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) snprintf(
buf2,128,
"%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);
853 size_t len=strlen(
name)+5;
858 snprintf(
s,len,
"%s(%d)",
name,
i+1);
865 h->data.uideal=(ideal)L->
m[
i].
data;
868 Print(
"//defining: %s as %d-th syzygy module\n",
s,
i+1);
873 Warn(
"cannot define %s",
s);
953 int add_row_shift = 0;
956 if (weights!=
NULL) add_row_shift=weights->
min_in();
985 l->m[0].rtyp=u->
Typ();
986 l->m[0].data=u->
Data();
989 l->m[0].attribute=*a;
996 l->m[0].attribute=
NULL;
1010 int add_row_shift=0;
1016 add_row_shift = ww->
min_in();
1017 (*weights) -= add_row_shift;
1024 res->data=(
void*)res_im;
1027 for(
int i=1;
i<=res_im->
rows();
i++)
1029 if (
IMATELEM(*res_im,1,
i)==0) { add_row_shift--; }
1034 if (weights!=
NULL)
delete weights;
1047 int add_row_shift=0;
1052 add_row_shift = ww->
min_in();
1053 (*weights) -= add_row_shift;
1058 if (weights!=
NULL)
delete weights;
1061 return reg+1+add_row_shift;
1065#define BREAK_LINE_LENGTH 80
1092 else if(strncmp(
s,
"cont;",5)==0)
1099 strcat(
s,
"\n;~\n");
1165 res->m[
i].data = (
void *)save->set;
1177 res->m[
i].data = (
void *)save->set;
1203 const char *
id =
name->name;
1208 WerrorS(
"object to declare is not a name");
1218 Werror(
"can not define `%s` in other package",
name->name);
1279 WerrorS(
"branchTo can only occur in a proc");
1287 if (ll!=(
l-1))
return FALSE;
1290 short *t=(
short*)
omAlloc(
l*
sizeof(
short));
1294 for(
i=1;
i<
l;
i++,
h=
h->next)
1299 Werror(
"arg %d is not a string",
i);
1303 b=
IsCmd((
char *)
h->Data(),tt);
1308 Werror(
"arg %d is not a type name",
i);
1315 Werror(
"last(%d.) arg.(%s) is not a proc(but %s(%d)), nesting=%d",
1328 if(
pi->data.s.body==
NULL )
1357 if (err==0)
Warn(
"too many arguments for %s",
IDID(currProc));
1381 if (strcmp(
p->name,
"#")==0)
1390 if (strcmp(
p->name,
"#")==0)
1392 is_default_list=
TRUE;
1400 if (is_default_list)
1453 WerrorS(
"object with a different type exists");
1471 Warn(
"'%s': no such identifier\n",
v->
name);
1474 package frompack=v->req_packhdl;
1488 v->req_packhdl=rootpack;
1489 if (
h==frompack->idroot)
1491 frompack->idroot=
h->next;
1495 idhdl hh=frompack->idroot;
1502 Werror(
"`%s` not found",
v->Name());
1506 h->next=rootpack->idroot;
1520 Werror(
"cannot export:%s of internal type %d",
v->
name,
v->rtyp);
1546 Werror(
"cannot export:%s of internal type %d",
v->
name,
v->rtyp);
1559 else if (
IDTYP(old)==
v->Typ())
1597 WerrorS(
"no ring active (9)");
1639 WarnS(
"package not found\n");
1660 #ifndef TEST_ZN_AS_ZP
1664 mpz_init_set_ui(modBase, (
long)32003);
1671 r->cf->has_simple_Inverse=1;
1684 r->block0 = (
int *)
omAlloc0(3 *
sizeof(
int *));
1685 r->block1 = (
int *)
omAlloc0(3 *
sizeof(
int *));
1704 if ((r==
NULL)||(r->VarOffset==
NULL))
1743 L->
m[0].
data=(
void *)(
long)r->cf->ch;
1749 for(
i=0;
i<r->N;
i++)
1755 L->
m[1].
data=(
void *)LL;
1772 if (r->block1[
i]-r->block0[
i] >=0 )
1774 j=r->block1[
i]-r->block0[
i];
1777 if ((r->wvhdl!=
NULL) && (r->wvhdl[
i]!=
NULL))
1779 for(;
j>=0;
j--) (*iv)[
j]=r->wvhdl[
i][
j];
1781 else switch (r->order[
i])
1790 for(;
j>=0;
j--) (*iv)[
j]=1;
1800 LLL->
m[1].
data=(
void *)iv;
1801 LL->
m[
i].
data=(
void *)LLL;
1804 L->
m[2].
data=(
void *)LL;
1815 L->
m[3].
data=(
void *)q;
1834 L->
m[0].
data=(
void *)0;
1844 L->
m[1].
data=(
void *)LL;
1868 L->
m[0].
data=(
void *)0;
1878 L->
m[1].
data=(
void *)LL;
1912 LL->
m[1].
data=(
void *) C->modExponent;
1914 L->
m[1].
data=(
void *)LL;
1941 LL->
m[1].
data=(
void *)
R->cf->modExponent;
1943 L->
m[1].
data=(
void *)LL;
1957 WerrorS(
"ring with polynomial data must be the base ring or compatible");
1970 else if ( C->extRing!=
NULL )
1980 Lc->m[0].data=(
void*)(
long)C->m_nfCharQ;
1987 Lc->m[1].data=(
void*)Lv;
1998 Loo->
m[1].
