10#include "factory/factory.h"
114 case LE:
return "<=";
115 case GE:
return ">=";
124 if (
s[1]==
'\0')
return s[0];
125 else if (
s[2]!=
'\0')
return 0;
128 case '.':
if (
s[1]==
'.')
return DOTDOT;
134 case '+':
if (
s[1]==
'+')
return PLUSPLUS;
138 case '<':
if (
s[1]==
'=')
return LE;
141 case '>':
if (
s[1]==
'=')
return GE;
143 case '!':
if (
s[1]==
'=')
return NOTEQUAL;
155 if(fullname) sprintf(
buf2,
"%s::%s",
"",
IDID(
h));
199 && (strlen(
IDPROC(
h)->libname)>0))
210 memset(buffer,0,
sizeof(buffer));
212 if ((
s=strchr(buffer,
'\n'))!=
NULL)
220 Print(
"..., %d char(s)",
l);
237 { number2 n=(number2)
IDDATA(
h);
243 Print(
" %d x %d (%s)",
269 ((
intvec*)(
v->Data()))->cols());
break;
273 case MODUL_CMD:
Print(
", rk %d\n", (
int)(((ideal)(
v->Data()))->rank));
break;
376 && (((ring)d)->idroot!=
NULL))
402 if (((ring)
h->data)->idroot!=
NULL)
427 package savePack=currPack;
434 if (strcmp(what,
"all")==0)
469 Werror(
"%s is undefined",what);
503 package save_p=currPack;
537 WarnS(
"Gerhard, use the option command");
567 rc += ((
intvec *)(
v->Data()))->length();
578 rc+=((
lists)
v->Data())->nr+1;
599 WerrorS(
"write: need at least two arguments");
609 Werror(
"cannot write to %s",
s);
636 Werror(
"can not map from ground field of %s to current ground field",
640 if (
IDELEMS(theMap)<src_ring->N)
644 (src_ring->N)*
sizeof(poly));
654 short src_lV = src_ring->isLPring;
655 short src_ncGenCount = src_ring->LPncGenCount;
656 short src_nVars = src_lV - src_ncGenCount;
657 int src_nblocks = src_ring->N / src_lV;
660 short dest_ncGenCount =
currRing->LPncGenCount;
663 for(
i=
IDELEMS(theMap);
i < src_lV - src_ncGenCount;
i++)
671 if (theMap->m[
i] !=
NULL)
679 for(
i = src_nVars;
i < src_lV;
i++)
681 short ncGenIndex =
i - src_nVars;
682 if (ncGenIndex < dest_ncGenCount)
696 for(
i = 1;
i < src_nblocks;
i++)
698 for(
int j = 0;
j < src_lV;
j++)
716 WerrorS(
"argument of a map must have a name");
728 save_r=
IDMAP(
w)->preimage;
738 ideal
id=(ideal)tmpW.
data;
746 for(
int j=
IDELEMS(theMap)-1;
j>=0 && !overflow;
j--)
748 if (theMap->m[
j]!=
NULL)
755 if ((
p!=
NULL) && (degs[
i]!=0) &&
756 ((
unsigned long)deg_monexp > (
currRing->bitmask / ((
unsigned long)degs[
i])/2)))
768 for(
int j=
IDELEMS(theMap)-1;
j>=0 && !overflow;
j--)
770 if (theMap->m[
j]!=
NULL)
773 poly
p=(poly)tmpW.
data;
776 ((
unsigned long)deg_monexp > (
currRing->bitmask / ((
unsigned long)deg)/2)))
790 Warn(
"possible OVERFLOW in map, max exponent is %ld",
currRing->bitmask/2);
809 char *tmp = theMap->preimage;
810 theMap->preimage=(
char*)1L;
813 theMap->preimage=tmp;
828 IDMAP(
w)->preimage=save_r;
836 Werror(
"%s undefined in %s",what,theMap->preimage);
841 Werror(
"cannot find preimage %s",theMap->preimage);
857 sprintf(
s,
"%s(%d)",
name,
i+1);
864 h->data.uideal=(ideal)L->
m[
i].
data;
867 Print(
"//defining: %s as %d-th syzygy module\n",
s,
i+1);
872 Warn(
"cannot define %s",
s);
952 int add_row_shift = 0;
955 if (weights!=
NULL) add_row_shift=weights->
min_in();
984 l->m[0].rtyp=u->
Typ();
985 l->m[0].data=u->
Data();
988 l->m[0].attribute=*a;
995 l->m[0].attribute=
NULL;
1009 int add_row_shift=0;
1015 add_row_shift = ww->
min_in();
1016 (*weights) -= add_row_shift;
1023 res->data=(
void*)res_im;
1026 for(
int i=1;
i<=res_im->
rows();
i++)
1028 if (
IMATELEM(*res_im,1,
i)==0) { add_row_shift--; }
1033 if (weights!=
NULL)
delete weights;
1046 int add_row_shift=0;
1051 add_row_shift = ww->
min_in();
1052 (*weights) -= add_row_shift;
1057 if (weights!=
NULL)
delete weights;
1060 return reg+1+add_row_shift;
1064#define BREAK_LINE_LENGTH 80
1091 else if(strncmp(
s,
"cont;",5)==0)
1098 strcat(
s,
"\n;~\n");
1164 res->m[
i].data = (
void *)save->set;
1176 res->m[
i].data = (
void *)save->set;
1202 const char *
id =
name->name;
1207 WerrorS(
"object to declare is not a name");
1217 Werror(
"can not define `%s` in other package",
name->name);
1278 WerrorS(
"branchTo can only occur in a proc");
1286 if (ll!=(
l-1))
return FALSE;
1289 short *t=(
short*)
omAlloc(
l*
sizeof(
short));
1293 for(
i=1;
i<
l;
i++,
h=
h->next)
1298 Werror(
"arg %d is not a string",
i);
1302 b=
IsCmd((
char *)
h->Data(),tt);
1307 Werror(
"arg %d is not a type name",
i);
1314 Werror(
"last(%d.) arg.(%s) is not a proc(but %s(%d)), nesting=%d",
1327 if(
pi->data.s.body==
NULL )
1356 if (err==0)
Warn(
"too many arguments for %s",
IDID(currProc));
1380 if (strcmp(
p->name,
"#")==0)
1389 if (strcmp(
p->name,
"#")==0)
1391 is_default_list=
TRUE;
1399 if (is_default_list)
1452 WerrorS(
"object with a different type exists");
1470 Warn(
"'%s': no such identifier\n",
v->
name);
1473 package frompack=v->req_packhdl;
1487 v->req_packhdl=rootpack;
1488 if (
h==frompack->idroot)
1490 frompack->idroot=
h->next;
1494 idhdl hh=frompack->idroot;
1501 Werror(
"`%s` not found",
v->Name());
1505 h->next=rootpack->idroot;
1519 Werror(
"cannot export:%s of internal type %d",
v->
name,
v->rtyp);
1545 Werror(
"cannot export:%s of internal type %d",
v->
name,
v->rtyp);
1558 else if (
IDTYP(old)==
v->Typ())
1596 WerrorS(
"no ring active (9)");
1638 WarnS(
"package not found\n");
1659 #ifndef TEST_ZN_AS_ZP
1663 mpz_init_set_ui(modBase, (
long)32003);
1670 r->cf->has_simple_Inverse=1;
1683 r->block0 = (
int *)
omAlloc0(3 *
sizeof(
int *));
1684 r->block1 = (
int *)
omAlloc0(3 *
sizeof(
int *));
1703 if ((r==
NULL)||(r->VarOffset==
NULL))
1742 L->
m[0].
data=(
void *)(
long)r->cf->ch;
1748 for(
i=0;
i<r->N;
i++)
1754 L->
m[1].
data=(
void *)LL;
1771 if (r->block1[
i]-r->block0[
i] >=0 )
1773 j=r->block1[
i]-r->block0[
i];
1776 if ((r->wvhdl!=
NULL) && (r->wvhdl[
i]!=
NULL))
1778 for(;
j>=0;
j--) (*iv)[
j]=r->wvhdl[
i][
j];
1780 else switch (r->order[
i])
1789 for(;
j>=0;
j--) (*iv)[
j]=1;
1799 LLL->
m[1].
data=(
void *)iv;
1800 LL->
m[
i].
data=(
void *)LLL;
1803 L->
m[2].
