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/*===========================================================================
R <- IPRESPRS(r,A,B)
Integral polynomial resultant, subresultant polynomial remainder
sequence algorithm.
Inputs
r : a BETA-digit, r > 0.
A,B : in Z[X1,...,Xr], A and B non-zero, deg(A) >= deg(B).
Outputs
R : the resultant of A and B, computed using the
(non-modular) subresultant prs algorithm.
===========================================================================*/
#ifdef _OLD_
Word IPRESPRS(Word r, Word A, Word B)
{
Word G1,G2,G3,Gh3,R,S,d0,d1,g1,h0,h1,hs0,hs1,i,n1,n2,n3,rp,a,b;
Step1: /* Initialize. */
a = PDEG(A);
b = PDEG(B);
if (a < b) {
G1 = B;
G2 = A; }
else {
G1 = A;
G2 = B; }
if (b == 0) {
R = 1; /* Added 2/97 */
for(i = 1; i < r; i++) R = LIST2(0,R); /* Added 2/97 */
goto Return; } /* Added 2/97 */
n1 = PDEG(G1);
n2 = PDEG(G2);
d0 = 0;
d1 = n1 - n2;
rp = r - 1;
i = 1;
Step2: /* Compute Gh_{i+2}. */
Gh3 = IPPSR(r,G1,G2);
if (Gh3 == 0) {
if (PDEG(S) > 0)
R = 0;
else {
R = PLDCF(S);
if (a < b) {
if (ODD(a) && ODD(b))
R = IPNEG(rp,R); } }
goto Return; }
if (EVEN(d1) == 1)
Gh3 = IPNEG(r,Gh3);
n3 = PDEG(Gh3);
Step3: /* Compute hi. */
if (i > 1) {
g1 = PLDCF(G1);
h1 = IPEXP(rp,g1,d0);
if (i > 2) {
hs0 = IPEXP(rp,h0,d0 - 1);
h1 = IPQ(rp,h1,hs0);
hs0 = 0; } }
Step4: /* Compute G_{i+2}. */
if (i == 1)
G3 = Gh3;
else {
hs1 = IPEXP(rp,h1,d1);
hs1 = IPPROD(rp,g1,hs1);
hs1 = LIST2(0,hs1);
G3 = IPQ(r,Gh3,hs1);
hs1 = 0;
Gh3 = 0; }
Step5: /* Update. */
S = G3;
n1 = n2;
n2 = n3;
d0 = d1;
d1 = n1 - n2;
G1 = G2;
G2 = G3;
if (i > 1)
h0 = h1;
i = i + 1;
goto Step2;
Return: /* Prepare for return. */
return(R);
}
#else
/*===========================================================================
R <- IPRESPRS(r,A,B)
Integral polynomial resultant, polynomial remainder sequence method.
Inputs
r : a BETA-digit, r > 0.
A, B : integral polynomials having positive degrees.
Output
R : the resultant of A and B.
===========================================================================*/
Word IPRESPRS(r,A,B)
BDigit r;
Word A,B;
{
Word G1,G2,G3,Gh3,R,g1,g2,gs1,gs2,h0,h1,h2,hs0,hs1;
BDigit d0,d1,i,n1,n2,n3,rp;
Step1: /* Initialize. */
if (PDEG(A) >= PDEG(B)) {
G1 = A;
G2 = B; }
else {
G1 = B;
G2 = A; }
n1 = PDEG(G1);
n2 = PDEG(G2);
d0 = 0;
d1 = n1 - n2;
rp = r - 1;
i = 1;
Step2: /* Compute Gh_{i+2} and n_{i+2}. */
Gh3 = IPPSR(r,G1,G2);
if (Gh3 == 0) {
R = 0;
goto Return; }
if (EVEN(d1))
Gh3 = IPNEG(r,Gh3);
n3 = PDEG(Gh3);
Step3: /* Compute h_i. */
if (i > 1) {
g1 = PLDCF(G1);
h1 = IPEXP(rp,g1,d0);
if (i > 2) {
hs0 = IPEXP(rp,h0,d0 - 1);
h1 = IPEQ(rp,h1,hs0); } }
Step4: /* Compute G_{i+2}. */
if (i == 1)
G3 = Gh3;
else {
hs1 = IPEXP(rp,h1,d1);
hs1 = IPPROD(rp,g1,hs1);
hs1 = PMON(hs1,0);
G3 = IPEQ(r,Gh3,hs1); }
Step5: /* Update. */
n1 = n2;
n2 = n3;
d0 = d1;
d1 = n1 - n2;
G1 = G2;
G2 = G3;
if (i > 1)
h0 = h1;
i = i + 1;
if (n2 > 0)
goto Step2;
Step6: /* Finish. */
g1 = PLDCF(G1);
g2 = PLDCF(G2);
if (d1 == 1)
R = g2;
else {
if (i == 2) {
R = IPEXP(rp,g2,d1);
if (d0 != 1) {
gs1 = IPEXP(rp,g1,d0 * d1 - d0);
R = IPEQ(rp,R,gs1); } }
else {
if (d0 == 1)
h1 = g1;
else {
hs0 = IPEXP(rp,h0,d0-1);
gs1 = IPEXP(rp,g1,d0);
h1 = IPEQ(rp,gs1,hs0); }
hs1 = IPEXP(rp,h1,d1-1);
gs2 = IPEXP(rp,g2,d1);
h2 = IPEQ(rp,gs2,hs1);
R = IPPROD(rp,g2,h2);
R = IPEQ(rp,R,g2); } }
Return: /* Return R. */
return(R);
}
#endif
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