Documentation

Symbolic Math Toolbox MuPAD Functions

MuPAD

MuPAD Language Fundamentals

Entering Commands

:= Assign variables
; Statement sequences
... Convert to a floating-point interval
_index Indexed access
indexval Indexed access to arrays and tables without evaluation
last Access a previously computed object
reset Re-initialize a session
unit Physical units
help Display a help page
info Prints short information
delete Delete the value of an identifier
freeIndets Free indeterminates of an expression
genident Create an unused identifier
id Identity map
indets Indeterminates of an expression
val Value of an object
alias Defines an abbreviation or a macro
unalias Deletes an alias-definition
anames Identifiers that have values or properties
unuse Undo the use command
use Use library functions by a short name

Operators and Elementary Operations

Arithmetic Operations
_invert Reciprocal of an expression
_subtract Subtract expressions
Set Operations
append Add elements to a list
card Cardinality of a set
contains Test if an entry exists in a container
in Membership
intersect Intersection of sets and/or intervals
minus Difference of sets and/or intervals
union Union of sets and/or intervals
revert Revert polynomials, lists, character strings and tables, invert series expansions
universe Set-theoretical universe
zip Combine lists
Expression Trees and Precedence
misc::genassop Generates an n-ary associative operator from a binary one

Special Values

FAIL Indicate a failed computation
NIL Singleton element of the domain DOM_NIL
null Generate the void object of type DOM_NULL
TRUE Boolean constant TRUE
FALSE Boolean constant FALSE
UNKNOWN Boolean constant UNKNOWN
undefined Undefined value
solvelib::BasicSet Basic 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
assign Perform assignments given as equations
assignElements Assign values to entries of an array, a list, or a table
length The "length" of a object (heuristic complexity)
match Pattern matching
nops Number of operands
op Operands of an object
piecewise Domain of conditionally defined objects
select Select operands
split Split an object
sysorder Compare objects according to the internal order
table Create a table
numeric::indets Search for indeterminates
prog::exprtree Visualize an expression as tree
prog::find Find operands of objects
prog::sort Sort objects by an index function
Operations on Lists
listlib::insert Insert an element into a list
listlib::insertAt Insert an element into a list at a given position
listlib::merge Merging two ordered lists
listlib::removeDuplicates Removes duplicate entries
listlib::removeDupSorted Remove duplicates of any element from ordered lists
listlib::setDifference Remove elements from a list
listlib::singleMerge Merging of two ordered lists without duplicates
listlib::sublist Search sublists
numeric::sort Sort a numerical list
poly2list Convert a polynomial to a list of terms
sort Sort a list
text2list Split a character string into a list of substrings
Operations on Strings
stringlib::collapseWhitespace Collapse whitespace in strings
stringlib::contains Test for substring
stringlib::format Formatting a string
stringlib::formatf Convert a floating-point number to a string
stringlib::formatTime Textual description of a time length
stringlib::lower Convert to lower-case
stringlib::maskMeta Mask regular expression special characters
stringlib::order Sorting procedure for Sort
stringlib::pos Position of a substring
stringlib::random Create a random string
stringlib::readText Read text file
stringlib::remove Delete substrings
stringlib::split Split a string
stringlib::subs Substitution in a string
stringlib::subsop Substitution in a string
stringlib::upper Convert to upper-case
stringlib::validIdent Validate identifier name
strmatch Match pattern in character string
substring Extract a substring from a string
Identification
Indeterminates, Expressions, Equations, Constants
Type::AlgebraicConstant Type representing algebraic constants
Type::Arithmetical Type representing arithmetical objects
Type::Boolean Type representing boolean expressions
Type::ConstantIdents Set of constant identifiers in MuPAD
Type::Constant Type representing constant objects
Type::Equation Type representing equations
Type::Function Type representing functions
Type::IndepOf Type representing objects that do not contain given identifiers
Type::Indeterminate Type representing indeterminates
Type::Property Type representing any property
Type::Relation Type representing relations
Type::Unknown Type representing variables
Numbers
Type::NegInt Type and property representing negative integers
Type::NegRat Type and property representing negative rational numbers
Type::Negative Type and property representing negative numbers
Type::NonNegInt Type and property representing nonnegative integers
Type::NonNegRat Type and property representing nonnegative rational numbers
Type::NonNegative Type and property representing nonnegative numbers
Type::PosInt Type and property representing positive integers
Type::PosRat Type and property representing positive rational numbers
Type::Positive Type and property representing positive numbers
Type::NonZero Type and property representing "unequal to zero"
Type::Zero Type and property representing zero
Type::Complex Type and property representing complex numbers
Type::Imaginary Type and property representing imaginary numbers
Type::Real Type and property representing real numbers
Type::Even Type and property representing even integers
Type::Integer Type and property representing integers
Type::Numeric Type representing numerical objects
Type::Odd Type and property representing odd integers
Type::Prime Type representing prime numbers
Type::Rational Type and property representing rational numbers
Type::Residue Property representing a residue class
Data Structures
Type::Interval Property representing intervals
Type::ListOf Type representing lists of objects with the same type
Type::ListProduct Type representing lists
Type::Intersection Type representing the intersection of several types
Type::PolyExpr Type representing polynomial expressions
Type::PolyOf Type representing polynomials
Type::Product Type representing sequences
Type::RatExpr Type representing rational expressions
Type::SequenceOf Type representing sequences
Type::Series Type representing truncated Puiseux, Laurent, and Taylor series expansions
Type::SetOf Type representing sets
Type::Set Type representing set-theoretic expressions
Type::Singleton Type representing exactly one object
Type::TableOfEntry Type representing tables with specified entries
Type::TableOfIndex Type representing tables with specified indices
Type::TableOf Type representing tables
Type::Union Type representing several types as one type object
Type Checking
domtype Data type of an object
has Check if an object occurs in another object
hastype Test if an object of a specified type occurs in another object
testtype Syntactical type checking
type Type of an object
Type::AnyType Type representing arbitrary MuPAD objects
Type::Predicate Type for testing object satisfying a given predicate
Conversion
coerce Type conversion
expr Convert into an element of a basic domain
expr2text Convert objects into character strings
int2text Convert an integer to a character string
interval Convert constant subexpressions to intervals
strprint Print into string
tbl2text Concatenate the strings in a table
text2expr Convert a character string to an expression
text2int Convert a character string to an integer
text2list Split a character string into a list of substrings
text2tbl Split a character string into a table of substrings
linalg::expr2Matrix Construct a matrix from equations
prog::exprlist Convert an expression into a nested list

MuPAD Symbols and Special Characters

Symbol::accentPrime Adds a prime accent to an identifier
Symbol::accentAsterisk Adds an asterisk accent to an identifier
Symbol::accentTilde Adds a tilde accent to an identifier
Symbol::accentHat Adds a hat accent to an identifier
Symbol::accentRightArrow Adds a right arrow accent to an identifier
Symbol::accentDot Adds a dot accent to an identifier
Symbol::accentDoubleDot Adds a double dot accent to an identifier
Symbol::accentTripleDot Adds a triple dot accent to an identifier
Symbol::accentOverBar Adds an overbar to an identifier
Symbol::accentUnderBar Adds an underbar to an identifier
Symbol::new Functional access to symbols
Symbol::subScript Combines two expressions to a new subscripted identifier
Symbol::subSuperScript Combines three expressions to a new combined sub- and superscripted identifier
Symbol::superScript Combines two expressions to a new superscripted identifier

