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/*======================================================================
T <- ACCCVBC(k,c,M,B1,b)
Are cell coordinates corresponding to variables in B1 constant?
(algebraic)
Inputs:
k : a level
c : a k-level cell
M : the minimal polynomial describing the coordinates of c's sample
point
B1: a (k + 1)-level polynomial that vanishes identically over c
b : the sample point for c
B1h: optional argument. If non-zero, B1h is a pointer to a Word in
which the function will store B1 evaluated at each coordinate that
was able to determine to be constant.
Output:
T : TRUE if ACCCVBC determines that the coordinates of c corresponding
to variables that appear in B1 are constant, UNDET if ACCCVBC
cannot be certain, FALSE if it knows there is a coordinate that is
not constant and that correspdonds to a variable that appears in B1.
======================================================================*/
#include "qepcad.h"
/* Prototypes for some local functions */
static Word SPECIALSUBS(Word k, Word M, Word a, Word Q);
static Word SECTIONPOLS(Word k, Word c, Word P);
Word QepcadCls::ACCCVBC(Word k, Word c, Word M, Word B1, Word b, Word* B1h)
{
Word d, nnf, dV, IV, i, I_i, c_i, L, Q, Qb, Qbs, F, Fp, a;
Step1: /* Initialization **********************************************/
a = NIL; /* this is the pseudo-sample point we're building up *******/
F = NIL; /* Useless now, could be usefull later. ********************/
d = 0; /* dimension of cell c_i. **********************************/
nnf = 0; /* number of variables not fixed. **************************/
dV = CINV(RED(PDEGV(k+1,B1))); /* vector of degrees of first k ******
variables of B1. ******************/
IV = LELTI(c,INDX); /* vector of indices of cell c. ******/
c_i = GVPC;
Step2: /* Loop over each level from 1 to k ****************************/
for(i = 1; i <= k; i++) {
I_i = LELTI(IV,i);
c_i = LELTI(LELTI(c_i,CHILD),I_i);
Step3: /* c_i is a section over a 0-dimensional cell ******************/
if ((I_i % 2 == 0) && d == 0) {
a = SUFFIX(a,LELTI(b,i));
continue; }
Step4: /* c_i is a section over a cell of dimension greater than zero */
if ((I_i % 2 == 0) && d > 0) {
for(L=SECTIONPOLS(i,c_i,GVPF),Qbs=1,Fp=NIL; L != NIL; L=RED(L)) {
Q = AFPFIP(i,LELTI(FIRST(L),PO_POLY));
Qb = SPECIALSUBS(i,M,a,Q); /* Qb can't be zero, by definition of
SECTIONPOLS */
Qbs = AFPEMV(nnf + 1,M,Qb,LELTI(b,i));
if (Qbs == 0) {
a = SUFFIX(a,LELTI(b,i));
break; }
else
Fp = COMP(Qb,Fp); }
if (L == NIL) {
F = CCONC(F,Fp);
nnf++;
a = SUFFIX(a,NIL);
} }
Step5: /* c_i is a sector *********************************************/
if (I_i % 2 == 1) {
d++;
nnf++;
a = SUFFIX(a,NIL); }
}
/*Step6: a is the psuedo-sample point, check that B1 is univariate at a. */
bool uniq = true;
/*
Changed to below 8/13/08
Word B1b = SPECIALSUBS(k+1,M,a,B1);
*/
Word B1b = SPECIALSUBS(k+1,M,a,AFPFIP(k+1,B1));
for(Word B1s = B1b; uniq && B1s != 0; B1s = PRED(B1s))
uniq = PCONST(nnf,PLDCF(B1s));
if (B1h != 0) *B1h = B1b;
return uniq ? TRUE : UNDET;
}
/*======================================================================
L <- SECTIONPOLS(k,c,P)
Inputs:
k : a level
c : a k-level cell
P : the QEPCAD data structure for the set of projection factors
associated with the CAD in which c resides.
Outputs:
L : the list of all k-level polynomials of which c is a section.
======================================================================*/
static Word SECTIONPOLS(Word k, Word c, Word P)
{
Word L,P_k,M,i;
L = NIL;
P_k = LELTI(P,k);
for(M = LELTI(c,MULSUB); M != NIL; M = RED(M)) {
i = FIRST(FIRST(M));
L = COMP(LELTI(P_k,i),L); }
return L;
}
/*======================================================================
Qp <- SPECIALSUBS(k,M,a,Q)
Special substitution - algebraic coordinates
k : a level
M : the minimal polynomial for an algebraic number alpha
a : a list of length not more than k, each element of
which is either an algebraic number in alpha or NIL
Q : an element of Q(alpha)[x_1,\ldots,x_k]
Output:
Qp: If a_i1, ..., a_it are the non-nil elements of a,
Qp is Q evaluated at x_i1 = a_i1, ... , x_it = a_it.
======================================================================*/
static Word SPECIALSUBS(Word k, Word M, Word a, Word Q)
{
Word r,i,Qp,L,x;
r = k;
i = 1;
Qp = Q;
for(L = a; L != NIL; L = RED(L)) {
x = FIRST(L);
if (x != NIL) {
Qp = AFPEV(r,M,Qp,i,x);
r--;
}
else
i++;
}
return Qp;
}
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