12 #include <factory/factory.h> 112 case LE:
return "<=";
113 case GE:
return ">=";
122 if (s[1]==
'\0')
return s[0];
123 else if (s[2]!=
'\0')
return 0;
126 case '.':
if (s[1]==
'.')
return DOTDOT;
132 case '+':
if (s[1]==
'+')
return PLUSPLUS;
136 case '<':
if (s[1]==
'=')
return LE;
137 else if (s[1]==
'>')
return NOTEQUAL;
139 case '>':
if (s[1]==
'=')
return GE;
141 case '!':
if (s[1]==
'=')
return NOTEQUAL;
153 if(fullname) sprintf(buf2,
"%s::%s",
"",
IDID(h));
154 else sprintf(buf2,
"%s",
IDID(h));
192 && (strlen(
IDPROC(h)->libname)>0))
205 if ((s=strchr(buffer,
'\n'))!=
NULL)
211 if((s!=
NULL) ||(l>20))
213 Print(
"..., %d char(s)",l);
229 { number2 n=(number2)
IDDATA(h);
235 Print(
" %d x %d (%s)",
368 && (((ring)d)->idroot!=
NULL))
419 package savePack=currPack;
426 if (strcmp(what,
"all")==0)
438 if (iterate)
list1(prefix,h,
TRUE,fullname);
461 Werror(
"%s is undefined",what);
495 package save_p=currPack;
529 Warn(
"Gerhard, use the option command");
591 WerrorS(
"write: need at least two arguments");
599 if ((l!=
NULL)&&(l->name!=
NULL)) s=l->name;
601 Werror(
"cannot write to %s",s);
628 Werror(
"can not map from ground field of %s to current ground field",
632 if (
IDELEMS(theMap)<src_ring->N)
636 (src_ring->N)*
sizeof(
poly));
637 for(i=
IDELEMS(theMap);i<src_ring->N;i++)
643 WerrorS(
"argument of a map must have a name");
650 memset(&tmpW,0,
sizeof(
sleftv));
655 save_r=
IDMAP(w)->preimage;
656 IDMAP(w)->preimage=0;
665 ideal
id=(ideal)tmpW.
data;
667 for(
int i=
IDELEMS(
id)-1;i>=0;i--)
673 for(
int j=
IDELEMS(theMap)-1;
j>=0 && !overflow;
j--)
675 if (theMap->m[
j]!=
NULL)
679 for(
int i=
IDELEMS(
id)-1;i>=0;i--)
682 if ((p!=
NULL) && (degs[i]!=0) &&
683 ((
unsigned long)deg_monexp > (
currRing->bitmask / ((
unsigned long)degs[i])/2)))
695 for(
int j=
IDELEMS(theMap)-1;
j>=0 && !overflow;
j--)
697 if (theMap->m[
j]!=
NULL)
703 ((
unsigned long)deg_monexp > (
currRing->bitmask / ((
unsigned long)deg)/2)))
712 Warn(
"possible OVERFLOW in map, max exponent is %ld",
currRing->bitmask/2);
728 char *tmp = theMap->preimage;
729 theMap->preimage=(
char*)1L;
732 theMap->preimage=tmp;
740 if (save_r!=
NULL)
IDMAP(w)->preimage=save_r;
747 IDMAP(w)->preimage=save_r;
755 Werror(
"%s undefined in %s",what,theMap->preimage);
760 Werror(
"cannot find preimage %s",theMap->preimage);
772 char *
s=(
char *)
omAlloc(strlen(name)+5);
776 sprintf(s,
"%s(%d)",name,i+1);
786 Print(
"//defining: %s as %d-th syzygy module\n",s,i+1);
791 Warn(
"cannot define %s",s);
871 int add_row_shift = 0;
874 if (weights!=
NULL) add_row_shift=weights->
min_in();
889 memset(&tmp,0,
sizeof(tmp));
909 memset(&tmp2,0,
sizeof(tmp2));
934 add_row_shift = ww->
min_in();
935 (*weights) -= add_row_shift;
942 res->
data=(
void*)res_im;
945 for(
int i=1;
i<=res_im->
rows();
i++)
947 if (
IMATELEM(*res_im,1,
i)==0) { add_row_shift--; }
952 if (weights!=
NULL)
delete weights;
970 add_row_shift = ww->
min_in();
971 (*weights) -= add_row_shift;
976 if (weights!=
NULL)
delete weights;
979 return reg+1+add_row_shift;
983 #define BREAK_LINE_LENGTH 80 1010 else if(strncmp(s,
"cont;",5)==0)
1017 strcat( s,
"\n;~\n");
1088 res->
m[
i].