Mathematics

Equation Solving

Symbolic Solvers
linsolve Solve a system of linear equations
poles Poles of expression or function
rec Domain of recurrence equations
RootOf Set of roots of a polynomial
solve Solve equations and inequalities
testeq Check the mathematical equivalence of expressions
solvelib::pdioe Solve polynomial Diophantine equations
Numeric Solvers
numeric::butcher Butcher parameters of Runge-Kutta schemes
numeric::cubicSpline Interpolation by cubic splines
numeric::cubicSpline2d Interpolation by 2-dimensional bi-cubic splines
numeric::fsolve Search for a numerical root of a system of equations
numeric::leastSquares Least squares solution of linear equations
numeric::linsolve Solve a system of linear equations
numeric::matlinsolve Solve a linear matrix equation
numeric::odesolve Numerical solution of an ordinary differential equation
numeric::odesolve2 Numerical solution of an ordinary differential equation
numeric::odesolveGeometric Numerical solution of an ordinary differential equation on a homogeneous manifold
numeric::ode2vectorfield Convert an ode system to vectorfield notation
numeric::odeToVectorField Convert an ode system to vectorfield notation
numeric::solve Numerical solution of equations (the float attribute of solve)
Ordinary Differential Equations
ode::exponentialSolutions Exponential solutions of a homogeneous linear ordinary differential equation
ode::polynomialSolutions Polynomial solutions of a homogeneous linear ordinary differential equation
ode::rationalSolutions Rational solutions of a homogeneous linear ordinary differential equation
ode::series Series solutions of an ordinary differential equation
ode::solve Solving ordinary differential equations
ode Domain of ordinary differential equations
ode::companionSystem Companion matrix of a linear homogeneous ordinary differential equation
ode::cyclicVector Transforms a linear differential system to an equivalent linear differential system with a companion matrix.
ode::dAlembert D'Alembert reduction of a linear homogeneous ordinary differential equation
ode::evalOde Applies an expression at a linear ordinary differential equation
ode::exponents Exponents of a linear ordinary differential equation
ode::getOrder Order of an ordinary differential equation
ode::indicialEquation Indicial equation of a linear ordinary differential equation
ode::isFuchsian Tests if a homogeneous linear ordinary differential equation is of Fuchsian type
ode::isLODE Test for a linear ordinary differential equation
ode::mkODE Builds a linear homogeneous ordinary differential equation from a list of coefficient functions
ode::normalize Normalized form of a linear ordinary differential equation
ode::ratSys Rational solutions of a first order homogeneous linear differential system
ode::scalarEquation Transforms a linear differential system to an equivalent scalar linear differential equation
ode::symmetricPower Symmetric power of a homogeneous linear ordinary differential equation
ode::unimodular Unimodular transformation of a linear ordinary differential equation
ode::vectorize Coefficients of a homogeneous linear ODE
ode::wronskian Wronskian of functions or of a linear homogeneous ordinary differential equation
Properties and Assumptions
assume Set permanent assumption
assumeAlso Add permanent assumption
assuming Set temporary assumption
assumingAlso Add temporary assumption
getprop Query properties of expressions
is Check a mathematical property of an expression
iszero Generic zero test
property::depends Dependence table with all properties of an expression
property::hasprop Does an object have properties?
property::showprops What assumptions are made?
unassume Delete the properties of an identifier
Utilities for the Solver
solvelib::cartesianPower Cartesian power of a set
solvelib::cartesianProduct Cartesian product of sets
solvelib::conditionalSort Possible sortings of a list depending on parameters
solvelib::getElement Get one element of a set
solvelib::isEmpty Predicate expressing the emptyness of a set
solvelib::isFinite Test whether a set is finite
solvelib::preImage Preimage of a set under a mapping
solvelib::splitVectorSet Factor a set of vectors into a cartesian product
solvelib::Union Union of a system of sets
solvelib::VectorImageSet Domain of set of vectors that are images of sets under mappings
Differential Algebraic Equations
daetools::findDecoupledBlocks Search for decoupled blocks in systems of equations
daetools::incidenceMatrix Find incidence matrix of system of equations
daetools::isLowIndexDAE Check if differential index of system equations is lower than 2
daetools::massMatrixForm Extract mass matrix and right side of semilinear system of differential algebraic equations
daetools::reduceDAEIndex Convert system of first-order differential algebraic equations to equivalent system of differential index 1
daetools::reduceDAEToODE Convert system of first-order quasilinear differential algebraic equations to equivalent system of differential index 0
daetools::reduceDifferentialOrder Reduce systems of higher-order differential equations to systems of first-order differential equations
daetools::reduceRedundancies Simplify system of first-order differential algebraic equations by eliminating redundant equations and variables

Formula Manipulation and Simplification

Simplification
factorout Factor out a given expression
normal Normalize an expression
radsimp Simplify radicals in arithmetical expressions
Rule Defining equivalence rules for mathematical expressions
simplify Simplify an expression
Simplify Simplify an expression
simplifyFraction Normalize an expression
simplifyRadical Simplify radicals in arithmetical expressions
Formula Rearrangement and Rewriting
collect Collect terms with the same powers
combine Combine terms of same algebraic structure
denom Denominator of a rational expression
expand Expand an expression
factor Factor a polynomial into irreducible polynomials
factorout Factor out a given expression
isolate Isolate variable or expression from equation
lhs Left hand side of equations, inequalities, relations, intervals, ranges and tables
rhs Right hand side of equations, inequalities, relations, intervals, ranges and tables
normal Normalize an expression
simplifyFraction Normalize an expression
numer Numerator of a rational expression
partfrac Partial fraction decomposition
radsimp Simplify radicals in arithmetical expressions
simplifyRadical Simplify radicals in arithmetical expressions
rationalize Transform an expression into a rational expression
rectform Rectangular form of a complex expression
rewrite Rewrite an expression
Substitution
subs Substitute into an object
subset Relation "is a subset of"
subsex Extended substitution
subsop Replace operands
Evaluation
block Create an object protected against evaluation
blockIdents Create a transparent block with some identifiers protected against evaluation
blockTransparent Create a transparent block protected against evaluation
unblock Replace blocks by their contents
context Evaluate an object in the enclosing context
eval Evaluate an object
evalassign Assignment with evaluation of the left hand side
evalAt Insert a value (evaluate at a point)
evalp Evaluate a polynomial at a point
freeze Create an inactive copy of a function
unfreeze Create an active copy of a frozen function
hold Delay evaluation
LEVEL Substitution depth of identifiers
level Evaluate an object with a specified substitution depth
MAXDEPTH Prevent infinite recursion during procedure calls
MAXEFFORT Maximum amount of work to spend on the computation
MAXLEVEL Prevent infinite recursion during evaluation
Properties and Assumptions
assume Set permanent assumption
assumeAlso Add permanent assumption
assuming Set temporary assumption
assumingAlso Add temporary assumption
getprop Query properties of expressions
is Check a mathematical property of an expression
iszero Generic zero test
property::depends Dependence table with all properties of an expression
property::hasprop Does an object have properties?
property::showprops What assumptions are made?
unassume Delete the properties of an identifier

