Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Symbolic Math Toolbox MuPAD Functions

Alphabetical List By Category

MuPAD

MuPAD Language Fundamentals

Entering Commands

:=Assign variables
;Statement sequences
...Convert to a floating-point interval
_indexIndexed access
indexvalIndexed access to arrays and tables without evaluation
%, lastAccess a previously computed object
resetRe-initialize a session
unitUnits of measurement
helpDisplay a help page
infoPrints short information
deleteDelete the value of an identifier
freeIndetsFree indeterminates of an expression
genidentCreate an unused identifier
idIdentity map
indetsIndeterminates of an expression
valValue of an object
aliasCreates an alias
unaliasDeletes an alias
anamesIdentifiers that have values or properties
unuseUndo export of library function
useUse library functions by a short name

Operators and Elementary Operations

Arithmetic Operations
_invertReciprocal of an expression
_subtractSubtract expressions
Set Operations
appendAdd elements to a list
cardCardinality of a set
containsTest if an entry exists in a container
inMembership
intersectIntersection of sets or intervals or both
minusDifference of sets or intervals or both
unionUnion of sets or intervals or both
revertRevert polynomials, lists, character strings and tables, invert series expansions
universeSet-theoretical universe
zipCombine lists
Expression Trees and Precedence
misc::genassopGenerates an n-ary associative operator from a binary one

Special Values

FAILIndicate a failed computation
NILSingleton element of the domain DOM_NIL
nullGenerate the void object of type DOM_NULL
TRUEBoolean constant TRUE
FALSEBoolean constant FALSE
UNKNOWNBoolean constant UNKNOWN
undefinedUndefined value
solvelib::BasicSetBasic infinite sets
C_Complex numbers
R_Real numbers
Q_Rational numbers
Z_Integers
N_Positive integers

Data Types

Data Structures
Common Operations
.Concatenate objects
..Range operator
assignPerform assignments given as equations
assignElementsAssign values to entries of an array, a list, or a table
lengthThe “length” of a object (heuristic complexity)
matchPattern matching
nopsNumber of operands
opOperands of an object
piecewiseDomain of conditionally defined objects
selectSelect operands
splitSplit an object
sysorderCompare objects according to the internal order
tableCreate a table
numeric::indetsSearch for indeterminates
prog::exprtreeVisualize an expression as tree
prog::findFind operands of objects
prog::sortSort objects by an index function
Operations on Lists
listlib::insertInsert an element into a list
listlib::insertAtInsert an element into a list at a given position
listlib::mergeMerging two ordered lists
listlib::removeDuplicatesRemoves duplicate entries
listlib::removeDupSortedRemove duplicates of any element from ordered lists
listlib::setDifferenceRemove elements from a list
listlib::singleMergeMerging of two ordered lists without duplicates
listlib::sublistSearch sublists
numeric::sortSort a numerical list
poly2listConvert a polynomial to a list of terms
sortSort a list
text2listSplit a character string into a list of substrings
Operations on Strings
stringlib::collapseWhitespaceCollapse whitespace in strings
stringlib::containsTest for substring
stringlib::formatFormatting a string
stringlib::formatfConvert a floating-point number to a string
stringlib::formatTimeTextual description of a time length
stringlib::lowerConvert to lower-case
stringlib::maskMetaMask regular expression special characters
stringlib::orderSorting procedure for Sort
stringlib::posPosition of a substring
stringlib::randomCreate a random string
stringlib::readTextRead text file
stringlib::removeDelete substrings
stringlib::splitSplit a string
stringlib::subsSubstitution in a string
stringlib::subsopSubstitution in a string
stringlib::upperConvert to upper-case
stringlib::validIdentValidate identifier name
strmatchMatch pattern in character string
substringExtract a substring from a string
Identification
Indeterminates, Expressions, Equations, Constants
Type::AlgebraicConstantType representing algebraic constants
Type::ArithmeticalType representing arithmetical objects
Type::BooleanType representing boolean expressions
Type::ConstantIdentsSet of constant identifiers in MuPAD
Type::ConstantType representing constant objects
Type::EquationType representing equations
Type::FunctionType representing functions
Type::IndepOfType representing objects that do not contain given identifiers
Type::IndeterminateType representing indeterminates
Type::PropertyType representing any property
Type::RelationType representing relations
Type::UnknownType representing variables
Numbers
Type::NegIntType and property representing negative integers
Type::NegRatType and property representing negative rational numbers
Type::NegativeType and property representing negative numbers
Type::NonNegIntType and property representing nonnegative integers
Type::NonNegRatType and property representing nonnegative rational numbers
Type::NonNegativeType and property representing nonnegative numbers
Type::PosIntType and property representing positive integers
Type::PosRatType and property representing positive rational numbers
Type::PositiveType and property representing positive numbers
Type::NonZeroType and property representing “unequal to zero”
Type::ZeroType and property representing zero
Type::ComplexType and property representing complex numbers
Type::ImaginaryType and property representing imaginary numbers
Type::RealType and property representing real numbers
Type::EvenType and property representing even integers
Type::IntegerType and property representing integers
Type::NumericType representing numerical objects
Type::OddType and property representing odd integers
Type::PrimeType representing prime numbers
Type::RationalType and property representing rational numbers
Type::ResidueProperty representing a residue class
Data Structures
Type::IntervalProperty representing intervals
Type::ListOfType representing lists of objects with the same type
Type::ListProductType representing lists
Type::IntersectionType representing the intersection of several types
Type::PolyExprType representing polynomial expressions
Type::PolyOfType representing polynomials
Type::ProductType representing sequences
Type::RatExprType representing rational expressions
Type::SequenceOfType representing sequences
Type::SeriesType representing truncated Puiseux, Laurent, and Taylor series expansions
Type::SetOfType representing sets
Type::SetType representing set-theoretic expressions
Type::SingletonType representing exactly one object
Type::TableOfEntryType representing tables with specified entries
Type::TableOfIndexType representing tables with specified indices
Type::TableOfType representing tables
Type::UnionType representing several types as one type object
Type Checking
domtypeData type of an object
hasCheck if an object occurs in another object
hastypeTest if an object of a specified type occurs in another object
testtypeSyntactical type checking
typeType of an object
Type::AnyTypeType representing arbitrary MuPAD objects
Type::PredicateType for testing object satisfying a given predicate
Conversion
coerceType conversion
exprConvert into an element of a basic domain
expr2textConvert objects into character strings
int2textConvert an integer to a character string
intervalConvert constant subexpressions to intervals
strprintPrint into string
tbl2textConcatenate the strings in a table
text2exprConvert a character string to an expression
text2intConvert a character string to an integer
text2listSplit a character string into a list of substrings
text2tblSplit a character string into a table of substrings
linalg::expr2MatrixConstruct a matrix from equations
prog::exprlistConvert an expression into a nested list