data=(
void *)iv;
2001 Lo->
m[0].
data=(
void*)Loo;
2004 Lc->m[2].data=(
void*)Lo;
2010 res->data=(
void*)
Lc;
2015 res->data=(
void *)(
long)C->ch;
2029 for(
i=0;
i<r->N;
i++)
2035 L->
m[1].
data=(
void *)LL;
2056 assume( r->block0[
i] == r->block1[
i] );
2057 const int s = r->block0[
i];
2063 else if (r->block1[
i]-r->block0[
i] >=0 )
2065 int bl=
j=r->block1[
i]-r->block0[
i];
2073 j+=r->wvhdl[
i][bl+1];
2076 if ((r->wvhdl!=
NULL) && (r->wvhdl[
i]!=
NULL))
2078 for(;
j>=0;
j--) (*iv)[
j]=r->wvhdl[
i][
j+(
j>bl)];
2080 else switch (r->order[
i])
2089 for(;
j>=0;
j--) (*iv)[
j]=1;
2099 LLL->
m[1].
data=(
void *)iv;
2100 LL->
m[
i].
data=(
void *)LLL;
2103 L->
m[2].
data=(
void *)LL;
2107 if (r->qideal==
NULL)
2138 WerrorS(
"ring with polynomial data must be the base ring or compatible");
2156 L->
m[0].
data=(
char*)r->cf; r->cf->ref++;
2171 || (r->qideal !=
NULL)
2178 WerrorS(
"ring with polynomial data must be the base ring or compatible");
2203 else if ( r->cf->extRing!=
NULL )
2213 Lc->m[0].data=(
void*)(
long)r->cf->m_nfCharQ;
2220 Lc->m[1].data=(
void*)Lv;
2231 Loo->
m[1].
data=(
void *)iv;
2234 Lo->
m[0].
data=(
void*)Loo;
2237 Lc->m[2].data=(
void*)Lo;
2248 L->
m[0].
data=(
void *)(
long)r->cf->ch;
2253 L->
m[0].
data=(
void *)r->cf;
2268 WerrorS(
"invalid coeff. field description, expecting 0");
2276 WerrorS(
"invalid coeff. field description, expecting precision list");
2284 WerrorS(
"invalid coeff. field description list, expected list(`int`,`int`)");
2287 int r1=(int)(
long)LL->
m[0].
data;
2288 int r2=(int)(
long)LL->
m[1].
data;
2298 WerrorS(
"invalid coeff. field description, expecting parameter name");
2320 unsigned int modExponent = 1;
2324 mpz_init_set_ui(modBase,0);
2335 number tmp= (number) LL->
m[0].
data;
2342 mpz_init_set_ui(modBase,(
unsigned long) LL->
m[0].
data);
2346 mpz_init_set_ui(modBase,0);
2350 modExponent = (
unsigned long) LL->
m[1].
data;
2358 if ((mpz_cmp_ui(modBase, 1) == 0) && (
mpz_sgn1(modBase) < 0))
2360 WerrorS(
"Wrong ground ring specification (module is 1)");
2363 if (modExponent < 1)
2365 WerrorS(
"Wrong ground ring specification (exponent smaller than 1)");
2374 else if (modExponent > 1)
2377 if ((mpz_cmp_ui(modBase, 2) == 0) && (modExponent <= 8*
sizeof(
unsigned long)))
2388 info.exp= modExponent;
2399 info.exp= modExponent;
2413 for(
i=0;
i<
R->N-1;
i++)
2415 for(
j=
i+1;
j<
R->N;
j++)
2417 if (strcmp(
R->names[
i],
R->names[
j])==0)
2422 size_t len=2+strlen(
R->names[
i]);
2424 snprintf(
R->names[
j],len,
"@%s",
R->names[
i]);
2442 snprintf(
R->names[
j],10,
"@@(%d)",
i+1);
2468 poly
p=(poly)
v->m[
i].Data();
2474 Werror(
"var name %d must be a string or a ring variable",
i+1);
2480 Werror(
"var name %d must be `string` (not %d)",
i+1,
v->m[
i].Typ());
2487 WerrorS(
"variable must be given as `list`");
2503 for (
int j=0;
j < n-1;
j++)
2510 &&(strcmp((
char*)vv->
m[0].
Data(),
"L")==0))
2512 number nn=(number)vv->
m[1].
Data();
2519 Werror(
"illegal argument for pseudo ordering L: %d",vv->
m[1].
Typ());
2526 if (bitmask!=0) n--;
2530 R->block0=(
int *)
omAlloc0((n+1)*
sizeof(int));
2531 R->block1=(
int *)
omAlloc0((n+1)*
sizeof(int));
2534 for (j_in_R= n-2; j_in_R>=0; j_in_R--)
2537 for(j_in_R=0,j_in_L=0;j_in_R<n-1;j_in_R++,j_in_L++)
2542 WerrorS(
"ordering must be list of lists");
2549 if (strcmp((
char*)vv->
m[0].