Calculus

Differentiation
D Differential operator for functions
diff Differentiate an expression or a polynomial
Integration
int Definite and indefinite integrals
int::addpattern Add patterns for integration
intlib::byparts Integration by parts
intlib::changevar Change of variable
intlib::intOverSet Integration over a set
intlib::printWarnings Enable or disable warnings
numeric::gldata Weights and abscissae of Gauss-Legendre quadrature
numeric::gtdata Weights and abscissae of Gauss-Tschebyscheff quadrature
numeric::int Numerical integration (the Float attribute of Int )
numeric::ncdata Weights and abscissae of Newton-Cotes quadrature
numeric::quadrature Numerical integration ( Quadrature )
Vector Analysis
curl Curl of a vector field
divergence Divergence of a vector field
gradient Vector gradient
hessian Hessian matrix of a scalar function
jacobian Jacobian matrix of a vector function
laplacian The Laplacian
potential The (scalar) potential of a gradient field
vectorPotential Vector potential of a three-dimensional vector field
Series
Expansion
asympt Compute an asymptotic series expansion
mtaylor Compute a multivariate Taylor series expansion
O Domain of order terms (Landau symbols)
ORDER Default number of terms in series expansions
pade Pade approximation
series Compute a generalized series expansion
taylor Compute a Taylor series expansion
theta Theta series
Summation
sum Definite and indefinite summation
sum::addpattern Add patterns for definite and indefinite summation
numeric::sum Numerical approximation of sums (the Float attribute of Sum )
Products
product Definite and indefinite products
numeric::product Numerical approximation of products
Limits
limit Compute a limit
Transforms
Fourier and Laplace Transforms
fourier Fourier transform
ifourier Inverse Fourier transform
ilaplace Inverse Laplace transform
laplace Laplace transform
Pref::fourierParameters Specify parameters for Fourier and inverse Fourier transforms
Z-Transform
iztrans Inverse Z transform
ztrans Z transform
Fast Fourier Transform
numeric::fft Fast Fourier Transform
numeric::invfft Inverse Fast Fourier Transform
New Patterns for Transforms
fourier::addpattern Add patterns for the Fourier transform
ifourier::addpattern Add patterns for the inverse Fourier transform
ilaplace::addpattern Add patterns for the inverse Laplace transform
iztrans::addpattern Add patterns for the inverse Z transform
laplace::addpattern Add patterns for the Laplace transform
ztrans::addpattern Add patterns for the Z transform
Properties and Assumptions
assume Set permanent assumption
assumeAlso Add permanent assumption
assuming Set temporary assumption
assumingAlso Add temporary assumption
getprop Query properties of expressions
is Check a mathematical property of an expression
iszero Generic zero test
property::depends Dependence table with all properties of an expression
property::hasprop Does an object have properties?
property::showprops What assumptions are made?
unassume Delete the properties of an identifier

Linear Algebra

Matrix and Vector Construction
array Create an array
bernstein Bernstein polynomials
bernsteinMatrix Bernstein matrix
densematrix Create a matrix or a vector
doprint Print large matrices
hfarray Create an array of hardware floats
matrix Create a matrix or a vector
hessian Hessian matrix of a scalar function
jacobian Jacobian matrix of a vector function
linalg::hessenberg Hessenberg matrix
linalg::hilbert Hilbert matrix
linalg::invhilbert Inverse of a Hilbert matrix
linalg::invpascal Inverse of a Pascal matrix
linalg::pascal Pascal matrix
linalg::randomMatrix Generate a random matrix
linalg::toeplitz Toeplitz matrix
linalg::vandermonde Vandermonde matrices and their inverses
linalg::invvandermonde Vandermonde matrices and their inverses
linalg::wiedemann Solving linear systems by Wiedemann's algorithm
Matrix Operations and Transformations
linalg::addCol Linear combination of matrix columns
linalg::addRow Linear combination of matrix rows
linalg::col Extract columns of a matrix
linalg::delCol Delete matrix columns
linalg::delRow Delete matrix rows
linalg::multCol Multiply columns with a scalar
linalg::multRow Multiply rows with a scalar
linalg::row Extract rows of a matrix
linalg::setCol Change a column of a matrix
linalg::setRow Change a row of a matrix
linalg::swapCol Swap two columns in a matrix
linalg::swapRow Swap two rows in a matrix
inverse Inverse of a matrix
transpose Transpose of a matrix
htranspose The Hermitian transpose of a matrix
linalg::pseudoInverse Moore-Penrose inverse of a matrix
numeric::inverse Inverse of a matrix
lllint Compute an LLL-reduced basis of a lattice
norm Compute the norm of a matrix, a vector, or a polynomial
linalg::concatMatrix Join matrices horizontally
linalg::crossProduct Cross product of three-dimensional vectors
linalg::kroneckerProduct Kronecker product of matrices
linalg::normalize Normalize a vector
linalg::ogCoordTab Table of orthogonal coordinate transformations
linalg::scalarProduct Scalar product of vectors
linalg::stackMatrix Join matrices vertically
linalg::submatrix Extract a submatrix or a subvector from a matrix or a vector, respectively
linalg::substitute Replace a part of a matrix by another matrix
linalg::sylvester Sylvester matrix of two polynomials
numeric::rotationMatrix Orthogonal matrix of the rotation about an axis
Linear Equations
det Determinant of a matrix
norm Compute the norm of a matrix, a vector, or a polynomial
linalg::cond Condition number of a matrix
linalg::matlinsolve Solving systems of linear equations
linalg::matlinsolveLU Solving the linear system given by an LU decomposition
linalg::rank Rank of a matrix
linalg::toeplitzSolve Solve a linear Toeplitz system
linalg::vandermondeSolve Solve a linear Vandermonde system
numeric::det Determinant of a matrix
numeric::inverse Inverse of a matrix
numeric::rank Numerical estimate of the rank of a matrix
Matrix Decomposition
linalg::factorCholesky The Cholesky decomposition of a matrix
linalg::factorLU LU-decomposition of a matrix
linalg::factorQR QR-decomposition of a matrix
linalg::frobeniusForm Frobenius form of a matrix
linalg::hermiteForm Hermite normal form of a matrix
linalg::inverseLU Computing the inverse of a matrix using LU-decomposition
linalg::jordanForm Jordan normal form of a matrix
linalg::smithForm Smith canonical form of a matrix
numeric::factorCholesky Cholesky factorization of a matrix
numeric::factorLU LU factorization of a matrix
numeric::factorQR QR factorization of a matrix
numeric::singularvalues Numerical singular values of a matrix
numeric::singularvectors Numerical singular value decomposition of a matrix
numeric::svd Numerical singular value decomposition of a matrix
Eigenvalues and Eigenvectors
linalg::eigenvalues Eigenvalues of a matrix
linalg::eigenvectors Eigenvectors of a matrix
numeric::eigenvalues Numerical eigenvalues of a matrix
numeric::eigenvectors Numerical eigenvalues and eigenvectors of a matrix
linalg::jordanForm Jordan normal form of a matrix
numeric::spectralRadius Spectral radius of a matrix
Vector Spaces and Subspaces
linalg::basis Basis for a vector space
linalg::gaussElim Gaussian elimination
linalg::gaussJordan Gauss-Jordan elimination
linalg::intBasis Basis for the intersection of vector spaces
linalg::matdim Dimension of a matrix
linalg::nrows Number of rows of a matrix
linalg::nullspace Basis for the null space of a matrix
linalg::orthog Orthogonalization of vectors
linalg::rank Rank of a matrix
linalg::sumBasis Basis for the sum of vector spaces
linalg::vecdim Number of components of a vector
numeric::rank Numerical estimate of the rank of a matrix
Matrix Analysis
curl Curl of a vector field
det Determinant of a matrix
divergence Divergence of a vector field
gradient Vector gradient
hessian Hessian matrix of a scalar function
jacobian Jacobian matrix of a vector function
laplacian The Laplacian
norm Compute the norm of a matrix, a vector, or a polynomial
potential The (scalar) potential of a gradient field
vectorPotential Vector potential of a three-dimensional vector field
numeric::det Determinant of a matrix
linalg::adjoint Adjoint of a matrix
linalg::angle Angle between two vectors
linalg::charmat Characteristic matrix
linalg::cond Condition number of a matrix
linalg::isHermitian Checks whether a matrix is Hermitian
linalg::isPosDef Test a matrix for positive definiteness
linalg::isUnitary Test whether a matrix is unitary
linalg::ncols Number of columns of a matrix
linalg::nonZeros Number of non-zero elements of a matrix
linalg::nrows Number of rows of a matrix
linalg::permanent Permanent of a matrix
linalg::tr Trace of a matrix
linalg::vectorOf Type specifier for vectors
Matrix Functions
funm General matrix function
linalg::sqrtMatrix Square root of a matrix
numeric::expMatrix Exponential of a matrix
numeric::fMatrix Functional calculus for numerical square matrices
Properties and Assumptions
assume Set permanent assumption
assumeAlso Add permanent assumption
assuming Set temporary assumption
assumingAlso Add temporary assumption
getprop Query properties of expressions
is Check a mathematical property of an expression
iszero Generic zero test
property::depends Dependence table with all properties of an expression
property::hasprop Does an object have properties?
property::showprops What assumptions are made?
unassume Delete the properties of an identifier

