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| R2012a Documentation → Symbolic Math Toolbox | |
Learn more about Symbolic Math Toolbox |
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| Contents | Index |
In MuPAD®, most of the provided functions are categorized into libraries and called with a prefix, such as linalg::eigenvalues or numeric::eigenvalues.
For convenience, a number of frequently used functions do not have such a prefix. These include the functions built into the MuPAD kernel such as the constructs of the MuPAD language. The current paper documents these basic functions.
=, <>, ~= – equations, inequalities and approximate equality
- – the negative of an expression
^ – raise an expression to a power
$ – create an expression sequence
%if – conditional creation of code by the parser
abs – the absolute value of a real or complex number
airyAi, airyBi – Airy's functions
alias, unalias – define or delete an abbreviation
anames – identifiers that have values or properties
and, or, not, xor, ==>, <=> – logical operators
append – add elements to a list
arcsin, arccos, arctan, arccsc, arcsec, arccot – the inverse trigonometric functions
arcsinh, arccosh, arctanh, arccsch, arcsech, arccoth – the inverse hyperbolic functions
arg – the argument (polar angle) of a complex number
args – access procedure parameters
array, hfarray – create an array
assert – assertions for debugging
assign – perform assignments given as equations
assignElements – assign values to entries of an array, a list, or a table
assume, assumeAlso – define a property
assuming, assumingAlso – evaluate under assumptions
asympt – compute an asymptotic series expansion
autoload – load an object on demand
bernoulli – Bernoulli numbers and polynomials
besselI, besselJ, besselK, besselY – the Bessel functions
binomial – binomial coefficients
block, blockIdents, blockTransparent, unblock – create an object protected against evaluation
break – terminate a loop or a case switch prematurely
buildnumber – The “build number” of MuPAD
builtin – representatives of C-functions of the MuPAD kernel
bytes – the memory used by the current MuPAD session
card – the cardinality of a set
ceil, floor, round, trunc – rounding to an integer
Ci, Chi – the cosine integral function
coeff – the coefficients of a polynomial
collect – collect terms with the same powers
combine – combine terms of the same algebraic structure
complexInfinity – complex infinity
conjugate – complex conjugation
contains – test if an entry exists in a container
content – the content of a polynomial
context – evaluate an object in the enclosing context
contfrac – the domain of continued fractions
copyClosure – copies the lexical closure of a procedure
D – differential operator for functions
debug – execute a procedure in single-step mode
dedekindEta – the Dedekind eta function
degree – the degree of a polynomial
degreevec – the exponents of the leading term of a polynomial
delete – delete the value of an identifier
denom – the denominator of a rational expression
densematrix – create a matrix or a vector
det – the determinant of a matrix
diff – differentiate an expression or a polynomial
DIGITS – the significant digits of floating point numbers
dilog – the dilogarithm function
dirac – the Dirac delta distribution
discont – discontinuities of a function
div – the integer part of a quotient
divergence – divergence of a vector field
domtype – the data type of an object
doprint – print large matrices
Ei – the exponential integral function
ellipticK, ellipticCK, ellipticF, ellipticE, ellipticCE, ellipticPi, ellipticCPi – elliptic integrals
ellipticNome – the elliptic nome
erf, erfc, erfi, inverf, inverfc – the error function and its relatives
error – raise a user-specified exception
euler – Euler numbers and polynomials
evalassign – assignment with evaluation of the left hand side
evalAt – insert a value (evaluate at a point)
evalp – evaluate a polynomial at a point
exp – the exponential function
expose – display the source code of a procedure or the entries of a domain
expr – convert into an element of a basic domain
expr2text – convert objects into character strings
external – create a module function environment
extnops – the number of operands of the internal representation a domain element
extop – the internal operands of a domain element
extsubsop – substitute operands of a domain element
fact2 – the double factorial function
factor – factor a polynomial into irreducible polynomials
factorout – factor out a given expression
FAIL – indicate a failed computation
FILEPATH – the pathname of a file that is currently loaded
finput – read MuPAD objects from a file
float – convert to a floating point number