data=(
void *)LL;
1813 pSetCoeff0(q->m[0],(number)(r->qideal->m[0]));
1814 L->
m[3].
data=(
void *)q;
1833 L->
m[0].
data=(
void *)0;
1843 L->
m[1].
data=(
void *)LL;
1867 L->
m[0].
data=(
void *)0;
1877 L->
m[1].
data=(
void *)LL;
1911 LL->
m[1].
data=(
void *) C->modExponent;
1913 L->
m[1].
data=(
void *)LL;
1940 LL->
m[1].
data=(
void *)
R->cf->modExponent;
1942 L->
m[1].
data=(
void *)LL;
1956 WerrorS(
"ring with polynomial data must be the base ring or compatible");
1969 else if ( C->extRing!=
NULL )
1979 Lc->m[0].data=(
void*)(
long)C->m_nfCharQ;
1986 Lc->m[1].data=(
void*)Lv;
1997 Loo->
m[1].
data=(
void *)iv;
2000 Lo->
m[0].
data=(
void*)Loo;
2003 Lc->m[2].data=(
void*)Lo;
2009 res->data=(
void*)
Lc;
2014 res->data=(
void *)(
long)C->ch;
2028 for(
i=0;
i<r->N;
i++)
2034 L->
m[1].
data=(
void *)LL;
2055 assume( r->block0[
i] == r->block1[
i] );
2056 const int s = r->block0[
i];
2062 else if (r->block1[
i]-r->block0[
i] >=0 )
2064 int bl=
j=r->block1[
i]-r->block0[
i];
2072 j+=r->wvhdl[
i][bl+1];
2075 if ((r->wvhdl!=
NULL) && (r->wvhdl[
i]!=
NULL))
2077 for(;
j>=0;
j--) (*iv)[
j]=r->wvhdl[
i][
j+(
j>bl)];
2079 else switch (r->order[
i])
2088 for(;
j>=0;
j--) (*iv)[
j]=1;
2098 LLL->
m[1].
data=(
void *)iv;
2099 LL->
m[
i].
data=(
void *)LLL;
2102 L->
m[2].
data=(
void *)LL;
2106 if (r->qideal==
NULL)
2137 WerrorS(
"ring with polynomial data must be the base ring or compatible");
2155 L->
m[0].
data=(
char*)r->cf; r->cf->ref++;
2170 || (r->qideal !=
NULL)
2177 WerrorS(
"ring with polynomial data must be the base ring or compatible");
2202 else if ( r->cf->extRing!=
NULL )
2212 Lc->m[0].data=(
void*)(
long)r->cf->m_nfCharQ;
2219 Lc->m[1].data=(
void*)Lv;
2230 Loo->
m[1].
data=(
void *)iv;
2233 Lo->
m[0].
data=(
void*)Loo;
2236 Lc->m[2].data=(
void*)Lo;
2247 L->
m[0].
data=(
void *)(
long)r->cf->ch;
2252 L->
m[0].
data=(
void *)r->cf;
2267 WerrorS(
"invalid coeff. field description, expecting 0");
2275 WerrorS(
"invalid coeff. field description, expecting precision list");
2283 WerrorS(
"invalid coeff. field description list, expected list(`int`,`int`)");
2286 int r1=(int)(
long)LL->
m[0].
data;
2287 int r2=(int)(
long)LL->
m[1].
data;
2297 WerrorS(
"invalid coeff. field description, expecting parameter name");
2319 unsigned int modExponent = 1;
2323 mpz_init_set_ui(modBase,0);
2334 number tmp= (number) LL->
m[0].
data;
2341 mpz_init_set_ui(modBase,(
unsigned long) LL->
m[0].
data);
2345 mpz_init_set_ui(modBase,0);
2349 modExponent = (
unsigned long) LL->
m[1].
data;
2357 if ((mpz_cmp_ui(modBase, 1) == 0) && (
mpz_sgn1(modBase) < 0))
2359 WerrorS(
"Wrong ground ring specification (module is 1)");
2362 if (modExponent < 1)
2364 WerrorS(
"Wrong ground ring specification (exponent smaller than 1)");
2373 else if (modExponent > 1)
2376 if ((mpz_cmp_ui(modBase, 2) == 0) && (modExponent <= 8*
sizeof(
unsigned long)))
2387 info.exp= modExponent;
2398 info.exp= modExponent;
2412 for(
i=0;
i<
R->N-1;
i++)
2414 for(
j=
i+1;
j<
R->N;
j++)
2416 if (strcmp(
R->names[
i],
R->names[
j])==0)
2421 R->names[
j]=(
char *)
omAlloc(2+strlen(
R->names[
i]));
2422 sprintf(
R->names[
j],
"@%s",
R->names[
i]);
2440 sprintf(
R->names[
j],
"@@(%d)",
i+1);
2466 poly
p=(poly)
v->m[
i].Data();
2472 Werror(
"var name %d must be a string or a ring variable",
i+1);
2478 Werror(
"var name %d must be `string` (not %d)",
i+1,
v->m[
i].Typ());
2485 WerrorS(
"variable must be given as `list`");
2501 for (
int j=0;
j < n-1;
j++)
2508 &&(strcmp((
char*)vv->
m[0].
Data(),
"L")==0))
2510 number nn=(number)vv->
m[1].
Data();
2517 Werror(
"illegal argument for pseudo ordering L: %d",vv->
m[1].
Typ());
2524 if (bitmask!=0) n--;
2528 R->block0=(
int *)
omAlloc0((n+1)*
sizeof(int));
2529 R->block1=(
int *)
omAlloc0((n+1)*
sizeof(int));
2532 for (j_in_R= n-2; j_in_R>=0; j_in_R--)
2535 for(j_in_R=0,j_in_L=0;j_in_R<n-1;j_in_R++,j_in_L++)
2540 WerrorS(
"ordering must be list of lists");
2547 if (strcmp((
char*)vv->
m[0].
Data(),
"L")==0)
2561 if (j_in_R==0)
R->block0[0]=1;
2578 if (jj<0)
R->block0[j_in_R]=1;
2579 else R->block0[j_in_R]=
R->block1[jj]+1;
2586 for(
int i=0;
i<
l;
i++) (*iv)[
i]=1;
2605 R->block1[j_in_R]=
si_max(
R->block0[j_in_R],
R->block0[j_in_R]+iv_len-1);
2606 if (
R->block1[j_in_R]>
R->N)
2608 if (
R->block0[j_in_R]>
R->N)
2613 R->block1[j_in_R]=
R->N;
2614 iv_len=
R->block1[j_in_R]-
R->block0[j_in_R]+1;
2619 switch (
R->order[j_in_R])
2628 R->wvhdl[j_in_R] =(
int *)
omAlloc(iv_len*
sizeof(
int));
2629 for (
i=0;
i<iv_len;
i++)
2631 R->wvhdl[j_in_R][
i]=(*iv)[
i];
2636 for (
i=0;
i<iv_len;
i++)
2638 R->wvhdl[j_in_R][
i]=(*iv)[
i];
2640 R->wvhdl[j_in_R][
i]=iv->
length() - iv_len;
2644 R->wvhdl[j_in_R][
i+1]=(*iv)[
i];
2649 for (
i=0;
i<iv->
length();
i++)
R->wvhdl[j_in_R][
i]=(*iv)[
i];
2650 R->block1[j_in_R]=
si_max(
R->block0[j_in_R],
R->block0[j_in_R]+(
int)
sqrt((
double)(iv->
length())));
2651 if (
R->block1[j_in_R]>
R->N)
2653 R->block1[j_in_R]=
R->N;
2666 for (
i=0;
i<iv_len;
i++)
2668 if (((*iv)[
i]!=1)&&(iv_len!=1))
2671 Warn(
"ignore weight %d for ord %d (%s) at pos %d\n>>%s<<",
2682 R->block1[j_in_R]=
R->block0[j_in_R]=0;
2686 R->block1[j_in_R]=
R->block0[j_in_R]=(*iv)[0];
2692 R->block1[j_in_R] =
R->block0[j_in_R] = 0;
2695 const int s = (*iv)[0];
2697 R->block1[j_in_R] =
R->block0[j_in_R] =
s;
2706 WerrorS(
"ring order not implemented");
2714 WerrorS(
"ordering name must be a (string,intvec)");
2723 if (
R->block1[j_in_R] !=
R->N)
2734 R->block0[j_in_R] <=
R->N)
2736 R->block1[j_in_R] =
R->N;
2740 Werror(
"ordering incomplete: size (%d) should be %d",
R->block1[j_in_R],
R->N);
2744 if (
R->block0[j_in_R]>
R->N)
2746 Werror(
"not enough variables (%d) for ordering block %d, scanned so far:",
R->N,j_in_R+1);
2747 for(
int ii=0;ii<=j_in_R;ii++)
2776 WerrorS(
"ordering must be given as `list`");
2779 if (bitmask!=0) {
R->bitmask=bitmask;
R->wanted_maxExp=bitmask; }
2811 int ch = (int)(
long)L->
m[0].
