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/*======================================================================
P <- PROJMC(r,A)
McCallum's projection excluding leading coeff's.
\Input
\parm{r} is a $\beta$--integer. $r = 3$.
\parm{A} is the list of distinct positive irreducible elements
of $Z[x_1,\ldots,x_r]$ of positive degree in $x_r$.
\Output
\parm{P} is the McCallum's projection of $A$.
======================================================================*/
#include "qepcad.h"
Word QepcadCls::PROJMCx(Word r, Word A)
{
Word A1,A2,Ap,Ap1,Ap2,App,D,P,R,W;
Step1: /* Obtain coefficients. */
P = NIL;
Step2: /* Obtain discriminants. */
Ap = A;
while (Ap != NIL) {
ADV(Ap,&A1,&Ap);
if (PCEQC && LELTI(A1,PO_TYPE) != PO_ECON) continue;
Ap1 = LELTI(A1,PO_POLY);
if (PDEG(Ap1) >= 2) {
D = IPDSCRQE(r,Ap1);
W = MPOLY(D,NIL,LIST1(LIST4(PO_DIS,0,0,A1)),PO_OTHER,PO_KEEP);
P = COMP(W,P); } }
Step3: /* Obtain resultants. */
Ap = A;
while (Ap != NIL) {
ADV(Ap,&A1,&Ap);
Ap1 = LELTI(A1,PO_POLY);
App = Ap;
while (App != NIL) {
ADV(App,&A2,&App);
if (PCEQC &&
LELTI(A1,PO_TYPE) != PO_ECON &&
LELTI(A2,PO_TYPE) != PO_ECON) continue;
Ap2 = LELTI(A2,PO_POLY);
R = IPRESQE(r,Ap1,Ap2);
W = MPOLY(R,NIL,LIST1(LIST6(PO_RES,0,0,A1,0,A2)),PO_OTHER,PO_KEEP);
P = COMP(W,P); } }
Step4: /* Finish. */
P = INV(P);
goto Return;
Return: /* Prepare for return. */
return(P);
}
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