Data(),
"L")==0)
2563 if (j_in_R==0)
R->block0[0]=1;
2580 if (jj<0)
R->block0[j_in_R]=1;
2581 else R->block0[j_in_R]=
R->block1[jj]+1;
2588 for(
int i=0;
i<
l;
i++) (*iv)[
i]=1;
2607 R->block1[j_in_R]=
si_max(
R->block0[j_in_R],
R->block0[j_in_R]+iv_len-1);
2608 if (
R->block1[j_in_R]>
R->N)
2610 if (
R->block0[j_in_R]>
R->N)
2615 R->block1[j_in_R]=
R->N;
2616 iv_len=
R->block1[j_in_R]-
R->block0[j_in_R]+1;
2621 switch (
R->order[j_in_R])
2630 R->wvhdl[j_in_R] =(
int *)
omAlloc(iv_len*
sizeof(
int));
2631 for (
i=0;
i<iv_len;
i++)
2633 R->wvhdl[j_in_R][
i]=(*iv)[
i];
2638 for (
i=0;
i<iv_len;
i++)
2640 R->wvhdl[j_in_R][
i]=(*iv)[
i];
2642 R->wvhdl[j_in_R][
i]=iv->
length() - iv_len;
2646 R->wvhdl[j_in_R][
i+1]=(*iv)[
i];
2651 for (
i=0;
i<iv->
length();
i++)
R->wvhdl[j_in_R][
i]=(*iv)[
i];
2652 R->block1[j_in_R]=
si_max(
R->block0[j_in_R],
R->block0[j_in_R]+(
int)
sqrt((
double)(iv->
length())));
2653 if (
R->block1[j_in_R]>
R->N)
2655 R->block1[j_in_R]=
R->N;
2668 for (
i=0;
i<iv_len;
i++)
2670 if (((*iv)[
i]!=1)&&(iv_len!=1))
2673 Warn(
"ignore weight %d for ord %d (%s) at pos %d\n>>%s<<",
2684 R->block1[j_in_R]=
R->block0[j_in_R]=0;
2688 R->block1[j_in_R]=
R->block0[j_in_R]=(*iv)[0];
2694 R->block1[j_in_R] =
R->block0[j_in_R] = 0;
2697 const int s = (*iv)[0];
2699 R->block1[j_in_R] =
R->block0[j_in_R] =
s;
2708 WerrorS(
"ring order not implemented");
2716 WerrorS(
"ordering name must be a (string,intvec)");
2725 if (
R->block1[j_in_R] !=
R->N)
2736 R->block0[j_in_R] <=
R->N)
2738 R->block1[j_in_R] =
R->N;
2742 Werror(
"ordering incomplete: size (%d) should be %d",
R->block1[j_in_R],
R->N);
2746 if (
R->block0[j_in_R]>
R->N)
2748 Werror(
"not enough variables (%d) for ordering block %d, scanned so far:",
R->N,j_in_R+1);
2749 for(
int ii=0;ii<=j_in_R;ii++)
2778 WerrorS(
"ordering must be given as `list`");
2781 if (bitmask!=0) {
R->bitmask=bitmask;
R->wanted_maxExp=bitmask; }
2813 int ch = (int)(
long)L->
m[0].
Data();
2823 Warn(
"%d is invalid characteristic of ground field. %d is used.", ch,
l);
2826 #ifndef TEST_ZN_AS_ZP
2830 mpz_init_set_ui(modBase,(
long) ch);
2837 R->cf->has_simple_Inverse=1;
2858 int ch = (int)(
long)LL->
m[0].
Data();
2859 while ((ch!=
fftable[is_gf_char]) && (
fftable[is_gf_char])) is_gf_char++;
2860 if (
fftable[is_gf_char]==0) is_gf_char=-1;
2881 WerrorS(
"could not create the specified coefficient field");
2885 if( extRing->qideal !=
NULL )
2889 extParam.
r = extRing;
2896 extParam.
r = extRing;
2905 WerrorS(
"coefficient field must be described by `int` or `list`");
2911 WerrorS(
"could not create coefficient field described by the input!");
2923 #ifdef HAVE_SHIFTBBA
2926 R->isLPring=isLetterplace;
2931 if ((bitmask!=0)&&(
R->wanted_maxExp==0))
R->wanted_maxExp=bitmask;
2938 ideal q=(ideal)L->
m[3].
Data();
2944 WerrorS(
"coefficient fields must be equal if q-ideal !=0");
2951 int par_perm_size=0;
2971 par_perm_size=
rPar(orig_ring);
2981 WerrorS(
"coefficient fields must be equal if q-ideal !=0");
2985 perm=(
int *)
omAlloc0((orig_ring->N+1)*
sizeof(int));
2986 if (par_perm_size!=0)
2987 par_perm=(
int *)
omAlloc0(par_perm_size*
sizeof(
int));
2991 maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
3000 else if (par_perm_size!=0)
3008 par_perm,par_perm_size);
3026 WerrorS(
"q-ideal must be given as `ideal`");
3075 ideal
id=(ideal)a->
Data();
3095 int n=(int)(
long)
b->Data();
3096 int d=(int)(
long)c->
Data();
3103 if ((d>n) || (d<1) || (n<1))
3108 int *choise = (
int*)
omAlloc(d*
sizeof(
int));
3112 temp=(ideal)id->
Data();
3127 p =
pCopy(temp->m[choise[
l-1]-1]);
3153 BOOLEAN minim=(int)(
long)
w->Data();
3155 int add_row_shift=0;
3161 add_row_shift = ww->
min_in();
3162 (*weights) -= add_row_shift;
3191 if ((fullres==
NULL) && (minres==
NULL))
3305 ideal F=(ideal)id->
Data();
3311 res->data=(
char *)iv;
3315 double wNsqr = (double)2.0 / (
double)n;
3317 x = (
int * )
omAlloc(2 * (n + 1) *
sizeof(int));
3319 for (
i = n;
i!=0;
i--)
3320 (*iv)[
i-1] =
x[
i + n + 1];
3338 res->data=(
void *)
b;
3364 spec.
