LaTeX to CAS translator
Jump to navigation
Jump to search
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 \theta}
... is translated to the CAS output ...
Semantic latex: \theta
Confidence: 0
Mathematica
Translation: \[Theta]
Information
Sub Equations
- \[Theta]
Free variables
- \[Theta]
Tests
Symbolic
Numeric
SymPy
Translation: Symbol('theta')
Information
Sub Equations
- Symbol('theta')
Free variables
- Symbol('theta')
Tests
Symbolic
Numeric
Maple
Translation: theta
Information
Sub Equations
- theta
Free variables
- theta
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
- Failed to parse (syntax error): {\displaystyle \frac{1 + m_1 m_2}{m_2 - m_1} = \cot\theta\}
Description
- angle
- angular coordinate
- center
- formula
- rotation angle
- affine transformation of the coordinate
- angle from the positive horizontal axis
- canonical equation
- canonical form parameter
- ellipse 's major axis
- expression
- general equation 's coefficient
- general form coefficient by the equation
- semi-major axis
- semi-minor axis
- quotient
- ellipse 's equation
- major axis
- ellipse
- order
- circumference
- function of the usual angle measure
- general case of an ellipse
- length of the semi-major axis
- origin at the center
- polar coordinate
- polar form
- angle by a degree
- complete elliptic integral of the second kind
- direction
- eccentricity
- elementary function
- focus
- other focus at angular coordinate
- point towards the center
- polar coordinate with the origin
- q-analog angle measure
- radian
- reference direction
- sign in the denominator
- focus at the origin
- function
- point
- line with equation
- family of ellipsis
- following measurement
- measure
Complete translation information:
{
"id" : "FORMULA_2554a2bb846cffd697389e5dc8912759",
"formula" : "\\theta",
"semanticFormula" : "\\theta",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "\\[Theta]",
"translationInformation" : {
"subEquations" : [ "\\[Theta]" ],
"freeVariables" : [ "\\[Theta]" ]
},
"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('theta')",
"translationInformation" : {
"subEquations" : [ "Symbol('theta')" ],
"freeVariables" : [ "Symbol('theta')" ]
},
"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" : "theta",
"translationInformation" : {
"subEquations" : [ "theta" ],
"freeVariables" : [ "theta" ]
},
"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" : 9,
"sentence" : 4,
"word" : 25
}, {
"section" : 14,
"sentence" : 0,
"word" : 18
}, {
"section" : 15,
"sentence" : 2,
"word" : 2
}, {
"section" : 28,
"sentence" : 2,
"word" : 12
} ],
"includes" : [ ],
"isPartOf" : [ "\\begin{align} A &= a^2 \\sin^2\\theta + b^2 \\cos^2\\theta \\\\ B &= 2\\left(b^2 - a^2\\right) \\sin\\theta \\cos\\theta \\\\ C &= a^2 \\cos^2\\theta + b^2 \\sin^2\\theta \\\\ D &= -2A x_\\circ - B y_\\circ \\\\ E &= - B x_\\circ - 2C y_\\circ \\\\ F &= A x_\\circ^2 + B x_\\circ y_\\circ + C y_\\circ^2 - a^2 b^2.\\end{align}", "\\begin{align} x &= \\left(X - x_\\circ\\right) \\cos\\theta + \\left(Y - y_\\circ\\right) \\sin\\theta \\\\ y &= -\\left(X - x_\\circ\\right) \\sin\\theta + \\left(Y - y_\\circ\\right) \\cos\\theta.\\end{align}", "\\begin{align} a, b &= \\frac{-\\sqrt{2 \\Big(A E^2 + C D^2 - B D E + (B^2 - 4 A C) F\\Big)\\left((A + C) \\pm \\sqrt{(A - C)^2 + B^2}\\right)}}{B^2 - 4 A C} \\\\ x_\\circ &= \\frac{2CD - BE}{B^2 - 4AC} \\\\[3pt] y_\\circ &= \\frac{2AE - BD}{B^2 - 4AC} \\\\[3pt] \\theta &= \\begin{cases} \\arctan\\left(\\frac{1}{B}\\left(C - A - \\sqrt{(A - C)^2 + B^2}\\right)\\right) & \\text{for } B \\ne 0 \\\\ 0 & \\text{for } B = 0,\\ A < C \\\\ 90^\\circ & \\text{for } B = 0,\\ A > C \\\\ \\end{cases}\\end{align}", "r(\\theta) = \\frac{ab}{\\sqrt{(b \\cos \\theta)^2 + (a\\sin \\theta)^2}}=\\frac{b}{\\sqrt{1 - (e\\cos\\theta)^2}}", "\\theta = 0", "r(\\theta)=\\frac{a (1-e^2)}{1 \\pm e\\cos\\theta}", "r=\\frac{a (1-e^2)}{1 - e\\cos(\\theta - \\phi)}", "\\frac{1 + m_1 m_2}{m_2 - m_1} = \\cot\\theta\\", "\\theta:", "C \\,=\\, 4a\\int_0^{\\pi/2}\\sqrt {1 - e^2 \\sin^2\\theta}\\ d\\theta \\,=\\, 4 a \\,E(e)", "E(e) \\,=\\, \\int_0^{\\pi/2}\\sqrt {1 - e^2 \\sin^2\\theta}\\ d\\theta" ],
