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 P_{\lambda}^{\mu}(z) = \frac{1}{\Gamma(1-\mu)} \left[\frac{1+z}{1-z}\right]^{\mu/2} \,_2F_1 \left(-\lambda, \lambda+1; 1-\mu; \frac{1-z}{2}\right),\qquad \text{for } \ |1-z|<2}
... is translated to the CAS output ...
Semantic latex: P_{\lambda}^{\mu}(z) = \frac{1}{\EulerGamma@{1 - \mu}} [\frac{1+z}{1-z}]_2^{\mu/2} F_1(- \lambda , \lambda + 1 ; 1 - \mu ; \frac{1-z}{2}) , \qquad for|1 - z|< 2
Confidence: 0.62649777776391
Mathematica
Translation: (Subscript[P, \[Lambda]])^\[Mu][z] == Divide[1,Gamma[1 - \[Mu]]]*(Subscript[Divide[1 + z,1 - z], 2])^(\[Mu]/2)*Subscript[F, 1][- \[Lambda], \[Lambda]+ 1 ; 1 - \[Mu];Divide[1 - z,2]]
Information
Sub Equations
- (Subscript[P, \[Lambda]])^\[Mu][z] = Divide[1,Gamma[1 - \[Mu]]]*(Subscript[Divide[1 + z,1 - z], 2])^(\[Mu]/2)*Subscript[F, 1][- \[Lambda], \[Lambda]+ 1 ; 1 - \[Mu];Divide[1 - z,2]]
Free variables
- \[Lambda]
- \[Mu]
- f
- o
- r
- z
Constraints
- f*o*r*Abs[1 - z] < 2
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- 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
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \EulerGamma [\EulerGamma]
Tests
Symbolic
Numeric
Maple
Translation: (P[lambda])^(mu)(z) = (1)/(GAMMA(1 - mu))*((1 + z)/(1 - z)[2])^(mu/2)*F[1](- lambda , lambda + 1 ; 1 - mu ;(1 - z)/(2))
Information
Sub Equations
- (P[lambda])^(mu)(z) = (1)/(GAMMA(1 - mu))*((1 + z)/(1 - z)[2])^(mu/2)*F[1](- lambda , lambda + 1 ; 1 - mu ;(1 - z)/(2))
Free variables
- f
- lambda
- mu
- o
- r
- z
Constraints
- f*o*r*abs(1 - z) < 2
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- 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
Is part of
Complete translation information:
{
"id" : "FORMULA_ba5e292c8adc5b7e37d9844ae7d737e0",
"formula" : "P_{\\lambda}^{\\mu}(z) = \\frac{1}{\\Gamma(1-\\mu)} \\left[\\frac{1+z}{1-z}\\right]^{\\mu/2} _2F_1 \\left(-\\lambda, \\lambda+1; 1-\\mu; \\frac{1-z}{2}\\right),\\qquad \\text{for } |1-z|<2",
"semanticFormula" : "P_{\\lambda}^{\\mu}(z) = \\frac{1}{\\EulerGamma@{1 - \\mu}} [\\frac{1+z}{1-z}]_2^{\\mu/2} F_1(- \\lambda , \\lambda + 1 ; 1 - \\mu ; \\frac{1-z}{2}) , \\qquad for|1 - z|< 2",
"confidence" : 0.6264977777639084,
"translations" : {
"Mathematica" : {
"translation" : "(Subscript[P, \\[Lambda]])^\\[Mu][z] == Divide[1,Gamma[1 - \\[Mu]]]*(Subscript[Divide[1 + z,1 - z], 2])^(\\[Mu]/2)*Subscript[F, 1][- \\[Lambda], \\[Lambda]+ 1 ; 1 - \\[Mu];Divide[1 - z,2]]",
"translationInformation" : {
"subEquations" : [ "(Subscript[P, \\[Lambda]])^\\[Mu][z] = Divide[1,Gamma[1 - \\[Mu]]]*(Subscript[Divide[1 + z,1 - z], 2])^(\\[Mu]/2)*Subscript[F, 1][- \\[Lambda], \\[Lambda]+ 1 ; 1 - \\[Mu];Divide[1 - z,2]]" ],
"freeVariables" : [ "\\[Lambda]", "\\[Mu]", "f", "o", "r", "z" ],
"constraints" : [ "f*o*r*Abs[1 - z] < 2" ],
"tokenTranslations" : {
"P" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"F" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\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" : "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: \\EulerGamma [\\EulerGamma]"
}
},
"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" : "(P[lambda])^(mu)(z) = (1)/(GAMMA(1 - mu))*((1 + z)/(1 - z)[2])^(mu/2)*F[1](- lambda , lambda + 1 ; 1 - mu ;(1 - z)/(2))",
"translationInformation" : {
"subEquations" : [ "(P[lambda])^(mu)(z) = (1)/(GAMMA(1 - mu))*((1 + z)/(1 - z)[2])^(mu/2)*F[1](- lambda , lambda + 1 ; 1 - mu ;(1 - z)/(2))" ],
"freeVariables" : [ "f", "lambda", "mu", "o", "r", "z" ],
"constraints" : [ "f*o*r*abs(1 - z) < 2" ],
"tokenTranslations" : {
"P" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"F" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\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"
}
},
"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" : [ "z", "\\lambda", "P_{\\lambda}^{\\mu}(z) = \\frac{1}{\\Gamma(1-\\mu)} \\left[\\frac{1+z}{1-z}\\right]^{\\mu/2} \\,_2F_1 \\left(-\\lambda, \\lambda+1; 1-\\mu; \\frac{1-z}{2}\\right),\\qquad \\text{for } \\ |1-z|<2", "\\Gamma", "\\mu", "P" ],
"isPartOf" : [ "P_{\\lambda}^{\\mu}(z) = \\frac{1}{\\Gamma(1-\\mu)} \\left[\\frac{1+z}{1-z}\\right]^{\\mu/2} \\,_2F_1 \\left(-\\lambda, \\lambda+1; 1-\\mu; \\frac{1-z}{2}\\right),\\qquad \\text{for } \\ |1-z|<2" ],
"definiens" : [ ]
}