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 F_1(a,b_1,b_2;c;x,y) = \sum_{r=0}^\infty \frac{(a)_r (b_1)_r (b_2)_r (c-a)_r} {(c+r-1)_r (c)_{2r} r!} \,x^r y^r {}_2F_{1}\left(a+r,b_1+r;c+2r;x\right){}_2F_{1}\left(a+r,b_2+r;c+2r;y\right)~.}
... is translated to the CAS output ...
Semantic latex: F_1(a , b_1 , b_2 ; c ; x , y) = \sum_{r=0}^\infty \frac{(a)_r (b_1)_r (b_2)_r (c-a)_r} {(c+r-1)_r (c)_{2r} r!} x^r y^r \genhyperF{2}{1}@{a + r , b_1 + r}{c + 2 r}{x} \genhyperF{2}{1}@{a + r , b_2 + r}{c + 2 r}{y}
Confidence: 0.44235989214356
Mathematica
Translation: Subscript[F, 1][a , Subscript[b, 1], Subscript[b, 2]; c ; x , y] == Sum[Divide[Subscript[a, r]*Subscript[Subscript[b, 1], r]*Subscript[Subscript[b, 2], r]*Subscript[c - a, r],Subscript[c + r - 1, r]*Subscript[c, 2*r]*(r)!]*(x)^(r)* (y)^(r)* HypergeometricPFQ[{a + r , Subscript[b, 1]+ r}, {c + 2*r}, x]*HypergeometricPFQ[{a + r , Subscript[b, 2]+ r}, {c + 2*r}, y], {r, 0, Infinity}, GenerateConditions->None]
Information
Sub Equations
- Subscript[F, 1][a , Subscript[b, 1], Subscript[b, 2]; c ; x , y] = Sum[Divide[Subscript[a, r]*Subscript[Subscript[b, 1], r]*Subscript[Subscript[b, 2], r]*Subscript[c - a, r],Subscript[c + r - 1, r]*Subscript[c, 2*r]*(r)!]*(x)^(r)* (y)^(r)* HypergeometricPFQ[{a + r , Subscript[b, 1]+ r}, {c + 2*r}, x]*HypergeometricPFQ[{a + r , Subscript[b, 2]+ r}, {c + 2*r}, y], {r, 0, Infinity}, GenerateConditions->None]
Free variables
- Subscript[b, 1]
- Subscript[b, 2]
- a
- c
- x
- y
Symbol info
- Generalized hypergeometric function; Example: \genhyperF{p}{q}@@@{a_1,...,a_p}{b_1,...,b_q}{z}
Will be translated to: HypergeometricPFQ[{$2}, {$3}, $4] Relevant links to definitions: DLMF: http://dlmf.nist.gov/16.2#E1 Mathematica: https://reference.wolfram.com/language/ref/HypergeometricPFQ.html
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \genhyperF [\genhyperF]
Tests
Symbolic
Numeric
Maple
Translation: F[1](a , b[1], b[2]; c ; x , y) = sum((a[r]*b[1][r]*b[2][r]*c - a[r])/(c + r - 1[r]*c[2*r]*factorial(r))*(x)^(r)* (y)^(r)* hypergeom([a + r , b[1]+ r], [c + 2*r], x)*hypergeom([a + r , b[2]+ r], [c + 2*r], y), r = 0..infinity)
Information
Sub Equations
- F[1](a , b[1], b[2]; c ; x , y) = sum((a[r]*b[1][r]*b[2][r]*c - a[r])/(c + r - 1[r]*c[2*r]*factorial(r))*(x)^(r)* (y)^(r)* hypergeom([a + r , b[1]+ r], [c + 2*r], x)*hypergeom([a + r , b[2]+ r], [c + 2*r], y), r = 0..infinity)
Free variables
- a
- b[1]
- b[2]
- c
- x
- y
Symbol info
- Generalized hypergeometric function; Example: \genhyperF{p}{q}@@@{a_1,...,a_p}{b_1,...,b_q}{z}
Will be translated to: hypergeom([$2], [$3], $4) Relevant links to definitions: DLMF: http://dlmf.nist.gov/16.2#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=hypergeom
- 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_9882f39d77d9d2877a654e90028107f2",
"formula" : "F_1(a,b_1,b_2;c;x,y) = \\sum_{r=0}^\\infty \\frac{(a)_r (b_1)_r (b_2)_r (c-a)_r} {(c+r-1)_r (c)_{2r} r!} x^r y^r {}_2F_{1}\\left(a+r,b_1+r;c+2r;x\\right){}_2F_{1}\\left(a+r,b_2+r;c+2r;y\\right)~",
"semanticFormula" : "F_1(a , b_1 , b_2 ; c ; x , y) = \\sum_{r=0}^\\infty \\frac{(a)_r (b_1)_r (b_2)_r (c-a)_r} {(c+r-1)_r (c)_{2r} r!} x^r y^r \\genhyperF{2}{1}@{a + r , b_1 + r}{c + 2 r}{x} \\genhyperF{2}{1}@{a + r , b_2 + r}{c + 2 r}{y}",
