Contents of the Maple V Release 2 Share Library =============================================== The routines have been grouped together under the following areas Algebra Analysis Combinatorics Engineering Graphics and Geometry Linear Algebra Number Theory Numerics Science System Tools Programming Examples Documentation Algebra ======= charsets (algebra/charsets, algebra/charsets.tex) A implementation of Ritt-Wu's characteristic sets method. Includes characteristic sets of (multivariate) polynomial sets, decomposing polynomial sets into ascending sets and irreducible ascending sets, decomposing algebraic varieties into irreducible components, factorizing polynomials over algebraic number fields and solving systems of polynomial equations. Dongming Wang, wang@risc.uni-linz.ac.at compoly (compoly) Implements a faster algorithm for polynomial decomposition (see Gutierrez et al.) that does not require factorization. Bruno Salvy, Francois Morain: salvy@inria.fr, morain@inria.fr galois (algebra/galois) Computes the Galois group of a polynomial of degree <= 7 Extends the functionality of the library routine galois from Q[x] to Q[t1,t2,...,tm][x] i.e. polynomials with polynomial coefficients. Note, the Galois group computed does not specialize correctly for particular values of the parameters t1, t2, ..., tm. The code is presently being extended to higher degree. R. Sommeling, T. Mattman, J McKay, mckay@vax2.concordia.ca GB (mod/GB) An implementation of Buchberger's algorithm for computing Grobner bases over finite fields, i.e. over Z_p(a,b,c,...)[x1,x2,...,xn] using either the term ordering total degree or pure lexicographic. Andreas Pirklbauer, andreas@think.com Dominik Gruntz, gruntz@inf.ethz.ch group.ms (algebra/group.ms) An application of Maple's group package to answering various questions about the small Rubik's cube. (IntBasis, IntBasis.tex) integral_basis Computes an integral basis for an algebraic number or function. genus Determines genus an algebraic curve: genus(f,x,y) computes the genus of a curve given by the polynomial f in x and y. This code is using a new method based on Puiseux series expansions, and should be considerably faster than the Maple library routine maxorder for large problems. Mark van Hoeij, hoeij@sci.kun.nl invar (algebra/invar, algebra/invar.tex (needs amsfonts), algebra/invar.dvi) The invar package is a package of routines mainly for computing the invariant ring of permutation groups or finite linear groups over Q or an algebraic number field. Gregor Kemper, kemper@kalliope.iwr.uni-heidelberg.de MatPade (algebra/MatPade, algebra/MatPade.ms) A set of functions to compute matrix-type Pade approximants. Examples of such approximants include Hermite Pade, Simultaneous Pade, right and left matrix Pade approximants. G. Labahn, glabahn@daisy.uwaterloo.ca polycon (engineer/polycon, engineer/polycon.tex) This package includes functions for analysis of polynomial and rational control systems, i.e. control systems of the type dx/dt=f(x(t),u(t)), y=h(x,u) or x(t+1)=f(x(t),u(t)), y=h(x,u) where h and all components of f are rational functions in x = (x1,...,xn) and u. Krister Forsman, krister@isy.liu.se trinom.ms (algebra/trinom.ms) An application to computing primitive trinomials over finite fields for use in error correcting codes and random number generators. This shows how to use Maple to compute with polynomials over finite fields. Michael Monagan, monagan@inf.ethz.ch SqrFree (mod/SqrFree, mod/SqrFree.tex) Computes the square-free factorization of a multivariate polynomial over a finite field -- Maple's Sqrfree(a) mod p only works for univariate polynomials. Steve Swanson, swany@math.purdue.edu, swany@math.lsa.umich.edu fields (algebra/fields, algebra/fields.ms, algebra/fields.dvi) Let N be a field extension of L, a field extension of K, such that N is finitely generated over K. This package uses Grobner basis methods to calculate the transcendence degree of N|L and the degree [N:L] if the field extension is algebraic, and related questions. The implementation works for K = Q or K = Q(alpha) a single algebraic extension of Q. Gregor Kemper, kemper@kalliope.iwr.uni-heidelberg.de Analysis ======== BesselH (hankel, hankel.ms) Implementation of Hankel Functions in terms of BesselJ and BesselY. Contains BesselH, evalf/BesselH, evalc/BesselH, expand/BesselH, simplify/BesselH, diff/BesselH. Douglas B. Meade, meade@math.scarolina.edu gfun.tex A LaTeX document summarizing the capabilities of the gfun package, for computing with sequences, series, and generating