/*************** -*- Mode: MACSYMA; Package: MAXIMA -*-  ******************/
/***************************************************************************
***                                                                    *****
***     Copyright (c) 1984 by William Schelter,University of Texas     *****
***     All rights reserved                                            *****
***************************************************************************/


1/(x^2+2);
1/(x^2+2)$
substpart(3/2,%,2,1,2);
1/(x^(3/2)+2)$
27*y^3+54*x*y^2+36*x^2*y+y+8*x^3+x+1;
27*y^3+54*x*y^2+36*x^2*y+y+8*x^3+x+1$
substpart(factor(piece),%,[1,2,3,5]);
(3*y+2*x)^3+y+x+1$
1/x+y/x-1/z;
-1/z+y/x+1/x$
substpart(xthru(piece),%,[2,3]);
(y+1)/x-1/z$
substpart("+",%,1,0);
-1/z+y+x+1$
ratsimp((k^2*x^2-1)*(cos(x)+eps)/(3*k+n[1])/(5*k-n[2]));
((k^2*x^2-1)*cos(x)+eps*k^2*x^2-eps)/(15*k^2+(5*n[1]-3*n[2])*k-n[1]*n[2])$
factor(%);
(k*x-1)*(k*x+1)*(cos(x)+eps)/((3*k+n[1])*(5*k-n[2]))$
substpart(ratsimp(piece),%,1,[1,2]);
(k^2*x^2-1)*(cos(x)+eps)/((3*k+n[1])*(5*k-n[2]))$
-substpart(-piece,%,1,1);
-((1-k^2*x^2)*(cos(x)+eps)/((3*k+n[1])*(5*k-n[2])))$
a+b/(x*(y+(a+b)*x)+1);
b/(x*(y+(b+a)*x)+1)+a$
substpart(multthru(piece),%,1,2,1);
b/(x*y+(b+a)*x^2+1)+a$
x . 'diff(f(x),x,2);
x . 'diff(f(x),x,2)$
substinpart(d^2,%,2);
x . d^2$
substinpart(f1,f[1](x+1),0);
f1(x+1)$