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/*======================================================================
L <- EVALSYS(S,t,R)
Eval System at rational number
Inputs:
S = (S_1,...,S_r), S_i a list of i-variate saclib pols
defining a system of equations.
t an integer, 1 <= t <= r
R a rational number
Outputs:
L : a system that is equivalent to S with R substituted for x_t.
NOTE: if Q is a polynomial in the system of positive
degree in x_s, where s > t, then Q will be represented
in L as an s-variate polynomial, despite the fact that
we know a priori that "x_t" will not exist in Q.
======================================================================*/
#include "qepcad.h"
Word EVALSYS(Word S, BDigit t, Word R)
{
Word r, L, i, S_i, Ap, a, A, is, As;
Step1: /* Construct the skelaton of L, the answer. */
r = LENGTH(S);
L = NIL;
for(i = 1; i <= r; i++)
if (i < t)
L = COMP(LELTI(S,i),L);
else
L = COMP(NIL,L);
L = CINV(L);
Step2: /* Sub R -> x_t for all levels >= t */
for(i = t; i <= r; i++)
{
for(S_i = LELTI(S,i); S_i != NIL; S_i = RED(S_i))
{
/* Make substitution */
Ap = IPRNEVAL(i,FIRST(S_i),t,R);
if (Ap == 0) continue;
IPSRP(i,Ap,&a,&A);
PSIMREP(i,A,&is,&As);
if (is == 0) { L = 1; goto Return; }
SLELTI(L,is,COMP(As,LELTI(L,is)));
}
}
Return: /* Prepare to return */
return L;
}
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