functions, with many beautiful examples. Bruno Salvy, salvy@rully.inria.fr Paul Zimmermann, zimmermann@inria.inria.fr guesss (guesss -- GUESS Sequence) A routine to guess the next values in a sequence. This routine searches for more general differential equations than the gfun package does. It uses a generalized continued fraction method to find the differential equation. Harm Derksen, hderksen@sci.kun.nl LambertW.ps A PostScript file documenting Lambert's W function (the W function in Maple). Describes known properties of the function, integration formulae and techniques, assymptotics, and gives many nice applications in various areas of mathematics, in particular solutions to ODE's. R. M. Corless (rcorless@uwovax.uwo.ca), D.J. Jeffrey, G. H. Gonnet, D. E. G. Hare (deghare@daisy.uwaterloo.ca) logmap.ms (calculus/logmap.ms) This worksheet explores the period-doubling bifurcation sequence of the discrete logistic map. Although numerical tools can be used, we believe it is useful to examine the polynomial algebra here in some detail. The worksheet makes use of polynomial factorization, discriminants, and numerical root finding. R. M. Corless, rcorless@uwovax.uwo.ca parfrac.ms (calculus/parfrac.ms) Shows how to use Maple to perform each step of a partial fraction decomposition for rational function integration. A good example of using Maple as a tool in teaching. Michael Monagan, monagan@inf.ethz.ch puiseux (IntBasis) Computes a Puiseux series expansion of an algebraic function. Especially intended for expansions about singular points where the result contains more than one branch. Mark van Hoeij, hoeij@sci.kun.nl ratlode (calculus/ratlode) Finds the rational solutions to a linear n'th order ODE in y(x) with rational coefficients, i.e. an equation of the form sum( a[i](x)*diff(y(x),x$i), i=0..n ) = b(x) where a[i](x) are rational functions in x over a field. Because of limitations in Maple, the implementation only works for coefficients which are transcendental extensions of Q. Manuel Bronstein, bronstei@inf.ethz.ch GRADIENT.ms (autodiff/GRADIENT.ms) A worksheet showing examples from automatic (algorithmic) differentiation using Maples D operator and the GRADIENT function to compute partial derivaties, gradients, and Jacobians of functions given as Maple procedures. Michael Monagan, monagan@inf.ethz.ch IntSolve (linalg/IntSolve) Version 1 of an integral equation solver. Note: this package requires the routines in the file linalg/Echelon. Honglin Ye & Robert M. Corless, rcorless@uwovax.uwo.ca Combinatorics ============= coxpoly (combinat/coxpoly) Computes the characteristic polynomial of the coxeter matrix of certain symbolically given quiver classes. Axel Boldt, 6500axel@ucsbuxa.ucsb.edu perm (combinat/perm, combinat/perm.tex, combinat/permgra1.ps, combinat/permgra2.ps) A package of routines for computing with permutation groups, including routines for computing orbits, subgroups, testing for conjugacy. There are also procedures used to represent and manipulate combinatorial structures. Yves Chiricota, chiricot@firmin.greco-prog.fr relpoly (combinat/relpoly, combinat/relpoly.ms) relpoly.ms The function relpoly(G,p) computes the all terminal reliability polynomial for a graph G with probability of edge failure p. Michael Monagan, monagan@inf.ethz.ch symmpoly (combinat/symmpoly) Utility routine for generating the symmetric polynomials. Michael Monagan, monagan@inf.ethz.ch Engineering =========== AnalSPT.in (engineer/AnalSPT.in) These procedures calculate the harmonic content of a single phase, thyristor controlled rectified sinewave for a firing angle y (degrees) and a frequency f (hertz) and plot the results either as a graph comparing the sum of harmonics with the original waveform or as a 3D plot of the harmonic magnitude. Alastair Rough, ROUGH@MANADON-ENGINEERING-COLLEGE.AC.UK Anal3PTB.in (engineer/Anal3PTB.in, engineer/harmonal) These procedures calculate the harmonic content of a 3 phase, thyristor bridge for a firing angle y (degrees) and a notional frequency 1 Hz and plot the results. Alastair Rough, ROUGH@MANADON-ENGINEERING-COLLEGE.AC.UK flash.ms (science/flash.ms) Flash calculations are used to determine the phase condition of a mixture at a specified temperature and pressure. Such computations lie at the heart of many process engineering calculations and are of central importance in many other applications as well (oil reservoir simulation for example). Ross Taylor, taylor@sun.soe.clarkson.edu filter.ms (engineer/filter.ms) An application to the analysis the