Maple Share Library:  Numerics
==============================

approx.ms	FILE: 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.
		AUTHOR: Keith Geddes, kogeddes@daisy.uwaterloo.ca

bpsline.ms	FILE: numerics/bspline.ms
		Uses the bspline package to compute B-spline segment
		polynomials for uniform and non-uniform knot sequences.
		AUTHOR: Michael Monagan, monagan@inf.ethz.ch
		
fit             > readshare(fit);
                A (linear) least squares fit of a curve to a set of data.
		fit(X, Y, B, v) fits the linear basis functions B in v
		to the X Y data points.
                AUTHOR: Dominik Gruntz, gruntz@inf.ethz.ch

fft             > readshare(fft, numerics);
fht             > readshare(fht, numerics);
		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.
		AUTHOR: Stephen Earl, Telephone 0332 529615 
		3 Faygate Crescent, Bexleyheath, Kent DA6 7NS, England

fortran.ms	FILE: numerics/fortran.ms
		A discussion of the pitfalls of naive use of symbolic
		computation when generating Fortran code.  The example is
		generating Fortran code for computing the inverse of a 3 by 3
		symmetric matrix.
		AUTHOR: Michael Monagan, monagan@inf.ethz.ch

ilp             > readshare(ilp, numerics);
                An integer linear programming algorithm for maximizing
                a linear function given a set of linear constraints.
                AUTHOR: Anu Pathria, pathria@arpa.berkeley.edu

intpak		> readshare(intpak, numerics); (68K)
		SEE ALSO: numerics/intpak.tex  (38K)
		Experimental interval arithmetic package.
		AUTHOR: A.E. Connell, R.M. Corless, rcorless@uwovax.uwo.ca

firsteuler      > readshare(ODE, plots); (50K)
impeuler        SEE ALSO plots/balloon.ms, plots/doubpend.ms
rungekutta	Routines for the numerical solution to first order ODE's
                AUTHOR: Daniel Schwalbe, schwalbe@macalstr.edu

macroC          > readshare(macroC, numerics); (60K)
                SEE ALSO: numerics/macroC.tex (50K)
                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.
                AUTHOR: Patrick Capolsini, capolsin@safir.unice.fr,
                AUTHOR:                    capolsin@sophia.inria.fr

macrofort       > readshare(macrofor, numerics); (45K)
                SEE ALSO: numerics/macrofor.tex (33K)
                A collection of routines for generating Fortran code.
                Macrofort allows for the generation of complete Fortran
                programs, including declarations and control structures.
                AUTHOR: Claude Gomez, gomez@amadeus.inria.fr

numerint.ms     FILE: numerics/numerint.ms
                A worksheet detailing how Maple's numerical integration 
                routines work, in particular showing how singularities in the
                integrand are handled by making use of Maple's series facility.
                AUTHOR: Keith Geddes, kogeddes@daisy.uwaterloo.ca

pade2		> readshare(pade2, numerics);
		The call pade2([f1,f2,...,fn],x=p,[d1,d2,...,dn]) computes a
                generalized 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
		AUTHOR: Harm Derksen, hderksen@sci.kun.nl

ratinterp	> readshare(rfinterp, numerics);
		Computes the rational function in x which interpolates the
		given data points x[i], y[i].
		AUTHOR: Carlos von Achenbach, achenbac@inf.ethz.ch

trans           > readshare(trans, numerics); (104K)
		SEE ALSO: numerics/trans.tex  (35K)
                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.
                AUTHOR: Johannes Grotendorst, j.grotendorst@kfa-juelich.de

traubjen        > readshare(traubjen, numerics);
                Traub-Jenkins algorithm for computing the complex
                roots of a polynomial in R[x] or C[x]
                AUTHOR: Bruno.Salvy@inria.fr

