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 f(t+\pi)=f(t), }

${\displaystyle f(t+\pi )=f(t),}$

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

Semantic latex: f(t + \cpi) = f(t)

Confidence: 0

Mathematica

Translation: f[t + Pi] == f[t]

Information

Sub Equations

f[t + Pi] = f[t]

Free variables

t

Symbol info

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Pi was translated to: Pi

Tests

Symbolic

Test expression: (f*(t + Pi))-(f*(t))

ERROR:

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

Numeric

SymPy

Translation: f(t + pi) == f(t)

Information

Sub Equations

f(t + pi) = f(t)

Free variables

t

Symbol info

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Pi was translated to: pi

Tests

Symbolic

Numeric

Maple

Translation: f(t + Pi) = f(t)

Information

Sub Equations

f(t + Pi) = f(t)

Free variables

t

Symbol info

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Pi was translated to: Pi

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$f(t)$

$t$

$\pi$

$f(t+p)=f(t)$

Is part of

$f(t+p)=f(t)$

Description

equation

number

Complete translation information:

{
  "id" : "FORMULA_fff8784c09d3848dde71e9aa20d7776a",
  "formula" : "f(t+\\pi)=f(t)",
  "semanticFormula" : "f(t + \\cpi) = f(t)",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "f[t + Pi] == f[t]",
      "translationInformation" : {
        "subEquations" : [ "f[t + Pi] = f[t]" ],
        "freeVariables" : [ "t" ],
        "tokenTranslations" : {
          "f" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\cpi" : "Pi was translated to: Pi"
        }
      },
      "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" : "f*(t + Pi)",
          "rhs" : "f*(t)",
          "testExpression" : "(f*(t + Pi))-(f*(t))",
          "testCalculations" : [ {
            "result" : "ERROR",
            "testTitle" : "Simple",
            "testExpression" : null,
            "resultExpression" : null,
            "wasAborted" : false,
            "conditionallySuccessful" : false
          } ]
        } ]
      }
    },
    "SymPy" : {
      "translation" : "f(t + pi) == f(t)",
      "translationInformation" : {
        "subEquations" : [ "f(t + pi) = f(t)" ],
        "freeVariables" : [ "t" ],
        "tokenTranslations" : {
          "f" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\cpi" : "Pi was translated to: pi"
        }
      }
    },
    "Maple" : {
      "translation" : "f(t + Pi) = f(t)",
      "translationInformation" : {
        "subEquations" : [ "f(t + Pi) = f(t)" ],
        "freeVariables" : [ "t" ],
        "tokenTranslations" : {
          "f" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\cpi" : "Pi was translated to: Pi"
        }
      }
    }
  },
  "positions" : [ {
    "section" : 0,
    "sentence" : 1,
    "word" : 8
  } ],
  "includes" : [ "f(t)", "t", "\\pi", "f(t+p) = f(t)" ],
  "isPartOf" : [ "f(t+p) = f(t)" ],
  "definiens" : [ {
    "definition" : "equation",
    "score" : 0.722
  }, {
    "definition" : "number",
    "score" : 0.6859086196238077
  } ]
}

Specify your own input

Formula input
Wikitext context	{{distinguish\|Hill equation (biochemistry)}} In [[mathematics]], the '''Hill equation''' or '''Hill differential equation''' is the second-order linear [[ordinary differential equation]] :<math> \frac{d^2y}{dt^2} + f(t) y = 0, </math> where <math> f(t)</math> is a [[periodic function]] by minimal period <math> \pi </math>. By these we mean that for all <math>t </math> :<math>f(t+\pi)=f(t), </math> and if <math> p</math> is a number with <math>0 < p < \pi </math>, the equation <math> f(t+p) = f(t) </math> must fail for some <math> t </math>.<ref>{{cite book\|last=Magnus\|first=W.\|last2=Winkler\|first2=S.\|title=Hill's equation\|year=2013\|publisher=Courier\|isbn=9780486150291}}</ref> It is named after [[George William Hill]], who introduced it in 1886.<ref>{{cite journal\|doi=10.1007/BF02417081\|authorlink=George William Hill\|first=G.W.\|last=Hill\|title=On the Part of the Motion of Lunar Perigee Which is a Function of the Mean Motions of the Sun and Moon\|journal=Acta Math.\|volume=8\|issue=1\|pages=1–36\|year=1886\|url=https://zenodo.org/record/1691491/files/article.pdf}}</ref> Because <math> f(t) </math> has period <math>\pi </math>, the Hill equation can be rewritten using the [[Fourier series]] of <math> f(t)</math>: :<math>\frac{d^2y}{dt^2}+\left(\theta_0+2\sum_{n=1}^\infty \theta_n \cos(2nt)+\sum_{m=1}^\infty \phi_m \sin(2mt) \right ) y=0. </math> Important special cases of Hill's equation include the [[Mathieu_function#Mathieu_equation\|Mathieu equation]] (in which only the terms corresponding to ''n'' = 0, 1 are included) and the [[Meissner equation]]. Hill's equation is an important example in the understanding of periodic differential equations. Depending on the exact shape of <math> f(t) </math>, solutions may stay bounded for all time, or the amplitude of the oscillations in solutions may grow exponentially.<ref>{{cite book \| last = Teschl \| given = Gerald \|authorlink=Gerald Teschl \| title = Ordinary Differential Equations and Dynamical Systems \| publisher=[[American Mathematical Society]] \| place = [[Providence, Rhode Island\|Providence]] \| year = 2012 \| isbn= 978-0-8218-8328-0 \| url = https://www.mat.univie.ac.at/~gerald/ftp/book-ode/}}</ref> The precise form of the solutions to Hill's equation is described by [[Floquet theory]]. Solutions can also be written in terms of Hill determinants. Aside from its original application to lunar stability, the Hill equation appears in many settings including the modeling of a [[quadrupole mass spectrometer]], as the one-dimensional [[Schrödinger equation]] of an electron in a crystal, [[quantum optics]] of two-level systems, and in [[Accelerator_physics#Beam_dynamics\|accelerator physics]]. ==References== {{Reflist}} <!--- * [[Heinrich Guggenheimer]] (1977) ''Applicable Geometry'', pages 73–98, Krieger, Huntington ISBN 0-88275-368-1 . --> ==External links== * {{springer\|title=Hill equation\|id=p/h047440}} * {{mathworld\|urlname=HillsDifferentialEquation\|title=Hill's Differential Equation}} *{{dlmf\|first=G.\|last=Wolf\|id=28.29\|title=Mathieu Functions and Hill’s Equation}} [[Category:Ordinary differential equations]] {{mathapplied-stub}}
	Purge cached results.

LaTeX to CAS translator

Mathematica

Information

Tests

Symbolic

Numeric

SymPy

Information

Tests

Symbolic

Numeric

Maple

Information

Tests

Symbolic

Numeric

Dependency Graph Information

Specify your own input

Navigation menu

Search