effects of a low pass filter (to suppress surge) on a change in signal or power frequency. Maple is used to solve the general equations derived from Kirchoff's laws and to plot the effect of the filter. Tom Lee (tom@steam.uwaterloo.ca) stepresp.ms (engineer/stepresp.ms) A second example of step response analysis of an RC circuit. Maple is used to solve the general equations derived from Kirchoff's laws and to plot the step response as a function of capacitance. Tom Lee (tom@steam.uwaterloo.ca) robotarm.ms (engineer/robotarm.ms) Application to solving the path planning problem for a simple two-link planar robot arm, common in assembly line operations. Maple is used to solve the kinematic equations in closed form and to animate two specific solutions. Tom Lee (tom@steam.uwaterloo.ca) shear.ms (engineer/shear.ms) An application to mechanical engineering. Two design problems for a machine element to solve equilibrium equations to obtain general solutions for shear and normal stresses. Tom Lee (tom@steam.uwaterloo.ca) (engineer/lagrange.ms) etc. A selection of mathematics tutorials for first/second year undergraduate engineering students. lagrange.ms Application of lagrange multiplies to minimize a function f(x,y) subject to q(x,y) = 0. nonlin.ms The geometric iteration and the Newton-Raphson iteration for approximating roots of non-linear equations in one variable. poten.ms Potential Fields using Green's Functions in 2 dimensions. The Neumann and Dirichlet problem. statval.ms Finding minima, maxima and saddle points in 2 dimensions. stream.ms Finding streamlines in 2 dimensional vector fields. Alastair Rough, ROUGH@MANADON-ENGINEERING-COLLEGE.AC.UK wheatsto.ms (science/wheatsto.ms) Kirchoff's laws are applied to the ``Wheatstone Bridge'' electrical circuit to define 6 linear equations in the currents. Maple is used to solve the linear system symbolically, i.e. in terms of the parameters R1, R2, R3, R3, R5, the resistances in the circuit. Tony Scott, tcscott@maths.ox.ac.uk Graphics and Geometry ===================== balloon.ms (plots/balloon.ms) A long flexible rope is coiled neatly on the group and a helium balloon is attached at one end. The motion of the balloon rising is modelled by an ODE, from Newtons second law of motion, solved numerically, and plotted. Daniel Schwalbe, schwalbe@macalstr.edu billiard.ms (geometry/billiard.ms) A Maple worksheet showing how to solve the billiard problem for a circular billiard table. This is an example of solving a difficult equation, first analytically, then numerically. The numerical solution shows the use of automatic differentiation to differentiate a program. Dominik Gruntz, gruntz@inf.ethz.ch directionfield (plots/ODE) phaseplot ODE is a package of tools for computing and plotting solutions to ODE's -- See Maple V Flight Manual, Brooks/Cole 1992 -- that is in the installed version of the Maple V Release 2 share library. This is an updated version where note the fieldplot routine has been renamed to directionfield and various improvements have been made. Daniel Schwalbe, schwalbe@macalstr.edu biology.ms (plots/biology.ms) Application of the plots/ODE package to a problem from biology where two polulations compete with each other for resources to survive. The biological system is modelled by two first order differential equations, and phase plots of the solutions are plotted showing examples of stable and unstable populations. Daniel Schwalbe, schwalbe@macalstr.edu doubpend.ms (plots/doubpend.ms) This worksheet uses the ODE package to approximate the solution to the differential equation associated to a double pendulum, i.e. a pendulum attached to a pendulum. The motion of the double pendulum is then animated. Daniel Schwalbe, schwalbe@macalstr.edu logistic.ms (plots/logistic.ms) The worksheet solves the logistics law of population growth P' = a*P - b*P^2. Given 3 populations P(t0), P(t0+delta), and P(t0+2*delta) Maple can solve for a and b. This is impressive. Daniel Schwalbe, schwalbe@macalstr.edu plotcurve (algcurve) algcurve (See also algcurve.tex in the Released share library) This is an updated version of the algcurve package. A package of routines for computing with algebraic curves in 2 dimensions. Includes facilities for computing singular points, tangents, inflection points, curve intersection points, as well as this routine for plotting curves. Stefan Schwendi, schwendi@iam.unibe.ch surfaces (geometry/surfaces) A set of procedures to calculate basic differential-geometric quantities of parametric surfaces in space. The