Polynomial Algebra

Polynomial Creation
genpoly Create a polynomial using b-adic expansion
laguerreL Laguerre polynomials and L function
orthpoly::chebyshev1 The Chebyshev polynomials of the first kind
orthpoly::chebyshev2 The Chebyshev polynomials of the second kind
orthpoly::curtz The Curtz polynomials
orthpoly::gegenbauer The Gegenbauer (ultraspherical) polynomials
orthpoly::hermite The Hermite polynomials
orthpoly::jacobi The Jacobi polynomials
orthpoly::laguerre The (generalized) Laguerre polynomials
orthpoly::legendre The Legendre polynomials
poly Create a polynomial
polylib::cyclotomic Cyclotomic polynomials
polylib::elemSym Elementary symmetric polynomials
polylib::Poly Domain of polynomials
polylib::randpoly Create a random polynomial
Polynomial Manipulation
divide Divide polynomials
interpolate Polynomial interpolation
irreducible Test irreducibility of a polynomial
pdivide Pseudo-division of polynomials
linalg::charpoly Characteristic polynomial of a matrix
linalg::companion Companion matrix of a univariate polynomial
linalg::minpoly Minimal polynomial of a matrix
polylib::decompose Functional decomposition of a polynomial
polylib::discrim Discriminant of a polynomial
polylib::divisors Divisors of a polynomial, polynomial expression, or Factored element
polylib::Dpoly Differential operator for polynomials
polylib::makerat Convert expression into rational function over a suitable field
polylib::minpoly Approximate minimal polynomial
polylib::primitiveElement Primitive element for tower of field extensions
polylib::primpart Primitive part of a polynomial
polylib::representByElemSym Represent symmetric by elementary symmetric polynomials
polylib::resultant Resultant of two polynomials
polylib::splitfield Splitting field of a polynomial
polylib::sqrfree Square-free factorization of polynomials
polylib::subresultant Subresultants of two polynomials
polylib::support Support of a polynomial
Elements of Polynomials
coeff Coefficients of a polynomial
content Content of a polynomial
degree Degree of a polynomial
degreevec Exponents of the leading term of a polynomial
icontent Content of a polynomial with rational coefficients
lcoeff Leading coefficient of a polynomial
ldegree Lowest degree of the terms in a polynomial
lmonomial Leading monomial of a polynomial
lterm Leading term of a polynomial
mapcoeffs Apply a function to the coefficients of a polynomial
monomials Sorted list of monomials of a polynomial
multcoeffs Multiply the coefficients of a polynomial with a factor
nterms Number of terms of a polynomial
nthcoeff N-th non-zero coefficient of a polynomial
nthmonomial N-th monomial of a polynomial
nthterm N-th term of a polynomial
poly2list Convert a polynomial to a list of terms
polylib::coeffRing Coefficient ring of a polynomial
polylib::sortMonomials Sorting monomials with respect to a term ordering
tcoeff Trailing coefficient of a polynomial
Groebner Algebra
groebner::dimension Dimension of the affine variety generated by polynomials
groebner::eliminate Eliminate variables
groebner::gbasis Computation of a reduced Gröbner basis
groebner::normalf Complete reduction modulo a polynomial ideal
groebner::spoly The S-polynomial of two polynomials
groebner::stronglyIndependentSets Strongly independent set of variables
Polynomial Roots
numeric::polyrootbound Bound for the roots of a univariate polynomial
numeric::polyroots Numerical roots of a univariate polynomial
numeric::polysysroots Numerical roots of a system of polynomial equations
numeric::realroot Numerical search for a real root of a real univariate function
numeric::realroots Isolate intervals containing real roots of a univariate function
polylib::realroots Isolate all real roots of a real univariate polynomial
Properties and Assumptions
assume Set permanent assumption
assumeAlso Add permanent assumption
assuming Set temporary assumption
assumingAlso Add temporary assumption
getprop Query properties of expressions
is Check a mathematical property of an expression
iszero Generic zero test
property::depends Dependence table with all properties of an expression
property::hasprop Does an object have properties?
property::showprops What assumptions are made?
unassume Delete the properties of an identifier