MuPAD Symbols and Special Characters

Symbol::accentPrimeAdds a prime accent to an identifier
Symbol::accentAsteriskAdds an asterisk accent to an identifier
Symbol::accentTildeAdds a tilde accent to an identifier
Symbol::accentHatAdds a hat accent to an identifier
Symbol::accentRightArrowAdds a right arrow accent to an identifier
Symbol::accentDotAdds a dot accent to an identifier
Symbol::accentDoubleDotAdds a double dot accent to an identifier
Symbol::accentTripleDotAdds a triple dot accent to an identifier
Symbol::accentOverBarAdds an overbar to an identifier
Symbol::accentUnderBarAdds an underbar to an identifier
Symbol::newFunctional access to symbols
Symbol::subScriptCombines two expressions to a new subscripted identifier
Symbol::subSuperScriptCombines three expressions to a new combined sub- and superscripted identifier
Symbol::superScriptCombines two expressions to a new superscripted identifier

Mathematics

Equation Solving

Symbolic Solvers
linsolveSolve a system of linear equations
polesPoles of expression or function
recDomain of recurrence equations
RootOfSet of roots of a polynomial
solveSolve equations and inequalities
testeqCheck the mathematical equivalence of expressions
solvelib::pdioeSolve polynomial Diophantine equations
Numeric Solvers
numeric::butcherButcher parameters of Runge-Kutta schemes
numeric::cubicSplineInterpolation by cubic splines
numeric::cubicSpline2dInterpolation by 2-dimensional bi-cubic splines
numeric::fsolveSearch for a numerical root of a system of equations
numeric::leastSquaresLeast squares solution of linear equations
numeric::linsolveSolve a system of linear equations
numeric::matlinsolveSolve a linear matrix equation
numeric::odesolveNumerical solution of an ordinary differential equation
numeric::odesolve2Numerical solution of an ordinary differential equation
numeric::odesolveGeometricNumerical solution of an ordinary differential equation on a homogeneous manifold
numeric::ode2vectorfieldConvert an ode system to vectorfield notation
numeric::odeToVectorFieldConvert an ode system to vectorfield notation
numeric::solveNumerical solution of equations (the float attribute of solve)
Ordinary Differential Equations
ode::exponentialSolutionsExponential solutions of a homogeneous linear ordinary differential equation
ode::polynomialSolutionsPolynomial solutions of a homogeneous linear ordinary differential equation
ode::rationalSolutionsRational solutions of a homogeneous linear ordinary differential equation
ode::seriesSeries solutions of an ordinary differential equation
ode::solveSolving ordinary differential equations
odeDomain of ordinary differential equations
ode::companionSystemCompanion matrix of a linear homogeneous ordinary differential equation
ode::cyclicVectorTransforms a linear differential system to an equivalent linear differential system with a companion matrix.
ode::dAlembertD'Alembert reduction of a linear homogeneous ordinary differential equation
ode::evalOdeApplies an expression at a linear ordinary differential equation
ode::exponentsExponents of a linear ordinary differential equation
ode::getOrderOrder of an ordinary differential equation
ode::indicialEquationIndicial equation of a linear ordinary differential equation
ode::isFuchsianTests if a homogeneous linear ordinary differential equation is of Fuchsian type
ode::isLODETest for a linear ordinary differential equation
ode::mkODEBuilds a linear homogeneous ordinary differential equation from a list of coefficient functions
ode::normalizeNormalized form of a linear ordinary differential equation
ode::ratSysRational solutions of a first order homogeneous linear differential system
ode::scalarEquationTransforms a linear differential system to an equivalent scalar linear differential equation
ode::symmetricPowerSymmetric power of a homogeneous linear ordinary differential equation
ode::unimodularUnimodular transformation of a linear ordinary differential equation
ode::vectorizeCoefficients of a homogeneous linear ODE
ode::wronskianWronskian of functions or of a linear homogeneous ordinary differential equation
Properties and Assumptions
assumeSet permanent assumption
assumeAlsoAdd permanent assumption
assumingSet temporary assumption
assumingAlsoAdd temporary assumption
getpropQuery properties of expressions
isCheck a mathematical property of an expression
iszeroGeneric zero test
property::dependsDependence table with all properties of an expression
property::haspropDoes an object have properties?
property::showpropsWhat assumptions are made?
unassumeDelete the properties of an identifier
Utilities for the Solver
solvelib::cartesianPowerCartesian power of a set
solvelib::cartesianProductCartesian product of sets
solvelib::conditionalSortPossible sortings of a list depending on parameters
solvelib::getElementGet one element of a set
solvelib::isEmptyPredicate expressing the emptyness of a set
solvelib::isFiniteTest whether a set is finite
solvelib::preImagePreimage of a set under a mapping
solvelib::splitVectorSetFactor a set of vectors into a cartesian product
solvelib::UnionUnion of a system of sets
solvelib::VectorImageSetDomain of set of vectors that are images of sets under mappings
Differential Algebraic Equations
daetools::findDecoupledBlocksSearch for decoupled blocks in systems of equations
daetools::incidenceMatrixFind incidence matrix of system of equations
daetools::isLowIndexDAECheck if differential index of system equations is lower than 2
daetools::massMatrixFormExtract mass matrix and right side of semilinear system of differential algebraic equations
daetools::reduceDAEIndexConvert system of first-order differential algebraic equations to equivalent system of differential index 1
daetools::reduceDAEToODEConvert system of first-order quasilinear differential algebraic equations to equivalent system of differential index 0
daetools::reduceDifferentialOrderReduce systems of higher-order differential equations to systems of first-order differential equations
daetools::reduceRedundanciesSimplify system of first-order differential algebraic equations by eliminating redundant equations and variables

Formula Manipulation and Simplification

Simplification
factoroutFactor out a given expression
normalNormalize an expression
radsimpSimplify radicals in arithmetical expressions
RuleDefining equivalence rules for mathematical expressions
simplifySimplify an expression
SimplifySimplify an expression
simplifyFractionNormalize an expression
simplifyRadicalSimplify radicals in arithmetical expressions
Formula Rearrangement and Rewriting
collectCollect terms with the same powers
combineCombine terms of same algebraic structure
denomDenominator of a rational expression
expandExpand an expression
factorFactor a polynomial into irreducible polynomials
factoroutFactor out a given expression
isolateIsolate variable or expression from equation
lhsLeft side of equations, inequalities, relations, intervals, ranges and tables
rhsRight side of equations, inequalities, relations, intervals, ranges and tables
normalNormalize an expression
simplifyFractionNormalize an expression
numerNumerator of a rational expression
partfracPartial fraction decomposition
radsimpSimplify radicals in arithmetical expressions
simplifyRadicalSimplify radicals in arithmetical expressions
rationalizeTransform an expression into a rational expression
rectformRectangular form of a complex expression
rewriteRewrite an expression
Substitution
subsSubstitute into an object
subsetRelation “is a subset of”
subsexExtended substitution
subsopReplace operands
Evaluation
blockCreate an object protected against evaluation
blockIdentsCreate a block with some identifiers protected against evaluation
blockTransparentCreate a transparent block protected against evaluation
unblockReplace blocks by their contents
contextEvaluate an object in the enclosing context
evalEvaluate an object
evalassignAssignment with evaluation of the left hand side
evalAtInsert a value (evaluate at a point)
evalpEvaluate a polynomial at a point
freezeCreate an inactive copy of a function
unfreezeCreate an active copy of a frozen function
holdDelay evaluation
LEVELSubstitution depth of identifiers
levelEvaluate an object with a specified substitution depth
MAXDEPTHPrevent infinite recursion during procedure calls
MAXEFFORTMaximum amount of work to spend on the computation
MAXLEVELPrevent infinite recursion during evaluation
Properties and Assumptions
assumeSet permanent assumption
assumeAlsoAdd permanent assumption
assumingSet temporary assumption
assumingAlsoAdd temporary assumption
getpropQuery properties of expressions
isCheck a mathematical property of an expression
iszeroGeneric zero test
property::dependsDependence table with all properties of an expression
property::haspropDoes an object have properties?
property::showpropsWhat assumptions are made?
unassumeDelete the properties of an identifier