procedures are intended to calculate first and second fundamental forms, metric determinant, Gauss curvature and Mean curvature. Tim Murdoch, murdoch@wlu.edu Linear Algebra ============== autoevalm (linalg/autoevalm) A utility routine to get Maple to automatically evaluate matrix expressions, e.g. instead of having to type evalm(A + B &* C); you can just type A + B &* C; Gene Johnson, ejohnson@umaxc.weeg.uiowa.edu eigen.ms (linalg/eigen.ms) A Maple worksheet tutorial on how to use the eigenvals and eigenvects and related commands to compute exact symbolic values for eigenvalues and eigenvectors of both numeric and symbolic matrices. This also includes a tutorial on computing with roots of polynomials using Maples RootOf notation. Michael Monagan, monagan@inf.ethz.ch lapack.ms (linalg/lapack.ms) On the front cover of the LAPACK User's Guide is a 6 by 6 matrix whose entries are +- the letters L A P A C K appearing in a particular pattern. This worksheet shows how we can use Maples symbolic linear algebra tools to find out exactly what is so special about this matrix. Michael Monagan, monagan@inf.ethz.ch magic (linalg/magic) Create an n by n magic square. Another family of matrices with interesting properties -- real eigenvalues. Dominik Gruntz, gruntz@inf.ethz.ch MatPade (algebra/MatPade, algebra/MatPade.ms) A set of functions to compute matrix-type Pade approximants. Examples of such approximants include Hermite Pade, Simultaneous Pade, right and left matrix Pade approximants. G. Labahn, glabahn@daisy.uwaterloo.ca McConnel.ms (science/McConnel.ms) A Maple worksheet on how to use matrix algebra, in particular matrix exponentials, for the symbolic solution of a system of first order differential equations in biochemistry, namely the McConnell equations. ==> See Science <== normform (linalg/normform) A package of routines for computing matrix normal forms. Contains: ismithex, smithex, frobenius, jordan, and ratjordan. The ismithex and smithex routines compute the Smith normal form over Z and F[x] respectively. The frobenius, jordan, and ratjordan routines compute the Frobenius, Jordan, and rational Jordan normal forms over a field K. These routines are typically faster than the routines in the Maple library, more general, and also compute the multiplier matrices. Example: F := frobenius(A,K,'P'); computes Frobenius normal form F, and the matrix P such that F = P^(-1) A P T.M.L. Mulders, mulders@sci.kun.nl, A.H.M. Levelt, ahml@sci.kun.nl Normform (mod/Normform) A package of routines for computing normal forms for matrices over the integers mod p. Contains Frobenius, Ratjordan, Jordan T.M.L. Mulders, mulders@sci.kun.nl, A.H.M. Levelt, ahml@sci.kun.nl pascal (linalg/pascal) Create an n by n Pascal matrix. A family of matrices with nice properties -- real eigenvalues, determinant = 1. Michael Monagan, monagan@inf.ethz.ch rrefshow (linalg/rrefshow) A utility routine for teaching purposes that allows the user to step through a matrix row reduction to Echelon form. Gene Johnson, ejohnson@umaxc.weeg.uiowa.edu sffdet (linalg/sffdet) Computes the determinant of a square matrix M using a variant of Bareiss's fraction free algorithm which is particularly suited to sparse matrices with integer or polynomial entries. Quyen Nguyen, nguyen@cis.udel.edu David Saunders, saunders@udel.edu sffge (linalg/sffge) Performs Bareiss' fraction free Gaussian elimination algorithm on a rectangular matrix of polynomial entries and returns the reduces matrix (in upper triangular form) and optionally the rank and determinant. This routine has the same functionality as the library routine linalg[ffgausselim] but is using a variation of Nguyen and Saunders algorithm which is suited to sparse matrices. Igor Berchtold, Michael Monagan, monagan@inf.ethz.ch Number Theory ============= isprime (isprime) An improved version of the probabilisitic isprime function. The new version replaces the previous 5 (default) strong pseudo-prime tests using bases 2,3,5,7,11 with one modified strong pseudo-prime test using base 2 and one Lucas test. The code for the Lucas test was written originally by Martin Schoenert. Gaston Gonnet, gonnet@inf.ethz.ch Numerics ======== approx.ms (numerics/approx.ms) Shows various numerical approximation techniques for developing efficient polynomial and rational function approximations to the function int(1/GAMMA(t),t=0..x)/x^2, including Taylor series, Pade approximation, Chebyshev series, Chebyshev-Pade approximation, and minimax approximations. Keith Geddes, kogeddes@daisy.uwaterloo.ca