t<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo stretchy=\"false\">⋅<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐒<\/mi><\/mrow><\/mrow><\/math>" }, { "input": "\\bold{P} = ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐏<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">=<\/mo><\/math>" }, { "input": "{\\scriptstyle \\partial \\Omega}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"1\"><mi>∂<\/mi><mi mathvariant=\"normal\">Ω<\/mi><\/mstyle><\/mrow><\/math>" }, { "input": "\\bold{T} \\cdot {\\rm d}^3\\boldsymbol{\\Sigma} = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐓<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">⋅<\/mo><msup><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Σ<\/mi><\/mrow><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "\\bold{P} = ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐏<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">=<\/mo><\/math>" }, { "input": "{\\scriptstyle \\partial \\Omega}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"1\"><mi>∂<\/mi><mi mathvariant=\"normal\">Ω<\/mi><\/mstyle><\/mrow><\/math>" }, { "input": "\\bold{T} \\cdot {\\rm d}^3\\boldsymbol{\\Sigma} = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">𝐓<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">⋅<\/mo><msup><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">d<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><\/mrow><\/msup><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">Σ<\/mi><\/mrow><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "\\overset{\\frown}{AB}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow><mrow data-mjx-texclass=\"ORD\"><mi>A<\/mi><mi>B<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">⌢<\/mo><\/mover><\/mrow><\/math>" }, { "input": "ax^2 + bx + c = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mi>b<\/mi><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mi>c<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "ax^2 + bx + c = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mi>b<\/mi><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mi>c<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "x={-b\\pm\\sqrt{b^2-4ac} \\over 2a}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo stretchy=\"false\">=<\/mo><mfrac><mrow><mo stretchy=\"false\">−<\/mo><mi>b<\/mi><mo stretchy=\"false\">±<\/mo><mrow data-mjx-texclass=\"ORD\"><msqrt><mrow data-mjx-texclass=\"ORD\"><msup><mi>b<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">−<\/mo><mn>4<\/mn><mi>a<\/mi><mi>c<\/mi><\/mrow><\/msqrt><\/mrow><\/mrow><mrow><mn>2<\/mn><mi>a<\/mi><\/mrow><\/mfrac><\/math>" }, { "input": "x={-b\\pm\\sqrt{b^2-4ac} \\over 2a}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo stretchy=\"false\">=<\/mo><mfrac><mrow><mo stretchy=\"false\">−<\/mo><mi>b<\/mi><mo stretchy=\"false\">±<\/mo><mrow data-mjx-texclass=\"ORD\"><msqrt><mrow data-mjx-texclass=\"ORD\"><msup><mi>b<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo stretchy=\"false\">−<\/mo><mn>4<\/mn><mi>a<\/mi><mi>c<\/mi><\/mrow><\/msqrt><\/mrow><\/mrow><mrow><mn>2<\/mn><mi>a<\/mi><\/mrow><\/mfrac><\/math>" }, { "input": "2 = \\left( \\frac{\\left(3-x\\right) \\times 2}{3-x} \\right)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>3<\/mn><mo stretchy=\"false\">−<\/mo><mi>x<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo stretchy=\"false\">×<\/mo><mn>2<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><mo stretchy=\"false\">−<\/mo><mi>x<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math>" }, { "input": "2 = \\left(\n\\frac{\\left(3-x\\right) \\times 2}{3-x}\n\\right)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>3<\/mn><mo stretchy=\"false\">−<\/mo><mi>x<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo stretchy=\"false\">×<\/mo><mn>2<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>3<\/mn><mo stretchy=\"false\">−<\/mo><mi>x<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math>" }, { "input": "S_{\\text{new}} = S_{\\text{old}} - \\frac{ \\left( 5-T \\right) ^2} {2}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>S<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mtext>new<\/mtext><\/mrow><\/mrow><\/msub><mo stretchy=\"false\">=<\/mo><msub><mi>S<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mtext>old<\/mtext><\/mrow><\/mrow><\/msub><mo stretchy=\"false\">−<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>5<\/mn><mo stretchy=\"false\">−<\/mo><mi>T<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "S_{\\text{new}} = S_{\\text{old}} - \\frac{ \\left( 5-T \\right) ^2} {2}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>S<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mtext>new<\/mtext><\/mrow><\/mrow><\/msub><mo stretchy=\"false\">=<\/mo><msub><mi>S<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mtext>old<\/mtext><\/mrow><\/mrow><\/msub><mo stretchy=\"false\">−<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mn>5<\/mn><mo stretchy=\"false\">−<\/mo><mi>T<\/mi><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\int_a^x \\!