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General\intro\Introduction to the Maple language and library Index\index\Index of help descriptions Datatypes\datatypes\Index of descriptions for Maple datatypes *\*\An infix multiplication operator +\+\An infix addition operator .\.\An infix catenation operator used to form names ..\..\An infix range operator <\<\An infix inequality operator <=\<=\Infix less than or equal to operator <>\<>\Infix not equal to operator =\=\Infix equality operator or infix equation generator ^\^\Infix exponentiation operator and\and\Infix logical and operator exprseq\exprseq\Expression sequences - usually used to form lists, sets and function calls float\float\Floating-point numbers and the Float function. fraction\fraction\Fractions, type rational, and type numeric. function\function\Functions. indexed\indexed\Indexed name formed as <name>[ <indexing expressions> ] integer\integer\Integers list\list\Sets and lists not\not\Unary logical negation operator or\or\Infix logical or operator procedure\procedure\Procedures. series\series\Generalized series expansion set\set\Sets and lists string\string\Names and strings table\table\Create a table uneval\uneval\Unevaluated expression formed with ' (unevaluation) quotes Expressions\expressions\Index of descriptions for Maple expressions. !\!\The postfix factorial operator "\"\An abbreviation for the last value computed by Maple. ""\""\An abbreviation for the second last value computed by Maple. """\"""\An abbreviation for the third last value computed by Maple. $\$\Infix expression repetition operator &\&\A neutral operator symbol. This used to indicate user defined infix operators *\*\An infix mulitiplication operator **\**\An infix exponentiation operator (equivalent to ^) +\+\An infix addition operator or prefix identity operator ,\,\Infix expression sequence operator -\-\An infix subtraction operator or a prefix negation operator .\.\An infix catenation operator used to form names. ..\..\An infix range operator. It consists of two or more dots. /\/\An infix division operator <\<\An infix inequality operator <=\<=\Infix less than or equal to operator <>\<>\Infix not equal to operator =\=\Infix equality operator or infix equation generator >\>\Infix greater than operator >=\>=\Infix greater than or equal to operator @\@\Infix composition operator @@\@@\Infix repeated composition operator ^\^\Infix exponentiation operator algebraic\algebraic\Expressions formed using standard algebraic operations and\and\Infix logical and operator arithop\arithop\General arithmetic operations arrays\arrays\Define an n-dimensional array (table indexed by numeric values) boolean\boolean\Expressions which evaluates to true or false concat\concat\Concatenation or dot operator constants\constants\False, gamma, infinity, true, Catalan, E, I, Pi ditto\ditto\The previous expression can be referenced by using the double quote (") symbol as a name. equations\equations\The mathematical relation of equality. expression\expression\A mathematical expression exprseq\exprseq\An expression sequence. These are usually used to form lists, sets and function calls functions\functions\Evaluated or unevaluated function applications indexed\indexed\Indexed name formed as <name>[ <indexing expressions> ] inequalities\inequalities\A mathematical relation. Intersect\Intersect\Set intersection operator lists\lists\Ordered collection of values formed by using enclosing list brackets "[" and "]" minus\minus\Infix set difference operator mod\mod\Computation over the integers modulo "m" names \names \Expressions that behave like names. Also see strings. neutral\neutral\User defined infix operators, generally non-commutative not\not\Unary logical negation operator operators\operators\A general description of the kind of operations available. or\or\Infix logical or operator precedence\precedence\Precedence of Maple operators procedures\procedures\User defined procedures written using the Maple language quotes\quotes\String quotes (`), previous expression ("), or leave unevaluated (') ranges\ranges\Expression ranges selection\selection\Selection operator used to extract a component from an aggregate object series\series\Generalized series expansion sets\sets\An unordered collection of values formed by using set braces "{" and "}" strings\strings\Maple names formed with ` (string) quotes tables\tables\Table data structures indexed either by numeric values or by arbitrary values uneval\uneval\Unevaluated expression formed with ' (unevaluation) quotes union\union\Infix set union operator Procedures\procedures\User defined procedures written using the Maple language Statements\statements\Index of descriptions for Maple statements. assignment\assignment\Associate a name with a Maple expression. break\break\Break out of a repetition (for/while/do) statement by\by\Indicate the step size in a do statement do\do\Repeat statement(s) with iterations controlled by optional for, while, and in clauses done\done\Terminate a Maple session elif\elif\Continuation of a Conditional statement else\else\The final clause of a Conditional statement empty\empty\Empty statement ERROR\ERROR\Error return from a procedure fi\fi\The terminator of an if statement for\for\Repeat a block of statements from\from\Indicate the starting point in a for clause if\if\Conditional statement with optional elif and else clauses next\next\Continue with next iteration of a repetition (for/while/do) statement od\od\The terminating expression of a do statement. quit\quit\Terminate Maple session. "Stop" and "done" are synonyms read\read\Read Maple statements from a file or loads values from a binary Maple file RETURN\RETURN\Explicit return from a procedure save\save\Save selected or all assigned variables along with their values to a file while\while\Conditional loop Tables\tables\Table data structures indexed either by numeric values or by arbitrary values Library\library\Commonly used Maple library functions and procedures $\$\Infix expression repetition operator @\@\Infix composition operator @@\@@\Infix repeated composition operator abs\abs\Absolute value of real or complex argument addressof\addressof\Obtain the address which points to an expression alias\alias\Define an abbreviation or denotation allvalues\allvalues\Evaluate all possible values of expressions involving RootOf's anames\anames\Sequence of assigned names appendto\appendto\Write output to a file in append mode arccos\arccos\Inverse trigonometric cosine function arccosh\arccosh\Inverse hyperbolic cosine function arccot\arccot\Inverse trigonometric cotangent function arccoth\arccoth\Inverse hyperbolic cotangent function arccsc\arccsc\Inverse trigonometric cosecant function arccsch\arccsch\Inverse hyperbolic cosecant function arcsec\arcsec\Inverse trigonometric secant function arcsech\arcsech\Inverse hyperbolic secant function arcsin\arcsin\Inverse trigonometric sine function arcsinh\arcsinh\Inverse hyperbolic sine function arctan\arctan\Inverse trigonometric tangent function arctanh\arctanh\Inverse hyperbolic tangent function array\array\Create an array assemble\assemble\Assemble a sequence of addresses into an object assign\assign\Perform assignments assigned\assigned\Check if a name is assigned asympt\asympt\Asymptotic expansion bernoulli\bernoulli\Bernoulli numbers and polynomials BesselI\BesselI\Modified Bessel function of the first kind I(v,x) BesselJ\BesselJ\Bessel function of the first kind J(v,x) BesselK\BesselK\Modified Bessel function of the second kind K(v,x) BesselY\BesselY\Bessel function of the second kind Y(v,x) Beta\Beta\Beta function: Beta(x,y) = GAMMA(x)*GAMMA(y)/GAMMA(x+y) binomial\binomial\Binomial coefficients cat\cat\Concatenating expressions chebyshev\chebyshev\Chebyshev series expansion chrem\chrem\Chinese Remainder Algorithm Ci\Ci\Cosine integral = gamma + ln(x) + int( (cos(t) 1)/t, t=0..x) coeff\coeff\Extract a coefficient of a polynomial coeffs\coeffs\Extract all coefficients of a multivariate polynomial collect\collect\Collect coefficients of like powers combine\combine\Combine terms into a single term exp\combine,exp\Combine exponentials ln\combine,ln\Combine logarithmic terms power\combine,power\Combine terms with powers Psi\combine,Psi\Combine Psi functions trig\combine,trig\Combine trigonometric terms compoly\compoly\Determine a possible composition of a polynomial content\content\Content of a multivariate polynomial Content\Content\Inert content function convert\convert\Convert an expression to a different form +\convert,+\Convert to sum *\convert,*\Convert to product array\convert,array\Convert to array base\convert,base\Convert between bases binary\convert,binary\Convert to binary form confrac\convert,confrac\Convert to continued-fraction form D\convert,D\Convert expressions involving derivatives to use the D operator decimal\convert,decimal\Convert to base 10 degrees\convert,degrees\Convert radians to degrees diff\convert,diff\Convert an expression of the form D(f)(x) to diff(f(x),x) double\convert,double\Convert a double precision floating point number from one format to another eqnlist\convert,eqnlist\Convert to a list of equations equality\convert,equality\Convert relations to equalities GAMMA\convert,GAMMA\Convert factorials and binomials to GAMMAs lessthan\convert,lessthan\Converts relations to `<` form lessequal\convert,lessequal\Converts relations to `<=` form exp\convert,exp\Convert trig functions to exponentials expln\convert,expln\Convert elementary functions to exp and ln expsincos\convert,expsincos\Convert trig functions to exp, sin, cos factorial\convert,factorial\Convert GAMMAs and binomials to factorials float\convert,float\Convert to floating-point hex\convert,hex\Convert to hexadecimal form horner\convert,horner\Convert a polynomial to Horner form hostfile\convert,hostfile\Convert Maple filename to host filename hypergeom\convert,hypergeom\Convert summations to hypergeometrics list\convert,list\Convert to a list listlist\convert,listlist\Convert to a list of lists ln\convert,ln\Convert arctrig functions to logarithms mathorner\convert,mathorner\Convert a polynomial to matrix Horner form matrix\convert,matrix\Convert an array or a list of lists to a matrix metric\convert,metric\Convert to metric units mod2\convert,mod2\Convert expression to mod 2 form multiset\convert,multiset\Convert to a multiset string\convert,string\Convert an expression to a string (name) name\convert,name\A synonym for convert,string octal\convert,octal\Convert to octal form parfrac\convert,parfrac\Convert to partial fraction form polar\convert,polar\Convert to polar form polynom\convert,polynom\Convert a series to polynomial form radians\convert,radians\Convert degrees to radians radical\convert,radical\Convert RootOf to radicals and I rational\convert,rational\Convert float to an approximate rational ratpoly\convert,ratpoly\Convert series to a rational polynomial RootOf\convert,RootOf\Convert radicals and I to RootOf notation series\convert,series\Convert to series set\convert,set\Convert to a set sincos\convert,sincos\Convert trig functions to sin, cos, sinh, cosh sqrfree\convert,sqrfree\Convert to square-free form tan\convert,tan\Convert trig function to tan trig\convert,trig\Convert all exponentials to trigonometric and hyperbolic trigonometric functions vector\convert,vector\Convert a list or an array to a Maple vector copy\copy\Create a duplicate array or table cos\cos\Trigonometric cosine function cosh\cosh\Hyperbolic cosine function cot\cot\Trigonometric cotangent function coth\coth\Hyperbolic cotangent function csc\csc\Trigonometric cosecant function csch\csch\Hyperbolic cosecant function D\D\Differential operator define\define\Define characteristics of an operator name forall\define,forall\Define a property for an operator group \define,group\Define characteristics of a group operator linear\define,linear\Define characteristics of a linear operator operator\define,operator\Define an operator by a list of properties degree\degree\Degree of a polynomial denom\denom\Denominator of an expression Det\Det\Inert determinant Diff\Diff\Partial differentiation diff\diff\Partial differentiation dilog\dilog\Dilogarithm integral = int( ln(t)/(1-t), t=1..x ) disassemble\disassemble\Break an object into its component addresses. discrim\discrim\Discriminant of a polynomial DistDeg\DistDeg\Distinct degree factorization divide\divide\Exact polynomial division Divide\Divide\Inert divide function dsolve\dsolve\Solve ordinary differential equations dsolve/numeric\dsolve,numeric\Numeric solution of ordinary differential equations Ei\Ei\Exponential integral = int( exp(t)/t, t= -infinity..x ) Eigenvals\Eigenvals\Compute the eigenvalues/vectors of a numeric matrix entries\entries\Entries of a table or array eqn\eqn\Produce output suitable for troff/eqn printing erf\erf\Error function = 2/sqrt(Pi) * int( exp(-t^2), t=0..x ) ERROR\ERROR\Error return from a procedure euler\euler\Euler numbers and polynomials Eval\Eval\Evaluate a polynomial eval\eval\Explicit evaluation evala\evala\Evaluate in an algebraic number field evalb\evalb\Evaluate as a boolean expression evalc\evalc\Evaluate in the complex number field evalc/polar\evalc,polar\Evaluate in the complex number field in polar form evalf\evalf\Evaluate using floating-point arithmetic evalf/hypergeom\evalf,hypergeom\Evaluate generalized hypergeometric function evalhf\evalhf\Evaluate an expression using hardware floating-point array\evalhf,array\Handling of arrays boolean\evalhf,boolean\Boolean expressions constant\evalhf,constant\Constants known to evalhf fcnlist\evalhf,fcnlist\List of functions handled fortran\evalhf,fortran\Evalhf's relation to Fortran function\evalhf,function\Handling of Maple functions var\evalhf,var\Passing arrays by value,result; var(name) evalm\evalm\Evaluate over the matrices evaln\evaln\Evaluate to a name example\example\Produce an example of a function or type exp\exp\The exponential function: exp(x) = sum(x^i/i!,i=0..infinity) expand\expand\Expand an expression Expand\Expand\Inert expand function factor\factor\Factor a multivariate polynomial Factor\Factor\Inert factor function factorial\factorial\The factorial function factorial(n) = n! Factors\Factors\Inert factors function fnormal\fnormal\Floating-point normalization fortran\fortran\Generate Fortran code frac\frac\Fractional part of a number FresnelC\FresnelC\Fresnel cosine integral = int( cos(Pi/2*t^2), t = 0..x ) FresnelS\FresnelS\Fresnel sine integral = int( sin(Pi/2*t^2), t = 0..x ) frontend\frontend\Process general expression into a rational expression fsolve\fsolve\Solve using floating-point arithmetic galois\galois\Compute the Galois group of an irreducible polynomial GAMMA\GAMMA\The gamma function GAMMA(z) = int( exp(-t)*t^(z-1), t=0..infinity ) and the incomplete Gamma function GAMMA(a,x) = int( exp(-t)*t^(a-1), t=x..infinity ) gc\gc\Garbage collection gcd\gcd\Greatest common divisor of polynomials Gcd\Gcd\Inert gcd function gcdex\gcdex\Extended Euclidean algorithm for polynomials Gcdex\Gcdex\Inert gcdex function genpoly\genpoly\Generate polynomial from integer n by Z-adic expansion has\has\Test for a specified subexpression hastype\hastype\Test for a specified type help\help\Descriptions