fft, fht (numerics/fft, numerics/fht) Maple routines for the calculation of the Fast Fourier and Hartley Transforms. The fft routine works for complex sequences and the fht routine works for real sequences. Stephen Earl, Telephone 0332 529615 3 Faygate Crescent, Bexleyheath, Kent DA6 7NS, England fortran.ms (numerics/fortran.ms) A discussion of the pitfalls of naive use of symbolic computation when generating Fortran code. The example is of generating Fortran code for computing the inverse of a 3 by 3 symmetric matrix. Michael Monagan, monagan@inf.ethz.ch intpak (numerics/intpak, numerics/intpak.tex) Experimental interval arithmetic package. A.E. Connell, R.M. Corless, rcorless@uwovax.uwo.ca ODE (plots/ODE) (routines: firsteuler, impeuler, rungekutta, rungekuttahf) Routines for the numerical solution to first order ODE's Daniel Schwable, SCHWALBEDA@SLUVCA.SLU.EDU pade2 (numerics/pade2) The call pade2([f1,f2,...,fn],x=p,[d1,d2,...,dn]) computes a generalised Pade approximation of the functions f1,f2,...,fn at x=p where the output polynomials [g1,g2,...,gn] in x (not all 0) satisfy (i) degree(g.i,x) <= d.i for all i (i) f1*g1+f2*g2+...+fn*gn has a zero of multiplicity d1+d2+...+dn+n-1 at x=p Harm Derksen, hderksen@sci.kun.nl trans (numerics/trans, numerics/trans.tex) Package of routines for rational function approximations to rational points, Taylor and asymptotic series, and functions Includes special numerical versions of the approximation algorithms to use the performance of the hardware floating point arithmetic. Johannes Grotendorst, j.grotendorst@kfa-juelich.de Science ======= biology.ms (plots/biology.ms) Application of the plots/ODE package to a problem from biology where two polulations compete with each other for resources to survive. The biological system is modelled by two first order differential equations, and phase plots of the solutions are plotted showing examples of stable and unstable populations. Daniel Schwalbe, schwalbe@macalstr.edu education (science/bohratom.ms, science/chemeqn.ms, science/heatcap.ms, science/Maxgas.ms, science/planck.ms, science/quantopt.ms) These six worksheets show different capabilities of Maple in solving four problems science at the educational level. bohratom.ms 1 (chemistry): shows Maple solving three non-linear equations symbolically arising from semi-classical mechanics, namely the Bohr theory applied to the Hydrogen atom. chemeqn.ms 2 (chemistry): shows Maple used to balance the coefficients in a chemical reaction. We are given a chemical equation and Maple's isolve command is used to find an integral solution. heatcap.ms 3 (statistical mechanics): obtains the mean energy and heat capacity of an Einstein solid. Maple is used to compute a symbolic infinite sum and compute symbolic limits. Maxgas.ms 4 (statistical mechanics): uses Maple to find the most probable speed of the Maxwell-Boltzman distribution. This involves differentiation and solving symbolically a non-linear equation. planck.ms 5 (statistical mechanics): uses Maple to compute a definite integral, the Stefan-Boltzman Law (of Blackbody radiation). quantopt.ms 6 (quantum optics): uses Maple to symbolically integrate a tripple integral and factor (simplify) the resulting formula. Tony Scott, Darren Redfern, Richard Pavelle, tcscott@maths.ox.ac.uk flash.ms (science/flash.ms) Flash calculations are used to determine the phase condition of a mixture at a specified temperature and pressure. Such computations lie at the heart of many process engineering calculations and are of central importance in many other applications as well (oil reservoir simulation for example). Ross Taylor, taylor@sun.soe.clarkson.edu kinetics (science/kinetics, science/kinetics.tex) (routines: odes, laws, steady) Given a reaction scheme these Maple procedures determine the system of differential equations, the associated conservation laws, and some of the species that have a zero steady state. Mark Holmes, holmem@rpi.edu McConnel.ms (science/McConnel.ms) A Maple worksheet on how to use matrix algebra, in particular matrix exponentials, for the symbolic solution of a system of first order differential equations in biochemistry, namely the McConnell equations. The McConnell equations are used to analyse data obtained from solute-cell transport experiments using the nuclear magnetic resonance (NMR) technique. The formal parameters involved in the solutions are determined by nonlinear least-squares fitting. Johannes Grotendorst, Paul Jansen, and Siegfried M. Schoberth j.grotendorst@kfa-juelich.de