Calculus

Differentiation
DDifferential operator for functions
diffDifferentiate an expression or a polynomial
Integration
intDefinite and indefinite integrals
int::addpatternAdd patterns for integration
intlib::bypartsIntegration by parts
intlib::changevarChange of variable
intlib::intOverSetIntegration over a set
intlib::printWarningsEnable or disable warnings
numeric::gldataWeights and abscissae of Gauss-Legendre quadrature
numeric::gtdataWeights and abscissae of Gauss-Tschebyscheff quadrature
numeric::intNumerical integration (the Float attribute of Int )
numeric::ncdataWeights and abscissae of Newton-Cotes quadrature
numeric::quadratureNumerical integration ( Quadrature )
Vector Analysis
curlCurl of a vector field
divergenceDivergence of a vector field
gradientVector gradient
hessianHessian matrix of a scalar function
jacobianJacobian matrix of a vector function
laplacianThe Laplacian
potentialThe (scalar) potential of a gradient field
vectorPotentialVector potential of a three-dimensional vector field
Series
Expansion
asymptCompute an asymptotic series expansion
mtaylorCompute a multivariate Taylor series expansion
ODomain of order terms (Landau symbols)
ORDERDefault number of terms in series expansions
padePade approximation
seriesCompute a generalized series expansion
taylorCompute a Taylor series expansion
Summation
sumDefinite and indefinite summation
sum::addpatternAdd patterns for definite and indefinite summation
numeric::sumNumerical approximation of sums (the Float attribute of Sum )
Products
productDefinite and indefinite products
numeric::productNumerical approximation of products
Limits
limitCompute a limit
Transforms
Fourier and Laplace Transforms
fourierFourier transform
ifourierInverse Fourier transform
ilaplaceInverse Laplace transform
laplaceLaplace transform
Pref::fourierParametersSpecify parameters for Fourier and inverse Fourier transforms
Z-Transform
iztransInverse Z transform
ztransZ transform
Fast Fourier Transform
numeric::fftFast Fourier Transform
numeric::invfftInverse Fast Fourier Transform
New Patterns for Transforms
fourier::addpatternAdd patterns for the Fourier transform
ifourier::addpatternAdd patterns for the inverse Fourier transform
ilaplace::addpatternAdd patterns for the inverse Laplace transform
iztrans::addpatternAdd patterns for the inverse Z transform
laplace::addpatternAdd patterns for the Laplace transform
ztrans::addpatternAdd patterns for the Z transform
Properties and Assumptions
assumeSet permanent assumption
assumeAlsoAdd permanent assumption
assumingSet temporary assumption
assumingAlsoAdd temporary assumption
getpropQuery properties of expressions
isCheck a mathematical property of an expression
iszeroGeneric zero test
property::dependsDependence table with all properties of an expression
property::haspropDoes an object have properties?
property::showpropsWhat assumptions are made?
unassumeDelete the properties of an identifier

Linear Algebra

Matrix and Vector Construction
arrayCreate an array
bernsteinBernstein polynomials
bernsteinMatrixBernstein matrix
densematrixCreate a matrix or a vector
doprintPrint large matrices
hfarrayCreate an array of hardware floating-point values
matrixCreate a matrix or a vector
hessianHessian matrix of a scalar function
jacobianJacobian matrix of a vector function
linalg::hessenbergHessenberg matrix
linalg::hilbertHilbert matrix
linalg::invhilbertInverse of a Hilbert matrix
linalg::invpascalInverse of a Pascal matrix
linalg::pascalPascal matrix
linalg::randomMatrixGenerate a random matrix
linalg::toeplitzToeplitz matrix
linalg::vandermondeVandermonde matrix
linalg::invvandermondeVandermonde matrices and their inverses
linalg::wiedemannSolving linear systems by Wiedemann's algorithm
Matrix Operations and Transformations
linalg::addColLinear combination of matrix columns
linalg::addRowLinear combination of matrix rows
linalg::colExtract columns of a matrix
linalg::delColDelete matrix columns
linalg::delRowDelete matrix rows
linalg::multColMultiply columns with a scalar
linalg::multRowMultiply rows with a scalar
linalg::rowExtract rows of a matrix
linalg::setColChange a column of a matrix
linalg::setRowChange a row of a matrix
linalg::swapColSwap two columns in a matrix
linalg::swapRowSwap two rows in a matrix
inverseInverse of a matrix
transposeTranspose of a matrix
htransposeHermitian transpose of a matrix
linalg::pseudoInverseMoore-Penrose inverse of a matrix
numeric::inverseInverse of a matrix
lllintCompute an LLL-reduced basis of a lattice
normCompute the norm of a matrix, a vector, or a polynomial
linalg::concatMatrixJoin matrices horizontally
linalg::crossProductCross product of three-dimensional vectors
linalg::kroneckerProductKronecker product of matrices
linalg::normalizeNormalize a vector
linalg::ogCoordTabTable of orthogonal coordinate transformations
linalg::scalarProductScalar product of vectors
linalg::stackMatrixJoin matrices vertically
linalg::submatrixExtract a submatrix or a subvector from a matrix or a vector, respectively
linalg::substituteReplace a part of a matrix by another matrix
linalg::sylvesterSylvester matrix of two polynomials
numeric::rotationMatrixOrthogonal matrix of the rotation about an axis
Linear Equations
detDeterminant of a matrix
normCompute the norm of a matrix, a vector, or a polynomial
linalg::condCondition number of a matrix
linalg::matlinsolveSolving systems of linear equations
linalg::matlinsolveLUSolving the linear system given by an LU decomposition
linalg::rankRank of a matrix
linalg::toeplitzSolveSolve a linear Toeplitz system
linalg::vandermondeSolveSolve a linear Vandermonde system
numeric::detDeterminant of a matrix
numeric::inverseInverse of a matrix
numeric::rankNumerical estimate of the rank of a matrix
Matrix Decomposition
linalg::factorCholeskyThe Cholesky decomposition of a matrix
linalg::factorLULU-decomposition of a matrix
linalg::factorQRQR-decomposition of a matrix
linalg::frobeniusFormFrobenius form of a matrix
linalg::hermiteFormHermite normal form of a matrix
linalg::inverseLUComputing the inverse of a matrix using LU-decomposition
linalg::jordanFormJordan normal form of a matrix
linalg::smithFormSmith normal form of a matrix
numeric::factorCholeskyCholesky factorization of a matrix
numeric::factorLULU factorization of a matrix
numeric::factorQRQR factorization of a matrix
numeric::singularvaluesNumerical singular values of a matrix
numeric::singularvectorsNumerical singular value decomposition of a matrix
numeric::svdNumerical singular value decomposition of a matrix
Eigenvalues and Eigenvectors
linalg::eigenvaluesEigenvalues of a matrix
linalg::eigenvectorsEigenvectors of a matrix
numeric::eigenvaluesNumerical eigenvalues of a matrix
numeric::eigenvectorsNumerical eigenvalues and eigenvectors of a matrix
linalg::jordanFormJordan normal form of a matrix
numeric::spectralRadiusSpectral radius of a matrix
Vector Spaces and Subspaces
linalg::basisBasis for a vector space
linalg::gaussElimGaussian elimination
linalg::gaussJordanGauss-Jordan elimination
linalg::intBasisBasis for the intersection of vector spaces
linalg::matdimDimension of a matrix
linalg::nrowsNumber of rows of a matrix
linalg::nullspaceBasis for the null space of a matrix
linalg::orthogOrthogonalization of vectors
linalg::rankRank of a matrix
linalg::sumBasisBasis for the sum of vector spaces
linalg::vecdimNumber of components of a vector
numeric::rankNumerical estimate of the rank of a matrix
Matrix Analysis
curlCurl of a vector field
detDeterminant of a matrix
divergenceDivergence of a vector field
gradientVector gradient
hessianHessian matrix of a scalar function
jacobianJacobian matrix of a vector function
laplacianThe Laplacian
normCompute the norm of a matrix, a vector, or a polynomial
potentialThe (scalar) potential of a gradient field
vectorPotentialVector potential of a three-dimensional vector field
numeric::detDeterminant of a matrix
linalg::adjointAdjoint of a matrix
linalg::angleAngle between two vectors
linalg::charmatCharacteristic matrix
linalg::condCondition number of a matrix
linalg::isHermitianChecks whether a matrix is Hermitian
linalg::isPosDefTest a matrix for positive definiteness
linalg::isUnitaryTest whether a matrix is unitary
linalg::ncolsNumber of columns of a matrix
linalg::nonZerosNumber of non-zero elements of a matrix
linalg::nrowsNumber of rows of a matrix
linalg::permanentPermanent of a matrix
linalg::trTrace of a matrix
linalg::vectorOfType specifier for vectors
Matrix Functions
funmGeneral matrix function
linalg::sqrtMatrixSquare root of a matrix
numeric::expMatrixExponential of a matrix
numeric::fMatrixFunctional calculus for numerical square matrices
Properties and Assumptions
assumeSet permanent assumption
assumeAlsoAdd permanent assumption
assumingSet temporary assumption
assumingAlsoAdd temporary assumption
getpropQuery properties of expressions
isCheck a mathematical property of an expression
iszeroGeneric zero test
property::dependsDependence table with all properties of an expression
property::haspropDoes an object have properties?
property::showpropsWhat assumptions are made?
unassumeDelete the properties of an identifier

