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{Li}(x)-\pi(x) = O(\sqrt{x}\log x)}
... is translated to the CAS output ...
Semantic latex: \operatorname{Li}(x) - \cpi(x) = O(\sqrt{x} \log x)
Confidence: 0
Mathematica
Translation: Li[x]- Pi*(x) == O[Sqrt[x]*Log[x]]
Information
Sub Equations
- Li[x]- Pi*(x) = O[Sqrt[x]*Log[x]]
Free variables
- x
Symbol info
- Pi was translated to: Pi
- Logarithm; Example: \log@@{z}
Will be translated to: Log[$0] Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 Mathematica: https://reference.wolfram.com/language/ref/Log.html
- Was interpreted as a function call because of a leading \operatorname.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Test expression: (Li[x]- Pi*(x))-(O*(Sqrt[x]*Log[x]))
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: Li(x)- pi*(x) == O(sqrt(x)*log(x))
Information
Sub Equations
- Li(x)- pi*(x) = O(sqrt(x)*log(x))
Free variables
- x
Symbol info
- Pi was translated to: pi
- Logarithm; Example: \log@@{z}
Will be translated to: log($0) Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#log
- Was interpreted as a function call because of a leading \operatorname.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Maple
Translation: Li(x)- Pi*(x) = O(sqrt(x)*log(x))
Information
Sub Equations
- Li(x)- Pi*(x) = O(sqrt(x)*log(x))
Free variables
- x
Symbol info
- Pi was translated to: Pi
- Logarithm; Example: \log@@{z}
Will be translated to: log($0) Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=log
- Was interpreted as a function call because of a leading \operatorname.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- Riemann hypothesis
Complete translation information:
{
"id" : "FORMULA_6b793e4d0f471b93f67b784fad45bec9",
"formula" : "\\operatorname{Li}(x)-\\pi(x) = O(\\sqrt{x}\\log x)",
"semanticFormula" : "\\operatorname{Li}(x) - \\cpi(x) = O(\\sqrt{x} \\log x)",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Li[x]- Pi*(x) == O[Sqrt[x]*Log[x]]",
"translationInformation" : {
"subEquations" : [ "Li[x]- Pi*(x) = O[Sqrt[x]*Log[x]]" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: Log[$0]\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.2#E2\nMathematica: https://reference.wolfram.com/language/ref/Log.html",
"Li" : "Was interpreted as a function call because of a leading \\operatorname.",
"O" : "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" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "Li[x]- Pi*(x)",
"rhs" : "O*(Sqrt[x]*Log[x])",
"testExpression" : "(Li[x]- Pi*(x))-(O*(Sqrt[x]*Log[x]))",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "Li(x)- pi*(x) == O(sqrt(x)*log(x))",
"translationInformation" : {
"subEquations" : [ "Li(x)- pi*(x) = O(sqrt(x)*log(x))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: pi",
"\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: log($0)\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.2#E2\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#log",
"Li" : "Was interpreted as a function call because of a leading \\operatorname.",
"O" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
},
"Maple" : {
"translation" : "Li(x)- Pi*(x) = O(sqrt(x)*log(x))",
"translationInformation" : {
"subEquations" : [ "Li(x)- Pi*(x) = O(sqrt(x)*log(x))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\cpi" : "Pi was translated to: Pi",
"\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: log($0)\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.2#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=log",
"Li" : "Was interpreted as a function call because of a leading \\operatorname.",
"O" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
}
},
"positions" : [ {
"section" : 6,
"sentence" : 2,
"word" : 11
} ],
"includes" : [ "\\pi(x)", "x)", "x", "O" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "Riemann hypothesis",
"score" : 0.6460746792928004
} ]
}