data = (
void *)save->set;
1098 for (i=hMu;i<hMu+
hMu2;i++)
1100 res->
m[
i].
data = (
void *)save->set;
1125 const char *
id = name->
name;
1127 memset(sy,0,
sizeof(
sleftv));
1130 WerrorS(
"object to declare is not a name");
1169 if (iiCurrProc!=
NULL)
1174 memset(&tmp,0,
sizeof(
sleftv));
1184 WerrorS(
"branchTo can only occur in a proc");
1192 if (ll!=(l-1))
return FALSE;
1195 short *t=(
short*)
omAlloc(l*
sizeof(
short));
1199 for(i=1;i<
l;i++,h=h->
next)
1204 Werror(
"arg %d is not a string",i);
1208 b=
IsCmd((
char *)h->Data(),tt);
1213 Werror(
"arg %d is not a type name",i);
1220 Werror(
"last arg (%d) is not a proc(%d), nest=%d",i,h->Typ(),
myynest);
1225 if (b && (h->rtyp==
IDHDL) && (h->e==
NULL))
1231 if(
pi->data.s.body==
NULL )
1248 pi,
pi->data.s.body_lineno-(iiCurrArgs==
NULL) );
1257 if (iiCurrArgs!=
NULL)
1259 if (err==0)
Warn(
"too many arguments for %s",
IDID(iiCurrProc));
1281 if (iiCurrArgs==
NULL)
1283 if (strcmp(p->
name,
"#")==0)
1292 if (strcmp(p->
name,
"#")==0)
1294 is_default_list=
TRUE;
1302 if (is_default_list)
1360 if (keepring)
IDRING(h)->ref--;
1372 Warn(
"'%s': no such identifier\n", v->
name);
1375 package frompack=v->req_packhdl;
1390 if (h==frompack->idroot)
1392 frompack->idroot=h->
next;
1396 idhdl hh=frompack->idroot;
1397 while ((hh!=
NULL) && (hh->
next!=h))
1407 h->
next=rootpack->idroot;
1543 WarnS(
"package not found\n");
1577 r->block0 = (
int *)
omAlloc0(3 *
sizeof(
int *));
1578 r->block1 = (
int *)
omAlloc0(3 *
sizeof(
int *));
1597 if (h!=
NULL)
return h;
1599 if (h!=
NULL)
return h;
1606 if (h!=
NULL)
return h;
1614 if (h!=
NULL)
return h;
1633 L->
m[0].
data=(
void *)(
long)r->cf->ch;
1639 for(i=0; i<r->N; i++)
1645 L->
m[1].
data=(
void *)LL;
1662 if (r->block1[i]-r->block0[i] >=0 )
1664 j=r->block1[
i]-r->block0[
i];
1667 if ((r->wvhdl!=
NULL) && (r->wvhdl[i]!=
NULL))
1669 for(;j>=0; j--) (*iv)[
j]=r->wvhdl[
i][
j];
1671 else switch (r->order[i])
1678 for(;j>=0; j--) (*iv)[
j]=1;
1688 LLL->
m[1].
data=(
void *)iv;
1689 LL->
m[
i].
data=(
void *)LLL;
1692 L->
m[2].
data=(
void *)LL;
1702 pSetCoeff0(q->m[0],(number)(r->qideal->m[0]));
1703 L->
m[3].
data=(
void *)q;
1722 L->
m[0].
data=(
void *)0;
1732 L->
m[1].
data=(
void *)LL;
1756 L->
m[0].
data=(
void *)0;
1766 L->
m[1].
data=(
void *)LL;
1800 LL->
m[1].
data=(
void *) C->modExponent;
1802 L->
m[1].
data=(
void *)LL;
1827 LL->
m[0].
data=
nlMapGMP((number) R->cf->modBase, R->cf, R->cf);
1829 LL->
m[1].
data=(
void *) R->cf->modExponent;
1831 L->
m[1].
data=(
void *)LL;
1845 WerrorS(
"ring with polynomial data must be the base ring or compatible");
1858 else if ( C->extRing!=
NULL )
1868 Lc->
m[0].
