LaTeX to CAS translator
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This mockup demonstrates the concept of TeX to Computer Algebra System (CAS) conversion.
The demo-application converts LaTeX functions which directly translate to CAS counterparts.
Functions without explicit CAS support are available for translation via a DRMF package (under development).
The following LaTeX input ...
{\displaystyle \, 2\pi }
... is translated to the CAS output ...
Semantic latex: 2 \cpi
Confidence: 0
Mathematica
Translation: 2*Pi
Information
Sub Equations
- 2*Pi
Symbol info
- Pi was translated to: Pi
Tests
Symbolic
Numeric
SymPy
Translation: 2*pi
Information
Sub Equations
- 2*pi
Symbol info
- Pi was translated to: pi
Tests
Symbolic
Numeric
Maple
Translation: 2*Pi
Information
Sub Equations
- 2*Pi
Symbol info
- Pi was translated to: Pi
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
- Failed to parse (unknown function "\cdotn"): {\displaystyle K(n)= e^{-(n^2-1)\zeta^\prime(-1)} \cdotn^{\frac{5}{12}}\cdot(2\pi)^{(n-1)/2}\,=\,(Ae^{-\frac{1}{12}})^{n^2-1}\cdot n^{\frac{5}{12}}\cdot (2\pi)^{(n-1)/2}}
Complete translation information:
{
"id" : "FORMULA_c3198a6dbef629ca31403b4ccdff3fc7",
"formula" : "2\\pi",
"semanticFormula" : "2 \\cpi",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "2*Pi",
"translationInformation" : {
"subEquations" : [ "2*Pi" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"SymPy" : {
"translation" : "2*pi",
"translationInformation" : {
"subEquations" : [ "2*pi" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: pi"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"Maple" : {
"translation" : "2*Pi",
"translationInformation" : {
"subEquations" : [ "2*Pi" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
}
},
"positions" : [ ],
"includes" : [ "\\, 2\\pi" ],
"isPartOf" : [ "K(n)= e^{-(n^2-1)\\zeta^\\prime(-1)} \\cdotn^{\\frac{5}{12}}\\cdot(2\\pi)^{(n-1)/2}\\,=\\,(Ae^{-\\frac{1}{12}})^{n^2-1}\\cdot n^{\\frac{5}{12}}\\cdot (2\\pi)^{(n-1)/2}", "\\, 0 < \\theta < 2\\pi", "\\, y=2\\pi x \\Rightarrow dx=dy/(2\\pi)", "G(nz)= K(n) n^{n^{2}z^{2}/2-nz} (2\\pi)^{-\\frac{n^2-n}{2}z}\\prod_{i=0}^{n-1}\\prod_{j=0}^{n-1}G\\left(z+\\frac{i+j}{n}\\right)", "\\log\\left( \\frac{G(1-z)}{G(z)} \\right)= z\\log\\left(\\frac{\\sin\\pi z}{\\pi}\\right)+\\log\\Gamma(z)+\\frac{1}{2\\pi}\\operatorname{Cl}_2(2\\pi z)", "z\\log(2\\sin \\pi z)-\\frac{1}{2\\pi}\\int_0^{2\\pi z}\\log\\left(2\\sin \\frac{y}{2} \\right)\\,dy", "\\operatorname{Lc}(z)=z\\log(2\\sin \\pi