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 p_r}
... is translated to the CAS output ...
Semantic latex: p_r
Confidence: 0
Mathematica
Translation: Subscript[p, r]
Information
Sub Equations
- Subscript[p, r]
Free variables
- Subscript[p, r]
- r
Tests
Symbolic
Numeric
SymPy
Translation: Symbol('{p}_{r}')
Information
Sub Equations
- Symbol('{p}_{r}')
Free variables
- Symbol('{p}_{r}')
- r
Tests
Symbolic
Numeric
Maple
Translation: p[r]
Information
Sub Equations
- p[r]
Free variables
- p[r]
- r
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- scalar product
- Orthogonal polynomial
- recurrence relation
- coefficient
- degree
- polynomial
- i.e. monic
- infinity
- maximal degree
- operation
- orthogonality
- starting point
- Golub-Welsch algorithm
- induction
- Newton 's method
- three-term recurrence for evaluation
- polynomial of degree
- asymptotic formula
- weight
- yield
- term of the orthogonal polynomial
- zero
- integrand
- orthogonal polynomial of degree
- same orthogonal polynomial
- i.e.
- correct degree
- node
- convention
- 3-term recurrence relation
- root of the polynomial
- Eq
- term
- integral expression for the weight
- L'Hôpital 's rule
- limit
- idea
- low degree
- lower degree
- proof
- property
- quotient
- remainder
- other hand
- eigenvalue of this tridiagonal matrix
- matrix form
- node for the Gaussian quadrature
- so-called Jacobi matrix
- standard basis vector
- three-term recurrence relation
- equation
- integral
- term in the bracket
- nontrivial polynomial of degree
- Gaussian quadrature formula
- nth degree
- integral expression
- right hand side
- continuous derivative
- side
- weight function
- expression in equation
- gauss-quadrature
Complete translation information:
{
"id" : "FORMULA_dd25403004ec2aad07ed9787d2dbfb2a",
"formula" : "p_r",
"semanticFormula" : "p_r",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Subscript[p, r]",
"translationInformation" : {
"subEquations" : [ "Subscript[p, r]" ],
"freeVariables" : [ "Subscript[p, r]", "r" ]
},
"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('{p}_{r}')",
"translationInformation" : {
"subEquations" : [ "Symbol('{p}_{r}')" ],
"freeVariables" : [ "Symbol('{p}_{r}')", "r" ]
},
"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" : "p[r]",
"translationInformation" : {
"subEquations" : [ "p[r]" ],
"freeVariables" : [ "p[r]", "r" ]
},
"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" : 8,
"sentence" : 0,
"word" : 2
}, {
"section" : 8,
"sentence" : 2,
"word" : 10
}, {
"section" : 8,
"sentence" : 7,
"word" : 5
}, {
"section" : 8,
"sentence" : 9,
"word" : 28
} ],
"includes" : [ "p_{n}", "p_s", "r" ],