\\!\\!\\int_a^s f(y)\\,dy\\,ds = \\int_a^x f(y)(x-y)\\,dy", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/munderover><\/mstyle><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>s<\/mi><\/mrow><\/munderover><\/mstyle><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>s<\/mi><mo stretchy=\"false\">=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/munderover><\/mstyle><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">−<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><\/math>" }, { "input": "\\int_a^x \\!\\!\\!\\int_a^s f(y)\\,dy\\,ds\n= \\int_a^x f(y)(x-y)\\,dy", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/munderover><\/mstyle><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mspace width=\"-0.167em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>s<\/mi><\/mrow><\/munderover><\/mstyle><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>s<\/mi><mo stretchy=\"false\">=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>x<\/mi><\/mrow><\/munderover><\/mstyle><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">−<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>y<\/mi><\/math>" }, { "input": "\\det(\\mathsf{A}-\\lambda\\mathsf{I}) = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>det<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">A<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">−<\/mo><mi>λ<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">I<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "\\det(\\mathsf{A}-\\lambda\\mathsf{I}) = 0", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>det<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">A<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">−<\/mo><mi>λ<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"sans-serif\">I<\/mi><\/mrow><\/mrow><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/math>" }, { "input": "\\sum_{i=0}^{n-1} i", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">−<\/mo><mn>1<\/mn><\/mrow><\/mrow><\/munderover><\/mstyle><mi>i<\/mi><\/math>" }, { "input": "\\sum_{i=0}^{n-1} i", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">−<\/mo><mn>1<\/mn><\/mrow><\/mrow><\/munderover><\/mstyle><mi>i<\/mi><\/math>" }, { "input": "\\sum_{m=1}^\\infty\\sum_{n=1}^\\infty\\frac{m^2\\,n}{3^m\\left(m\\,3^n+n\\,3^m\\right)}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>m<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msup><mi>m<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>n<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msup><mn>3<\/mn><mrow data-mjx-texclass=\"ORD\"><mi>m<\/mi><\/mrow><\/msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mi>m<\/mi><mspace width=\"0.167em\"><\/mspace><msup><mn>3<\/mn><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mi>n<\/mi><mspace width=\"0.167em\"><\/mspace><msup><mn>3<\/mn><mrow data-mjx-texclass=\"ORD\"><mi>m<\/mi><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\sum_{m=1}^\\infty\\sum_{n=1}^\\infty\\frac{m^2\\,n}\n{3^m\\left(m\\,3^n+n\\,3^m\\right)}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>m<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">=<\/mo><mn>1<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msup><mi>m<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mspace width=\"0.167em\"><\/mspace><mi>n<\/mi><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msup><mn>3<\/mn><mrow data-mjx-texclass=\"ORD\"><mi>m<\/mi><\/mrow><\/msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mi>m<\/mi><mspace width=\"0.167em\"><\/mspace><msup><mn>3<\/mn><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><mo stretchy=\"false\">+<\/mo><mi>n<\/mi><mspace width=\"0.167em\"><\/mspace><msup><mn>3<\/mn><mrow data-mjx-texclass=\"ORD\"><mi>m<\/mi><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "u'' + p(x)u' + q(x)u=f(x),\\quad x>a", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>u<\/mi><mo>″<\/mo><\/msup><mo stretchy=\"false\">+<\/mo><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><msup><mi>u<\/mi><mo>′<\/mo><\/msup><mo stretchy=\"false\">+<\/mo><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mi>u<\/mi><mo stretchy=\"false\">=<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>,<\/mo><mspace width=\"1em\"><\/mspace><mi>x<\/mi><mo>><\/mo><mi>a<\/mi><\/math>" }, { "input": "u'' + p(x)u' + q(x)u=f(x),\\quad