forceGarbageCollection – force a garbage collection
forget – clear the remember table of a procedure
frac – the fractional part of a number
frame – create a new frame, change to an existing frame
frandom – generate random floating point numbers
fread – read and execute a file
freeIndets – the free indeterminates of an expression
freeze, unfreeze – create an inactive or active copy of a function
fresnelC, fresnelS – the Fresnel functions
funcenv – create a function environment
gamma, lngamma – the gamma function
gcd – the greatest common divisor of polynomials
gcdex – the extended Euclidean algorithm for polynomials
genident – create an unused identifier
genpoly – create a polynomial using b-adic expansion
getlasterror – retrieve the last error number and text
getpid – the process ID of the running MuPAD kernel
getprop – query properties of expressions
ground – ground term (constant coefficient) of a polynomial
harmonic – the harmonic function
has – check if an object occurs in another object
hastype – test if an object of a specified type occurs in another object
heaviside – the Heaviside step function
hessian – Hessian matrix of a scalar function
HISTORY – the maximal number of elements in the history table
history – access an entry of the history table
hull, ... – convert to a floating point interval
hypergeom – the hypergeometric functions
icontent – the content of a polynomial with rational coefficients
ifactor – factor an integer into primes
igamma – the incomplete Gamma function
igcd – the greatest common divisor of integers and complex numbers with integer real and imaginary parts
igcdex – the extended Euclidean algorithm for two integers
ilcm – the least common multiple of integers
indets – the indeterminates of an expression
indexval – indexed access to arrays and tables without evaluation
infinity – real positive infinity
info – prints short information
input – interactive input of MuPAD objects
int – definite and indefinite integrals
int::addpattern – add patterns for integration
int2text – convert an integer to a character string
interpolate – polynomial interpolation
intersect, minus, union – intersection of sets and/or intervals
interval – convert constant subexpressions to intervals
inverse – the inverse of a matrix
_invert – the reciprocal of an expression
irreducible – test irreducibility of a polynomial
is – check a mathematical property of an expression
ithprime – the 
-th prime number
jacobiAM – Jacobi amplitude function
jacobiSN, jacobiCN, jacobiDN, jacobiCD, jacobiSD, jacobiND, jacobiDC, jacobiNC, jacobiSC, jacobiNS, jacobiDS, jacobiCS – the Jacobian elliptic functions
jacobian – Jacobian matrix of a vector function
jacobiZeta – Jacobian Zeta function
kroneckerDelta – Kronecker's delta symbol
kummerU – the confluent hypergeometric KummerU function
laguerreL – Laguerre polynomials and L function
lambertW – the Lambert function
last – access a previously computed object
lasterror – reproduce the last error
_lazy_and, _lazy_or – “lazy” evaluation of Boolean expressions
lcm – the least common multiple of polynomials
lcoeff – the leading coefficient of a polynomial
ldegree – the lowest degree of the terms in a polynomial
length – the “length” of a MuPAD object (heuristic complexity)
LEVEL – substitution depth of identifiers
level – evaluate an object with a specified substitution depth
lhs, rhs – the left, respectively right hand side of equations, inequalities, relations, intervals, ranges and tables
LIBPATH, PACKAGEPATH, READPATH, WRITEPATH – file search paths
linsolve – solve a system of linear equations
lllint – compute an LLL-reduced basis of a lattice
lmonomial – the leading monomial of a polynomial
loadproc – load an object on demand
log – logarithm to arbitrary base
lterm – the leading term of a polynomial
map – apply a function to all operands of an object
mapcoeffs – apply a function to the coefficients of a polynomial
maprat – apply a function to a rationalized expression
matrix – create a matrix or a vector
MAXDEPTH – prevent infinite recursion during procedure calls
MAXEFFORT – the maximum amount of work to spend on the computation
MAXLEVEL – prevent infinite recursion during evaluation
meijerG – the Meijer G function
mod, modp, mods – the modulo operator
monomials – sorted list of monomials of a polynomial
mtaylor – compute a multivariate Taylor series expansion
multcoeffs – multiply the coefficients of a polynomial with a factor
newDomain – create a new data type (domain)
nextprime – the next prime number
NIL – the singleton element of the domain DOM_NIL
norm – compute the norm of a matrix, a vector, or a polynomial
normal, simplifyFraction – normalize an expression
