[ { "input": "e^{i \\pi} + 1 = 0\\,\\!", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/mspace><\/mspace><\/math>", "skipped": false }, { "input": "e^{i \\pi} + 1 = 0\\,\\!", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/mspace><\/mspace><\/math>", "skipped": false }, { "input": "\\definecolor{red}{RGB}{255,0,0}\\pagecolor{red}e^{i \\pi} + 1 = 0\\,\\!", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/mspace><\/mspace><\/math>", "skipped": false }, { "input": "\\sqrt{\\pi}", "params": { "alt": "Square root of pi" }, "output": "π<\/mi><\/msqrt><\/mrow><\/math>" }, { "input": "\\sqrt{\\pi}", "params": { "alt": "square root of pi" }, "output": "π<\/mi><\/msqrt><\/mrow><\/math>" }, { "input": "\\pi", "params": { "title": "pi" }, "output": "π<\/mi><\/math>" }, { "input": "\\pi", "params": { "title": "pi" }, "output": "π<\/mi><\/math>" }, { "input": "\\text{abc}", "params": [], "output": "abc<\/mtext><\/mrow><\/math>" }, { "input": "\\alpha\\,\\!", "params": [], "output": "α<\/mi><\/mspace><\/mspace><\/math>" }, { "input": " f(x) = x^2\\,\\!", "params": [], "output": "f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>x<\/mi>2<\/mn><\/mrow><\/msup><\/mspace><\/mspace><\/math>" }, { "input": "\\sqrt{2}", "params": [], "output": "2<\/mn><\/msqrt><\/mrow><\/math>" }, { "input": "\\sqrt{1-e^2}\\!", "params": [], "output": "1<\/mn>−<\/mo>e<\/mi>2<\/mn><\/mrow><\/msup><\/mrow><\/msqrt><\/mrow><\/mspace><\/math>" }, { "input": "\\sqrt{1-z^3}\\!", "params": [], "output": "1<\/mn>−<\/mo>z<\/mi>3<\/mn><\/mrow><\/msup><\/mrow><\/msqrt><\/mrow><\/mspace><\/math>" }, { "input": "x", "params": [], "output": "x<\/mi><\/math>" }, { "input": "\\dot{a}, \\ddot{a}, \\acute{a}, \\grave{a} \\!", "params": [], "output": "a<\/mi>\u02d9<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>\u00a8<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>\u00b4<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>`<\/mo><\/mover><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\check{a}, \\breve{a}, \\tilde{a}, \\bar{a} \\!", "params": [], "output": "a<\/mi>\u02c7<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>\u02d8<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>~<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>\u00af<\/mo><\/mover><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\hat{a}, \\widehat{a}, \\vec{a} \\!", "params": [], "output": "a<\/mi>^<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>^<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>\u2192<\/mo><\/mover><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\exp_a b = a^b, \\exp b = e^b, 10^m \\!", "params": [], "output": "exp<\/mi>a<\/mi><\/mrow><\/msub>b<\/mi>=<\/mo>a<\/mi>b<\/mi><\/mrow><\/msup>,<\/mo>exp<\/mi>⁡<\/mo>b<\/mi>=<\/mo>e<\/mi>b<\/mi><\/mrow><\/msup>,<\/mo>1<\/mn>0<\/mn>m<\/mi><\/mrow><\/msup><\/mspace><\/math>" }, { "input": "\\ln c, \\lg d = \\log e, \\log_{10} f \\!", "params": [], "output": "ln<\/mi>⁡<\/mo>c<\/mi>,<\/mo>lg<\/mi>⁡<\/mo>d<\/mi>=<\/mo>log<\/mi>⁡<\/mo>e<\/mi>,<\/mo>log<\/mi>1<\/mn>0<\/mn><\/mrow><\/mrow><\/msub>f<\/mi><\/mspace><\/math>", "skipped": false }, { "input": "\\sin a, \\cos b, \\tan c, \\cot d, \\sec e, \\csc f\\!", "params": [], "output": "sin<\/mi>⁡<\/mo>a<\/mi>,<\/mo>cos<\/mi>⁡<\/mo>b<\/mi>,<\/mo>tan<\/mi>⁡<\/mo>c<\/mi>,<\/mo>cot<\/mi>⁡<\/mo>d<\/mi>,<\/mo>sec<\/mi>⁡<\/mo>e<\/mi>,<\/mo>csc<\/mi>⁡<\/mo>f<\/mi><\/mspace><\/math>" }, { "input": "\\arcsin h, \\arccos i, \\arctan j \\!", "params": [], "output": "arcsin<\/mi>⁡<\/mo>h<\/mi>,<\/mo>arccos<\/mi>⁡<\/mo>i<\/mi>,<\/mo>arctan<\/mi>⁡<\/mo>j<\/mi><\/mspace><\/math>" }, { "input": "\\sinh k, \\cosh l, \\tanh m, \\coth n \\!", "params": [], "output": "sinh<\/mi>⁡<\/mo>k<\/mi>,<\/mo>cosh<\/mi>⁡<\/mo>l<\/mi>,<\/mo>tanh<\/mi>⁡<\/mo>m<\/mi>,<\/mo>coth<\/mi>⁡<\/mo>n<\/mi><\/mspace><\/math>" }, { "input": "\\operatorname{sh}\\,k, \\operatorname{ch}\\,l, \\operatorname{th}\\,m, \\operatorname{coth}\\,n \\!", "params": [], "output": "sh<\/mi>⁡<\/mo><\/mspace>k<\/mi>,<\/mo>ch<\/mi>⁡<\/mo><\/mspace>l<\/mi>,<\/mo>th<\/mi>⁡<\/mo><\/mspace>m<\/mi>,<\/mo>coth<\/mi>⁡<\/mo><\/mspace>n<\/mi><\/mspace><\/math>" }, { "input": "\\operatorname{argsh}\\,o, \\operatorname{argch}\\,p, \\operatorname{argth}\\,q \\!", "params": [], "output": "argsh<\/mi>⁡<\/mo><\/mspace>o<\/mi>,<\/mo>argch<\/mi>⁡<\/mo><\/mspace>p<\/mi>,<\/mo>argth<\/mi>⁡<\/mo><\/mspace>q<\/mi><\/mspace><\/math>" }, { "input": "\\sgn r, \\left\\vert s \\right\\vert \\!", "params": [], "output": "sgn<\/mi>⁡<\/mo>r<\/mi>,<\/mo>|<\/mo>s<\/mi>|<\/mo><\/mrow><\/mspace><\/math>" }, { "input": "\\min(x,y), \\max(x,y) \\!", "params": [], "output": "min<\/mi>⁡<\/mo>(<\/mo>x<\/mi>,<\/mo>y<\/mi>)<\/mo>,<\/mo>max<\/mi>⁡<\/mo>(<\/mo>x<\/mi>,<\/mo>y<\/mi>)<\/mo><\/mspace><\/math>" }, { "input": "\\min x, \\max y, \\inf s, \\sup t \\!", "params": [], "output": "min<\/mi>⁡<\/mo>x<\/mi>,<\/mo>max<\/mi>⁡<\/mo>y<\/mi>,<\/mo>inf<\/mi>⁡<\/mo>s<\/mi>,<\/mo>sup<\/mi>⁡<\/mo>t<\/mi><\/mspace><\/math>" }, { "input": "\\lim u, \\liminf v, \\limsup w \\!", "params": [], "output": "lim<\/mi>⁡<\/mo>u<\/mi>,<\/mo>lim inf<\/mi>⁡<\/mo>v<\/mi>,<\/mo>lim sup<\/mi>⁡<\/mo>w<\/mi><\/mspace><\/math>" }, { "input": "\\dim p, \\deg q, \\det m, \\ker\\phi \\!", "params": [], "output": "dim<\/mi>⁡<\/mo>p<\/mi>,<\/mo>deg<\/mi>⁡<\/mo>q<\/mi>,<\/mo>det<\/mi>⁡<\/mo>m<\/mi>,<\/mo>ker<\/mi>⁡<\/mo>ϕ<\/mi><\/mspace><\/math>" }, { "input": "\\Pr j, \\hom l, \\lVert z \\rVert, \\arg z \\!", "params": [], "output": "Pr<\/mi>⁡<\/mo>j<\/mi>,<\/mo>hom<\/mi>⁡<\/mo>l<\/mi>,<\/mo>‖<\/mo>z<\/mi>‖<\/mo>,<\/mo>arg<\/mi>⁡<\/mo>z<\/mi><\/mspace><\/math>" }, { "input": "dt, \\operatorname{d}\\!t, \\partial t, \\nabla\\psi\\!", "params": [], "output": "d<\/mi>t<\/mi>,<\/mo>d<\/mi>⁡<\/mo><\/mspace>t<\/mi>,<\/mo>∂<\/mi>t<\/mi>,<\/mo>∇<\/mi>ψ<\/mi><\/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": "d<\/mi>y<\/mi>\/<\/mo>d<\/mi>x<\/mi>,<\/mo>d<\/mi>⁡<\/mo><\/mspace>y<\/mi>\/<\/mo>d<\/mi>⁡<\/mo><\/mspace>x<\/mi>,<\/mo>d<\/mi>y<\/mi><\/mrow>d<\/mi>x<\/mi><\/mrow><\/mfrac>,<\/mo>d<\/mi>⁡<\/mo><\/mspace>y<\/mi><\/mrow>d<\/mi>⁡<\/mo><\/mspace>x<\/mi><\/mrow><\/mfrac>,<\/mo>∂<\/mi>2<\/mn><\/mrow><\/msup><\/mrow>∂<\/mi>x<\/mi>1<\/mn><\/mrow><\/msub>∂<\/mi>x<\/mi>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>y<\/mi><\/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": "′<\/mi>,<\/mo>‵<\/mi>,<\/mo>f<\/mi>′<\/mi><\/mrow><\/msup>,<\/mo>f<\/mi>′<\/mo><\/msup>,<\/mo>f<\/mi>″<\/mo><\/msup>,<\/mo>f<\/mi>(<\/mo>3<\/mn>)<\/mo><\/mrow><\/mrow><\/msup><\/mspace>,<\/mo>y<\/mi>\u02d9<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>y<\/mi>\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": "∞<\/mi>,<\/mo>ℵ<\/mi>,<\/mo>∁<\/mi>,<\/mo>∍<\/mo>,<\/mo>ð<\/mi>,<\/mo>Ⅎ<\/mi>,<\/mo>ℏ<\/mi><\/mspace><\/math>" }, { "input": "\\Im, \\imath, \\jmath, \\Bbbk, \\ell, \\mho, \\wp, \\Re, \\circledS \\!", "params": [], "output": "ℑ<\/mi>,<\/mo>ı<\/mi>,<\/mo>ȷ<\/mi>,<\/mo>k<\/mi>,<\/mo>ℓ<\/mi>,<\/mo>℧<\/mi>,<\/mo>℘<\/mi>,<\/mo>ℜ<\/mi>,<\/mo>Ⓢ<\/mi><\/mspace><\/math>" }, { "input": "s_k \\equiv 0 \\pmod{m} \\!", "params": [], "output": "s<\/mi>k<\/mi><\/mrow><\/msub>≡<\/mo>0<\/mn><\/mspace>(<\/mo>mod<\/mi><\/mspace>m<\/mi>)<\/mo><\/mrow><\/mspace><\/math>" }, { "input": "a\\,\\bmod\\,b \\!", "params": [], "output": "a<\/mi><\/mspace>mod<\/mo><\/mspace><\/mrow><\/mrow><\/mrow>b<\/mi><\/mspace><\/math>", "skipped": false, "comemnt": "implement macros later tbd" }, { "input": "\\gcd(m, n), \\operatorname{lcm}(m, n)", "params": [], "output": "gcd<\/mi>⁡<\/mo>(<\/mo>m<\/mi>,<\/mo>n<\/mi>)<\/mo>,<\/mo>lcm<\/mi>⁡<\/mo>(<\/mo>m<\/mi>,<\/mo>n<\/mi>)<\/mo><\/math>" }, { "input": "\\mid, \\nmid, \\shortmid, \\nshortmid \\!", "params": [], "output": "∣<\/mo>,<\/mo>∤<\/mo>,<\/mo>∣<\/mo>,<\/mo>∤<\/mo><\/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": "x<\/mi>3<\/mn><\/mrow><\/msup>+<\/mo>y<\/mi>3<\/mn><\/mrow><\/msup><\/mrow>2<\/mn><\/mrow><\/mfrac>3<\/mn><\/mrow><\/mroot><\/mrow><\/mspace><\/math>" }, { "input": "\\surd, \\sqrt{2}, \\sqrt[n]{}, \\sqrt[3]{x^3+y^3 \\over 2} \\!", "params": [], "output": "√<\/mo>,<\/mo>2<\/mn><\/msqrt><\/mrow>,<\/mo>n<\/mi><\/mrow><\/mroot><\/mrow>,<\/mo>x<\/mi>3<\/mn><\/mrow><\/msup>+<\/mo>y<\/mi>3<\/mn><\/mrow><\/msup><\/mrow>2<\/mn><\/mrow><\/mfrac>3<\/mn><\/mrow><\/mroot><\/mrow><\/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": "+<\/mo>,<\/mo>−<\/mo>,<\/mo>±<\/mo>,<\/mo>∓<\/mo>,<\/mo>∔<\/mo><\/mspace><\/math>" }, { "input": "\\times, \\div, \\divideontimes, \/, \\backslash \\!", "params": [], "output": "×<\/mo>,<\/mo>÷<\/mo>,<\/mo>⋇<\/mo>,<\/mo>\/<\/mo>,<\/mo>∖<\/mi><\/mspace><\/math>" }, { "input": "\\cdot, * \\ast, \\star, \\circ, \\bullet \\!", "params": [], "output": "⋅<\/mo>,<\/mo>*<\/mo>∗<\/mo>,<\/mo>⋆<\/mo>,<\/mo>∘<\/mo>,<\/mo>∙<\/mo><\/mspace><\/math>" }, { "input": "\\boxplus, \\boxminus, \\boxtimes, \\boxdot \\!", "params": [], "output": "⊞<\/mo>,<\/mo>⊟<\/mo>,<\/mo>⊠<\/mo>,<\/mo>⊡<\/mo><\/mspace><\/math>" }, { "input": "\\oplus, \\ominus, \\otimes, \\oslash, \\odot\\!", "params": [], "output": "⊕<\/mo>,<\/mo>⊖<\/mo>,<\/mo>⊗<\/mo>,<\/mo>⊘<\/mo>,<\/mo>⊙<\/mo><\/mspace><\/math>" }, { "input": "\\circleddash, \\circledcirc, \\circledast \\!", "params": [], "output": "⊝<\/mo>,<\/mo>⊚<\/mo>,<\/mo>⊛<\/mo><\/mspace><\/math>" }, { "input": "\\bigoplus, \\bigotimes, \\bigodot \\!", "params": [], "output": "⨁<\/mo>,<\/mo>⨂<\/mo>,<\/mo>⨀<\/mo><\/mspace><\/math>" }, { "input": "\\{ \\}, \\O \\empty \\emptyset, \\varnothing \\!", "params": [], "output": "{<\/mo>}<\/mo>,<\/mo>∅<\/mi>∅<\/mi>∅<\/mi>,<\/mo>∅<\/mi><\/mspace><\/math>" }, { "input": "\\in, \\notin \\not\\in, \\ni, \\not\\ni \\!", "params": [], "output": "∈<\/mo>,<\/mo>∉<\/mo>∉<\/mo>,<\/mo>∋<\/mo>,<\/mo>∌<\/mo><\/mspace><\/math>" }, { "input": "\\cap, \\Cap, \\sqcap, \\bigcap \\!", "params": [], "output": "∩<\/mo>,<\/mo>⋒<\/mo>,<\/mo>⊓<\/mo>,<\/mo>⋂<\/mo><\/mspace><\/math>" }, { "input": "\\cup, \\Cup, \\sqcup, \\bigcup, \\bigsqcup, \\uplus, \\biguplus \\!", "params": [], "output": "∪<\/mo>,<\/mo>⋓<\/mo>,<\/mo>⊔<\/mo>,<\/mo>⋃<\/mo>,<\/mo>⨆<\/mo>,<\/mo>⊎<\/mo>,<\/mo>⨄<\/mo><\/mspace><\/math>" }, { "input": "\\setminus, \\smallsetminus, \\times \\!", "params": [], "output": "∖<\/mo>,<\/mo>∖<\/mo>,<\/mo>×<\/mo><\/mspace><\/math>" }, { "input": "\\subset, \\Subset, \\sqsubset \\!", "params": [], "output": "⊂<\/mo>,<\/mo>⋐<\/mo>,<\/mo>⊏<\/mo><\/mspace><\/math>" }, { "input": "\\supset, \\Supset, \\sqsupset \\!", "params": [], "output": "⊃<\/mo>,<\/mo>⋑<\/mo>,<\/mo>⊐<\/mo><\/mspace><\/math>" }, { "input": "\\subseteq, \\nsubseteq, \\subsetneq, \\varsubsetneq, \\sqsubseteq \\!", "params": [], "output": "⊆<\/mo>,<\/mo>⊈<\/mo>,<\/mo>⊊<\/mo>,<\/mo>⊊<\/mo>,<\/mo>⊑<\/mo><\/mspace><\/math>" }, { "input": "\\supseteq, \\nsupseteq, \\supsetneq, \\varsupsetneq, \\sqsupseteq \\!", "params": [], "output": "⊇<\/mo>,<\/mo>⊉<\/mo>,<\/mo>⊋<\/mo>,<\/mo>⊋<\/mo>,<\/mo>⊒<\/mo><\/mspace><\/math>" }, { "input": "\\subseteqq, \\nsubseteqq, \\subsetneqq, \\varsubsetneqq \\!", "params": [], "output": "⫅<\/mo>,<\/mo>⊈<\/mo>,<\/mo>⫋<\/mo>,<\/mo>⫋<\/mo><\/mspace><\/math>" }, { "input": "\\supseteqq, \\nsupseteqq, \\supsetneqq, \\varsupsetneqq \\!", "params": [], "output": "⫆<\/mo>,<\/mo>⊉<\/mo>,<\/mo>⫌<\/mo>,<\/mo>⫌<\/mo><\/mspace><\/math>" }, { "input": "=, \\ne, \\neq, \\equiv, \\not\\equiv \\!", "params": [], "output": "=<\/mo>,<\/mo>≠<\/mo>,<\/mo>≠<\/mo>,<\/mo>≡<\/mo>,<\/mo>≢<\/mo><\/mspace><\/math>" }, { "input": "\\doteq, \\doteqdot, \\overset{\\underset{\\mathrm{def}}{}}{=}, := \\!", "params": [], "output": "≐<\/mo>,<\/mo>≑<\/mo>,<\/mo>=<\/mo><\/mrow>d<\/mi>e<\/mi>f<\/mi><\/mrow><\/mrow><\/mrow><\/mover><\/mrow>,<\/mo>:<\/mo>=<\/mo><\/mspace><\/math>" }, { "input": "\\sim, \\nsim, \\backsim, \\thicksim, \\simeq, \\backsimeq, \\eqsim, \\cong, \\ncong \\!", "params": [], "output": "∼<\/mo>,<\/mo>≁<\/mo>,<\/mo>∽<\/mo>,<\/mo>∼<\/mo>,<\/mo>≃<\/mo>,<\/mo>⋍<\/mo>,<\/mo>≂<\/mo>,<\/mo>≅<\/mo>,<\/mo>≆<\/mo><\/mspace><\/math>" }, { "input": "\\approx, \\thickapprox, \\approxeq, \\asymp, \\propto, \\varpropto \\!", "params": [], "output": "≈<\/mo>,<\/mo>≈<\/mo>,<\/mo>≊<\/mo>,<\/mo>≍<\/mo>,<\/mo>∝<\/mo>,<\/mo>∝<\/mo><\/mspace><\/math>" }, { "input": "<, \\nless, \\ll, \\not\\ll, \\lll, \\not\\lll, \\lessdot \\!", "params": [], "output": "<<\/mo>,<\/mo>≮<\/mo>,<\/mo>≪<\/mo>,<\/mo>≪̸<\/mo>,<\/mo>⋘<\/mo>,<\/mo>⋘̸<\/mo>,<\/mo>⋖<\/mo><\/mspace><\/math>" }, { "input": ">, \\ngtr, \\gg, \\not\\gg, \\ggg, \\not\\ggg, \\gtrdot \\!", "params": [], "output": "><\/mo>,<\/mo>≯<\/mo>,<\/mo>≫<\/mo>,<\/mo>≫̸<\/mo>,<\/mo>⋙<\/mo>,<\/mo>⋙̸<\/mo>,<\/mo>⋗<\/mo><\/mspace><\/math>" }, { "input": "\\le \\leq, \\lneq, \\leqq, \\nleqq, \\lneqq, \\lvertneqq \\!", "params": [], "output": "≤<\/mo>≤<\/mo>,<\/mo>⪇<\/mo>,<\/mo>≦<\/mo>,<\/mo>≰<\/mo>,<\/mo>≨<\/mo>,<\/mo>≨<\/mo><\/mspace><\/math>" }, { "input": "\\ge \\geq, \\gneq, \\geqq, \\ngeqq, \\gneqq, \\gvertneqq \\!", "params": [], "output": "≥<\/mo>≥<\/mo>,<\/mo>⪈<\/mo>,<\/mo>≧<\/mo>,<\/mo>≱<\/mo>,<\/mo>≩<\/mo>,<\/mo>≩<\/mo><\/mspace><\/math>" }, { "input": "\\lessgtr \\lesseqgtr \\lesseqqgtr \\gtrless \\gtreqless \\gtreqqless \\!", "params": [], "output": "≶<\/mo>⋚<\/mo>⪋<\/mo>≷<\/mo>⋛<\/mo>⪌<\/mo><\/mspace><\/math>" }, { "input": "\\leqslant, \\nleqslant, \\eqslantless \\!", "params": [], "output": "⩽<\/mo>,<\/mo>⪇<\/mo>,<\/mo>⪕<\/mo><\/mspace><\/math>" }, { "input": "\\geqslant, \\ngeqslant, \\eqslantgtr \\!", "params": [], "output": "⩾<\/mo>,<\/mo>⪈<\/mo>,<\/mo>⪖<\/mo><\/mspace><\/math>" }, { "input": "\\lesssim, \\lnsim, \\lessapprox, \\lnapprox \\!", "params": [], "output": "≲<\/mo>,<\/mo>⋦<\/mo>,<\/mo>⪅<\/mo>,<\/mo>⪉<\/mo><\/mspace><\/math>" }, { "input": " \\gtrsim, \\gnsim, \\gtrapprox, \\gnapprox \\,", "params": [], "output": "≳<\/mo>,<\/mo>⋧<\/mo>,<\/mo>⪆<\/mo>,<\/mo>⪊<\/mo><\/mspace><\/math>" }, { "input": "\\prec, \\nprec, \\preceq, \\npreceq, \\precneqq \\!", "params": [], "output": "≺<\/mo>,<\/mo>⊀<\/mo>,<\/mo>⪯<\/mo>,<\/mo>⋠<\/mo>,<\/mo>⪵<\/mo><\/mspace><\/math>" }, { "input": "\\succ, \\nsucc, \\succeq, \\nsucceq, \\succneqq \\!", "params": [], "output": "≻<\/mo>,<\/mo>⊁<\/mo>,<\/mo>⪰<\/mo>,<\/mo>⋡<\/mo>,<\/mo>⪶<\/mo><\/mspace><\/math>" }, { "input": "\\preccurlyeq, \\curlyeqprec \\,", "params": [], "output": "≼<\/mo>,<\/mo>⋞<\/mo><\/mspace><\/math>" }, { "input": "\\succcurlyeq, \\curlyeqsucc \\,", "params": [], "output": "≽<\/mo>,<\/mo>⋟<\/mo><\/mspace><\/math>" }, { "input": "\\precsim, \\precnsim, \\precapprox, \\precnapprox \\,", "params": [], "output": "≾<\/mo>,<\/mo>⋨<\/mo>,<\/mo>⪷<\/mo>,<\/mo>⪹<\/mo><\/mspace><\/math>" }, { "input": "\\succsim, \\succnsim, \\succapprox, \\succnapprox \\,", "params": [], "output": "≿<\/mo>,<\/mo>⋩<\/mo>,<\/mo>⪸<\/mo>,<\/mo>⪺<\/mo><\/mspace><\/math>" }, { "input": "\\parallel, \\nparallel, \\shortparallel, \\nshortparallel \\!", "params": [], "output": "∥<\/mo>,<\/mo>∦<\/mo>,<\/mo>∥<\/mo>,<\/mo>∦<\/mo><\/mspace><\/math>" }, { "input": "\\perp, \\angle, \\sphericalangle, \\measuredangle, 45^\\circ \\!", "params": [], "output": "⊥<\/mo>,<\/mo>∠<\/mi>,<\/mo>∢<\/mi>,<\/mo>∡<\/mi>,<\/mo>4<\/mn>5<\/mn>∘<\/mo><\/mrow><\/msup><\/mspace><\/math>" }, { "input": "\\Box, \\blacksquare, \\diamond, \\Diamond \\lozenge, \\blacklozenge, \\bigstar \\!", "params": [], "output": "◻<\/mi>,<\/mo>◼<\/mi>,<\/mo>⋄<\/mo>,<\/mo>◊<\/mi>◊<\/mi>,<\/mo>⧫<\/mi>,<\/mo>★<\/mi><\/mspace><\/math>" }, { "input": "\\bigcirc, \\triangle \\bigtriangleup, \\bigtriangledown \\!", "params": [], "output": "◯<\/mo>,<\/mo>△<\/mi>△<\/mo>,<\/mo>▽<\/mo><\/mspace><\/math>" }, { "input": "\\vartriangle, \\triangledown\\!", "params": [], "output": "△<\/mo>,<\/mo>▽<\/mi><\/mspace><\/math>" }, { "input": "\\blacktriangle, \\blacktriangledown, \\blacktriangleleft, \\blacktriangleright \\!", "params": [], "output": "▴<\/mi>,<\/mo>▾<\/mi>,<\/mo>◂<\/mo>,<\/mo>▸<\/mo><\/mspace><\/math>" }, { "input": "\\forall, \\exists, \\nexists \\!", "params": [], "output": "∀<\/mi>,<\/mo>∃<\/mi>,<\/mo>∄<\/mi><\/mspace><\/math>" }, { "input": "\\therefore, \\because, \\And \\!", "params": [], "output": "∴<\/mo>,<\/mo>∵<\/mo>,<\/mo>&<\/mi><\/mspace><\/math>" }, { "input": "\\or \\lor \\vee, \\curlyvee, \\bigvee \\!", "params": [], "output": "∨<\/mo>∨<\/mo>∨<\/mo>,<\/mo>⋎<\/mo>,<\/mo>⋁<\/mo><\/mspace><\/math>" }, { "input": "\\and \\land \\wedge, \\curlywedge, \\bigwedge \\!", "params": [], "output": "∧<\/mo>∧<\/mo>∧<\/mo>,<\/mo>⋏<\/mo>,<\/mo>⋀<\/mo><\/mspace><\/math>" }, { "input": "\\bar{q}, \\bar{abc}, \\overline{q}, \\overline{abc}, \\!", "params": [], "output": "q<\/mi>\u00af<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>a<\/mi>b<\/mi>c<\/mi><\/mrow>\u00af<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>q<\/mi>‾<\/mo><\/mover><\/mrow>,<\/mo>a<\/mi>b<\/mi>c<\/mi><\/mrow>‾<\/mo><\/mover><\/mrow>,<\/mo><\/mspace><\/math>" }, { "input": "\\lnot \\neg, \\not\\operatorname{R}, \\bot, \\top \\!", "params": [], "output": "¬<\/mi>¬<\/mi>,<\/mo>⧸<\/mtext><\/mpadded><\/mrow>R<\/mi>⁡<\/mo>,<\/mo>⊥<\/mi>,<\/mo>⊤<\/mi><\/mspace><\/math>" }, { "input": "\\vdash \\dashv, \\vDash, \\Vdash, \\models \\!", "params": [], "output": "⊢<\/mo>⊣<\/mo>,<\/mo>⊨<\/mo>,<\/mo>⊩<\/mo>,<\/mo>⊨<\/mo><\/mspace><\/math>" }, { "input": "\\Vvdash \\nvdash \\nVdash \\nvDash \\nVDash \\!", "params": [], "output": "⊪<\/mo>⊬<\/mo>⊮<\/mo>⊭<\/mo>⊯<\/mo><\/mspace><\/math>" }, { "input": "\\ulcorner \\urcorner \\llcorner \\lrcorner \\,", "params": [], "output": "⌜<\/mo>⌝<\/mo>⌞<\/mo>⌟<\/mo><\/mspace><\/math>" }, { "input": "\\Rrightarrow, \\Lleftarrow \\!", "params": [], "output": "⇛<\/mo>,<\/mo>⇚<\/mo><\/mspace><\/math>" }, { "input": "\\Rightarrow, \\nRightarrow, \\Longrightarrow \\implies\\!", "params": [], "output": "⇒<\/mo>,<\/mo>⇏<\/mo>,<\/mo>⟹<\/mo><\/mstyle>⟹<\/mo><\/mstyle><\/mspace><\/math>" }, { "input": "\\Leftarrow, \\nLeftarrow, \\Longleftarrow \\!", "params": [], "output": "⇐<\/mo>,<\/mo>⇍<\/mo>,<\/mo>⟸<\/mo><\/mspace><\/math>" }, { "input": "\\Leftrightarrow, \\nLeftrightarrow, \\Longleftrightarrow \\iff \\!", "params": [], "output": "⇔<\/mo>,<\/mo>⇎<\/mo>,<\/mo>⟺<\/mo><\/mstyle>⟺<\/mo><\/mstyle><\/mspace><\/math>" }, { "input": "\\Uparrow, \\Downarrow, \\Updownarrow \\!", "params": [], "output": "⇑<\/mo>,<\/mo>⇓<\/mo>,<\/mo>⇕<\/mo><\/mspace><\/math>" }, { "input": "\\rightarrow \\to, \\nrightarrow, \\longrightarrow\\!", "params": [], "output": "→<\/mo>→<\/mo>,<\/mo>↛<\/mo>,<\/mo>⟶<\/mo><\/mspace><\/math>" }, { "input": "\\leftarrow \\gets, \\nleftarrow, \\longleftarrow\\!", "params": [], "output": "←<\/mo>←<\/mo>,<\/mo>↚<\/mo>,<\/mo>⟵<\/mo><\/mspace><\/math>" }, { "input": "\\leftrightarrow, \\nleftrightarrow, \\longleftrightarrow \\!", "params": [], "output": "↔<\/mo>,<\/mo>↮<\/mo>,<\/mo>⟷<\/mo><\/mspace><\/math>" }, { "input": "\\uparrow, \\downarrow, \\updownarrow \\!", "params": [], "output": "↑<\/mo>,<\/mo>↓<\/mo>,<\/mo>↕<\/mo><\/mspace><\/math>" }, { "input": "\\nearrow, \\swarrow, \\nwarrow, \\searrow \\!", "params": [], "output": "↗<\/mo>,<\/mo>↙<\/mo>,<\/mo>↖<\/mo>,<\/mo>↘<\/mo><\/mspace><\/math>" }, { "input": "\\mapsto, \\longmapsto \\!", "params": [], "output": "↦<\/mo>,<\/mo>⟼<\/mo><\/mspace><\/math>" }, { "input": "\\rightharpoonup \\rightharpoondown \\leftharpoonup \\leftharpoondown \\upharpoonleft \\upharpoonright \\downharpoonleft \\downharpoonright \\rightleftharpoons \\leftrightharpoons \\,\\!", "params": [], "output": "⇀<\/mo>⇁<\/mo>↼<\/mo>↽<\/mo>↿<\/mo>↾<\/mo>⇃<\/mo>⇂<\/mo>⇌<\/mo>⇋<\/mo><\/mspace><\/mspace><\/math>" }, { "input": "\\curvearrowleft \\circlearrowleft \\Lsh \\upuparrows \\rightrightarrows \\rightleftarrows \\rightarrowtail \\looparrowright \\,\\!", "params": [], "output": "↶<\/mo>↺<\/mo>↰<\/mo>⇈<\/mo>⇉<\/mo>⇄<\/mo>↣<\/mo>↬<\/mo><\/mspace><\/mspace><\/math>" }, { "input": "\\curvearrowright \\circlearrowright \\Rsh \\downdownarrows \\leftleftarrows \\leftrightarrows \\leftarrowtail \\looparrowleft \\,\\!", "params": [], "output": "↷<\/mo>↻<\/mo>↱<\/mo>⇊<\/mo>⇇<\/mo>⇆<\/mo>↢<\/mo>↫<\/mo><\/mspace><\/mspace><\/math>" }, { "input": "\\hookrightarrow \\hookleftarrow \\multimap \\leftrightsquigarrow \\rightsquigarrow \\twoheadrightarrow \\twoheadleftarrow \\!", "params": [], "output": "↪<\/mo>↩<\/mo>⊸<\/mo>↭<\/mo>⇝<\/mo>↠<\/mo>↞<\/mo><\/mspace><\/math>" }, { "input": "\\amalg \\P \\S \\% \\dagger \\ddagger \\ldots \\cdots \\!", "params": [], "output": "⨿<\/mo>¶<\/mo>§<\/mi>%<\/mi>†<\/mo>‡<\/mo>…<\/mo>⋯<\/mo><\/mspace><\/math>" }, { "input": "\\smile \\frown \\wr \\triangleleft \\triangleright\\!", "params": [], "output": "⌣<\/mo>⌢<\/mo>≀<\/mo>◃<\/mo>▹<\/mo><\/mspace><\/math>" }, { "input": "\\diamondsuit, \\heartsuit, \\clubsuit, \\spadesuit, \\Game, \\flat, \\natural, \\sharp \\!", "params": [], "output": "♢<\/mi>,<\/mo>♡<\/mi>,<\/mo>♣<\/mi>,<\/mo>♠<\/mi>,<\/mo>⅁<\/mi>,<\/mo>♭<\/mi>,<\/mo>♮<\/mi>,<\/mo>♯<\/mi><\/mspace><\/math>" }, { "input": "\\diagup \\diagdown \\centerdot \\ltimes \\rtimes \\leftthreetimes \\rightthreetimes \\!", "params": [], "output": "╱<\/mi>╲<\/mi>⋅<\/mo>⋉<\/mo>⋊<\/mo>⋋<\/mo>⋌<\/mo><\/mspace><\/math>" }, { "input": "\\eqcirc \\circeq \\triangleq \\bumpeq \\Bumpeq \\doteqdot \\risingdotseq \\fallingdotseq \\!", "params": [], "output": "≖<\/mo>≗<\/mo>≜<\/mo>≏<\/mo>≎<\/mo>≑<\/mo>≓<\/mo>≒<\/mo><\/mspace><\/math>" }, { "input": "\\intercal \\barwedge \\veebar \\doublebarwedge \\between \\pitchfork \\!", "params": [], "output": "⊺<\/mo>⊼<\/mo>⊻<\/mo>⩞<\/mo>≬<\/mo>⋔<\/mo><\/mspace><\/math>" }, { "input": "\\vartriangleleft \\ntriangleleft \\vartriangleright \\ntriangleright \\!", "params": [], "output": "⊲<\/mo>⋪<\/mo>⊳<\/mo>⋫<\/mo><\/mspace><\/math>" }, { "input": "\\trianglelefteq \\ntrianglelefteq \\trianglerighteq \\ntrianglerighteq \\!", "params": [], "output": "⊴<\/mo>⋬<\/mo>⊵<\/mo>⋭<\/mo><\/mspace><\/math>" }, { "input": "a^2", "params": [], "output": "a<\/mi>2<\/mn><\/mrow><\/msup><\/math>" }, { "input": "a_2", "params": [], "output": "a<\/mi>2<\/mn><\/mrow><\/msub><\/math>" }, { "input": "10^{30} a^{2+2}", "params": [], "output": "1<\/mn>0<\/mn>3<\/mn>0<\/mn><\/mrow><\/mrow><\/msup>a<\/mi>2<\/mn>+<\/mo>2<\/mn><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "a_{i,j} b_{f'}", "params": [], "output": "a<\/mi>i<\/mi>,<\/mo>j<\/mi><\/mrow><\/mrow><\/msub>b<\/mi>f<\/mi>′<\/mo><\/msup><\/mrow><\/mrow><\/msub><\/math>" }, { "input": "x_2^3", "params": [], "output": "x<\/mi>2<\/mn><\/mrow>3<\/mn><\/mrow><\/msubsup><\/math>" }, { "input": "{x_2}^3 \\,\\!", "params": [], "output": "x<\/mi>2<\/mn><\/mrow><\/msub>3<\/mn><\/mrow><\/msup><\/mspace><\/mspace><\/math>" }, { "input": "10^{10^{8}}", "params": [], "output": "1<\/mn>0<\/mn>1<\/mn>0<\/mn>8<\/mn><\/mrow><\/msup><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "\\sideset{_1^2}{_3^4}\\prod_a^b", "params": [], "output": "∏<\/mo>3<\/mn><\/mrow>4<\/mn><\/mrow>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mmultiscripts><\/mstyle>a<\/mi><\/mrow>b<\/mi><\/mrow><\/munderover><\/mrow><\/math>" }, { "input": "{}_1^2\\!\\Omega_3^4", "params": [], "output": "1<\/mn><\/mrow>2<\/mn><\/mrow><\/msubsup><\/mspace>Ω<\/mi>3<\/mn><\/mrow>4<\/mn><\/mrow><\/msubsup><\/math>" }, { "input": "\\overset{\\alpha}{\\omega}", "params": [], "output": "ω<\/mi><\/mrow>α<\/mi><\/mover><\/mrow><\/math>" }, { "input": "\\underset{\\alpha}{\\omega}", "params": [], "output": "ω<\/mi>α<\/mi><\/munder><\/mrow><\/math>" }, { "input": "\\overset{\\alpha}{\\underset{\\gamma}{\\omega}}", "params": [], "output": "ω<\/mi>γ<\/mi><\/munder><\/mrow><\/mrow>α<\/mi><\/mover><\/mrow><\/math>" }, { "input": "\\stackrel{\\alpha}{\\omega}", "params": [], "output": "ω<\/mi><\/mrow>α<\/mi><\/mrow><\/mover><\/mrow><\/mrow><\/math>" }, { "input": "x', y'', f', f''", "params": [], "output": "x<\/mi>′<\/mo><\/msup>,<\/mo>y<\/mi>″<\/mo><\/msup>,<\/mo>f<\/mi>′<\/mo><\/msup>,<\/mo>f<\/mi>″<\/mo><\/msup><\/math>" }, { "input": "x^\\prime, y^{\\prime\\prime}", "params": [], "output": "x<\/mi>′<\/mi><\/mrow><\/msup>,<\/mo>y<\/mi>′<\/mi>′<\/mi><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "\\dot{x}, \\ddot{x}", "params": [], "output": "x<\/mi>\u02d9<\/mo><\/mover><\/mrow><\/mrow>,<\/mo>x<\/mi>\u00a8<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": " \\hat a \\ \\bar b \\ \\vec c", "params": [], "output": "a<\/mi>^<\/mo><\/mover><\/mrow><\/mrow> <\/mtext>b<\/mi>\u00af<\/mo><\/mover><\/mrow><\/mrow> <\/mtext>c<\/mi>\u2192<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": " \\overrightarrow{a b} \\ \\overleftarrow{c d} \\ \\widehat{d e f}", "params": [], "output": "a<\/mi>b<\/mi><\/mrow>→<\/mo><\/mover><\/mrow> <\/mtext>c<\/mi>d<\/mi><\/mrow>←<\/mo><\/mover><\/mrow> <\/mtext>d<\/mi>e<\/mi>f<\/mi><\/mrow>^<\/mo><\/mover><\/mrow><\/mrow><\/math>" }, { "input": " \\overline{g h i} \\ \\underline{j k l}", "params": [], "output": "g<\/mi>h<\/mi>i<\/mi><\/mrow>‾<\/mo><\/mover><\/mrow> <\/mtext>j<\/mi>k<\/mi>l<\/mi><\/mrow>_<\/mo><\/munder><\/mrow><\/math>" }, { "input": "\\overset{\\frown} {AB}", "params": [], "output": "A<\/mi>B<\/mi><\/mrow><\/mrow>⌢<\/mo><\/mover><\/mrow><\/math>" }, { "input": " A \\xleftarrow{n+\\mu-1} B \\xrightarrow[T]{n\\pm i-1} C", "params": [], "output": "A<\/mi>\u2190<\/mo><\/mstyle>n<\/mi>+<\/mo>μ<\/mi>−<\/mo>1<\/mn><\/mrow><\/mspace><\/mpadded><\/mover>B<\/mi>\u2192<\/mo><\/mstyle>T<\/mi><\/mrow><\/mspace><\/mpadded>n<\/mi>±<\/mo>i<\/mi>−<\/mo>1<\/mn><\/mrow><\/mpadded><\/munderover><\/mrow>C<\/mi><\/math>" }, { "input": "\\overbrace{ 1+2+\\cdots+100 }^{5050}", "params": [], "output": "1<\/mn>+<\/mo>2<\/mn>+<\/mo>⋯<\/mo>+<\/mo>1<\/mn>0<\/mn>0<\/mn><\/mrow>⏞<\/mo><\/mover><\/mrow>5<\/mn>0<\/mn>5<\/mn>0<\/mn><\/mrow><\/mrow><\/mover><\/math>" }, { "input": "\\underbrace{ a+b+\\cdots+z }_{26}", "params": [], "output": "a<\/mi>+<\/mo>b<\/mi>+<\/mo>⋯<\/mo>+<\/mo>z<\/mi><\/mrow>⏟<\/mo><\/munder><\/mrow>2<\/mn>6<\/mn><\/mrow><\/mrow><\/munder><\/math>" }, { "input": "\\sum_{k=1}^N k^2", "params": [], "output": "∑<\/mo>k<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/munderover><\/mstyle>k<\/mi>2<\/mn><\/mrow><\/msup><\/math>" }, { "input": "\\textstyle \\sum_{k=1}^N k^2", "params": [], "output": "∑<\/mo>k<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/msubsup>k<\/mi>2<\/mn><\/mrow><\/msup><\/mstyle><\/math>" }, { "input": "\\frac{\\sum_{k=1}^N k^2}{a}", "params": [], "output": "∑<\/mo>k<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/munderover><\/mstyle>k<\/mi>2<\/mn><\/mrow><\/msup><\/mrow><\/mrow>a<\/mi><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\frac{\\displaystyle \\sum_{k=1}^N k^2}{a}", "params": [], "output": "∑<\/mo>k<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/munderover><\/mstyle>k<\/mi>2<\/mn><\/mrow><\/msup><\/mstyle><\/mrow><\/mrow>a<\/mi><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\frac{\\sum\\limits^{^N}_{k=1} k^2}{a}", "params": [], "output": "∑<\/mo>k<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/msup><\/mrow><\/munderover>k<\/mi>2<\/mn><\/mrow><\/msup><\/mrow><\/mrow>a<\/mi><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\prod_{i=1}^N x_i", "params": [], "output": "∏<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/munderover><\/mstyle>x<\/mi>i<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\textstyle \\prod_{i=1}^N x_i", "params": [], "output": "∏<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/msubsup>x<\/mi>i<\/mi><\/mrow><\/msub><\/mstyle><\/math>" }, { "input": "\\coprod_{i=1}^N x_i", "params": [], "output": "∐<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/munderover><\/mstyle>x<\/mi>i<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\textstyle \\coprod_{i=1}^N x_i", "params": [], "output": "∐<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>N<\/mi><\/mrow><\/msubsup>x<\/mi>i<\/mi><\/mrow><\/msub><\/mstyle><\/math>" }, { "input": "\\lim_{n \\to \\infty}x_n", "params": [], "output": "lim<\/mi>n<\/mi>→<\/mo>∞<\/mi><\/mrow><\/mrow><\/munder>x<\/mi>n<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\textstyle \\lim_{n \\to \\infty}x_n", "params": [], "output": "lim<\/mi>n<\/mi>→<\/mo>∞<\/mi><\/mrow><\/mrow><\/munder>x<\/mi>n<\/mi><\/mrow><\/msub><\/mstyle><\/math>" }, { "input": "\\int\\limits_{1}^{3}\\frac{e^3\/x}{x^2}\\, dx", "params": [], "output": "∫<\/mo>1<\/mn><\/mrow>3<\/mn><\/mrow><\/munderover>e<\/mi>3<\/mn><\/mrow><\/msup>\/<\/mo>x<\/mi><\/mrow><\/mrow>x<\/mi>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mrow><\/mspace>d<\/mi>x<\/mi><\/math>" }, { "input": "\\int_{1}^{3}\\frac{e^3\/x}{x^2}\\, dx", "params": [], "output": "∫<\/mo>1<\/mn><\/mrow>3<\/mn><\/mrow><\/munderover><\/mstyle>e<\/mi>3<\/mn><\/mrow><\/msup>\/<\/mo>x<\/mi><\/mrow><\/mrow>x<\/mi>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac><\/mrow><\/mspace>d<\/mi>x<\/mi><\/math>" }, { "input": "\\textstyle \\int\\limits_{-N}^{N} e^x\\, dx", "params": [], "output": "∫<\/mo>−<\/mo>N<\/mi><\/mrow><\/mrow>N<\/mi><\/mrow><\/munderover>e<\/mi>x<\/mi><\/mrow><\/msup><\/mspace>d<\/mi>x<\/mi><\/mstyle><\/math>" }, { "input": "\\textstyle \\int_{-N}^{N} e^x\\, dx", "params": [], "output": "∫<\/mo>−<\/mo>N<\/mi><\/mrow><\/mrow>N<\/mi><\/mrow><\/msubsup>e<\/mi>x<\/mi><\/mrow><\/msup><\/mspace>d<\/mi>x<\/mi><\/mstyle><\/math>" }, { "input": "\\iint\\limits_D \\, dx\\,dy", "params": [], "output": "∬<\/mo>D<\/mi><\/mrow><\/munder><\/mspace>d<\/mi>x<\/mi><\/mspace>d<\/mi>y<\/mi><\/math>" }, { "input": "\\iiint\\limits_E \\, dx\\,dy\\,dz", "params": [], "output": "∭<\/mo>E<\/mi><\/mrow><\/munder><\/mspace>d<\/mi>x<\/mi><\/mspace>d<\/mi>y<\/mi><\/mspace>d<\/mi>z<\/mi><\/math>" }, { "input": "\\iiiint\\limits_F \\, dx\\,dy\\,dz\\,dt", "params": [], "output": "⨌<\/mo>F<\/mi><\/mrow><\/munder><\/mspace>d<\/mi>x<\/mi><\/mspace>d<\/mi>y<\/mi><\/mspace>d<\/mi>z<\/mi><\/mspace>d<\/mi>t<\/mi><\/math>" }, { "input": "\\int_{(x,y)\\in C} x^3\\, dx + 4y^2\\, dy", "params": [], "output": "∫<\/mo>(<\/mo>x<\/mi>,<\/mo>y<\/mi>)<\/mo>∈<\/mo>C<\/mi><\/mrow><\/mrow><\/munder>x<\/mi>3<\/mn><\/mrow><\/msup><\/mspace>d<\/mi>x<\/mi>+<\/mo>4<\/mn>y<\/mi>2<\/mn><\/mrow><\/msup><\/mspace>d<\/mi>y<\/mi><\/math>" }, { "input": "\\oint_{(x,y)\\in C} x^3\\, dx + 4y^2\\, dy", "params": [], "output": "∮<\/mo><\/mstyle>(<\/mo>x<\/mi>,<\/mo>y<\/mi>)<\/mo>∈<\/mo>C<\/mi><\/mrow><\/mrow><\/msub>x<\/mi>3<\/mn><\/mrow><\/msup><\/mspace>d<\/mi>x<\/mi>+<\/mo>4<\/mn>y<\/mi>2<\/mn><\/mrow><\/msup><\/mspace>d<\/mi>y<\/mi><\/math>", "skipped": false }, { "input": "\\bigcap_{i=_1}^n E_i", "params": [], "output": "⋂<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow><\/msub><\/mrow><\/mrow>n<\/mi><\/mrow><\/munderover><\/mstyle>E<\/mi>i<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\bigcup_{i=_1}^n E_i", "params": [], "output": "⋃<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow><\/msub><\/mrow><\/mrow>n<\/mi><\/mrow><\/munderover><\/mstyle>E<\/mi>i<\/mi><\/mrow><\/msub><\/math>" }, { "input": "\\frac{2}{4}=0.5", "params": [], "output": "2<\/mn><\/mrow>4<\/mn><\/mrow><\/mfrac><\/mrow>=<\/mo>0<\/mn>.<\/mo>5<\/mn><\/math>" }, { "input": "\\tfrac{2}{4} = 0.5", "params": [], "output": "2<\/mn><\/mrow>4<\/mn><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>=<\/mo>0<\/mn>.<\/mo>5<\/mn><\/math>" }, { "input": "\\dfrac{2}{4} = 0.5 \\qquad \\dfrac{2}{c + \\dfrac{2}{d + \\dfrac{2}{4}}} = a", "params": [], "output": "2<\/mn><\/mrow>4<\/mn><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>=<\/mo>0<\/mn>.