version 1.3, 2002/09/27 08:40:48 |
version 1.6, 2002/10/25 02:43:40 |
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/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.2 2002/09/26 09:07:42 noro Exp $ */ |
/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.5 2002/10/23 07:54:58 noro Exp $ */ |
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#include "ca.h" |
#include "ca.h" |
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Line 6 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp); |
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Line 6 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp); |
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void gcdsf_main(VL vl,P *pa,int m,P *r); |
void gcdsf_main(VL vl,P *pa,int m,P *r); |
void ugcdsf(P *pa,int m,P *r); |
void ugcdsf(P *pa,int m,P *r); |
void head_monomial(V v,P p,P *coef,P *term); |
void head_monomial(V v,P p,P *coef,P *term); |
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void sqfrsfmain(VL vl,P f,DCP *dcp); |
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void pthrootsf(P f,Q m,P *r); |
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void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp); |
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void gcdsf(VL vl,P *pa,int k,P *r); |
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void mfctrsfmain(VL vl, P f, DCP *dcp); |
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int next_evaluation_point(int *mev,int n); |
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void estimatelc_sf(VL vl,P c,DCP dc,int *mev,P *lcp); |
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void mfctrsf_hensel(VL vl,int *mev,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up); |
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void lex_lc(P f,P *c) |
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{ |
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if ( !f || NUM(f) ) |
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*c = f; |
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else |
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lex_lc(COEF(DC(f)),c); |
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} |
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DCP append_dc(DCP dc,DCP dct) |
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{ |
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DCP dcs; |
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if ( !dc ) |
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return dct; |
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else { |
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for ( dcs = dc; NEXT(dcs); dcs = NEXT(dcs) ); |
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NEXT (dcs) = dct; |
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return dc; |
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} |
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} |
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void sqfrsf(VL vl, P f, DCP *dcp) |
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{ |
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DCP dc,dct; |
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Obj obj; |
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P t,s,c; |
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VL tvl,nvl; |
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simp_ff((Obj)f,&obj); f = (P)obj; |
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lex_lc(f,&c); divsp(vl,f,c,&t); f = t; |
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monomialfctr(vl,f,&t,&dc); f = t; |
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clctv(vl,f,&tvl); vl = tvl; |
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if ( !vl ) |
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; |
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else if ( !NEXT(vl) ) { |
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sfusqfr(f,&dct); |
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dc = append_dc(dc,NEXT(dct)); |
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} else { |
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t = f; |
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for ( tvl = vl; tvl; tvl = NEXT(tvl) ) { |
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reordvar(vl,tvl->v,&nvl); |
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cont_pp_mv_sf(vl,NEXT(nvl),t,&c,&s); t = s; |
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sqfrsf(vl,c,&dct); |
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dc = append_dc(dc,NEXT(dct)); |
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} |
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sqfrsfmain(vl,t,&dct); |
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dc = append_dc(dc,dct); |
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} |
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NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)c; NEXT(dct) = dc; |
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*dcp = dct; |
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} |
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void sqfrsfmain(VL vl,P f,DCP *dcp) |
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{ |
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VL tvl; |
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DCP dc,dct,dcs; |
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P t,s; |
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Q m,m1; |
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V v; |
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clctv(vl,f,&tvl); vl = tvl; |
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dc = 0; |
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t = f; |
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for ( tvl = vl; tvl; tvl = NEXT(tvl) ) { |
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v = tvl->v; |
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partial_sqfrsf(vl,v,t,&s,&dct); t = s; |
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dc = append_dc(dc,dct); |
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} |
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if ( !NUM(t) ) { |
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STOQ(characteristic_sf(),m); |
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pthrootsf(t,m,&s); |
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sqfrsfmain(vl,s,&dct); |
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for ( dcs = dct; dcs; dcs = NEXT(dcs) ) { |
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mulq(DEG(dcs),m,&m1); DEG(dcs) = m1; |
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} |
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dc = append_dc(dc,dct); |
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} |
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*dcp = dc; |
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} |
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void pthrootsf(P f,Q m,P *r) |
