File: [local] / OpenXM_contrib2 / asir2000 / lib / bfct (download)
Revision 1.8, Thu Dec 14 09:13:37 2000 UTC (23 years, 5 months ago) by noro
Branch: MAIN
Changes since 1.7: +13 -4
lines
The bug in weyl_minipoly may be fixed.
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/*
* Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
* All rights reserved.
*
* FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
* non-exclusive and royalty-free license to use, copy, modify and
* redistribute, solely for non-commercial and non-profit purposes, the
* computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
* conditions of this Agreement. For the avoidance of doubt, you acquire
* only a limited right to use the SOFTWARE hereunder, and FLL or any
* third party developer retains all rights, including but not limited to
* copyrights, in and to the SOFTWARE.
*
* (1) FLL does not grant you a license in any way for commercial
* purposes. You may use the SOFTWARE only for non-commercial and
* non-profit purposes only, such as academic, research and internal
* business use.
* (2) The SOFTWARE is protected by the Copyright Law of Japan and
* international copyright treaties. If you make copies of the SOFTWARE,
* with or without modification, as permitted hereunder, you shall affix
* to all such copies of the SOFTWARE the above copyright notice.
* (3) An explicit reference to this SOFTWARE and its copyright owner
* shall be made on your publication or presentation in any form of the
* results obtained by use of the SOFTWARE.
* (4) In the event that you modify the SOFTWARE, you shall notify FLL by
* e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
* for such modification or the source code of the modified part of the
* SOFTWARE.
*
* THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
* MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
* EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
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* MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
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* OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
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* DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
* ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
* FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
* DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
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*
* $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.8 2000/12/14 09:13:37 noro Exp $
*/
/* requires 'primdec' */
/* annihilating ideal of F^s */
def ann(F)
{
V = vars(F);
N = length(V);
D = newvect(N);
for ( I = 0; I < N; I++ )
D[I] = [deg(F,V[I]),V[I]];
qsort(D,compare_first);
for ( V = [], I = N-1; I >= 0; I-- )
V = cons(D[I][1],V);
for ( I = N-1, DV = []; I >= 0; I-- )
DV = cons(strtov("d"+rtostr(V[I])),DV);
W = append([y1,y2,t],V);
DW = append([dy1,dy2,dt],DV);
B = [1-y1*y2,t-y1*F];
for ( I = 0; I < N; I++ ) {
B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
}
dp_nelim(2);
G0 = dp_weyl_gr_main(B,append(W,DW),0,0,6);
G1 = [];
for ( T = G0; T != []; T = cdr(T) ) {
E = car(T); VL = vars(E);
if ( !member(y1,VL) && !member(y2,VL) )
G1 = cons(E,G1);
}
G2 = map(subst,G1,dt,1);
G3 = map(b_subst,G2,t);