Polynomial Algebra

Polynomial Creation
genpolyCreate a polynomial using b-adic expansion
laguerreLLaguerre polynomials and L function
orthpoly::chebyshev1The Chebyshev polynomials of the first kind
orthpoly::chebyshev2The Chebyshev polynomials of the second kind
orthpoly::curtzThe Curtz polynomials
orthpoly::gegenbauerThe Gegenbauer (ultraspherical) polynomials
orthpoly::hermiteThe Hermite polynomials
orthpoly::jacobiThe Jacobi polynomials
orthpoly::laguerreThe (generalized) Laguerre polynomials
orthpoly::legendreThe Legendre polynomials
polyCreate a polynomial
polylib::cyclotomicCyclotomic polynomials
polylib::elemSymElementary symmetric polynomials
polylib::PolyDomain of polynomials
polylib::randpolyCreate a random polynomial
Polynomial Manipulation
divideDivide polynomials
interpolatePolynomial interpolation
irreducibleTest irreducibility of a polynomial
pdividePseudo-division of polynomials
linalg::charpolyCharacteristic polynomial of a matrix
linalg::companionCompanion matrix of a univariate polynomial
linalg::minpolyMinimal polynomial of a matrix
polylib::decomposeFunctional decomposition of a polynomial
polylib::discrimDiscriminant of a polynomial
polylib::divisorsDivisors of a polynomial, polynomial expression, or Factored element
polylib::DpolyDifferential operator for polynomials
polylib::makeratConvert expression into rational function over a suitable field
polylib::minpolyApproximate minimal polynomial
polylib::primitiveElementPrimitive element for tower of field extensions
polylib::primpartPrimitive part of a polynomial
polylib::representByElemSymRepresent symmetric by elementary symmetric polynomials
polylib::resultantResultant of two polynomials
polylib::splitfieldSplitting field of a polynomial
polylib::sqrfreeSquare-free factorization of polynomials
polylib::subresultantSubresultants of two polynomials
polylib::supportSupport of a polynomial
Elements of Polynomials
coeffCoefficients of a polynomial
contentContent of a polynomial
degreeDegree of a polynomial
degreevecExponents of the leading term of a polynomial
icontentContent of a polynomial with rational coefficients
lcoeffLeading coefficient of a polynomial
ldegreeLowest degree of the terms in a polynomial
lmonomialLeading monomial of a polynomial
ltermLeading term of a polynomial
mapcoeffsApply a function to the coefficients of a polynomial
monomialsSorted list of monomials of a polynomial
multcoeffsMultiply the coefficients of a polynomial with a factor
ntermsNumber of terms of a polynomial
nthcoeffN-th non-zero coefficient of a polynomial
nthmonomialN-th monomial of a polynomial
nthtermN-th term of a polynomial
poly2listConvert a polynomial to a list of terms
polylib::coeffRingCoefficient ring of a polynomial
polylib::sortMonomialsSorting monomials with respect to a term ordering
tcoeffTrailing coefficient of a polynomial
Groebner Algebra
groebner::dimensionDimension of the affine variety generated by polynomials
groebner::eliminateEliminate variables
groebner::gbasisComputation of a reduced Gröbner basis
groebner::normalfComplete reduction modulo a polynomial ideal
groebner::spolyThe S-polynomial of two polynomials
groebner::stronglyIndependentSetsStrongly independent set of variables
Polynomial Roots
numeric::polyrootboundBound for the roots of a univariate polynomial
numeric::polyrootsNumerical roots of a univariate polynomial
numeric::polysysrootsNumerical roots of a system of polynomial equations
numeric::realrootNumerical search for a real root of a real univariate function
numeric::realrootsIsolate intervals containing real roots of a univariate function
polylib::realrootsIsolate all real roots of a real univariate polynomial
Properties and Assumptions
assumeSet permanent assumption
assumeAlsoAdd permanent assumption
assumingSet temporary assumption
assumingAlsoAdd temporary assumption
getpropQuery properties of expressions
isCheck a mathematical property of an expression
iszeroGeneric zero test
property::dependsDependence table with all properties of an expression
property::haspropDoes an object have properties?
property::showpropsWhat assumptions are made?
unassumeDelete the properties of an identifier

