version 1.14, 2001/01/10 04:30:35 |
version 1.17, 2002/01/28 01:02:03 |
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* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, |
* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, |
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. |
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. |
* |
* |
* $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.13 2000/12/27 07:17:39 noro Exp $ |
* $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.16 2001/01/18 00:52:32 noro Exp $ |
*/ |
*/ |
/* requires 'primdec' */ |
/* requires 'primdec' */ |
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Line 212 def generic_bfct(F,V,DV,W) |
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Line 212 def generic_bfct(F,V,DV,W) |
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N = length(V); |
N = length(V); |
N2 = N*2; |
N2 = N*2; |
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/* If W is a list, convert it to a vector */ |
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if ( type(W) == 4 ) |
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W = newvect(length(W),W); |
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dp_weyl_set_weight(W); |
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/* create a term order M in D<x,d> (DRL) */ |
/* create a term order M in D<x,d> (DRL) */ |
M = newmat(N2,N2); |
M = newmat(N2,N2); |
for ( J = 0; J < N2; J++ ) |
for ( J = 0; J < N2; J++ ) |
Line 244 def generic_bfct(F,V,DV,W) |
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Line 249 def generic_bfct(F,V,DV,W) |
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FH = map(dp_dtop,map(dp_homo,map(dp_ptod,F,VDV)),VDVH); |
FH = map(dp_dtop,map(dp_homo,map(dp_ptod,F,VDV)),VDVH); |
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/* compute a groebner basis of FH w.r.t. MWH */ |
/* compute a groebner basis of FH w.r.t. MWH */ |
GH = dp_weyl_gr_main(FH,VDVH,0,1,MWH); |
dp_gr_flags(["Top",1,"NoRA",1]); |
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GH = dp_weyl_gr_main(FH,VDVH,0,1,11); |
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dp_gr_flags(["Top",0,"NoRA",0]); |
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/* dehomigenize GH */ |
/* dehomigenize GH */ |
G = map(subst,GH,h,1); |
G = map(subst,GH,h,1); |
Line 344 def bfct_via_gbfct(F) |
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Line 351 def bfct_via_gbfct(F) |
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return subst(R,s,-s-1); |
return subst(R,s,-s-1); |
} |
} |
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/* use an order s.t. [t,x,y,z,...,dt,dx,dy,dz,...,h] */ |
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def bfct_via_gbfct_weight(F,V) |
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{ |
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N = length(V); |
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D = newvect(N); |
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Wt = getopt(weight); |
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if ( type(Wt) == 4 ) { |
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Tdeg = w_tdeg(F,V,Wt); |
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WtV = newvect(2*(N+1)+1); |
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WtV[0] = Tdeg; |
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WtV[N+1] = 1; |
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/* wdeg(V[I])=Wt[I], wdeg(DV[I])=Tdeg-Wt[I]+1 */ |
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for ( I = 1; I <= N; I++ ) { |
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WtV[I] = Wt[I-1]; |
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WtV[N+1+I] = Tdeg-Wt[I-1]+1; |
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} |
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WtV[2*(N+1)] = 1; |
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dp_set_weight(WtV); |
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} |
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for ( I = N-1, DV = []; I >= 0; I-- ) |
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DV = cons(strtov("d"+rtostr(V[I])),DV); |
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B = [t-F]; |
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for ( I = 0; I < N; I++ ) { |
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B = cons(DV[I]+diff(F,V[I])*dt,B); |
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} |
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V1 = cons(t,V); DV1 = cons(dt,DV); |
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W = newvect(N+1); |
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W[0] = 1; |
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R = generic_bfct(B,V1,DV1,W); |
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return subst(R,s,-s-1); |
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} |
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/* use an order s.t. [x,y,z,...,t,dx,dy,dz,...,dt,h] */ |
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def bfct_via_gbfct_weight_1(F,V) |
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{ |
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N = length(V); |
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D = newvect(N); |
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Wt = getopt(weight); |
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if ( type(Wt) == 4 ) { |
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Tdeg = w_tdeg(F,V,Wt); |
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WtV = newvect(2*(N+1)); |
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/* wdeg(V[I])=Wt[I], wdeg(DV[I])=Tdeg-Wt[I]+1 */ |
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for ( I = 0; I < N; I++ ) { |
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WtV[I] = Wt[I]; |
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WtV[N+1+I] = Tdeg-Wt[I]+1; |
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} |
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WtV[N] = Tdeg; |
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WtV[2*N+1] = 1; |
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dp_set_weight(WtV); |
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} |
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for ( I = N-1, DV = []; I >= 0; I-- ) |
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DV = cons(strtov("d"+rtostr(V[I])),DV); |
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B = [t-F]; |
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for ( I = 0; I < N; I++ ) { |
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B = cons(DV[I]+diff(F,V[I])*dt,B); |
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} |
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V1 = append(V,[t]); DV1 = append(DV,[dt]); |
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W = newvect(N+1); |
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W[N] = 1; |
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R = generic_bfct(B,V1,DV1,W); |
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return subst(R,s,-s-1); |
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} |
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def weyl_minipolym(G,V,O,M,V0) |
def weyl_minipolym(G,V,O,M,V0) |
{ |
{ |
N = length(V); |
N = length(V); |
Line 362 def weyl_minipolym(G,V,O,M,V0) |
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Line 438 def weyl_minipolym(G,V,O,M,V0) |
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GI = cons(I,GI); |
GI = cons(I,GI); |
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U = dp_mod(dp_ptod(V0,V),M,[]); |
U = dp_mod(dp_ptod(V0,V),M,[]); |
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U = dp_weyl_nf_mod(GI,U,PS,1,M); |
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T = dp_mod(<<0>>,M,[]); |
T = dp_mod(<<0>>,M,[]); |
TT = dp_mod(dp_ptod(1,V),M,[]); |
TT = dp_mod(dp_ptod(1,V),M,[]); |
Line 541 def v_factorial(V,N) |
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Line 618 def v_factorial(V,N) |
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{ |
{ |
for ( J = N-1, R = 1; J >= 0; J-- ) |
for ( J = N-1, R = 1; J >= 0; J-- ) |
R *= V-J; |
R *= V-J; |
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return R; |
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} |
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def w_tdeg(F,V,W) |
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{ |
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dp_set_weight(newvect(length(W),W)); |
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T = dp_ptod(F,V); |
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for ( R = 0; T; T = cdr(T) ) { |
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D = dp_td(T); |
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if ( D > R ) R = D; |
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} |
return R; |
return R; |
} |
} |
end$ |
end$ |