Mathematical Constants and Functions

Constants
complexInfinity Complex infinity
infinity Real positive infinity
FAIL Indicate a failed computation
NIL Singleton element of the domain DOM_NIL
null Generate the void object of type DOM_NULL
TRUE Boolean constant TRUE
FALSE Boolean constant FALSE
UNKNOWN Boolean constant UNKNOWN
undefined Undefined value
C_ Complex numbers
R_ Real numbers
Q_ Rational numbers
Z_ Integers
N_ Positive integers
Complex Numbers
abs Absolute value of a real or complex number
arg Argument (polar angle) of a complex number
Re Real part of an arithmetical expression
Im Imaginary part of an arithmetical expression
sign Sign of a real or complex number
signIm Sign of the imaginary part of a complex number
Exponents and Logarithms
exp Exponential function
ln Natural logarithm
log Logarithm to arbitrary base
log10 Logarithm to base 10
log2 Logarithm to base 2
^ Raise an expression to a power
sqrt Square root function
surd N -th root
Trigonometric Functions
sin Sine function
cos Cosine function
tan Tangent function
cot Cotangent function
sec Secant function
csc Cosecant function
arcsin Inverse sine function
arccos Inverse cosine function
arctan Inverse tangent function
arccot Inverse cotangent function
arcsec Inverse secant function
arccsc Inverse cosecant function
Hyperbolic Functions
sinh Hyperbolic sine function
cosh Hyperbolic cosine function
tanh Hyperbolic tangent function
coth Hyperbolic cotangent function
sech Hyperbolic secant function
csch Hyperbolic cosecant function
arcsinh Inverse of the hyperbolic sine function
arccosh Inverse of the hyperbolic cosine function
arctanh Inverse of the hyperbolic tangent function
arccoth Inverse of the hyperbolic cotangent function
arcsech Inverse of the hyperbolic secant function
arccsch Inverse of the hyperbolic cosecant function
Special Functions
Dirac and Heaviside Functions
dirac The Dirac delta distribution
heaviside The Heaviside step function
kroneckerDelta Kronecker's delta symbol
rectangularPulse Rectangular pulse function
rectpulse Rectangular pulse function
triangularPulse Triangular pulse function
tripulse Triangular pulse function
Pref::heavisideAtOrigin Set value of Heaviside function at origin
Gamma Functions
beta Beta function
binomial Binomial coefficients
gamma Gamma function
lngamma Log-gamma function
igamma Incomplete gamma function
pochhammer The Pochhammer symbol
psi Digamma/polygamma function
Zeta Function and Polylogarithms
dilog Dilogarithm function
polylog Polylogarithm function
zeta The Riemann zeta function
Airy and Bessel Functions
airyAi Airy function of the first kind
airyBi Airy function of the second kind
besselI Modified Bessel functions of the first kind
besselJ Bessel functions of the first kind
besselK Modified Bessel functions of the second kind
besselY Bessel functions of the second kind
Exponential and Trigonometric Integrals
Ci Cosine integral function
Chi Hyperbolic cosine integral function
dawson Dawson's integral
Ei Exponential integral function
Li Integral logarithm
Si Sine integral function
Ssi Shifted sine integral function
Shi Hyperbolic sine integral function
Error Functions and Fresnel Functions
erf Error function
erfc Complementary error function
erfi Imaginary error function
inverf Inverse of the error function
inverfc Inverse of the complementary error function
fresnelC The Fresnel cosine integral function
fresnelS The Fresnel sine integral function
Hypergeometric and Whittaker Functions
hypergeom Hypergeometric functions
kummerU Confluent hypergeometric KummerU function
meijerG The Meijer G function
whittakerM The Whittaker M function
whittakerW The Whittaker W function
Elliptic Integrals
ellipticK Complete elliptic integral of the first kind
ellipticCK Complementary complete elliptic integral of the first kind
ellipticF Incomplete elliptic integral of the first kind
ellipticE Complete and incomplete elliptic integrals of the second kind
ellipticCE Complementary complete elliptic integral of the second kind
ellipticPi Complete and incomplete elliptic integrals of the third kind
ellipticCPi Complementary complete elliptic integral of the third kind
ellipticNome Elliptic nome
jacobiAM Jacobi amplitude function am
jacobiSN Jacobi elliptic function sn
jacobiCN Jacobi elliptic function cn
jacobiDN Jacobi elliptic function dn
jacobiCD Jacobi elliptic function cd
jacobiSD Jacobi elliptic function sd
jacobiND Jacobi elliptic function nd
jacobiDC Jacobi elliptic function dc
jacobiNC Jacobi elliptic function nc
jacobiSC Jacobi elliptic function sc
jacobiNS Jacobi elliptic function ns
jacobiDS Jacobi elliptic function ds
jacobiCS Jacobi elliptic function cs
jacobiZeta Jacobi Zeta function
Lambert W and Wright Functions
lambertW The Lambert function
wrightOmega The Wright ω function

Numbers and Precision

Precision Control
float Convert to a floating-point number
Pref::floatFormat Representation of floating-point numbers
Pref::outputDigits Set the number of digits in floating-point outputs
Pref::trailingZeroes Trailing zeroes when printing floating-point numbers
Operations on Numbers
ceil Rounding up to the next integer
floor Rounding down to the next integer
conjugate Complex conjugation
frac Fractional part of a number
ground Ground term (constant coefficient) of a polynomial
Im Imaginary part of an arithmetical expression
max Maximum of numbers
min Minimum of numbers
misc::pslq Heuristic detection of relations between real numbers
numeric::complexRound Round a complex number towards the real or imaginary axis
numeric::rationalize Approximate a floating-point number by a rational number
Re Real part of an arithmetical expression
round Rounding to the nearest integer
trunc Rounding towards zero