data=(
void*)(
long)C->m_nfCharQ;
1875 Lc->
m[1].
data=(
void*)Lv;
1886 Loo->
m[1].
data=(
void *)iv;
1889 Lo->
m[0].
data=(
void*)Loo;
1892 Lc->
m[2].
data=(
void*)Lo;
1898 res->
data=(
void*)Lc;
1903 res->
data=(
void *)(
long)C->ch;
1924 WerrorS(
"ring with polynomial data must be the base ring or compatible");
1942 L->
m[0].
data=(
char*)r->cf; r->cf->ref++;
1948 for(i=0; i<r->N; i++)
1951 LL->m[
i].data=(
void *)
omStrDup(r->names[i]);
1954 L->
m[1].
data=(
void *)LL;
1974 assume( r->block0[i] == r->block1[i] );
1975 const int s = r->block0[
i];
1976 assume( -2 < s && s < 2);
1981 else if (r->block1[i]-r->block0[i] >=0 )
1983 int bl=j=r->block1[
i]-r->block0[
i];
1991 j+=r->wvhdl[
i][bl+1];
1994 if ((r->wvhdl!=
NULL) && (r->wvhdl[i]!=
NULL))
1996 for(;j>=0; j--) (*iv)[
j]=r->wvhdl[
i][j+(j>bl)];
1998 else switch (r->order[i])
2005 for(;j>=0; j--) (*iv)[
j]=1;
2015 LLL->
m[1].
data=(
void *)iv;
2016 LL->m[
i].data=(
void *)LLL;
2019 L->
m[2].
data=(
void *)LL;
2023 if (r->qideal==
NULL)
2028 #ifdef HAVE_PLURAL // NC! in rDecompose 2049 || (r->qideal !=
NULL)
2056 WerrorS(
"ring with polynomial data must be the base ring or compatible");
2081 else if ( r->cf->extRing!=
NULL )
2091 Lc->
m[0].
data=(
void*)(
long)r->cf->m_nfCharQ;
2098 Lc->
m[1].
data=(
void*)Lv;
2109 Loo->
m[1].
data=(
void *)iv;
2112 Lo->
m[0].
data=(
void*)Loo;
2115 Lc->
m[2].
data=(
void*)Lo;
2121 L->
m[0].
data=(
void*)Lc;
2126 L->
m[0].
data=(
void *)(
long)r->cf->ch;
2133 for(i=0; i<r->N; i++)
2139 L->
m[1].
data=(
void *)LL;
2160 assume( r->block0[i] == r->block1[i] );
2161 const int s = r->block0[
i];
2167 else if (r->block1[i]-r->block0[i] >=0 )
2169 int bl=j=r->block1[
i]-r->block0[
i];
2177 j+=r->wvhdl[
i][bl+1];
2180 if ((r->wvhdl!=
NULL) && (r->wvhdl[i]!=
NULL))
2182 for(;j>=0; j--) (*iv)[
j]=r->wvhdl[
i][j+(j>bl)];
2184 else switch (r->order[i])
2191 for(;j>=0; j--) (*iv)[
j]=1;
2201 LLL->
m[1].
data=(
void *)iv;
2202 LL->
m[
i].
data=(
void *)LLL;
2205 L->
m[2].
data=(
void *)LL;
2209 if (r->qideal==
NULL)
2214 #ifdef HAVE_PLURAL // NC! in rDecompose 2233 WerrorS(
"invalid coeff. field description, expecting 0");
2241 WerrorS(
"invalid coeff. field description, expecting precision list");
2251 WerrorS(
"invalid coeff. field description list");
2254 int r1=(int)(
long)LL->
m[0].
data;
2255 int r2=(int)(
long)LL->
m[1].
data;
2277 R->cf->float_len=
si_min(r1,32767);
2278 R->cf->float_len2=
si_min(r2,32767);
2287 WerrorS(
"invalid coeff. field description, expecting parameter name");
2304 unsigned int modExponent = 1;
2308 mpz_init_set_ui(modBase,0);
2319 number tmp= (number) LL->
m[0].
data;
2326 mpz_init_set_ui(modBase,(
unsigned long) LL->
m[0].
data);
2330 mpz_init_set_ui(modBase,0);
2334 modExponent = (
unsigned long) LL->
m[1].
