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(e^{i\varphi},s,a)=L\big(\tfrac{\varphi}{2\pi},a,s\big)= \frac{1}{a^s} + \frac{1}{2\Gamma(s)}\int_{0}^{\infty}\frac{t^{s-1}e^{-at}\big(e^{i\varphi}-e^{-t}\big)}{\cosh{t}-\cos{\varphi}}\,dt, }
... is translated to the CAS output ...
Semantic latex: \Phi(\expe^{\iunit \varphi} , s , a) = L(\tfrac{\varphi}{2 \cpi} , a , s) = \frac{1}{a^s} + \frac{1}{2\Gamma(s)} \int_{0}^{\infty} \frac{t^{s-1} \expe^{-at}(\expe^{\iunit \varphi} - \expe^{-t})}{\cosh{t}-\cos{\varphi}} \diff{t}
Confidence: 0
Mathematica
Translation: \[CapitalPhi][Exp[I*\[CurlyPhi]], s , a] == L[Divide[\[CurlyPhi],2*Pi], a , s] == Divide[1,(a)^(s)]+Divide[1,2*\[CapitalGamma][s]]*Integrate[Divide[(t)^(s - 1)* Exp[- a*t]*(Exp[I*\[CurlyPhi]]- Exp[- t]),Cosh[t]- Cos[\[CurlyPhi]]], {t, 0, Infinity}, GenerateConditions->None]
Information
Sub Equations
- \[CapitalPhi][Exp[I*\[CurlyPhi]], s , a] = L[Divide[\[CurlyPhi],2*Pi], a , s]
- L[Divide[\[CurlyPhi],2*Pi], a , s] = Divide[1,(a)^(s)]+Divide[1,2*\[CapitalGamma][s]]*Integrate[Divide[(t)^(s - 1)* Exp[- a*t]*(Exp[I*\[CurlyPhi]]- Exp[- t]),Cosh[t]- Cos[\[CurlyPhi]]], {t, 0, Infinity}, GenerateConditions->None]
Free variables
- \[CapitalGamma]
- \[CapitalPhi]
- \[CurlyPhi]
- a
- s
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: Cos[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Mathematica: https://reference.wolfram.com/language/ref/Cos.html
- Hyperbolic cosine; Example: \cosh@@{z}
Will be translated to: Cosh[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.28#E2 Mathematica: https://reference.wolfram.com/language/ref/Cosh.html
- Recognizes e with power as the exponential function. It was translated as a function.
- Pi was translated to: Pi
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Imaginary unit was translated to: I
- 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).
Tests
Symbolic
Test expression: (\[CapitalPhi]*(Exp[I*\[CurlyPhi]], s , a))-(L*(Divide[\[CurlyPhi],2*Pi], a , s))
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Test expression: (L*(Divide[\[CurlyPhi],2*Pi], a , s))-(Divide[1,(a)^(s)]+Divide[1,2*\[CapitalGamma]*(s)]*Integrate[Divide[(t)^(s - 1)* Exp[- a*t]*(Exp[I*\[CurlyPhi]]- Exp[- t]),Cosh[t]- Cos[\[CurlyPhi]]], {t, 0, Infinity}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: Symbol('Phi')(exp(I*Symbol(r'\varphi')), s , a) == L((Symbol(r'\varphi'))/(2*pi), a , s) == (1)/((a)**(s))+(1)/(2*Symbol('Gamma')(s))*integrate(((t)**(s - 1)* exp(- a*t)*(exp(I*Symbol(r'\varphi'))- exp(- t)))/(cosh(t)- cos(Symbol(r'\varphi'))), (t, 0, oo))
Information
Sub Equations
- Symbol('Phi')(exp(I*Symbol(r'\varphi')), s , a) = L((Symbol(r'\varphi'))/(2*pi), a , s)
- L((Symbol(r'\varphi'))/(2*pi), a , s) = (1)/((a)**(s))+(1)/(2*Symbol('Gamma')(s))*integrate(((t)**(s - 1)* exp(- a*t)*(exp(I*Symbol(r'\varphi'))- exp(- t)))/(cosh(t)- cos(Symbol(r'\varphi'))), (t, 0, oo))
Free variables
- Symbol('Gamma')
- Symbol('Phi')
- Symbol(r'\varphi')
- a
- s
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: cos($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#cos
- Hyperbolic cosine; Example: \cosh@@{z}
Will be translated to: cosh($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.28#E2 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#cosh
- Recognizes e with power as the exponential function. It was translated as a function.