Data();
2821 Warn(
"%d is invalid characteristic of ground field. %d is used.", ch,
l);
2824 #ifndef TEST_ZN_AS_ZP
2828 mpz_init_set_ui(modBase,(
long) ch);
2835 R->cf->has_simple_Inverse=1;
2856 int ch = (int)(
long)LL->
m[0].
Data();
2857 while ((ch!=
fftable[is_gf_char]) && (
fftable[is_gf_char])) is_gf_char++;
2858 if (
fftable[is_gf_char]==0) is_gf_char=-1;
2879 WerrorS(
"could not create the specified coefficient field");
2883 if( extRing->qideal !=
NULL )
2887 extParam.
r = extRing;
2894 extParam.
r = extRing;
2904 WerrorS(
"coefficient field must be described by `int` or `list`");
2910 WerrorS(
"could not create coefficient field described by the input!");
2922 #ifdef HAVE_SHIFTBBA
2925 R->isLPring=isLetterplace;
2930 if ((bitmask!=0)&&(
R->wanted_maxExp==0))
R->wanted_maxExp=bitmask;
2937 ideal q=(ideal)L->
m[3].
Data();
2943 WerrorS(
"coefficient fields must be equal if q-ideal !=0");
2950 int par_perm_size=0;
2970 par_perm_size=
rPar(orig_ring);
2980 WerrorS(
"coefficient fields must be equal if q-ideal !=0");
2984 perm=(
int *)
omAlloc0((orig_ring->N+1)*
sizeof(int));
2985 if (par_perm_size!=0)
2986 par_perm=(
int *)
omAlloc0(par_perm_size*
sizeof(
int));
2990 maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
2999 else if (par_perm_size!=0)
3007 par_perm,par_perm_size);
3025 WerrorS(
"q-ideal must be given as `ideal`");
3074 ideal
id=(ideal)a->
Data();
3094 int n=(int)(
long)
b->Data();
3095 int d=(int)(
long)c->
Data();
3102 if ((d>n) || (d<1) || (n<1))
3107 int *choise = (
int*)
omAlloc(d*
sizeof(
int));
3111 temp=(ideal)id->
Data();
3126 p =
pCopy(temp->m[choise[
l-1]-1]);
3152 BOOLEAN minim=(int)(
long)
w->Data();
3154 int add_row_shift=0;
3160 add_row_shift = ww->
min_in();
3161 (*weights) -= add_row_shift;
3190 if ((fullres==
NULL) && (minres==
NULL))
3302 ideal F=(ideal)id->
Data();
3308 res->data=(
char *)iv;
3312 double wNsqr = (double)2.0 / (
double)n;
3314 x = (
int * )
omAlloc(2 * (n + 1) *
sizeof(int));
3316 for (
i = n;
i!=0;
i--)
3317 (*iv)[
i-1] =
x[
i + n + 1];
3335 res->data=(
void *)
b;
3361 spec.
mu = (int)(
long)(
l->m[0].Data( ));
3362 spec.
pg = (int)(
long)(
l->m[1].Data( ));
3363 spec.
n = (int)(
long)(
l->m[2].Data( ));
3371 for(
int i=0;
i<spec.
n;
i++ )
3374 spec.
w[
i] = (*mul)[
i];
3405 for(
int i=0;
i<spec.
n;
i++ )
3409 (*mult)[
i] = spec.
w[
i];
3419 L->
m[0].
data = (
void*)(
long)spec.
mu;
3420 L->
m[1].
data = (
void*)(
long)spec.
pg;
3421 L->
m[2].
data = (
void*)(
long)spec.
n;
3472 WerrorS(
"the list is too short" );
3475 WerrorS(
"the list is too long" );
3479 WerrorS(
"first element of the list should be int" );
3482 WerrorS(
"second element of the list should be int" );
3485 WerrorS(
"third element of the list should be int" );
3488 WerrorS(
"fourth element of the list should be intvec" );
3491 WerrorS(
"fifth element of the list should be intvec" );
3494 WerrorS(
"sixth element of the list should be intvec" );
3498 WerrorS(
"first element of the list should be positive" );
3501 WerrorS(
"wrong number of numerators" );
3504 WerrorS(
"wrong number of denominators" );
3507 WerrorS(
"wrong number of multiplicities" );
3511 WerrorS(
"the Milnor number should be positive" );
3514 WerrorS(
"the geometrical genus should be nonnegative" );
3517 WerrorS(
"all numerators should be positive" );
3520 WerrorS(
"all denominators should be positive" );
3523 WerrorS(
"all multiplicities should be positive" );
3527 WerrorS(
"it is not symmetric" );
3530 WerrorS(
"it is not monotonous" );
3534 WerrorS(
"the Milnor number is wrong" );
3537 WerrorS(
"the geometrical genus is wrong" );
3541 WerrorS(
"unspecific error" );
3577 ( fast==2 ? 2 : 1 ) );
3587 ( fast==0 || (*node)->weight<=smax ) )
3609 cmp =
pCmp( (*node)->mon,
f );
3632 (*node)->nf =
search->nf;
3636 while( cmp<0 &&
f!=(poly)
NULL );
3649 if( (*node)->weight<=(
Rational)1 ) pg++;
3650 if( (*node)->weight==smax ) z++;
3651 if( (*node)->weight>weight_prev ) n++;
3653 weight_prev = (*node)->weight;
3654 node = &((*node)->next);
3676 cmp =
pCmp( (*node)->mon,
f );
3689 while( cmp<0 &&
f!=(poly)
NULL );
3705 n = ( z > 0 ? 2*n - 1 : 2*n );
3720 ( fast==0 ||
search->weight<=smax );
3746 for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3749 (*den) [n2] = (*den)[n1];
3750 (*mult)[n2] = (*mult)[n1];
3758 if( fast==0 || fast==1 )
3762 for(
int n1=0, n2=n-1 ; n1<n2 && symmetric==
TRUE; n1++, n2-- )
3765 (*
den) [n1]!= (*
den)[n2] ||
3772 if( symmetric==
FALSE )
3782 (*L)->m[0].data = (
void*)(
long)
mu;
3799 (*L)->m[0].data = (
void*)(
long)
mu;
3800 (*L)->m[1].data = (
void*)(
long)pg;
3801 (*L)->m[2].data = (
void*)(
long)n;
3802 (*L)->m[3].data = (
void*)nom;
3803 (*L)->m[4].data = (
void*)
den;
3804 (*L)->m[5].data = (
void*)
mult;
3813 #ifdef SPECTRUM_DEBUG
3814 #ifdef SPECTRUM_PRINT
3815 #ifdef SPECTRUM_IOSTREAM
3816 cout <<
"spectrumCompute\n";
3817 if( fast==0 ) cout <<
" no optimization" << endl;
3818 if( fast==1 ) cout <<
" weight optimization" << endl;
3819 if( fast==2 ) cout <<
" symmetry optimization" << endl;
3821 fputs(
"spectrumCompute\n",stdout );
3822 if( fast==0 ) fputs(
" no optimization\n", stdout );
3823 if( fast==1 ) fputs(
" weight optimization\n", stdout );
3824 if( fast==2 ) fputs(
" symmetry optimization\n", stdout );
3868 #ifdef SPECTRUM_DEBUG
3869 #ifdef SPECTRUM_PRINT
3870 #ifdef SPECTRUM_IOSTREAM
3871 cout <<
"\n computing the Jacobi ideal...\n";
3873 fputs(
"\n computing the Jacobi ideal...\n",stdout );
3882 #ifdef SPECTRUM_DEBUG
3883 #ifdef SPECTRUM_PRINT
3884 #ifdef SPECTRUM_IOSTREAM
3887 fputs(
" ", stdout );
3898 #ifdef SPECTRUM_DEBUG
3899 #ifdef SPECTRUM_PRINT
3900 #ifdef SPECTRUM_IOSTREAM
3902 cout <<
" computing a standard basis..." << endl;
3904 fputs(
"\n", stdout );
3905 fputs(
" computing a standard basis...\n", stdout );
3913 #ifdef SPECTRUM_DEBUG
3914 #ifdef SPECTRUM_PRINT
3917 #ifdef SPECTRUM_IOSTREAM
3920 fputs(
" ",stdout );
3965 #ifdef SPECTRUM_DEBUG
3966 #ifdef SPECTRUM_PRINT
3967 #ifdef SPECTRUM_IOSTREAM
3968 cout <<
"\n computing the highest corner...\n";
3970 fputs(
"\n computing the highest corner...\n", stdout );
3975 poly hc = (poly)
NULL;
3979 if( hc!=(poly)
NULL )
3994 #ifdef SPECTRUM_DEBUG
3995 #ifdef SPECTRUM_PRINT
3996 #ifdef SPECTRUM_IOSTREAM
3999 fputs(
" ", stdout );
4009 #ifdef SPECTRUM_DEBUG
4010 #ifdef SPECTRUM_PRINT
4011 #ifdef SPECTRUM_IOSTREAM
4012 cout <<
"\n computing the newton polygon...\n";
4014 fputs(
"\n computing the newton polygon...\n", stdout );
4021 #ifdef SPECTRUM_DEBUG
4022 #ifdef SPECTRUM_PRINT
4031 #ifdef SPECTRUM_DEBUG
4032 #ifdef SPECTRUM_PRINT
4033 #ifdef SPECTRUM_IOSTREAM
4034 cout <<
"\n computing the weight corner...\n";
4036 fputs(
"\n computing the weight corner...\n", stdout );
4041 poly wc = ( fast==0 ?