<\/mo>5<\/mn><\/mspace>2<\/mn><\/mrow>c<\/mi>+<\/mo>2<\/mn><\/mrow>d<\/mi>+<\/mo>2<\/mn><\/mrow>4<\/mn><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>=<\/mo>a<\/mi><\/math>" }, { "input": "\\cfrac{2}{c + \\cfrac{2}{d + \\cfrac{2}{4}}} = a", "params": [], "output": "<\/mpadded><\/mrow>2<\/mn><\/mrow><\/mstyle><\/mrow><\/mpadded><\/mrow>c<\/mi>+<\/mo><\/mpadded><\/mrow>2<\/mn><\/mrow><\/mstyle><\/mrow><\/mpadded><\/mrow>d<\/mi>+<\/mo><\/mpadded><\/mrow>2<\/mn><\/mrow><\/mstyle><\/mrow><\/mpadded><\/mrow>4<\/mn><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><\/mrow><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><\/mrow><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow>=<\/mo>a<\/mi><\/math>" }, { "input": "\\cfrac{x}{1 + \\cfrac{\\cancel{y}}{\\cancel{y}}} = \\cfrac{x}{2}", "params": [], "output": "<\/mpadded><\/mrow>x<\/mi><\/mrow><\/mstyle><\/mrow><\/mpadded><\/mrow>1<\/mn>+<\/mo><\/mpadded><\/mrow>y<\/mi><\/menclose><\/mrow><\/mstyle><\/mrow><\/mpadded><\/mrow>y<\/mi><\/menclose><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><\/mrow><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow>=<\/mo><\/mpadded><\/mrow>x<\/mi><\/mrow><\/mstyle><\/mrow><\/mpadded><\/mrow>2<\/mn><\/mrow><\/mstyle><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\binom{n}{k}", "params": [], "output": "(<\/mo><\/mrow>n<\/mi><\/mrow>k<\/mi><\/mrow><\/mfrac>)<\/mo><\/mrow><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "\\tbinom{n}{k}", "params": [], "output": "(<\/mo><\/mrow>n<\/mi><\/mrow>k<\/mi><\/mrow><\/mfrac>)<\/mo><\/mrow><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "\\dbinom{n}{k}", "params": [], "output": "(<\/mo><\/mrow>n<\/mi><\/mrow>k<\/mi><\/mrow><\/mfrac>)<\/mo><\/mrow><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "\\begin{matrix} x & y \\\\ z & v\n\\end{matrix}", "params": [], "output": "<\/mo>x<\/mi><\/mtd>y<\/mi><\/mtd><\/mtr>z<\/mi><\/mtd>v<\/mi><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\\begin{vmatrix} x & y \\\\ z & v\n\\end{vmatrix}", "params": [], "output": "|<\/mo>x<\/mi><\/mtd>y<\/mi><\/mtd><\/mtr>z<\/mi><\/mtd>v<\/mi><\/mtd><\/mtr><\/mtable>|<\/mo><\/mrow><\/math>" }, { "input": "\\begin{Vmatrix} x & y \\\\ z & v\n\\end{Vmatrix}", "params": [], "output": "‖<\/mo>x<\/mi><\/mtd>y<\/mi><\/mtd><\/mtr>z<\/mi><\/mtd>v<\/mi><\/mtd><\/mtr><\/mtable>‖<\/mo><\/mrow><\/math>" }, { "input": "\\begin{bmatrix} 0 & \\cdots & 0 \\\\ \\vdots\n& \\ddots & \\vdots \\\\ 0 & \\cdots &\n0\\end{bmatrix} ", "params": [], "output": "[<\/mo>0<\/mn><\/mtd>⋯<\/mo><\/mtd>0<\/mn><\/mtd><\/mtr>⋮<\/mo><\/mtd>⋱<\/mo><\/mtd>⋮<\/mo><\/mtd><\/mtr>0<\/mn><\/mtd>⋯<\/mo><\/mtd>0<\/mn><\/mtd><\/mtr><\/mtable>]<\/mo><\/mrow><\/math>" }, { "input": "\\begin{Bmatrix} x & y \\\\ z & v\n\\end{Bmatrix}", "params": [], "output": "{<\/mo>x<\/mi><\/mtd>y<\/mi><\/mtd><\/mtr>z<\/mi><\/mtd>v<\/mi><\/mtd><\/mtr><\/mtable>}<\/mo><\/mrow><\/math>" }, { "input": "\\begin{pmatrix} x & y \\\\ z & v\n\\end{pmatrix}", "params": [], "output": "(<\/mo>x<\/mi><\/mtd>y<\/mi><\/mtd><\/mtr>z<\/mi><\/mtd>v<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/math>" }, { "input": "\n\\bigl( \\begin{smallmatrix}\na&b\\\\ c&d\n\\end{smallmatrix} \\bigr)\n", "params": [], "output": "(<\/mo><\/mo>a<\/mi><\/mtd>b<\/mi><\/mtd><\/mtr>c<\/mi><\/mtd>d<\/mi><\/mtd><\/mtr><\/mtable><\/mrow>)<\/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": "f<\/mi>(<\/mo>n<\/mi>)<\/mo>=<\/mo>{<\/mo>n<\/mi>\/<\/mo>2<\/mn>,<\/mo><\/mtd>if <\/mtext><\/mrow>n<\/mi> is even<\/mtext><\/mrow><\/mtd><\/mtr>3<\/mn>n<\/mi>+<\/mo>1<\/mn>,<\/mo><\/mtd>if <\/mtext><\/mrow>n<\/mi> 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": "f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mtd>=<\/mo>(<\/mo>a<\/mi>+<\/mo>b<\/mi>)<\/mo>2<\/mn><\/mrow><\/msup><\/mtd><\/mtr><\/mtd>=<\/mo>a<\/mi>2<\/mn><\/mrow><\/msup>+<\/mo>2<\/mn>a<\/mi>b<\/mi>+<\/mo>b<\/mi>2<\/mn><\/mrow><\/msup><\/mtd><\/mtr><\/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": "f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mtd>=<\/mo>(<\/mo>a<\/mi>−<\/mo>b<\/mi>)<\/mo>2<\/mn><\/mrow><\/msup><\/mtd><\/mtr><\/mtd>=<\/mo>a<\/mi>2<\/mn><\/mrow><\/msup>−<\/mo>2<\/mn>a<\/mi>b<\/mi>+<\/mo>b<\/mi>2<\/mn><\/mrow><\/msup><\/mtd><\/mtr><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\\begin{array}{lcl}\nz & = & a \\\\\nf(x,y,z) & = & x + y + z\n\\end{array}", "params": [], "output": "z<\/mi><\/mtd>=<\/mo><\/mtd>a<\/mi><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>,<\/mo>y<\/mi>,<\/mo>z<\/mi>)<\/mo><\/mtd>=<\/mo><\/mtd>x<\/mi>+<\/mo>y<\/mi>+<\/mo>z<\/mi><\/mtd><\/mtr><\/mtable><\/math>" }, { "input": "\\begin{array}{lcr}\nz & = & a \\\\\nf(x,y,z) & = & x + y + z\n\\end{array}", "params": [], "output": "z<\/mi><\/mtd>=<\/mo><\/mtd>a<\/mi><\/mtd><\/mtr>f<\/mi>(<\/mo>x<\/mi>,<\/mo>y<\/mi>,<\/mo>z<\/mi>)<\/mo><\/mtd>=<\/mo><\/mtd>x<\/mi>+<\/mo>y<\/mi>+<\/mo>z<\/mi><\/mtd><\/mtr><\/mtable><\/math>" }, { "input": "f(x) \\,\\!", "params": [], "output": "f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mspace><\/mspace><\/math>" }, { "input": "= \\sum_{n=0}^\\infty a_n x^n ", "params": [], "output": "=<\/mo>∑<\/mo>n<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>a<\/mi>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/mrow><\/msup><\/math>" }, { "input": "= a_0+a_1x+a_2x^2+\\cdots", "params": [], "output": "=<\/mo>a<\/mi>0<\/mn><\/mrow><\/msub>+<\/mo>a<\/mi>1<\/mn><\/mrow><\/msub>x<\/mi>+<\/mo>a<\/mi>2<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn><\/mrow><\/msup>+<\/mo>⋯<\/mo><\/math>" }, { "input": "f(x) \\,\\!", "params": [], "output": "f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mspace><\/mspace><\/math>" }, { "input": "= \\sum_{n=0}^\\infty a_n x^n ", "params": [], "output": "=<\/mo>∑<\/mo>n<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>a<\/mi>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/mrow><\/msup><\/math>" }, { "input": "= a_0 +a_1x+a_2x^2+\\cdots", "params": [], "output": "=<\/mo>a<\/mi>0<\/mn><\/mrow><\/msub>+<\/mo>a<\/mi>1<\/mn><\/mrow><\/msub>x<\/mi>+<\/mo>a<\/mi>2<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn><\/mrow><\/msup>+<\/mo>⋯<\/mo><\/math>" }, { "input": "\\begin{cases} 3x + 5y + z \\\\ 7x - 2y + 4z \\\\ -6x + 3y + 2z \\end{cases}", "params": [], "output": "{<\/mo>3<\/mn>x<\/mi>+<\/mo>5<\/mn>y<\/mi>+<\/mo>z<\/mi><\/mtd><\/mtr>7<\/mn>x<\/mi>−<\/mo>2<\/mn>y<\/mi>+<\/mo>4<\/mn>z<\/mi><\/mtd><\/mtr>−<\/mo>6<\/mn>x<\/mi>+<\/mo>3<\/mn>y<\/mi>+<\/mo>2<\/mn>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": "a<\/mi><\/mtd>b<\/mi><\/mtd>S<\/mi><\/mtd><\/mtr>0<\/mn><\/mtd>0<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd>0<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd>1<\/mn><\/mtd>0<\/mn><\/mtd><\/mtr><\/mtd><\/mtr><\/mtable><\/math>" }, { "input": "( \\frac{1}{2} )", "params": [], "output": "(<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac><\/mrow>)<\/mo><\/math>" }, { "input": "\\left ( \\frac{1}{2} \\right )", "params": [], "output": "(<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow><\/math>" }, { "input": "\\left ( \\frac{a}{b} \\right )", "params": [], "output": "(<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow><\/math>" }, { "input": "\\left [ \\frac{a}{b} \\right ] \\quad \\left \\lbrack \\frac{a}{b} \\right \\rbrack", "params": [], "output": "[<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>]<\/mo><\/mrow><\/mspace>[<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>]<\/mo><\/mrow><\/math>" }, { "input": "\\left \\{ \\frac{a}{b} \\right \\} \\quad \\left \\lbrace \\frac{a}{b} \\right \\rbrace", "params": [], "output": "{<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>}<\/mo><\/mrow><\/mspace>{<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>}<\/mo><\/mrow><\/math>" }, { "input": "\\left \\langle \\frac{a}{b} \\right \\rangle", "params": [], "output": "⟨<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>⟩<\/mo><\/mrow><\/math>" }, { "input": "\\left | \\frac{a}{b} \\right \\vert \\quad \\left \\Vert \\frac{c}{d} \\right \\|", "params": [], "output": "|<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>|<\/mo><\/mrow><\/mspace>‖<\/mo>c<\/mi><\/mrow>d<\/mi><\/mrow><\/mfrac><\/mrow>‖<\/mo><\/mrow><\/math>" }, { "input": "\\left \\lfloor \\frac{a}{b} \\right \\rfloor \\quad \\left \\lceil \\frac{c}{d} \\right \\rceil", "params": [], "output": "⌊<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>⌋<\/mo><\/mrow><\/mspace>⌈<\/mo>c<\/mi><\/mrow>d<\/mi><\/mrow><\/mfrac><\/mrow>⌉<\/mo><\/mrow><\/math>" }, { "input": "\\left \/ \\frac{a}{b} \\right \\backslash", "params": [], "output": "\/<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>\\<\/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": "↑<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>↓<\/mo><\/mrow><\/mspace>⇑<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>⇓<\/mo><\/mrow><\/mspace>↕<\/mo>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow>⇕<\/mo><\/mrow><\/math>" }, { "input": "\\left [ 0,1 \\right )", "params": [], "output": "[<\/mo>0<\/mn>,<\/mo>1<\/mn>)<\/mo><\/mrow><\/math>" }, { "input": "\\left \\langle \\psi \\right |", "params": [], "output": "⟨<\/mo>ψ<\/mi>|<\/mo><\/mrow><\/math>" }, { "input": "\\left . \\frac{A}{B} \\right \\} \\to X", "params": [], "output": "<\/mo>A<\/mi><\/mrow>B<\/mi><\/mrow><\/mfrac><\/mrow>}<\/mo><\/mrow>→<\/mo>X<\/mi><\/math>" }, { "input": "\\big( \\Big( \\bigg( \\Bigg( \\dots \\Bigg] \\bigg] \\Big] \\big]", "params": [], "output": "(<\/mo>(<\/mo>(<\/mo>(<\/mo>…<\/mo>]<\/mo>]<\/mo>]<\/mo>]<\/mo><\/math>" }, { "input": "\\big\\{ \\Big\\{ \\bigg\\{ \\Bigg\\{ \\dots \\Bigg\\rangle \\bigg\\rangle \\Big\\rangle \\big\\rangle", "params": [], "output": "{<\/mo>{<\/mo>{<\/mo>{<\/mo>…<\/mo>⟩<\/mo>⟩<\/mo>⟩<\/mo>⟩<\/mo><\/math>" }, { "input": "\\big\\| \\Big\\| \\bigg\\| \\Bigg\\| \\dots \\Bigg| \\bigg| \\Big| \\big|", "params": [], "output": "‖<\/mo>‖<\/mo>‖<\/mo>‖<\/mo>…<\/mo>|<\/mo>|<\/mo>|<\/mo>|<\/mo><\/math>" }, { "input": "\\big\\lfloor \\Big\\lfloor \\bigg\\lfloor \\Bigg\\lfloor \\dots \\Bigg\\rceil \\bigg\\rceil \\Big\\rceil \\big\\rceil", "params": [], "output": "⌊<\/mo>⌊<\/mo>⌊<\/mo>⌊<\/mo>…<\/mo>⌉<\/mo>⌉<\/mo>⌉<\/mo>⌉<\/mo><\/math>" }, { "input": "\\big\\uparrow \\Big\\uparrow \\bigg\\uparrow \\Bigg\\uparrow \\dots \\Bigg\\Downarrow \\bigg\\Downarrow \\Big\\Downarrow \\big\\Downarrow", "params": [], "output": "↑<\/mo>↑<\/mo>↑<\/mo>↑<\/mo>…<\/mo>⇓<\/mo>⇓<\/mo>⇓<\/mo>⇓<\/mo><\/math>" }, { "input": "\\big\\updownarrow \\Big\\updownarrow \\bigg\\updownarrow \\Bigg\\updownarrow \\dots \\Bigg\\Updownarrow \\bigg\\Updownarrow \\Big\\Updownarrow \\big\\Updownarrow", "params": [], "output": "↕<\/mo>↕<\/mo>↕<\/mo>↕<\/mo>…<\/mo>⇕<\/mo>⇕<\/mo>⇕<\/mo>⇕<\/mo><\/math>" }, { "input": "\\big \/ \\Big \/ \\bigg \/ \\Bigg \/ \\dots \\Bigg\\backslash \\bigg\\backslash \\Big\\backslash \\big\\backslash", "params": [], "output": "\/<\/mo>\/<\/mo>\/<\/mo>\/<\/mo>…<\/mo>\\<\/mo>\\<\/mo>\\<\/mo>\\<\/mo><\/math>" }, { "input": "x^2 + y^2 + z^2 = 1 \\,", "params": [], "output": "x<\/mi>2<\/mn><\/mrow><\/msup>+<\/mo>y<\/mi>2<\/mn><\/mrow><\/msup>+<\/mo>z<\/mi>2<\/mn><\/mrow><\/msup>=<\/mo>1<\/mn><\/mspace><\/math>" }, { "input": "\\Alpha \\Beta \\Gamma \\Delta \\Epsilon \\Zeta \\Eta \\Theta \\!", "params": [], "output": "A<\/mi><\/mrow>B<\/mi><\/mrow>Γ<\/mi>Δ<\/mi>E<\/mi><\/mrow>Z<\/mi><\/mrow>H<\/mi><\/mrow>Θ<\/mi><\/mspace><\/math>" }, { "input": "\\Iota \\Kappa \\Lambda \\Mu \\Nu \\Xi \\Pi \\Rho \\!", "params": [], "output": "I<\/mi><\/mrow>K<\/mi><\/mrow>Λ<\/mi>M<\/mi><\/mrow>N<\/mi><\/mrow>Ξ<\/mi>Π<\/mi>P<\/mi><\/mrow><\/mspace><\/math>" }, { "input": "\\Sigma \\Tau \\Upsilon \\Phi \\Chi \\Psi \\Omega \\!", "params": [], "output": "Σ<\/mi>T<\/mi><\/mrow>Υ<\/mi>Φ<\/mi>X<\/mi><\/mrow>Ψ<\/mi>Ω<\/mi><\/mspace><\/math>" }, { "input": "\\alpha \\beta \\gamma \\delta \\epsilon \\zeta \\eta \\theta \\!", "params": [], "output": "α<\/mi>β<\/mi>γ<\/mi>δ<\/mi>ϵ<\/mi>ζ<\/mi>η<\/mi>θ<\/mi><\/mspace><\/math>" }, { "input": "\\iota \\kappa \\lambda \\mu \\nu \\xi \\pi \\rho \\!", "params": [], "output": "ι<\/mi>κ<\/mi>λ<\/mi>μ<\/mi>ν<\/mi>ξ<\/mi>π<\/mi>ρ<\/mi><\/mspace><\/math>" }, { "input": "\\sigma \\tau \\upsilon \\phi \\chi \\psi \\omega \\!", "params": [], "output": "σ<\/mi>τ<\/mi>υ<\/mi>ϕ<\/mi>χ<\/mi>ψ<\/mi>ω<\/mi><\/mspace><\/math>" }, { "input": "\\varepsilon \\digamma \\varkappa \\varpi \\!", "params": [], "output": "ε<\/mi>ϝ<\/mi>ϰ<\/mi>ϖ<\/mi><\/mspace><\/math>" }, { "input": "\\varrho \\varsigma \\vartheta \\varphi \\!", "params": [], "output": "ϱ<\/mi>ς<\/mi>ϑ<\/mi>φ<\/mi><\/mspace><\/math>" }, { "input": "\\aleph \\beth \\gimel \\daleth \\!", "params": [], "output": "ℵ<\/mi>ℶ<\/mi>ℷ<\/mi>ℸ<\/mi><\/mspace><\/math>" }, { "input": "\\mathbb{ABCDEFGHI} \\!", "params": [], "output": "𝔸<\/mi>𝔹<\/mi>ℂ<\/mi>𝔻<\/mi>𝔼<\/mi>𝔽<\/mi>𝔾<\/mi>ℍ<\/mi>𝕀<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathbb{JKLMNOPQR} \\!", "params": [], "output": "𝕁<\/mi>𝕂<\/mi>𝕃<\/mi>𝕄<\/mi>ℕ<\/mi>𝕆<\/mi>ℙ<\/mi>ℚ<\/mi>ℝ<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathbb{STUVWXYZ} \\!", "params": [], "output": "𝕊<\/mi>𝕋<\/mi>𝕌<\/mi>𝕍<\/mi>𝕎<\/mi>𝕏<\/mi>𝕐<\/mi>ℤ<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathbf{ABCDEFGHI} \\!", "params": [], "output": "𝐀<\/mi>𝐁<\/mi>𝐂<\/mi>𝐃<\/mi>𝐄<\/mi>𝐅<\/mi>𝐆<\/mi>𝐇<\/mi>𝐈<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathbf{JKLMNOPQR} \\!", "params": [], "output": "𝐉<\/mi>𝐊<\/mi>𝐋<\/mi>𝐌<\/mi>𝐍<\/mi>𝐎<\/mi>𝐏<\/mi>𝐐<\/mi>𝐑<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathbf{STUVWXYZ} \\!", "params": [], "output": "𝐒<\/mi>𝐓<\/mi>𝐔<\/mi>𝐕<\/mi>𝐖<\/mi>𝐗<\/mi>𝐘<\/mi>𝐙<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathbf{abcdefghijklm} \\!", "params": [], "output": "𝐚<\/mi>𝐛<\/mi>𝐜<\/mi>𝐝<\/mi>𝐞<\/mi>𝐟<\/mi>𝐠<\/mi>𝐡<\/mi>𝐢<\/mi>𝐣<\/mi>𝐤<\/mi>𝐥<\/mi>𝐦<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathbf{nopqrstuvwxyz} \\!", "params": [], "output": "𝐧<\/mi>𝐨<\/mi>𝐩<\/mi>𝐪<\/mi>𝐫<\/mi>𝐬<\/mi>𝐭<\/mi>𝐮<\/mi>𝐯<\/mi>𝐰<\/mi>𝐱<\/mi>𝐲<\/mi>𝐳<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathbf{0123456789} \\!", "params": [], "output": "𝟎<\/mn>𝟏<\/mn>𝟐<\/mn>𝟑<\/mn>𝟒<\/mn>𝟓<\/mn>𝟔<\/mn>𝟕<\/mn>𝟖<\/mn>𝟗<\/mn><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\Alpha\\Beta\\Gamma\\Delta\\Epsilon\\Zeta\\Eta\\Theta} \\!", "params": [], "output": "A<\/mi><\/mrow>B<\/mi><\/mrow>Γ<\/mi>Δ<\/mi>E<\/mi><\/mrow>Z<\/mi><\/mrow>H<\/mi><\/mrow>Θ<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\Iota\\Kappa\\Lambda\\Mu\\Nu\\Xi\\Pi\\Rho} \\!", "params": [], "output": "I<\/mi><\/mrow>K<\/mi><\/mrow>Λ<\/mi>M<\/mi><\/mrow>N<\/mi><\/mrow>Ξ<\/mi>Π<\/mi>P<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\Sigma\\Tau\\Upsilon\\Phi\\Chi\\Psi\\Omega} \\!", "params": [], "output": "Σ<\/mi>T<\/mi><\/mrow>Υ<\/mi>Φ<\/mi>X<\/mi><\/mrow>Ψ<\/mi>Ω<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\alpha\\beta\\gamma\\delta\\epsilon\\zeta\\eta\\theta} \\!", "params": [], "output": "α<\/mi>β<\/mi>γ<\/mi>δ<\/mi>ϵ<\/mi>ζ<\/mi>η<\/mi>θ<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\iota\\kappa\\lambda\\mu\\nu\\xi\\pi\\rho} \\!", "params": [], "output": "ι<\/mi>κ<\/mi>λ<\/mi>μ<\/mi>ν<\/mi>ξ<\/mi>π<\/mi>ρ<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\sigma\\tau\\upsilon\\phi\\chi\\psi\\omega} \\!", "params": [], "output": "σ<\/mi>τ<\/mi>υ<\/mi>ϕ<\/mi>χ<\/mi>ψ<\/mi>ω<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\varepsilon\\digamma\\varkappa\\varpi} \\!", "params": [], "output": "ε<\/mi>ϝ<\/mi>ϰ<\/mi>ϖ<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\boldsymbol{\\varrho\\varsigma\\vartheta\\varphi} \\!", "params": [], "output": "ϱ<\/mi>ς<\/mi>ϑ<\/mi>φ<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathit{0123456789} \\!", "params": [], "output": "0<\/mn>1<\/mn>2<\/mn>3<\/mn>4<\/mn>5<\/mn>6<\/mn>7<\/mn>8<\/mn>9<\/mn><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathit{\\Alpha\\Beta\\Gamma\\Delta\\Epsilon\\Zeta\\Eta\\Theta} \\!", "params": [], "output": "A<\/mi><\/mrow>B<\/mi><\/mrow>Γ<\/mi>Δ<\/mi>E<\/mi><\/mrow>Z<\/mi><\/mrow>H<\/mi><\/mrow>Θ<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathit{\\Iota\\Kappa\\Lambda\\Mu\\Nu\\Xi\\Pi\\Rho} \\!", "params": [], "output": "I<\/mi><\/mrow>K<\/mi><\/mrow>Λ<\/mi>M<\/mi><\/mrow>N<\/mi><\/mrow>Ξ<\/mi>Π<\/mi>P<\/mi><\/mrow><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathit{\\Sigma\\Tau\\Upsilon\\Phi\\Chi\\Psi\\Omega} \\!", "params": [], "output": "Σ<\/mi>T<\/mi><\/mrow>Υ<\/mi>Φ<\/mi>X<\/mi><\/mrow>Ψ<\/mi>Ω<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathrm{ABCDEFGHI} \\!", "params": [], "output": "A<\/mi>B<\/mi>C<\/mi>D<\/mi>E<\/mi>F<\/mi>G<\/mi>H<\/mi>I<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathrm{JKLMNOPQR} \\!", "params": [], "output": "J<\/mi>K<\/mi>L<\/mi>M<\/mi>N<\/mi>O<\/mi>P<\/mi>Q<\/mi>R<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathrm{STUVWXYZ} \\!", "params": [], "output": "S<\/mi>T<\/mi>U<\/mi>V<\/mi>W<\/mi>X<\/mi>Y<\/mi>Z<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathrm{abcdefghijklm} \\!", "params": [], "output": "a<\/mi>b<\/mi>c<\/mi>d<\/mi>e<\/mi>f<\/mi>g<\/mi>h<\/mi>i<\/mi>j<\/mi>k<\/mi>l<\/mi>m<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathrm{nopqrstuvwxyz} \\!", "params": [], "output": "n<\/mi>o<\/mi>p<\/mi>q<\/mi>r<\/mi>s<\/mi>t<\/mi>u<\/mi>v<\/mi>w<\/mi>x<\/mi>y<\/mi>z<\/mi><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathrm{0123456789} \\!", "params": [], "output": "0<\/mn>1<\/mn>2<\/mn>3<\/mn>4<\/mn>5<\/mn>6<\/mn>7<\/mn>8<\/mn>9<\/mn><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{ABCDEFGHI} \\!", "params": [], "output": "A<\/mi>B<\/mi>C<\/mi>D<\/mi>E<\/mi>F<\/mi>G<\/mi>H<\/mi>I<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{JKLMNOPQR} \\!", "params": [], "output": "J<\/mi>K<\/mi>L<\/mi>M<\/mi>N<\/mi>O<\/mi>P<\/mi>Q<\/mi>R<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{STUVWXYZ} \\!", "params": [], "output": "S<\/mi>T<\/mi>U<\/mi>V<\/mi>W<\/mi>X<\/mi>Y<\/mi>Z<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{abcdefghijklm} \\!", "params": [], "output": "a<\/mi>b<\/mi>c<\/mi>d<\/mi>e<\/mi>f<\/mi>g<\/mi>h<\/mi>i<\/mi>j<\/mi>k<\/mi>l<\/mi>m<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{nopqrstuvwxyz} \\!", "params": [], "output": "n<\/mi>o<\/mi>p<\/mi>q<\/mi>r<\/mi>s<\/mi>t<\/mi>u<\/mi>v<\/mi>w<\/mi>x<\/mi>y<\/mi>z<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{0123456789} \\!", "params": [], "output": "0<\/mn>1<\/mn>2<\/mn>3<\/mn>4<\/mn>5<\/mn>6<\/mn>7<\/mn>8<\/mn>9<\/mn><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{\\Alpha \\Beta \\Gamma \\Delta \\Epsilon \\Zeta \\Eta \\Theta} \\!", "params": [], "output": "A<\/mi><\/mrow>B<\/mi><\/mrow>Γ<\/mi>Δ<\/mi>E<\/mi><\/mrow>Z<\/mi><\/mrow>H<\/mi><\/mrow>Θ<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{\\Iota \\Kappa \\Lambda \\Mu \\Nu \\Xi \\Pi \\Rho} \\!", "params": [], "output": "I<\/mi><\/mrow>K<\/mi><\/mrow>Λ<\/mi>M<\/mi><\/mrow>N<\/mi><\/mrow>Ξ<\/mi>Π<\/mi>P<\/mi><\/mrow><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathsf{\\Sigma \\Tau \\Upsilon \\Phi \\Chi \\Psi \\Omega}\\!", "params": [], "output": "Σ<\/mi>T<\/mi><\/mrow>Υ<\/mi>Φ<\/mi>X<\/mi><\/mrow>Ψ<\/mi>Ω<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathcal{ABCDEFGHI} \\!", "params": [], "output": "𝒜<\/mi>ℬ<\/mi>𝒞<\/mi>𝒟<\/mi>ℰ<\/mi>ℱ<\/mi>𝒢<\/mi>ℋ<\/mi>ℐ<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathcal{JKLMNOPQR} \\!", "params": [], "output": "𝒥<\/mi>𝒦<\/mi>ℒ<\/mi>ℳ<\/mi>𝒩<\/mi>𝒪<\/mi>𝒫<\/mi>𝒬<\/mi>ℛ<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathcal{STUVWXYZ} \\!", "params": [], "output": "𝒮<\/mi>𝒯<\/mi>𝒰<\/mi>𝒱<\/mi>𝒲<\/mi>𝒳<\/mi>𝒴<\/mi>𝒵<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathfrak{ABCDEFGHI} \\!", "params": [], "output": "𝔄<\/mi>𝔅<\/mi>ℭ<\/mi>𝔇<\/mi>𝔈<\/mi>𝔉<\/mi>𝔊<\/mi>ℌ<\/mi>ℑ<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathfrak{JKLMNOPQR} \\!", "params": [], "output": "𝔍<\/mi>𝔎<\/mi>𝔏<\/mi>𝔐<\/mi>𝔑<\/mi>𝔒<\/mi>𝔓<\/mi>𝔔<\/mi>ℜ<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathfrak{STUVWXYZ} \\!", "params": [], "output": "𝔖<\/mi>𝔗<\/mi>𝔘<\/mi>𝔙<\/mi>𝔚<\/mi>𝔛<\/mi>𝔜<\/mi>ℤ<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathfrak{abcdefghijklm} \\!", "params": [], "output": "𝔞<\/mi>𝔟<\/mi>𝔠<\/mi>𝔡<\/mi>𝔢<\/mi>𝔣<\/mi>𝔤<\/mi>𝔥<\/mi>𝔦<\/mi>𝔧<\/mi>𝔨<\/mi>𝔩<\/mi>𝔪<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathfrak{nopqrstuvwxyz} \\!", "params": [], "output": "𝔫<\/mi>𝔬<\/mi>𝔭<\/mi>𝔮<\/mi>𝔯<\/mi>𝔰<\/mi>𝔱<\/mi>𝔲<\/mi>𝔳<\/mi>𝔴<\/mi>𝔵<\/mi>𝔶<\/mi>𝔷<\/mi><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "\\mathfrak{0123456789} \\!", "params": [], "output": "0<\/mn>1<\/mn>2<\/mn>3<\/mn>4<\/mn>5<\/mn>6<\/mn>7<\/mn>8<\/mn>9<\/mn><\/mrow><\/mrow><\/mrow><\/mspace><\/math>" }, { "input": "x y z", "params": [], "output": "x<\/mi>y<\/mi>z<\/mi><\/math>" }, { "input": "\\text{x y z}", "params": [], "output": "x y z<\/mtext><\/mrow><\/math>" }, { "input": "\\text{if} n \\text{is even}", "params": [], "output": "if<\/mtext><\/mrow>n<\/mi>is even<\/mtext><\/mrow><\/math>" }, { "input": "\\text{if }n\\text{ is even}", "params": [], "output": "if <\/mtext><\/mrow>n<\/mi> is even<\/mtext><\/mrow><\/math>" }, { "input": "\\text{if}~n\\ \\text{is even}", "params": [], "output": "if<\/mtext><\/mrow>n<\/mi> <\/mtext>is even<\/mtext><\/mrow><\/math>" }, { "input": "{\\color{Blue}x^2}+{\\color{YellowOrange}2x}-{\\color{OliveGreen}1}", "params": [], "output": "x<\/mi>2<\/mn><\/mrow><\/msup><\/mstyle><\/mrow>+<\/mo>2<\/mn><\/mstyle>x<\/mi><\/mstyle><\/mrow>−<\/mo>1<\/mn><\/mstyle><\/mrow><\/math>" }, { "input": "x_{1,2}=\\frac{-b\\pm\\sqrt{\\color{Red}b^2-4ac}}{2a}", "params": [], "output": "x<\/mi>1<\/mn>,<\/mo>2<\/mn><\/mrow><\/mrow><\/msub>=<\/mo>−<\/mo>b<\/mi>±<\/mo>b<\/mi>2<\/mn><\/mrow><\/msup><\/mstyle>−<\/mo><\/mstyle>4<\/mn><\/mstyle>a<\/mi><\/mstyle>c<\/mi><\/mstyle><\/mrow><\/msqrt><\/mrow><\/mrow><\/mrow>2<\/mn>a<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "e^{i \\pi} + 1 = 0", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/math>" }, { "input": "\\definecolor{orange}{RGB}{255,165,0}\\pagecolor{orange}e^{i \\pi} + 1 = 0", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/math>" }, { "input": "e^{i \\pi} + 1 = 0\\,\\!", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/mspace><\/mspace><\/math>" }, { "input": "\\definecolor{orange}{RGB}{255,165,0}\\pagecolor{orange}e^{i \\pi} + 1 = 0", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/math>" }, { "input": "e^{i \\pi} + 1 = 0", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/math>" }, { "input": "\\definecolor{orange}{RGB}{255,165,0}\\pagecolor{orange}e^{i \\pi} + 1 = 0", "params": [], "output": "e<\/mi>i<\/mi>π<\/mi><\/mrow><\/mrow><\/msup>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/math>" }, { "input": "\\color{Apricot}\\text{Apricot}", "params": [], "output": "Apricot<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Aquamarine}\\text{Aquamarine}", "params": [], "output": "Aquamarine<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Bittersweet}\\text{Bittersweet}", "params": [], "output": "Bittersweet<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Black}\\text{Black}", "params": [], "output": "Black<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Blue}\\text{Blue}", "params": [], "output": "Blue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{BlueGreen}\\text{BlueGreen}", "params": [], "output": "BlueGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{BlueViolet}\\text{BlueViolet}", "params": [], "output": "BlueViolet<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{BrickRed}\\text{BrickRed}", "params": [], "output": "BrickRed<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Brown}\\text{Brown}", "params": [], "output": "Brown<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{BurntOrange}\\text{BurntOrange}", "params": [], "output": "BurntOrange<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{CadetBlue}\\text{CadetBlue}", "params": [], "output": "CadetBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{CarnationPink}\\text{CarnationPink}", "params": [], "output": "CarnationPink<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Cerulean}\\text{Cerulean}", "params": [], "output": "Cerulean<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{CornflowerBlue}\\text{CornflowerBlue}", "params": [], "output": "CornflowerBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Cyan}\\text{Cyan}", "params": [], "output": "Cyan<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Dandelion}\\text{Dandelion}", "params": [], "output": "Dandelion<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{DarkOrchid}\\text{DarkOrchid}", "params": [], "output": "DarkOrchid<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Emerald}\\text{Emerald}", "params": [], "output": "Emerald<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{ForestGreen}\\text{ForestGreen}", "params": [], "output": "ForestGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Fuchsia}\\text{Fuchsia}", "params": [], "output": "Fuchsia<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Goldenrod}\\text{Goldenrod}", "params": [], "output": "Goldenrod<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Gray}\\text{Gray}", "params": [], "output": "Gray<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Green}\\text{Green}", "params": [], "output": "Green<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{GreenYellow}\\text{GreenYellow}", "params": [], "output": "GreenYellow<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{JungleGreen}\\text{JungleGreen}", "params": [], "output": "JungleGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Lavender}\\text{Lavender}", "params": [], "output": "Lavender<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{LimeGreen}\\text{LimeGreen}", "params": [], "output": "LimeGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Magenta}\\text{Magenta}", "params": [], "output": "Magenta<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Mahogany}\\text{Mahogany}", "params": [], "output": "Mahogany<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Maroon}\\text{Maroon}", "params": [], "output": "Maroon<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Melon}\\text{Melon}", "params": [], "output": "Melon<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{MidnightBlue}\\text{MidnightBlue}", "params": [], "output": "MidnightBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Mulberry}\\text{Mulberry}", "params": [], "output": "Mulberry<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{NavyBlue}\\text{NavyBlue}", "params": [], "output": "NavyBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{OliveGreen}\\text{OliveGreen}", "params": [], "output": "OliveGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Orange}\\text{Orange}", "params": [], "output": "Orange<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{OrangeRed}\\text{OrangeRed}", "params": [], "output": "OrangeRed<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Orchid}\\text{Orchid}", "params": [], "output": "Orchid<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Peach}\\text{Peach}", "params": [], "output": "Peach<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Periwinkle}\\text{Periwinkle}", "params": [], "output": "Periwinkle<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{PineGreen}\\text{PineGreen}", "params": [], "output": "PineGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Plum}\\text{Plum}", "params": [], "output": "Plum<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{ProcessBlue}\\text{ProcessBlue}", "params": [], "output": "ProcessBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Purple}\\text{Purple}", "params": [], "output": "Purple<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RawSienna}\\text{RawSienna}", "params": [], "output": "RawSienna<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Red}\\text{Red}", "params": [], "output": "Red<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RedOrange}\\text{RedOrange}", "params": [], "output": "RedOrange<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RedViolet}\\text{RedViolet}", "params": [], "output": "RedViolet<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Rhodamine}\\text{Rhodamine}", "params": [], "output": "Rhodamine<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RoyalBlue}\\text{RoyalBlue}", "params": [], "output": "RoyalBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RoyalPurple}\\text{RoyalPurple}", "params": [], "output": "RoyalPurple<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{RubineRed}\\text{RubineRed}", "params": [], "output": "RubineRed<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Salmon}\\text{Salmon}", "params": [], "output": "Salmon<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{SeaGreen}\\text{SeaGreen}", "params": [], "output": "SeaGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Sepia}\\text{Sepia}", "params": [], "output": "Sepia<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{SkyBlue}\\text{SkyBlue}", "params": [], "output": "SkyBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{SpringGreen}\\text{SpringGreen}", "params": [], "output": "SpringGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Tan}\\text{Tan}", "params": [], "output": "Tan<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{TealBlue}\\text{TealBlue}", "params": [], "output": "TealBlue<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Thistle}\\text{Thistle}", "params": [], "output": "Thistle<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Turquoise}\\text{Turquoise}", "params": [], "output": "Turquoise<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{Violet}\\text{Violet}", "params": [], "output": "Violet<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{VioletRed}\\text{VioletRed}", "params": [], "output": "VioletRed<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\pagecolor{Black}\\color{White}\\text{White}", "params": { "style": "background: black" }, "output": "White<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{WildStrawberry}\\text{WildStrawberry}", "params": [], "output": "WildStrawberry<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\pagecolor{Black}\\color{Yellow}\\text{Yellow}", "params": { "style": "background: black" }, "output": "Yellow<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{YellowGreen}\\text{YellowGreen}", "params": [], "output": "YellowGreen<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "\\color{YellowOrange}\\text{YellowOrange}", "params": [], "output": "YellowOrange<\/mtext><\/mrow><\/mstyle><\/math>" }, { "input": "a \\qquad b", "params": [], "output": "a<\/mi><\/mspace>b<\/mi><\/math>" }, { "input": "a \\quad b", "params": [], "output": "a<\/mi><\/mspace>b<\/mi><\/math>" }, { "input": "a\\ b", "params": [], "output": "a<\/mi> <\/mtext>b<\/mi><\/math>" }, { "input": "a \\mbox{ } b", "params": [], "output": "a<\/mi> <\/mtext><\/mrow>b<\/mi><\/math>" }, { "input": "a\\;b", "params": [], "output": "a<\/mi><\/mspace>b<\/mi><\/math>" }, { "input": "a\\,b", "params": [], "output": "a<\/mi><\/mspace>b<\/mi><\/math>" }, { "input": "ab", "params": [], "output": "a<\/mi>b<\/mi><\/math>" }, { "input": "\\mathit{ab}", "params": [], "output": "a<\/mi>b<\/mi><\/mrow><\/mrow><\/mrow><\/math>" }, { "input": "a\\!b", "params": [], "output": "a<\/mi><\/mspace>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": "0<\/mn>+<\/mo>1<\/mn>+<\/mo>2<\/mn>+<\/mo>3<\/mn>+<\/mo>4<\/mn>+<\/mo>5<\/mn>+<\/mo>6<\/mn>+<\/mo>7<\/mn>+<\/mo>8<\/mn>+<\/mo>9<\/mn>+<\/mo>1<\/mn>0<\/mn>+<\/mo>1<\/mn>1<\/mn>+<\/mo>1<\/mn>2<\/mn>+<\/mo>1<\/mn>3<\/mn>+<\/mo>1<\/mn>4<\/mn>+<\/mo>1<\/mn>5<\/mn>+<\/mo>1<\/mn>6<\/mn>+<\/mo>1<\/mn>7<\/mn>+<\/mo>1<\/mn>8<\/mn>+<\/mo>1<\/mn>9<\/mn>+<\/mo>2<\/mn>0<\/mn>+<\/mo>⋯<\/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": "0<\/mn>+<\/mo>1<\/mn>+<\/mo>2<\/mn>+<\/mo>3<\/mn>+<\/mo>4<\/mn>+<\/mo>5<\/mn>+<\/mo>6<\/mn>+<\/mo>7<\/mn>+<\/mo>8<\/mn>+<\/mo>9<\/mn>+<\/mo>1<\/mn>0<\/mn>+<\/mo>1<\/mn>1<\/mn>+<\/mo>1<\/mn>2<\/mn>+<\/mo>1<\/mn>3<\/mn>+<\/mo>1<\/mn>4<\/mn>+<\/mo>1<\/mn>5<\/mn>+<\/mo>1<\/mn>6<\/mn>+<\/mo>1<\/mn>7<\/mn>+<\/mo>1<\/mn>8<\/mn>+<\/mo>1<\/mn>9<\/mn>+<\/mo>2<\/mn>0<\/mn>+<\/mo>⋯<\/mo><\/mrow><\/math>" }, { "input": "\\int_{-N}^{N} e^x\\, dx", "params": [], "output": "∫<\/mo>−<\/mo>N<\/mi><\/mrow><\/mrow>N<\/mi><\/mrow><\/munderover><\/mstyle>e<\/mi>x<\/mi><\/mrow><\/msup><\/mspace>d<\/mi>x<\/mi><\/math>" }, { "input": "\\sum_{i=0}^\\infty 2^{-i}", "params": { "display": "inline" }, "output": "∑<\/mo>i<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>2<\/mn>−<\/mo>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": "geometric series:<\/mtext><\/mrow><\/mspace>∑<\/mo>i<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>2<\/mn>−<\/mo>i<\/mi><\/mrow><\/mrow><\/msup>=<\/mo>2<\/mn><\/mtd><\/mtr><\/mtable><\/mrow><\/math>" }, { "input": "\\sum_{i=0}^\\infty 2^{-i}", "params": [], "output": "∑<\/mo>i<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>2<\/mn>−<\/mo>i<\/mi><\/mrow><\/mrow><\/msup><\/math>" }, { "input": "\\text{geometric series:}\\quad \\sum_{i=0}^\\infty 2^{-i}=2 ", "params": [], "output": "geometric series:<\/mtext><\/mrow><\/mspace>∑<\/mo>i<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>2<\/mn>−<\/mo>i<\/mi><\/mrow><\/mrow><\/msup>=<\/mo>2<\/mn><\/math>" }, { "input": "\\iint", "params": [], "output": "∬<\/mo><\/math>" }, { "input": "\\oint", "params": [], "output": "∮<\/mo><\/mstyle><\/math>", "skipped": false }, { "input": "\\iint\\limits_{S}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\subset\\!\\supset \\mathbf D \\cdot \\mathrm{d}\\mathbf A", "params": [], "output": "∬<\/mo>S<\/mi><\/mrow><\/munder><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace>⊂<\/mo><\/mspace>⊃<\/mo>𝐃<\/mi><\/mrow>⋅<\/mo>d<\/mi><\/mrow>𝐀<\/mi><\/mrow><\/math>" }, { "input": "\\int\\!\\!\\!\\!\\int_{\\partial V}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\;\\;\\;\\bigcirc\\,\\,\\mathbf D\\cdot\\mathrm{d}\\mathbf A", "params": [], "output": "∫<\/mo><\/mspace><\/mspace><\/mspace><\/mspace>∫<\/mo>∂<\/mi>V<\/mi><\/mrow><\/mrow><\/munder><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace>◯<\/mo><\/mspace><\/mspace>𝐃<\/mi><\/mrow>⋅<\/mo>d<\/mi><\/mrow>𝐀<\/mi><\/mrow><\/math>" }, { "input": "\\int\\!\\!\\!\\!\\!\\int\\!\\!\\!\\!\\!\\int_{\\partial V}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\;\\;\\;\\subset\\!\\supset \\mathbf D\\cdot\\mathrm{d}\\mathbf A", "params": [], "output": "∫<\/mo><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace>∫<\/mo><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace>∫<\/mo>∂<\/mi>V<\/mi><\/mrow><\/mrow><\/munder><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace>⊂<\/mo><\/mspace>⊃<\/mo>𝐃<\/mi><\/mrow>⋅<\/mo>d<\/mi><\/mrow>𝐀<\/mi><\/mrow><\/math>" }, { "input": "\\int\\!\\!\\!\\!\\!\\int\\!\\!\\!\\!\\!\\int_{\\partial V}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\;\\;\\;\\bigcirc\\,\\,\\mathbf D\\;\\cdot\\mathrm{d}\\mathbf A", "params": [], "output": "∫<\/mo><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace>∫<\/mo><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace>∫<\/mo>∂<\/mi>V<\/mi><\/mrow><\/mrow><\/munder><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace><\/mspace>◯<\/mo><\/mspace><\/mspace>𝐃<\/mi><\/mrow><\/mspace>⋅<\/mo>d<\/mi><\/mrow>𝐀<\/mi><\/mrow><\/math>" }, { "input": "{\\scriptstyle S}", "params": [], "output": "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": "(<\/mo>∇<\/mi>×<\/mo>𝐅<\/mi><\/mrow><\/mrow>)<\/mo>⋅<\/mo>d<\/mi><\/mrow><\/mrow>𝐒<\/mi><\/mrow><\/mrow>=<\/mo>∮<\/mo><\/mstyle>∂<\/mi>S<\/mi><\/mrow><\/mrow><\/msub>𝐅<\/mi><\/mrow><\/mrow>⋅<\/mo>d<\/mi><\/mrow><\/mrow>ℓ<\/mi><\/mrow><\/math>", "skipped": false }, { "input": "{\\scriptstyle S}", "params": [], "output": "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": "(<\/mo>∇<\/mi>×<\/mo>𝐅<\/mi><\/mrow><\/mrow>)<\/mo>⋅<\/mo>d<\/mi><\/mrow><\/mrow>𝐒<\/mi><\/mrow><\/mrow>=<\/mo>∮<\/mo><\/mstyle>∂<\/mi>S<\/mi><\/mrow><\/mrow><\/msub>𝐅<\/mi><\/mrow><\/mrow>⋅<\/mo>d<\/mi><\/mrow><\/mrow>ℓ<\/mi><\/mrow><\/math>", "skipped": false }, { "input": "\\oint_C \\bold{B} \\cdot {\\rm d} \\boldsymbol{\\ell} = \\mu_0 ", "params": [], "output": "∮<\/mo><\/mstyle>C<\/mi><\/mrow><\/msub>𝐁<\/mi><\/mrow><\/mrow>⋅<\/mo>d<\/mi><\/mrow><\/mrow>ℓ<\/mi><\/mrow>=<\/mo>μ<\/mi>0<\/mn><\/mrow><\/msub><\/math>", "skipped": false }, { "input": "{\\scriptstyle S}", "params": [], "output": "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": "(<\/mo>𝐉<\/mi><\/mrow><\/mrow>+<\/mo>ϵ<\/mi>0<\/mn><\/mrow><\/msub>∂<\/mi>𝐄<\/mi><\/mrow><\/mrow><\/mrow><\/mrow>∂<\/mi>t<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow>⋅<\/mo>d<\/mi><\/mrow><\/mrow>𝐒<\/mi><\/mrow><\/mrow><\/math>" }, { "input": "\\oint_{\\partial S} \\bold{B} \\cdot {\\rm d} \\boldsymbol{\\ell} = \\mu_0 ", "params": [], "output": "∮<\/mo><\/mstyle>∂<\/mi>S<\/mi><\/mrow><\/mrow><\/msub>𝐁<\/mi><\/mrow><\/mrow>⋅<\/mo>d<\/mi><\/mrow><\/mrow>ℓ<\/mi><\/mrow>=<\/mo>μ<\/mi>0<\/mn><\/mrow><\/msub><\/math>" }, { "input": "{\\scriptstyle S}", "params": [], "output": "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": "(<\/mo>𝐉<\/mi><\/mrow><\/mrow>+<\/mo>ϵ<\/mi>0<\/mn><\/mrow><\/msub>∂<\/mi>𝐄<\/mi><\/mrow><\/mrow><\/mrow><\/mrow>∂<\/mi>t<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow>⋅<\/mo>d<\/mi><\/mrow><\/mrow>𝐒<\/mi><\/mrow><\/mrow><\/math>" }, { "input": "\\bold{P} = ", "params": [], "output": "𝐏<\/mi><\/mrow><\/mrow>=<\/mo><\/math>" }, { "input": "{\\scriptstyle \\partial \\Omega}", "params": [], "output": "∂<\/mi>Ω<\/mi><\/mstyle><\/mrow><\/math>" }, { "input": "\\bold{T} \\cdot {\\rm d}^3\\boldsymbol{\\Sigma} = 0", "params": [], "output": "𝐓<\/mi><\/mrow><\/mrow>⋅<\/mo>d<\/mi><\/mrow><\/mrow>3<\/mn><\/mrow><\/msup>Σ<\/mi><\/mrow>=<\/mo>0<\/mn><\/math>" }, { "input": "\\bold{P} = ", "params": [], "output": "𝐏<\/mi><\/mrow><\/mrow>=<\/mo><\/math>" }, { "input": "{\\scriptstyle \\partial \\Omega}", "params": [], "output": "∂<\/mi>Ω<\/mi><\/mstyle><\/mrow><\/math>" }, { "input": "\\bold{T} \\cdot {\\rm d}^3\\boldsymbol{\\Sigma} = 0", "params": [], "output": "𝐓<\/mi><\/mrow><\/mrow>⋅<\/mo>d<\/mi><\/mrow><\/mrow>3<\/mn><\/mrow><\/msup>Σ<\/mi><\/mrow>=<\/mo>0<\/mn><\/math>" }, { "input": "\\overset{\\frown}{AB}", "params": [], "output": "A<\/mi>B<\/mi><\/mrow><\/mrow>⌢<\/mo><\/mover><\/mrow><\/math>" }, { "input": "ax^2 + bx + c = 0", "params": [], "output": "a<\/mi>x<\/mi>2<\/mn><\/mrow><\/msup>+<\/mo>b<\/mi>x<\/mi>+<\/mo>c<\/mi>=<\/mo>0<\/mn><\/math>" }, { "input": "ax^2 + bx + c = 0", "params": [], "output": "a<\/mi>x<\/mi>2<\/mn><\/mrow><\/msup>+<\/mo>b<\/mi>x<\/mi>+<\/mo>c<\/mi>=<\/mo>0<\/mn><\/math>" }, { "input": "x={-b\\pm\\sqrt{b^2-4ac} \\over 2a}", "params": [], "output": "x<\/mi>=<\/mo>−<\/mo>b<\/mi>±<\/mo>b<\/mi>2<\/mn><\/mrow><\/msup>−<\/mo>4<\/mn>a<\/mi>c<\/mi><\/mrow><\/msqrt><\/mrow><\/mrow>2<\/mn>a<\/mi><\/mrow><\/mfrac><\/math>" }, { "input": "x={-b\\pm\\sqrt{b^2-4ac} \\over 2a}", "params": [], "output": "x<\/mi>=<\/mo>−<\/mo>b<\/mi>±<\/mo>b<\/mi>2<\/mn><\/mrow><\/msup>−<\/mo>4<\/mn>a<\/mi>c<\/mi><\/mrow><\/msqrt><\/mrow><\/mrow>2<\/mn>a<\/mi><\/mrow><\/mfrac><\/math>" }, { "input": "2 = \\left( \\frac{\\left(3-x\\right) \\times 2}{3-x} \\right)", "params": [], "output": "2<\/mn>=<\/mo>(<\/mo>(<\/mo>3<\/mn>−<\/mo>x<\/mi>)<\/mo><\/mrow>×<\/mo>2<\/mn><\/mrow><\/mrow>3<\/mn>−<\/mo>x<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow><\/math>" }, { "input": "2 = \\left(\n\\frac{\\left(3-x\\right) \\times 2}{3-x}\n\\right)", "params": [], "output": "2<\/mn>=<\/mo>(<\/mo>(<\/mo>3<\/mn>−<\/mo>x<\/mi>)<\/mo><\/mrow>×<\/mo>2<\/mn><\/mrow><\/mrow>3<\/mn>−<\/mo>x<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow><\/math>" }, { "input": "S_{\\text{new}} = S_{\\text{old}} - \\frac{ \\left( 5-T \\right) ^2} {2}", "params": [], "output": "S<\/mi>new<\/mtext><\/mrow><\/mrow><\/msub>=<\/mo>S<\/mi>old<\/mtext><\/mrow><\/mrow><\/msub>−<\/mo>(<\/mo>5<\/mn>−<\/mo>T<\/mi>)<\/mo><\/mrow>2<\/mn><\/mrow><\/msup><\/mrow>2<\/mn><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "S_{\\text{new}} = S_{\\text{old}} - \\frac{ \\left( 5-T \\right) ^2} {2}", "params": [], "output": "S<\/mi>new<\/mtext><\/mrow><\/mrow><\/msub>=<\/mo>S<\/mi>old<\/mtext><\/mrow><\/mrow><\/msub>−<\/mo>(<\/mo>5<\/mn>−<\/mo>T<\/mi>)<\/mo><\/mrow>2<\/mn><\/mrow><\/msup><\/mrow>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": "∫<\/mo>a<\/mi><\/mrow>x<\/mi><\/mrow><\/munderover><\/mstyle><\/mspace><\/mspace><\/mspace>∫<\/mo>a<\/mi><\/mrow>s<\/mi><\/mrow><\/munderover><\/mstyle>f<\/mi>(<\/mo>y<\/mi>)<\/mo><\/mspace>d<\/mi>y<\/mi><\/mspace>d<\/mi>s<\/mi>=<\/mo>∫<\/mo>a<\/mi><\/mrow>x<\/mi><\/mrow><\/munderover><\/mstyle>f<\/mi>(<\/mo>y<\/mi>)<\/mo>(<\/mo>x<\/mi>−<\/mo>y<\/mi>)<\/mo><\/mspace>d<\/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": "∫<\/mo>a<\/mi><\/mrow>x<\/mi><\/mrow><\/munderover><\/mstyle><\/mspace><\/mspace><\/mspace>∫<\/mo>a<\/mi><\/mrow>s<\/mi><\/mrow><\/munderover><\/mstyle>f<\/mi>(<\/mo>y<\/mi>)<\/mo><\/mspace>d<\/mi>y<\/mi><\/mspace>d<\/mi>s<\/mi>=<\/mo>∫<\/mo>a<\/mi><\/mrow>x<\/mi><\/mrow><\/munderover><\/mstyle>f<\/mi>(<\/mo>y<\/mi>)<\/mo>(<\/mo>x<\/mi>−<\/mo>y<\/mi>)<\/mo><\/mspace>d<\/mi>y<\/mi><\/math>" }, { "input": "\\det(\\mathsf{A}-\\lambda\\mathsf{I}) = 0", "params": [], "output": "det<\/mi>⁡<\/mo>(<\/mo>A<\/mi><\/mrow><\/mrow>−<\/mo>λ<\/mi>I<\/mi><\/mrow><\/mrow>)<\/mo>=<\/mo>0<\/mn><\/math>" }, { "input": "\\det(\\mathsf{A}-\\lambda\\mathsf{I}) = 