z)+\\frac{1}{2\\pi} \\operatorname{Cl}_2(2\\pi z)", "\\log G(1+z) = \\frac{z}{2}\\log 2\\pi -\\left( \\frac{z+(1+\\gamma)z^2}{2} \\right) + \\sum_{k=2}^{\\infty}(-1)^k\\frac{\\zeta(k)}{k+1}z^{k+1}", "2\\pi \\log\\left( \\frac{G(1-z)}{G(1+z)} \\right)= 2\\pi z\\log\\left(\\frac{\\sin\\pi z}{\\pi} \\right) + \\operatorname{Cl}_2(2\\pi z)", "G(1+z)=(2\\pi)^{z/2} \\exp\\left(- \\frac{z+z^2(1+\\gamma)}{2} \\right) \\, \\prod_{k=1}^\\infty \\left\\{ \\left(1+\\frac{z}{k}\\right)^k \\exp\\left(\\frac{z^2}{2k}-z\\right) \\right\\}", "\\begin{align}& \\sum_{k=1}^\\infty \\Bigg\\{ (k+z)\\log \\left(1+\\frac{z}{k}\\right)-\\frac{z^2}{2k}-z \\Bigg\\} \\\\[5pt]= {} & {-z}\\log z-\\frac{z}{2}\\log 2\\pi +\\frac{z}{2} +\\frac{z^2}{2}- \\frac{z^2 \\gamma}{2}- z\\log\\Gamma(z) +\\log G(1+z)\\end{align}", "\\int_0^z \\log \\Gamma(x)\\,dx=\\frac{z(1-z)}{2}+\\frac{z}{2}\\log 2\\pi +z\\log\\Gamma(z) -\\log G(1+z)", "\\log G(1-z) = \\log G(1+z)-z\\log 2\\pi+ \\int_0^z \\pi x \\cot \\pi x \\, dx", "\\int_0^z \\log \\Gamma(x)\\,dx=\\frac{z(1-z)}{2}+\\frac{z}{2}\\log 2\\pi -(1-z)\\log\\Gamma(z) -\\log G(z)\\,", "\\, 2\\pi", "2\\pi \\log\\left( \\frac{G(1-z)}{G(1+z)} \\right)= 2\\pi z\\log\\left(\\frac{\\sin\\pi z}{\\pi} \\right)+\\operatorname{Cl}_2(2\\pi z)\\, . \\, \\Box", "\\begin{align}\\log G(z+1) = {} & \\frac{z^2}{2} \\log z - \\frac{3z^2}{4} + \\frac{z}{2}\\log 2\\pi -\\frac{1}{12} \\log z \\\\ & {} + \\left(\\frac{1}{12}-\\log A \\right) +\\sum_{k=1}^N \\frac{B_{2k + 2}}{4k\\left(k + 1\\right)z^{2k}}+O\\left(\\frac{1}{z^{2N + 2}}\\right).\\end{align}", "\\begin{align} G(1+z) &= \\exp \\left[ \\frac{z}{2}\\log 2\\pi -\\left( \\frac{z+(1+\\gamma)z^2}{2} \\right) + \\sum_{k=2}^{\\infty}(-1)^k\\frac{\\zeta(k)}{k+1}z^{k+1} \\right] \\\\&=(2\\pi)^{z/2}\\exp\\left[ -\\frac{z+(1+\\gamma)z^2}{2} \\right] \\exp \\left[\\sum_{k=2}^{\\infty}(-1)^k\\frac{\\zeta(k)}{k+1}z^{k+1} \\right].\\end{align}", "\\begin{align}& z\\log \\Gamma(z)-\\log G(1+z)=-z \\log\\left(\\frac{1}{\\Gamma (z)}\\right)-\\log G(1+z) \\\\[5pt]= {} & {-z} \\left[ \\log z+\\gamma z +\\sum_{k=1}^\\infty \\Bigg\\{ \\log\\left(1+\\frac{z}{k} \\right) -\\frac{z}{k} \\Bigg\\} \\right] \\\\[5pt]& {} -\\left[ \\frac{z}{2}\\log 2\\pi -\\frac{z}{2}-\\frac{z^2}{2} -\\frac{z^2 \\gamma}{2} + \\sum_{k=1}^\\infty \\Bigg\\{k\\log\\left(1+\\frac{z}{k}\\right) +\\frac{z^2}{2k} -z \\Bigg\\} \\right]\\end{align}", "\\log \\Gamma \\left(\\frac{1}{2}-z \\right) + B_1(z) \\log 2\\pi+\\frac{1}{2}\\log 2+\\pi \\int_0^z B_1(x) \\tan \\pi x \\,dx" ],
"definiens" : [ ]
}