"isPartOf" : [ "p_{n-1}(x)", "p_n(x)", "p_{k}(x)", "\\frac{1}{b}p_{n+1}\\left(x_i\\right)", "p_{n}", "\\frac{p_{n}(x)}{x-x_{i}}", "\\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", "p_{n+1}(x)", "p_n(x) = 0", "p_{n}(x)", "\\int_{a}^{b}\\omega(x)\\frac{p_{n}(x)}{x-x_{i}}dx=\\frac{a_{n}}{a_{n-1}p_{n-1}(x_{i})}\\int_{a}^{b}\\omega(x)p_{n-1}(x)^{2}dx", "p_{n}(x_{i})", "w_{i} = \\frac{1}{p'_{n}(x_{i})}\\int_{a}^{b}\\omega(x)\\frac{p_{n}(x)}{x-x_{i}}dx", "\\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}}", "p_{n-1}(x_{i})", "\\frac{p_{n}(x)}{x-x_{i}} = a_{n}x^{n-1} + s(x)", "p_{n+1}(x_{i}) = (a)p_{n}(x_{i}) + (b)p_{n-1}(x_{i})", "w_{i} = \\frac{a_{n}}{a_{n-1}}\\frac{\\int_{a}^{b}\\omega(x)p_{n-1}\\left(x\\right)^{2}dx}{p'_{n}(x_{i})p_{n-1}(x_{i})}", "q(x) = p_{n-1}(x)", "\\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{p_{n}(x)}{x-x_{i}}dx=\\frac{1}{q(x_{i})}\\int_{a}^{b}\\omega(x)\\frac{q(x)p_{n}(x)}{x-x_{i}}dx", "(p_r, p_s) = 0", "(p_r) = r", "p_{r+1}(x) = (x - a_{r,r})p_r(x) - a_{r,r-1}p_{r-1}(x)\\cdots - a_{r,0}p_0(x)", "a_{r,s} = \\frac{\\left(xp_r, p_s\\right)}{\\left(p_s, p_s\\right)}", "p_0(x) = 1", "p_0", "(p_1,p_0)=(x-a_{0,0})(p_0,p_0)=(xp_0,p_0)-a_{0,0}(p_0,p_0)=(xp_0,p_0)-(xp_0,p_0)=0", "p_0, p_1, \\ldots, p_r", "p_{r+1}", "(p_{r+1}, p_s) = (xp_r, p_s) - a_{r,r}(p_r, p_s) - a_{r,r-1}(p_{r-1}, p_s)\\cdots - a_{r,0}(p_0, p_s)", "p_s", "(p_{r+1},p_s)=(xp_r,p_s)-a_{r,s}(p_s,p_s)=(xp_r,p_s)-(xp_r,p_s)=0", "(xp_r, p_s) = (p_r, xp_s) = 0", "p_{r+1}(x)=(x-a_{r,r})p_r(x)-a_{r,r-1}p_{r-1}(x)", "p_{r+1}(x)=(x-a_r)p_r(x)-b_rp_{r-1}(x)", "p_{-1}(x) \\equiv 0", "a_r:=\\frac{(xp_r,p_r)}{(p_r,p_r)},\\qquad b_r:=\\frac{(xp_r,p_{r-1})}{(p_{r-1},p_{r-1})}=\\frac{(p_r,p_r)}{(p_{r-1},p_{r-1})}", "(xp_r, p_{r-1}) = (p_r, xp_{r-1}) = (p_r, p_r)", "J\\tilde{P} = x\\tilde{P} - p_n(x) \\times \\mathbf{e}_n", "\\tilde{P} = \\begin{bmatrix} p_0(x) & p_1(x) & \\ldots & p_{n-1}(x) \\end{bmatrix}^\\mathsf{T}", "\\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" : "scalar product",
"score" : 0.8900228770769254
}, {
"definition" : "Orthogonal polynomial",
"score" : 0.8795546074619977
}, {
"definition" : "recurrence relation",
"score" : 0.8725592315754308
}, {
"definition" : "coefficient",
"score" : 0.8553505819306981
}, {
"definition" : "degree",
"score" : 0.8447739738694751
}, {
"definition" : "polynomial",
"score" : 0.695757365000427
}, {
"definition" : "i.e. monic",
"score" : 0.6839477168404777
}, {
"definition" : "infinity",
"score" : 0.6839477168404777
}, {
"definition" : "maximal degree",
"score" : 0.6839477168404777
}, {
"definition" : "operation",
"score" : 0.6246224871382262
}, {
"definition" : "orthogonality",
"score" : 0.5927925509888069
}, {
"definition" : "starting point",
"score" : 0.5927925509888069
}, {
"definition" : "Golub-Welsch algorithm",
"score" : 0.5262687197903358
}, {
"definition" : "induction",
"score" : 0.5262687197903358
}, {
"definition" : "Newton 's method",
"score" : 0.5262687197903358
}, {
"definition" : "three-term recurrence for evaluation",
"score" : 0.5262687197903358
}, {
"definition" : "polynomial of degree",
"score" : 0.5083996414013885
}, {
"definition" : "asymptotic formula",
"score" : 0.479011540030968
}, {
"definition" : "weight",
"score" : 0.47467359482739613
}, {
"definition" : "yield",
"score" : 0.4643761949482384