- Pi was translated to: pi
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Imaginary unit was translated to: I
- 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).
Tests
Symbolic
Numeric
Maple
Translation: Phi(exp(I*varphi), s , a) = L((varphi)/(2*Pi), a , s) = (1)/((a)^(s))+(1)/(2*Gamma(s))*int(((t)^(s - 1)* exp(- a*t)*(exp(I*varphi)- exp(- t)))/(cosh(t)- cos(varphi)), t = 0..infinity)
Information
Sub Equations
- Phi(exp(I*varphi), s , a) = L((varphi)/(2*Pi), a , s)
- L((varphi)/(2*Pi), a , s) = (1)/((a)^(s))+(1)/(2*Gamma(s))*int(((t)^(s - 1)* exp(- a*t)*(exp(I*varphi)- exp(- t)))/(cosh(t)- cos(varphi)), t = 0..infinity)
Free variables
- Gamma
- Phi
- a
- s
- varphi
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: cos($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos
- Hyperbolic cosine; Example: \cosh@@{z}
Will be translated to: cosh($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.28#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cosh
- Recognizes e with power as the exponential function. It was translated as a function.
- Pi was translated to: Pi
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Imaginary unit was translated to: I
- 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).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_398a38c6530a3e7df8b1a5dcd9f4a747",
"formula" : "\\Phi(e^{i\\varphi},s,a)=L(\\tfrac{\\varphi}{2\\pi},a,s)= \\frac{1}{a^s} + \\frac{1}{2\\Gamma(s)}\\int_{0}^{\\infty}\\frac{t^{s-1}e^{-at}(e^{i\\varphi}-e^{-t})}{\\cosh{t}-\\cos{\\varphi}}dt",
"semanticFormula" : "\\Phi(\\expe^{\\iunit \\varphi} , s , a) = L(\\tfrac{\\varphi}{2 \\cpi} , a , s) = \\frac{1}{a^s} + \\frac{1}{2\\Gamma(s)} \\int_{0}^{\\infty} \\frac{t^{s-1} \\expe^{-at}(\\expe^{\\iunit \\varphi} - \\expe^{-t})}{\\cosh{t}-\\cos{\\varphi}} \\diff{t}",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "\\[CapitalPhi][Exp[I*\\[CurlyPhi]], s , a] == L[Divide[\\[CurlyPhi],2*Pi], a , s] == Divide[1,(a)^(s)]+Divide[1,2*\\[CapitalGamma][s]]*Integrate[Divide[(t)^(s - 1)* Exp[- a*t]*(Exp[I*\\[CurlyPhi]]- Exp[- t]),Cosh[t]- Cos[\\[CurlyPhi]]], {t, 0, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "\\[CapitalPhi][Exp[I*\\[CurlyPhi]], s , a] = L[Divide[\\[CurlyPhi],2*Pi], a , s]", "L[Divide[\\[CurlyPhi],2*Pi], a , s] = Divide[1,(a)^(s)]+Divide[1,2*\\[CapitalGamma][s]]*Integrate[Divide[(t)^(s - 1)* Exp[- a*t]*(Exp[I*\\[CurlyPhi]]- Exp[- t]),Cosh[t]- Cos[\\[CurlyPhi]]], {t, 0, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[CapitalGamma]", "\\[CapitalPhi]", "\\[CurlyPhi]", "a", "s" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: Cos[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nMathematica: https://reference.wolfram.com/language/ref/Cos.html",
"\\cosh" : "Hyperbolic cosine; Example: \\cosh@@{z}\nWill be translated to: Cosh[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.28#E2\nMathematica: https://reference.wolfram.com/language/ref/Cosh.html",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\cpi" : "Pi was translated to: Pi",
"L" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\iunit" : "Imaginary unit was translated to: I",
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\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" : 2,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 2,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "\\[CapitalPhi]*(Exp[I*\\[CurlyPhi]], s , a)",
"rhs" : "L*(Divide[\\[CurlyPhi],2*Pi], a , s)",
"testExpression" : "(\\[CapitalPhi]*(Exp[I*\\[CurlyPhi]], s , a))-(L*(Divide[\\[CurlyPhi],2*Pi], a , s))",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