mu = (int)(
long)(
l->m[0].Data( ));
3365 spec.
pg = (int)(
long)(
l->m[1].Data( ));
3366 spec.
n = (int)(
long)(
l->m[2].Data( ));
3374 for(
int i=0;
i<spec.
n;
i++ )
3377 spec.
w[
i] = (*mul)[
i];
3408 for(
int i=0;
i<spec.
n;
i++ )
3412 (*mult)[
i] = spec.
w[
i];
3422 L->
m[0].
data = (
void*)(
long)spec.
mu;
3423 L->
m[1].
data = (
void*)(
long)spec.
pg;
3424 L->
m[2].
data = (
void*)(
long)spec.
n;
3475 WerrorS(
"the list is too short" );
3478 WerrorS(
"the list is too long" );
3482 WerrorS(
"first element of the list should be int" );
3485 WerrorS(
"second element of the list should be int" );
3488 WerrorS(
"third element of the list should be int" );
3491 WerrorS(
"fourth element of the list should be intvec" );
3494 WerrorS(
"fifth element of the list should be intvec" );
3497 WerrorS(
"sixth element of the list should be intvec" );
3501 WerrorS(
"first element of the list should be positive" );
3504 WerrorS(
"wrong number of numerators" );
3507 WerrorS(
"wrong number of denominators" );
3510 WerrorS(
"wrong number of multiplicities" );
3514 WerrorS(
"the Milnor number should be positive" );
3517 WerrorS(
"the geometrical genus should be nonnegative" );
3520 WerrorS(
"all numerators should be positive" );
3523 WerrorS(
"all denominators should be positive" );
3526 WerrorS(
"all multiplicities should be positive" );
3530 WerrorS(
"it is not symmetric" );
3533 WerrorS(
"it is not monotonous" );
3537 WerrorS(
"the Milnor number is wrong" );
3540 WerrorS(
"the geometrical genus is wrong" );
3544 WerrorS(
"unspecific error" );
3580 ( fast==2 ? 2 : 1 ) );
3590 ( fast==0 || (*node)->weight<=smax ) )
3612 cmp =
pCmp( (*node)->mon,
f );
3635 (*node)->nf =
search->nf;
3639 while( cmp<0 &&
f!=(poly)
NULL );
3652 if( (*node)->weight<=(
Rational)1 ) pg++;
3653 if( (*node)->weight==smax ) z++;
3654 if( (*node)->weight>weight_prev ) n++;
3656 weight_prev = (*node)->weight;
3657 node = &((*node)->next);
3679 cmp =
pCmp( (*node)->mon,
f );
3692 while( cmp<0 &&
f!=(poly)
NULL );
3708 n = ( z > 0 ? 2*n - 1 : 2*n );
3723 ( fast==0 ||
search->weight<=smax );
3749 for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3752 (*den) [n2] = (*den)[n1];
3753 (*mult)[n2] = (*mult)[n1];
3761 if( fast==0 || fast==1 )
3765 for(
int n1=0, n2=n-1 ; n1<n2 && symmetric==
TRUE; n1++, n2-- )
3768 (*
den) [n1]!= (*
den)[n2] ||
3775 if( symmetric==
FALSE )
3785 (*L)->m[0].data = (
void*)(
long)
mu;
3802 (*L)->m[0].data = (
void*)(
long)
mu;
3803 (*L)->m[1].data = (
void*)(
long)pg;
3804 (*L)->m[2].data = (
void*)(
long)n;
3805 (*L)->m[3].data = (
void*)nom;
3806 (*L)->m[4].data = (
void*)
den;
3807 (*L)->m[5].data = (
void*)
mult;
3816 #ifdef SPECTRUM_DEBUG
3817 #ifdef SPECTRUM_PRINT
3818 #ifdef SPECTRUM_IOSTREAM
3819 cout <<
"spectrumCompute\n";
3820 if( fast==0 ) cout <<
" no optimization" << endl;
3821 if( fast==1 ) cout <<
" weight optimization" << endl;
3822 if( fast==2 ) cout <<
" symmetry optimization" << endl;
3824 fputs(
"spectrumCompute\n",stdout );
3825 if( fast==0 ) fputs(
" no optimization\n", stdout );
3826 if( fast==1 ) fputs(
" weight optimization\n", stdout );
3827 if( fast==2 ) fputs(
" symmetry optimization\n", stdout );
3871 #ifdef SPECTRUM_DEBUG
3872 #ifdef SPECTRUM_PRINT
3873 #ifdef SPECTRUM_IOSTREAM
3874 cout <<
"\n computing the Jacobi ideal...\n";
3876 fputs(
"\n computing the Jacobi ideal...\n",stdout );
3885 #ifdef SPECTRUM_DEBUG
3886 #ifdef SPECTRUM_PRINT
3887 #ifdef SPECTRUM_IOSTREAM
3890 fputs(
" ", stdout );
3901 #ifdef SPECTRUM_DEBUG
3902 #ifdef SPECTRUM_PRINT
3903 #ifdef SPECTRUM_IOSTREAM
