LOAD('LRATS)$
/* LRATS FASL contains two functions related to MACSYMA's 
        RATSUBST.  The first is LRATSUBST(LIST_OF_EQUATIONS,EXP)
	which provides the user with a RATSUBST capability for
	multiple substitution similar to the existing capability
	of SUBST.  Recall that SUBST can carry out multiple substi-
	tutions: */
SUBST([A=B,C=D],A+C);
/* LRATSUBST works in an analogous way: */
LRATSUBST([A^2=B,C^2=D],(A+E)*C*(A+C));
/* If only one substitution is desired, then a single
	equation may be given as first argument: */
LRATSUBST(A^2=B,A^3);
/* Another function contained in LRATS FASL is FULLRATSUBST,
	which is equivalent to RATSUBST except that it recurses until
	its result stops changing.  Note the difference between the
	two results: */
RATSUBST(B*A,A^2,A^3);
FULLRATSUBST(B*A,A^2,A^3);
/* FULLRATSUBST will also accept a list of equations or a single
	equation as first argument. */
FULLRATSUBST([A^2=B,B^2=C,C^2=A],A^3*B*C);
FULLRATSUBST(A^2=B*A,A^3);
/*  FULLRATSUBST can be dangerous, so care must be taken to avoid
	infinite recursion.  An example of the kind of difficulty
	that can arise is given below: */
/* runs out of core in DOE MACSYMA without GC */
ERRCATCH(FULLRATSUBST(B*A^2,A^2,A^3));