pCopy( hc ) :
4046 #ifdef SPECTRUM_DEBUG
4047 #ifdef SPECTRUM_PRINT
4048 #ifdef SPECTRUM_IOSTREAM
4051 fputs(
" ", stdout );
4061 #ifdef SPECTRUM_DEBUG
4062 #ifdef SPECTRUM_PRINT
4063 #ifdef SPECTRUM_IOSTREAM
4064 cout <<
"\n computing NF...\n" << endl;
4066 fputs(
"\n computing NF...\n", stdout );
4075 #ifdef SPECTRUM_DEBUG
4076 #ifdef SPECTRUM_PRINT
4078 #ifdef SPECTRUM_IOSTREAM
4081 fputs(
"\n", stdout );
4106 WerrorS(
"polynomial is zero" );
4109 WerrorS(
"polynomial has constant term" );
4112 WerrorS(
"not a singularity" );
4115 WerrorS(
"the singularity is not isolated" );
4118 WerrorS(
"highest corner cannot be computed" );
4121 WerrorS(
"principal part is degenerate" );
4127 WerrorS(
"unknown error occurred" );
4144 WerrorS(
"only works for local orderings" );
4152 WerrorS(
"does not work in quotient rings" );
4198 WerrorS(
"only works for local orderings" );
4203 WerrorS(
"does not work in quotient rings" );
4262 else if(
l->nr > 5 )
4300 int mu = (int)(
long)(
l->m[0].Data( ));
4301 int pg = (int)(
long)(
l->m[1].Data( ));
4302 int n = (int)(
long)(
l->m[2].Data( ));
4313 if( n !=
num->length( ) )
4317 else if( n !=
den->length( ) )
4321 else if( n != mul->
length( ) )
4341 for(
i=0;
i<n;
i++ )
4343 if( (*
num)[
i] <= 0 )
4347 if( (*
den)[
i] <= 0 )
4351 if( (*mul)[
i] <= 0 )
4363 for(
i=0,
j=n-1;
i<=
j;
i++,
j-- )
4366 (*den)[
i] != (*den)[
j] ||
4367 (*mul)[
i] != (*mul)[
j] )
4377 for(
i=0,
j=1;
i<n/2;
i++,
j++ )
4379 if( (*
num)[
i]*(*den)[
j] >= (*num)[
j]*(*den)[
i] )
4389 for(
mu=0,
i=0;
i<n;
i++ )
4394 if(
mu != (
int)(long)(
l->m[0].Data( )) )
4403 for( pg=0,
i=0;
i<n;
i++ )
4405 if( (*
num)[
i]<=(*den)[
i] )
4411 if( pg != (
int)(long)(
l->m[1].Data( )) )
4440 WerrorS(
"first argument is not a spectrum:" );
4445 WerrorS(
"second argument is not a spectrum:" );
4478 int k = (int)(
long)second->
Data( );
4482 WerrorS(
"first argument is not a spectrum" );
4487 WerrorS(
"second argument should be positive" );
4513 BOOLEAN qh=(((int)(
long)
w->Data())==1);
4524 WerrorS(
"first argument is not a spectrum" );
4529 WerrorS(
"second argument is not a spectrum" );
4572 WerrorS(
"Ground field not implemented!");
4592 LP->
m= (int)(
long)(
v->Data());
4598 LP->
n= (int)(
long)(
v->Data());
4604 LP->
m1= (int)(
long)(
v->Data());
4610 LP->
m2= (int)(
long)(
v->Data());
4616 LP->
m3= (int)(
long)(
v->Data());
4619 Print(
"m (constraints) %d\n",LP->
m);
4620 Print(
"n (columns) %d\n",LP->
n);
4644 lres->
m[4].
data=(
void*)(
long)LP->
m;
4647 lres->
m[5].
data=(
void*)(
long)LP->
n;
4649 res->data= (
void*)lres;
4656 ideal gls = (ideal)(arg1->
Data());
4657 int imtype= (int)(
long)arg2->
Data();
4680 gls= (poly)(arg1->
Data());
4681 int howclean= (int)(
long)arg3->
Data();
4685 WerrorS(
"Input polynomial is constant!");
4694 rlist->
Init( r[0] );
4695 for(
int i=r[0];
i>0;
i--)
4710 WerrorS(
"Ground field not implemented!");
4717 unsigned long int ii = (
unsigned long int)arg2->
Data();
4742 if ( (vpos !=
i) && (
pGetExp( piter,
i ) != 0) )
4744 WerrorS(
"The input polynomial must be univariate!");
4752 number * pcoeffs= (number *)
omAlloc( (deg+1) *
sizeof( number ) );
4754 for (
i= deg;
i >= 0;
i-- )
4769 for (
i=deg;
i >= 0;
i--)
4777 roots->
solver( howclean );
4785 rlist->
Init( elem );
4789 for (
j= 0;
j < elem;
j++ )
4798 for (
j= 0;
j < elem;
j++ )
4802 rlist->
m[
j].
data=(
void *)dummy;
4815 res->data= (
void*)rlist;
4824 p= (ideal)arg1->
Data();
4825 w= (ideal)arg2->
Data();
4836 int tdg= (int)(
long)arg3->
Data();
4843 WerrorS(
"Last input parameter must be > 0!");
4851 if (
m != (
int)
pow((
double)tdg+1,(
double)n) )
4853 Werror(
"Size of second input ideal must be equal to %d!",
4854 (
int)
pow((
double)tdg+1,(
double)n));
4861 WerrorS(
"Ground field not implemented!");
4866 number *pevpoint= (number *)
omAlloc( n *
sizeof( number ) );
4867 for (
i= 0;
i < n;
i++ )
4876 WerrorS(
"Elements of first input ideal must not be equal to -1, 0, 1!");
4885 WerrorS(
"Elements of first input ideal must be numbers!");
4888 pevpoint[
i]=
nCopy( tmp );
4892 number *wresults= (number *)
omAlloc(
m *
sizeof( number ) );
4893 for (
i= 0;
i <
m;
i++ )
4902 WerrorS(
"Elements of second input ideal must be numbers!");
4917 res->data= (
void*)rpoly;
4932 else gls= (ideal)(
v->Data());
4938 else imtype= (int)(
long)
v->Data();
4943 ideal test_id=
idInit(1,1);
4947 if (gls->m[
j]!=
NULL)
4949 test_id->m[0]=gls->m[
j];
4953 WerrorS(
"Newton polytope not of expected dimension");
4967 unsigned long int ii=(
unsigned long int)
v->Data();
4975 else howclean= (int)(
long)
v->Data();
5004 WerrorS(
"Error occurred during matrix setup!");
5017 WerrorS(
"Unsuitable input ideal: Minor of resultant matrix is singular!");
5023 if ( interpolate_det )
5029 if ( interpolate_det )
5036 for (
i=0;
i < c;
i++)
pWrite(iproots[
i]->getPoly());
5038 for (
i=0;
i < c;
i++)
pWrite(muiproots[
i]->getPoly());
5042 arranger=
new rootArranger( iproots, muiproots, howclean );
5053 WerrorS(
"Solver was unable to find any roots!");
5059 for (
i=0;
i <
count;
i++)
delete iproots[
i];
5062 for (
i=0;
i <
count;
i++)
delete muiproots[
i];
5069 res->data= (
void *)listofroots;
5093 onepoint->
Init(elem);
5094 for (
j= 0;
j < elem;
j++ )
5110 listofroots->
m[
i].
