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 \mathrm{bei}_n(x) = \left(\frac{x}{2}\right)^n \sum_{k \geq 0} \frac{\sin\left[\left(\frac{3n}{4} + \frac{k}{2}\right)\pi\right]}{k! \Gamma(n + k + 1)} \left(\frac{x^2}{4}\right)^k .}
... is translated to the CAS output ...
Semantic latex: \Kelvinbei{n}@@{(x)} =(\frac{x}{2})^n \sum_{k \geq 0} \frac{\sin [(\frac{3n}{4} + \frac{k}{2}) \cpi]}{k! \EulerGamma@{n + k + 1}}(\frac{x^2}{4})^k
Confidence: 0.66866523996064
Mathematica
Translation: KelvinBei[n, x] == (Divide[x,2])^(n)* Sum[Divide[Sin[(Divide[3*n,4]+Divide[k,2])*Pi],(k)!*Gamma[n + k + 1]]*(Divide[(x)^(2),4])^(k), {k, 0, Infinity}, GenerateConditions->None]
Information
Sub Equations
- KelvinBei[n, x] = (Divide[x,2])^(n)* Sum[Divide[Sin[(Divide[3*n,4]+Divide[k,2])*Pi],(k)!*Gamma[n + k + 1]]*(Divide[(x)^(2),4])^(k), {k, 0, Infinity}, GenerateConditions->None]
Free variables
- n
- x
Symbol info
- Pi was translated to: Pi
- Kelvin Function BEI; Example: \Kelvinbei{\nu}@@{x}
Will be translated to: KelvinBei[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/10.61#E1 Mathematica: https://reference.wolfram.com/language/ref/KelvinBei.html
- Sine; Example: \sin@@{z}
Will be translated to: Sin[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Mathematica: https://reference.wolfram.com/language/ref/Sin.html
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: Gamma[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Mathematica: https://reference.wolfram.com/language/ref/Gamma.html
Tests
Symbolic
Test expression: (KelvinBei[n, x])-((Divide[x,2])^(n)* Sum[Divide[Sin[(Divide[3*n,4]+Divide[k,2])*Pi],(k)!*Gamma[n + k + 1]]*(Divide[(x)^(2),4])^(k), {k, 0, Infinity}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \Kelvinbei [\Kelvinbei]
Tests
Symbolic
Numeric
Maple
Translation: KelvinBei(n, x) = ((x)/(2))^(n)* sum((sin(((3*n)/(4)+(k)/(2))*Pi))/(factorial(k)*GAMMA(n + k + 1))*(((x)^(2))/(4))^(k), k = 0..infinity)
Information
Sub Equations
- KelvinBei(n, x) = ((x)/(2))^(n)* sum((sin(((3*n)/(4)+(k)/(2))*Pi))/(factorial(k)*GAMMA(n + k + 1))*(((x)^(2))/(4))^(k), k = 0..infinity)
Free variables
- n
- x
Symbol info
- Pi was translated to: Pi
- Kelvin Function BEI; Example: \Kelvinbei{\nu}@@{x}
Will be translated to: KelvinBei($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/10.61#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=KelvinBei
- Sine; Example: \sin@@{z}
Will be translated to: sin($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: GAMMA($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- series expansion
- integer
Complete translation information:
{
"id" : "FORMULA_eaeb48a91ce81d0193ab3b9c4dec9892",
"formula" : "\\mathrm{bei}_n(x) = \\left(\\frac{x}{2}\\right)^n \\sum_{k \\geq 0} \\frac{\\sin\\left[\\left(\\frac{3n}{4} + \\frac{k}{2}\\right)\\pi\\right]}{k! \\Gamma(n + k + 1)} \\left(\\frac{x^2}{4}\\right)^k",
"semanticFormula" : "\\Kelvinbei{n}@@{(x)} =(\\frac{x}{2})^n \\sum_{k \\geq 0} \\frac{\\sin [(\\frac{3n}{4} + \\frac{k}{2}) \\cpi]}{k! \\EulerGamma@{n + k + 1}}(\\frac{x^2}{4})^k",
"confidence" : 0.6686652399606361,
"translations" : {
"Mathematica" : {
"translation" : "KelvinBei[n, x] == (Divide[x,2])^(n)* Sum[Divide[Sin[(Divide[3*n,4]+Divide[k,2])*Pi],(k)!*Gamma[n + k + 1]]*(Divide[(x)^(2),4])^(k), {k, 0, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "KelvinBei[n, x] = (Divide[x,2])^(n)* Sum[Divide[Sin[(Divide[3*n,4]+Divide[k,2])*Pi],(k)!*Gamma[n + k + 1]]*(Divide[(x)^(2),4])^(k), {k, 0, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"\\Kelvinbei" : "Kelvin Function BEI; Example: \\Kelvinbei{\\nu}@@{x}\nWill be translated to: KelvinBei[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/10.61#E1\nMathematica: https://reference.wolfram.com/language/ref/KelvinBei.html",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: Sin[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nMathematica: https://reference.wolfram.com/language/ref/Sin.html",
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: Gamma[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMathematica: https://reference.wolfram.com/language/ref/Gamma.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "KelvinBei[n, x]",
"rhs" : "(Divide[x,2])^(n)* Sum[Divide[Sin[(Divide[3*n,4]+Divide[k,2])*Pi],(k)!*Gamma[n + k + 1]]*(Divide[(x)^(2),4])^(k), {k, 0, Infinity}, GenerateConditions->None]",
"testExpression" : "(KelvinBei[n, x])-((Divide[x,2])^(n)* Sum[Divide[Sin[(Divide[3*n,4]+Divide[k,2])*Pi],(k)!*Gamma[n + k + 1]]*(Divide[(x)^(2),4])^(k), {k, 0, Infinity}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\Kelvinbei [\\Kelvinbei]"
}
}
},
"Maple" : {
"translation" : "KelvinBei(n, x) = ((x)/(2))^(n)* sum((sin(((3*n)/(4)+(k)/(2))*Pi))/(factorial(k)*GAMMA(n + k + 1))*(((x)^(2))/(4))^(k), k = 0..infinity)",
"translationInformation" : {
"subEquations" : [ "KelvinBei(n, x) = ((x)/(2))^(n)* sum((sin(((3*n)/(4)+(k)/(2))*Pi))/(factorial(k)*GAMMA(n + k + 1))*(((x)^(2))/(4))^(k), k = 0..infinity)" ],
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"\\Kelvinbei" : "Kelvin Function BEI; Example: \\Kelvinbei{\\nu}@@{x}\nWill be translated to: KelvinBei($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/10.61#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=KelvinBei",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: sin($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin",
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: GAMMA($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA"
}
}
}
},
"positions" : [ {
"section" : 2,
"sentence" : 0,
"word" : 10
} ],
"includes" : [ "x", "\\Gamma(z)", "x)", "n", "_{n}(x)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "series expansion",
"score" : 0.722
}, {
"definition" : "integer",
"score" : 0.6460746792928004
} ]
}