data;
2342 if ((mpz_cmp_ui(modBase, 1) == 0) && (mpz_cmp_ui(modBase, 0) < 0))
2344 WerrorS(
"Wrong ground ring specification (module is 1)");
2347 if (modExponent < 1)
2349 WerrorS(
"Wrong ground ring specification (exponent smaller than 1)");
2353 if (mpz_cmp_ui(modBase, 0) == 0)
2358 else if (modExponent > 1)
2361 if ((mpz_cmp_ui(modBase, 2) == 0) && (modExponent <= 8*
sizeof(
unsigned long)))
2372 info.
exp= modExponent;
2383 info.
exp= modExponent;
2397 for(i=0;i<R->N-1;i++)
2399 for(j=i+1;j<R->N;j++)
2401 if (strcmp(R->names[i],R->names[j])==0)
2404 Warn(
"name conflict var(%d) and var(%d): `%s`, rename to `@%s`",i+1,j+1,R->names[i],R->names[i]);
2406 R->names[
j]=(
char *)
omAlloc(2+strlen(R->names[i]));
2407 sprintf(R->names[j],
"@%s",R->names[i]);
2413 for(i=0;i<
rPar(R); i++)
2419 Warn(
"name conflict par(%d) and var(%d): `%s`, renaming the VARIABLE to `@@(%d)`",i+1,j+1,R->names[j],i+1);
2425 sprintf(R->names[j],
"@@(%d)",i+1);
2457 Werror(
"var name %d must be a string or a ring variable",i+1);
2463 Werror(
"var name %d must be `string`",i+1);
2470 WerrorS(
"variable must be given as `list`");
2486 for (
int j=0;
j < n-1;
j++)
2493 &&(strcmp((
char*)vv->
m[0].
Data(),
"L")==0))
2495 number nn=(number)vv->
m[1].
Data();
2502 Werror(
"illegal argument for pseudo ordering L: %d",vv->
m[1].
Typ());
2509 if (bitmask!=0) n--;
2513 R->block0=(
int *)
omAlloc0(n*
sizeof(
int));
2514 R->block1=(
int *)
omAlloc0(n*
sizeof(
int));
2517 for (j_in_R= n-2; j_in_R>=0; j_in_R--)
2520 for(j_in_R=0,j_in_L=0;j_in_R<n-1;j_in_R++,j_in_L++)
2525 WerrorS(
"ordering must be list of lists");
2532 if (strcmp((
char*)vv->
m[0].
Data(),
"L")==0)
2540 WerrorS(
"ordering name must be a (string,intvec)(1)");
2545 if (j_in_R==0) R->block0[0]=1;
2562 if (jj<0) R->block0[j_in_R]=1;
2563 else R->block0[j_in_R]=R->block1[jj]+1;
2573 R->block1[j_in_R]=
si_max(R->block0[j_in_R],R->block0[j_in_R]+iv_len-1);
2574 if (R->block1[j_in_R]>R->N)
2576 R->block1[j_in_R]=R->N;
2577 iv_len=R->block1[j_in_R]-R->block0[j_in_R]+1;
2582 switch (R->order[j_in_R])
2591 R->wvhdl[j_in_R] =(
int *)
omAlloc(iv_len*
sizeof(
int));
2592 for (i=0; i<iv_len;i++)
2594 R->wvhdl[j_in_R][
i]=(*iv)[
i];
2598 R->wvhdl[j_in_R] =(
int *)
omAlloc((iv->
length()+1)*
sizeof(
int));
2599 for (i=0; i<iv_len;i++)
2601 R->wvhdl[j_in_R][
i]=(*iv)[
i];
2603 R->wvhdl[j_in_R][
i]=iv->
length() - iv_len;
2605 for (; i<iv->
length(); i++)
2607 R->wvhdl[j_in_R][i+1]=(*iv)[
i];
2611 R->wvhdl[j_in_R] =(
int *)
omAlloc((iv->
length())*
sizeof(
int));
2612 for (i=0; i<iv->
length();i++) R->wvhdl[j_in_R][i]=(*iv)[
i];
2613 R->block1[j_in_R]=
si_max(R->block0[j_in_R],R->block0[j_in_R]+(
int)
sqrt((
double)(iv->
length()-1)));
2614 if (R->block1[j_in_R]>R->N)
2616 WerrorS(
"ordering matrix too big");
2634 R->block1[j_in_R]=R->block0[j_in_R]=0;
2638 R->block1[j_in_R]=R->block0[j_in_R]=(*iv)[0];
2644 R->block1[j_in_R] = R->block0[j_in_R] = 0;
2647 const int s = (*iv)[0];
2648 assume( -2 < s && s < 2 );
2649 R->block1[j_in_R] = R->block0[j_in_R] =
s;
2662 WerrorS(
"ordering name must be a (string,intvec)");
