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/*======================================================================
S <- SUBST(c,k,M,b,B)
Substitute the sample point into the projection factors.
\Input
\parm{c} is a cell.
\parm{k} is a positive $\beta$--integer.
\parm{M} is the integral minimal polynomial of an algebraic number $\alpha$.
\parm{b} is the $k$-tuple coordinates of a sample point.
\parm{B} is a list~$(B_1,\ldots,B_m)$ of
$(k+1)$--variate integral polynomials.
\Output
\parm{S} is the list~$(S_1,\ldots,,S_m)
where $S_i = B_i(b_1,\ldots,b_k,x_{k+1})$.
======================================================================*/
#include "qepcad.h"
Word QepcadCls::SUBST(Word c, Word k, Word M, Word b, Word B)
{
Word B1,Bp,S,S1;
Word P,L,Sp,T1,T2,G,Q,f,i;
Step1: /* Substitute. */
f = UNDET;
L = NIL;
S = NIL;
Bp = B;
i = 0;
while (Bp != NIL)
{
i++;
ADV(Bp,&B1,&Bp);
S1 = IPAFME(k + 1,M,B1,b);
/* This is just to warn me that previously we'd be in trouble! */
if (PCVERBOSE && S1 == 0 && k + 1 != GVNV) {
SWRITE("@A");
}
Step2: /* Check if S1 vanishes and, if so, whether this invalidates McCallum's projection*/
if (S1 == 0 && (PCPROPEC == TRUE ||
MEMBER('m',REDI(PCPROJOP,k)) ||
MEMBER('p',REDI(PCPROJOP,k)))
&& PFPRDQ(LELTI(LELTI(GVPF,k + 1),i))) {
if (CELLDIM(c) > 0) {
f = ACCCVBC(k,c,M,B1,b);
if (f != TRUE && !NZFOPQ(c,k,M,b,B1) && PFCOICQ(k+1,B1,c,GVPF,GVPC) != TRUE) {
SWRITE("WARNING! Projection factor ");
IPDWRITE(k+1,B1,GVVL);
SWRITE("\nis everywhere zero");
SWRITE(" in the cylinder ");
SWRITE("over the cell ");
LWRITE(LELTI(c,INDX));
SWRITE(" of positive dimension. The McCallum projection ");
SWRITE("may not be valid.\n"); }
}
if (f == TRUE || CELLDIM(c) == 0) {
P = DELINPOL(k,B1,M,b);
if (P != NIL && CELLDIM(c) == 0) {
L = COMP(P,L); }
else if (P != NIL && CELLDIM(c) > 0) {
SWRITE("WARNING! A projection factor is everywhere zero");
SWRITE(" in the cylinder \n");
SWRITE("over the cell ");
LWRITE(LELTI(c,INDX));
SWRITE(" of poistive dimension. The McCallum projection \n");
SWRITE("may not be valid.\n");
}
}
}
S = COMP(S1,S);
}
Step3: /* Searches non-zero substituted projection factors to see if the factors
of necessary delineating polynomials are included. ONLY IN 0-dim case! */
while(L != NIL) {
ADV(L,&P,&L);
P = AFUPGS(M,P); /* gets squarefree part */
for(Sp = S; Sp != NIL && PDEG(P) > 0; Sp = RED(Sp)) {
Q = FIRST(Sp);
if (Q != 0) {
AFUPGC(M,P,Q,&G,&T1,&T2);
if (PDEG(G) != 0)
P = T1; }
}
if (PDEG(P) > 0) {
SWRITE("Error! Delineating polynomial should be added over cell");
OWRITE(LELTI(c,INDX));
SWRITE("!\n");
}
else {
if (GVNFV > k+1) {
SWRITE("Warning! Some ");
IWRITE(k+1);
SWRITE("-level projection factor is acting as a \n");
SWRITE("delineating polynomial for another! CAD Simplification does not\n");
SWRITE("take this into account!\n");
GVPFASDPFLAG = TRUE;
}
}
}
S = INV(S);
goto Return;
Return: /* Prepare for return. */
return(S);
}
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