Mathematical Constants and Functions

Constants
complexInfinityComplex infinity
infinityReal positive infinity
FAILIndicate a failed computation
NILSingleton element of the domain DOM_NIL
nullGenerate the void object of type DOM_NULL
TRUEBoolean constant TRUE
FALSEBoolean constant FALSE
UNKNOWNBoolean constant UNKNOWN
undefinedUndefined value
C_Complex numbers
R_Real numbers
Q_Rational numbers
Z_Integers
N_Positive integers
Complex Numbers
absAbsolute value of a real or complex number
argArgument (polar angle) of a complex number
ReReal part of an arithmetical expression
ImImaginary part of an arithmetical expression
signSign of a real or complex number
signImSign of the imaginary part of a complex number
Exponents and Logarithms
expExponential function
lnNatural logarithm
logLogarithm to arbitrary base
log10Logarithm to base 10
log2Logarithm to base 2
^Raise an expression to a power
sqrtSquare root function
surdN -th root
Trigonometric Functions
sinSine function
cosCosine function
tanTangent function
cotCotangent function
secSecant function
cscCosecant function
arcsinInverse sine function
arccosInverse cosine function
arctanInverse tangent function
arccotInverse cotangent function
arcsecInverse secant function
arccscInverse cosecant function
Hyperbolic Functions
sinhHyperbolic sine function
coshHyperbolic cosine function
tanhHyperbolic tangent function
cothHyperbolic cotangent function
sechHyperbolic secant function
cschHyperbolic cosecant function
arcsinhInverse of the hyperbolic sine function
arccoshInverse of the hyperbolic cosine function
arctanhInverse of the hyperbolic tangent function
arccothInverse of the hyperbolic cotangent function
arcsechInverse of the hyperbolic secant function
arccschInverse of the hyperbolic cosecant function
Special Functions
Dirac and Heaviside Functions
diracThe Dirac delta distribution
heavisideThe Heaviside step function
kroneckerDeltaKronecker's delta symbol
rectangularPulseRectangular pulse function
rectpulseRectangular pulse function
triangularPulseTriangular pulse function
tripulseTriangular pulse function
Pref::heavisideAtOriginSet value of Heaviside function at origin
Gamma Functions
betaBeta function
binomialBinomial coefficients
gammaGamma function
lngammaLogarithmic gamma function
igammaIncomplete gamma function
pochhammerThe Pochhammer symbol
psiDigamma/polygamma function
Zeta Function and Polylogarithms
dilogDilogarithm function
polylogPolylogarithm function
zetaThe Riemann zeta function
Airy and Bessel Functions
airyAiAiry function of the first kind
airyBiAiry function of the second kind
besselIModified Bessel functions of the first kind
besselJBessel functions of the first kind
besselKModified Bessel functions of the second kind
besselYBessel functions of the second kind
Error and Exponential Integral Functions
erfError function
erfcComplementary error function
erfiImaginary error function
inverfInverse of the error function
inverfcInverse of the complementary error function
CiCosine integral function
ChiHyperbolic cosine integral function
SiSine integral function
SsiShifted sine integral function
ShiHyperbolic sine integral function
EiExponential integral function
LiIntegral logarithm
fresnelCThe Fresnel cosine integral function
fresnelSThe Fresnel sine integral function
dawsonDawson's integral
Hypergeometric and Whittaker Functions
hypergeomHypergeometric functions
kummerUConfluent hypergeometric KummerU function
meijerGThe Meijer G function
whittakerMThe Whittaker M function
whittakerWThe Whittaker W function
Elliptic Integrals
ellipticKComplete elliptic integral of the first kind
ellipticCKComplementary complete elliptic integral of the first kind
ellipticFIncomplete elliptic integral of the first kind
ellipticEComplete and incomplete elliptic integrals of the second kind
ellipticCEComplementary complete elliptic integral of the second kind
ellipticPiComplete and incomplete elliptic integrals of the third kind
ellipticCPiComplementary complete elliptic integral of the third kind
ellipticNomeElliptic nome
jacobiAMJacobi amplitude function am
jacobiSNJacobi elliptic function sn
jacobiCNJacobi elliptic function cn
jacobiDNJacobi elliptic function dn
jacobiCDJacobi elliptic function cd
jacobiSDJacobi elliptic function sd
jacobiNDJacobi elliptic function nd
jacobiDCJacobi elliptic function dc
jacobiNCJacobi elliptic function nc
jacobiSCJacobi elliptic function sc
jacobiNSJacobi elliptic function ns
jacobiDSJacobi elliptic function ds
jacobiCSJacobi elliptic function cs
jacobiZetaJacobi Zeta function
Lambert W and Wright Functions
lambertWThe Lambert function
wrightOmegaThe Wright ω function

Numbers and Precision

Precision Control
floatConvert to a floating-point number
Pref::floatFormatRepresentation of floating-point numbers
Pref::outputDigitsSet the number of digits in floating-point outputs
Pref::trailingZeroesTrailing zeroes when printing floating-point numbers
Operations on Numbers
ceilRound up to the next integer
floorRound down to the next integer
conjugateComplex conjugation
fracFractional part of a number
groundGround term (constant coefficient) of a polynomial
ImImaginary part of an arithmetical expression
maxMaximum of numbers
minMinimum of numbers
misc::pslqHeuristic detection of relations between real numbers
numeric::complexRoundRound a complex number towards the real or imaginary axis
numeric::rationalizeApproximate a floating-point number by a rational number
ReReal part of an arithmetical expression
roundRounding to the nearest integer
truncRounding towards zero

