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 x^n}
... is translated to the CAS output ...
Semantic latex: x^n
Confidence: 0
Mathematica
Translation: (x)^(n)
Information
Sub Equations
- (x)^(n)
Free variables
- n
- x
Tests
Symbolic
Numeric
SymPy
Translation: (x)**(n)
Information
Sub Equations
- (x)**(n)
Free variables
- n
- x
Tests
Symbolic
Numeric
Maple
Translation: (x)^(n)
Information
Sub Equations
- (x)^(n)
Free variables
- n
- x
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- polynomial of degree
- yield
- coefficient
- integrand
- weight
- integral expression for the weight
- L'Hôpital 's rule
- limit
- side
- integral expression
- term of the orthogonal polynomial
- term
- note
- term in the bracket
- rule
- i.e.
- Lagrange interpolation one
- value
- relation
- degree
- Gaussian quadrature
- Chebyshev -- Gauss
- Gauss-Jacobi quadrature rule
- orthogonal polynomial of degree
- choice of node
- different point
- nontrivial polynomial of degree
- Common weight
- approximation
- point
- common domain of integration
- continuous derivative
Complete translation information:
{
"id" : "FORMULA_b41952e9dfed8e1ed562fddafeca7c70",
"formula" : "x^n",
"semanticFormula" : "x^n",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "(x)^(n)",
"translationInformation" : {
"subEquations" : [ "(x)^(n)" ],
"freeVariables" : [ "n", "x" ]
},
"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" : "(x)**(n)",
"translationInformation" : {
"subEquations" : [ "(x)**(n)" ],
"freeVariables" : [ "n", "x" ]
},
"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" : "(x)^(n)",
"translationInformation" : {
"subEquations" : [ "(x)^(n)" ],
"freeVariables" : [ "n", "x" ]
},
"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" : 5,
"sentence" : 3,
"word" : 10
} ],
"includes" : [ "n", "x^{k}", "x" ],
"isPartOf" : [ "\\sqrt{1 - x^2}", "\\int_{-1}^1 f(x)\\,dx \\approx \\sum_{i=1}^n w_i f(x_i)", "r(x) = \\sum_{i=1}^{n}r(x_{i})\\prod_{\\begin{smallmatrix}1\\leq j\\leq n\\\\j\\neq i\\end{smallmatrix}}\\frac{x-x_{j}}{x_{i}-x_{j}}", "\\frac{1}{\\sqrt{1 - x^2}}", "\\sum_{i=1}^n w_i h(x_i) = \\sum_{i=1}^n w_i r(x_i)", "\\int_a^b f(x)\\,dx \\approx \\frac{b-a}{2} \\sum_{i=1}^n w_i f\\left(\\frac{b-a}{2}\\xi_i + \\frac{a+b}{2}\\right)", "\\int_{a}^{b}\\omega(x)r(x)dx= \\sum_{i=1}^{n}r(x_{i})\\int_{a}^{b}\\omega(x)\\prod_{\\begin{smallmatrix}1\\leq j\\leq n\\\\j\\neq i\\end{smallmatrix}}\\frac{x-x_{j}}{x_{i}-x_{j}}dx", "x^{k}", "\\int_{-1}^1 f(x)\\,dx = \\int_{-1}^1 \\left(1 - x\\right)^\\alpha \\left(1 + x\\right)^\\beta g(x)\\,dx \\approx \\sum_{i=1}^n w_i' g\\left(x_i'\\right)", "\\int_a^b \\omega(x) \\, x^k p_n(x) \\, dx = 0, \\quad \\text{for all } k = 0, 1, \\ldots, n - 1", "\\int_a^b\\omega(x)\\frac{x^kp_n(x)}{x-x_i}dx= x_i^k\\int_{a}^{b}\\omega(x)\\frac{p_n(x)}{x-x_i}dx", "\\frac{p_{n}(x)}{x-x_{i}} = a_{n}x^{n-1} + s(x)", "\\int_{a}^{b}\\omega(x)\\frac{p_{n}(x)}{x-x_{i}}dx=\\frac{a_{n}}{p_{n-1}(x_{i})}\\int_{a}^{b}\\omega(x)p_{n-1}(x)x^{n-1}dx", "x^{n-1} = \\left(x^{n-1} - \\frac{p_{n-1}(x)}{a_{n-1}}\\right) + \\frac{p_{n-1}(x)}{a_{n-1}}", "\\int_a^b \\omega(x)\\,f(x)\\,dx - \\sum_{i=1}^n w_i\\,f(x_i) = \\frac{f^{(2n)}(\\xi)}{(2n)!} \\, (p_n, p_n)" ],
"definiens" : [ {
"definition" : "polynomial of degree",
"score" : 0.8545405215115502
}, {
"definition" : "yield",
"score" : 0.8507024064224206
}, {
"definition" : "coefficient",
"score" : 0.845991813538057
}, {
"definition" : "integrand",
"score" : 0.713233936054274
}, {
"definition" : "weight",
"score" : 0.7035711338549921
}, {
"definition" : "integral expression for the weight",
"score" : 0.6329188778482951
}, {
"definition" : "L'Hôpital 's rule",
"score" : 0.6329188778482951
}, {
"definition" : "limit",
"score" : 0.6329188778482951
}, {
"definition" : "side",
"score" : 0.6329188778482951
}, {
"definition" : "integral expression",
"score" : 0.5930849375172879
}, {
"definition" : "term of the orthogonal polynomial",
"score" : 0.5930849375172879
}, {
"definition" : "term",
"score" : 0.5672486918673748
}, {
"definition" : "note",
"score" : 0.48015757177699975
}, {
"definition" : "term in the bracket",
"score" : 0.4148602823111834
}, {
"definition" : "rule",
"score" : 0.4121193857436087
}, {
"definition" : "i.e.",
"score" : 0.4017036074432621
}, {
"definition" : "Lagrange interpolation one",
"score" : 0.3862474978250166
}, {
"definition" : "value",
"score" : 0.3862474978250166
}, {
"definition" : "relation",
"score" : 0.37217380952380946
}, {
"definition" : "degree",
"score" : 0.3478993797251958
}, {
"definition" : "Gaussian quadrature",
"score" : 0.34128422477700016
}, {
"definition" : "Chebyshev -- Gauss",
"score" : 0.3412842247769857
}, {
"definition" : "Gauss-Jacobi quadrature rule",
"score" : 0.3412842247769857
}, {
"definition" : "orthogonal polynomial of degree",
"score" : 0.3412842247769857
}, {
"definition" : "choice of node",
"score" : 0.33608242914761716
}, {
"definition" : "different point",
"score" : 0.3178322344112588
}, {
"definition" : "nontrivial polynomial of degree",
"score" : 0.3145950988780003
}, {
"definition" : "Common weight",
"score" : 0.31459433390952196
}, {
"definition" : "approximation",
"score" : 0.2747603935785291
}, {
"definition" : "point",
"score" : 0.2747603935785291
}, {
"definition" : "common domain of integration",
"score" : 0.27476039357851473
}, {
"definition" : "continuous derivative",
"score" : 0.22750321381914684
} ]
}