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{ |
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DCP dc,dc0,dct; |
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N qn,rn; |
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if ( NUM(f) ) |
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pthrootgfs(f,r); |
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else { |
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dc = DC(f); |
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dc0 = 0; |
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for ( dc0 = 0; dc; dc = NEXT(dc) ) { |
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NEXTDC(dc0,dct); |
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pthrootsf(COEF(dc),m,&COEF(dct)); |
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if ( DEG(dc) ) { |
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divn(NM(DEG(dc)),NM(m),&qn,&rn); |
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if ( rn ) |
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error("pthrootsf : cannot happen"); |
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NTOQ(qn,1,DEG(dct)); |
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} else |
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DEG(dct) = 0; |
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} |
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NEXT(dct) = 0; |
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MKP(VR(f),dc0,*r); |
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} |
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} |
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void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp) |
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{ |
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P ps[2]; |
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DCP dc0,dc; |
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int m; |
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P t,flat,flat1,g,df,q; |
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diffp(vl,f,v,&df); |
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if ( !df ) { |
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*dcp = 0; |
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*r = f; |
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return; |
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} |
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ps[0] = f; ps[1] = df; |
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gcdsf(vl,ps,2,&g); |
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divsp(vl,f,g,&flat); |
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m = 0; |
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t = f; |
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dc0 = 0; |
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while ( !NUM(flat) ) { |
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while ( divtp(vl,t,flat,&q) ) { |
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t = q; m++; |
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} |
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ps[0] = t; ps[1] = flat; |
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gcdsf(vl,ps,2,&flat1); |
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divsp(vl,flat,flat1,&g); |
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flat = flat1; |
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NEXTDC(dc0,dc); |
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COEF(dc) = g; |
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STOQ(m,DEG(dc)); |
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} |
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NEXT(dc) = 0; |
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*dcp = dc0; |
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*r = t; |
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} |
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void gcdsf(VL vl,P *pa,int k,P *r) |
void gcdsf(VL vl,P *pa,int k,P *r) |
{ |
{ |
P *ps,*pl,*pm; |
P *ps,*pl,*pm; |
Line 113 void ugcdsf(P *pa,int m,P *r) |
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Line 263 void ugcdsf(P *pa,int m,P *r) |
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sfumtop(v,w1,r); |
sfumtop(v,w1,r); |
} |
} |
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/* deg(HT(p),v), where p is considered as distributed poly over F[v] */ |
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int gethdeg(VL vl,V v,P p) |
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{ |
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DCP dc; |
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Q dmax; |
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P cmax; |
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if ( !p ) |
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return -1; |
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else if ( NUM(p) ) |
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return 0; |
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else if ( VR(p) != v ) |
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/* HT(p) = HT(lc(p))*x^D */ |
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return gethdeg(vl,v,COEF(DC(p))); |
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else { |
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/* VR(p) = v */ |
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dc = DC(p); dmax = DEG(dc); cmax = COEF(dc); |
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for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) |
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if ( compp(vl,COEF(dc),cmax) > 0 ) { |
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dmax = DEG(dc); cmax = COEF(dc); |
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} |
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return QTOS(dmax); |
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} |
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} |
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/* all the pa[i]'s have the same variables (=vl) */ |
/* all the pa[i]'s have the same variables (=vl) */ |
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void gcdsf_main(VL vl,P *pa,int m,P *r) |
void gcdsf_main(VL vl,P *pa,int m,P *r) |
Line 131 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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Line 305 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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ugcdsf(pa,m,r); |
ugcdsf(pa,m,r); |
return; |
return; |
} |
} |
/* find v s.t. min(deg(pa[i],v)) is minimal */ |
/* find v s.t. min(deg(pa[i],v)+gethdeg(pa[i],v)) is minimal */ |
tvl = vl; |
tvl = vl; |
do { |
do { |
v = tvl->v; |
v = tvl->v; |
i = 0; |
i = 0; |
do { |
do { |
d = getdeg(v,pa[i]); |
d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]); |
if ( i == 0 || (d < d0) ) { |
if ( i == 0 || (d < d0) ) { |