Statistics

Supported Distributions
Cumulative Distribution Functions
stats::betaCDFCumulative distribution function of the beta distribution
stats::binomialCDFThe (discrete) cumulative distribution function of the binomial distribution
stats::cauchyCDFCumulative distribution function of the Cauchy distribution
stats::chisquareCDFCumulative distribution function of the chi-square distribution
stats::empiricalCDFEmpirical (discrete) cumulative distribution function of a finite data sample
stats::erlangCDFCumulative distribution function of the Erlang distribution
stats::exponentialCDFCumulative distribution function of the exponential distribution
stats::fCDFCumulative distribution function of Fisher's f-distribution (fratio distribution)
stats::finiteCDFCumulative distribution function of a finite sample space
stats::gammaCDFCumulative distribution function of the gamma distribution
stats::geometricCDFThe (discrete) cumulative distribution function of the geometric distribution
stats::hypergeometricCDFThe (discrete) cumulative probability function of the hypergeometric distribution
stats::logisticCDFCumulative distribution function of the logistic distribution
stats::lognormalCDFCumulative distribution function of the log-normal distribution
stats::normalCDFCumulative distribution function of the normal distribution
stats::poissonCDFThe (discrete) cumulative distribution function of the Poisson distribution
stats::tCDFCumulative distribution function of Student's t-distribution
stats::uniformCDFCumulative distribution function of the uniform distribution
stats::weibullCDFCumulative distribution function of the Weibull distribution
Probability Density Functions
stats::betaPDFProbability density function of the beta distribution
stats::cauchyPDFProbability density function of the Cauchy distribution
stats::chisquarePDFProbability density function of the chi-square distribution
stats::erlangPDFProbability density function of the Erlang distribution
stats::exponentialPDFProbability density function of the exponential distribution
stats::fPDFProbability density function of Fisher's f-distribution (fratio distribution)
stats::gammaPDFProbability density function of the gamma distribution
stats::logisticPDFProbability density function of the logistic distribution
stats::lognormalPDFProbability density function of the log-normal distribution
stats::normalPDFProbability density function of the normal distribution
stats::tPDFProbability density function of Student's t-distribution
stats::uniformPDFProbability density function of the uniform distribution
stats::weibullPDFProbability density function of the Weibull distribution
Probability Functions
stats::binomialPFProbability function of the binomial distribution
stats::empiricalPFProbability function of a finite data sample
stats::finitePFProbability function of a finite sample space
stats::geometricPFProbability function of the geometric distribution
stats::hypergeometricPFProbability function of the hypergeometric distribution
stats::poissonPFProbability function of the Poisson distribution
Quantile Functions
stats::betaQuantileQuantile function of the beta distribution
stats::binomialQuantileQuantile function of the binomial distribution
stats::cauchyQuantileQuantile function of the Cauchy distribution
stats::chisquareQuantileQuantile function of the chi-square distribution
stats::empiricalQuantileQuantile function of the empirical distribution
stats::erlangQuantileQuantile function of the Erlang distribution
stats::exponentialQuantileQuantile function of the exponential distribution
stats::fQuantileQuantile function of Fisher's f-distribution (fratio distribution)
stats::finiteQuantileQuantile function of a finite sample space
stats::gammaQuantileQuantile function of the gamma distribution
stats::geometricQuantileQuantile function of the geometric distribution
stats::hypergeometricQuantileQuantile function of the hypergeometric distribution
stats::logisticQuantileQuantile function of the logistic distribution
stats::lognormalQuantileQuantile function of the log-normal distribution
stats::normalQuantileQuantile function of the normal distribution
stats::poissonQuantileQuantile function of the Poisson distribution
stats::tQuantileQuantile function of Student's t-distribution
stats::uniformQuantileQuantile function of the uniform distribution
stats::weibullQuantileQuantile function of the Weibull distribution
Random Number Generators
frandomGenerate random floating-point numbers
randomGenerate random integer numbers
stats::betaRandomGenerate a random number generator for beta deviates
stats::binomialRandomGenerate a random number generator for binomial deviates
stats::cauchyRandomGenerate a random number generator for Cauchy deviates
stats::chisquareRandomGenerate a random number generator for chi-square deviates
stats::empiricalRandomGenerate a random generator for uniformly distributed elements of a data sample
stats::erlangRandomGenerate a random number generator for Erlang deviates
stats::exponentialRandomGenerate a random number generator for exponential deviates
stats::fRandomGenerate a random number generator for Fisher's f-deviates (fratio deviates)
stats::finiteRandomGenerate a random generator for elements of a finite sample space
stats::gammaRandomGenerate a random number generator for gamma deviates
stats::geometricRandomGenerate a random number generator for geometric deviates
stats::hypergeometricRandomGenerate a random number generator for hypergeometric deviates
stats::logisticRandomGenerate a random number generator for logistic deviates
stats::lognormalRandomGenerate a random number generator for log-normal deviates
stats::normalRandomGenerate a random number generator for normal deviates
stats::poissonRandomGenerate a random number generator for Poisson deviates
stats::tRandomGenerate a random number generator for Student deviates (t-deviates)
stats::uniformRandomGenerate a random number generator for uniformly continous deviates
stats::weibullRandomGenerate a random number generator for Weibull deviates
Data Import
import::csvRead CSV data from an ASCII file
import::readbitmapRead bitmap data
import::readdataRead data from an ASCII file
import::readlispParse Lisp-formatted string
stats::sampleDomain of statistical samples
Operations on Data Samples
stats::calcApply functions to a sample
stats::colSelect and rearrange columns of a sample
stats::concatColConcatenate samples column-wise
stats::concatRowConcatenate samples row-wise
stats::rowSelect and re-arrange rows of a sample
stats::sampleDomain of statistical samples
stats::sample2listConvert a sample to a list of lists
stats::selectRowSelect rows of a sample
stats::sortSampleSort the rows of a sample
stats::tabulateStatistics of duplicate rows in a sample
stats::unzipColExtract columns from a list of lists
stats::zipColConvert a sequence of columns to a list of lists
Descriptive Statistics
numeric::gaussAGMGauss' arithmetic geometric mean
stats::correlationCorrelation between data samples
stats::correlationMatrixCompute the correlation matrix associated with a covariance matrix
stats::covarianceCovariance of data samples
stats::cutoffDiscard outliers
stats::winsorizeClamp (winsorize) extremal values
stats::frequencyTally numerical data into classes and count frequencies
stats::geometricMeanGeometric mean of a data sample
stats::harmonicMeanHarmonic mean of a data sample
stats::kurtosisKurtosis (excess) of a data sample
stats::meanArithmetic mean of a data sample
stats::meandevMean deviation of a data sample
stats::medianMedian value of a data sample
stats::modalModal (most frequent) value(s) in a data sample
stats::momentThe K-th moment of a data sample
stats::obliquityObliquity (skewness) of a data sample
stats::quadraticMeanQuadratic mean of a data sample
stats::stdevStandard deviation of a data sample
stats::varianceVariance of a data sample
Regression Analysis
stats::hodrickPrescottFilterThe Hodrick-Prescott filter
stats::linRegLinear regression (least squares fit)
stats::regRegression (general linear and nonlinear least squares fit)
Hypothesis Testing
stats::csGOFTClassical chi-square goodness-of-fit test
stats::equiprobableCellsDivide the real line into equiprobable intervals
stats::ksGOFTThe Kolmogorov-Smirnov goodness-of-fit test
stats::swGOFTThe Shapiro-Wilk goodness-of-fit test for normality
stats::tTestT-test for a mean

