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(\omega, s, \alpha) = \sum_{n=0}^\infty \frac {\omega^n} {(n+\alpha)^s} = \sum_{m=0}^{q-1} \sum_{n=0}^\infty \frac {\omega^{qn + m}}{(qn + m + \alpha)^s} = \sum_{m=0}^{q-1} \omega^m q^{-s} \zeta(s,\frac{m + \alpha}{q})}
... is translated to the CAS output ...
Semantic latex: \Phi(\omega, s, \alpha) = \sum_{n=0}^\infty \frac {\omega^n} {(n+\alpha)^s} = \sum_{m=0}^{q-1} \sum_{n=0}^\infty \frac {\omega^{qn + m}}{(qn + m + \alpha)^s} = \sum_{m=0}^{q-1} \omega^m q^{-s} \zeta(s,\frac{m + \alpha}{q})
Confidence: 0
Mathematica
Translation: \[CapitalPhi][\[Omega], s , \[Alpha]] == Sum[Divide[\[Omega]^(n),(n + \[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[\[Omega]^(q*n + m),(q*n + m + \[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None], {m, 0, q - 1}, GenerateConditions->None] == Sum[\[Omega]^(m)* (q)^(- s)* \[Zeta][s ,Divide[m + \[Alpha],q]], {m, 0, q - 1}, GenerateConditions->None]
Information
Sub Equations
- \[CapitalPhi][\[Omega], s , \[Alpha]] = Sum[Divide[\[Omega]^(n),(n + \[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None]
- Sum[Divide[\[Omega]^(n),(n + \[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None] = Sum[Sum[Divide[\[Omega]^(q*n + m),(q*n + m + \[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None], {m, 0, q - 1}, GenerateConditions->None]
- Sum[Sum[Divide[\[Omega]^(q*n + m),(q*n + m + \[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None], {m, 0, q - 1}, GenerateConditions->None] = Sum[\[Omega]^(m)* (q)^(- s)* \[Zeta][s ,Divide[m + \[Alpha],q]], {m, 0, q - 1}, GenerateConditions->None]
Free variables
- \[Alpha]
- \[CapitalPhi]
- \[Omega]
- \[Zeta]
- q
- s
Symbol info
- 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.
- 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
SymPy
Translation: Symbol('Phi')(Symbol('omega'), s , Symbol('alpha')) == Sum(((Symbol('omega'))**(n))/((n + Symbol('alpha'))**(s)), (n, 0, oo)) == Sum(Sum(((Symbol('omega'))**(q*n + m))/((q*n + m + Symbol('alpha'))**(s)), (n, 0, oo)), (m, 0, q - 1)) == Sum((Symbol('omega'))**(m)* (q)**(- s)* Symbol('zeta')(s ,(m + Symbol('alpha'))/(q)), (m, 0, q - 1))
Information
Sub Equations
- Symbol('Phi')(Symbol('omega'), s , Symbol('alpha')) = Sum(((Symbol('omega'))**(n))/((n + Symbol('alpha'))**(s)), (n, 0, oo))
- Sum(((Symbol('omega'))**(n))/((n + Symbol('alpha'))**(s)), (n, 0, oo)) = Sum(Sum(((Symbol('omega'))**(q*n + m))/((q*n + m + Symbol('alpha'))**(s)), (n, 0, oo)), (m, 0, q - 1))
- Sum(Sum(((Symbol('omega'))**(q*n + m))/((q*n + m + Symbol('alpha'))**(s)), (n, 0, oo)), (m, 0, q - 1)) = Sum((Symbol('omega'))**(m)* (q)**(- s)* Symbol('zeta')(s ,(m + Symbol('alpha'))/(q)), (m, 0, q - 1))
Free variables
- Symbol('Phi')
- Symbol('alpha')
- Symbol('omega')
- Symbol('zeta')
- q
- s
Symbol info
- 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.
