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 \Phi(z,s,a)=z^{-a}\Gamma(1-s)\sum_{k=-\infty}^\infty [2k\pi i-\log(z)]^{s-1}e^{2k\pi ai} }
... is translated to the CAS output ...
Semantic latex: \Phi(z , s , a) = z^{-a} \Gamma(1 - s) \sum_{k=-\infty}^\infty [2 k \cpi \iunit - \log(z)]^{s-1} \expe^{2 k \cpi a \iunit}
Confidence: 0
Mathematica
Translation: \[CapitalPhi][z , s , a] == (z)^(- a)* \[CapitalGamma]*(1 - s)*Sum[(2*k*Pi*I - Log[z])^(s - 1)* Exp[2*k*Pi*a*I], {k, - Infinity, Infinity}, GenerateConditions->None]
Information
Sub Equations
- \[CapitalPhi][z , s , a] = (z)^(- a)* \[CapitalGamma]*(1 - s)*Sum[(2*k*Pi*I - Log[z])^(s - 1)* Exp[2*k*Pi*a*I], {k, - Infinity, Infinity}, GenerateConditions->None]
Free variables
- \[CapitalGamma]
- \[CapitalPhi]
- a
- s
- z
Symbol info
- Pi was translated to: Pi
- Logarithm; Example: \log@@{z}
Will be translated to: Log[$0] Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 Mathematica: https://reference.wolfram.com/language/ref/Log.html
- Recognizes e with power as the exponential function. It was translated as a function.
- Imaginary unit was translated to: I
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Test expression: (\[CapitalPhi]*(z , s , a))-((z)^(- a)* \[CapitalGamma]*(1 - s)*Sum[(2*k*Pi*I - Log[z])^(s - 1)* Exp[2*k*Pi*a*I], {k, - Infinity, Infinity}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: Symbol('Phi')(z , s , a) == (z)**(- a)* Symbol('Gamma')*(1 - s)*Sum((2*k*pi*I - log(z))**(s - 1)* exp(2*k*pi*a*I), (k, - oo, oo))
Information
Sub Equations
- Symbol('Phi')(z , s , a) = (z)**(- a)* Symbol('Gamma')*(1 - s)*Sum((2*k*pi*I - log(z))**(s - 1)* exp(2*k*pi*a*I), (k, - oo, oo))
Free variables
- Symbol('Gamma')
- Symbol('Phi')
- a
- s
- z
Symbol info
- Pi was translated to: pi
- Logarithm; Example: \log@@{z}
Will be translated to: log($0) Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#log
- Recognizes e with power as the exponential function. It was translated as a function.
- Imaginary unit was translated to: I
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Maple
Translation: Phi(z , s , a) = (z)^(- a)* Gamma*(1 - s)*sum((2*k*Pi*I - log(z))^(s - 1)* exp(2*k*Pi*a*I), k = - infinity..infinity)
Information
Sub Equations
- Phi(z , s , a) = (z)^(- a)* Gamma*(1 - s)*sum((2*k*Pi*I - log(z))^(s - 1)* exp(2*k*Pi*a*I), k = - infinity..infinity)
Free variables
- Gamma
- Phi
- a
- s
- z
Symbol info
- Pi was translated to: Pi
- Logarithm; Example: \log@@{z}
Will be translated to: log($0) Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=log
- Recognizes e with power as the exponential function. It was translated as a function.
- Imaginary unit was translated to: I
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_e3f20db22a7bc9467a2e0a677af1892a",
"formula" : "\\Phi(z,s,a)=z^{-a}\\Gamma(1-s)\\sum_{k=-\\infty}^\\infty\n[2k\\pi i-\\log(z)]^{s-1}e^{2k\\pi ai}",
"semanticFormula" : "\\Phi(z , s , a) = z^{-a} \\Gamma(1 - s) \\sum_{k=-\\infty}^\\infty [2 k \\cpi \\iunit - \\log(z)]^{s-1} \\expe^{2 k \\cpi a \\iunit}",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "\\[CapitalPhi][z , s , a] == (z)^(- a)* \\[CapitalGamma]*(1 - s)*Sum[(2*k*Pi*I - Log[z])^(s - 1)* Exp[2*k*Pi*a*I], {k, - Infinity, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "\\[CapitalPhi][z , s , a] = (z)^(- a)* \\[CapitalGamma]*(1 - s)*Sum[(2*k*Pi*I - Log[z])^(s - 1)* Exp[2*k*Pi*a*I], {k, - Infinity, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[CapitalGamma]", "\\[CapitalPhi]", "a", "s", "z" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: Log[$0]\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.2#E2\nMathematica: https://reference.wolfram.com/language/ref/Log.html",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I",
"\\Phi" : "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" : "\\[CapitalPhi]*(z , s , a)",
"rhs" : "(z)^(- a)* \\[CapitalGamma]*(1 - s)*Sum[(2*k*Pi*I - Log[z])^(s - 1)* Exp[2*k*Pi*a*I], {k, - Infinity, Infinity}, GenerateConditions->None]",
"testExpression" : "(\\[CapitalPhi]*(z , s , a))-((z)^(- a)* \\[CapitalGamma]*(1 - s)*Sum[(2*k*Pi*I - Log[z])^(s - 1)* Exp[2*k*Pi*a*I], {k, - Infinity, Infinity}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "Symbol('Phi')(z , s , a) == (z)**(- a)* Symbol('Gamma')*(1 - s)*Sum((2*k*pi*I - log(z))**(s - 1)* exp(2*k*pi*a*I), (k, - oo, oo))",
"translationInformation" : {
"subEquations" : [ "Symbol('Phi')(z , s , a) = (z)**(- a)* Symbol('Gamma')*(1 - s)*Sum((2*k*pi*I - log(z))**(s - 1)* exp(2*k*pi*a*I), (k, - oo, oo))" ],
"freeVariables" : [ "Symbol('Gamma')", "Symbol('Phi')", "a", "s", "z" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: pi",
"\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: log($0)\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.2#E2\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#log",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I",
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
},
"Maple" : {
"translation" : "Phi(z , s , a) = (z)^(- a)* Gamma*(1 - s)*sum((2*k*Pi*I - log(z))^(s - 1)* exp(2*k*Pi*a*I), k = - infinity..infinity)",
"translationInformation" : {
"subEquations" : [ "Phi(z , s , a) = (z)^(- a)* Gamma*(1 - s)*sum((2*k*Pi*I - log(z))^(s - 1)* exp(2*k*Pi*a*I), k = - infinity..infinity)" ],
"freeVariables" : [ "Gamma", "Phi", "a", "s", "z" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: log($0)\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.2#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=log",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I",
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
}
},
"positions" : [ ],
"includes" : [ "a", "\\Phi(z,s,a)", "z", "s", "\\Phi(z,s,a)=z^{-a}\\Gamma(1-s)\\sum_{k=-\\infty}^\\infty[2k\\pi i-\\log(z)]^{s-1}e^{2k\\pi ai}" ],
"isPartOf" : [ "\\Phi(z,s,a)=z^{-a}\\Gamma(1-s)\\sum_{k=-\\infty}^\\infty[2k\\pi i-\\log(z)]^{s-1}e^{2k\\pi ai}" ],
"definiens" : [ ]
}