LaTeX to CAS translator
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 \mathbf{K}_\alpha(x)}
... is translated to the CAS output ...
Semantic latex: \StruveK{\alpha}@{x}
Confidence: 0.6977631659498
Mathematica
Translation: StruveH[\[Alpha], x] - BesselY[\[Alpha], x]
Information
Sub Equations
- StruveH[\[Alpha], x] - BesselY[\[Alpha], x]
Free variables
- \[Alpha]
- x
Symbol info
- Associated Struve funtion; Example: \StruveK{\nu}@{z}
Will be translated to: StruveH[$0, $1] - BesselY[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E5 Mathematica: https://reference.wolfram.com/language/ref/StruveH.html
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \StruveK [\StruveK]
Tests
Symbolic
Numeric
Maple
Translation: StruveH(alpha, x) - BesselY(alpha, x)
Information
Sub Equations
- StruveH(alpha, x) - BesselY(alpha, x)
Free variables
- alpha
- x
Symbol info
- Associated Struve funtion; Example: \StruveK{\nu}@{z}
Will be translated to: StruveH($0, $1) - BesselY($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E5 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveH
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
- Failed to parse (unknown function "\taud"): {\displaystyle \mathbf{H}_\alpha(x)=\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^1(1-t^2)^{\alpha-\frac{1}{2}}\sin xtdt=\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\frac{\pi}{2}\sin(x\cos\tau)\sin^{2\alpha}\taud\tau=\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\frac{\pi}{2}\sin(x\sin\tau)\cos^{2\alpha}\taud\tau}
- Failed to parse (unknown function "\taud"): {\displaystyle \mathbf{K}_\alpha(x)=\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\infty(1+t^2)^{\alpha-\frac{1}{2}}e^{-xt}dt=\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\infty e^{-x\sinh\tau}\cosh^{2\alpha}\taud\tau}
- Failed to parse (unknown function "\taud"): {\displaystyle \mathbf{L}_\alpha(x)=\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^1(1-t^2)^{\alpha-\frac{1}{2}}\sinh xtdt=\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\frac{\pi}{2}\sinh(x\cos\tau)\sin^{2\alpha}\taud\tau=\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\frac{\pi}{2}\sinh(x\sin\tau)\cos^{2\alpha}\taud\tau}
- Failed to parse (unknown function "\taud"): {\displaystyle \mathbf{M}_\alpha(x)=-\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^1(1-t^2)^{\alpha-\frac{1}{2}}e^{-xt}dt=-\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\frac{\pi}{2}e^{-x\cos\tau}\sin^{2\alpha}\taud\tau=-\frac{2\left(\frac{x}{2}\right)^\alpha}{\sqrt\pi\Gamma\left(\alpha+\frac{1}{2}\right)}\int_0^\frac{\pi}{2}e^{-x\sin\tau}\cos^{2\alpha}\taud\tau}
Description
- second-kind version
- solution
- non-homogeneous Bessel 's differential equation
- Struve function
- modified Struve function
- mathematics
- hypergeometric function
- gamma function
- Struve
- power series
- Neumann function
- recurrence relation
- Gauss
- definition of the Struve function
- term of the Poisson 's integral representation
- value
- term
- order
Complete translation information:
{
"id" : "FORMULA_f5255aadaf5da07961cce09847acbcec",
"formula" : "\\mathbf{K}_\\alpha(x)",
"semanticFormula" : "\\StruveK{\\alpha}@{x}",
"confidence" : 0.6977631659497951,
"translations" : {
"Mathematica" : {
"translation" : "StruveH[\\[Alpha], x] - BesselY[\\[Alpha], x]",
"translationInformation" : {
"subEquations" : [ "StruveH[\\[Alpha], x] - BesselY[\\[Alpha], x]" ],
"freeVariables" : [ "\\[Alpha]", "x" ],
"tokenTranslations" : {
"\\StruveK" : "Associated Struve funtion; Example: \\StruveK{\\nu}@{z}\nWill be translated to: StruveH[$0, $1] - BesselY[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E5\nMathematica: https://reference.wolfram.com/language/ref/StruveH.html",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\StruveK [\\StruveK]"
}
},
"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" : "StruveH(alpha, x) - BesselY(alpha, x)",
"translationInformation" : {
"subEquations" : [ "StruveH(alpha, x) - BesselY(alpha, x)" ],
"freeVariables" : [ "alpha", "x" ],
"tokenTranslations" : {
"\\StruveK" : "Associated Struve funtion; Example: \\StruveK{\\nu}@{z}\nWill be translated to: StruveH($0, $1) - BesselY($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E5\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveH",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : [ {
"section" : 0,
"sentence" : 2,
"word" : 6
} ],
"includes" : [ "\\alpha", "\\mathbf{H}_{\\alpha}(x)", "\\mathbf{L}_{\\alpha}(x)", "\\mathbf{M}_\\alpha(x)", "\\mathbf{H}_{\\alpha}(z)", "x", "Y_{\\alpha}(x)" ],
"isPartOf" : [ "\\mathbf{H}_{\\alpha}(x)", "\\mathbf{K}_\\alpha(x)=\\mathbf{H}_\\alpha(x)-Y_\\alpha(x)", "\\mathbf{L}_{\\alpha}(x)", "-ie^{-i\\alpha\\pi / 2}\\mathbf{H}_{\\alpha}(ix)", "\\mathbf{M}_\\alpha(x)", "\\mathbf{M}_\\alpha(x)=\\mathbf{L}_\\alpha(x)-I_\\alpha(x)", "\\mathbf{H}_{\\alpha}(z)", "\\mathbf{H}_\\alpha(z) = \\sum_{m=0}^\\infty \\frac{(-1)^m}{\\Gamma \\left (m+\\frac{3}{2} \\right ) \\Gamma \\left (m+\\alpha+\\frac{3}{2} \\right )} \\left({\\frac{z}{2}}\\right)^{2m+\\alpha+1}", "\\mathbf{H}_\\alpha(x)=\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^1(1-t^2)^{\\alpha-\\frac{1}{2}}\\sin xtdt=\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\frac{\\pi}{2}\\sin(x\\cos\\tau)\\sin^{2\\alpha}\\taud\\tau=\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\frac{\\pi}{2}\\sin(x\\sin\\tau)\\cos^{2\\alpha}\\taud\\tau", "\\mathbf{K}_\\alpha(x)=\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\infty(1+t^2)^{\\alpha-\\frac{1}{2}}e^{-xt}dt=\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\infty e^{-x\\sinh\\tau}\\cosh^{2\\alpha}\\taud\\tau", "\\mathbf{L}_\\alpha(x)=\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^1(1-t^2)^{\\alpha-\\frac{1}{2}}\\sinh xtdt=\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\frac{\\pi}{2}\\sinh(x\\cos\\tau)\\sin^{2\\alpha}\\taud\\tau=\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\frac{\\pi}{2}\\sinh(x\\sin\\tau)\\cos^{2\\alpha}\\taud\\tau", "\\mathbf{M}_\\alpha(x)=-\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^1(1-t^2)^{\\alpha-\\frac{1}{2}}e^{-xt}dt=-\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\frac{\\pi}{2}e^{-x\\cos\\tau}\\sin^{2\\alpha}\\taud\\tau=-\\frac{2\\left(\\frac{x}{2}\\right)^\\alpha}{\\sqrt\\pi\\Gamma\\left(\\alpha+\\frac{1}{2}\\right)}\\int_0^\\frac{\\pi}{2}e^{-x\\sin\\tau}\\cos^{2\\alpha}\\taud\\tau", "\\mathbf{H}_\\alpha(x) - Y_\\alpha(x) = \\frac{\\left(\\frac{x}{2}\\right)^{\\alpha-1}}{\\sqrt{\\pi} \\Gamma \\left (\\alpha+\\frac{1}{2} \\right )} + O\\left(\\left (\\tfrac{x}{2}\\right)^{\\alpha-3}\\right)", "Y_{\\alpha}(x)", "\\begin{align}\\mathbf{H}_{\\alpha -1}(x) + \\mathbf{H}_{\\alpha+1}(x) &= \\frac{2\\alpha}{x} \\mathbf{H}_\\alpha (x) + \\frac{\\left (\\frac{x}{2}\\right)^{\\alpha}}{\\sqrt{\\pi}\\Gamma \\left (\\alpha + \\frac{3}{2} \\right )}, \\\\\\mathbf{H}_{\\alpha -1}(x) - \\mathbf{H}_{\\alpha+1}(x) &= 2 \\frac{d}{dx} \\left (\\mathbf{H}_\\alpha(x) \\right) - \\frac{ \\left( \\frac{x}{2} \\right)^\\alpha}{\\sqrt{\\pi}\\Gamma \\left (\\alpha + \\frac{3}{2} \\right )}.\\end{align}", "\\mathbf{H}_{\\alpha}(z) = \\frac{z^{\\alpha+1}}{2^{\\alpha}\\sqrt{\\pi} \\Gamma \\left (\\alpha+\\tfrac{3}{2} \\right )} {}_1F_2 \\left (1,\\tfrac{3}{2}, \\alpha+\\tfrac{3}{2},-\\tfrac{z^2}{4} \\right )" ],
"definiens" : [ {
"definition" : "second-kind version",
"score" : 0.8811165303034428
}, {
"definition" : "solution",
"score" : 0.8023902964963254
}, {
"definition" : "non-homogeneous Bessel 's differential equation",
"score" : 0.7001020293281626
}, {
"definition" : "Struve function",
"score" : 0.6999318073895041
}, {
"definition" : "modified Struve function",
"score" : 0.6432331635625809
}, {
"definition" : "mathematics",
"score" : 0.5775629775816605
}, {
"definition" : "hypergeometric function",
"score" : 0.44694132238726914
}, {
"definition" : "gamma function",
"score" : 0.40173148469210224
}, {
"definition" : "Struve",
"score" : 0.3892005821042821
}, {
"definition" : "power series",
"score" : 0.3750415938246384
}, {
"definition" : "Neumann function",
"score" : 0.3522700134674619
}, {
"definition" : "recurrence relation",
"score" : 0.35175394239749164
}, {
"definition" : "Gauss",
"score" : 0.3515992754597499
}, {
"definition" : "definition of the Struve function",
"score" : 0.33280406830999054
}, {
"definition" : "term of the Poisson 's integral representation",
"score" : 0.29297012797898336
}, {
"definition" : "value",
"score" : 0.29297012797898336
}, {
"definition" : "term",
"score" : 0.28507544426127884
}, {
"definition" : "order",
"score" : 0.14390819054992784
} ]
}