2671 if (R->block1[j_in_R] != R->N)
2682 R->block0[j_in_R] <= R->N)
2684 R->block1[j_in_R] = R->N;
2688 Werror(
"ordering incomplete: size (%d) should be %d",R->block1[j_in_R],R->N);
2692 if (R->block0[j_in_R]>R->N)
2694 Werror(
"not enough variables (%d) for ordering block %d, scanned so far:",R->N,j_in_R+1);
2695 for(
int ii=0;ii<=j_in_R;ii++)
2696 Werror(
"ord[%d]: %s from v%d to v%d",ii+1,
rSimpleOrdStr(R->order[ii]),R->block0[ii],R->block1[ii]);
2711 R->block0=(
int*)
omRealloc0Size(R->block0,n*
sizeof(
int),(n+1)*
sizeof(
int));
2712 R->block1=(
int*)
omRealloc0Size(R->block1,n*
sizeof(
int),(n+1)*
sizeof(
int));
2724 WerrorS(
"ordering must be given as `list`");
2727 if (bitmask!=0) R->bitmask=bitmask*2;
2759 int ch = (int)(
long)L->
m[0].
Data();
2769 Warn(
"%d is invalid characteristic of ground field. %d is used.", ch, l);
2792 int ch = (int)(
long)LL->
m[0].
Data();
2793 while ((ch!=
fftable[is_gf_char]) && (
fftable[is_gf_char])) is_gf_char++;
2794 if (
fftable[is_gf_char]==0) is_gf_char=-1;
2815 WerrorS(
"could not create the specified coefficient field");
2819 if( extRing->qideal !=
NULL )
2823 extParam.
r = extRing;
2830 extParam.
r = extRing;
2840 WerrorS(
"coefficient field must be described by `int` or `list`");
2846 WerrorS(
"could not create coefficient field described by the input!");
2864 ideal q=(ideal)L->
m[3].
Data();
2870 WerrorS(
"coefficient fields must be equal if q-ideal !=0");
2877 int par_perm_size=0;
2896 par_perm_size=
rPar(orig_ring);
2906 WerrorS(
"coefficient fields must be equal if q-ideal !=0");
2910 perm=(
int *)
omAlloc0((orig_ring->N+1)*
sizeof(int));
2911 if (par_perm_size!=0)
2912 par_perm=(
int *)
omAlloc0(par_perm_size*
sizeof(
int));
2916 maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
2925 else if (par_perm_size!=0)
2930 for(i=
IDELEMS(q)-1; i>=0; i--)
2933 par_perm,par_perm_size);
2935 pTest(dest_id->m[i]);
2951 WerrorS(
"q-ideal must be given as `ideal`");
2979 while (i>=0) {
omfree(R->names[i]); i--; }
3000 ideal
id=(ideal)a->
Data();
3003 for (i=1; i<=
IDELEMS(
id); i++)
3010 res->
data=(
char *)result;
3020 int n=(int)(
long)b->
Data();
3021 int d=(int)(
long)c->
Data();
3028 if ((d>n) || (d<1) || (n<1))
3033 int *choise = (
int*)
omAlloc(d*
sizeof(
int));
3037 temp=(ideal)id->
Data();
3050 if (choise[l-1]<=
IDELEMS(temp))
3052 p =
pCopy(temp->m[choise[l-1]-1]);
3053 if (sign == -1) p =
pNeg(p);
3065 res->
data=(
char *)result;
3080 int add_row_shift=0;
3086 add_row_shift = ww->
min_in();
3087 (*weights) -= add_row_shift;
3100 memset(&tmp,0,
sizeof(tmp));
3114 const int length = syzstr->
length;
3116 if ((fullres==
NULL) && (minres==
NULL))
3142 for (
int i=(length)-1;
i>=0;
i--)
3154 for (
int i=length-1;
i>=0;
i--)
3229 ideal F=(ideal)id->
Data();
3235 res->
data=(
char *)iv;
3239 double wNsqr = (double)2.0 / (
double)n;
3241 x = (
int * )
omAlloc(2 * (n + 1) *
sizeof(int));
3243 for (i = n; i!=0; i--)
3244 (*iv)[i-1] = x[i + n + 1];
3262 res->
data=(
void *)b;
3280 #ifdef HAVE_SPECTRUM 3288 spec.
mu = (int)(
long)(l->
m[0].