Discrete Mathematics

Number Theory
Divisors
gcdGreatest common divisor of polynomials
gcdexExtended Euclidean algorithm for polynomials
igcdGreatest common divisor of integers and complex numbers with integer real and imaginary parts
igcdexExtended Euclidean algorithm for two integers
numlib::igcdmultExtended Euclidean algorithm for integers
ilcmLeast common multiple of integers
lcmLeast common multiple of polynomials
numlib::divisorsDivisors of an integer
numlib::numdivisorsNumber of divisors of an integer
numlib::OmegaNumber of prime divisors (with multiplicity)
numlib::sumdivisorsSum of divisors of an integer
Primes
isprimePrimality test
ithprimeI-th prime number
nextprimeNext prime number
prevprimeNext smaller prime
numlib::checkPrimalityCertificateTest the primality certificate
numlib::OmegaNumber of prime divisors (with multiplicity)
numlib::piNumber of primes up to a given bound
numlib::proveprimePrimality proving using elliptic curves
numlib::primedivisorsPrime factors of an integer
Factorizations
factFactorial function
fact2Double factorial function
ifactorFactor an integer into primes
isqrtInteger square root
numlib::ispowerTest for perfect powers
numlib::issqrTest for perfect squares
numlib::factorGaussIntFactorization of Gaussian integers
numlib::numprimedivisorsNumber of prime factors of an integer
numlib::primedivisorsPrime factors of an integer
Modular Arithmetic
divInteger part of a quotient
modModulo operator
modpPositive modulo function
modsSymmetric modulo function
numlib::isquadresTest for quadratic residues
numlib::orderOrder of a residue class
numlib::primrootPrimitive roots
numlib::reconstructRationalRational number reconstruction
numlib::sqrtmodpSquare root of a quadratic residue modulo a prime
powermodCompute a modular power of a number or a polynomial
remRemainder after division
Congruences
divInteger part of a quotient
modModulo operator
numlib::cornacchiaCornachia's algorithm
numlib::ichremChinese remainder theorem for integers
numlib::jacobiJacobi symbol
numlib::legendreLegendre symbol
numlib::lincongruenceLinear congruence
numlib::mrootsModular roots of polynomials
numlib::msqrtsModular square roots
Sequences of Numbers
bernoulliBernoulli numbers and polynomials
contfracDomain of continued fractions
eulerEuler numbers and polynomials
numlib::contfracDomain of continued fractions
numlib::contfracPeriodicPeriodic continued fraction expansions
numlib::decimalInfinite representation of rational numbers
numlib::fibonacciFibonacci numbers
numlib::mersenneMersenne primes
numlib::sumOfDigitsSum of digits of an integer
randomGenerate random integer numbers
Number Theoretic Functions
dedekindEtaThe Dedekind eta function
thetaTheta series
numlib::g_adicG-adic representation of a nonnegative integer
harmonicHarmonic function
numlib::invphiInverse of the Euler phi function
numlib::LambdaVon Mangoldt's function
numlib::lambdaCarmichael function
numlib::moebiusMöbius function
numlib::phiEuler phi function
Conversions
numlib::fromAsciiDecoding of ASCII codes
numlib::sqrt2cfracContinued fraction expansion of square roots
numlib::toAsciiASCII encoding of a string
Linear Optimization
linopt::cornersReturn the feasible corners of a linear program
linopt::maximizeMaximize a linear or mixed-integer program
linopt::minimizeMinimize a linear or mixed-integer program
linopt::plot_dataPlot the feasible region of a linear program
linopt::TransparentReturn the ordinary simplex tableau of a linear program
linopt::Transparent::autostepPerform the next simplex step
linopt::Transparent::clean_basisDelete all slack variables of the first phase from the basis
linopt::Transparent::convertTransform the given tableau into a structure printable on screen
linopt::Transparent::dual_pricesGet the dual solution belonging to the given tableau
linopt::Transparent::phaseI_tableauStart an ordinary phase one of a 2-phase simplex algorithm
linopt::Transparent::phaseII_tableauStart phase two of a 2-phase simplex algorithm
linopt::Transparent::resultGet the basic feasible solution belonging to the given simplex tableau
linopt::Transparent::simplexFinish the current phase of the 2-phase simplex algorithm
linopt::Transparent::suggestSuggest the next step in the simplex algorithm
linopt::Transparent::userstepPerform a user defined simplex step
Boolean Algebra
boolBoolean evaluation
_lazy_and“short circuit and” of Boolean expressions
_lazy_or“short circuit or” of Boolean expressions
Graph Theory
Creation
GraphCreates new graph
Graph::createCircleGraphGenerates a circle Graph
Graph::createCompleteGraphGenerates a complete graph
Graph::createGraphFromMatrixTransfers a squared matrix into a directed graph
Graph::createRandomEdgeWeightsSets random weights to edges
Graph::createRandomEdgeCostsSets random costs to edges
Graph::createRandomGraphGenerates a random graph.
Graph::createRandomVertexWeightsSets random weights to vertices
Graph::plotBipartiteGraphPlots a Graph in a bipartite layout
Graph::plotCircleGraphPlots a Graph in a circle layout
Graph::plotGridGraphPlots a Graph in a grid layout
Modification
Graph::addEdgesAdds one or several edges to a graph
Graph::addVerticesAdds one or several vertices to a graph
Graph::contractContracts vertices
Graph::convertSSQConverts a Graph into a single source single sink Graph
Graph::printEdgeCostInformationPrints the edge costs of a graph
Graph::printEdgeDescInformationPrints the edge descriptions of a graph
Graph::printEdgeInformationPrints the edges of a graph
Graph::printEdgeWeightInformationPrints the edge weights of a graph
Graph::printGraphInformationPrints the edges of a graph
Graph::printVertexInformationPrints vertex information of a graph
Graph::removeEdgeRemoves one or several edges from a graph
Graph::removeVertexRemoves one or several vertices from a graph
Graph::revertReverts the edges of a graph.
Graph::setEdgeCostsAssigns edge costs to edges.
Graph::setEdgeDescriptionsAssigns edge Descriptions to edges.
Graph::setEdgeWeightsAssigns edge weights to edges.
Graph::setVertexWeightsAssigns vertex weights to vertices.
Analysis
Graph::getAdjacentEdgesEnteringReturns the incident edges.
Graph::getAdjacentEdgesLeavingReturns the adjacent edges.
Graph::getBestAdjacentEdgeReturns the "best" incident edges.
Graph::getEdgeCostsReturns a table with the edge costs.
Graph::getEdgeDescriptionsReturns a table with the edge descriptions.
Graph::getEdgesReturns a list with all edges
Graph::getEdgesEnteringReturns the incoming edges
Graph::getEdgesLeavingReturns the outgoing edges
Graph::getEdgeNumberReturns the number of edges.
Graph::getEdgeWeightsReturns a table with the edge weights.
Graph::getSubGraphReturns a subgraph.
Graph::getVertexNumberReturns the number of vertices.
Graph::getVertexWeightsReturns a table with the vertex weights.
Graph::getVerticesReturns a list with all vertices
Graph::admissibleFlowChecks a flow for admissibility in a Graph
Graph::bipartiteFinds out if a graph is bipartite.
Graph::breadthFirstSearchMakes a breadth first Search in a graph.
Graph::checkForVerticesChecks if all vertices in edges really exist.
Graph::chromaticNumberChromatic number of a graph
Graph::chromaticPolynomialCalculates a chromatic polynomial
Graph::depthFirstSearchMakes a depth first Search in a graph.
Graph::residualGraphComputes the residual graph
Graph::shortestPathAllPairsShortest paths from and to all vertices
Graph::shortestPathSingleSourceShortest paths from one single vertex
Graph::stronglyConnectedComponentsFinds the strongly connected components
Graph::topSortTopological sorting of the vertices
Graph::inDegreeReturns the indegree of one or more vertices.
Graph::isConnectedFinds out if the graph is connected
Graph::isDirectedFinds out if the graph is directed
Graph::isEdgeFinds out if the edges exists
Graph::isVertexFinds out if special vertices exist in the Graph
Graph::longestPathLongest paths from one single node
Graph::maxFlowComputes a maximal flow through a graph
Graph::minCostComputes a minimal cost flow
Graph::minCutComputes a minimal cut
Graph::minimumSpanningTreeCreates a MST
Graph::outDegreeReturns the outdegree of one or more vertices.
Combinatorics
combinat::bellBell numbers
combinat::cartesianProductCartesian product
combinat::catalanCatalan numbers
combinat::chooseSubsets of a given size
combinat::compositionsCompositions of an integer
combinat::modStirlingModified Stirling numbers
combinat::partitionsPartitions of an integer
combinat::permutePermutations of a list
combinat::powersetSubsets of a set
combinat::stirling1Stirling numbers of the first kind
combinat::stirling2Stirling numbers of the second kind
combinat::subwordsSubwords of a word