}, {
"definition" : "term of the orthogonal polynomial",
"score" : 0.4187906509053051
}, {
"definition" : "zero",
"score" : 0.41879065090030204
}, {
"definition" : "integrand",
"score" : 0.4187836061987369
}, {
"definition" : "orthogonal polynomial of degree",
"score" : 0.4187836053147102
}, {
"definition" : "same orthogonal polynomial",
"score" : 0.41371425056515165
}, {
"definition" : "i.e.",
"score" : 0.383024625345215
}, {
"definition" : "correct degree",
"score" : 0.38235638864614735
}, {
"definition" : "node",
"score" : 0.36464793863894107
}, {
"definition" : "convention",
"score" : 0.350211185515873
}, {
"definition" : "3-term recurrence relation",
"score" : 0.34969511444590257
}, {
"definition" : "root of the polynomial",
"score" : 0.3426251035304757
}, {
"definition" : "Eq",
"score" : 0.3402936249371742
}, {
"definition" : "term",
"score" : 0.3402936249371742
}, {
"definition" : "integral expression for the weight",
"score" : 0.3401381939721649
}, {
"definition" : "L'Hôpital 's rule",
"score" : 0.3401381939721649
}, {
"definition" : "limit",
"score" : 0.3401381939721649
}, {
"definition" : "idea",
"score" : 0.34013819303095405
}, {
"definition" : "low degree",
"score" : 0.34013819303095405
}, {
"definition" : "lower degree",
"score" : 0.34013819303095405
}, {
"definition" : "proof",
"score" : 0.34013819303095405
}, {
"definition" : "property",
"score" : 0.34013819303095405
}, {
"definition" : "quotient",
"score" : 0.34013819303095405
}, {
"definition" : "remainder",
"score" : 0.34013819303095405
}, {
"definition" : "other hand",
"score" : 0.32134375084967315
}, {
"definition" : "eigenvalue of this tridiagonal matrix",
"score" : 0.31347914375992064
}, {
"definition" : "matrix form",
"score" : 0.31347914375992064
}, {
"definition" : "node for the Gaussian quadrature",
"score" : 0.31347914375992064
}, {
"definition" : "so-called Jacobi matrix",
"score" : 0.31347914375992064
}, {
"definition" : "standard basis vector",
"score" : 0.31347914375992064
}, {
"definition" : "three-term recurrence relation",
"score" : 0.31347914375992064
}, {
"definition" : "equation",
"score" : 0.3134535482804917
}, {
"definition" : "integral",
"score" : 0.3134535482804917
}, {
"definition" : "term in the bracket",
"score" : 0.31344906713196863
}, {
"definition" : "nontrivial polynomial of degree",
"score" : 0.3134483021634902
}, {
"definition" : "Gaussian quadrature formula",
"score" : 0.29510245707057825
}, {
"definition" : "nth degree",
"score" : 0.27361437207880523
}, {
"definition" : "integral expression",
"score" : 0.27361436183748605
}, {
"definition" : "right hand side",
"score" : 0.2263571923194374
}, {
"definition" : "continuous derivative",
"score" : 0.22635718214723086
}, {
"definition" : "side",
"score" : 0.22635718207811822
}, {
"definition" : "weight function",
"score" : 0.17763492063492065
}, {
"definition" : "expression in equation",
"score" : 0.13245235423813345
}, {
"definition" : "gauss-quadrature",
"score" : 0.13244710812113195
} ]
}