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 C_n^{(\alpha)}(z)=\sum_{k=0}^{\lfloor n/2\rfloor} (-1)^k\frac{\Gamma(n-k+\alpha)}{\Gamma(\alpha)k!(n-2k)!}(2z)^{n-2k}. }
... is translated to the CAS output ...
Semantic latex: \ultrasphpoly{\alpha}{n}@{z} = \sum_{k=0}^{\floor{n / 2}}(- 1)^k \frac{\Gamma(n-k+\alpha)}{\Gamma(\alpha)k!(n-2k)!}(2 z)^{n-2k}
Confidence: 0.67541445472108
Mathematica
Translation: GegenbauerC[n, \[Alpha], z] == Sum[(- 1)^(k)*Divide[\[CapitalGamma][n - k + \[Alpha]],\[CapitalGamma][\[Alpha]]* (k)!*(n - 2*k)!]*(2*z)^(n - 2*k), {k, 0, Floor[n/2]}, GenerateConditions->None]
Information
Sub Equations
- GegenbauerC[n, \[Alpha], z] = Sum[(- 1)^(k)*Divide[\[CapitalGamma][n - k + \[Alpha]],\[CapitalGamma][\[Alpha]]* (k)!*(n - 2*k)!]*(2*z)^(n - 2*k), {k, 0, Floor[n/2]}, GenerateConditions->None]
Free variables
- \[Alpha]
- \[CapitalGamma]
- n
- z
Symbol info
- Ultraspherical Gegenbauer polynomial; Example: \ultrasphpoly{\lambda}{n}@{x}
Will be translated to: GegenbauerC[$1, $0, $2] Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r3 Mathematica: https://reference.wolfram.com/language/ref/GegenbauerC.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.
- Floor; Example: \floor{x}
Will be translated to: Floor[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r16 Mathematica: https://reference.wolfram.com/language/ref/Floor.html
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Test expression: (GegenbauerC[n, \[Alpha], z])-(Sum[(- 1)^(k)*Divide[\[CapitalGamma]*(n - k + \[Alpha]),\[CapitalGamma]*(\[Alpha])*(k)!*(n - 2*k)!]*(2*z)^(n - 2*k), {k, 0, Floor[n/2]}, 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: \ultrasphpoly [\ultrasphpoly]
Tests
Symbolic
Numeric
Maple
Translation: GegenbauerC(n, alpha, z) = sum((- 1)^(k)*(Gamma(n - k + alpha))/(Gamma(alpha)* factorial(k)*factorial(n - 2*k))*(2*z)^(n - 2*k), k = 0..floor(n/2))
Information
Sub Equations
- GegenbauerC(n, alpha, z) = sum((- 1)^(k)*(Gamma(n - k + alpha))/(Gamma(alpha)* factorial(k)*factorial(n - 2*k))*(2*z)^(n - 2*k), k = 0..floor(n/2))
Free variables
- Gamma
- alpha
- n
- z
Symbol info
- Ultraspherical Gegenbauer polynomial; Example: \ultrasphpoly{\lambda}{n}@{x}
Will be translated to: GegenbauerC($1, $0, $2) Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r3 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GegenbauerC
- 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.
- Floor; Example: \floor{x}
Will be translated to: floor($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r16 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=floor
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Complete translation information:
{
"id" : "FORMULA_820b3cc4c65eb72900257f18225d1e91",
"formula" : "C_n^{(\\alpha)}(z)=\\sum_{k=0}^{\\lfloor n/2\\rfloor} (-1)^k\\frac{\\Gamma(n-k+\\alpha)}{\\Gamma(\\alpha)k!(n-2k)!}(2z)^{n-2k}",
"semanticFormula" : "\\ultrasphpoly{\\alpha}{n}@{z} = \\sum_{k=0}^{\\floor{n / 2}}(- 1)^k \\frac{\\Gamma(n-k+\\alpha)}{\\Gamma(\\alpha)k!(n-2k)!}(2 z)^{n-2k}",
"confidence" : 0.675414454721077,
"translations" : {
"Mathematica" : {
"translation" : "GegenbauerC[n, \\[Alpha], z] == Sum[(- 1)^(k)*Divide[\\[CapitalGamma][n - k + \\[Alpha]],\\[CapitalGamma][\\[Alpha]]* (k)!*(n - 2*k)!]*(2*z)^(n - 2*k), {k, 0, Floor[n/2]}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "GegenbauerC[n, \\[Alpha], z] = Sum[(- 1)^(k)*Divide[\\[CapitalGamma][n - k + \\[Alpha]],\\[CapitalGamma][\\[Alpha]]* (k)!*(n - 2*k)!]*(2*z)^(n - 2*k), {k, 0, Floor[n/2]}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Alpha]", "\\[CapitalGamma]", "n", "z" ],
"tokenTranslations" : {
"\\ultrasphpoly" : "Ultraspherical Gegenbauer polynomial; Example: \\ultrasphpoly{\\lambda}{n}@{x}\nWill be translated to: GegenbauerC[$1, $0, $2]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r3\nMathematica: https://reference.wolfram.com/language/ref/GegenbauerC.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",
"\\floor" : "Floor; Example: \\floor{x}\nWill be translated to: Floor[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r16\nMathematica: https://reference.wolfram.com/language/ref/Floor.html",
"\\Gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
},
"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" : "GegenbauerC[n, \\[Alpha], z]",
"rhs" : "Sum[(- 1)^(k)*Divide[\\[CapitalGamma]*(n - k + \\[Alpha]),\\[CapitalGamma]*(\\[Alpha])*(k)!*(n - 2*k)!]*(2*z)^(n - 2*k), {k, 0, Floor[n/2]}, GenerateConditions->None]",
"testExpression" : "(GegenbauerC[n, \\[Alpha], z])-(Sum[(- 1)^(k)*Divide[\\[CapitalGamma]*(n - k + \\[Alpha]),\\[CapitalGamma]*(\\[Alpha])*(k)!*(n - 2*k)!]*(2*z)^(n - 2*k), {k, 0, Floor[n/2]}, 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: \\ultrasphpoly [\\ultrasphpoly]"
}
}
},
"Maple" : {
"translation" : "GegenbauerC(n, alpha, z) = sum((- 1)^(k)*(Gamma(n - k + alpha))/(Gamma(alpha)* factorial(k)*factorial(n - 2*k))*(2*z)^(n - 2*k), k = 0..floor(n/2))",
"translationInformation" : {
"subEquations" : [ "GegenbauerC(n, alpha, z) = sum((- 1)^(k)*(Gamma(n - k + alpha))/(Gamma(alpha)* factorial(k)*factorial(n - 2*k))*(2*z)^(n - 2*k), k = 0..floor(n/2))" ],
"freeVariables" : [ "Gamma", "alpha", "n", "z" ],
"tokenTranslations" : {
"\\ultrasphpoly" : "Ultraspherical Gegenbauer polynomial; Example: \\ultrasphpoly{\\lambda}{n}@{x}\nWill be translated to: GegenbauerC($1, $0, $2)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r3\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GegenbauerC",
"\\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",
"\\floor" : "Floor; Example: \\floor{x}\nWill be translated to: floor($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r16\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=floor",
"\\Gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
}
},
"positions" : [ {
"section" : 1,
"sentence" : 8,
"word" : 2
} ],
"includes" : [ "C_{n}^{(\\alpha)}(x)", "\\alpha", "n" ],
"isPartOf" : [ ],
"definiens" : [ ]
}