data=(
void *)onepoint;
5118 listofroots->
Init( 0 );
5132 if (rg==
NULL)
return;
5156 Warn(
"deleting denom_list for ring change to %s",
IDID(
h));
5170 if ((rg!=
NULL) && (rg->idroot==
NULL))
5198 if((*iv)[
i]>=0) { neg=
FALSE;
break; }
5203 (*iv)[
i]= - (*iv)[
i];
5212 if((*iv)[
i]>=0) { neg=
FALSE;
break; }
5217 (*iv)[
i]= -(*iv)[
i];
5226 if((*iv)[
i]!=1) { all_one=
FALSE;
break; }
5232 (*iv2)[2]=iv->
length()-2;
5244 if((*iv)[
i]!=1) { all_one=
FALSE;
break; }
5250 (*iv2)[2]=iv->
length()-2;
5291 (*iv)[2] += (*iv2)[2];
5298 if (!change)
h=
h->next;
5306 int last = 0, o=0, n = 1,
i=0, typ = 1,
j;
5318 R->wanted_maxExp=(*iv)[2]*2+1;
5331 WerrorS(
"invalid combination of orderings");
5339 WerrorS(
"more than one ordering c/C specified");
5345 R->block0=(
int *)
omAlloc0(n*
sizeof(
int));
5346 R->block1=(
int *)
omAlloc0(n*
sizeof(
int));
5349 int *weights=(
int*)
omAlloc0((
R->N+1)*
sizeof(int));
5352 for (
j=0;
j < n-1;
j++)
5383 R->block0[n] =
last+1;
5386 R->wvhdl[n][
i-2] = (*iv)[
i];
5388 if (weights[
last]==0) weights[
last]=(*iv)[
i]*typ;
5401 R->block0[n] =
last+1;
5403 else last += (*iv)[0];
5408 if (weights[
i]==0) weights[
i]=typ;
5420 const int s = (*iv)[2];
5430 const int s = (*iv)[2];
5432 if( 1 <
s ||
s < -1 )
return TRUE;
5448 R->block0[n] =
last+1;
5453 R->wvhdl[n][
i-2]=(*iv)[
i];
5455 if (weights[
last]==0) weights[
last]=(*iv)[
i]*typ;
5457 last=
R->block0[n]-1;
5462 R->block0[n] =
last+1;
5465 if (
R->block1[n]-
R->block0[n]+2>=iv->
length())
5466 WarnS(
"missing module weights");
5467 for (
i=2;
i<=(
R->block1[n]-
R->block0[n]+2);
i++)
5469 R->wvhdl[n][
i-2]=(*iv)[
i];
5471 if (weights[
last]==0) weights[
last]=(*iv)[
i]*typ;
5473 R->wvhdl[n][
i-2]=iv->
length() -3 -(
R->block1[n]-
R->block0[n]);
5476 R->wvhdl[n][
i-1]=(*iv)[
i];
5478 last=
R->block0[n]-1;
5483 R->block0[n] =
last+1;
5491 if (weights[
last]==0) weights[
last]=(*iv)[
i]*typ;
5493 last=
R->block0[n]-1;
5499 if (Mtyp==0)
return TRUE;
5500 if (Mtyp==-1) typ = -1;
5504 R->wvhdl[n][
i-2]=(*iv)[
i];
5506 R->block0[n] =
last+1;
5509 for(
i=
R->block1[n];
i>=
R->block0[n];
i--)
5511 if (weights[
i]==0) weights[
i]=typ;
5521 Werror(
"Internal Error: Unknown ordering %d", (*iv)[1]);
5528 Werror(
"mismatch of number of vars (%d) and ordering (>=%d vars)",
5536 for(
i=1;
i<=
R->N;
i++)
5537 {
if (weights[
i]<0) {
R->OrdSgn=-1;
break; }}
5551 if (
R->block1[n] !=
R->N)
5562 R->block0[n] <=
R->N)
5564 R->block1[n] =
R->N;
5568 Werror(
"mismatch of number of vars (%d) and ordering (%d vars)",
5587 *
p = (
char*)sl->
name;
5655 WerrorS(
"parameter expected");
5662 for(
int i=pars-1;
i>=0;
i--)
5674 int ch = (int)(
long)pn->
Data();
5685 if ((ch<2)||(ch!=ch2))
5687 Warn(
"%d is invalid as characteristic of the ground field. 32003 is used.", ch);
5690 #ifndef TEST_ZN_AS_ZP
5694 mpz_init_set_ui(modBase, (
long)ch);
5701 cf->has_simple_Inverse=1;
5714 if ((ch!=0) && (ch!=
IsPrime(ch)) && (pars == 1))
5726 if ((ch!=0) && (ch!=
IsPrime(ch)))
5728 WerrorS(
"too many parameters");
5736 WerrorS(
"parameter expected");
5742 extParam.
r =
rDefault( ch, pars, names);
5743 for(
int i=pars-1;
i>=0;
i--)
5756 && ((strcmp(pn->
name,
"real")==0) || (strcmp(pn->
name,
"complex")==0)))
5759 BOOLEAN complex_flag=(strcmp(pn->
name,
"complex")==0);
5762 float_len=(int)(
long)pnn->
Data();
5763 float_len2=float_len;
5767 float_len2=(int)(
long)pnn->
Data();
5802 else if ((pn->
name !=
NULL) && (strcmp(pn->
name,
"integer") == 0))
5806 unsigned int modExponent = 1;
5807 mpz_init_set_si(modBase, 0);
5814 mpz_set_ui(modBase, (
long) pnn->
Data());
5818 modExponent = (long) pnn->
Data();
5823 mpz_mul_ui(modBase, modBase, (
int)(
long) pnn->
Data());
5836 if ((mpz_cmp_ui(modBase, 1) == 0) && (
mpz_sgn1(modBase) < 0))
5838 WerrorS(
"Wrong ground ring specification (module is 1)");
5841 if (modExponent < 1)
5843 WerrorS(
"Wrong ground ring specification (exponent smaller than 1");
5848 if (modExponent > 1 &&
cf ==
NULL)
5850 if ((mpz_cmp_ui(modBase, 2) == 0) && (modExponent <= 8*
sizeof(
unsigned long)))
5861 WerrorS(
"modulus must not be 0 or parameter not allowed");
5867 info.exp= modExponent;
5876 WerrorS(
"modulus must not be 0 or parameter not allowed");
5882 info.exp= modExponent;
5893 extParam.
r = (ring)pn->
Data();
5906 WerrorS(
"Wrong or unknown ground field specification");
5912 Print(
"pn[%p]: type: %d [%s]: %p, name: %s", (
void*)
p,
p->Typ(),
Tok2Cmdname(
p->Typ()),
p->Data(), (
p->name ==
NULL?