Data( ));
3289 spec.
pg = (int)(
long)(l->
m[1].
Data( ));
3290 spec.
n = (int)(
long)(l->
m[2].
Data( ));
3298 for(
int i=0;
i<spec.
n;
i++ )
3301 spec.
w[
i] = (*mul)[
i];
3332 for(
int i=0;
i<spec.
n;
i++ )
3336 (*mult)[
i] = spec.
w[
i];
3346 L->
m[0].
data = (
void*)(
long)spec.
mu;
3347 L->
m[1].
data = (
void*)(
long)spec.
pg;
3348 L->
m[2].
data = (
void*)(
long)spec.
n;
3349 L->
m[3].
data = (
void*)num;
3350 L->
m[4].
data = (
void*)den;
3351 L->
m[5].
data = (
void*)mult;
3399 WerrorS(
"the list is too short" );
3402 WerrorS(
"the list is too long" );
3406 WerrorS(
"first element of the list should be int" );
3409 WerrorS(
"second element of the list should be int" );
3412 WerrorS(
"third element of the list should be int" );
3415 WerrorS(
"fourth element of the list should be intvec" );
3418 WerrorS(
"fifth element of the list should be intvec" );
3421 WerrorS(
"sixth element of the list should be intvec" );
3425 WerrorS(
"first element of the list should be positive" );
3428 WerrorS(
"wrong number of numerators" );
3431 WerrorS(
"wrong number of denominators" );
3434 WerrorS(
"wrong number of multiplicities" );
3438 WerrorS(
"the Milnor number should be positive" );
3441 WerrorS(
"the geometrical genus should be nonnegative" );
3444 WerrorS(
"all numerators should be positive" );
3447 WerrorS(
"all denominators should be positive" );
3450 WerrorS(
"all multiplicities should be positive" );
3454 WerrorS(
"it is not symmetric" );
3457 WerrorS(
"it is not monotonous" );
3461 WerrorS(
"the Milnor number is wrong" );
3464 WerrorS(
"the geometrical genus is wrong" );
3468 WerrorS(
"unspecific error" );
3504 ( fast==2 ? 2 : 1 ) );
3514 ( fast==0 || (*node)->weight<=smax ) )
3536 cmp =
pCmp( (*node)->mon,f );
3559 (*node)->nf = search->
nf;
3563 while( cmp<0 && f!=(
poly)NULL );
3565 search = search->
next;
3576 if( (*node)->weight<=(
Rational)1 ) pg++;
3577 if( (*node)->weight==smax ) z++;
3578 if( (*node)->weight>weight_prev ) n++;
3580 weight_prev = (*node)->weight;
3581 node = &((*node)->next);
3603 cmp =
pCmp( (*node)->mon,f );
3618 search = search->
next;
3632 n = ( z > 0 ? 2*n - 1 : 2*n );
3647 ( fast==0 || search->
weight<=smax );
3648 search=search->
next )
3673 for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3676 (*den) [n2] = (*den)[n1];
3677 (*mult)[n2] = (*mult)[n1];
3685 if( fast==0 || fast==1 )
3689 for(
int n1=0, n2=n-1 ; n1<n2 && symmetric==
TRUE; n1++, n2-- )
3691 if( (*mult)[n1]!=(*mult)[n2] ||
3692 (*den) [n1]!= (*den)[n2] ||
3699 if( symmetric==
FALSE )
3709 (*L)->m[0].data = (
void*)(
long)
mu;
3726 (*L)->m[0].data = (
void*)(
long)
mu;
3727 (*L)->m[1].data = (
void*)(
long)pg;
3728 (*L)->m[2].data = (
void*)(
long)n;
3729 (*L)->m[3].data = (
void*)nom;
3730 (*L)->m[4].data = (
void*)den;
3731 (*L)->m[5].data = (
void*)mult;
3740 #ifdef SPECTRUM_DEBUG 3741 #ifdef SPECTRUM_PRINT 3742 #ifdef SPECTRUM_IOSTREAM 3743 cout <<