of syntax, datatypes, and functions Hermite\Hermite\Compute the Hermite normal form of a matrix mod p icontent\icontent\Integer content of a polynomial if\if\Conditional statement with optional elif and else clauses ifactor\ifactor\Integer factorization igcd\igcd\Greatest common divisor of integers igcdex\igcdex\Extended Euclidean algorithm for integers ilcm\ilcm\Least common multiple of integers indets\indets\Find indeterminates of an expression indices\indices\Indices of a table or array Int\Int\Definite and indefinite integration int\int\Definite and indefinite integration int/series\int,series\Integration of a series structure interface\interface\Set or query user interface variables Interp\Interp\Inert interp function interp\interp\Polynomial interpolation intersect\intersect\Set intersection operator iquo\iquo\Integer quotient irem\irem\Integer remainder Irreduc\Irreduc\Inert irreducibility function irreduc\irreduc\Polynomial irreducibility test isolve\isolve\Solve equations for integer solutions isprime\isprime\Primality test isqrt\isqrt\Integer square root ithprime\ithprime\Determine the i'th prime laplace\laplace\Laplace transform latex\latex\Produce output suitable for latex printing functions\latex,functions\How latex formats functions names\latex,names\How latex formats names lcm\lcm\Least common multiple of polynomials lcoeff\lcoeff\Leading coefficient of a multivariate polynomial ldegree\ldegree\Low degree of a polynomial leadterm\leadterm\Find the leading term of a series expansion length\length\Length of an object lexorder\lexorder\Test for lexicographical order lhs\lhs\Left hand side of an expression limit\limit\Calculate limits dir\limit,dir\Directional limits multi\limit,multi\Multidirectional limits return\limit,return\Values returned by limit Limit \Limit\Inert form of limit ln\ln\Natural logarithm (logarithm with base E = 2.71828...) log\log\Initially assigned the name ln. Typically, the user assigns to this a function that computes logarithms to some other base. lprint\lprint\Linear printing of expression macro\macro\Define an macro abbreviation map\map\Apply a procedure to each operand of an expression match\match\Pattern matching max\max\Maximum of numbers maxnorm\maxnorm\Infinity norm of a polynomial MeijerG\MeijerG\Special case of the general Meijer G function mellin\mellin\Mellin transform member\member\Test for membership in a set or list min\min\Minimum of numbers minus\minus\Infix set difference operator modp\modp\Computation over the integers modulo "m" modp1\modp1\Univariate polynomial arithmetic modulo n mods\mods\Computation over the integers modulo "m" msolve\msolve\Solve equations in Z mod m nextprime\nextprime\Determine the next largest prime nops\nops\The number of operands of an expression norm\norm\Norm of a polynomial Normal\Normal\Inert normal function normal\normal\Normalize a rational expression Nullspace\Nullspace\Compute the nullspace of a matrix mod p numer\numer\Numerator of an expression op\op\Extract operands from an expression order\order\Determine the truncation order of a series plot\plot\Create a 2-dimensional plot of functions plot3d\plot3d\Three-dimensional plotting plotsetup\plotsetup\Set up appropriate parameters for plotting pointto\pointto\Obtain the expression pointed to by an address Power\Power\Inert power function Powmod\Powmod\Inert power function with remainder Prem\Prem\Inert prem function prem\prem\Pseudo-remainder of polynomials prevprime\prevprime\Determine the next smallest prime Primitive\Primitive\Test whether a polynomial is primitive mod p Primpart\Primpart\Inert primitive part function. primpart\primpart\Primitive part of a multivariate polynomial print\print\Pretty-printing of expressions product\product\Definite and indefinite product Product\Product\Inert form of product. Psi\Psi\Polygamma function Psi(x) = diff( ln(GAMMA(x)), x ) and its derivatives Psi(n,x) = diff(Psi(x),x$n) Quo\Quo\Inert quo function. quo\quo\Quotient of polynomials radsimp\radsimp\Simplification of an expression containing radicals rand\rand\Random number generator randpoly\randpoly\Random polynomial generator Randpoly\Randpoly\Random polynomial over a finite field readlib\readlib\Read a library file to define a specified name readstat\readstat\Read one statement from the input stream Rem\Rem\Inert rem function rem\rem\Remainder of polynomials resultant\resultant\Compute the resultant of two polynomials Resultant\Resultant\Inert resultant function RETURN\RETURN\Explicit return from a procedure rhs\rhs\Right hand side of an expression RootOf\RootOf\A representation for roots of equations Roots\Roots\Roots of a polynomial mod n roots\roots\Roots of a univariate polynomial round\round\Round a number to an integer rsolve\rsolve\Recurrence equation solver sec\sec\Trigonometric secant function sech\sech\Hyperbolic secant function select\select\Selection from a list, set, sum, or product seq\seq\Create a sequence series\series\Generalized series expansion series/leadterm\series,leadterm\Find the leading term of a series expansion Si\Si\Sine integral = int( sin(t)/t, t=0..x ) sign\sign\Sign of a number or a polynomial signum\signum\Sign function for real and complex expressions simplify\simplify\Apply simplification rules to an expression atsign\simplify,atsign\Simplify expressions involving operators GAMMA\simplify,GAMMA\Simplifications involving the GAMMA function hypergeom\simplify,hypergeom\Simplify hypergeometric expressions power\simplify,power\Simplify powers radical\simplify,radical\Simplify expressions with radicals RootOf\simplify,RootOf\Simplify expressions with the RootOf function siderels\simplify,siderels\Simplify with respect to side relations sqrt\simplify,sqrt\Simplify square roots trig\simplify,trig\Simplify trigonometric expressions sin\sin\Trigonometric sine function sinh\sinh\Hyperbolic sine function Smith\Smith\Compute the Smith normal form of a matrix mod p solve\solve\Solve equations floats\solve,floats\Expressions involving floating-point numbers functions\solve,functions\For a variable which is used as a function name identity\solve,identity\Expressions involving identities ineqs\solve,ineqs\Inequalities linear\solve,linear\Systems of linear equations radical\solve,radical\Expressions involving radicals of unknowns scalar\solve,scalar\Scalar case (a single variable and equation) series\solve,series\Expressions involving general series system\solve,system\Systems of equations, multiple equations or unknowns sort\sort\Sort a list of values or a polynomial Sprem\Sprem\Inert sprem function sprem\sprem\Sparse pseudo-remainder of polynomials Sqrfree\Sqrfree\Inert square free factorization function sqrt\sqrt\Square root subs\subs\Substitute subexpressions into an expression subsop\subsop\Substitute for specified operands in an expression substring\substring\Extract a substring from a string sum\sum\Definite and indefinite summation Sum\Sum\Inert form of summation Svd\Svd\Compute the singular values/vectors of a numeric matrix system\system\Invoke a command in the host operating system table\table\Create a table tan\tan\Trigonometric tangent function tanh\tanh\Hyperbolic tangent function taylor\taylor\Taylor series expansion tcoeff\tcoeff\Trailing coefficient of a multivariate polynomial testeq\testeq\Random polynomial-time equivalence tester time\time\Total CPU time used for the session trace\trace\Trace procedures in order to debug them traperror\traperror\Trap an error condition trunc\trunc\Truncate a number to an integer type\type\Type-checking function .\type,.\Check for an expression of type `.