"confidence" : 0.44235989214355975,
"translations" : {
"Mathematica" : {
"translation" : "Subscript[F, 1][a , Subscript[b, 1], Subscript[b, 2]; c ; x , y] == Sum[Divide[Subscript[a, r]*Subscript[Subscript[b, 1], r]*Subscript[Subscript[b, 2], r]*Subscript[c - a, r],Subscript[c + r - 1, r]*Subscript[c, 2*r]*(r)!]*(x)^(r)* (y)^(r)* HypergeometricPFQ[{a + r , Subscript[b, 1]+ r}, {c + 2*r}, x]*HypergeometricPFQ[{a + r , Subscript[b, 2]+ r}, {c + 2*r}, y], {r, 0, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "Subscript[F, 1][a , Subscript[b, 1], Subscript[b, 2]; c ; x , y] = Sum[Divide[Subscript[a, r]*Subscript[Subscript[b, 1], r]*Subscript[Subscript[b, 2], r]*Subscript[c - a, r],Subscript[c + r - 1, r]*Subscript[c, 2*r]*(r)!]*(x)^(r)* (y)^(r)* HypergeometricPFQ[{a + r , Subscript[b, 1]+ r}, {c + 2*r}, x]*HypergeometricPFQ[{a + r , Subscript[b, 2]+ r}, {c + 2*r}, y], {r, 0, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "Subscript[b, 1]", "Subscript[b, 2]", "a", "c", "x", "y" ],
"tokenTranslations" : {
"\\genhyperF" : "Generalized hypergeometric function; Example: \\genhyperF{p}{q}@@@{a_1,...,a_p}{b_1,...,b_q}{z}\nWill be translated to: HypergeometricPFQ[{$2}, {$3}, $4]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/16.2#E1\nMathematica: https://reference.wolfram.com/language/ref/HypergeometricPFQ.html",
"F" : "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" : "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: \\genhyperF [\\genhyperF]"
}
},
"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" : "F[1](a , b[1], b[2]; c ; x , y) = sum((a[r]*b[1][r]*b[2][r]*c - a[r])/(c + r - 1[r]*c[2*r]*factorial(r))*(x)^(r)* (y)^(r)* hypergeom([a + r , b[1]+ r], [c + 2*r], x)*hypergeom([a + r , b[2]+ r], [c + 2*r], y), r = 0..infinity)",
"translationInformation" : {
"subEquations" : [ "F[1](a , b[1], b[2]; c ; x , y) = sum((a[r]*b[1][r]*b[2][r]*c - a[r])/(c + r - 1[r]*c[2*r]*factorial(r))*(x)^(r)* (y)^(r)* hypergeom([a + r , b[1]+ r], [c + 2*r], x)*hypergeom([a + r , b[2]+ r], [c + 2*r], y), r = 0..infinity)" ],
"freeVariables" : [ "a", "b[1]", "b[2]", "c", "x", "y" ],
"tokenTranslations" : {
"\\genhyperF" : "Generalized hypergeometric function; Example: \\genhyperF{p}{q}@@@{a_1,...,a_p}{b_1,...,b_q}{z}\nWill be translated to: hypergeom([$2], [$3], $4)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/16.2#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=hypergeom",
"F" : "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" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
}
},
"positions" : [ ],
"includes" : [ "y", "F_{1}", "_{2}F_{1}", "F_1(a,b_1,b_2;c;x,y) = \\sum_{r=0}^\\infty \\frac{(a)_r (b_1)_r (b_2)_r (c-a)_r} {(c+r-1)_r (c)_{2r} r!} \\,x^r y^r {}_2F_{1}\\left(a+r,b_1+r;c+2r;x\\right){}_2F_{1}\\left(a+r,b_2+r;c+2r;y\\right)", "F", "x" ],
"isPartOf" : [ "F_1(a,b_1,b_2;c;x,y) = \\sum_{r=0}^\\infty \\frac{(a)_r (b_1)_r (b_2)_r (c-a)_r} {(c+r-1)_r (c)_{2r} r!} \\,x^r y^r {}_2F_{1}\\left(a+r,b_1+r;c+2r;x\\right){}_2F_{1}\\left(a+r,b_2+r;c+2r;y\\right)" ],
"definiens" : [ ]
}