LaTeX to CAS translator

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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) = \lim_{\varepsilon \to 0+} \left( \int_0^{1-\varepsilon} \frac{dt}{\ln t} + \int_{1+\varepsilon}^x \frac{dt}{\ln t} \right)}

... is translated to the CAS output ...

Semantic latex: \operatorname{li}(x) = \lim_{\varepsilon \to 0+} \left(\int_0^{1-\varepsilon} \frac{\diff{t}}{\ln t} + \int_{1+\varepsilon}^x \frac{\diff{t}}{\ln t} \right)

Confidence: 0

Mathematica

Translation: li[x] == Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \[CurlyEpsilon]}, GenerateConditions->None]+ Integrate[Divide[1,Log[t]], {t, 1 + \[CurlyEpsilon], x}, GenerateConditions->None], \[CurlyEpsilon] -> 0, Direction -> "FromAbove", GenerateConditions->None]

Information

Sub Equations

  • li[x] = Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \[CurlyEpsilon]}, GenerateConditions->None]+ Integrate[Divide[1,Log[t]], {t, 1 + \[CurlyEpsilon], x}, GenerateConditions->None], \[CurlyEpsilon] -> 0, Direction -> "FromAbove", GenerateConditions->None]

Free variables

  • x

Symbol info

  • Was interpreted as a function call because of a leading \operatorname.
  • Natural logarithm; Example: \ln@@{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

Tests

Symbolic

Test expression: (li[x])-(Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \[CurlyEpsilon]}, GenerateConditions->None]+ Integrate[Divide[1,Log[t]], {t, 1 + \[CurlyEpsilon], x}, GenerateConditions->None], \[CurlyEpsilon] -> 0, Direction -> "FromAbove", GenerateConditions->None])

ERROR: 

{
    "result": "ERROR",
    "testTitle": "Simple",
    "testExpression": null,
    "resultExpression": null,
    "wasAborted": false,
    "conditionallySuccessful": false
}
Numeric

SymPy

Translation: li(x) == limit(integrate((1)/(ln(t)), (t, 0, 1 - Symbol(r'\varepsilon')))+ integrate((1)/(ln(t)), (t, 1 + Symbol(r'\varepsilon'), x)), Symbol(r'\varepsilon'), 0, dir='+')

Information

Sub Equations

  • li(x) = limit(integrate((1)/(ln(t)), (t, 0, 1 - Symbol(r'\varepsilon')))+ integrate((1)/(ln(t)), (t, 1 + Symbol(r'\varepsilon'), x)), Symbol(r'\varepsilon'), 0, dir='+')

Free variables

  • x

Symbol info

  • Was interpreted as a function call because of a leading \operatorname.
  • Natural logarithm; Example: \ln@@{z}

Will be translated to: ln($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

Tests

Symbolic
Numeric

Maple

Translation: li(x) = limit(int((1)/(ln(t)), t = 0..1 - varepsilon)+ int((1)/(ln(t)), t = 1 + varepsilon..x), varepsilon = 0, right)

Information

Sub Equations

  • li(x) = limit(int((1)/(ln(t)), t = 0..1 - varepsilon)+ int((1)/(ln(t)), t = 1 + varepsilon..x), varepsilon = 0, right)

Free variables

  • x

Symbol info

  • Was interpreted as a function call because of a leading \operatorname.
  • Natural logarithm; Example: \ln@@{z}

Will be translated to: ln($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=ln

Tests

Symbolic
Numeric

Dependency Graph Information

Includes

  • Failed to parse (syntax error): {\displaystyle 0+}}
  • Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0+}(}

Description

  • varepsilon
  • int
  • ln t
  • TeX Source
  • dt
  • Formula
  • frac
  • Gold ID
  • li
  • link
  • operatorname
  • right
  • x

Complete translation information: 

