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_{i=0}^n\binom{n}{i}(q-1)^i\mathcal{K}_r(i; n,q)\mathcal{K}_s(i; n,q) = q^n(q-1)^r\binom{n}{r}\delta_{r,s}. }
... is translated to the CAS output ...
Semantic latex: \sum_{i=0}^n\binom{n}{i}(q-1)^i\mathcal{K}_r(i; n,q)\mathcal{K}_s(i; n,q) = q^n(q-1)^r\binom{n}{r}\delta_{r,s}
Confidence: 0
Mathematica
Translation: Sum[Binomial[n,i]*(q - 1)^(i)* Subscript[K, r][i ; n , q]* Subscript[K, s][i ; n , q], {i, 0, n}, GenerateConditions->None] == (q)^(n)*(q - 1)^(r)*Binomial[n,r]*Subscript[\[Delta], r , s]
Information
Sub Equations
- Sum[Binomial[n,i]*(q - 1)^(i)* Subscript[K, r][i ; n , q]* Subscript[K, s][i ; n , q], {i, 0, n}, GenerateConditions->None] = (q)^(n)*(q - 1)^(r)*Binomial[n,r]*Subscript[\[Delta], r , s]
Free variables
- Subscript[\[Delta], r , s]
- n
- q
- r
- s
Symbol info
- You use a typical letter for a constant [the imaginary unit == the principal square root of -1].
We keep it like it is! But you should know that Mathematica uses I for this constant. If you want to translate it as a constant, use the corresponding DLMF macro \iunit
- 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).
Tests
Symbolic
Numeric
SymPy
Translation: Sum(binomial(n,i)*(q - 1)**(i)* Symbol('{K}_{r}')(i ; n , q)* Symbol('{K}_{s}')(i ; n , q), (i, 0, n)) == (q)**(n)*(q - 1)**(r)*binomial(n,r)*Symbol('{Symbol('delta')}_{r , s}')
Information
Sub Equations
- Sum(binomial(n,i)*(q - 1)**(i)* Symbol('{K}_{r}')(i ; n , q)* Symbol('{K}_{s}')(i ; n , q), (i, 0, n)) = (q)**(n)*(q - 1)**(r)*binomial(n,r)*Symbol('{Symbol('delta')}_{r , s}')
Free variables
- Symbol('{Symbol('delta')}_{r , s}')
- n
- q
- r
- s
Symbol info
- You use a typical letter for a constant [the imaginary unit == the principal square root of -1].
We keep it like it is! But you should know that SymPy uses I for this constant. If you want to translate it as a constant, use the corresponding DLMF macro \iunit
- 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).
Tests
Symbolic
Numeric
Maple
Translation: sum(binomial(n,i)*(q - 1)^(i)* K[r](i ; n , q)* K[s](i ; n , q), i = 0..n) = (q)^(n)*(q - 1)^(r)*binomial(n,r)*delta[r , s]
Information
Sub Equations
- sum(binomial(n,i)*(q - 1)^(i)* K[r](i ; n , q)* K[s](i ; n , q), i = 0..n) = (q)^(n)*(q - 1)^(r)*binomial(n,r)*delta[r , s]
Free variables
- delta[r , s]
- n
- q
- r
- s
Symbol info
- You use a typical letter for a constant [the imaginary unit == the principal square root of -1].
We keep it like it is! But you should know that Maple uses I for this constant. If you want to translate it as a constant, use the corresponding DLMF macro \iunit
- 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).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- non-negative integer
Complete translation information:
{
"id" : "FORMULA_d65b1937893f9781b6fe503c1b692ff3",
"formula" : "\\sum_{i=0}^n\\binom{n}{i}(q-1)^i\\mathcal{K}_r(i; n,q)\\mathcal{K}_s(i; n,q) = q^n(q-1)^r\\binom{n}{r}\\delta_{r,s}",
"semanticFormula" : "\\sum_{i=0}^n\\binom{n}{i}(q-1)^i\\mathcal{K}_r(i; n,q)\\mathcal{K}_s(i; n,q) = q^n(q-1)^r\\binom{n}{r}\\delta_{r,s}",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Sum[Binomial[n,i]*(q - 1)^(i)* Subscript[K, r][i ; n , q]* Subscript[K, s][i ; n , q], {i, 0, n}, GenerateConditions->None] == (q)^(n)*(q - 1)^(r)*Binomial[n,r]*Subscript[\\[Delta], r , s]",
"translationInformation" : {
"subEquations" : [ "Sum[Binomial[n,i]*(q - 1)^(i)* Subscript[K, r][i ; n , q]* Subscript[K, s][i ; n , q], {i, 0, n}, GenerateConditions->None] = (q)^(n)*(q - 1)^(r)*Binomial[n,r]*Subscript[\\[Delta], r , s]" ],
"freeVariables" : [ "Subscript[\\[Delta], r , s]", "n", "q", "r", "s" ],
"tokenTranslations" : {
"i" : "You use a typical letter for a constant [the imaginary unit == the principal square root of -1].\nWe keep it like it is! But you should know that Mathematica uses I for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\iunit\n",
"\\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",
"K" : "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(binomial(n,i)*(q - 1)**(i)* Symbol('{K}_{r}')(i ; n , q)* Symbol('{K}_{s}')(i ; n , q), (i, 0, n)) == (q)**(n)*(q - 1)**(r)*binomial(n,r)*Symbol('{Symbol('delta')}_{r , s}')",
"translationInformation" : {
"subEquations" : [ "Sum(binomial(n,i)*(q - 1)**(i)* Symbol('{K}_{r}')(i ; n , q)* Symbol('{K}_{s}')(i ; n , q), (i, 0, n)) = (q)**(n)*(q - 1)**(r)*binomial(n,r)*Symbol('{Symbol('delta')}_{r , s}')" ],
"freeVariables" : [ "Symbol('{Symbol('delta')}_{r , s}')", "n", "q", "r", "s" ],
"tokenTranslations" : {
"i" : "You use a typical letter for a constant [the imaginary unit == the principal square root of -1].\nWe keep it like it is! But you should know that SymPy uses I for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\iunit\n",
"\\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",
"K" : "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(binomial(n,i)*(q - 1)^(i)* K[r](i ; n , q)* K[s](i ; n , q), i = 0..n) = (q)^(n)*(q - 1)^(r)*binomial(n,r)*delta[r , s]",
"translationInformation" : {
"subEquations" : [ "sum(binomial(n,i)*(q - 1)^(i)* K[r](i ; n , q)* K[s](i ; n , q), i = 0..n) = (q)^(n)*(q - 1)^(r)*binomial(n,r)*delta[r , s]" ],
"freeVariables" : [ "delta[r , s]", "n", "q", "r", "s" ],
"tokenTranslations" : {
"i" : "You use a typical letter for a constant [the imaginary unit == the principal square root of -1].\nWe keep it like it is! But you should know that Maple uses I for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\iunit\n",
"\\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",
"K" : "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" : 4,
"sentence" : 0,
"word" : 5
} ],
"includes" : [ "q", "r,s", "n" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "non-negative integer",
"score" : 0.7125985104912714
} ]
}