# Symbolic Math Toolbox MuPAD Functions

#### 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

### 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
##### 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
##### 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

#### 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

#### 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