` algebraic\type,algebraic\Check for an algebraic expression algext\type,algext\Check for an algebraic extension algfun\type,algfun\Check for an algebraic function algnum\type,algnum\Check for an algebraic number algnumext\type,algnumext\Check for an algebraic number extension anything\type,anything\Check for any type array\type,array\Check for an array boolean\type,boolean\Check for type Boolean constant\type,constant\Check for a constant cubic\type,cubic\Check for cubic functions even\type,even\Check for an even integer evenfunc\type,evenfunc\Check for an even function expanded\type,expanded\Check for an expanded polynomial facint\type,facint\Test for factored integer form float\type,float\Check for an object of type float fraction\type,fraction\Check for an object of type fraction integer\type,integer\Check for an integer laurent\type,laurent\Check for Laurent series linear\type,linear\Check for linear functions list\type,list\Check for a list listlist\type,listlist\Check for a list of lists logical\type,logical\Check for type logical mathfunc\type,mathfunc\Check for mathematical functions matrix\type,matrix\Check for a matrix monomial\type,monomial\Check for a monomial negative\type,negative\Check for a negative number negint\type,negint\Check for a negative integer nonneg\type,nonneg\Check for a non-negative number nonnegint\type,nonnegint\Check for a non-negative integer numeric\type,numeric\Check for an object of type numeric odd\type,odd\Check for an odd integer oddfunc\type,oddfunc\Check for an odd function operator\type,operator\Check for a functional operator PLOT\type,PLOT\Check for a PLOT data structure PLOT3D\type,PLOT3D\Check for a PLOT3D data structure point\type,point\Check for a point polynom\type,polynom\Check for a polynomial posint\type,posint\Check for a positive integer positive\type,positive\Check for a positive number primeint\type,primeint\Check for a prime integer quadratic\type,quadratic\Check for quadratic functions quartic\type,quartic\Check for quartic functions radext\type,radext\Check for an algebraic extension in terms of radicals radfun\type,radfun\Check for a radical function radfunext\type,radfunext\Check for a radical function extension radical\type,radical\Check for fractional powers radnum\type,radnum\Check for an algebraic number in terms of radicals radnumext\type,radnumext\Check for a radical number extension range\type,range\Check for a range rational\type,rational\Check for an object of type rational ratpoly\type,ratpoly\Check for a rational polynomial realcons\type,realcons\Check for a real constant relation\type,relation\Check for type relation scalar\type,scalar\Check for scalar (in the matrix sense) set\type,set\Check for a set sqrt\type,sqrt\Check for a square root square\type,square\Check for a perfect square taylor\type,taylor\Check for Taylor series trig\type,trig\Check for trigonometric functions type\type,type\Check for type expressions vector\type,vector\Check for vector (one-dimensional array) unames\unames\Sequence of unassigned names unapply\unapply\Returns an operator from an expression and arguments union\union\Infix set union operator userinfo\userinfo\Print useful information to the user whattype\whattype\Query the basic data type of an expression with\with\Define the names of functions from a library package words\words\Query memory usage (words used) writeto\writeto\Write output to a file Zeta\Zeta\Riemann zeta function Zeta(s) = sum(1/i^s,i=1..infinity), its derivatives Zeta(n,s) = diff(Zeta(s),s$n), and with 3 arguments Zeta(n,s,q) = diff(Zeta(0,s,q),s$n) where Zeta(0,s,q) = sum(1/(i+q)^s,i=1..infinity) zip\zip\Zip together two lists or vectors ztrans\ztrans\Z transform Miscellaneous\libmisc\Miscellaneous Maple library procedures atatsign\atatsign\The repeated composition operator atsign\atsign\The composition operator bernstein\bernstein\Bernstein polynomial approximating a function bianchi\bianchi\Find the Bianchi type of any 3-dimensional Lie algebra bspline\bspline\Compute the B-spline segment polynomials C\C\Generate C code cartan\cartan\Compute connection and curvature using Cartan's structure equations coeftayl\coeftayl\Coefficient of (multivariate) expression commutat\commutat\Commutator routines convergs\convergs\Print convergents of continued fraction cost\cost\Operation evaluation count debever\debever\Newman-Penrose spin and curvature using Debever's formalism dinterp\dinterp\Probabilistic degree interpolation Dirac\Dirac\The Dirac delta function edit\edit\Expression editor ellipsoid\ellipsoid\Surface area of an ellipsoid erfc\erfc\Complementary error function = 1-erf(x) eulermac\eulermac\Euler-Maclaurin summation evalgf\evalgf\Evaluate in an algebraic extension of a finite field evalr\evalr\Evaluate an expression using range arithmetic extrema\extrema\Find relative extrema of an expression factors\factors\Factor a multivariate polynomial FFT\FFT\Fast Fourier transform finance\finance\Amount, interest, payment, or periods fixdiv\fixdiv\Compute the fixed divisor of a polynomial forget\forget\Remove an entry or entries from a remember table freeze\freeze\Replace an expression by a name Functions\Functions\Maple functions GF\GF\Galois Field Package heap\heap\Priority Queue Data Structure Heaviside\Heaviside\The Heaviside step function history\history\Maintain a history of all values computed hypergeom\hypergeom\Generalized hypergeometric function ifactors\ifactors\Integer factorization invlaplace\invlaplace\Inverse Laplace transform invztrans\invztrans\Inverse Z transform iratrecon\iratrecon\Rational reconstruction iroot\iroot\Integer n-th root iscont\iscont\Test continuity on an interval isolate\isolate\Isolate a subexpression to left-side of an equation isqrfree\isqrfree\Integer square free factorization issqr\issqr\Test if an integer is a perfect square lattice\lattice\Find a reduced basis of a lattice minimize\minimize\Compute the minimum minpoly\minpoly\Find minimum polynomial with an approximate root modpol\modpol\Expression evaluation in a quotient field MOLS\MOLS\Mutually orthogonal Latin squares mtaylor\mtaylor\Multivariate Taylor series expansion oframe\oframe\Orthonormal tetrads in the Ellis-MacCallum formalism optimize\optimize\Common subexpression optimization petrov\petrov\Finds the Petrov classification of the Weyl tensor poisson\poisson\Poisson series expansion priqueue\priqueue\Priority Queue Functions procbody\procbody\Create a ``neutralized form'' of a procedure procmake\procmake\Create a Maple procedure profile\profile\Space & time profile of a proc proot\proot\N-th root of a polynomial psqrt\psqrt\Square root of a polynomial realroot\realroot\Isolating intervals for real roots of a polynomial recipoly\recipoly\Determine whether a polynomial is self-reciprocal residue\residue\Compute the algebraic residue of an expression search\search\Substring search shake\shake\Compute a bounding interval showtime\showtime\Display time and space statistics for commands singular\singular\Find singularities of an expression sinterp\sinterp\Sparse multivariate modular polynomial interpolation sqrfree\sqrfree\Convert to square-free form sturm\sturm\Number of real roots of a polynomial in an interval tensor\tensor\Compute curvature tensors in a coordinate basis thiele\thiele\Thiele's continued fraction interpolation formula translate\translate\Linear translation of a polynomial trigsubs\trigsubs\Handling trigonometric identities unassign\unassign\Unassign names W\W\The function satisfying W(x) * exp(W(x)) = x write\write\Buffered output Packages\packages\Index of descriptions for packages of library functions combinat\combinat\Introduction