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 \operatorname{Si}(x) - \operatorname{si}(x) = \int_0^\infty\frac{\sin t}{t}\,dt = \frac{\pi}{2} \quad \text{ or } \quad \operatorname{Si}(x) = \frac{\pi}{2} + \operatorname{si}(x) ~.}
... is translated to the CAS output ...
Semantic latex: \operatorname{Si}(x) - \operatorname{si}(x) = \int_0^\infty \frac{\sin t}{t} \diff{t} = \frac{\cpi}{2} \quad or \quad \operatorname{Si}(x) = \frac{\cpi}{2} + \operatorname{si}(x)
Confidence: 0
Mathematica
Translation: Si[x]- si[x] == Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Pi,2]
Information
Sub Equations
- Si[x]- si[x] = Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None]
- Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None] = Divide[Pi,2]
Free variables
- o
- r
- x
Constraints
- o*r*Si[x] == Divide[Pi,2]+ si[x]
Symbol info
- Pi was translated to: Pi
- Was interpreted as a function call because of a leading \operatorname.
- Was interpreted as a function call because of a leading \operatorname.
- Sine; Example: \sin@@{z}
Will be translated to: Sin[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Mathematica: https://reference.wolfram.com/language/ref/Sin.html
Tests
Symbolic
Test expression: (Si[x]- si[x])-(Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Test expression: (Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None])-(Divide[Pi,2])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: Si(x)- si(x) == integrate((sin(t))/(t), (t, 0, oo)) == (pi)/(2)
Information
Sub Equations
- Si(x)- si(x) = integrate((sin(t))/(t), (t, 0, oo))
- integrate((sin(t))/(t), (t, 0, oo)) = (pi)/(2)
Free variables
- o
- r
- x
Constraints
- o*r*Si(x) == (pi)/(2)+ si(x)
Symbol info
- Pi was translated to: pi
- Was interpreted as a function call because of a leading \operatorname.
- Was interpreted as a function call because of a leading \operatorname.
- Sine; Example: \sin@@{z}
Will be translated to: sin($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#sin
Tests
Symbolic
Numeric
Maple
Translation: Si(x)- si(x) = int((sin(t))/(t), t = 0..infinity) = (Pi)/(2)
Information
Sub Equations
- Si(x)- si(x) = int((sin(t))/(t), t = 0..infinity)
- int((sin(t))/(t), t = 0..infinity) = (Pi)/(2)
Free variables
- o
- r
- x
Constraints
- o*r*Si(x) = (Pi)/(2)+ si(x)
Symbol info
- Pi was translated to: Pi
- Was interpreted as a function call because of a leading \operatorname.
- Was interpreted as a function call because of a leading \operatorname.
- Sine; Example: \sin@@{z}
Will be translated to: sin($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_3719bd08e8536b9500f4a5bd384a3dda",
"formula" : "\\operatorname{Si}(x) - \\operatorname{si}(x) = \\int_0^\\infty\\frac{\\sin t}{t}dt = \\frac{\\pi}{2} \\quad \\text{ or } \\quad \\operatorname{Si}(x) = \\frac{\\pi}{2} + \\operatorname{si}(x) ~",
"semanticFormula" : "\\operatorname{Si}(x) - \\operatorname{si}(x) = \\int_0^\\infty \\frac{\\sin t}{t} \\diff{t} = \\frac{\\cpi}{2} \\quad or \\quad \\operatorname{Si}(x) = \\frac{\\cpi}{2} + \\operatorname{si}(x)",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Si[x]- si[x] == Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Pi,2]",
"translationInformation" : {
"subEquations" : [ "Si[x]- si[x] = Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None]", "Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None] = Divide[Pi,2]" ],
"freeVariables" : [ "o", "r", "x" ],
"constraints" : [ "o*r*Si[x] == Divide[Pi,2]+ si[x]" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"Si" : "Was interpreted as a function call because of a leading \\operatorname.",
"si" : "Was interpreted as a function call because of a leading \\operatorname.",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: Sin[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nMathematica: https://reference.wolfram.com/language/ref/Sin.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 2,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 2,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "Si[x]- si[x]",
"rhs" : "Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None]",
"testExpression" : "(Si[x]- si[x])-(Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
}, {
"lhs" : "Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None]",
"rhs" : "Divide[Pi,2]",
"testExpression" : "(Integrate[Divide[Sin[t],t], {t, 0, Infinity}, GenerateConditions->None])-(Divide[Pi,2])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "Si(x)- si(x) == integrate((sin(t))/(t), (t, 0, oo)) == (pi)/(2)",
"translationInformation" : {
"subEquations" : [ "Si(x)- si(x) = integrate((sin(t))/(t), (t, 0, oo))", "integrate((sin(t))/(t), (t, 0, oo)) = (pi)/(2)" ],
"freeVariables" : [ "o", "r", "x" ],
"constraints" : [ "o*r*Si(x) == (pi)/(2)+ si(x)" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: pi",
"Si" : "Was interpreted as a function call because of a leading \\operatorname.",
"si" : "Was interpreted as a function call because of a leading \\operatorname.",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: sin($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#sin"
}
}
},
"Maple" : {
"translation" : "Si(x)- si(x) = int((sin(t))/(t), t = 0..infinity) = (Pi)/(2)",
"translationInformation" : {
"subEquations" : [ "Si(x)- si(x) = int((sin(t))/(t), t = 0..infinity)", "int((sin(t))/(t), t = 0..infinity) = (Pi)/(2)" ],
"freeVariables" : [ "o", "r", "x" ],
"constraints" : [ "o*r*Si(x) = (Pi)/(2)+ si(x)" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"Si" : "Was interpreted as a function call because of a leading \\operatorname.",
"si" : "Was interpreted as a function call because of a leading \\operatorname.",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: sin($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin"
}
}
}
},
"positions" : [ ],
"includes" : [ "\\pi", "\\operatorname{Si}(x) - \\operatorname{si}(x) = \\int_0^\\infty\\frac{\\sin t}{t}\\,dt = \\frac{\\pi}{2} \\quad \\text{ or } \\quad \\operatorname{Si}(x) = \\frac{\\pi}{2} + \\operatorname{si}(x)", "si(x)", "Si", "x", "Si(x)" ],
"isPartOf" : [ "\\operatorname{Si}(x) - \\operatorname{si}(x) = \\int_0^\\infty\\frac{\\sin t}{t}\\,dt = \\frac{\\pi}{2} \\quad \\text{ or } \\quad \\operatorname{Si}(x) = \\frac{\\pi}{2} + \\operatorname{si}(x)" ],
"definiens" : [ ]
}