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));