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 \sum^{b-1}_{s=a}w_n^{(c)}(s,a,b)w_m^{(c)}(s,a,b)\rho(s)[\Delta x(s-\frac{1}{2}) ]=\delta_{nm}d_n^2}
... is translated to the CAS output ...
Semantic latex: \sum_{s=a}^{b-1} w_n^{(c)}(s , a , b) w_m^{(c)}(s , a , b) \rho(s) [\Delta x(s - \frac{1}{2})] = \delta_{nm} d_n^2
Confidence: 0
Mathematica
Translation: Sum[(Subscript[w, n])^(c)[s , a , b]* (Subscript[w, m])^(c)[s , a , b]* \[Rho][s]*(\[CapitalDelta]*x*(s -Divide[1,2])), {s, a, b - 1}, GenerateConditions->None] == Subscript[\[Delta], n, m]*(Subscript[d, n])^(2)
Information
Sub Equations
- Sum[(Subscript[w, n])^(c)[s , a , b]* (Subscript[w, m])^(c)[s , a , b]* \[Rho][s]*(\[CapitalDelta]*x*(s -Divide[1,2])), {s, a, b - 1}, GenerateConditions->None] = Subscript[\[Delta], n, m]*(Subscript[d, n])^(2)
Free variables
- Subscript[\[Delta], n, m]
- Subscript[d, n]
- \[CapitalDelta]
- \[Rho]
- a
- b
- c
- m
- n
- x
Symbol info
- Could be the first 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: Sum((Symbol('{w}_{n}'))**(c)(s , a , b)* (Symbol('{w}_{m}'))**(c)(s , a , b)* Symbol('rho')(s)*(Symbol('Delta')*x*(s -(1)/(2))), (s, a, b - 1)) == Symbol('{Symbol('delta')}_{n, m}')*(Symbol('{d}_{n}'))**(2)
Information
Sub Equations
- Sum((Symbol('{w}_{n}'))**(c)(s , a , b)* (Symbol('{w}_{m}'))**(c)(s , a , b)* Symbol('rho')(s)*(Symbol('Delta')*x*(s -(1)/(2))), (s, a, b - 1)) = Symbol('{Symbol('delta')}_{n, m}')*(Symbol('{d}_{n}'))**(2)
Free variables
- Symbol('Delta')
- Symbol('rho')
- Symbol('{Symbol('delta')}_{n, m}')
- Symbol('{d}_{n}')
- a
- b
- c
- m
- n
- x
Symbol info
- Could be the first 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: sum((w[n])^(c)(s , a , b)* (w[m])^(c)(s , a , b)* rho(s)*(Delta*x*(s -(1)/(2))), s = a..b - 1) = delta[n, m]*(d[n])^(2)
Information
Sub Equations
- sum((w[n])^(c)(s , a , b)* (w[m])^(c)(s , a , b)* rho(s)*(Delta*x*(s -(1)/(2))), s = a..b - 1) = delta[n, m]*(d[n])^(2)
Free variables
- Delta
- a
- b
- c
- d[n]
- delta[n, m]
- m
- n
- rho
- x
Symbol info
- Could be the first 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
Description
- orthogonality condition
- Dual Hahn polynomial
Complete translation information:
{
"id" : "FORMULA_657ec9a2e460e61adc6857260291be56",
"formula" : "\\sum^{b-1}_{s=a}w_n^{(c)}(s,a,b)w_m^{(c)}(s,a,b)\\rho(s)[\\Delta x(s-\\frac{1}{2}) ]=\\delta_{nm}d_n^2",
"semanticFormula" : "\\sum_{s=a}^{b-1} w_n^{(c)}(s , a , b) w_m^{(c)}(s , a , b) \\rho(s) [\\Delta x(s - \\frac{1}{2})] = \\delta_{nm} d_n^2",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Sum[(Subscript[w, n])^(c)[s , a , b]* (Subscript[w, m])^(c)[s , a , b]* \\[Rho][s]*(\\[CapitalDelta]*x*(s -Divide[1,2])), {s, a, b - 1}, GenerateConditions->None] == Subscript[\\[Delta], n, m]*(Subscript[d, n])^(2)",
"translationInformation" : {
"subEquations" : [ "Sum[(Subscript[w, n])^(c)[s , a , b]* (Subscript[w, m])^(c)[s , a , b]* \\[Rho][s]*(\\[CapitalDelta]*x*(s -Divide[1,2])), {s, a, b - 1}, GenerateConditions->None] = Subscript[\\[Delta], n, m]*(Subscript[d, n])^(2)" ],
"freeVariables" : [ "Subscript[\\[Delta], n, m]", "Subscript[d, n]", "\\[CapitalDelta]", "\\[Rho]", "a", "b", "c", "m", "n", "x" ],
"tokenTranslations" : {
"\\delta" : "Could be the first Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\rho" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"w" : "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" : "Sum((Symbol('{w}_{n}'))**(c)(s , a , b)* (Symbol('{w}_{m}'))**(c)(s , a , b)* Symbol('rho')(s)*(Symbol('Delta')*x*(s -(1)/(2))), (s, a, b - 1)) == Symbol('{Symbol('delta')}_{n, m}')*(Symbol('{d}_{n}'))**(2)",
"translationInformation" : {
"subEquations" : [ "Sum((Symbol('{w}_{n}'))**(c)(s , a , b)* (Symbol('{w}_{m}'))**(c)(s , a , b)* Symbol('rho')(s)*(Symbol('Delta')*x*(s -(1)/(2))), (s, a, b - 1)) = Symbol('{Symbol('delta')}_{n, m}')*(Symbol('{d}_{n}'))**(2)" ],
"freeVariables" : [ "Symbol('Delta')", "Symbol('rho')", "Symbol('{Symbol('delta')}_{n, m}')", "Symbol('{d}_{n}')", "a", "b", "c", "m", "n", "x" ],
"tokenTranslations" : {
"\\delta" : "Could be the first Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\rho" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"w" : "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" : "sum((w[n])^(c)(s , a , b)* (w[m])^(c)(s , a , b)* rho(s)*(Delta*x*(s -(1)/(2))), s = a..b - 1) = delta[n, m]*(d[n])^(2)",
"translationInformation" : {
"subEquations" : [ "sum((w[n])^(c)(s , a , b)* (w[m])^(c)(s , a , b)* rho(s)*(Delta*x*(s -(1)/(2))), s = a..b - 1) = delta[n, m]*(d[n])^(2)" ],
"freeVariables" : [ "Delta", "a", "b", "c", "d[n]", "delta[n, m]", "m", "n", "rho", "x" ],
"tokenTranslations" : {
"\\delta" : "Could be the first Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\rho" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"w" : "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" : [ {
"section" : 1,
"sentence" : 0,
"word" : 8
} ],
"includes" : [ "n" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "orthogonality condition",
"score" : 0.722
}, {
"definition" : "Dual Hahn polynomial",
"score" : 0.6859086196238077
} ]
}