d0 = d; i0 = i; v0 = v; |
d0 = d; i0 = i; v0 = v; |
} |
} |
Line 298 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp) |
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Line 472 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp) |
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ps[i] = C(t); |
ps[i] = C(t); |
ugcdsf(ps,m,c); |
ugcdsf(ps,m,c); |
divsp(vl,p,*c,pp); |
divsp(vl,p,*c,pp); |
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} |
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void mfctrsf(VL vl, P f, DCP *dcp) |
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{ |
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DCP dc0,dc,dct,dcs,dcr; |
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Obj obj; |
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simp_ff((Obj)f,&obj); f = (P)obj; |
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sqfrsf(vl,f,&dct); |
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dc = dc0 = dct; dct = NEXT(dct); NEXT(dc) = 0; |
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for ( ; dct; dct = NEXT(dct) ) { |
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mfctrsfmain(vl,COEF(dct),&dcs); |
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for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) |
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DEG(dcr) = DEG(dct); |
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for ( ; NEXT(dc); dc = NEXT(dc) ); |
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NEXT(dc) = dcs; |
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} |
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*dcp = dc0; |
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} |
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/* f : sqfr, non const */ |
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void mfctrsfmain(VL vl, P f, DCP *dcp) |
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{ |
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VL tvl,nvl,rvl; |
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DCP dc,dc0,dc1,dc2,dct,lcfdc; |
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int imin,inext,i,n,k,np; |
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int *da; |
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V vx,vy; |
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V *va; |
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P gcd,g,df,dfmin; |
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P pa[2]; |
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P g0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s; |
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GFS ev,evy; |
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P *fp0; |
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int *mev,*win; |
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clctv(vl,f,&tvl); vl = tvl; |
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if ( !vl ) |
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error("mfctrsfmain : cannot happen"); |
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if ( !NEXT(vl) ) { |
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/* univariate */ |
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ufctrsf(f,&dc); |
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/* remove lc */ |
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*dcp = NEXT(dc); |
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return; |
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} |
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for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ ); |
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va = (V *)ALLOCA(n*sizeof(int)); |
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da = (int *)ALLOCA(n*sizeof(int)); |
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/* find v s.t. diff(f,v) is nonzero and deg(f,v) is minimal */ |
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imin = -1; |
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for ( i = 0, tvl = vl; i < n; tvl = NEXT(tvl), i++ ) { |
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va[i] = tvl->v; |
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da[i] = getdeg(va[i],f); |
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diffp(vl,f,va[i],&df); |
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if ( !df ) |
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continue; |
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if ( imin < 0 || da[i] < da[imin] ) { |
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dfmin = df; |
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imin = i; |
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} |
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} |
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/* find v1 neq v s.t. deg(f,v) is minimal */ |
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inext = -1; |
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for ( i = 0; i < n; i++ ) { |
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if ( i == imin ) |
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continue; |
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if ( inext < 0 || da[i] < da[inext] ) |
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inext = i; |
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} |
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pa[0] = f; |
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pa[1] = dfmin; |
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gcdsf_main(vl,pa,2,&gcd); |
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if ( !NUM(gcd) ) { |
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/* f = gcd * f/gcd */ |
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mfctrsfmain(vl,gcd,&dc1); |
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divsp(vl,f,gcd,&g); |
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mfctrsfmain(vl,g,&dc2); |
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for ( dct = dc1; NEXT(dct); dct = NEXT(dct) ); |
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NEXT(dct) = dc2; |
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*dcp = dc1; |
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return; |
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} |
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/* create vl s.t. vl[0] = va[imin], vl[1] = va[inext] */ |
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nvl = 0; |
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NEXTVL(nvl,tvl); tvl->v = va[imin]; |
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NEXTVL(nvl,tvl); tvl->v = va[inext]; |
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for ( i = 0; i < n; i++ ) { |
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if ( i == imin || i == inext ) |
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continue; |
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NEXTVL(nvl,tvl); tvl->v = va[i]; |
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} |
