Основы Maple

Robert M. Corless
Department of Applied Mathematics
University of Western Ontario
London, Canada

Copyright 2001 by Robert M. Corless
All rights reserved

Programming in Maple

Программирование в Maple

Sample Maple programs

Пример программ Maple

Parametric solution of algebraic equations

Параметрическое решение алгебраических уравнений

> restart;

>read "D:/books/ess/programs/parsolve.mpl";

>eq1 := u^2 + v^2 = a^2;

>sol1 := parsolve( eq1 , [u,v], t);

$sol1 := {v = t/(1+t^2)^(1/2)*a, u = 1/(1+t^2)^(1/2)...$

>seq( normal( subs( sol, eq1 )), sol=sol1 );

>sol2 := parsolve( eq1, [u=-a,v=0], s );

$sol2 := {v = 2*s*a/(s^2+1), u = -a*(s^2-1)/(s^2+1)}...$

>seq( normal( eval( eq1, sol )), sol=sol2 );

>eq3 := s^2 + s*t + t^2 = a^2;

> parsolve( eq3, [s=0,t=a], u);

${s = -a*(1+2*u)/(1+u+u^2), t = -a*(-1+u^2)/(1+u+u^2...$

>Folium := parsolve( x^3 - 3*a*x*y + y^3 = 0, [x,y], t);

$Folium := {x = 3*t*a/(1+t^3), y = 3*t^2*a/(1+t^3)}$

>plot( eval([x/a, y/a, t=-5..5], Folium ), view=[-2..2,-2..2], colour=black, scaling=CONSTRAINED );

>Foley := parsolve( x^5 - 5*x*y^3 + y^5, [x,y], u);

$Foley := {x = 5*u^3/(1+u^5), y = 5*u^4/(1+u^5)}$

>plot( eval([x,y,u=-8..8],Foley), numpoints=101, view=[-4..4,-4..4], colour=black, scaling=CONSTRAINED );

> _EnvExplicit := false;

>f := randpoly([x,y], degree=5, sparse);

> simpler := parsolve( f, [x,y], s );

С официального разрешения © 2002 Waterloo Maple, Inc