0", "params": [], "output": "det<\/mi>⁡<\/mo>(<\/mo>A<\/mi><\/mrow><\/mrow>−<\/mo>λ<\/mi>I<\/mi><\/mrow><\/mrow>)<\/mo>=<\/mo>0<\/mn><\/math>" }, { "input": "\\sum_{i=0}^{n-1} i", "params": [], "output": "∑<\/mo>i<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>n<\/mi>−<\/mo>1<\/mn><\/mrow><\/mrow><\/munderover><\/mstyle>i<\/mi><\/math>" }, { "input": "\\sum_{i=0}^{n-1} i", "params": [], "output": "∑<\/mo>i<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>n<\/mi>−<\/mo>1<\/mn><\/mrow><\/mrow><\/munderover><\/mstyle>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": "∑<\/mo>m<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>∑<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>m<\/mi>2<\/mn><\/mrow><\/msup><\/mspace>n<\/mi><\/mrow><\/mrow>3<\/mn>m<\/mi><\/mrow><\/msup>(<\/mo>m<\/mi><\/mspace>3<\/mn>n<\/mi><\/mrow><\/msup>+<\/mo>n<\/mi><\/mspace>3<\/mn>m<\/mi><\/mrow><\/msup>)<\/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": "∑<\/mo>m<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>∑<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>m<\/mi>2<\/mn><\/mrow><\/msup><\/mspace>n<\/mi><\/mrow><\/mrow>3<\/mn>m<\/mi><\/mrow><\/msup>(<\/mo>m<\/mi><\/mspace>3<\/mn>n<\/mi><\/mrow><\/msup>+<\/mo>n<\/mi><\/mspace>3<\/mn>m<\/mi><\/mrow><\/msup>)<\/mo><\/mrow><\/mrow><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "u'' + p(x)u' + q(x)u=f(x),\\quad x>a", "params": [], "output": "u<\/mi>″<\/mo><\/msup>+<\/mo>p<\/mi>(<\/mo>x<\/mi>)<\/mo>u<\/mi>′<\/mo><\/msup>+<\/mo>q<\/mi>(<\/mo>x<\/mi>)<\/mo>u<\/mi>=<\/mo>f<\/mi>(<\/mo>x<\/mi>)<\/mo>,<\/mo><\/mspace>x<\/mi>><\/mo>a<\/mi><\/math>" }, { "input": "u'' + p(x)u' + q(x)u=f(x),\\quad x>a", "params": [], "output": "u<\/mi>″<\/mo><\/msup>+<\/mo>p<\/mi>(<\/mo>x<\/mi>)<\/mo>u<\/mi>′<\/mo><\/msup>+<\/mo>q<\/mi>(<\/mo>x<\/mi>)<\/mo>u<\/mi>=<\/mo>f<\/mi>(<\/mo>x<\/mi>)<\/mo>,<\/mo><\/mspace>x<\/mi>><\/mo>a<\/mi><\/math>" }, { "input": "|\\bar{z}| = |z|, |(\\bar{z})^n| = |z|^n, \\arg(z^n) = n \\arg(z)", "params": [], "output": "|<\/mo>z<\/mi>\u00af<\/mo><\/mover><\/mrow><\/mrow>|<\/mo>=<\/mo>|<\/mo>z<\/mi>|<\/mo>,<\/mo>|<\/mo>(<\/mo>z<\/mi>\u00af<\/mo><\/mover><\/mrow><\/mrow>)<\/mo>n<\/mi><\/mrow><\/msup>|<\/mo>=<\/mo>|<\/mo>z<\/mi>|<\/mo>n<\/mi><\/mrow><\/msup>,<\/mo>arg<\/mi>⁡<\/mo>(<\/mo>z<\/mi>n<\/mi><\/mrow><\/msup>)<\/mo>=<\/mo>n<\/mi>arg<\/mi>⁡<\/mo>(<\/mo>z<\/mi>)<\/mo><\/math>" }, { "input": "|\\bar{z}| = |z|,\n|(\\bar{z})^n| = |z|^n,\n\\arg(z^n) = n \\arg(z)", "params": [], "output": "|<\/mo>z<\/mi>\u00af<\/mo><\/mover><\/mrow><\/mrow>|<\/mo>=<\/mo>|<\/mo>z<\/mi>|<\/mo>,<\/mo>|<\/mo>(<\/mo>z<\/mi>\u00af<\/mo><\/mover><\/mrow><\/mrow>)<\/mo>n<\/mi><\/mrow><\/msup>|<\/mo>=<\/mo>|<\/mo>z<\/mi>|<\/mo>n<\/mi><\/mrow><\/msup>,<\/mo>arg<\/mi>⁡<\/mo>(<\/mo>z<\/mi>n<\/mi><\/mrow><\/msup>)<\/mo>=<\/mo>n<\/mi>arg<\/mi>⁡<\/mo>(<\/mo>z<\/mi>)<\/mo><\/math>" }, { "input": "\\lim_{z\\rightarrow z_0} f(z)=f(z_0)", "params": [], "output": "lim<\/mi>z<\/mi>→<\/mo>z<\/mi>0<\/mn><\/mrow><\/msub><\/mrow><\/mrow><\/munder>f<\/mi>(<\/mo>z<\/mi>)<\/mo>=<\/mo>f<\/mi>(<\/mo>z<\/mi>0<\/mn><\/mrow><\/msub>)<\/mo><\/math>" }, { "input": "\\lim_{z\\rightarrow z_0} f(z)=f(z_0)", "params": [], "output": "lim<\/mi>z<\/mi>→<\/mo>z<\/mi>0<\/mn><\/mrow><\/msub><\/mrow><\/mrow><\/munder>f<\/mi>(<\/mo>z<\/mi>)<\/mo>=<\/mo>f<\/mi>(<\/mo>z<\/mi>0<\/mn><\/mrow><\/msub>)<\/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": "ϕ<\/mi>n<\/mi><\/mrow><\/msub>(<\/mo>κ<\/mi>)<\/mo>=<\/mo>1<\/mn><\/mrow>4<\/mn>π<\/mi>2<\/mn><\/mrow><\/msup>κ<\/mi>2<\/mn><\/mrow><\/msup><\/mrow><\/mrow><\/mfrac><\/mrow>∫<\/mo>0<\/mn><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>sin<\/mi>⁡<\/mo>(<\/mo>κ<\/mi>R<\/mi>)<\/mo><\/mrow><\/mrow>κ<\/mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>∂<\/mi><\/mrow>∂<\/mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>[<\/mo>R<\/mi>2<\/mn><\/mrow><\/msup>∂<\/mi>D<\/mi>n<\/mi><\/mrow><\/msub>(<\/mo>R<\/mi>)<\/mo><\/mrow><\/mrow>∂<\/mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>]<\/mo><\/mrow><\/mspace>d<\/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": "ϕ<\/mi>n<\/mi><\/mrow><\/msub>(<\/mo>κ<\/mi>)<\/mo>=<\/mo>1<\/mn><\/mrow>4<\/mn>π<\/mi>2<\/mn><\/mrow><\/msup>κ<\/mi>2<\/mn><\/mrow><\/msup><\/mrow><\/mrow><\/mfrac><\/mrow>∫<\/mo>0<\/mn><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>sin<\/mi>⁡<\/mo>(<\/mo>κ<\/mi>R<\/mi>)<\/mo><\/mrow><\/mrow>κ<\/mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>∂<\/mi><\/mrow>∂<\/mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>[<\/mo>R<\/mi>2<\/mn><\/mrow><\/msup>∂<\/mi>D<\/mi>n<\/mi><\/mrow><\/msub>(<\/mo>R<\/mi>)<\/mo><\/mrow><\/mrow>∂<\/mi>R<\/mi><\/mrow><\/mrow><\/mfrac><\/mrow>]<\/mo><\/mrow><\/mspace>d<\/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": "ϕ<\/mi>n<\/mi><\/mrow><\/msub>(<\/mo>κ<\/mi>)<\/mo>=<\/mo>0<\/mn>.<\/mo>0<\/mn>3<\/mn>3<\/mn>C<\/mi>n<\/mi><\/mrow>2<\/mn><\/mrow><\/msubsup>κ<\/mi>−<\/mo>1<\/mn>1<\/mn>\/<\/mo>3<\/mn><\/mrow><\/mrow><\/msup>,<\/mo><\/mspace>1<\/mn><\/mrow>L<\/mi>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/mrow>≪<\/mo>κ<\/mi>≪<\/mo>1<\/mn><\/mrow>l<\/mi>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": "ϕ<\/mi>n<\/mi><\/mrow><\/msub>(<\/mo>κ<\/mi>)<\/mo>=<\/mo>0<\/mn>.<\/mo>0<\/mn>3<\/mn>3<\/mn>C<\/mi>n<\/mi><\/mrow>2<\/mn><\/mrow><\/msubsup>κ<\/mi>−<\/mo>1<\/mn>1<\/mn>\/<\/mo>3<\/mn><\/mrow><\/mrow><\/msup>,<\/mo><\/mspace>1<\/mn><\/mrow>L<\/mi>0<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/mrow>≪<\/mo>κ<\/mi>≪<\/mo>1<\/mn><\/mrow>l<\/mi>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": "f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>{<\/mo>1<\/mn><\/mtd>−<\/mo>1<\/mn>≤<\/mo>x<\/mi><<\/mo>0<\/mn><\/mtd><\/mtr>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac><\/mrow><\/mtd>x<\/mi>=<\/mo>0<\/mn><\/mtd><\/mtr>1<\/mn>−<\/mo>x<\/mi>2<\/mn><\/mrow><\/msup><\/mtd>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": "f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>{<\/mo>1<\/mn><\/mtd>−<\/mo>1<\/mn>≤<\/mo>x<\/mi><<\/mo>0<\/mn><\/mtd><\/mtr>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac><\/mrow><\/mtd>x<\/mi>=<\/mo>0<\/mn><\/mtd><\/mtr>1<\/mn>−<\/mo>x<\/mi>2<\/mn><\/mrow><\/msup><\/mtd>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": "p<\/mi><\/mrow><\/msub>F<\/mi>q<\/mi><\/mrow><\/msub>(<\/mo>a<\/mi>1<\/mn><\/mrow><\/msub>,<\/mo>…<\/mo>,<\/mo>a<\/mi>p<\/mi><\/mrow><\/msub>;<\/mo>c<\/mi>1<\/mn><\/mrow><\/msub>,<\/mo>…<\/mo>,<\/mo>c<\/mi>q<\/mi><\/mrow><\/msub>;<\/mo>z<\/mi>)<\/mo>=<\/mo>∑<\/mo>n<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>(<\/mo>a<\/mi>1<\/mn><\/mrow><\/msub>)<\/mo>n<\/mi><\/mrow><\/msub>⋯<\/mo>(<\/mo>a<\/mi>p<\/mi><\/mrow><\/msub>)<\/mo>n<\/mi><\/mrow><\/msub><\/mrow><\/mrow>(<\/mo>c<\/mi>1<\/mn><\/mrow><\/msub>)<\/mo>n<\/mi><\/mrow><\/msub>⋯<\/mo>(<\/mo>c<\/mi>q<\/mi><\/mrow><\/msub>)<\/mo>n<\/mi><\/mrow><\/msub><\/mrow><\/mrow><\/mfrac><\/mrow>z<\/mi>n<\/mi><\/mrow><\/msup><\/mrow>n<\/mi>!<\/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": "p<\/mi><\/mrow><\/msub>F<\/mi>q<\/mi><\/mrow><\/msub>(<\/mo>a<\/mi>1<\/mn><\/mrow><\/msub>,<\/mo>…<\/mo>,<\/mo>a<\/mi>p<\/mi><\/mrow><\/msub>;<\/mo>c<\/mi>1<\/mn><\/mrow><\/msub>,<\/mo>…<\/mo>,<\/mo>c<\/mi>q<\/mi><\/mrow><\/msub>;<\/mo>z<\/mi>)<\/mo>=<\/mo>∑<\/mo>n<\/mi>=<\/mo>0<\/mn><\/mrow><\/mrow>∞<\/mi><\/mrow><\/munderover><\/mstyle>(<\/mo>a<\/mi>1<\/mn><\/mrow><\/msub>)<\/mo>n<\/mi><\/mrow><\/msub>⋯<\/mo>(<\/mo>a<\/mi>p<\/mi><\/mrow><\/msub>)<\/mo>n<\/mi><\/mrow><\/msub><\/mrow><\/mrow>(<\/mo>c<\/mi>1<\/mn><\/mrow><\/msub>)<\/mo>n<\/mi><\/mrow><\/msub>⋯<\/mo>(<\/mo>c<\/mi>q<\/mi><\/mrow><\/msub>)<\/mo>n<\/mi><\/mrow><\/msub><\/mrow><\/mrow><\/mfrac><\/mrow>z<\/mi>n<\/mi><\/mrow><\/msup><\/mrow>n<\/mi>!<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><\/math>" }, { "input": "\\frac{a}{b}\\ \\tfrac{a}{b}", "params": [], "output": "a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow> <\/mtext>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "\\frac{a}{b}\\ \\tfrac{a}{b}", "params": [], "output": "a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow> <\/mtext>a<\/mi><\/mrow>b<\/mi><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow><\/math>" }, { "input": "S=dD\\,\\sin\\alpha\\!", "params": [], "output": "S<\/mi>=<\/mo>d<\/mi>D<\/mi><\/mspace>sin<\/mi>⁡<\/mo>α<\/mi><\/mspace><\/math>" }, { "input": "S=dD\\,\\sin\\alpha\\!", "params": [], "output": "S<\/mi>=<\/mo>d<\/mi>D<\/mi><\/mspace>sin<\/mi>⁡<\/mo>α<\/mi><\/mspace><\/math>" }, { "input": "V=\\frac16\\pi h\\left[3\\left(r_1^2+r_2^2\\right)+h^2\\right]", "params": [], "output": "V<\/mi>=<\/mo>1<\/mn><\/mrow>6<\/mn><\/mrow><\/mfrac><\/mrow>π<\/mi>h<\/mi>[<\/mo>3<\/mn>(<\/mo>r<\/mi>1<\/mn><\/mrow>2<\/mn><\/mrow><\/msubsup>+<\/mo>r<\/mi>2<\/mn><\/mrow>2<\/mn><\/mrow><\/msubsup>)<\/mo><\/mrow>+<\/mo>h<\/mi>2<\/mn><\/mrow><\/msup>]<\/mo><\/mrow><\/math>" }, { "input": "V=\\frac16\\pi h\\left[3\\left(r_1^2+r_2^2\\right)+h^2\\right]", "params": [], "output": "V<\/mi>=<\/mo>1<\/mn><\/mrow>6<\/mn><\/mrow><\/mfrac><\/mrow>π<\/mi>h<\/mi>[<\/mo>3<\/mn>(<\/mo>r<\/mi>1<\/mn><\/mrow>2<\/mn><\/mrow><\/msubsup>+<\/mo>r<\/mi>2<\/mn><\/mrow>2<\/mn><\/mrow><\/msubsup>)<\/mo><\/mrow>+<\/mo>h<\/mi>2<\/mn><\/mrow><\/msup>]<\/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": "u<\/mi><\/mtd>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>(<\/mo>x<\/mi>+<\/mo>y<\/mi>)<\/mo><\/mspace><\/mtd>x<\/mi><\/mtd>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>(<\/mo>u<\/mi>+<\/mo>v<\/mi>)<\/mo><\/mtd><\/mtr>v<\/mi><\/mtd>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>(<\/mo>x<\/mi>−<\/mo>y<\/mi>)<\/mo><\/mspace><\/mtd>y<\/mi><\/mtd>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>(<\/mo>u<\/mi>−<\/mo>v<\/mi>)<\/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": "u<\/mi><\/mtd>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>(<\/mo>x<\/mi>+<\/mo>y<\/mi>)<\/mo><\/mspace><\/mtd>x<\/mi><\/mtd>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>(<\/mo>u<\/mi>+<\/mo>v<\/mi>)<\/mo><\/mtd><\/mtr>v<\/mi><\/mtd>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>(<\/mo>x<\/mi>−<\/mo>y<\/mi>)<\/mo><\/mspace><\/mtd>y<\/mi><\/mtd>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/msqrt><\/mrow><\/mrow><\/mfrac><\/mrow><\/mstyle><\/mrow>(<\/mo>u<\/mi>−<\/mo>v<\/mi>)<\/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|2+2", "params": [], "output": "<\/math>" }, { "input": " with a thumbnail- math enabled [[Image:foobar.jpg|thumb|2+2", "params": [], "output": "w<\/mi>i<\/mi>t<\/mi>h<\/mi>a<\/mi>t<\/mi>h<\/mi>u<\/mi>m<\/mi>b<\/mi>n<\/mi>a<\/mi>i<\/mi>l<\/mi>−<\/mo>m<\/mi>a<\/mi>t<\/mi>h<\/mi>e<\/mi>n<\/mi>a<\/mi>b<\/mi>l<\/mi>e<\/mi>d<\/mi>[<\/mo>[<\/mo>I<\/mi>m<\/mi>a<\/mi>g<\/mi>e<\/mi>:<\/mo>f<\/mi>o<\/mi>o<\/mi>b<\/mi>a<\/mi>r<\/mi>.<\/mo>j<\/mi>p<\/mi>g<\/mi>|<\/mo>t<\/mi>h<\/mi>u<\/mi>m<\/mi>b<\/mi>|<\/mo><<\/mo>m<\/mi>a<\/mi>t<\/mi>h<\/mi>><\/mo>2<\/mn>+<\/mo>2<\/mn><\/math>" }, { "input": "