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/*======================================================================
P <- PROJMCmod(r,A)
A "safe" half-way implementation of the improved McCallum projection.
We ignore equational constraints!
\Input
\parm{r} is a $\beta$--integer.
\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 "safe" half-way improved McCallum's projection of $A$.
======================================================================*/
#include "qepcad.h"
#include <iostream>
#include <sstream>
#include <cstdlib>
using namespace std;
Word QepcadCls::PROJMCmod(Word r, Word A)
{
Word A1,A2,Ap,Ap1,Ap2,App,D,L,Lh,P,R,W,i,t,Q,j,S;
Word Ls, Lc,LL,f,rp,fp,T1,fef,esu,AssTmp,Sf;
Step1: /* Obtain coefficients. */
P = NIL;
Ap = A;
while (Ap != NIL) {
ADV(Ap,&A1,&Ap);
Ap1 = LELTI(A1,PO_POLY);
/* Deal with projection points!: NOT REALLY IMPLEMENTED RIGHT NOW! */
if (LELTI(A1,PO_TYPE) == PO_POINT) {
W = MPOLY(RED(Ap1),NIL,LIST1(LIST2(PT_PRJ,A1)),PO_POINT,PO_KEEP);
P = COMP(W,P);
continue;
}
/* Handle the leading coefficient! */
L = PLDCF(Ap1);
Lh = NIL;
t = 0;
/*-- TEST NEW --*/
if (experimentalExtensionFlag)
{
bool qfc = qfrCheckNonVanishing(r-1,L,GVNA.W,GVNQFF.W,GVVL.W);
if (qfc) continue;
}
/*-- END TEST NEW --*/
if (!VERIFYCONSTSIGN(r-1,IPIP(r-1,ISIGNF(PLBCF(r-1,L)),L),1,GVNA.W)) {
W = MPOLY(L,NIL,LIST1(LIST3(PO_LCO,0,A1)),PO_OTHER,PO_KEEP);
P = COMP(W,P);
Lh = COMP(L,Lh);
t = 1; }
/* If r = 2 OR r-1 is in free variable space, the leading coefficient is always enough! */
if ((t && (r == 2 || (PCMZERROR && r-1 <= GVNFV)))
|| (experimentalExtensionFlag && qfrCheckNonNullified(r,Ap1,GVNA.W,GVNQFF.W,GVVL.W))
)
t = 0;
else if (t) {
T1 = ACLOCK();
/**************
If every factor of the leading coefficient is
1 identically non-zero, OR
2 of a level corresponding to a FULLDE or FULLDA quantifier, OR
3 in free variable space when the PCMZERROR option is used, OR
4 has no common zero with the system of all other coefficients
Then ... we need only include the leading coefficient.
****************/
/* Loop over each factor f of L, the leading coefficient of Ap1 */
IPFAC(r-1,L,&Ls,&Lc,&LL);
S = 0;
fef = 1; /* For every factor ... initially true. */
for(Word LLp = LL; t != 0 && fef && LLp != NIL; LLp = RED(LLp))
{
f = SECOND(FIRST(LLp));
PSIMREP(r-1,f,&rp,&fp);
Word tf = 0;
/* Test 1: identically non-zero */
//--ORIGINAL-- tf = tf || VERIFYCONSTSIGN(r-1,f,1,GVNA.W);
tf = tf || (experimentalExtensionFlag && qfrCheckNonVanishing(r-1,f,GVNA.W,GVNQFF.W,GVVL.W));
/* Test 2: of a level corresponding to a FULLDE or FULLDA quantifier */
j = rp - GVNFV;
Q = j > 0 ? LELTI(GVQ,j) : NIL;
tf = tf || (Q == FULLDE || Q == FULLDA);
/* Test 3: in free variable space when the PCMZERROR option is used */
tf = tf || (PCMZERROR && rp <= GVNFV);
/* Test 4: has no common zero with the system of all other coefficients */