G4 = map(subst,G3,t,-1-s);
return G4;
}
def indicial1(F,V)
{
W = append([y1,t],V);
N = length(V);
B = [t-y1*F];
for ( I = N-1, DV = []; I >= 0; I-- )
DV = cons(strtov("d"+rtostr(V[I])),DV);
DW = append([dy1,dt],DV);
for ( I = 0; I < N; I++ ) {
B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
}
dp_nelim(1);
/* we use homogenization (heuristically determined) */
G0 = dp_weyl_gr_main(B,append(W,DW),1,0,6);
G1 = map(subst,G0,y1,1);
Mat = newmat(2,2,[[-1,1],[0,1]]);
G2 = map(psi,G1,t,dt);
G3 = map(subst,G2,t,-s-1);
return G3;
}
def psi(F,T,DT)
{
D = dp_ptod(F,[T,DT]);
Wmax = weight(D);
D1 = dp_rest(D);
for ( ; D1; D1 = dp_rest(D1) )
if ( weight(D1) > Wmax )
Wmax = weight(D1);
for ( D1 = D, Dmax = 0; D1; D1 = dp_rest(D1) )
if ( weight(D1) == Wmax )
Dmax += dp_hm(D1);
if ( Wmax >= 0 )
Dmax = dp_weyl_mul(<<Wmax,0>>,Dmax);
else
Dmax = dp_weyl_mul(<<0,-Wmax>>,Dmax);
Rmax = dp_dtop(Dmax,[T,DT]);
R = b_subst(subst(Rmax,DT,1),T);
return R;
}
def weight(D)
{
V = dp_etov(D);
return V[1]-V[0];
}
def compare_first(A,B)
{
A0 = car(A);
B0 = car(B);
if ( A0 > B0 )
return 1;
else if ( A0 < B0 )
return -1;
else
return 0;
}
/* b-function of F ? */
def bfct(F)
{
V = vars(F);
N = length(V);
D = newvect(N);
for ( I = 0; I < N; I++ )
D[I] = [deg(F,V[I]),V[I]];
qsort(D,compare_first);
for ( V = [], I = 0; I < N; I++ )
V = cons(D[I][1],V);
for ( I = N-1, DV = []; I >= 0; I-- )
DV = cons(strtov("d"+rtostr(V[I])),DV);
V1 = cons(s,V); DV1 = cons(ds,DV);
G0 = indicial1(F,reverse(V));
G1 = dp_weyl_gr_main(G0,append(V1,DV1),0,1,0);
Minipoly = weyl_minipoly(G1,append(V1,DV1),0,s);
return Minipoly;
}
def weyl_minipolym(G,V,O,M,V0)
{
N = length(V);
Len = length(G);
dp_ord(O);
setmod(M);
PS = newvect(Len);
PS0 = newvect(Len);
for ( I = 0, T = G; T != []; T = cdr(T), I++ )
PS0[I] = dp_ptod(car(T),V);
for ( I = 0, T = G; T != []; T = cdr(T), I++ )
PS[I] = dp_mod(dp_ptod(car(T),V),M,[]);
for ( I = Len - 1, GI = []; I >= 0; I-- )
GI = cons(I,GI);
U = dp_mod(dp_ptod(V0,V),M,[]);
T = dp_mod(<<0>>,M,[]);
TT = dp_mod(dp_ptod(1,V),M,[]);
G = H = [[TT,T]];
for ( I = 1; ; I++ ) {
T = dp_mod(<<I>>,M,[]);
TT = dp_weyl_nf_mod(GI,dp_weyl_mul_mod(TT,U,M),PS,1,M);
H = cons([TT,T],H);
L = dp_lnf_mod([TT,T],G,M);
if ( !L[0] )
return dp_dtop(L[1],[V0]);
else
G = insert(G,L);
}
}
def weyl_minipoly(G0,V0,O0,V)
{
for ( I = 0; ; I++ ) {
Prime = lprime(I);
MP = weyl_minipolym(G0,V0,O0,Prime,V);
for ( D = deg(MP,V), TL = [], J = 0; J <= D; J++ )
TL = cons(V^J,TL);
dp_ord(O0);
NF = weyl_gennf(G0,TL,V0,O0)[0];
LHS = weyl_nf_tab(-car(TL),NF,V0);
B = weyl_hen_ttob(cdr(TL),NF,LHS,V0,Prime);
if ( B ) {
R = ptozp(B[1]*car(TL)+B[0]);
return R;
}
}
}
def weyl_gennf(G,TL,V,O)
{
N = length(V); Len = length(G); dp_ord(O); PS = newvect(Len);
for ( I = 0, T = G, HL = []; T != []; T = cdr(T), I++ ) {
PS[I] = dp_ptod(car(T),V); HL = cons(dp_ht(PS[I]),HL);
}
for ( I = 0, DTL = []; TL != []; TL = cdr(TL) )
DTL = cons(dp_ptod(car(TL),V),DTL);
for ( I = Len - 1, GI = []; I >= 0; I-- )
GI = cons(I,GI);
T = car(DTL); DTL = cdr(DTL);
H = [weyl_nf(GI,T,T,PS)];
T0 = time()[0];
while ( DTL != [] ) {
T = car(DTL); DTL = cdr(DTL);
if ( dp_gr_print() )
print(".",2);
if ( L = search_redble(T,H) ) {
DD = dp_subd(T,L[1]);
NF = weyl_nf(GI,dp_weyl_mul(L[0],dp_subd(T,L[1])),dp_hc(L[1])*T,PS);
} else
NF = weyl_nf(GI,T,T,PS);