to the "combinat" package bell\combinat,bell\Compute Bell numbers binomial\combinat,binomial\Binomial coefficients cartprod\combinat,cartprod\Iterate over a list of lists character\combinat,character\Compute character table for a symmetric group Chi\combinat,Chi\Compute Chi function for partitions of a symmetry group combine\combinat,combine\Construct the combinations of a list composition\combinat,composition\K-compositions of an integer decodepart\combinat,decodepart\Compute canonical partition represented by integer encodepart\combinat,encodepart\Compute canonical integer representing partition fibonacci\combinat,fibonacci\Compute Fibonacci numbers or polynomials firstpart\combinat,firstpart\First partition in canonical partition sequence inttovec\combinat,inttovec\Vector referenced by integer in canonical ordering lastpart\combinat,lastpart\Last partition in canonical partition sequence multinomial\combinat,multinomial\Compute the multinomial coefficients nextpart\combinat,nextpart\Next partition in canonical partition sequence numbcomb\combinat,numbcomb\Count the number of combinations numbcomp\combinat,numbcomp\The number of k-compositions of an integer numbpart\combinat,numbpart\The number of partitions of an integer numbperm\combinat,numbperm\Count the number of permutations partition\combinat,partition\Partition an integer permute\combinat,permute\Construct the permutations of a list powerset\combinat,powerset\Construct the power set of a set prevpart\combinat,prevpart\Previous partition in canonical partition sequence randcomb\combinat,randcomb\Construct a random combination randpart\combinat,randpart\Construct a random partition randperm\combinat,randperm\Construct a random permutation stirling1\combinat,stirling1\Stirling numbers of the first kind stirling2\combinat,stirling2\Stirling numbers of the second kind subsets\combinat,subsets\Iterate over the power set of a set or list vectoint\combinat,vectoint\Index of vector in canonical ordering difforms\difforms\Introduction to the "difforms" package &^\difforms,&^\Wedge product of differential forms d\difforms,d\Exterior differentiation defform\difforms,defform\Define a constant, scalar, or form formpart\difforms,formpart\Find part of an expression which is a form mixpar\difforms,mixpar\Ensure equality of mixed partial derivatives parity\difforms,parity\Extension of mod 2 scalarpart\difforms,scalarpart\Find part of an expression which is a scalar simpform\difforms,simpform\Simplify an expression involving forms wdegree\difforms,wdegree\Degree of a form geom3d\geom3d\Introduction to the "geom3d" package angle\geom3d,angle\Find angle between two lines, two planes, or a line and plane area\geom3d,area\Compute the area of a triangle or the surface of a sphere are_collinear\geom3d,are_collinear\Test if three points are collinear are_concurrent\geom3d,are_concurrent\Test if three lines are concurrent are_parallel\geom3d,are_parallel\Test if lines or planes are parallel are_perpendicular\geom3d,are_perpendicular\Test if lines or planes are perpendicular are_tangent\geom3d,are_tangent\Test if a line, plane, or sphere and a sphere are tangent center\geom3d,center\Find the center of a given sphere centroid\geom3d,centroid\Compute the centroid tetrahedron, triangle, or point list coordinates\geom3d,coordinates\Return the coordinates of a given point coplanar\geom3d,coplanar\Test if four points or two lines are coplanar distance\geom3d,distance\Distance between two points, two lines, or a point and a line inter\geom3d,inter\Find the intersections between two lines or planes midpoint\geom3d,midpoint\Find the midpoint of the segment joining 2 points onsegment\geom3d,onsegment\Find the point which divides a segment in a given ratio on_plane\geom3d,on_plane\Test if a point or a list or set of points are on a plane on_sphere\geom3d,on_sphere\Test if a point or a list or set of points are on a sphere parallel\geom3d,parallel\Find a parallel plane or line going through a given point perpendicular\geom3d,perpendicular\Find perpendicular plane or line going through a point powerps\geom3d,powerps\Power of a given point with respect to a given sphere projection\geom3d,projection\Find projection of a given point or line on a line or plane radius\geom3d,radius\Compute the radius of a given sphere rad_plane\geom3d,rad_plane\Find the radical plane of two given sphere reflect\geom3d,reflect\Find reflection of a given point or line in a line or plane sphere\geom3d,sphere\Define a sphere symmetric\geom3d,symmetric\Find the symmetric point of a point with respect to a point tangent\geom3d,tangent\Find the tangent plane of a point on a given sphere tetrahedron\geom3d,tetrahedron\Define a tetrahedron triangle3d\geom3d,triangle3d\Define the triangles in three-dimensional space volume\geom3d,volume\Compute the volume of a tetrahedron or a sphere geometry\geometry\Introduction to the "geometry" package altitude\geometry,altitude\Find the altitude of a given triangle Appolonius\geometry,Appolonius\Find the Appolonius circles of three given circles. area\geometry,area\Compute the area of a triangle, square, or circle are_collinear\geometry,are_collinear\Test if three points are collinear are_concurrent\geometry,are_concurrent\Test if three lines are concurrent are_harmonic\geometry,are_harmonic\Test if pair of points is harmonic conjugate to another are_orthogonal\geometry,are_orthogonal\Test if two circles are orthogonal to each other are_parallel\geometry,are_parallel\Test if two lines are parallel to each other are_perpendicular\geometry,are_perpendicular\Test if two lines are perpendicular to each other are_similar\geometry,are_similar\Test if two triangles are similar are_tangent\geometry,are_tangent\Test if a line and a circle or two circles are tangent bisector\geometry,bisector\Find the bisector of a given triangle center\geometry,center\Find the center of a given circle centroid\geometry,centroid\Centroid of a triangle, set, or list of points on a plane circumcircle\geometry,circumcircle\Find the circumcircle of a given triangle conic\geometry,conic\Find the conic going through five points convexhull\geometry,convexhull\Find convex hull enclosing the given points coordinates\geometry,coordinates\Compute the coordinates of a given point detailf\geometry,detailf\Floating-point information about points, circles, and lines. diameter\geometry,diameter\Compute the diameter of a given set or list of points distance\geometry,distance\Find the distance between two points or a point and a line ellipse\geometry,ellipse\Define the ellipse Eulercircle\geometry,Eulercircle\Find the Euler circle of a given triangle Eulerline\geometry,Eulerline\Find the Euler line of a given triangle excircle\geometry,excircle\Find three excircles of a given triangle find_angle\geometry,find_angle\Find the angle between two lines or two circles Gergonnepoint\geometry,Gergonnepoint\Find the Gergonne point of a given triangle harmonic\geometry,harmonic\Find a point which is harmonic conjugate to two others incircle\geometry,incircle\Find the incircle of a given triangle inter\geometry,inter\Find the intersections between two lines and/or circles inversion\geometry,inversion\Inversion of a point, line, or circle wrt a given circle is_equilateral\geometry,is_equilateral\Test if a given triangle is equilateral is_right\geometry,is_right\Test if a given triangle is a right triangle make_square\geometry,make_square\Construct squares median\geometry,median\Find the median of a given triangle midpoint\geometry,midpoint\Find the midpoint of the segment joining two points Nagelpoint\geometry,Nagelpoint\Find