OpenXM_contrib2/asir2000/lib/sp - diff

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Diff for /OpenXM_contrib2/asir2000/lib/sp between version 1.4 and 1.18

version 1.4, 2000/03/17 01:33:49

version 1.18, 2018/04/06 07:40:44

Line 1

/* $OpenXM: OpenXM_contrib2/asir2000/lib/sp,v 1.3 2000/03/10 09:22:39 noro Exp $ */

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* $OpenXM: OpenXM_contrib2/asir2000/lib/sp,v 1.17 2016/02/04 04:17:21 noro Exp $

sp : functions related to algebraic number fields

Revision History:

2000/03/10 noro fixed several bugs

2001/10/12 noro if USE_PARI_FACTOR is nonzero, pari factor is called

2000/03/10 noro fixed several bugs around gathering algebraic numbers

1999/08/24 noro modified for 1999 release version

#include "defs.h"

extern ASCENT,GCDTIME,UFTIME,RESTIME,SQTIME,PRINT$

extern Ord$

extern SpOrd$

extern USE_PARI_FACTOR$

/* gen_sp can handle non-monic poly */

def gen_sp(P)

{

P = ptozp(P);

V = var(P);

D = deg(P,V);

LC = coef(P,D,V);

F = LC^(D-1)*subst(P,V,V/LC);

/* F must be monic */

L = sp(F);

return cons(map(subst,car(L),V,LC*V),cdr(L));

}

def sp(P)

{

RESTIME=UFTIME=GCDTIME=SQTIME=0;

Line 147 def flatmf(L) {

Line 211 def flatmf(L) {

def af(P,AL)

{

RESTIME=UFTIME=GCDTIME=SQTIME=0;

V = var(P);

LC = coef(P,deg(P,V),V);

if ( ntype(LC) != 1 )

P = simpalg(1/LC*P);

S = reverse(asq(P));

for ( L = []; S != []; S = cdr(S) ) {

FM = car(S); F = FM[0]; M = FM[1];

Line 163 def af_sp(P,AL,HINT)

Line 231 def af_sp(P,AL,HINT)

{

if ( !P || type(P) == NUM )

return [P];

V = var(P);

LC = coef(P,deg(P,V),V);

if ( ntype(LC) != 1 )

P = simpalg(1/LC*P);

P1 = simpcoef(simpalg(P));

return af_spmain(P1,AL,1,HINT,P1,[]);

}

Line 544 def simpcoef(P) {

Line 616 def simpcoef(P) {

}

def ufctrhint_heuristic(P,HINT,PP,SHIFT) {

if ( USE_PARI_FACTOR )

return pari_ufctr(P);

else

return asir_ufctrhint_heuristic(P,HINT,PP,SHIFT);

}

def pari_ufctr(P) {

F = pari(factor,P);

S = size(F);

for ( I = S[0]-1, R = []; I >= 0; I-- )

R = cons(vtol(F[I]),R);

return cons([1,1],R);

}

def asir_ufctrhint_heuristic(P,HINT,PP,SHIFT) {

V = var(P); D = deg(P,V);

if ( D == HINT )

return [[P,1]];

Line 580 def ufctrhint2(P,HINT,PP,AL)

Line 667 def ufctrhint2(P,HINT,PP,AL)

return [[P,1]];

if ( AL == [] )

return ufctrhint(P,HINT);

/* if P != norm(PP) then call the generic ufctrhint() */

for ( T = AL, E = 1; T != []; T = cdr(T) ) {

D = defpoly(car(T)); E *= deg(D,var(D));

}

if ( E*deg(PP,var(PP)) != deg(P,var(P)) )

return ufctrhint(P,HINT);

/* P = norm(PP) */

L = resfctr(algptorat(PP),map(defpoly,AL),map(algtorat,AL),P);

for ( T = reverse(L[1]), DL = []; T != []; T = cdr(T) )

DL = cons(deg(car(car(T)),a_),DL);

Line 724 def norm_ch_lag(V,VM,P,P0) {

Line 820 def norm_ch_lag(V,VM,P,P0) {

def cr_gcda(P1,P2)

{

if ( !(V = var(P1)) || !var(P2) )

if ( !P1 )

return P2;

if ( !P2 )

return P1;

if ( !var(P1) || !var(P2) )

return 1;