Statistics

Supported Distributions
Cumulative Distribution Functions
stats::betaCDF Cumulative distribution function of the beta distribution
stats::binomialCDF The (discrete) cumulative distribution function of the binomial distribution
stats::cauchyCDF Cumulative distribution function of the Cauchy distribution
stats::chisquareCDF Cumulative distribution function of the chi-square distribution
stats::empiricalCDF Empirical (discrete) cumulative distribution function of a finite data sample
stats::erlangCDF Cumulative distribution function of the Erlang distribution
stats::exponentialCDF Cumulative distribution function of the exponential distribution
stats::fCDF Cumulative distribution function of Fisher's f-distribution (fratio distribution)
stats::finiteCDF Cumulative distribution function of a finite sample space
stats::gammaCDF Cumulative distribution function of the gamma distribution
stats::geometricCDF The (discrete) cumulative distribution function of the geometric distribution
stats::hypergeometricCDF The (discrete) cumulative probability function of the hypergeometric distribution
stats::logisticCDF Cumulative distribution function of the logistic distribution
stats::lognormalCDF Cumulative distribution function of the log-normal distribution
stats::normalCDF Cumulative distribution function of the normal distribution
stats::poissonCDF The (discrete) cumulative distribution function of the Poisson distribution
stats::tCDF Cumulative distribution function of Student's t-distribution
stats::uniformCDF Cumulative distribution function of the uniform distribution
stats::weibullCDF Cumulative distribution function of the Weibull distribution
Probability Density Functions
stats::betaPDF Probability density function of the beta distribution
stats::cauchyPDF Probability density function of the Cauchy distribution
stats::chisquarePDF Probability density function of the chi-square distribution
stats::erlangPDF Probability density function of the Erlang distribution
stats::exponentialPDF Probability density function of the exponential distribution
stats::fPDF Probability density function of Fisher's f-distribution (fratio distribution)
stats::gammaPDF Probability density function of the gamma distribution
stats::logisticPDF Probability density function of the logistic distribution
stats::lognormalPDF Probability density function of the log-normal distribution
stats::normalPDF Probability density function of the normal distribution
stats::tPDF Probability density function of Student's t-distribution
stats::uniformPDF Probability density function of the uniform distribution
stats::weibullPDF Probability density function of the Weibull distribution
Probability Functions
stats::binomialPF Probability function of the binomial distribution
stats::empiricalPF Probability function of a finite data sample
stats::finitePF Probability function of a finite sample space
stats::geometricPF Probability function of the geometric distribution
stats::hypergeometricPF Probability function of the hypergeometric distribution
stats::poissonPF Probability function of the Poisson distribution
Quantile Functions
stats::betaQuantile Quantile function of the beta distribution
stats::binomialQuantile Quantile function of the binomial distribution
stats::cauchyQuantile Quantile function of the Cauchy distribution
stats::chisquareQuantile Quantile function of the chi-square distribution
stats::empiricalQuantile Quantile function of the empirical distribution
stats::erlangQuantile Quantile function of the Erlang distribution
stats::exponentialQuantile Quantile function of the exponential distribution
stats::fQuantile Quantile function of Fisher's f-distribution (fratio distribution)
stats::finiteQuantile Quantile function of a finite sample space
stats::gammaQuantile Quantile function of the gamma distribution
stats::geometricQuantile Quantile function of the geometric distribution
stats::hypergeometricQuantile Quantile function of the hypergeometric distribution
stats::logisticQuantile Quantile function of the logistic distribution
stats::lognormalQuantile Quantile function of the log-normal distribution
stats::normalQuantile Quantile function of the normal distribution
stats::poissonQuantile Quantile function of the Poisson distribution
stats::tQuantile Quantile function of Student's t-distribution
stats::uniformQuantile Quantile function of the uniform distribution
stats::weibullQuantile Quantile function of the Weibull distribution
Random Number Generators
frandom Generate random floating-point numbers
random Generate random integer numbers
stats::betaRandom Generate a random number generator for beta deviates
stats::binomialRandom Generate a random number generator for binomial deviates
stats::cauchyRandom Generate a random number generator for Cauchy deviates
stats::chisquareRandom Generate a random number generator for chi-square deviates
stats::empiricalRandom Generate a random generator for uniformly distributed elements of a data sample
stats::erlangRandom Generate a random number generator for Erlang deviates
stats::exponentialRandom Generate a random number generator for exponential deviates
stats::fRandom Generate a random number generator for Fisher's f-deviates (fratio deviates)
stats::finiteRandom Generate a random generator for elements of a finite sample space
stats::gammaRandom Generate a random number generator for gamma deviates
stats::geometricRandom Generate a random number generator for geometric deviates
stats::hypergeometricRandom Generate a random number generator for hypergeometric deviates
stats::logisticRandom Generate a random number generator for logistic deviates
stats::lognormalRandom Generate a random number generator for log-normal deviates
stats::normalRandom Generate a random number generator for normal deviates
stats::poissonRandom Generate a random number generator for Poisson deviates
stats::tRandom Generate a random number generator for Student deviates (t-deviates)
stats::uniformRandom Generate a random number generator for uniformly continous deviates
stats::weibullRandom Generate a random number generator for Weibull deviates
Data Import
import::csv Read CSV data from an ASCII file
import::readbitmap Read bitmap data
import::readdata Read data from an ASCII file
import::readlisp Parse Lisp-formatted string
stats::sample Domain of statistical samples
Operations on Data Samples
stats::calc Apply functions to a sample
stats::col Select and rearrange columns of a sample
stats::concatCol Concatenate samples column-wise
stats::concatRow Concatenate samples row-wise
stats::row Select and re-arrange rows of a sample
stats::sample Domain of statistical samples
stats::sample2list Convert a sample to a list of lists
stats::selectRow Select rows of a sample
stats::sortSample Sort the rows of a sample
stats::tabulate Statistics of duplicate rows in a sample
stats::unzipCol Extract columns from a list of lists
stats::zipCol Convert a sequence of columns to a list of lists
Descriptive Statistics
numeric::gaussAGM Gauss' arithmetic geometric mean
stats::correlation Correlation between data samples
stats::correlationMatrix Compute the correlation matrix associated with a covariance matrix
stats::covariance Covariance of data samples
stats::cutoff Discard outliers
stats::winsorize Clamp (winsorize) extremal values
stats::frequency Tally numerical data into classes and count frequencies
stats::geometricMean Geometric mean of a data sample
stats::harmonicMean Harmonic mean of a data sample
stats::kurtosis Kurtosis (excess) of a data sample
stats::mean Arithmetic mean of a data sample
stats::meandev Mean deviation of a data sample
stats::median Median value of a data sample
stats::modal Modal (most frequent) value(s) in a data sample
stats::moment The K-th moment of a data sample
stats::obliquity Obliquity (skewness) of a data sample
stats::quadraticMean Quadratic mean of a data sample
stats::stdev Standard deviation of a data sample
stats::variance Variance of a data sample
Regression Analysis
stats::hodrickPrescottFilter The Hodrick-Prescott filter
stats::linReg Linear regression (least squares fit)
stats::reg Regression (general linear and nonlinear least squares fit)
Hypothesis Testing
stats::csGOFT Classical chi-square goodness-of-fit test
stats::equiprobableCells Divide the real line into equiprobable intervals
stats::ksGOFT The Kolmogorov-Smirnov goodness-of-fit test
stats::swGOFT The Shapiro-Wilk goodness-of-fit test for normality
stats::tTest T-test for a mean