NOTEBOOKFILE, NOTEBOOKPATH – Notebook file name and path
nterms – the number of terms of a polynomial
nthcoeff – the n-th non-zero coefficient of a polynomial
nthmonomial – the n-th monomial of a polynomial
nthterm – the n-th term of a polynomial
null – generate the void object of type DOM_NULL
numer – the numerator of a rational expression
O – the domain of order terms (Landau symbols)
ode – the domain of ordinary differential equations
op – the operands of an object
operator – define a new operator symbol
ORDER – the default number of terms in series expansions
package – load a package of new library functions
partfrac – compute a partial fraction decomposition
pathname – create a platform dependent path name
pdivide – pseudo-division of polynomials
piecewise – the domain of conditionally defined objects
plot, display – display graphical objects on the screen
plotfunc2d – function plots in 2D
plotfunc3d – function plots in 3D
pochhammer – the Pochhammer symbol
poly2list – convert a polynomial to a list of terms
polylog – the polylogarithm function
potential – the (scalar) potential of a gradient field
powermod – compute a modular power of a number or a polynomial
PRETTYPRINT – control the formatting of output
prevprime – next smaller prime
print – print objects to the screen
product – definite and indefinite products
protect – protect an identifier
protocol – create a protocol of a MuPAD session
psi – the digamma/polygamma function
radsimp, simplifyRadical – simplify radicals in arithmetical expressions
random – generate random integer numbers
rationalize – transform an expression into a rational expression
Re, Im – real and imaginary part of an arithmetical expression
read – search, read, and execute a file
readbytes, writebytes – read and write binary data
repeat, while – “repeat” and “while” loops
rec – the domain of recurrence equations
rectform – rectangular form of a complex expression
rectpulse – rectangular pulse function
reset – re-initialize a MuPAD session
revert – revert polynomials, lists, character strings and tables, invert series expansions
rewrite – rewrite an expression
RootOf – the set of roots of a polynomial
Rule – defining equivalence rules for mathematical expressions
save – save the state of an identifier
series – compute a (generalized) series expansion
setuserinfo – set an information level
share – create a unique data representation
Si, Ssi, Shi – the sine integral function
sign – the sign of a real or complex number
signIm – the sign of the imaginary part of a complex number
simplify – simplify an expression
Simplify – simplify an expression
sin, cos, tan, csc, sec, cot – the trigonometric functions
sinh, cosh, tanh, csch, sech, coth – the hyperbolic functions
slot – method or entry of a domain or a function environment
slotAssignCounter – counts slot assignments
solve – solve equations and inequalities
sqrt – the square root function
strmatch – match a pattern in a character string
subs – substitute into an object
subset – the relation “is a subset of”
subsex – extended substitution
substring – extract a substring from a string
_subtract – subtract expressions
sum – definite and indefinite summation
sum::addpattern – add patterns for definite and indefinite summation
sysname – the name of the operating system
sysorder – compare objects according to the internal order
system – execute a command of the operating system
taylor – compute a Taylor series expansion
tbl2text – concatenate the strings in a table
tcoeff – the trailing coefficient of a polynomial
testargs – decide whether procedure arguments should be tested
testeq – check the mathematical equivalence of expressions
testtype – syntactical type checking
text2expr – convert a character string to an expression
text2int – convert a character string to an integer
text2list, text2tbl – split a character string into a list or table of substrings
textinput – interactive input of text
TEXTWIDTH – the maximum number of characters in an output line
transpose, htranspose – the transpose of a matrix
tripulse – triagular pulse function
TRUE, FALSE, UNKNOWN – Boolean constant TRUE
unassume – delete the properties of an identifier
universe – the set-theoretical universe
unprotect – remove protection of identifiers
use, unuse – use library functions by a short name
userinfo – print progress information
vectorPotential – vector potential of a three-dimensional vector field
version – the version number of the MuPAD library
warning – print a warning message
whittakerM, whittakerW – the Whittaker functions
wrightOmega – the Wright ω function
write – write the values of variables into a file
zeta – the Riemann zeta function
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