Graphics

2-D and 3-D Plots

2-D Function Plots
plotDisplay graphical objects on the screen
displayDisplay graphical objects on screen
plotfunc2dFunction plots in 2D
plot::easyEasy plotting
3-D Function Plots
plotfunc3dFunction plots in 3D
Scatter Plots
plot::delaunayCompute the Delaunay triangulation of a set of points
plot::hullCompute the convex hull of a set of points

Annotations and Appearance

Colors
RGB::ColorNamesFind predefined colors by name
RGB::plotColorPaletteDisplay predefined colors
RGB::colorNameFind names of predefined colors
RGB::fromWaveLengthGet the RGB color of monochromatic light
RGB::randomPick a color uniformly at random in RGB color space
RGB::toHSVConvert RGB colors to HSV
RGB::fromHSVConvert HSV colors to RGB
Default Settings
plot::getDefaultGet current default setting of attributes
plot::setDefaultSet default setting of attributes

Export

plot::copyMake a physical copy of a plot object
plot::modifyMake a physical copy of a plot object setting new values of attributes in the same call

Programming Basics

Control Flow

%ifConditional creation of code by the parser
break, _breakTerminate a loop or a Case switch prematurely
case, of, otherwise, end_case, _caseSwitch statement
endClose a block statement
for, from, to, step, end_for, _for_in, downto, _for_downtoFor loop
if, then, elif, else, end_if, _ifIf-statement (conditional branch in a program)
next, _nextSkip a step in a loop
repeat, until, end_repeat, _repeat“repeat” loop
while, end_while, _while“while” loop
returnExit a procedure

Functions and Procedures

exposeDisplay the source code of a procedure or the entries of a domain
procDefine a procedure
saveSave the state of an identifier
prog::waitWait for a while

Interactive Input

inputInteractive input of objects
textinputInteractive input of text
Pref::postInputActions after input
Pref::postOutputActions after output

Data and File Management

Data Import and Export

export::stlExport STL data
import::csvRead CSV data from an ASCII file
import::readbitmapRead bitmap data
import::readdataRead data from an ASCII file
import::readlispParse Lisp-formatted string

File Operations

fcloseClose a file
finputRead objects from file
fnameGet a file's name
fopenOpen file
fprintWrite data to file
freadRead and execute file
ftextinputRead text file
pathnameCreate a platform dependent path name
protocolCreate a protocol of a session
readSearch, read, and execute file
readbytesRead binary data from a file
writebytesWrite binary data to a file
writeWrite values of variables into file
Pref::verboseReadShows reading of files

Advanced Software Development

Functional Programming

@Compose functions
@@Iterate a function
copyClosureCopies the lexical closure of a procedure
discontDiscontinuities of a function
funcenvCreate a function environment
mapApply a function to all operands of an object
mapratApply a function to a rationalized expression
operatorDefine a new operator symbol
fp::applyApply function to arguments
fp::bottomFunction that never returns
fp::curryCurry an n-ary function
fp::expr_unapplyCreate a functional expression from an expression
fp::fixargsCreate function by fixing all but one argument
fp::fixedptReturns fixed point of a function
fp::foldCreate function which iterates over sequences
fp::nestRepeated composition of function
fp::nestvalsRepeated composition returning intermediate values
fp::unapplyCreate a procedure from an expression
misc::breakmapStops the mapping currently done by maprec
misc::maprecMap a function to subexpressions of an expression
Pref::typeCheckType checking of formal parameters
Pref::warnDeadProcEnvWarnings about wrong usage of lexical scope
prog::getnameName of an object
prog::getOptionsGet and verify options within a procedure
prog::isGlobalInformation about reserved identifiers

Debugging

argsAccess procedure parameters
assertAssertions for debugging
debugExecute a procedure in single-step mode
forceGarbageCollectionForce a garbage collection
prog::traceObserve functions
prog::tracedFind traced functions
prog::untraceTerminates observation of functions

Code Performance

rtimeMeasure real time
timeMeasure CPU time
Pref::maxTimeTime limit for computations
prog::ntimeHardware independent time unit
prog::profileDisplay timing data of nested function calls

Memory Usage

bytesMemory used by the current session
forgetClear the remember table of a procedure
historyAccess an entry of the history table
Pref::maxMemSet a memory limit for the session
Pref::reportInformations during evaluation
prog::rememberExtended remember mechanism for procedures

Error Handling

errorRaise a user-specified exception
getlasterrorRetrieve the last error number and text
lasterrorReproduce the last error
traperrorTrap errors
warningPrint a warning message

Testing and Code Verification

testargsDecide whether procedure arguments should be tested
prog::checkChecking objects
prog::initLoading objects
prog::tcovReport on test coverage (passed program lines)
prog::testAutomatic comparing of calculation results
prog::testexitClosing tests
prog::testinitInitialize tests

Custom Functionality Integration

protectProtect an identifier
unprotectRemove protection of identifiers

Object-Oriented Programming

Domains
Domain Operations
extnopsNumber of operands of the internal representation a domain element
extopInternal operands of a domain element
extsubsopSubstitute operands of a domain element
newCreate a domain element
newDomainCreate a new data type (domain)
slotMethod or entry of a domain or a function environment
slotAssignCounterCounts slot assignments

Code Generation

generate::CGenerate C formatted string
generate::fortranGenerate Fortran formatted string
generate::MathMLGenerate MathML from expressions
generate::MATLABGenerate MATLAB formatted string
generate::optimizeGenerate optimized code
generate::SimscapeGenerate Simscape equation
generate::TeXGenerate formatted string from expressions

Notebook Interface

Typeset Math and Other Output Modes

printPrint objects to the screen
output::asciiAbbreviateGenerates a procedure for creating an ASCII formatted output
output::fencePut delimiters around multiline strings
output::mathTextPretty output of text combined with formulas
output::ordinalOrdinal numbers
output::romanRoman numerals
output::subexprAbbreviates a expression
output::tableFormPrinting objects in table form
output::treeDisplay of trees
Pref::abbreviateOutputControls the use of abbreviations in outputs
Pref::outputModify the screen output of objects

Customizations and Preferences

Pref::aliasControls the output of aliased expressions
Pref::autoExpansionLimitSet a limit for automatic expansions
Pref::autoPlotAutomatically plot graphical objects
Pref::callBackInformations during evaluation
Pref::ignoreNoDebugControls debugging of procedures
Pref::keepOrderOrder of terms in sum outputs
Pref::userOptionsAdditional options when starting MuPAD
Pref::heavisideAtOriginSet value of Heaviside function at origin

Version

buildnumberThe Build number of
versionVersion number of the MuPAD library
Pref::kernelVersion number of the presently used kernel

MATLAB and MuPAD Integration

MuPAD to MATLAB Code Conversion

generate::MATLABGenerate MATLAB formatted string
Was this topic helpful?