x>a", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msup><mi>u<\/mi><mo>″<\/mo><\/msup><mo stretchy=\"false\">+<\/mo><mi>p<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><msup><mi>u<\/mi><mo>′<\/mo><\/msup><mo stretchy=\"false\">+<\/mo><mi>q<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mi>u<\/mi><mo stretchy=\"false\">=<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>,<\/mo><mspace width=\"1em\"><\/mspace><mi>x<\/mi><mo>><\/mo><mi>a<\/mi><\/math>" }, { "input": "|\\bar{z}| = |z|, |(\\bar{z})^n| = |z|^n, \\arg(z^n) = n \\arg(z)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">|<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>z<\/mi><mo>\u00af<\/mo><\/mover><\/mrow><\/mrow><mo stretchy=\"false\">|<\/mo><mo stretchy=\"false\">=<\/mo><mo stretchy=\"false\">|<\/mo><mi>z<\/mi><mo stretchy=\"false\">|<\/mo><mo>,<\/mo><mo stretchy=\"false\">|<\/mo><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>z<\/mi><mo>\u00af<\/mo><\/mover><\/mrow><\/mrow><msup><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><mo stretchy=\"false\">|<\/mo><mo stretchy=\"false\">=<\/mo><mo stretchy=\"false\">|<\/mo><mi>z<\/mi><msup><mo stretchy=\"false\">|<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><mo>,<\/mo><mi>arg<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><msup><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mi>n<\/mi><mi>arg<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><\/math>" }, { "input": "|\\bar{z}| = |z|,\n|(\\bar{z})^n| = |z|^n,\n\\arg(z^n) = n \\arg(z)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">|<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>z<\/mi><mo>\u00af<\/mo><\/mover><\/mrow><\/mrow><mo stretchy=\"false\">|<\/mo><mo stretchy=\"false\">=<\/mo><mo stretchy=\"false\">|<\/mo><mi>z<\/mi><mo stretchy=\"false\">|<\/mo><mo>,<\/mo><mo stretchy=\"false\">|<\/mo><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>z<\/mi><mo>\u00af<\/mo><\/mover><\/mrow><\/mrow><msup><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><mo stretchy=\"false\">|<\/mo><mo stretchy=\"false\">=<\/mo><mo stretchy=\"false\">|<\/mo><mi>z<\/mi><msup><mo stretchy=\"false\">|<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><mo>,<\/mo><mi>arg<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><msup><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mi>n<\/mi><mi>arg<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><\/math>" }, { "input": "\\lim_{z\\rightarrow z_0} f(z)=f(z_0)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mi form=\"prefix\">lim<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>z<\/mi><mo stretchy=\"false\">→<\/mo><msub><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mrow><\/munder><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><msub><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><mo stretchy=\"false\">)<\/mo><\/math>" }, { "input": "\\lim_{z\\rightarrow z_0} f(z)=f(z_0)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><munder><mi form=\"prefix\">lim<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>z<\/mi><mo stretchy=\"false\">→<\/mo><msub><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mrow><\/munder><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><msub><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><mo stretchy=\"false\">)<\/mo><\/math>" }, { "input": "\\phi_n(\\kappa)\n= \\frac{1}{4\\pi^2\\kappa^2} \\int_0^\\infty \\frac{\\sin(\\kappa R)}{\\kappa R} \\frac{\\partial}{\\partial R} \\left[R^2\\frac{\\partial D_n(R)}{\\partial R}\\right]\\,dR", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>ϕ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>κ<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><msup><mi>π<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><msup><mi>κ<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mrow><\/mfrac><\/mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>sin<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>κ<\/mi><mi>R<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>κ<\/mi><mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><msup><mi>R<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><msub><mi>D<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>R<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>R<\/mi><\/math>" }, { "input": "\\phi_n(\\kappa) =\n\\frac{1}{4\\pi^2\\kappa^2} \\int_0^\\infty\n\\frac{\\sin(\\kappa R)}{\\kappa R}\n\\frac{\\partial}{\\partial R}\n\\left[R^2\\frac{\\partial D_n(R)}{\\partial