3905 cout <<
" computing a standard basis..." << endl;
3907 fputs(
"\n", stdout );
3908 fputs(
" computing a standard basis...\n", stdout );
3916 #ifdef SPECTRUM_DEBUG
3917 #ifdef SPECTRUM_PRINT
3920 #ifdef SPECTRUM_IOSTREAM
3923 fputs(
" ",stdout );
3968 #ifdef SPECTRUM_DEBUG
3969 #ifdef SPECTRUM_PRINT
3970 #ifdef SPECTRUM_IOSTREAM
3971 cout <<
"\n computing the highest corner...\n";
3973 fputs(
"\n computing the highest corner...\n", stdout );
3978 poly hc = (poly)
NULL;
3982 if( hc!=(poly)
NULL )
3997 #ifdef SPECTRUM_DEBUG
3998 #ifdef SPECTRUM_PRINT
3999 #ifdef SPECTRUM_IOSTREAM
4002 fputs(
" ", stdout );
4012 #ifdef SPECTRUM_DEBUG
4013 #ifdef SPECTRUM_PRINT
4014 #ifdef SPECTRUM_IOSTREAM
4015 cout <<
"\n computing the newton polygon...\n";
4017 fputs(
"\n computing the newton polygon...\n", stdout );
4024 #ifdef SPECTRUM_DEBUG
4025 #ifdef SPECTRUM_PRINT
4034 #ifdef SPECTRUM_DEBUG
4035 #ifdef SPECTRUM_PRINT
4036 #ifdef SPECTRUM_IOSTREAM
4037 cout <<
"\n computing the weight corner...\n";
4039 fputs(
"\n computing the weight corner...\n", stdout );
4044 poly wc = ( fast==0 ?
pCopy( hc ) :
4049 #ifdef SPECTRUM_DEBUG
4050 #ifdef SPECTRUM_PRINT
4051 #ifdef SPECTRUM_IOSTREAM
4054 fputs(
" ", stdout );
4064 #ifdef SPECTRUM_DEBUG
4065 #ifdef SPECTRUM_PRINT
4066 #ifdef SPECTRUM_IOSTREAM
4067 cout <<
"\n computing NF...\n" << endl;
4069 fputs(
"\n computing NF...\n", stdout );
4078 #ifdef SPECTRUM_DEBUG
4079 #ifdef SPECTRUM_PRINT
4081 #ifdef SPECTRUM_IOSTREAM
4084 fputs(
"\n", stdout );
4109 WerrorS(
"polynomial is zero" );
4112 WerrorS(
"polynomial has constant term" );
4115 WerrorS(
"not a singularity" );
4118 WerrorS(
"the singularity is not isolated" );
4121 WerrorS(
"highest corner cannot be computed" );
4124 WerrorS(
"principal part is degenerate" );
4130 WerrorS(
"unknown error occurred" );
4147 WerrorS(
"only works for local orderings" );
4155 WerrorS(
"does not work in quotient rings" );
4201 WerrorS(
"only works for local orderings" );
4206 WerrorS(
"does not work in quotient rings" );
4265 else if(
l->nr > 5 )
4303 int mu = (int)(
long)(
l->m[0].Data( ));
4304 int pg = (int)(
long)(
l->m[1].Data( ));
4305 int n = (int)(
long)(
l->m[2].Data( ));
4316 if( n !=
num->length( ) )
4320 else if( n !=
den->length( ) )
4324 else if( n != mul->
length( ) )
4344 for(
i=0;
i<n;
i++ )
4346 if( (*
num)[
i] <= 0 )
4350 if( (*
den)[
i] <= 0 )
4354 if( (*mul)[
i] <= 0 )
4366 for(
i=0,
j=n-1;
i<=
j;
i++,
j-- )
4369 (*den)[
i] != (*den)[
j] ||
4370 (*mul)[
i] != (*mul)[
j] )
4380 for(
i=0,
j=1;
i<n/2;
i++,
j++ )
4382 if( (*
num)[
i]*(*den)[
j] >= (*num)[
j]*(*den)[
i] )
4392 for(
mu=0,
i=0;
i<n;
i++ )
4397 if(
mu != (
int)(long)(
l->m[0].Data( )) )
4406 for( pg=0,
i=0;
i<n;
i++ )
4408 if( (*
num)[
i]<=(*den)[
i] )
4414 if( pg != (
int)(long)(
l->m[1].Data( )) )
4443 WerrorS(
"first argument is not a spectrum:" );
4448 WerrorS(
"second argument is not a spectrum:" );
4481 int k = (int)(
long)second->
Data( );
4485 WerrorS(
"first argument is not a spectrum" );
4490 WerrorS(
"second argument should be positive" );
4516 BOOLEAN qh=(((int)(
long)
w->Data())==1);
4527 WerrorS(
"first argument is not a spectrum" );
4532 WerrorS(
"second argument is not a spectrum" );
4575 WerrorS(
"Ground field not implemented!");
4595 LP->
m= (int)(
long)(
v->Data());
4601 LP->
n= (int)(
long)(
v->Data());
4607 LP->
m1= (int)(
long)(
v->Data());
4613 LP->
m2= (int)(
long)(
v->Data());
4619 LP->
m3= (int)(
long)(
v->Data());
4622 Print(
"m (constraints) %d\n",LP->
m);
4623 Print(
"n (columns) %d\n",LP->
n);
4647 lres->
m[4].