NF = remove_cont(NF);
H = cons(NF,H);
}
print("");
TNF = time()[0]-T0;
if ( dp_gr_print() )
print("gennf(TAB="+rtostr(TTAB)+" NF="+rtostr(TNF)+")");
return [H,PS,GI];
}
def weyl_nf(B,G,M,PS)
{
for ( D = 0; G; ) {
for ( U = 0, L = B; L != []; L = cdr(L) ) {
if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
GCD = igcd(dp_hc(G),dp_hc(R));
CG = idiv(dp_hc(R),GCD); CR = idiv(dp_hc(G),GCD);
U = CG*G-dp_weyl_mul(CR*dp_subd(G,R),R);
if ( !U )
return [D,M];
D *= CG; M *= CG;
break;
}
}
if ( U )
G = U;
else {
D += dp_hm(G); G = dp_rest(G);
}
}
return [D,M];
}
def weyl_nf_mod(B,G,PS,Mod)
{
for ( D = 0; G; ) {
for ( U = 0, L = B; L != []; L = cdr(L) ) {
if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
CR = dp_hc(G)/dp_hc(R);
U = G-dp_weyl_mul_mod(CR*dp_mod(dp_subd(G,R),Mod,[]),R,Mod);
if ( !U )
return D;
break;
}
}
if ( U )
G = U;
else {
D += dp_hm(G); G = dp_rest(G);
}
}
return D;
}
def weyl_hen_ttob(T,NF,LHS,V,MOD)
{
T0 = time()[0]; M = etom(weyl_leq_nf(T,NF,LHS,V)); TE = time()[0] - T0;
T0 = time()[0]; U = henleq(M,MOD); TH = time()[0] - T0;
if ( dp_gr_print() ) {
print("(etom="+rtostr(TE)+" hen="+rtostr(TH)+")");
}
return U ? vtop(T,U,LHS) : 0;
}
def weyl_leq_nf(TL,NF,LHS,V)
{
TLen = length(NF);
T = newvect(TLen); M = newvect(TLen);
for ( I = 0; I < TLen; I++ ) {
T[I] = dp_ht(NF[I][1]);
M[I] = dp_hc(NF[I][1]);
}
Len = length(TL); INDEX = newvect(Len); COEF = newvect(Len);
for ( L = TL, J = 0; L != []; L = cdr(L), J++ ) {
D = dp_ptod(car(L),V);
for ( I = 0; I < TLen; I++ )
if ( D == T[I] )
break;
INDEX[J] = I; COEF[J] = strtov("u"+rtostr(J));
}
if ( !LHS ) {
COEF[0] = 1; NM = 0; DN = 1;
} else {
NM = LHS[0]; DN = LHS[1];
}
for ( J = 0, S = -NM; J < Len; J++ ) {
DNJ = M[INDEX[J]];
GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
DN *= CS;
}
for ( D = S, E = []; D; D = dp_rest(D) )
E = cons(dp_hc(D),E);
BOUND = LHS ? 0 : 1;
for ( I = Len - 1, W = []; I >= BOUND; I-- )
W = cons(COEF[I],W);
return [E,W];
}
def weyl_nf_tab(A,NF,V)
{
TLen = length(NF);
T = newvect(TLen); M = newvect(TLen);
for ( I = 0; I < TLen; I++ ) {
T[I] = dp_ht(NF[I][1]);
M[I] = dp_hc(NF[I][1]);
}
A = dp_ptod(A,V);
for ( Z = A, Len = 0; Z; Z = dp_rest(Z), Len++ );
INDEX = newvect(Len); COEF = newvect(Len);
for ( Z = A, J = 0; Z; Z = dp_rest(Z), J++ ) {
D = dp_ht(Z);
for ( I = 0; I < TLen; I++ )
if ( D == T[I] )
break;
INDEX[J] = I; COEF[J] = dp_hc(Z);
}
for ( J = 0, S = 0, DN = 1; J < Len; J++ ) {
DNJ = M[INDEX[J]];
GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
DN *= CS;
}
return [S,DN];
}
def remove_zero(L)
{
for ( R = []; L != []; L = cdr(L) )
if ( car(L) )
R = cons(car(L),R);
return R;
}
def z_subst(F,V)
{
for ( ; V != []; V = cdr(V) )
F = subst(F,car(V),0);
return F;
}
def flatmf(L) {
for ( S = []; L != []; L = cdr(L) )
if ( type(F=car(car(L))) != NUM )
S = append(S,[F]);
return S;
}
def member(A,L) {
for ( ; L != []; L = cdr(L) )
if ( A == car(L) )
return 1;
return 0;
}
def intersection(A,B)
{
for ( L = []; A != []; A = cdr(A) )
if ( member(car(A),B) )
L = cons(car(A),L);
return L;
}
def b_subst(F,V)
{
D = deg(F,V);
C = newvect(D+1);
for ( I = D; I >= 0; I-- )
C[I] = coef(F,I,V);
for ( I = 0, R = 0; I <= D; I++ )
if ( C[I] )
R += C[I]*v_factorial(V,I);
return R;
}
def v_factorial(V,N)
{
for ( J = N-1, R = 1; J >= 0; J-- )
R *= V-J;
return R;
}
end$