R}\\right]\\,dR", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>ϕ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>κ<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mn>4<\/mn><msup><mi>π<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><msup><mi>κ<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mrow><\/mrow><\/mfrac><\/mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∫<\/mo><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>sin<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>κ<\/mi><mi>R<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>κ<\/mi><mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><msup><mi>R<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><msub><mi>D<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>R<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>∂<\/mi><mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><mspace width=\"0.167em\"><\/mspace><mi>d<\/mi><mi>R<\/mi><\/math>" }, { "input": "\\phi_n(\\kappa) = 0.033C_n^2\\kappa^{-11\/3},\\quad \\frac{1}{L_0}\\ll\\kappa\\ll\\frac{1}{l_0}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>ϕ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>κ<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mo stretchy=\"false\">.<\/mo><mn>0<\/mn><mn>3<\/mn><mn>3<\/mn><msubsup><mi>C<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>κ<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mn>1<\/mn><mn>1<\/mn><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mn>3<\/mn><\/mrow><\/mrow><\/msup><mo>,<\/mo><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><msub><mi>L<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/mrow><mo stretchy=\"false\">≪<\/mo><mi>κ<\/mi><mo stretchy=\"false\">≪<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><msub><mi>l<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\phi_n(\\kappa) =\n0.033C_n^2\\kappa^{-11\/3},\\quad\n\\frac{1}{L_0}\\ll\\kappa\\ll\\frac{1}{l_0}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>ϕ<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mi>κ<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><mo stretchy=\"false\">.<\/mo><mn>0<\/mn><mn>3<\/mn><mn>3<\/mn><msubsup><mi>C<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msubsup><msup><mi>κ<\/mi><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">−<\/mo><mn>1<\/mn><mn>1<\/mn><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mn>3<\/mn><\/mrow><\/mrow><\/msup><mo>,<\/mo><mspace width=\"1em\"><\/mspace><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><msub><mi>L<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/mrow><mo stretchy=\"false\">≪<\/mo><mi>κ<\/mi><mo stretchy=\"false\">≪<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><msub><mi>l<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "f(x) = \\begin{cases}1 & -1 \\le x < 0 \\\\\n\\frac{1}{2} & x = 0 \\\\ 1 - x^2 & \\text{otherwise}\\end{cases}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">{<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\" columnalign=\"left left\"><mtr><mtd><mn>1<\/mn><\/mtd><mtd><mo stretchy=\"false\">−<\/mo><mn>1<\/mn><mo stretchy=\"false\">≤<\/mo><mi>x<\/mi><mo><<\/mo><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mfrac><\/mrow><\/mtd><mtd><mi>x<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd><mn>1<\/mn><mo stretchy=\"false\">−<\/mo><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mtd><mtd><mrow data-mjx-texclass=\"ORD\"><mtext>otherwise<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\nf(x) =\n\\begin{cases}\n1 & -1 \\le x < 0 \\\\\n\\frac{1}{2} & x = 0 \\\\\n1 - x^2 & \\text{otherwise}\n\\end{cases}\n", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>f<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\">{<\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\" columnalign=\"left left\"><mtr><mtd><mn>1<\/mn><\/mtd><mtd><mo stretchy=\"false\">−<\/mo><mn>1<\/mn><mo stretchy=\"false\">≤<\/mo><mi>x<\/mi><mo><<\/mo><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/mfrac><\/mrow><\/mtd><mtd><mi>x<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd><mn>1<\/mn><mo stretchy=\"false\">−<\/mo><msup><mi>x<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><\/mtd><mtd><mrow data-mjx-texclass=\"ORD\"><mtext>otherwise<\/mtext><\/mrow><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "{}_pF_q(a_1,\\dots,a_p;c_1,\\dots,c_q;z) = \\sum_{n=0}^\\infty \\frac{(a_1)_n\\cdots(a_p)_n}{(c_1)_n\\cdots(c_q)_n}\\frac{z^n}{n!