phase.ms (science/phase.ms) Simple Thermodynamic Calculations including bubble and dew point determination, creating and plotting phase diagrams. Ross Taylor, taylor@sun.soe.clarkson.edu pendulum.ms (science/pendulum.ms) Models the motion of a pendulum in a fluid as a second order ODE, solves the ODE analytically using Maple, and then plots the motion for different fluid resistances. David Harper, D.Harper@qmw.ac.uk shottraj.ms (science/shottraj.ms) Uses Maple to solve symbolically and plot the solution of a second order ODE which describes the motion of a bullet shot straight up into the air. Michael Monagan, monagan@inf.ethz.ch wheatsto.ms (science/wheatsto.ms) Kirchoff's laws are applied to the ``Wheatstone Bridge'' electrical circuit to define 6 linear equations in the currents. Maple is used to solve the linear system symbolically, i.e. in terms of the parameters R1, R2, R3, R3, R5, the resistances in the circuit. Tony Scott, tcscott@maths.ox.ac.uk System Tools ============ arctanh (convert/arctanh) Rewrite all logarithms and inverse hyperbolic trig functions in an expression in terms of arctanh. Vincent Broman, broman@nosc.mil eps (eps) This is a maple program to generate encapsulated postscript for a Maple plot. It provides control over a number of parameters including scaling - default is [.13,.13] output file - default is mplot.eps rotation - default is none Stanly Devitt, jsdevitt@maplesoft.on.cA maclaurinsubs (macsubs) Replaces functions in an expression with Maclaurin series (a formal Sum). No checking for convergence is made. Vincent Broman, broman@nosc.mil macroC (macroC, macroC.tex) MacroC is a Maple package for generating C language code without having to leave Maple. All C structures can be generated and the resulting code can be optimized. (Note: the Maple library routine C only handles expressions). Based on Claude Gomez' macrofort package for Fortran. Patrick Capolsini, capolsin@safir.unice.fr, capolsin@sophia.inria.fr mathematica (math) The mathematica function converts a Maple expression in the equivalent Mathematica expression -- as a string. This in includes integrals, matrices, simple operators as well as polynomials, and formulae. Dominik Gruntz, gruntz@inf.ethz.ch reorder (reorder) Utility routine to reorder the order in which two or more sums, limits, or integrals appear in an expression. Vincent Broman, broman@nosc.mil sprint (sprint) Utility routine "short print" for displaying large expressions. Best understood by looking at an example. > sprint(e); x 1/3 [1 + ------, - <<+2>> + <<*2>> - 1/3] <<+2>> The terms <<+2>> and <<*2>> stand for expressions which are a sum (respectively product) of two terms. This allows the user to look at the structure (top levels) of a large expression. Michael Monagan, monagan@inf.ethz.ch undistribute (undist) Factors out of integrands, summands, and limits any factors which are constant with respect to the index. Vincent Broman, broman@nosc.mil Programming Examples ==================== BesselH (hankel, hankel.ms) Implementation of Hankel Functions in terms of BesselJ and BesselY. Contains BesselH, evalf/BesselH, evalc/BesselH, expand/BesselH, simplify/BesselH, diff/BesselH. Douglas B. Meade, meade@math.scarolina.edu gdegree (gdegree) An example of programming with Maple expressions (formulae). This program computes the degree of an expression allowing rational and symbolic exponents. Michael Monagan, monagan@inf.ethz.ch program.tex (program.tex) "Programming in Maple: The Basics" An introduction to programming in Maple with exercises. Michael Monagan, monagan@inf.ethz.ch symmpoly (combinat/symmpoly) Utility routine for generating the symmetric polynomials. Michael Monagan, monagan@inf.ethz.ch Documentation (under directory doc) ============= A4.sty A LaTeX style file for European size paper fullpage.sty A LaTeX style file for American size paper maple.sty A LaTeX style file for including Maple input/output in a \begin{maple} ... \end{maple} MapleBooks A list of books on Maple including course texts Maple.tex "The Maple Computer Algebra System" A overview of Maple's capabilites Michael Monagan, monagan@inf.ethz.ch summary A summary of the new features in Maple V Release 2 and the changes from Maple V Release 1 to Release 2. summary.tex This is a LaTeX version of the summary file. summary.ms This is a Maple worksheet of the summary file. Contains some nice examples of the new plotting and graphics capabilities in Release 2 and gives some updated information Michael Monagan and Ron Neumann, monagan@inf.ethz.ch