- 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(omega , s , alpha) = sum(((omega)^(n))/((n + alpha)^(s)), n = 0..infinity) = sum(sum(((omega)^(q*n + m))/((q*n + m + alpha)^(s)), n = 0..infinity), m = 0..q - 1) = sum((omega)^(m)* (q)^(- s)* zeta(s ,(m + alpha)/(q)), m = 0..q - 1)
Information
Sub Equations
- Phi(omega , s , alpha) = sum(((omega)^(n))/((n + alpha)^(s)), n = 0..infinity)
- sum(((omega)^(n))/((n + alpha)^(s)), n = 0..infinity) = sum(sum(((omega)^(q*n + m))/((q*n + m + alpha)^(s)), n = 0..infinity), m = 0..q - 1)
- sum(sum(((omega)^(q*n + m))/((q*n + m + alpha)^(s)), n = 0..infinity), m = 0..q - 1) = sum((omega)^(m)* (q)^(- s)* zeta(s ,(m + alpha)/(q)), m = 0..q - 1)
Free variables
- Phi
- alpha
- omega
- q
- s
- zeta
Symbol info
- 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.
- 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_2df8c33ae0585e530cb3a0b15f6685df",
"formula" : "\\Phi(\\omega, s, \\alpha) = \\sum_{n=0}^\\infty\n\\frac {\\omega^n} {(n+\\alpha)^s} = \\sum_{m=0}^{q-1} \\sum_{n=0}^\\infty \\frac {\\omega^{qn + m}}{(qn + m + \\alpha)^s} = \\sum_{m=0}^{q-1} \\omega^m q^{-s} \\zeta(s,\\frac{m + \\alpha}{q})",
"semanticFormula" : "\\Phi(\\omega, s, \\alpha) = \\sum_{n=0}^\\infty\n\\frac {\\omega^n} {(n+\\alpha)^s} = \\sum_{m=0}^{q-1} \\sum_{n=0}^\\infty \\frac {\\omega^{qn + m}}{(qn + m + \\alpha)^s} = \\sum_{m=0}^{q-1} \\omega^m q^{-s} \\zeta(s,\\frac{m + \\alpha}{q})",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "\\[CapitalPhi][\\[Omega], s , \\[Alpha]] == Sum[Divide[\\[Omega]^(n),(n + \\[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[\\[Omega]^(q*n + m),(q*n + m + \\[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None], {m, 0, q - 1}, GenerateConditions->None] == Sum[\\[Omega]^(m)* (q)^(- s)* \\[Zeta][s ,Divide[m + \\[Alpha],q]], {m, 0, q - 1}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "\\[CapitalPhi][\\[Omega], s , \\[Alpha]] = Sum[Divide[\\[Omega]^(n),(n + \\[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None]", "Sum[Divide[\\[Omega]^(n),(n + \\[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None] = Sum[Sum[Divide[\\[Omega]^(q*n + m),(q*n + m + \\[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None], {m, 0, q - 1}, GenerateConditions->None]", "Sum[Sum[Divide[\\[Omega]^(q*n + m),(q*n + m + \\[Alpha])^(s)], {n, 0, Infinity}, GenerateConditions->None], {m, 0, q - 1}, GenerateConditions->None] = Sum[\\[Omega]^(m)* (q)^(- s)* \\[Zeta][s ,Divide[m + \\[Alpha],q]], {m, 0, q - 1}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Alpha]", "\\[CapitalPhi]", "\\[Omega]", "\\[Zeta]", "q", "s" ],
"tokenTranslations" : {
"\\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",
"\\zeta" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\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" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"SymPy" : {
