/*************** -*- 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)$