{
  "id" : "FORMULA_36fb8f8330168b8f8acda0dc36851474",
  "formula" : "\\operatorname{li}(x) = \\lim_{\\varepsilon \\to 0+} \\left( \\int_0^{1-\\varepsilon} \\frac{dt}{\\ln t} + \\int_{1+\\varepsilon}^x \\frac{dt}{\\ln t} \\right)",
  "semanticFormula" : "\\operatorname{li}(x) = \\lim_{\\varepsilon \\to 0+} \\left(\\int_0^{1-\\varepsilon} \\frac{\\diff{t}}{\\ln t} + \\int_{1+\\varepsilon}^x \\frac{\\diff{t}}{\\ln t} \\right)",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "li[x] == Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \\[CurlyEpsilon]}, GenerateConditions->None]+ Integrate[Divide[1,Log[t]], {t, 1 + \\[CurlyEpsilon], x}, GenerateConditions->None], \\[CurlyEpsilon] -> 0, Direction -> \"FromAbove\", GenerateConditions->None]",
      "translationInformation" : {
        "subEquations" : [ "li[x] = Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \\[CurlyEpsilon]}, GenerateConditions->None]+ Integrate[Divide[1,Log[t]], {t, 1 + \\[CurlyEpsilon], x}, GenerateConditions->None], \\[CurlyEpsilon] -> 0, Direction -> \"FromAbove\", GenerateConditions->None]" ],
        "freeVariables" : [ "x" ],
        "tokenTranslations" : {
          "li" : "Was interpreted as a function call because of a leading \\operatorname.",
          "\\ln" : "Natural logarithm; Example: \\ln@@{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"
        }
      },
      "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]",
          "rhs" : "Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \\[CurlyEpsilon]}, GenerateConditions->None]+ Integrate[Divide[1,Log[t]], {t, 1 + \\[CurlyEpsilon], x}, GenerateConditions->None], \\[CurlyEpsilon] -> 0, Direction -> \"FromAbove\", GenerateConditions->None]",
          "testExpression" : "(li[x])-(Limit[Integrate[Divide[1,Log[t]], {t, 0, 1 - \\[CurlyEpsilon]}, GenerateConditions->None]+ Integrate[Divide[1,Log[t]], {t, 1 + \\[CurlyEpsilon], x}, GenerateConditions->None], \\[CurlyEpsilon] -> 0, Direction -> \"FromAbove\", GenerateConditions->None])",
          "testCalculations" : [ {
            "result" : "ERROR",
            "testTitle" : "Simple",
            "testExpression" : null,
            "resultExpression" : null,
            "wasAborted" : false,
            "conditionallySuccessful" : false
          } ]
        } ]
      }
    },
    "SymPy" : {
      "translation" : "li(x) == limit(integrate((1)/(ln(t)), (t, 0, 1 - Symbol(r'\\varepsilon')))+ integrate((1)/(ln(t)), (t, 1 + Symbol(r'\\varepsilon'), x)), Symbol(r'\\varepsilon'), 0, dir='+')",
      "translationInformation" : {
        "subEquations" : [ "li(x) = limit(integrate((1)/(ln(t)), (t, 0, 1 - Symbol(r'\\varepsilon')))+ integrate((1)/(ln(t)), (t, 1 + Symbol(r'\\varepsilon'), x)), Symbol(r'\\varepsilon'), 0, dir='+')" ],
        "freeVariables" : [ "x" ],
        "tokenTranslations" : {
          "li" : "Was interpreted as a function call because of a leading \\operatorname.",
          "\\ln" : "Natural logarithm; Example: \\ln@@{z}\nWill be translated to: ln($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"
        }
      }
    },
    "Maple" : {
      "translation" : "li(x) = limit(int((1)/(ln(t)), t = 0..1 - varepsilon)+ int((1)/(ln(t)), t = 1 + varepsilon..x), varepsilon = 0, right)",
      "translationInformation" : {
        "subEquations" : [ "li(x) = limit(int((1)/(ln(t)), t = 0..1 - varepsilon)+ int((1)/(ln(t)), t = 1 + varepsilon..x), varepsilon = 0, right)" ],
        "freeVariables" : [ "x" ],
        "tokenTranslations" : {
          "li" : "Was interpreted as a function call because of a leading \\operatorname.",
          "\\ln" : "Natural logarithm; Example: \\ln@@{z}\nWill be translated to: ln($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=ln"
        }
      }
    }
  },
  "positions" : [ {
    "section" : 1,
    "sentence" : 0,
    "word" : 8
  } ],
  "includes" : [ "0+}", "0+}(" ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "varepsilon",
    "score" : 0.8835270181497158
  }, {
    "definition" : "int",
    "score" : 0.8144453757286602
  }, {
    "definition" : "ln t",
    "score" : 0.8144453757286602
  }, {
    "definition" : "TeX Source",
    "score" : 0.722
  }, {
    "definition" : "dt",
    "score" : 0.657257825973014
  }, {
    "definition" : "Formula",
    "score" : 0.657257825973014
  }, {
    "definition" : "frac",
    "score" : 0.657257825973014
  }, {
    "definition" : "Gold ID",
    "score" : 0.657257825973014
  }, {
    "definition" : "li",
    "score" : 0.657257825973014
  }, {
    "definition" : "link",
    "score" : 0.657257825973014
  }, {
    "definition" : "operatorname",
    "score" : 0.657257825973014
  }, {
    "definition" : "right",
    "score" : 0.657257825973014
  }, {
    "definition" : "x",
    "score" : 0.657257825973014
  } ]
}

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