"NULL" :
p->name) );
5934 WerrorS(
"Invalid ground field specification");
5958 WerrorS(
"name of ring variable expected");
6011 int *perm=(
int *)
omAlloc0((org_ring->N+1)*
sizeof(int));
6028 WerrorS(
"name of ring variable expected");
6038 for(;
i<org_ring->N;
i++)
6040 if (strcmp(org_ring->names[
i],
R->names[
j])==0)
6048 Werror(
"variable %d (%s) not in basering",
j+1,
R->names[
j]);
6061 for(
j=
R->block0[
i];j<=R->block1[
i];
j++)
6065 if (min_var==-1) min_var=perm[
j];
6073 R->block0[
i]=min_var;
6074 R->block1[
i]=max_var;
6078 R->wvhdl[
i]=(
int*)
omAlloc0((max_var-min_var+1)*
sizeof(int));
6079 for(
j=org_ring->block0[
i];j<=org_ring->block1[
i];
j++)
6083 R->wvhdl[
i][perm[
j]-
R->block0[
i]]=
6084 org_ring->wvhdl[
i][
j-org_ring->block0[
i]];
6110 R->order[
j-1]=
R->order[
j];
6111 R->block0[
j-1]=
R->block0[
j];
6112 R->block1[
j-1]=
R->block1[
j];
6114 R->wvhdl[
j-1]=
R->wvhdl[
j];
6122 while (
R->order[n]==0) n--;
6125 if (
R->block1[n] !=
R->N)
6136 R->block0[n] <=
R->N)
6138 R->block1[n] =
R->N;
6142 Werror(
"mismatch of number of vars (%d) and ordering (%d vars) in block %d",
6143 R->N,
R->block1[n],n);
6149 R->OrdSgn = org_ring->OrdSgn;
6172 if ((r->ref<=0)&&(r->order!=
NULL))
6182 if (
j==0)
WarnS(
"killing the basering for level 0");
6187 while (r->idroot!=
NULL)
6190 killhdl2(r->idroot,&(r->idroot),r);
6237 Warn(
"deleting denom_list for ring change from %s",
IDID(
h));
6311 ideal I=(ideal)u->
Data();
6314 for(
i=I->nrows*I->ncols-1;
i>=0;
i--)
6326 switch (
p->language)
6335 if(
p->libname!=
NULL)
6336 Print(
",%s",
p->libname);
6351 tmp_in.
data=(
void*)(
long)(*aa)[
i];
6359 Werror(
"apply fails at index %d",
i+1);
6362 if (
i==0) { memcpy(
res,&tmp_out,
sizeof(tmp_out)); }
6367 memcpy(curr,&tmp_out,
sizeof(tmp_out));
6389 res->data=(
void *)
l;
6396 for(
int i=0;
i<=aa->
nr;
i++)
6399 tmp_in.
Copy(&(aa->
m[
i]));
6408 Werror(
"apply fails at index %d",
i+1);
6411 if (
i==0) { memcpy(
res,&tmp_out,
sizeof(tmp_out)); }
6416 memcpy(curr,&tmp_out,
sizeof(tmp_out));
6439 WerrorS(
"first argument to `apply` must allow an index");
6449 char assume_yylinebuf[80];
6451 int lev=(long)a->
Data();
6458 if (bo) {
WerrorS(
"syntax error in ASSUME");
return TRUE;}
6460 if (
b->Data()==
NULL) {
Werror(
"ASSUME failed:%s",assume_yylinebuf);
return TRUE;}
6472 char *ss=(
char*)
omAlloc(strlen(a)+strlen(
s)+30);
6474 int end_s=strlen(
s);
6475 while ((end_s>0) && ((
s[end_s]<=
' ')||(
s[end_s]==
';'))) end_s--;
6478 sprintf(
name,
"%s->%s",a,
s);
6480 int start_s=end_s-1;
6481 while ((start_s>=0) && (
s[start_s]!=
';')) start_s--;
6484 sprintf(ss,
"parameter def %s;return(%s);\n",a,
s);
6489 sprintf(ss,
"parameter def %s;%s;return(%s);\n",a,
s,
s+start_s+1);
6549 sprintf(
buf,
"wrong length of parameters(%d), expected ",t);
6551 sprintf(
buf,
"par. %d is of type `%s`, expected ",nr,
Tok2Cmdname(t));
6552 for(
int i=1;
i<=
T[0];
i++)
6557 if (
i<
T[0]) strcat(
buf,
",");
6567 if (type_list[0]==0)
return TRUE;
6570 if (
l!=(
int)type_list[0])
6575 for(
int i=1;
i<=
l;
i++,args=args->
next)
6577 short t=type_list[
i];
6581 || (t!=args->
Typ()))
Rational pow(const Rational &a, int e)
struct for passing initialization parameters to naInitChar
void atSet(idhdl root, char *name, void *data, int typ)
void * atGet(idhdl root, const char *name, int t, void *defaultReturnValue)
static int si_max(const int a, const int b)
static int si_min(const int a, const int b)
for(int i=0;i<=n;i++) degsf[i]
void mu(int **points, int sizePoints)
CanonicalForm map(const CanonicalForm &primElem, const Variable &alpha, const CanonicalForm &F, const Variable &beta)
map from to such that is mapped onto
unsigned char * proc[NUM_PROC]
poly singclap_resultant(poly f, poly g, poly x, const ring r)
ideal singclap_factorize(poly f, intvec **v, int with_exps, const ring r)
matrix singclap_irrCharSeries(ideal I, const ring r)
int * Zp_roots(poly p, const ring r)
idhdl get(const char *s, int lev)
void show(int mat=0, int spaces=0) const
virtual number getSubDet()
virtual ideal getMatrix()
virtual IStateType initState() const
complex root finder for univariate polynomials based on laguers algorithm
gmp_complex * getRoot(const int i)
void fillContainer(number *_coeffs, number *_ievpoint, const int _var, const int _tdg, const rootType _rt, const int _anz)
bool solver(const int polishmode=PM_NONE)
Linear Programming / Linear Optimization using Simplex - Algorithm.
BOOLEAN mapFromMatrix(matrix m)
matrix mapToMatrix(matrix m)
Class used for (list of) interpreter objects.
void CleanUp(ring r=currRing)
void Clean(ring r=currRing)
INLINE_THIS void Init(int l=0)
void delete_node(spectrumPolyNode **)
int mult_spectrum(spectrum &)
int mult_spectrumh(spectrum &)
Base class for solving 0-dim poly systems using u-resultant.
rootContainer ** specializeInU(BOOLEAN matchUp=false, const number subDetVal=NULL)
rootContainer ** interpolateDenseSP(BOOLEAN matchUp=false, const number subDetVal=NULL)
resMatrixBase * accessResMat()
vandermonde system solver for interpolating polynomials from their values
poly numvec2poly(const number *q)
number * interpolateDense(const number *q)
Solves the Vandermode linear system \sum_{i=1}^{n} x_i^k-1 w_i = q_k, k=1,..,n.
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE long n_Int(number &n, const coeffs r)
conversion of n to an int; 0 if not possible in Z/pZ: the representing int lying in (-p/2 ....
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
static FORCE_INLINE BOOLEAN nCoeff_is_GF(const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Z(const coeffs r)
@ n_R
single prescision (6,6) real numbers
@ n_Q
rational (GMP) numbers
@ n_Znm
only used if HAVE_RINGS is defined
@ n_algExt
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic
@ n_Zn
only used if HAVE_RINGS is defined
@ n_long_R
real floating point (GMP) numbers
@ n_Z2m
only used if HAVE_RINGS is defined
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
@ n_Z
only used if HAVE_RINGS is defined
@ n_long_C
complex floating point (GMP) numbers
short float_len2
additional char-flags, rInit
static FORCE_INLINE BOOLEAN nCoeff_is_numeric(const coeffs r)
static FORCE_INLINE void n_MPZ(mpz_t result, number &n, const coeffs r)
conversion of n to a GMP integer; 0 if not possible
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
const char * par_name
parameter name
static FORCE_INLINE char const ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
const unsigned short fftable[]
static FORCE_INLINE void nSetChar(const coeffs r)
initialisations after each ring change
static FORCE_INLINE BOOLEAN nCoeff_is_Ring(const coeffs r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
static FORCE_INLINE char * nCoeffName(const coeffs cf)
static FORCE_INLINE number n_InitMPZ(mpz_t n, const coeffs r)
conversion of a GMP integer to number
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
short float_len
additional char-flags, rInit
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
static FORCE_INLINE BOOLEAN nCoeff_is_long_C(const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
Creation data needed for finite fields.
const CanonicalForm int s
const Variable & v
< [in] a sqrfree bivariate poly
const ExtensionInfo & info
< [in] sqrfree poly
int search(const CFArray &A, const CanonicalForm &F, int i, int j)
search for F in A between index i and j
char name(const Variable &v)
void WerrorS(const char *s)
VAR char my_yylinebuf[80]
if(!FE_OPT_NO_SHELL_FLAG)(void) system(sys)
char *(* fe_fgets_stdin)(const char *pr, char *s, int size)
void newBuffer(char *s, feBufferTypes t, procinfo *pi, int lineno)
ideal maMapIdeal(const ideal map_id, const ring preimage_r, const ideal image_id, const ring image_r, const nMapFunc nMap)
polynomial map for ideals/module/matrix map_id: the ideal to map map_r: the base ring for map_id imag...