if (!tf)
{
/* Get coeff sys for reductum & see if it's unsat */
if (S == 0) {
AssTmp = (GVNA == NIL) ? TRUE : CHANGEASSUMPTIONSLEVEL(GVNA.W,r-1,1);
S = COEFSYS(r,PRED(Ap1));
if (S != 1) S = SIMPLIFYSYSLIST(r-1,S,AssTmp); }
if (S == 1) { t = 0; continue; }
/* Add f to S and do a quick test for unsat */
Sf = NIL; for(Word Sp = S; Sp != NIL; Sp = RED(Sp)) Sf = COMP(COMP(f,FIRST(Sp)),Sf);
Sf = SIMPLIFYSYSLIST(r-1,Sf,AssTmp);
tf = tf || Sf == 1;
/* Last resort: Try to determine unsat-ness via CAD! */
if (!tf)
{
QepcadCls Q;
esu = 1; /* Every System Unsat flag */
for(; esu && Sf != NIL; Sf = RED(Sf))
esu = (SYSSOLVECAD(r-1,FIRST(Sf),GVNA == NIL ? TRUE : GVNA.W,GVVL,Q) == NIL);
/* NOTE: "projection points" need to be implemented so when SYSSOLVECAD returns
a list of points, we simply add those to the projection points, rather than
giving up and adding all coefficients! */
tf = esu;
}
}
fef = fef && tf;
}
t = !fef;
T1 = ACLOCK() - T1;
if (PCVERBOSE) {
SWRITE("LDCF sufficiency check took "); IWRITE(T1); SWRITE("ms\n");
if (!t)
SWRITE("Found LDCF sufficient for ");
else
SWRITE("Unable to determine LDCF sufficiency for ");
IPDWRITE(r,Ap1,GVVL);
SWRITE("\n");
}
}
/* Handle the rest of the coefficients as needed. */
i = 0;
while (t) {
Ap1 = PRED(Ap1); i++; L = PLDCF(Ap1);
t = 0;
if (Ap1 != 0)
if (!PCONST(r - 1,L))
if (!IPFZT(r - 1,Lh)) {
W = MPOLY(L,NIL,LIST1(LIST3(PO_LCO,i,A1)),PO_OTHER,PO_KEEP);
P = COMP(W,P);
Lh = COMP(L,Lh);
t = 1; } }
}
Step2: /* Obtain discriminants. */
Ap = A;
while (Ap != NIL) {
ADV(Ap,&A1,&Ap);
if (LELTI(A1,PO_TYPE) == PO_POINT) continue;
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);
if (LELTI(A1,PO_TYPE) == PO_POINT) continue;
Ap1 = LELTI(A1,PO_POLY);
App = Ap;
while (App != NIL) {
ADV(App,&A2,&App);
if (LELTI(A2,PO_TYPE) == PO_POINT) continue;
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);
}
/* QepcadCls Q; Word G; */
/* for(t = 0; t == 0 && Sp != NIL; Sp = RED(Sp)) */
/* if ((G = SYSSOLVECAD(r-1,FIRST(Sp),GVNA == NIL ? TRUE : GVNA.W,GVVL,Q)) != NIL) */
/* { */
/* /* If there are finitely many solutions, add those points as projection */
/* points. * / */
/* // if (ISLIST(G) && G != NIL) { */
/* if (ISLIST(G) && G == NIL) { //-- JUST HERE BECAUSE LIFTING DOESN'T SUPPORT POINTS */
/* for(Word Lp = G; Lp != NIL; Lp = RED(Lp)) { */
/* /* ADD POINTS to PROJECTION POLS! * / */
/* Word X = NIL; /* List of all sample points up to and inluding FIRST(G) * / */
/* Word c = Q.GVPC; */
/* for(Word I = LELTI(FIRST(Lp),INDX); I != NIL; I = RED(I)) */
/* { */
/* c = LELTI(LELTI(c,CHILD),FIRST(I)); */
/* Word s = LELTI(c,SAMPLE); */
/* X = COMP(ISPRIMIT(s) ? (LENGTH(s) > 3 ? FOURTH(s) : s) : s,X); */
/* } */
/* W = MPOLY(X,NIL,LIST1(LIST2(PT_NUL,A1)),PO_POINT,PO_KEEP); */
/* P = COMP(W,P); */
/* } */
/* } */
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