the Nagel point of a given triangle onsegment\geometry,onsegment\Find the point which divides a segment in a given ratio on_circle\geometry,on_circle\Test if a point, a list or set of points lies on a circle on_line\geometry,on_line\Test if a point, a list or a set of points lies on a line orthocenter\geometry,orthocenter\Compute orthocenter of a triangle, set, or point list parallel\geometry,parallel\Find line through a point parallel to another line perpendicular\geometry,perpendicular\Find line through point perpendicular to another line perpen_bisector\geometry,perpen_bisector\Find perpendicular bisector of a line polar_point\geometry,polar_point\Polar-line of a point with respect to a circle or conic pole_line\geometry,pole_line\Pole of a given line with respect to a circle or conic powerpc\geometry,powerpc\Power of a given point with respect to a given circle projection\geometry,projection\Find the projection of a given point on a given line radius\geometry,radius\Compute the radius of a given circle rad_axis\geometry,rad_axis\Find the radical axis of two given circles rad_center\geometry,rad_center\Find the radical center of three given circles randpoint\geometry,randpoint\Find a random point on a line or a circle reflect\geometry,reflect\Find the reflection of a given point with respect to a line rotate\geometry,rotate\Find point of rotation of a point with respect to a point sides\geometry,sides\Compute the sides of a given triangle or a given square similitude\geometry,similitude\Find the insimilitude and outsimilitude of two circles Simsonline\geometry,Simsonline\Find the Simson line of a given triangle with respect... square\geometry,square\Define the squares symmetric\geometry,symmetric\Find the symmetric point of a point with respect a point tangent\geometry,tangent\Find the tangents of a point with respect to a circle tangentpc\geometry,tangentpc\Find the tangent of a point on a circle grobner\grobner\Introduction to the "grobner" package finduni\grobner,finduni\Find smallest univariate polynomial in ideal generated by... finite\grobner,finite\Decide if algebraic system has (at most) finitely many sol'ns gbasis\grobner,gbasis\Compute reduced, minimal Grobner basis gsolve\grobner,gsolve\Prepare the given algebraic system for solving leadmon\grobner,leadmon\Compute the leading monomial of a polynomial normalf\grobner,normalf\Reduced form of a polynomial modulo an ideal solvable\grobner,solvable\Decide if given algebraic system is solvable spoly\grobner,spoly\Compute the S polynomial of two polynomials group\group\Introduction to the "group" package centralizer\group,centralizer\Find the centralizer of a set of permutations cosets\group,cosets\Find a complete list of right coset representatives cosrep\group,cosrep\Element as product of subgroup element and right coset rep groupmember\group,groupmember\Test if a permutation is in a given group grouporder\group,grouporder\Compute the order of a group inter\group,inter\Find the intersection of two permutation groups invperm\group,invperm\Find inverse of a permutation isnormal\group,isnormal\Determine whether a subgroup is normal mulperms\group,mulperms\Multiply two permutations in disjoint cycle notation normalizer\group,normalizer\Find the normalizer of a subgroup permrep\group,permrep\Find a permutation representation of a group pres\group,pres\Find a presentation for a subgroup of a group liesymm\liesymm\Introduction to the "liesymm" package &mod\liesymm,&mod\Reduce a form modulo an exterior ideal &^\liesymm,&^\Wedge product of differential forms annul\liesymm,annul\Annul a set of differential forms close\liesymm,close\Compute the closure of a set of differential forms d\liesymm,d\The exterior derivative determine\liesymm,determine\Find the determining equations for the isovectors of a pde getcoeff\liesymm,getcoeff\Extract the coefficient part of a basis wedge product getform\liesymm,getform\Extracts the basis element of a single wedge product hasclosure\liesymm,hasclosure\Verify closure with respect to d() hook\liesymm,hook\Inner product (hook) Lie\liesymm,Lie\The Lie derivative Lrank\liesymm,Lrank\The Lie Rank of a set of forms makeforms\liesymm,makeforms\Construct a set of differential forms from a pde mixpar\liesymm,mixpar\Order the mixed partials setup\liesymm,setup\Define the coordinates value\liesymm,value\Force evaluation of derivatives wcollect\liesymm,wcollect\Regroup the terms as a sum of products wdegree\liesymm,wdegree\Compute the wedge degree of a form wedgeset\liesymm,wedgeset\Find the coordinate set wsubs\liesymm,wsubs\Replace part of a wedge product linalg\linalg\Introduction to the "linalg" package add\linalg,add\Matrix or vector addition addcol\linalg,addcol\Form linear combinations of matrix columns addrow\linalg,addrow\Form linear combinations of matrix rows adj\linalg,adj\Compute the adjoint of a matrix adjoint\linalg,adjoint\Compute the adjoint of a matrix angle\linalg,angle\Compute the angle between vectors augment\linalg,augment\Join two or more matrices together horizontally backsub\linalg,backsub\Back substitution on a matrix band\linalg,band\Create a band matrix basis\linalg,basis\Find a basis for a vector space bezout\linalg,bezout\Create the Bezout matrix of two polynomials BlockDiagonal\linalg,BlockDiagonal\Create a block diagonal matrix charmat\linalg,charmat\Construct the characteristic matrix charpoly\linalg,charpoly\Compute the characteristic polynomial of a matrix col\linalg,col\Extract column(s) of a matrix as vectors(s) coldim\linalg,coldim\Determine the column dimension of a matrix colspace\linalg,colspace\Compute a basis for the column space colspan\linalg,colspan\Compute spanning vectors for the column space companion\linalg,companion\Return a companion matrix associated with a polynomial concat\linalg,concat\Join two or more matrices together horizontally cond\linalg,cond\Condition number of a matrix copyinto\linalg,copyinto\Move entries from one matrix into another crossprod\linalg,crossprod\Vector cross product curl\linalg,curl\Curl of a vector definite\linalg,definite\Test for positive (negative) definite matrices delcols\linalg,delcols\Delete columns of a matrix delrows\linalg,delrows\Delete rows of a matrix det\linalg,det\Determinant of a matrix diag\linalg,diag\Create a block diagonal matrix diverge\linalg,diverge\Compute the divergence of a vector function dotprod\linalg,dotprod\Vector dot (scalar) product eigenvals\linalg,eigenvals\Compute the eigenvalues of a matrix eigenvects\linalg,eigenvects\Find the eigenvectors of a matrix equal\linalg,equal\Determine whether two matrices are equal exponential\linalg,exponential\Matrix exponential extend\linalg,extend\Enlarge a matrix ffgausselim\linalg,ffgausselim\Fraction-free Gaussian elimination on a matrix fibonacci\linalg,fibonacci\Fibonacci matrix frobenius\linalg,frobenius\Compute the Frobenius form of a matrix gausselim\linalg,gausselim\Gaussian elimination on a matrix gaussjord\linalg,gaussjord\Reduced row Echelon form (Gauss-Jordan elimination) genmatrix\linalg,genmatrix\Generate the coefficient matrix from equations grad\linalg,grad\Vector gradient of an expression GramSchmidt\linalg,GramSchmidt\Compute orthogonal vectors hadamard\linalg,hadamard\Bound on coefficients of the determinant of a matrix hermite\linalg,hermite\Hermite normal form (reduced row echelon form) hessian\linalg,hessian\Compute the Hessian matrix of an expression hilbert\linalg,hilbert\Create a Hilbert matrix htranspose\linalg,htranspose\Compute the Hermitian transpose of a matrix ihermite\linalg,ihermite\Integer-only Hermite normal form