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/*======================================================================
Jp <- GROUPSAMEPJ(r,J)
Group the same projection polynomials.
\Input
\parm{r} is the positive BETA-integer.
\parm{J} is a list of polynomial in r variables.
\Output
\parm{J'} is the list such that same elements are grouped.
======================================================================*/
#include "qepcad.h"
/* Projection point equal */
BDigit PRJPNTEQUAL(Word A, Word B)
{
if (LENGTH(A) != LENGTH(B))
return 0;
/* Both primitive */
Word a = FIRST(A), b = FIRST(B);
if (ISPRIMIT(a) && ISPRIMIT(b)) {
Word aC,aK,ac,bC,bK,bc;
FIRST3(a,&aC,&aK,&ac);
FIRST3(b,&bC,&bK,&bc);
if (!EQUAL(aC,bC)) return 0;
if (EQUAL(FIRST(aK),SECOND(aK)) && EQUAL(aK,bK)) return 1;
if (EQUAL(FIRST(aK),SECOND(aK)) && EQUAL(FIRST(bK),SECOND(bK)) && !EQUAL(aK,bK)) return 0;
if (RNCOMP(SECOND(aK),FIRST(bK)) <= 0 || RNCOMP(FIRST(aK),SECOND(bK)) >= 0) return 0;
return EQUAL(ac,bc);
}
/* Both Not Primitive */
if (!ISPRIMIT(a) && !ISPRIMIT(b)) {
if (!PRJPNTEQUAL(LIST1(SECOND(A)),LIST1(SECOND(B)))) return 0;
Word aC,aK,aM,aI,ac,bC,bK,G,Af,Bf;
FIRST5(a,&aC,&aK,&aM,&aI,&ac);
FIRST2(b,&bC,&bK);
if (EQUAL(FIRST(aK),SECOND(aK)) && EQUAL(FIRST(bK),SECOND(bK)) && !EQUAL(aK,bK)) return 0;
if (RNCOMP(SECOND(aK),FIRST(bK)) <= 0 || RNCOMP(FIRST(aK),SECOND(bK)) >= 0) return 0;
if (EQUAL(aC,bC)) return 1;
AFUPGC(aM,aC,bC,&G,&Af,&Bf);
if (PDEG(G) < 1) return 0;
Word KL = LIST2(FIRST(aK),LIST2(1,1));
Word KR = LIST2(SECOND(aK),LIST2(1,1));
Word sL = AFSIGN(aM,aI,AFPEMV(1,aM,G,KL));
Word sR = AFSIGN(aM,aI,AFPEMV(1,aM,G,KR));
return (EQUAL(KL,KR) && sL == 0) || (sL == 1 && sR == -1) || (sL == -1 && sR == 1);
}
/* One primitive, the other not */
if (ISPRIMIT(a) != ISPRIMIT(b)) {
SWRITE("This condition not implemented in PRJPNTEQUAL!\n");
FAIL("PRJPNTEQUAL","Incomplete Implementation Error!");
}
return -1;
}
Word GROUPSAMEPJ(Word r, Word J)
{
Word J1,Jp,Js,t, Js1, Jt, J2, Jt2, i;
Step1: /* Group. */
Jp = NIL; Js = J;
i = 0;
while (Js != NIL)
{
ADV(Js,&J1,&Js);
Js1 = LELTI(J1,PO_POLY);
Jt = Jp;
t = 0;
while (Jt != NIL)
{
ADV(Jt,&J2,&Jt);
Jt2 = LELTI(J2,PO_POLY);
if ((LELTI(J1,PO_TYPE) == PO_POINT && LELTI(J2,PO_TYPE) == PO_POINT
&& PRJPNTEQUAL(Js1,Jt2)) ||
(LELTI(J1,PO_TYPE) != PO_POINT && LELTI(J2,PO_TYPE) != PO_POINT
&& EQUAL(Js1,Jt2)))
{
SLELTI(J2,PO_PARENT,CONC(LELTI(J2,PO_PARENT),LELTI(J1,PO_PARENT)));
t = 1;
break;
}
}
if (t == 0)
{
i = i + 1;
SLELTI(J1,PO_LABEL,LIST3(LFS("J"),r,i));
Jp = COMP(J1,Jp);
}
}
Jp = INV(Jp);
Return: /* Prepare for return. */
return(Jp);
}
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