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 D_-(x) = i F(-ix) = -\frac{\sqrt{\pi}}{2} \left[ e^{x^2} - w(-ix) \right]}
... is translated to the CAS output ...
Semantic latex: D_-(x) = \iunit F(- \iunit x) = - \frac{\sqrt{\cpi}}{2} [\expe^{x^2} - w(- \iunit x)]
Confidence: 0
Mathematica
Translation: Subscript[D, -][x] == I*F[- I*x] == -Divide[Sqrt[Pi],2]*(Exp[(x)^(2)]- w[- I*x])
Information
Sub Equations
- Subscript[D, -][x] = I*F[- I*x]
- I*F[- I*x] = -Divide[Sqrt[Pi],2]*(Exp[(x)^(2)]- w[- I*x])
Free variables
- x
Symbol info
- Pi was translated to: Pi
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Recognizes e with power as the exponential function. It was translated as a function.
- 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
SymPy
Translation: Symbol('{D}_{-}')(x) == I*F(- I*x) == -(sqrt(pi))/(2)*(exp((x)**(2))- w(- I*x))
Information
Sub Equations
- Symbol('{D}_{-}')(x) = I*F(- I*x)
- I*F(- I*x) = -(sqrt(pi))/(2)*(exp((x)**(2))- w(- I*x))
Free variables
- x
Symbol info
- Pi was translated to: pi
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Recognizes e with power as the exponential function. It was translated as a function.
- 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: D[-](x) = I*F(- I*x) = -(sqrt(Pi))/(2)*(exp((x)^(2))- w(- I*x))
Information
Sub Equations
- D[-](x) = I*F(- I*x)
- I*F(- I*x) = -(sqrt(Pi))/(2)*(exp((x)^(2))- w(- I*x))
Free variables
- x
Symbol info
- Pi was translated to: Pi
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Recognizes e with power as the exponential function. It was translated as a function.
- 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
Description
- entire complex plane
- Dawson function
- term
- erfi
- Faddeeva function
Complete translation information:
{
"id" : "FORMULA_7e0e13bac033ba8ef229ce6f5c661822",
"formula" : "D_-(x) = i F(-ix) = -\\frac{\\sqrt{\\pi}}{2} \\left[ e^{x^2} - w(-ix) \\right]",
"semanticFormula" : "D_-(x) = \\iunit F(- \\iunit x) = - \\frac{\\sqrt{\\cpi}}{2} [\\expe^{x^2} - w(- \\iunit x)]",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Subscript[D, -][x] == I*F[- I*x] == -Divide[Sqrt[Pi],2]*(Exp[(x)^(2)]- w[- I*x])",
"translationInformation" : {
"subEquations" : [ "Subscript[D, -][x] = I*F[- I*x]", "I*F[- I*x] = -Divide[Sqrt[Pi],2]*(Exp[(x)^(2)]- w[- I*x])" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"D" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I",
"F" : "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" : "Symbol('{D}_{-}')(x) == I*F(- I*x) == -(sqrt(pi))/(2)*(exp((x)**(2))- w(- I*x))",
"translationInformation" : {
"subEquations" : [ "Symbol('{D}_{-}')(x) = I*F(- I*x)", "I*F(- I*x) = -(sqrt(pi))/(2)*(exp((x)**(2))- w(- I*x))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: pi",
"D" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I",
"F" : "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" : "D[-](x) = I*F(- I*x) = -(sqrt(Pi))/(2)*(exp((x)^(2))- w(- I*x))",
"translationInformation" : {
"subEquations" : [ "D[-](x) = I*F(- I*x)", "I*F(- I*x) = -(sqrt(Pi))/(2)*(exp((x)^(2))- w(- I*x))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"D" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I",
"F" : "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" : 4,
"word" : 29
} ],
"includes" : [ "w(z)", "F(x)", "x", "F(y)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "entire complex plane",
"score" : 0.6460746792928004
}, {
"definition" : "Dawson function",
"score" : 0.5500952380952381
}, {
"definition" : "term",
"score" : 0.5500952380952381
}, {
"definition" : "erfi",
"score" : 0.5049074255814494
}, {
"definition" : "Faddeeva function",
"score" : 0.46655930748162855
} ]
}