int iiTestConvert(int inputType, int outputType)
const char * Tok2Cmdname(int tok)
void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge)
void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void hKill(monf xmem, int Nvar)
void hDelete(scfmon ev, int ev_length)
void hPure(scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
void hSupp(scfmon stc, int Nstc, varset var, int *Nvar)
void hLexR(scfmon rad, int Nrad, varset var, int Nvar)
scfmon hInit(ideal S, ideal Q, int *Nexist)
void hRadical(scfmon rad, int *Nrad, int Nvar)
#define idDelete(H)
delete an ideal
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
static BOOLEAN idIsZeroDim(ideal i)
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
#define idMaxIdeal(D)
initialise the maximal ideal (at 0)
int idGetNumberOfChoise(int t, int d, int begin, int end, int *choise)
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
STATIC_VAR int * multiplicity
static BOOLEAN length(leftv result, leftv arg)
intvec * ivCopy(const intvec *o)
#define IMATELEM(M, I, J)
int IsCmd(const char *n, int &tok)
BOOLEAN iiExprArith1(leftv res, leftv a, int op)
BOOLEAN iiAssign(leftv l, leftv r, BOOLEAN toplevel)
BOOLEAN iiConvert(int inputType, int outputType, int index, leftv input, leftv output, const struct sConvertTypes *dConvertTypes)
idhdl ggetid(const char *n)
void killhdl2(idhdl h, idhdl *ih, ring r)
idhdl enterid(const char *s, int lev, int t, idhdl *root, BOOLEAN init, BOOLEAN search)
VAR proclevel * procstack
idhdl packFindHdl(package r)
EXTERN_VAR omBin sleftv_bin
INST_VAR sleftv iiRETURNEXPR
char * iiGetLibProcBuffer(procinfo *pi, int part)
procinfo * iiInitSingularProcinfo(procinfov pi, const char *libname, const char *procname, int, long pos, BOOLEAN pstatic)
lists rDecompose(const ring r)
@ semicListWrongNumberOfNumerators
@ semicListFirstElementWrongType
@ semicListSecondElementWrongType
@ semicListFourthElementWrongType
@ semicListWrongNumberOfDenominators
@ semicListThirdElementWrongType
@ semicListWrongNumberOfMultiplicities
@ semicListFifthElementWrongType
@ semicListSixthElementWrongType
BOOLEAN iiApplyINTVEC(leftv res, leftv a, int op, leftv proc)
BOOLEAN jjVARIABLES_P(leftv res, leftv u)
lists rDecompose_list_cf(const ring r)
int iiOpsTwoChar(const char *s)
BOOLEAN spaddProc(leftv result, leftv first, leftv second)
BOOLEAN jjMINRES(leftv res, leftv v)
BOOLEAN killlocals_list(int v, lists L)
BOOLEAN iiParameter(leftv p)
STATIC_VAR BOOLEAN iiNoKeepRing
int iiDeclCommand(leftv sy, leftv name, int lev, int t, idhdl *root, BOOLEAN isring, BOOLEAN init_b)
static void rRenameVars(ring R)
void iiCheckPack(package &p)
BOOLEAN iiCheckTypes(leftv args, const short *type_list, int report)
check a list of arguemys against a given field of types return TRUE if the types match return FALSE (...
BOOLEAN iiApply(leftv res, leftv a, int op, leftv proc)
void list_cmd(int typ, const char *what, const char *prefix, BOOLEAN iterate, BOOLEAN fullname)
VAR BOOLEAN iiDebugMarker
ring rInit(leftv pn, leftv rv, leftv ord)
leftv iiMap(map theMap, const char *what)
int iiRegularity(lists L)
BOOLEAN nuLagSolve(leftv res, leftv arg1, leftv arg2, leftv arg3)
find the (complex) roots an univariate polynomial Determines the roots of an univariate polynomial us...
BOOLEAN rDecompose_CF(leftv res, const coeffs C)
static void rDecomposeC_41(leftv h, const coeffs C)
void iiMakeResolv(resolvente r, int length, int rlen, char *name, int typ0, intvec **weights)
BOOLEAN iiARROW(leftv r, char *a, char *s)
BOOLEAN semicProc3(leftv res, leftv u, leftv v, leftv w)
BOOLEAN syBetti1(leftv res, leftv u)
BOOLEAN iiApplyLIST(leftv res, leftv a, int op, leftv proc)
idhdl rDefault(const char *s)
static void rDecomposeC(leftv h, const ring R)
int exprlist_length(leftv v)
BOOLEAN mpKoszul(leftv res, leftv c, leftv b, leftv id)
poly iiHighCorner(ideal I, int ak)
BOOLEAN spectrumfProc(leftv result, leftv first)
lists listOfRoots(rootArranger *self, const unsigned int oprec)
static void jjINT_S_TO_ID(int n, int *e, leftv res)
lists scIndIndset(ideal S, BOOLEAN all, ideal Q)
BOOLEAN nuVanderSys(leftv res, leftv arg1, leftv arg2, leftv arg3)
COMPUTE: polynomial p with values given by v at points p1,..,pN derived from p; more precisely: consi...
BOOLEAN jjCHARSERIES(leftv res, leftv u)
void rDecomposeCF(leftv h, const ring r, const ring R)
BOOLEAN iiApplyIDEAL(leftv, leftv, int, leftv)
static void list1(const char *s, idhdl h, BOOLEAN c, BOOLEAN fullname)
void list_error(semicState state)
BOOLEAN mpJacobi(leftv res, leftv a)
const char * iiTwoOps(int t)
BOOLEAN iiBranchTo(leftv, leftv args)
BOOLEAN jjBETTI2_ID(leftv res, leftv u, leftv v)
BOOLEAN iiTestAssume(leftv a, leftv b)
void iiSetReturn(const leftv source)
BOOLEAN iiAssignCR(leftv r, leftv arg)
BOOLEAN spmulProc(leftv result, leftv first, leftv second)
spectrumState spectrumCompute(poly h, lists *L, int fast)
idhdl rFindHdl(ring r, idhdl n)
syStrategy syConvList(lists li)
BOOLEAN spectrumProc(leftv result, leftv first)
BOOLEAN iiDefaultParameter(leftv p)
void rComposeC(lists L, ring R)
BOOLEAN iiCheckRing(int i)
#define BREAK_LINE_LENGTH
spectrumState spectrumStateFromList(spectrumPolyList &speclist, lists *L, int fast)
BOOLEAN syBetti2(leftv res, leftv u, leftv w)
ring rSubring(ring org_ring, sleftv *rv)
BOOLEAN kWeight(leftv res, leftv id)
static leftv rOptimizeOrdAsSleftv(leftv ord)
BOOLEAN rSleftvOrdering2Ordering(sleftv *ord, ring R)
static BOOLEAN rComposeOrder(const lists L, const BOOLEAN check_comp, ring R)
spectrum spectrumFromList(lists l)
static idhdl rSimpleFindHdl(const ring r, const idhdl root, const idhdl n)
syStrategy syForceMin(lists li)
static void iiReportTypes(int nr, int t, const short *T)
void rDecomposeRing(leftv h, const ring R)
BOOLEAN jjRESULTANT(leftv res, leftv u, leftv v, leftv w)
static BOOLEAN iiInternalExport(leftv v, int toLev)
static void rDecompose_23456(const ring r, lists L)
void copy_deep(spectrum &spec, lists l)
void killlocals_rec(idhdl *root, int v, ring r)
BOOLEAN nuMPResMat(leftv res, leftv arg1, leftv arg2)
returns module representing the multipolynomial resultant matrix Arguments 2: ideal i,...
semicState list_is_spectrum(lists l)
static void killlocals0(int v, idhdl *localhdl, const ring r)
BOOLEAN semicProc(leftv res, leftv u, leftv v)
BOOLEAN loSimplex(leftv res, leftv args)
Implementation of the Simplex Algorithm.
