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/*======================================================================
P <- PROJCO(r,A)
Collins' projection.
\Input
\parm{r} is a $\beta$--integer. $r \geq 2$.
\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 Collins' projection of $A$.
======================================================================*/
#include "qepcad.h"
Word QepcadCls::PROJCO(Word r, Word A)
{
Word A1,A2,Ap,Ap1,Ap2,App,D,L,L1,P,R,R1,R11,R2,R21,Rp,Rp1,Rp11,Rp2,
Rpp,Rs2,S1,Sp1,T,W,ap1,b,d,i,i1,i2,k,t;
Step1: /* $r = 2$. */
if (r > 2) goto Step2;
P = NIL; Ap = A;
while (Ap != NIL) {
ADV(Ap,&A1,&Ap);
if (PCEQC && LELTI(A1,PO_TYPE) != PO_ECON) continue;
Ap1 = LELTI(A1,PO_POLY);
W = MPOLY(PLDCF(Ap1),NIL,LIST1(LIST3(PO_LCO,0,A1)),PO_OTHER,PO_KEEP);
P = COMP(W,P);
if (PDEG(Ap1) >= 2) {
D = IPDSCRQE(2,Ap1);
W = MPOLY(D,NIL,LIST1(LIST4(PO_DIS,0,0,A1)),PO_OTHER,PO_KEEP);
P = COMP(W,P); } }
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);
T = IPRESQE(2,Ap1,Ap2);
W = MPOLY(T,NIL,LIST1(LIST6(PO_RES,0,0,A1,0,A2)),PO_OTHER,PO_KEEP);
P = COMP(W,P); } }
P = INV(P);
goto Return;
Step2: /* Determine number of reducta needed for each $A_i$. */
Ap = A; R = NIL;
while (Ap != NIL) {
ADV(Ap,&A1,&Ap);
Ap1 = LELTI(A1,PO_POLY);
R1 = LIST1(Ap1);
ap1 = PLDCF(Ap1);
S1 = LIST1(ap1);
b = PCONST(r - 1,ap1);
d = 0;
Ap1 = PRED(Ap1);
while (!b && !d && Ap1 != 0) {
R1 = COMP(Ap1,R1);
ap1 = PLDCF(Ap1);
b = PCONST(r - 1,ap1);
if (!b) {
S1 = COMP(ap1,S1);
d = IPFZT(r - 1,S1); }
Ap1 = PRED(Ap1); }
R1 = INV(R1);
R = COMP(R1,R); }
R = INV(R);
Step3: /* Process each $R_i$. */
P = NIL; Rp = R; Ap = A;
while (Rp != NIL) {
ADV(Rp,&R1,&Rp); ADV(Ap,&A1,&Ap);
if (PCEQC && LELTI(A1,PO_TYPE) != PO_ECON) continue;
S1 = NIL;
i = 0;
do {
ADV(R1,&R11,&R1);
W = MPOLY(PLDCF(R11),NIL,LIST1(LIST3(PO_LCO,i,A1)),
PO_OTHER,PO_KEEP);
P = COMP(W,P);
if (PDEG(R11) >= 2) {
Rp11 = IPDMV(r,R11);
L = IPPSCT(r,R11,Rp11,S1);
k = 0;
while (L != NIL) {
ADV(L,&L1,&L);
W = MPOLY(L1,NIL,LIST1(LIST4(PO_DIS,k,i,A1)),PO_OTHER,PO_KEEP);
P = COMP(W,P);
k = k + 1; }
S1 = COMP(PLDCF(R11),S1); }
i = i + 1; }
while (R1 != NIL); }
Step4: /* Process pairs $R_i$, $R_j$. */
Rp = R; Ap = A;
while (Rp != NIL) {
ADV(Rp,&R1,&Rp); ADV(Ap,&A1,&Ap);
Rpp = Rp; App = Ap;
while (Rpp != NIL) {
ADV(Rpp,&R2,&Rpp); ADV(App,&A2,&App);
if (PCEQC &&
LELTI(A1,PO_TYPE) != PO_ECON &&
LELTI(A2,PO_TYPE) != PO_ECON) continue;
S1 = NIL;
Rp1 = R1;
i1 = 0;
do {
ADV(Rp1,&R11,&Rp1);
if (PDEG(R11) >= 1) {
Rs2 = NIL;
Rp2 = R2;
Sp1 = S1;
do {
ADV(Rp2,&R21,&Rp2);
Rs2 = COMP(R21,Rs2);
Sp1 = COMP(PLDCF(R21),Sp1);
t = IPFZT(r - 1,Sp1); }
while (t != 1 && Rp2 != NIL);
Rs2 = INV(Rs2);
Sp1 = S1;
i2 = 0;
do {
ADV(Rs2,&R21,&Rs2);
if (PDEG(R21) >= 1) {
L = IPPSCT(r,R11,R21,Sp1);
k = 0;
while (L != NIL) {
ADV(L,&L1,&L);
W = MPOLY(L1,NIL,LIST1(LIST6(PO_RES,k,i1,A1,i2,A2)),
PO_OTHER,PO_KEEP);
P = COMP(W,P);
k = k + 1; }
Sp1 = COMP(PLDCF(R21),Sp1); }
i2 = i2 + 1; }
while (Rs2 != NIL); }
S1 = COMP(PLDCF(R11),S1);
i1 = i1 + 1; }
while (Rp1 != NIL); } }
Step5: /* Finish. */
P = INV(P);
goto Return;
Return: /* Prepare for return. */
return(P);
}
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