data=(
void*)(
long)LP->
m;
4650 lres->
m[5].
data=(
void*)(
long)LP->
n;
4652 res->data= (
void*)lres;
4659 ideal gls = (ideal)(arg1->
Data());
4660 int imtype= (int)(
long)arg2->
Data();
4683 gls= (poly)(arg1->
Data());
4684 int howclean= (int)(
long)arg3->
Data();
4688 WerrorS(
"Input polynomial is constant!");
4697 rlist->
Init( r[0] );
4698 for(
int i=r[0];
i>0;
i--)
4713 WerrorS(
"Ground field not implemented!");
4720 unsigned long int ii = (
unsigned long int)arg2->
Data();
4745 if ( (vpos !=
i) && (
pGetExp( piter,
i ) != 0) )
4747 WerrorS(
"The input polynomial must be univariate!");
4755 number * pcoeffs= (number *)
omAlloc( (deg+1) *
sizeof( number ) );
4757 for (
i= deg;
i >= 0;
i-- )
4772 for (
i=deg;
i >= 0;
i--)
4780 roots->
solver( howclean );
4788 rlist->
Init( elem );
4792 for (
j= 0;
j < elem;
j++ )
4801 for (
j= 0;
j < elem;
j++ )
4805 rlist->
m[
j].
data=(
void *)dummy;
4818 res->data= (
void*)rlist;
4827 p= (ideal)arg1->
Data();
4828 w= (ideal)arg2->
Data();
4839 int tdg= (int)(
long)arg3->
Data();
4846 WerrorS(
"Last input parameter must be > 0!");
4854 if (
m != (
int)
pow((
double)tdg+1,(
double)n) )
4856 Werror(
"Size of second input ideal must be equal to %d!",
4857 (
int)
pow((
double)tdg+1,(
double)n));
4864 WerrorS(
"Ground field not implemented!");
4869 number *pevpoint= (number *)
omAlloc( n *
sizeof( number ) );
4870 for (
i= 0;
i < n;
i++ )
4879 WerrorS(
"Elements of first input ideal must not be equal to -1, 0, 1!");
4888 WerrorS(
"Elements of first input ideal must be numbers!");
4891 pevpoint[
i]=
nCopy( tmp );
4895 number *wresults= (number *)
omAlloc(
m *
sizeof( number ) );
4896 for (
i= 0;
i <
m;
i++ )
4905 WerrorS(
"Elements of second input ideal must be numbers!");
4920 res->data= (
void*)rpoly;
4935 else gls= (ideal)(
v->Data());
4941 else imtype= (int)(
long)
v->Data();
4946 ideal test_id=
idInit(1,1);
4950 if (gls->m[
j]!=
NULL)
4952 test_id->m[0]=gls->m[
j];
4956 WerrorS(
"Newton polytope not of expected dimension");
4970 unsigned long int ii=(
unsigned long int)
v->Data();
4978 else howclean= (int)(
long)
v->Data();
5007 WerrorS(
"Error occurred during matrix setup!");
5020 WerrorS(
"Unsuitable input ideal: Minor of resultant matrix is singular!");
5026 if ( interpolate_det )
5032 if ( interpolate_det )
5039 for (
i=0;
i < c;
i++)
pWrite(iproots[
i]->getPoly());
5041 for (
i=0;
i < c;
i++)
pWrite(muiproots[
i]->getPoly());
5045 arranger=
new rootArranger( iproots, muiproots, howclean );
5056 WerrorS(
"Solver was unable to find any roots!");
5062 for (
i=0;
i <
count;
i++)
delete iproots[
i];
5065 for (
i=0;
i <
count;
i++)
delete muiproots[
i];
5072 res->data= (
void *)listofroots;
5096 onepoint->
Init(elem);
5097 for (
j= 0;
j < elem;
j++ )
5113 listofroots->
m[
i].