}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mrow data-mjx-texclass=\"ORD\"\/><mrow data-mjx-texclass=\"ORD\"><mi>p<\/mi><\/mrow><\/msub><msub><mi>F<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>q<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><mo>,<\/mo><mo>…<\/mo><mo>,<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>p<\/mi><\/mrow><\/msub><mo>;<\/mo><msub><mi>c<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><mo>,<\/mo><mo>…<\/mo><mo>,<\/mo><msub><mi>c<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>q<\/mi><\/mrow><\/msub><mo>;<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><msub><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">⋯<\/mo><mo stretchy=\"false\">(<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>p<\/mi><\/mrow><\/msub><msub><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(<\/mo><msub><mi>c<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><msub><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">⋯<\/mo><mo stretchy=\"false\">(<\/mo><msub><mi>c<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>q<\/mi><\/mrow><\/msub><msub><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mrow><\/mfrac><\/mrow><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><msup><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "{}_pF_q(a_1,\\dots,a_p;c_1,\\dots,c_q;z)\n= \\sum_{n=0}^\\infty\n\\frac{(a_1)_n\\cdots(a_p)_n}{(c_1)_n\\cdots(c_q)_n}\n\\frac{z^n}{n!}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mrow data-mjx-texclass=\"ORD\"\/><mrow data-mjx-texclass=\"ORD\"><mi>p<\/mi><\/mrow><\/msub><msub><mi>F<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>q<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><mo>,<\/mo><mo>…<\/mo><mo>,<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>p<\/mi><\/mrow><\/msub><mo>;<\/mo><msub><mi>c<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><mo>,<\/mo><mo>…<\/mo><mo>,<\/mo><msub><mi>c<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>q<\/mi><\/mrow><\/msub><mo>;<\/mo><mi>z<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><munderover><mo stretchy=\"false\">∑<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">=<\/mo><mn>0<\/mn><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"normal\">∞<\/mi><\/mrow><\/munderover><\/mstyle><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><msub><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">⋯<\/mo><mo stretchy=\"false\">(<\/mo><msub><mi>a<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>p<\/mi><\/mrow><\/msub><msub><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(<\/mo><msub><mi>c<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><\/msub><msub><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><mo stretchy=\"false\">⋯<\/mo><mo stretchy=\"false\">(<\/mo><msub><mi>c<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>q<\/mi><\/mrow><\/msub><msub><mo stretchy=\"false\">)<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msub><\/mrow><\/mrow><\/mfrac><\/mrow><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><msup><mi>z<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><\/mrow><\/msup><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi>n<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\frac{a}{b}\\ \\tfrac{a}{b}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mtext> <\/mtext><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "\\frac{a}{b}\\ \\tfrac{a}{b}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><mtext> <\/mtext><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>b<\/mi><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "S=dD\\,\\sin\\alpha\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>S<\/mi><mo stretchy=\"false\">=<\/mo><mi>d<\/mi><mi>D<\/mi><mspace width=\"0.167em\"><\/mspace><mi>sin<\/mi><mo>⁡<\/mo><mi>α<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "S=dD\\,\\sin\\alpha\\!", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>S<\/mi><mo stretchy=\"false\">=<\/mo><mi>d<\/mi><mi>D<\/mi><mspace width=\"0.167em\"><\/mspace><mi>sin<\/mi><mo>⁡<\/mo><mi>α<\/mi><mspace width=\"-0.167em\"><\/mspace><\/math>" }, { "input": "V=\\frac16\\pi h\\left[3\\left(r_1^2+r_2^2\\right)+h^2\\right]", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>V<\/mi><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>6<\/mn><\/mrow><\/mfrac><\/mrow><mi>π<\/mi><mi>h<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mn>3<\/mn><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msubsup><mi>r<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msubsup><mo stretchy=\"false\">+<\/mo><msubsup><mi>r<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msubsup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo stretchy=\"false\">+<\/mo><msup><mi>h<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math>" }, { "input": "V=\\frac16\\pi h\\left[3\\left(r_1^2+r_2^2\\right)+h^2\\right]", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>V<\/mi><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>6<\/mn><\/mrow><\/mfrac><\/mrow><mi>π<\/mi><mi>h<\/mi><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">[<\/mo><mn>3<\/mn><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><msubsup><mi>r<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msubsup><mo