indexfunc\linalg,indexfunc\Determine the indexing function of an array innerprod\linalg,innerprod\Calculate the inner product intbasis\linalg,intbasis\Determine a basis for the intersection of spaces inverse\linalg,inverse\Compute the inverse of a matrix ismith\linalg,ismith\Integer-only Smith normal form iszero\linalg,iszero\Determine whether a matrix is zero jacobian\linalg,jacobian\Compute the Jacobian matrix of a vector function jordan\linalg,jordan\Compute the Jordan form of a matrix JordanBlock\linalg,JordanBlock\Return a Jordan block matrix kernel\linalg,kernel\Compute a basis for the null space laplacian\linalg,laplacian\Compute the Laplacian leastsqrs\linalg,leastsqrs\Least-squares solution of equations linsolve\linalg,linsolve\Solution of linear equations matrix\linalg,matrix\Create a matrix minor\linalg,minor\Compute a minor of a matrix minpoly\linalg,minpoly\Compute the minimum polynomial of a matrix mulcol\linalg,mulcol\Multiply a column of a matrix by an expression mulrow\linalg,mulrow\Multiply a row of a matrix by an expression multiply\linalg,multiply\Matrix-matrix or matrix-vector multiplication norm\linalg,norm\Norm of a matrix or vector nullspace\linalg,nullspace\Compute a basis for the null space orthog\linalg,orthog\Test for orthogonal matrices permanent\linalg,permanent\Compute the permanent of a matrix pivot\linalg,pivot\Pivot about a matrix entry potential\linalg,potential\Compute the potential of a vector field randmatrix\linalg,randmatrix\Random matrix generator range\linalg,range\Compute a basis for the column space rank\linalg,rank\Rank of a matrix row\linalg,row\Extract row(s) of a matrix as vector(s) rowdim\linalg,rowdim\Determine the row dimension of a matrix rowspace\linalg,rowspace\Compute a basis for the row space rowspan\linalg,rowspan\Compute spanning vectors for the row space rref\linalg,rref\Reduced row Echelon form scalarmul\linalg,scalarmul\Multiply a matrix or vector by an expression singularvals\linalg,singularvals\Compute the singular values of a matrix smith\linalg,smith\Compute the Smith normal form of a matrix stack\linalg,stack\Join two or more matrices together vertically submatrix\linalg,submatrix\Extract a specified submatrix from a matrix subvector\linalg,subvector\Extract a specified vector from a matrix sumbasis\linalg,sumbasis\Determine a basis for the sum of vector spaces swapcol\linalg,swapcol\Swap two columns in a matrix swaprow\linalg,swaprow\Swap two rows in a matrix sylvester\linalg,sylvester\Create Sylvester matrix from two polynomials toeplitz\linalg,toeplitz\Create a Toeplitz matrix trace\linalg,trace\The trace of a matrix transpose\linalg,transpose\Compute the transpose of a matrix vandermonde\linalg,vandermonde\Create a Vandermonde matrix vecpotent\linalg,vecpotent\Compute the vector potential vectdim\linalg,vectdim\Determine the dimension of a vector vector\linalg,vector\Create a vector logic\logic\Introduction to the "logic" package bequal\logic,bequal\Logical equivalence of two expressions bsimp\logic,bsimp\Boolean expression simplification canon\logic,canon\Canonical representation of expression convert/frominert\logic,frominert\Replace inert operators by system operators convert/MOD2\logic,MOD2\Convert boolean expression to equivalent modulo 2 format convert/toinert\logic,toinert\Convert system defined operators to inert ones distrib\logic,distrib\Expand a boolean expression dual\logic,dual\Construct the dual of a boolean expression environ\logic,environ\Set level of automatic logical simplification randbool\logic,randbool\Construct a random boolean function satisfy\logic,satisfy\Return a valuation satisfying an expression tautology\logic,tautology\Test for tautology np\np\Introduction to the "np" package conj\np,conj\Newman-Penrose complex conjugation operator D\np,D\Newman-Penrose Pfaffian operators eqns\np,eqns\Initialization and display of NP equations suball\np,suball\Substitution utility for Newman-Penrose package V\np,V\Newman-Penrose Pfaffian operators V_D\np,V_D\Newman-Penrose commutators X\np,X\Newman-Penrose Pfaffian operators X_D\np,X_D\Newman-Penrose commutators X_V\np,X_V\Newman-Penrose commutators Y\np,Y\Newman-Penrose Pfaffian operators Y_D\np,Y_D\Newman-Penrose commutators Y_V\np,Y_V\Newman-Penrose commutators Y_X\np,Y_X\Newman-Penrose commutators numtheory\numtheory\Introduction to the "numtheory" package B\numtheory,B\N'th Bernoulli number bernoulli\numtheory,bernoulli\Bernoulli numbers and polynomials cfrac\numtheory,cfrac\Continued fraction convergents cyclotomic\numtheory,cyclotomic\Calculate cyclotomic polynomial divisors\numtheory,divisors\Positive divisors of an integer E\numtheory,E\N'th Euler number euler\numtheory,euler\Euler numbers and polynomials F\numtheory,F\N'th Fermat number factorset\numtheory,factorset\Prime factors of an integer fermat\numtheory,fermat\N'th Fermat number GIgcd\numtheory,GIgcd\Gcd of Gaussian integers ifactor\numtheory,ifactor\Integer factorization imagunit\numtheory,imagunit\Square root of -1 mod n isolve\numtheory,isolve\Solve equations for integer solutions isprime\numtheory,isprime\Primality test issqrfree\numtheory,issqrfree\Test if integer is square free ithprime\numtheory,ithprime\Determine the i'th prime J\numtheory,J\Jacobi symbol jacobi\numtheory,jacobi\Jacobi symbol L\numtheory,L\Legendre symbol lambda\numtheory,lambda\Carmichael's lambda function legendre\numtheory,legendre\Legendre symbol M\numtheory,M\N'th Mersenne prime mcombine\numtheory,mcombine\Chinese remaindering mersenne\numtheory,mersenne\N'th Mersenne prime mipolys\numtheory,mipolys\Number of monic irreducible univariate polynomials mlog\numtheory,mlog\Discrete logarithm mobius\numtheory,mobius\Mobius function mroot\numtheory,mroot\Modular root msqrt\numtheory,msqrt\Modular square root nextprime\numtheory,nextprime\Determine the next largest prime nthpow\numtheory,nthpow\Find largest nth power in a number order\numtheory,order\Order of a number phi\numtheory,phi\Totient function pprimroot\numtheory,pprimroot\Compute a pseudo primitive root prevprime\numtheory,prevprime\Determine the next smallest prime primroot\numtheory,primroot\Compute a primitive root rootsunity\numtheory,rootsunity\Roots of unity safeprime\numtheory,safeprime\Compute a safe prime sigma\numtheory,sigma\Sum of divisors tau\numtheory,tau\Number of divisors orthopoly\orthopoly\Introduction to the "orthopoly" package G\orthopoly,G\Gegenbauer (ultraspherical) polynomial H\orthopoly,H\Hermite polynomial L\orthopoly,L\Laguerre polynomial P\orthopoly,P\Legendre and Jacobi polynomials T\orthopoly,T\Chebyshev polynomial (of the first kind) U\orthopoly,U\Chebyshev polynomial of the second kind plots\plots\Introduction to the "plots" package conformal\plots,conformal\Conformal plot of a complex function cylinderplot\plots,cylinderplot\Plot a 3D surface in cylindrical coordinates display\plots,display\Display a set of 2D plot structures display3d\plots,display3d\Display a set of 3D plot structures matrixplot\plots,matrixplot\3D plot with z values determined by a matrix pointplot\plots,pointplot\Create a 3D point plot polarplot\plots,polarplot\Plot a 2D curve in polar coordinates replot\plots,replot\Redo a plot spacecurve\plots,spacecurve\Plotting of 3D space curves sparsematrixplot\plots,sparsematrixplot\2D plot of nonzero values of a matrix sphereplot\plots,sphereplot\Plot a 3D surface in spherical coordinates tubeplot\plots,tubeplot\Three-dimensional tube plotting powseries\powseries\Introduction to the "powseries" package add\powseries,add\Addition of formal power series compose\powseries,compose\Composition of formal power series