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NEXT(tvl) = 0; |
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reorderp(nvl,vl,f,&g); |
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vx = nvl->v; |
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vy = NEXT(nvl)->v; |
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MKV(vx,x); |
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MKV(vy,y); |
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/* remaining variables */ |
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rvl = NEXT(NEXT(nvl)); |
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if ( !rvl ) { |
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/* bivariate */ |
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sfbfctr(g,vx,vy,getdeg(vx,g),&dc1); |
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for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) { |
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NEXTDC(dc0,dc); |
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DEG(dc) = ONE; |
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reorderp(vl,nvl,COEF(dc1),&COEF(dc)); |
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} |
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NEXT(dc) = 0; |
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*dcp = dc0; |
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return; |
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} |
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/* n >= 3; nvl = (vx,vy,X) */ |
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/* find good evaluation pt for X */ |
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mev = (int *)CALLOC(n-2,sizeof(int)); |
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while ( 1 ) { |
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for ( g0 = g, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) { |
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indextogfs(mev[i],&ev); |
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substp(nvl,g0,tvl->v,(P)ev,&t); g0 = t; |
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} |
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pa[0] = g0; |
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diffp(nvl,g0,vx,&pa[1]); |
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if ( pa[1] ) { |
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gcdsf(nvl,pa,2,&gcd); |
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/* XXX maybe we have to accept the case where gcd is a poly of y */ |
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if ( NUM(gcd) ) |
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break; |
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} |
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if ( next_evaluation_point(mev,n-2) ) |
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error("mfctrsfhmain : short of evaluation points"); |
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} |
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/* g0 = g(x,y,mev) */ |
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/* separate content; g0 may have the content wrt x */ |
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cont_pp_sfp(nvl,g0,&c0,&pp0); |
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/* factorize pp0; spp0 = pp0(x,y+evy) = prod dc */ |
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sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); |
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if ( !NEXT(dc) ) { |
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/* f is irreducible */ |
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NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0; |
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*dcp = dc; |
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return; |
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} |
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/* shift c0; c0 <- c0(y+evy) */ |
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addp(nvl,y,(P)evy,&t); |
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substp(nvl,c0,vy,t,&s); |
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c0 = s; |
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/* now f(x,y+ev,mev) = c0 * prod dc */ |
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/* factorize lc_x(f) */ |
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lcf = COEF(DC(f)); |
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mfctrsf(nvl,lcf,&lcfdc); lcfdc = NEXT(lcfdc); |
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/* np = number of bivariate factors */ |
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for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ ); |
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fp0 = (P *)ALLOCA((np+1)*sizeof(P)); |
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for ( i = 0, dct = dc; i < np; dct = NEXT(dct), i++ ) |
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fp0[i] = COEF(dct); |
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fp0[np] = 0; |
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win = W_ALLOC(np+1); |
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for ( k = 1, win[0] = 1, --np; ; ) { |
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itogfs(1,&u0); |
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/* u0 = product of selected factors */ |
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for ( i = 0; i < k; i++ ) { |
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mulp(nvl,u0,fp0[win[i]],&t); u0 = t; |
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} |
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/* we have to consider the content */ |
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/* g0(y+yev) = c0*u0*v0 */ |
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mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,c,dc,mev,&lcu); |
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divsp(nvl,pp0,u0,&v0); |
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mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,c,dc,mev,&lcv); |
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mfctrsf_hensel(nvl,mev,f,pp0,u0,v0,lcu,lcv,&u); |
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} |
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} |
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int next_evaluation_point(int *mev,int n) |
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{ |
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} |
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void estimatelc_sf(VL vl,P c,DCP dc,int *mev,P *lcp) |
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{ |
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} |
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void mfctrsf_hensel(VL vl,int *mev,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up) |
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{ |
} |
} |