stretchy=\"false\">+<\/mo><msubsup><mi>r<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msubsup><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo stretchy=\"false\">+<\/mo><msup><mi>h<\/mi><mrow data-mjx-texclass=\"ORD\"><mn>2<\/mn><\/mrow><\/msup><mo data-mjx-texclass=\"CLOSE\">]<\/mo><\/mrow><\/math>" }, { "input": "\\begin{align}\nu & = \\tfrac{1}{\\sqrt{2}}(x+y) \\qquad & x &= \\tfrac{1}{\\sqrt{2}}(u+v)\\\\\nv & = \\tfrac{1}{\\sqrt{2}}(x-y) \\qquad & y &= \\tfrac{1}{\\sqrt{2}}(u-v)\n\\end{align}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\" rowspacing=\"3pt\"><mtr><mtd><mi>u<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"2em\"><\/mspace><\/mtd><mtd><mi>x<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">(<\/mo><mi>u<\/mi><mo stretchy=\"false\">+<\/mo><mi>v<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><\/mtr><mtr><mtd><mi>v<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">−<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"2em\"><\/mspace><\/mtd><mtd><mi>y<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">(<\/mo><mi>u<\/mi><mo stretchy=\"false\">−<\/mo><mi>v<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\\begin{align}\nu & = \\tfrac{1}{\\sqrt{2}}(x+y) \\qquad & x &= \\tfrac{1}{\\sqrt{2}}(u+v) \\\\\nv & = \\tfrac{1}{\\sqrt{2}}(x-y) \\qquad & y &= \\tfrac{1}{\\sqrt{2}}(u-v)\n\\end{align}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\" rowspacing=\"3pt\"><mtr><mtd><mi>u<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">+<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"2em\"><\/mspace><\/mtd><mtd><mi>x<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">(<\/mo><mi>u<\/mi><mo stretchy=\"false\">+<\/mo><mi>v<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><\/mtr><mtr><mtd><mi>v<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">−<\/mo><mi>y<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"2em\"><\/mspace><\/mtd><mtd><mi>y<\/mi><\/mtd><mtd><mo stretchy=\"false\">=<\/mo><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1<\/mn><\/mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><mo stretchy=\"false\">(<\/mo><mi>u<\/mi><mo stretchy=\"false\">−<\/mo><mi>v<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": " with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped <math> tags. [[Image:foobar.jpg|thumb|<math>2+2", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><\/math>" }, { "input": " with a thumbnail- math enabled [[Image:foobar.jpg|thumb|<math>2+2", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>w<\/mi><mi>i<\/mi><mi>t<\/mi><mi>h<\/mi><mi>a<\/mi><mi>t<\/mi><mi>h<\/mi><mi>u<\/mi><mi>m<\/mi><mi>b<\/mi><mi>n<\/mi><mi>a<\/mi><mi>i<\/mi><mi>l<\/mi><mo stretchy=\"false\">−<\/mo><mi>m<\/mi><mi>a<\/mi><mi>t<\/mi><mi>h<\/mi><mi>e<\/mi><mi>n<\/mi><mi>a<\/mi><mi>b<\/mi><mi>l<\/mi><mi>e<\/mi><mi>d<\/mi><mo stretchy=\"false\">[<\/mo><mo stretchy=\"false\">[<\/mo><mi>I<\/mi><mi>m<\/mi><mi>a<\/mi><mi>g<\/mi><mi>e<\/mi><mo stretchy=\"false\">:<\/mo><mi>f<\/mi><mi>o<\/mi><mi>o<\/mi><mi>b<\/mi><mi>a<\/mi><mi>r<\/mi><mo stretchy=\"false\">.<\/mo><mi>j<\/mi><mi>p<\/mi><mi>g<\/mi><mo stretchy=\"false\">|<\/mo><mi>t<\/mi><mi>h<\/mi><mi>u<\/mi><mi>m<\/mi><mi>b<\/mi><mo stretchy=\"false\">|<\/mo><mo><<\/mo><mi>m<\/mi><mi>a<\/mi><mi>t<\/mi><mi>h<\/mi><mo>><\/mo><mn>2<\/mn><mo stretchy=\"false\">+<\/mo><mn>2<\/mn><\/math>" }, { "input": "<script>alert(document.cookies);<\/script>", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo><<\/mo><mi>s<\/mi><mi>c<\/mi><mi>r<\/mi><mi>i<\/mi><mi>p<\/mi><mi>t<\/mi><mo>><\/mo><mi>a<\/mi><mi>l<\/mi><mi>e<\/mi><mi>r<\/mi><mi>t<\/mi><mo stretchy=\"false\">(<\/mo><mi>d<\/mi><mi>o<\/mi><mi>c<\/mi><mi>u<\/mi><mi>m<\/mi><mi>e<\/mi><mi>n<\/mi><mi>t<\/mi><mo stretchy=\"false\">.<\/mo><mi>c<\/mi><mi>o<\/mi><mi>o<\/mi><mi>k<\/mi><mi>i<\/mi><mi>e<\/mi><mi>s<\/mi><mo stretchy=\"false\">)<\/mo><mo>;<\/mo><mo><<\/mo><mo lspace=\"0\" rspace=\"0\">\/<\/mo><mi>s<\/mi><mi>c<\/mi><mi>r<\/mi><mi>i<\/mi><mi>p<\/mi><mi>t<\/mi><mo>><\/mo><\/math>" }, { "input": "\\widehat{x}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>x<\/mi><mo stretchy=\"true\">^<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": "\\widetilde{x}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>x<\/mi><mo stretchy=\"true\">~<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": "\\euro 200", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>€<\/mo><\/mrow><mn>2<\/mn><mn>0<\/mn><mn>0<\/mn><\/math>" }, { "input": "\\geneuro", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>€<\/mo><\/mrow><\/math>" }, { "input": "\\geneuronarrow", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>€<\/mo><\/mrow><\/math>" }, { "input": "\\geneurowide", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>€<\/mo><\/mrow><\/math>" }, { "input": "\\officialeuro", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>€<\/mo><\/mrow><\/math>" }, { "input": "\\digamma", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>ϝ<\/mi><\/math>" }, { "input": "\\Coppa\\coppa\\varcoppa", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>Ϙ<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mo>ϙ<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mo>ϙ<\/mo><\/mrow><\/math>" }, { "input": "\\Digamma", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>Ϝ<\/mo><\/mrow><\/math>" }, { "input": "\\Koppa\\koppa", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>Ϟ<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mo>ϟ<\/mo><\/mrow><\/math>" }, { "input": "\\Sampi\\sampi", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>Ϡ<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mo>ϡ<\/mo><\/mrow><\/math>" }, { "input": "\\Stigma\\stigma\\varstigma", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>Ϛ<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mo>ϛ<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mo>ϛ<\/mo><\/mrow><\/math>" }, { "input": "\\text{next years}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>next years<\/mtext><\/mrow><\/math>" }, { "input": "\\text{next year's}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>next year's<\/mtext><\/mrow><\/math>" }, { "input": "\\text{`next' year}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mtext>`next' year<\/mtext><\/mrow><\/math>" }, { "input": "\\sin x", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sin<\/mi><mo>⁡<\/mo><mi>x<\/mi><\/math>" }, { "input": "\\sin(x)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sin<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/math>" }, { "input": "\\sin{x}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sin<\/mi><mo>⁡<\/mo><mi>x<\/mi><\/math>" }, { "input": "\\sin x \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sin<\/mi><mo>⁡<\/mo><mi>x<\/mi><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\sin(x) \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sin<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\sin{x} \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>sin<\/mi><mo>⁡<\/mo><mi>x<\/mi><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\sen x", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sen<\/mi><mo>⁡<\/mo><mi>x<\/mi><\/math>" }, { "input": "\\sen(x)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sen<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/math>" }, { "input": "\\sen{x}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sen<\/mi><mo>⁡<\/mo><mi>x<\/mi><\/math>" }, { "input": "\\sen x \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sen<\/mi><mo>⁡<\/mo><mi>x<\/mi><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\sen(x) \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sen<\/mi><mo>⁡<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\sen{x} \\,", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sen<\/mi><mo>⁡<\/mo><mi>x<\/mi><mspace width=\"0.167em\"><\/mspace><\/math>" }, { "input": "\\operatorname{sen}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi data-mjx-texclass=\"OP\" mathvariant=\"normal\">sen<\/mi><\/math>" }, { "input": "\\dot \\vec B", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mi>B<\/mi><mo>\u2192<\/mo><\/mover><\/mrow><\/mrow><mo>\u02d9<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": "\\tilde \\mathcal{M}", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mover><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"-tex-calligraphic\">ℳ<\/mi><\/mrow><\/mrow><mo>~<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": "", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><\/math>", "skipped": false }, { "input": " ", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><\/math>", "skipped": false }, { "input": "\\left(\\begin{smallmatrix}a & b\\\\ c & d\\end{smallmatrix}\\right)", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-texclass=\"OPEN\"><\/mo><mtable columnspacing=\"1em\" rowspacing=\"4pt\"><mtr><mtd><mi>a<\/mi><\/mtd><mtd><mi>b<\/mi><\/mtd><\/mtr><mtr><mtd><mi>c<\/mi><\/mtd><mtd><mi>d<\/mi><\/mtd><\/mtr><\/mtable><\/mrow><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/math>" }, { "input": "\\AA", "params": [], "output": "<math class=\"mwe-math-element\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mo>Å<\/mo><\/mrow><\/math>" } ]
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