BOOLEAN jjPROC(leftv res, leftv u, leftv v)
ring rCompose(const lists L, const BOOLEAN check_comp, const long bitmask, const int isLetterplace)
BOOLEAN loNewtonP(leftv res, leftv arg1)
compute Newton Polytopes of input polynomials
BOOLEAN iiApplyBIGINTMAT(leftv, leftv, int, leftv)
BOOLEAN jjBETTI2(leftv res, leftv u, leftv v)
const char * lastreserved
static BOOLEAN rSleftvList2StringArray(leftv sl, char **p)
lists syConvRes(syStrategy syzstr, BOOLEAN toDel, int add_row_shift)
BOOLEAN iiWRITE(leftv, leftv v)
void paPrint(const char *n, package p)
static resolvente iiCopyRes(resolvente r, int l)
BOOLEAN kQHWeight(leftv res, leftv v)
void rComposeRing(lists L, ring R)
BOOLEAN iiExport(leftv v, int toLev)
BOOLEAN jjBETTI(leftv res, leftv u)
void spectrumPrintError(spectrumState state)
lists getList(spectrum &spec)
BOOLEAN nuUResSolve(leftv res, leftv args)
solve a multipolynomial system using the u-resultant Input ideal must be 0-dimensional and (currRing-...
BOOLEAN jjVARIABLES_ID(leftv res, leftv u)
void rDecomposeRing_41(leftv h, const coeffs C)
static BOOLEAN rComposeVar(const lists L, ring R)
ideal kStd(ideal F, ideal Q, tHomog h, intvec **w, intvec *hilb, int syzComp, int newIdeal, intvec *vw, s_poly_proc_t sp)
VAR denominator_list DENOMINATOR_LIST
BOOLEAN nc_CallPlural(matrix cc, matrix dd, poly cn, poly dn, ring r, bool bSetupQuotient, bool bCopyInput, bool bBeQuiet, ring curr, bool dummy_ring=false)
returns TRUE if there were errors analyze inputs, check them for consistency detects nc_type,...
char * lString(lists l, BOOLEAN typed, int dim)
BOOLEAN lRingDependend(lists L)
resolvente liFindRes(lists L, int *len, int *typ0, intvec ***weights)
lists liMakeResolv(resolvente r, int length, int reallen, int typ0, intvec **weights, int add_row_shift)
void maFindPerm(char const *const *const preim_names, int preim_n, char const *const *const preim_par, int preim_p, char const *const *const names, int n, char const *const *const par, int nop, int *perm, int *par_perm, n_coeffType ch)
BOOLEAN maApplyFetch(int what, map theMap, leftv res, leftv w, ring preimage_r, int *perm, int *par_perm, int P, nMapFunc nMap)
matrix mpNew(int r, int c)
create a r x c zero-matrix
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
#define MATELEM(mat, i, j)
1-based access to matrix
void mult(unsigned long *result, unsigned long *a, unsigned long *b, unsigned long p, int dega, int degb)
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
ideal loNewtonPolytope(const ideal id)
EXTERN_VAR size_t gmp_output_digits
uResultant::resMatType determineMType(int imtype)
mprState mprIdealCheck(const ideal theIdeal, const char *name, uResultant::resMatType mtype, BOOLEAN rmatrix=false)
char * complexToStr(gmp_complex &c, const unsigned int oprec, const coeffs src)
gmp_float sqrt(const gmp_float &a)
void setGMPFloatDigits(size_t digits, size_t rest)
Set size of mantissa digits - the number of output digits (basis 10) the size of mantissa consists of...
void report(const char *fmt, const char *name)
The main handler for Singular numbers which are suitable for Singular polynomials.
#define nPrint(a)
only for debug, over any initalized currRing
#define SHORT_REAL_LENGTH
#define omFreeSize(addr, size)
#define omCheckAddr(addr)
#define omReallocSize(addr, o_size, size)
#define omCheckAddrSize(addr, size)
#define omFreeBin(addr, bin)
#define omFreeBinAddr(addr)
#define omRealloc0Size(addr, o_size, size)
poly p_PermPoly(poly p, const int *perm, const ring oldRing, const ring dst, nMapFunc nMap, const int *par_perm, int OldPar, BOOLEAN use_mult)
#define __pp_Mult_nn(p, n, r)
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
static void p_Setm(poly p, const ring r)
static void p_Delete(poly *p, const ring r)
static unsigned pLength(poly a)
static poly p_Init(const ring r, omBin bin)
static poly p_Copy(poly p, const ring r)
returns a copy of p
static long p_Totaldegree(poly p, const ring r)
#define __p_Mult_nn(p, n, r)
void rChangeCurrRing(ring r)
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Compatiblity layer for legacy polynomial operations (over currRing)
static long pTotaldegree(poly p)
#define pIsConstant(p)
like above, except that Comp must be 0
#define pCmp(p1, p2)
pCmp: args may be NULL returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
#define pGetVariables(p, e)
#define pGetExp(p, i)
Exponent.
#define pCopy(p)
return a copy of the poly
ideal idrCopyR(ideal id, ring src_r, ring dest_r)
void PrintS(const char *s)
void Werror(const char *fmt,...)
BOOLEAN rComplete(ring r, int force)
this needs to be called whenever a new ring is created: new fields in ring are created (like VarOffse...
const char * rSimpleOrdStr(int ord)
int rTypeOfMatrixOrder(const intvec *order)
ring rAssure_HasComp(const ring r)
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
BOOLEAN rCheckIV(const intvec *iv)
rRingOrder_t rOrderName(char *ordername)
void rDelete(ring r)
unconditionally deletes fields in r
BOOLEAN rEqual(ring r1, ring r2, BOOLEAN qr)
returns TRUE, if r1 equals r2 FALSE, otherwise Equality is determined componentwise,...
void rSetSyzComp(int k, const ring r)
static BOOLEAN rField_is_R(const ring r)
static BOOLEAN rField_is_Zp_a(const ring r)
static BOOLEAN rField_is_Z(const ring r)
static BOOLEAN rField_is_Zp(const ring r)
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
static BOOLEAN rField_is_long_C(const ring r)
static int rBlocks(const ring r)
static ring rIncRefCnt(ring r)
static BOOLEAN rField_is_Zn(const ring r)
static int rPar(const ring r)
(r->cf->P)
static int rInternalChar(const ring r)
static BOOLEAN rIsLPRing(const ring r)
@ ringorder_a64
for int64 weights
@ ringorder_rs
opposite of ls
@ ringorder_aa
for idElimination, like a, except pFDeg, pWeigths ignore it
@ ringorder_IS
Induced (Schreyer) ordering.
static BOOLEAN rField_is_Q_a(const ring r)
static BOOLEAN rField_is_Q(const ring r)
static void rDecRefCnt(ring r)
static char const ** rParameter(const ring r)
(r->cf->parameter)
static BOOLEAN rField_is_long_R(const ring r)
static BOOLEAN rField_is_numeric(const ring r)
static BOOLEAN rField_is_GF(const ring r)
static short rVar(const ring r)
#define rVar(r) (r->N)
BOOLEAN rHasLocalOrMixedOrdering(const ring r)
#define rField_is_Ring(R)
int status int void size_t count
int status int void * buf
BOOLEAN slWrite(si_link l, leftv v)
ideal idInit(int idsize, int rank)
initialise an ideal / module
intvec * id_QHomWeight(ideal id, const ring r)
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
BOOLEAN hasAxis(ideal J, int k, const ring r)
int hasOne(ideal J, const ring r)
BOOLEAN ringIsLocal(const ring r)
poly computeWC(const newtonPolygon &np, Rational max_weight, const ring r)
void computeNF(ideal stdJ, poly hc, poly wc, spectrumPolyList *NF, const ring r)
BOOLEAN hasLinearTerm(poly h, const ring r)
BOOLEAN hasConstTerm(poly h, const ring r)
INST_VAR sleftv sLastPrinted
BOOLEAN RingDependend(int t)
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
void syMinimizeResolvente(resolvente res, int length, int first)
void syKillComputation(syStrategy syzstr, ring r=currRing)
resolvente syReorder(resolvente res, int length, syStrategy syzstr, BOOLEAN toCopy=TRUE, resolvente totake=NULL)
intvec * syBettiOfComputation(syStrategy syzstr, BOOLEAN minim=TRUE, int *row_shift=NULL, intvec *weights=NULL)
void syKillEmptyEntres(resolvente res, int length)
struct for passing initialization parameters to naInitChar
THREAD_VAR double(* wFunctional)(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
void wCall(poly *s, int sl, int *x, double wNsqr, const ring R)
double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)