evalpow\powseries,evalpow\General evaluator for power series expressions inverse\powseries,inverse\Multiplicative inverse of a formal power series multconst\powseries,multconst\Multiplication of a power series by a constant multiply\powseries,multiply\Multiplication of formal power series negative\powseries,negative\Negation of a formal power series powcreate\powseries,powcreate\Create formal power series powdiff\powseries,powdiff\Differentiation of a formal power series powexp\powseries,powexp\Exponentiation of a formal power series powint\powseries,powint\Integration of a formal power series powlog\powseries,powlog\Logarithm of a formal power series powpoly\powseries,powpoly\Create a formal power series from a polynomial powsolve\powseries,powsolve\Solve linear differential equations as power series quotient\powseries,quotient\Quotient of two formal power series reversion\powseries,reversion\Reversion of formal power series subtract\powseries,subtract\Subtraction of two formal power series tpsform\powseries,tpsform\Truncated power series form of a formal series projgeom\projgeom\Introduction to the "projgeom" package collinear\projgeom,collinear\Test whether three given points are collinear concur\projgeom,concur\Test whether three given lines are concurrent conjugate\projgeom,conjugate\Check whether two given points are conjugate wrt a conic ctangent\projgeom,ctangent\Tangent lines to a conic from any point in a complex plane fpconic\projgeom,fpconic\Coefficients of equation of conic going through five points harmonic\projgeom,harmonic\Point which is harmonic conjugate to another wrt 2 others inter\projgeom,inter\Find the intersection of two given lines join\projgeom,join\Find the line joining two given points lccutc\projgeom,lccutc\The intersection of a conic and a line in a complex plane lccutr\projgeom,lccutr\The intersection of a conic and a line in a real plane lccutr2p\projgeom,lccutr2p\Intersection of conic and a line joining two points linemeet\projgeom,linemeet\Find a line which is concurrent to two given lines midpoint\projgeom,midpoint\Find the midpoint of the line joining two points onsegment\projgeom,onsegment\Find the point which divides a segment in a given ratio polarp\projgeom,polarp\The polar line of a given point with respect to a conic poleline\projgeom,poleline\The pole of a given line with respect to a conic ptangent\projgeom,ptangent\Find the tangent line to the conic at a point on it rtangent\projgeom,rtangent\Tangent lines to a conic from any point in real ext'd plane tangentte\projgeom,tangentte\Check if a given line touches a given conic tharmonic\projgeom,tharmonic\Test if pair of points is harmonic conjugate to another simplex\simplex\Introduction to the "simplex" package basis\simplex,basis\Computes a list of variables, corresponds to the basis convexhull\simplex,convexhull\Find convex hull enclosing the given points cterm\simplex,cterm\Computes the list of constants from the system dual\simplex,dual\Computes the dual of a linear program feasible\simplex,feasible\Determine if system is feasible or not maximize\simplex,maximize\Maximize a linear program minimize\simplex,minimize\Minimize a linear program pivot\simplex,pivot\Construct a new set of equations given a pivot pivoteqn\simplex,pivoteqn\Returns a sublist of equations given a pivot pivotvar\simplex,pivotvar\Returns a variable with positive coefficient ratio\simplex,ratio\Returns a list of ratios setup\simplex,setup\Constructs a set of equations with variables on the lhs standardize\simplex,standardize\Converts a set of equations to type "<=" stats\stats\Introduction to the "stats" package addrecord\stats,addrecord\Add records to a statistical matrix average\stats,average\Calculate the average of some numbers ChiSquare\stats,ChiSquare\Evaluate the Chi squared function correlation\stats,correlation\Evaluate the correlation coefficient covariance\stats,covariance\Calculate the covariance evalstat\stats,evalstat\Manipulation of statistical data Exponential\stats,Exponential\The exponential distribution Fdist\stats,Fdist\Variance Ratio Distribution Ftest\stats,Ftest\Test Prob(F > x) getkey\stats,getkey\Returns the key from a statistical matrix linregress\stats,linregress\Linear regression median\stats,median\The median of the given data mode\stats,mode\The mode of the given data multregress\stats,multregress\Multiple regression N\stats,N\Values for a Normal Distribution projection\stats,projection\Create a projection matrix putkey\stats,putkey\Add a key to a matrix Q\stats,Q\Tail of a N(0,1) distribution RandBeta\stats,RandBeta\Random number generator for the Beta distribution RandChiSquare\stats,RandChiSquare\Random number generator Chi Square distribution RandExponential\stats,RandExponential\Random number generator for exponential distribution RandFdist\stats,RandFdist\Random number generator F distribution RandGamma\stats,RandGamma\Random number generator for the Gamma distribution RandNormal\stats,RandNormal\Random number generator for normal distribution RandPoisson\stats,RandPoisson\Random number generator Poisson distribution RandStudentsT\stats,RandStudentsT\Random number generator Student T distribution RandUniform\stats,RandUniform\Uniform random number generator regression\stats,regression\Generalized regression routine removekey\stats,removekey\Take the key away from a statistical matrix Rsquared\stats,Rsquared\Square of the correlation coefficient sdev\stats,sdev\Standard deviation serr\stats,serr\Standard error statplot\stats,statplot\Statistical plotting StudentsT\stats,StudentsT\The Student's T distribution Uniform\stats,Uniform\The Uniform distribution variance\stats,variance\Compute the variance of a set of data student\student\Introduction to the "student" package changevar\student,changevar\Perform a change of variables combine\student,combine\Combine terms into a single term completesquare\student,completesquare\Complete the square D\student,D\Differential operator distance\student,distance\Compute the distance between Points Int\student,Int\Inert form of int (integration function) intercept\student,intercept\Compute the points of intersection of two curves intparts\student,intparts\Perform integration by parts isolate\student,isolate\Isolate a subexpression to left-side of an equation leftbox\student,leftbox\Graph an approximation to an integral leftsum\student,leftsum\Numerical approximation to an integral Limit\student,Limit\Inert form of limit makeproc\student,makeproc\Convert an expression into a Maple procedure maximize\student,maximize\Compute the maximum middlesum\student,middlesum\Numerical approximation to an integral midpoint\student,midpoint\Compute the midpoint of a line segment minimize\student,minimize\Compute the minimum powsubs\student,powsubs\Substitute for factors of an expression rightbox\student,rightbox\Graph an approximation to an integral rightsum\student,rightsum\Numerical approximation to an integral showtangent\student,showtangent\Plot a function and its tangent line simpson\student,simpson\Numerical approximation to an integral slope\student,slope\Compute the slope of a line Sum\student,Sum\Inert form of sum trapezoid\student,trapezoid\Numerical approximation to an integral value\student,value\Evaluate inert functions (formerly student,Eval) totorder\totorder\Introduction to the "totorder" package assume\totorder,assume\Define total ordering on a sequence of names forget\totorder,forget\Deletes relationships within the ordering of names is\totorder,is\Make queries with respect to the ordering of names ordering\totorder,ordering\Print out the current total ordering of names