}, {
"lhs" : "L*(Divide[\\[CurlyPhi],2*Pi], a , s)",
"rhs" : "Divide[1,(a)^(s)]+Divide[1,2*\\[CapitalGamma]*(s)]*Integrate[Divide[(t)^(s - 1)* Exp[- a*t]*(Exp[I*\\[CurlyPhi]]- Exp[- t]),Cosh[t]- Cos[\\[CurlyPhi]]], {t, 0, Infinity}, GenerateConditions->None]",
"testExpression" : "(L*(Divide[\\[CurlyPhi],2*Pi], a , s))-(Divide[1,(a)^(s)]+Divide[1,2*\\[CapitalGamma]*(s)]*Integrate[Divide[(t)^(s - 1)* Exp[- a*t]*(Exp[I*\\[CurlyPhi]]- Exp[- t]),Cosh[t]- Cos[\\[CurlyPhi]]], {t, 0, Infinity}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "Symbol('Phi')(exp(I*Symbol(r'\\varphi')), s , a) == L((Symbol(r'\\varphi'))/(2*pi), a , s) == (1)/((a)**(s))+(1)/(2*Symbol('Gamma')(s))*integrate(((t)**(s - 1)* exp(- a*t)*(exp(I*Symbol(r'\\varphi'))- exp(- t)))/(cosh(t)- cos(Symbol(r'\\varphi'))), (t, 0, oo))",
"translationInformation" : {
"subEquations" : [ "Symbol('Phi')(exp(I*Symbol(r'\\varphi')), s , a) = L((Symbol(r'\\varphi'))/(2*pi), a , s)", "L((Symbol(r'\\varphi'))/(2*pi), a , s) = (1)/((a)**(s))+(1)/(2*Symbol('Gamma')(s))*integrate(((t)**(s - 1)* exp(- a*t)*(exp(I*Symbol(r'\\varphi'))- exp(- t)))/(cosh(t)- cos(Symbol(r'\\varphi'))), (t, 0, oo))" ],
"freeVariables" : [ "Symbol('Gamma')", "Symbol('Phi')", "Symbol(r'\\varphi')", "a", "s" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: cos($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#cos",
"\\cosh" : "Hyperbolic cosine; Example: \\cosh@@{z}\nWill be translated to: cosh($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.28#E2\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#cosh",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\cpi" : "Pi was translated to: pi",
"L" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\iunit" : "Imaginary unit was translated to: I",
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\Gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
},
"Maple" : {
"translation" : "Phi(exp(I*varphi), s , a) = L((varphi)/(2*Pi), a , s) = (1)/((a)^(s))+(1)/(2*Gamma(s))*int(((t)^(s - 1)* exp(- a*t)*(exp(I*varphi)- exp(- t)))/(cosh(t)- cos(varphi)), t = 0..infinity)",
"translationInformation" : {
"subEquations" : [ "Phi(exp(I*varphi), s , a) = L((varphi)/(2*Pi), a , s)", "L((varphi)/(2*Pi), a , s) = (1)/((a)^(s))+(1)/(2*Gamma(s))*int(((t)^(s - 1)* exp(- a*t)*(exp(I*varphi)- exp(- t)))/(cosh(t)- cos(varphi)), t = 0..infinity)" ],
"freeVariables" : [ "Gamma", "Phi", "a", "s", "varphi" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: cos($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos",
"\\cosh" : "Hyperbolic cosine; Example: \\cosh@@{z}\nWill be translated to: cosh($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.28#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cosh",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\cpi" : "Pi was translated to: Pi",
"L" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\iunit" : "Imaginary unit was translated to: I",
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\Gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
}
},
"positions" : [ ],
"includes" : [ "a", "\\Phi(z,s,a)", "L(\\lambda, \\alpha, s)", "s", "\\Phi(e^{i\\varphi},s,a)=L\\big(\\tfrac{\\varphi}{2\\pi},a,s\\big)= \\frac{1}{a^s} + \\frac{1}{2\\Gamma(s)}\\int_{0}^{\\infty}\\frac{t^{s-1}e^{-at}\\big(e^{i\\varphi}-e^{-t}\\big)}{\\cosh{t}-\\cos{\\varphi}}\\,dt" ],
"isPartOf" : [ "\\Phi(e^{i\\varphi},s,a)=L\\big(\\tfrac{\\varphi}{2\\pi},a,s\\big)= \\frac{1}{a^s} + \\frac{1}{2\\Gamma(s)}\\int_{0}^{\\infty}\\frac{t^{s-1}e^{-at}\\big(e^{i\\varphi}-e^{-t}\\big)}{\\cosh{t}-\\cos{\\varphi}}\\,dt" ],
"definiens" : [ ]
}