Discrete Mathematics

Number Theory
Divisors
gcd Greatest common divisor of polynomials
gcdex Extended Euclidean algorithm for polynomials
igcd Greatest common divisor of integers and complex numbers with integer real and imaginary parts
igcdex Extended Euclidean algorithm for two integers
numlib::igcdmult Extended Euclidean algorithm for integers
ilcm Least common multiple of integers
lcm Least common multiple of polynomials
numlib::divisors Divisors of an integer
numlib::numdivisors Number of divisors of an integer
numlib::Omega Number of prime divisors (with multiplicity)
numlib::sumdivisors Sum of divisors of an integer
Primes
isprime Primality test
ithprime I-th prime number
nextprime Next prime number
prevprime Next smaller prime
numlib::checkPrimalityCertificate Test the primality certificate
numlib::Omega Number of prime divisors (with multiplicity)
numlib::pi Number of primes up to a given bound
numlib::proveprime Primality proving using elliptic curves
numlib::primedivisors Prime factors of an integer
Factorizations
fact Factorial function
fact2 Double factorial function
ifactor Factor an integer into primes
isqrt Integer square root
numlib::ispower Test for perfect powers
numlib::issqr Test for perfect squares
numlib::factorGaussInt Factorization of Gaussian integers
numlib::numprimedivisors Number of prime factors of an integer
numlib::primedivisors Prime factors of an integer
Modular Arithmetic
div Integer part of a quotient
mod Modulo operator
modp Positive modulo function
mods Symmetric modulo function
numlib::isquadres Test for quadratic residues
numlib::order Order of a residue class
numlib::primroot Primitive roots
numlib::reconstructRational Rational number reconstruction
numlib::sqrtmodp Square root of a quadratic residue modulo a prime
powermod Compute a modular power of a number or a polynomial
rem Remainder after division
Congruences
div Integer part of a quotient
mod Modulo operator
numlib::cornacchia Cornachia's algorithm
numlib::ichrem Chinese remainder theorem for integers
numlib::jacobi Jacobi symbol
numlib::legendre Legendre symbol
numlib::lincongruence Linear congruence
numlib::mroots Modular roots of polynomials
numlib::msqrts Modular square roots
Sequences of Numbers
bernoulli Bernoulli numbers and polynomials
contfrac Domain of continued fractions
euler Euler numbers and polynomials
numlib::contfrac Domain of continued fractions
numlib::contfracPeriodic Periodic continued fraction expansions
numlib::decimal Infinite representation of rational numbers
numlib::fibonacci Fibonacci numbers
numlib::mersenne Mersenne primes
numlib::sumOfDigits Sum of digits of an integer
random Generate random integer numbers
Number Theoretic Functions
dedekindEta The Dedekind eta function
numlib::g_adic G-adic representation of a nonnegative integer
harmonic Harmonic function
numlib::invphi Inverse of the Euler phi function
numlib::Lambda Von Mangoldt's function
numlib::lambda Carmichael function
numlib::moebius Möbius function
numlib::phi Euler phi function
Conversions
numlib::fromAscii Decoding of ASCII codes
numlib::sqrt2cfrac Continued fraction expansion of square roots
numlib::toAscii ASCII encoding of a string
Linear Optimization
linopt::corners Return the feasible corners of a linear program
linopt::maximize Maximize a linear or mixed-integer program
linopt::minimize Minimize a linear or mixed-integer program
linopt::plot_data Plot the feasible region of a linear program
linopt::Transparent Return the ordinary simplex tableau of a linear program
linopt::Transparent::autostep Perform the next simplex step
linopt::Transparent::clean_basis Delete all slack variables of the first phase from the basis
linopt::Transparent::convert Transform the given tableau into a structure printable on screen
linopt::Transparent::dual_prices Get the dual solution belonging to the given tableau
linopt::Transparent::phaseI_tableau Start an ordinary phase one of a 2-phase simplex algorithm
linopt::Transparent::phaseII_tableau Start phase two of a 2-phase simplex algorithm
linopt::Transparent::result Get the basic feasible solution belonging to the given simplex tableau
linopt::Transparent::simplex Finish the current phase of the 2-phase simplex algorithm
linopt::Transparent::suggest Suggest the next step in the simplex algorithm
linopt::Transparent::userstep Perform a user defined simplex step
Boolean Algebra
bool Boolean evaluation
_lazy_and "lazy and" of Boolean expressions
_lazy_or "lazy or" of Boolean expressions
Graph Theory
Creation
Graph Creates new graph
Graph::createCircleGraph Generates a circle Graph
Graph::createCompleteGraph Generates a complete graph
Graph::createGraphFromMatrix Transfers a squared matrix into a directed graph
Graph::createRandomEdgeWeights Sets random weights to edges
Graph::createRandomEdgeCosts Sets random costs to edges
Graph::createRandomGraph Generates a random graph.
Graph::createRandomVertexWeights Sets random weights to vertices
Graph::plotBipartiteGraph Plots a Graph in a bipartite layout
Graph::plotCircleGraph Plots a Graph in a circle layout
Graph::plotGridGraph Plots a Graph in a grid layout
Modification
Graph::addEdges Adds one or several edges to a graph
Graph::addVertices Adds one or several vertices to a graph
Graph::contract Contracts vertices
Graph::convertSSQ Converts a Graph into a single source single sink Graph
Graph::printEdgeCostInformation Prints the edge costs of a graph
Graph::printEdgeDescInformation Prints the edge descriptions of a graph
Graph::printEdgeInformation Prints the edges of a graph
Graph::printEdgeWeightInformation Prints the edge weights of a graph
Graph::printGraphInformation Prints the edges of a graph
Graph::printVertexInformation Prints vertex information of a graph
Graph::removeEdge Removes one or several edges from a graph
Graph::removeVertex Removes one or several vertices from a graph
Graph::revert Reverts the edges of a graph.
Graph::setEdgeCosts Assigns edge costs to edges.
Graph::setEdgeDescriptions Assigns edge Descriptions to edges.
Graph::setEdgeWeights Assigns edge weights to edges.
Graph::setVertexWeights Assigns vertex weights to vertices.
Analysis
Graph::getAdjacentEdgesEntering Returns the incident edges.
Graph::getAdjacentEdgesLeaving Returns the adjacent edges.
Graph::getBestAdjacentEdge Returns the "best" incident edges.
Graph::getEdgeCosts Returns a table with the edge costs.
Graph::getEdgeDescriptions Returns a table with the edge descriptions.
Graph::getEdges Returns a list with all edges
Graph::getEdgesEntering Returns the incoming edges
Graph::getEdgesLeaving Returns the outgoing edges
Graph::getEdgeNumber Returns the number of edges.
Graph::getEdgeWeights Returns a table with the edge weights.
Graph::getSubGraph Returns a subgraph.
Graph::getVertexNumber Returns the number of vertices.
Graph::getVertexWeights Returns a table with the vertex weights.
Graph::getVertices Returns a list with all vertices
Graph::admissibleFlow Checks a flow for admissibility in a Graph
Graph::bipartite Finds out if a graph is bipartite.
Graph::breadthFirstSearch Makes a breadth first Search in a graph.
Graph::checkForVertices Checks if all vertices in edges really exist.
Graph::chromaticNumber Chromatic number of a graph
Graph::chromaticPolynomial Calculates a chromatic polynomial
Graph::depthFirstSearch Makes a depth first Search in a graph.
Graph::residualGraph Computes the residual graph
Graph::shortestPathAllPairs Shortest paths from and to all vertices
Graph::shortestPathSingleSource Shortest paths from one single vertex
Graph::stronglyConnectedComponents Finds the strongly connected components
Graph::topSort Topological sorting of the vertices
Graph::inDegree Returns the indegree of one or more vertices.
Graph::isConnected Finds out if the graph is connected
Graph::isDirected Finds out if the graph is directed
Graph::isEdge Finds out if the edges exists
Graph::isVertex Finds out if special vertices exist in the Graph
Graph::longestPath Longest paths from one single node
Graph::maxFlow Computes a maximal flow through a graph
Graph::minCost Computes a minimal cost flow
Graph::minCut Computes a minimal cut
Graph::minimumSpanningTree Creates a MST
Graph::outDegree Returns the outdegree of one or more vertices.
Combinatorics
combinat::bell Bell numbers
combinat::cartesianProduct Cartesian product
combinat::catalan Catalan numbers
combinat::choose Subsets of a given size
combinat::compositions Compositions of an integer
combinat::modStirling Modified Stirling numbers
combinat::partitions Partitions of an integer
combinat::permute Permutations of a list
combinat::powerset Subsets of a set
combinat::stirling1 Stirling numbers of the first kind
combinat::stirling2 Stirling numbers of the second kind
combinat::subwords Subwords of a word