data=(
void *)onepoint;
5121 listofroots->
Init( 0 );
5135 if (rg==
NULL)
return;
5159 Warn(
"deleting denom_list for ring change to %s",
IDID(
h));
5173 if ((rg!=
NULL) && (rg->idroot==
NULL))
5201 if((*iv)[
i]>=0) { neg=
FALSE;
break; }
5206 (*iv)[
i]= - (*iv)[
i];
5215 if((*iv)[
i]>=0) { neg=
FALSE;
break; }
5220 (*iv)[
i]= -(*iv)[
i];
5229 if((*iv)[
i]!=1) { all_one=
FALSE;
break; }
5235 (*iv2)[2]=iv->
length()-2;
5247 if((*iv)[
i]!=1) { all_one=
FALSE;
break; }
5253 (*iv2)[2]=iv->
length()-2;
5294 (*iv)[2] += (*iv2)[2];
5301 if (!change)
h=
h->next;
5309 int last = 0, o=0, n = 1,
i=0, typ = 1,
j;
5321 R->wanted_maxExp=(*iv)[2]*2+1;
5334 WerrorS(
"invalid combination of orderings");
5342 WerrorS(
"more than one ordering c/C specified");
5348 R->block0=(
int *)
omAlloc0(n*
sizeof(
int));
5349 R->block1=(
int *)
omAlloc0(n*
sizeof(
int));
5352 int *weights=(
int*)
omAlloc0((
R->N+1)*
sizeof(int));
5355 for (
j=0;
j < n-1;
j++)
5386 R->block0[n] =
last+1;
5389 R->wvhdl[n][
i-2] = (*iv)[
i];
5391 if (weights[
last]==0) weights[
last]=(*iv)[
i]*typ;
5404 R->block0[n] =
last+1;
5406 else last += (*iv)[0];
5411 if (weights[
i]==0) weights[
i]=typ;
5423 const int s = (*iv)[2];
5433 const int s = (*iv)[2];
5435 if( 1 <
s ||
s < -1 )
return TRUE;
5451 R->block0[n] =
last+1;
5456 R->wvhdl[n][
i-2]=(*iv)[
i];
5458 if (weights[
last]==0) weights[
last]=(*iv)[
i]*typ;
5460 last=
R->block0[n]-1;
5465 R->block0[n] =
last+1;
5468 if (
R->block1[n]-
R->block0[n]+2>=iv->
length())
5469 WarnS(
"missing module weights");
5470 for (
i=2;
i<=(
R->block1[n]-
R->block0[n]+2);
i++)
5472 R->wvhdl[n][
i-2]=(*iv)[
i];
5474 if (weights[
last]==0) weights[
last]=(*iv)[
i]*typ;
5476 R->wvhdl[n][
i-2]=iv->
length() -3 -(
R->block1[n]-
R->block0[n]);
5479 R->wvhdl[n][
i-1]=(*iv)[
i];
5481 last=
R->block0[n]-1;
5486 R->block0[n] =
last+1;
5494 if (weights[
last]==0) weights[
last]=(*iv)[
i]*typ;
5496 last=
R->block0[n]-1;
5502 if (Mtyp==0)
return TRUE;
5503 if (Mtyp==-1) typ = -1;
5507 R->wvhdl[n][
i-2]=(*iv)[
i];
5509 R->block0[n] =
last+1;
5512 for(
i=
R->block1[n];
i>=
R->block0[n];
i--)
5514 if (weights[
i]==0) weights[
i]=typ;
5524 Werror(
"Internal Error: Unknown ordering %d", (*iv)[1]);
5531 Werror(
"mismatch of number of vars (%d) and ordering (>=%d vars)",
5539 for(
i=1;
i<=
R->N;
i++)
5540 {
if (weights[
i]<0) {
R->OrdSgn=-1;
break; }}
5554 if (
R->block1[n] !=
R->N)
5565 R->block0[n] <=
R->N)
5567 R->block1[n] =
R->N;
5571 Werror(
"mismatch of number of vars (%d) and ordering (%d vars)",
5590 *
p = (
char*)sl->
name;
5658 WerrorS(
"parameter expected");
5665 for(
int i=pars-1;
i>=0;
i--)
5677 int ch = (int)(
long)pn->
Data();
5688 if ((ch<2)||(ch!=ch2))
5690 Warn(
"%d is invalid as characteristic of the ground field. 32003 is used.", ch);
5693 #ifndef TEST_ZN_AS_ZP
5697 mpz_init_set_ui(modBase, (
long)ch);
5704 cf->has_simple_Inverse=1;
5717 if ((ch!=0) && (ch!=
IsPrime(ch)) && (pars == 1))
5729 if ((ch!=0) && (ch!=
IsPrime(ch)))
5731 WerrorS(
"too many parameters");
5739 WerrorS(
"parameter expected");
5745 extParam.
r =
rDefault( ch, pars, names);
5746 for(
int i=pars-1;
i>=0;
i--)
5759 && ((strcmp(pn->
name,
"real")==0) || (strcmp(pn->
name,
"complex")==0)))
5762 BOOLEAN complex_flag=(strcmp(pn->
name,
"complex")==0);
5765 float_len=(int)(
long)pnn->
Data();
5766 float_len2=float_len;
5770 float_len2=(int)(
long)pnn->
Data();
5805 else if ((pn->
name !=
NULL) && (strcmp(pn->
name,
"integer") == 0))
5809 unsigned int modExponent = 1;
5810 mpz_init_set_si(modBase, 0);
5817 mpz_set_ui(modBase, (
long) pnn->
Data());
5821 modExponent = (long) pnn->
Data();
5826 mpz_mul_ui(modBase, modBase, (
int)(
long) pnn->
Data());
5839 if ((mpz_cmp_ui(modBase, 1) == 0) && (
mpz_sgn1(modBase) < 0))
5841 WerrorS(
"Wrong ground ring specification (module is 1)");
5844 if (modExponent < 1)
5846 WerrorS(
"Wrong ground ring specification (exponent smaller than 1");
5851 if (modExponent > 1 &&
cf ==
NULL)
5853 if ((mpz_cmp_ui(modBase, 2) == 0) && (modExponent <= 8*
sizeof(
unsigned long)))
5864 WerrorS(
"modulus must not be 0 or parameter not allowed");
5870 info.exp= modExponent;
5879 WerrorS(
"modulus must not be 0 or parameter not allowed");
5885 info.exp= modExponent;
5895 ring r=(ring)pn->
Data();
5896 if (r->qideal==
NULL)
5903 else if (
IDELEMS(r->qideal)==1)
5912 WerrorS(
"algebraic extension ring must have one minpoly");
5918 WerrorS(
"Wrong or unknown ground field specification");
5924 Print(
"pn[%p]: type: %d [%s]: %p, name: %s", (
void*)
p,
p->Typ(),
Tok2Cmdname(
p->Typ()),
p->Data(), (
p->name ==
NULL?