V = var(P1);

EXT = union_sort(getalgtreep(P1),getalgtreep(P2));

if ( EXT == [] )

return gcd(P1,P2);

Line 753 def cr_gcda(P1,P2)

Line 854 def cr_gcda(P1,P2)

break;

if ( J != length(DL) )

continue;

Ord = 2; NOSUGAR = 1;

SpOrd = 2; NOSUGAR = 1;

T = ag_mod(G1 % MOD,G2 % MOD,ML,VL,MOD);

if ( dp_gr_print() )

print(".");

Line 967 def ag_mod(F1,F2,D,VL,MOD)

Line 1068 def ag_mod(F1,F2,D,VL,MOD)

VL = cons(V,VL); B = append([F1,F2],D); N = length(VL);

while ( 1 ) {

FLAGS = dp_gr_flags(); dp_gr_flags(["Reverse",1,"NoSugar",1]);

G = dp_gr_mod_main(B,VL,0,MOD,Ord);

G = dp_gr_mod_main(B,VL,0,MOD,SpOrd);

dp_gr_flags(FLAGS);

if ( length(G) == 1 )

return 1;

Line 1201 def ag_mod_single6(F1,F2,D,MOD)

Line 1302 def ag_mod_single6(F1,F2,D,MOD)

def inverse_by_gr_mod(C,D,MOD)

{

Ord = 2;

SpOrd = 2;

dp_gr_flags(["NoSugar",1]);

G = dp_gr_mod_main(cons(x*C-1,D),cons(x,vars(D)),0,MOD,Ord);

G = dp_gr_mod_main(cons(x*C-1,D),cons(x,vars(D)),0,MOD,SpOrd);

dp_gr_flags(["NoSugar",0]);

if ( length(G) == 1 )

return 1;

Line 1262 def resfctr(F,L,V,N)

Line 1363 def resfctr(F,L,V,N)

N = ptozp(N);

V0 = var(N);

DN = diff(N,V0);

for ( I = 0, J = 2, Len = deg(N,V0)+1; I < 5; J++ ) {

LC = coef(N,deg(N,V0),V0);

M = prime(J);

LCD = coef(DN,deg(DN,V0),V0);

G = gcd(N,DN,M);

J = 2;

if ( !deg(G,V0) ) {

while ( 1 ) {

I++;

Len = deg(N,V0)+1;

T = nfctr_mod(N,M);

for ( I = 0; I < 5; J++ ) {

if ( T < Len ) {

M = prime(J);

Len = T; M0 = M;

if ( !(LC%M) || !(LCD%M))

}

continue;

}

G = gcd(N,DN,M);

}

if ( !deg(G,V0) ) {

S = spm(L,V,M0);

I++;

T = nfctr_mod(N,M);

if ( T < Len ) {

Len = T; M0 = M;

}

S = spm(L,V,M0);

if ( S ) break;

}

T = resfctr_mod(F,S,M0);

return [T,S,M0];

}

Line 1287 def resfctr_mod(F,L,M)

Line 1397 def resfctr_mod(F,L,M)

C = res(var(MP),B,MP) % M;

R = cons(flatten(cdr(modfctr(C,M))),R);

}

return R;

return reverse(R);

}

def flatten(L)

Line 1303 def spm(L,V,M)

Line 1413 def spm(L,V,M)

U = modfctr(car(L),M);

for ( T = cdr(U), R = []; T != []; T = cdr(T) ) {

S = car(T);

if ( S[1] > 1 ) return 0;

R = cons([subst(S[0],var(S[0]),a_),[var(S[0]),a_]],R);

}

return R;

}

L1 = spm(cdr(L),cdr(V),M);

if ( !L1 ) return 0;

F0 = car(L); V0 = car(V); VR = cdr(V);

for ( T = L1, R = []; T != []; T = cdr(T) ) {

S = car(T);

Line 1315 def spm(L,V,M)

Line 1427 def spm(L,V,M)

U = fctr_mod(F1,V0,S[0],M);

VS = var(S[0]);

for ( W = U; W != []; W = cdr(W) ) {

if ( car(W)[1] > 1 ) return 0;

A = car(car(W));

if ( deg(A,V0) == 1 ) {

A = monic_mod(A,V0,S[0],M);

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