"translation" : "Symbol('Phi')(Symbol('omega'), s , Symbol('alpha')) == Sum(((Symbol('omega'))**(n))/((n + Symbol('alpha'))**(s)), (n, 0, oo)) == Sum(Sum(((Symbol('omega'))**(q*n + m))/((q*n + m + Symbol('alpha'))**(s)), (n, 0, oo)), (m, 0, q - 1)) == Sum((Symbol('omega'))**(m)* (q)**(- s)* Symbol('zeta')(s ,(m + Symbol('alpha'))/(q)), (m, 0, q - 1))",
"translationInformation" : {
"subEquations" : [ "Symbol('Phi')(Symbol('omega'), s , Symbol('alpha')) = Sum(((Symbol('omega'))**(n))/((n + Symbol('alpha'))**(s)), (n, 0, oo))", "Sum(((Symbol('omega'))**(n))/((n + Symbol('alpha'))**(s)), (n, 0, oo)) = Sum(Sum(((Symbol('omega'))**(q*n + m))/((q*n + m + Symbol('alpha'))**(s)), (n, 0, oo)), (m, 0, q - 1))", "Sum(Sum(((Symbol('omega'))**(q*n + m))/((q*n + m + Symbol('alpha'))**(s)), (n, 0, oo)), (m, 0, q - 1)) = Sum((Symbol('omega'))**(m)* (q)**(- s)* Symbol('zeta')(s ,(m + Symbol('alpha'))/(q)), (m, 0, q - 1))" ],
"freeVariables" : [ "Symbol('Phi')", "Symbol('alpha')", "Symbol('omega')", "Symbol('zeta')", "q", "s" ],
"tokenTranslations" : {
"\\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",
"\\zeta" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\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" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"Maple" : {
"translation" : "Phi(omega , s , alpha) = sum(((omega)^(n))/((n + alpha)^(s)), n = 0..infinity) = sum(sum(((omega)^(q*n + m))/((q*n + m + alpha)^(s)), n = 0..infinity), m = 0..q - 1) = sum((omega)^(m)* (q)^(- s)* zeta(s ,(m + alpha)/(q)), m = 0..q - 1)",
"translationInformation" : {
"subEquations" : [ "Phi(omega , s , alpha) = sum(((omega)^(n))/((n + alpha)^(s)), n = 0..infinity)", "sum(((omega)^(n))/((n + alpha)^(s)), n = 0..infinity) = sum(sum(((omega)^(q*n + m))/((q*n + m + alpha)^(s)), n = 0..infinity), m = 0..q - 1)", "sum(sum(((omega)^(q*n + m))/((q*n + m + alpha)^(s)), n = 0..infinity), m = 0..q - 1) = sum((omega)^(m)* (q)^(- s)* zeta(s ,(m + alpha)/(q)), m = 0..q - 1)" ],
"freeVariables" : [ "Phi", "alpha", "omega", "q", "s", "zeta" ],
"tokenTranslations" : {
"\\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",
"\\zeta" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\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" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
}
},
"positions" : [ ],
"includes" : [ "\\Phi(z,s,a)", "\\Phi(z, s, \\alpha) = \\sum_{n=0}^\\infty\\frac { z^n} {(n+\\alpha)^s}", "\\Phi(\\omega, s, \\alpha) = \\sum_{n=0}^\\infty\\frac {\\omega^n} {(n+\\alpha)^s} = \\sum_{m=0}^{q-1} \\sum_{n=0}^\\infty \\frac {\\omega^{qn + m}}{(qn + m + \\alpha)^s} = \\sum_{m=0}^{q-1} \\omega^m q^{-s} \\zeta(s,\\frac{m + \\alpha}{q})", "s", "n= 0" ],
"isPartOf" : [ "\\Phi(\\omega, s, \\alpha) = \\sum_{n=0}^\\infty\\frac {\\omega^n} {(n+\\alpha)^s} = \\sum_{m=0}^{q-1} \\sum_{n=0}^\\infty \\frac {\\omega^{qn + m}}{(qn + m + \\alpha)^s} = \\sum_{m=0}^{q-1} \\omega^m q^{-s} \\zeta(s,\\frac{m + \\alpha}{q})" ],
"definiens" : [ ]
}