"NULL" :
p->name) );
5946 WerrorS(
"Invalid ground field specification");
5970 WerrorS(
"name of ring variable expected");
6023 int *perm=(
int *)
omAlloc0((org_ring->N+1)*
sizeof(int));
6040 WerrorS(
"name of ring variable expected");
6050 for(;
i<org_ring->N;
i++)
6052 if (strcmp(org_ring->names[
i],
R->names[
j])==0)
6060 Werror(
"variable %d (%s) not in basering",
j+1,
R->names[
j]);
6073 for(
j=
R->block0[
i];j<=R->block1[
i];
j++)
6077 if (min_var==-1) min_var=perm[
j];
6085 R->block0[
i]=min_var;
6086 R->block1[
i]=max_var;
6090 R->wvhdl[
i]=(
int*)
omAlloc0((max_var-min_var+1)*
sizeof(int));
6091 for(
j=org_ring->block0[
i];j<=org_ring->block1[
i];
j++)
6095 R->wvhdl[
i][perm[
j]-
R->block0[
i]]=
6096 org_ring->wvhdl[
i][
j-org_ring->block0[
i]];
6122 R->order[
j-1]=
R->order[
j];
6123 R->block0[
j-1]=
R->block0[
j];
6124 R->block1[
j-1]=
R->block1[
j];
6126 R->wvhdl[
j-1]=
R->wvhdl[
j];
6134 while (
R->order[n]==0) n--;
6137 if (
R->block1[n] !=
R->N)
6148 R->block0[n] <=
R->N)
6150 R->block1[n] =
R->N;
6154 Werror(
"mismatch of number of vars (%d) and ordering (%d vars) in block %d",
6155 R->N,
R->block1[n],n);
6161 R->OrdSgn = org_ring->OrdSgn;
6184 if ((r->ref<=0)&&(r->order!=
NULL))
6194 if (
j==0)
WarnS(
"killing the basering for level 0");
6199 while (r->idroot!=
NULL)
6202 killhdl2(r->idroot,&(r->idroot),r);
6249 Warn(
"deleting denom_list for ring change from %s",
IDID(
h));
6323 ideal I=(ideal)u->
Data();
6326 for(
i=I->nrows*I->ncols-1;
i>=0;
i--)
6338 switch (
p->language)
6347 if(
p->libname!=
NULL)
6348 Print(
",%s",
p->libname);
6363 tmp_in.
data=(
void*)(
long)(*aa)[
i];
6371 Werror(
"apply fails at index %d",
i+1);
6374 if (
i==0) { memcpy(
res,&tmp_out,
sizeof(tmp_out)); }
6379 memcpy(curr,&tmp_out,
sizeof(tmp_out));
6401 res->data=(
void *)
l;
6408 for(
int i=0;
i<=aa->
nr;
i++)
6411 tmp_in.
Copy(&(aa->
m[
i]));
6420 Werror(
"apply fails at index %d",
i+1);
6423 if (
i==0) { memcpy(
res,&tmp_out,
sizeof(tmp_out)); }
6428 memcpy(curr,&tmp_out,
sizeof(tmp_out));
6451 WerrorS(
"first argument to `apply` must allow an index");
6461 char assume_yylinebuf[80];
6463 int lev=(long)a->
Data();
6470 if (bo) {
WerrorS(
"syntax error in ASSUME");
return TRUE;}
6472 if (
b->Data()==
NULL) {
Werror(
"ASSUME failed:%s",assume_yylinebuf);
return TRUE;}
6484 size_t len=strlen(a)+strlen(
s)+30;
6487 int end_s=strlen(
s);
6488 while ((end_s>0) && ((
s[end_s]<=
' ')||(
s[end_s]==
';'))) end_s--;
6491 snprintf(
name,len,
"%s->%s",a,
s);
6493 int start_s=end_s-1;
6494 while ((start_s>=0) && (
s[start_s]!=
';')) start_s--;
6497 snprintf(ss,len,
"parameter def %s;return(%s);\n",a,
s);
6502 snprintf(ss,len,
"parameter def %s;%s;return(%s);\n",a,
s,
s+start_s+1);
6562 snprintf(
buf,250,
"wrong length of parameters(%d), expected ",t);
6564 snprintf(
buf,250,
"par. %d is of type `%s`, expected ",nr,
Tok2Cmdname(t));
6565 for(
int i=1;
i<=
T[0];
i++)
6570 if (
i<
T[0]) strcat(
buf,
",");
6580 if (type_list[0]==0)
return TRUE;
6583 if (
l!=(
int)type_list[0])
6588 for(
int i=1;
i<=
l;
i++,args=args->
next)
6590 short t=type_list[
i];
6594 || (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
static void rDecomposeRing_41(leftv h, const coeffs C)
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)
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)
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)
static int pLength(poly a)
#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 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 ...
Compatibility 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)