Graphics

2-D and 3-D Plots

2-D Function Plots
plot Display graphical objects on the screen
display Display graphical objects on the screen
plotfunc2d Function plots in 2D
plot::easy Easy plotting
3-D Function Plots
plotfunc3d Function plots in 3D
Scatter Plots
plot::delaunay Compute the Delaunay triangulation of a set of points
plot::hull Compute the convex hull of a set of points

Annotations and Appearance

Colors
RGB::ColorNames Find predefined colors by name
RGB::plotColorPalette Display predefined colors
RGB::colorName Find names of predefined colors
RGB::fromWaveLength Get the RGB color of monochromatic light
RGB::random Pick a color uniformly at random in RGB color space
RGB::toHSV Convert RGB colors to HSV
RGB::fromHSV Convert HSV colors to RGB
Default Settings
plot::getDefault Get current default setting of attributes
plot::setDefault Set default setting of attributes

Export

plot::copy Make a physical copy of a plot object
plot::modify Make a physical copy of a plot object setting new values of attributes in the same call

Programming Basics

Control Flow

%if Conditional creation of code by the parser
break Terminate a loop or a Case switch prematurely
case Switch statement
end Close a block statement
for For loop
if If-statement (conditional branch in a program)
next Skip a step in a loop
repeat "repeat" loop
while "while" loop
return Exit a procedure

Functions and Procedures

expose Display the source code of a procedure or the entries of a domain
proc Define a procedure
save Save the state of an identifier
prog::wait Wait for a while

Interactive Input

input Interactive input of objects
textinput Interactive input of text
Pref::postInput Actions after input
Pref::postOutput Actions after output

Data and File Management

Data Import and Export

export::stl Export STL data
import::csv Read CSV data from an ASCII file
import::readbitmap Read bitmap data
import::readdata Read data from an ASCII file
import::readlisp Parse Lisp-formatted string

File Operations

fclose Close a file
finput Read objects from file
fname Get a file's name
fopen Open file
fprint Write data to file
fread Read and execute file
ftextinput Read text file
pathname Create a platform dependent path name
protocol Create a protocol of a session
read Search, read, and execute file
readbytes Read binary data from a file
writebytes Write binary data to a file
write Write values of variables into file
Pref::verboseRead Shows reading of files

Advanced Software Development

Functional Programming

@ Compose functions
@@ Iterate a function
copyClosure Copies the lexical closure of a procedure
discont Discontinuities of a function
funcenv Create a function environment
map Apply a function to all operands of an object
maprat Apply a function to a rationalized expression
operator Define a new operator symbol
fp::apply Apply function to arguments
fp::bottom Function that never returns
fp::curry Curry an n-ary function
fp::expr_unapply Create a functional expression from an expression
fp::fixargs Create function by fixing all but one argument
fp::fixedpt Returns fixed point of a function
fp::fold Create function which iterates over sequences
fp::nest Repeated composition of function
fp::nestvals Repeated composition returning intermediate values
fp::unapply Create a procedure from an expression
misc::breakmap Stops the mapping currently done by maprec
misc::maprec Map a function to subexpressions of an expression
Pref::typeCheck Type checking of formal parameters
Pref::warnDeadProcEnv Warnings about wrong usage of lexical scope
prog::getname Name of an object
prog::getOptions Get and verify options within a procedure
prog::isGlobal Information about reserved identifiers

Debugging

args Access procedure parameters
assert Assertions for debugging
debug Execute a procedure in single-step mode
forceGarbageCollection Force a garbage collection
prog::trace Observe functions
prog::traced Find traced functions
prog::untrace Terminates observation of functions

Code Performance

rtime Measure real time
time Measure CPU time
Pref::maxTime Time limit for computations
prog::ntime Hardware independent time unit
prog::profile Display timing data of nested function calls

Memory Usage

bytes Memory used by the current session
forget Clear the remember table of a procedure
history Access an entry of the history table
Pref::maxMem Set a memory limit for the session
Pref::report Informations during evaluation
prog::remember Extended remember mechanism for procedures

Error Handling

error Raise a user-specified exception
getlasterror Retrieve the last error number and text
lasterror Reproduce the last error
traperror Trap errors
warning Print a warning message

Testing and Code Verification

testargs Decide whether procedure arguments should be tested
prog::check Checking objects
prog::init Loading objects
prog::tcov Report on test coverage (passed program lines)
prog::test Automatic comparing of calculation results
prog::testexit Closing tests
prog::testinit Initialize tests

Custom Functionality Integration

protect Protect an identifier
unprotect Remove protection of identifiers

Object-Oriented Programming

Domains
Domain Operations
extnops Number of operands of the internal representation a domain element
extop Internal operands of a domain element
extsubsop Substitute operands of a domain element
new Create a domain element
newDomain Create a new data type (domain)
slot Method or entry of a domain or a function environment
slotAssignCounter Counts slot assignments

Code Generation

generate::C Generate C formatted string
generate::fortran Generate Fortran formatted string
generate::MathML Generate MathML from expressions
generate::MATLAB Generate MATLAB formatted string
generate::optimize Generate optimized code
generate::Simscape Generate Simscape equation
generate::TeX Generate formatted string from expressions

Notebook Interface

Typeset Math and Other Output Modes

print Print objects to the screen
output::asciiAbbreviate Generates a procedure for creating an ASCII formatted output
output::fence Put delimiters around multiline strings
output::mathText Pretty output of text combined with formulas
output::ordinal Ordinal numbers
output::roman Roman numerals
output::subexpr Abbreviates a expression
output::tableForm Printing objects in table form
output::tree Display of trees
Pref::abbreviateOutput Controls the use of abbreviations in outputs
Pref::output Modify the screen output of objects

Customizations and Preferences

Pref::alias Controls the output of aliased expressions
Pref::autoExpansionLimit Set a limit for automatic expansions
Pref::autoPlot Automatically plot graphical objects
Pref::callBack Informations during evaluation
Pref::ignoreNoDebug Controls debugging of procedures
Pref::keepOrder Order of terms in sum outputs
Pref::userOptions Additional options when starting MuPAD
Pref::heavisideAtOrigin Set value of Heaviside function at origin

Version

buildnumber The Build number of
version Version number of the MuPAD library
Pref::kernel Version number of the presently used kernel
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