"definiens" : [ {
"definition" : "angle",
"score" : 0.8039148947084266
}, {
"definition" : "angular coordinate",
"score" : 0.7975333247310152
}, {
"definition" : "center",
"score" : 0.7827687341984797
}, {
"definition" : "formula",
"score" : 0.7827687341984797
}, {
"definition" : "rotation angle",
"score" : 0.722
}, {
"definition" : "affine transformation of the coordinate",
"score" : 0.6896778755706364
}, {
"definition" : "angle from the positive horizontal axis",
"score" : 0.6896778755706364
}, {
"definition" : "canonical equation",
"score" : 0.6896778755706364
}, {
"definition" : "canonical form parameter",
"score" : 0.6896778755706364
}, {
"definition" : "ellipse 's major axis",
"score" : 0.6896778755706364
}, {
"definition" : "expression",
"score" : 0.6896778755706364
}, {
"definition" : "general equation 's coefficient",
"score" : 0.6896778755706364
}, {
"definition" : "general form coefficient by the equation",
"score" : 0.6896778755706364
}, {
"definition" : "semi-major axis",
"score" : 0.6896778755706364
}, {
"definition" : "semi-minor axis",
"score" : 0.6896778755706364
}, {
"definition" : "quotient",
"score" : 0.4328619939524455
}, {
"definition" : "ellipse 's equation",
"score" : 0.40617210308498164
}, {
"definition" : "major axis",
"score" : 0.40617210308498164
}, {
"definition" : "ellipse",
"score" : 0.3970721724437041
}, {
"definition" : "order",
"score" : 0.3751459896300362
}, {
"definition" : "circumference",
"score" : 0.34586835176111275
}, {
"definition" : "function of the usual angle measure",
"score" : 0.34586835176111275
}, {
"definition" : "general case of an ellipse",
"score" : 0.34586835176111275
}, {
"definition" : "length of the semi-major axis",
"score" : 0.34586835176111275
}, {
"definition" : "origin at the center",
"score" : 0.34586835176111275
}, {
"definition" : "polar coordinate",
"score" : 0.34586835176111275
}, {
"definition" : "polar form",
"score" : 0.34586835176111275
}, {
"definition" : "angle by a degree",
"score" : 0.31917846089364893
}, {
"definition" : "complete elliptic integral of the second kind",
"score" : 0.31917846089364893
}, {
"definition" : "direction",
"score" : 0.31917846089364893
}, {
"definition" : "eccentricity",
"score" : 0.31917846089364893
}, {
"definition" : "elementary function",
"score" : 0.31917846089364893
}, {
"definition" : "focus",
"score" : 0.31917846089364893
}, {
"definition" : "other focus at angular coordinate",
"score" : 0.31917846089364893
}, {
"definition" : "point towards the center",
"score" : 0.31917846089364893
}, {
"definition" : "polar coordinate with the origin",
"score" : 0.31917846089364893
}, {
"definition" : "q-analog angle measure",
"score" : 0.31917846089364893
}, {
"definition" : "radian",
"score" : 0.31917846089364893
}, {
"definition" : "reference direction",
"score" : 0.31917846089364893
}, {
"definition" : "sign in the denominator",
"score" : 0.31917846089364893
}, {
"definition" : "focus at the origin",
"score" : 0.2793445205626417
}, {
"definition" : "function",
"score" : 0.2793445205626417
}, {
"definition" : "point",
"score" : 0.2793445205626417
}, {
"definition" : "line with equation",
"score" : 0.23933260810146667
}, {
"definition" : "family of ellipsis",
"score" : 0.23208734080327384
}, {
"definition" : "following measurement",
"score" : 0.23208734080327384
}, {
"definition" : "measure",
"score" : 0.23208734080327384
} ]
}