"spectrumCompute\n";
3744 if( fast==0 ) cout <<
" no optimization" << endl;
3745 if( fast==1 ) cout <<
" weight optimization" << endl;
3746 if( fast==2 ) cout <<
" symmetry optimization" << endl;
3748 fputs(
"spectrumCompute\n",stdout );
3749 if( fast==0 ) fputs(
" no optimization\n", stdout );
3750 if( fast==1 ) fputs(
" weight optimization\n", stdout );
3751 if( fast==2 ) fputs(
" symmetry optimization\n", stdout );
3795 #ifdef SPECTRUM_DEBUG 3796 #ifdef SPECTRUM_PRINT 3797 #ifdef SPECTRUM_IOSTREAM 3798 cout <<
"\n computing the Jacobi ideal...\n";
3800 fputs(
"\n computing the Jacobi ideal...\n",stdout );
3809 #ifdef SPECTRUM_DEBUG 3810 #ifdef SPECTRUM_PRINT 3811 #ifdef SPECTRUM_IOSTREAM 3814 fputs(
" ", stdout );
3825 #ifdef SPECTRUM_DEBUG 3826 #ifdef SPECTRUM_PRINT 3827 #ifdef SPECTRUM_IOSTREAM 3829 cout <<
" computing a standard basis..." << endl;
3831 fputs(
"\n", stdout );
3832 fputs(
" computing a standard basis...\n", stdout );
3840 #ifdef SPECTRUM_DEBUG 3841 #ifdef SPECTRUM_PRINT 3842 for( i=0; i<
IDELEMS(stdJ); i++ )
3844 #ifdef SPECTRUM_IOSTREAM 3847 fputs(
" ",stdout );
3892 #ifdef SPECTRUM_DEBUG 3893 #ifdef SPECTRUM_PRINT 3894 #ifdef SPECTRUM_IOSTREAM 3895 cout <<
"\n computing the highest corner...\n";
3897 fputs(
"\n computing the highest corner...\n", stdout );
3906 if( hc!=(
poly)NULL )
3921 #ifdef SPECTRUM_DEBUG 3922 #ifdef SPECTRUM_PRINT 3923 #ifdef SPECTRUM_IOSTREAM 3926 fputs(
" ", stdout );
3936 #ifdef SPECTRUM_DEBUG 3937 #ifdef SPECTRUM_PRINT 3938 #ifdef SPECTRUM_IOSTREAM 3939 cout <<
"\n computing the newton polygon...\n";
3941 fputs(
"\n computing the newton polygon...\n", stdout );
3948 #ifdef SPECTRUM_DEBUG 3949 #ifdef SPECTRUM_PRINT 3958 #ifdef SPECTRUM_DEBUG 3959 #ifdef SPECTRUM_PRINT 3960 #ifdef SPECTRUM_IOSTREAM 3961 cout <<
"\n computing the weight corner...\n";
3963 fputs(
"\n computing the weight corner...\n", stdout );
3973 #ifdef SPECTRUM_DEBUG 3974 #ifdef SPECTRUM_PRINT 3975 #ifdef SPECTRUM_IOSTREAM 3978 fputs(
" ", stdout );
3988 #ifdef SPECTRUM_DEBUG 3989 #ifdef SPECTRUM_PRINT 3990 #ifdef SPECTRUM_IOSTREAM 3991 cout <<
"\n computing NF...\n" << endl;
3993 fputs(
"\n computing NF...\n", stdout );
4002 #ifdef SPECTRUM_DEBUG 4003 #ifdef SPECTRUM_PRINT 4005 #ifdef SPECTRUM_IOSTREAM 4008 fputs(
"\n", stdout );
4033 WerrorS(
"polynomial is zero" );
4036 WerrorS(
"polynomial has constant term" );
4039 WerrorS(
"not a singularity" );
4042 WerrorS(
"the singularity is not isolated" );
4045 WerrorS(
"highest corner cannot be computed" );
4048 WerrorS(
"principal part is degenerate" );
4054 WerrorS(
"unknown error occurred" );
4071 WerrorS(
"only works for local orderings" );
4079 WerrorS(
"does not work in quotient rings" );
4092 result->
data = (
char*)L;
4125 WerrorS(
"only works for local orderings" );
4130 WerrorS(
"does not work in quotient rings" );
4143 result->
data = (
char*)L;
4189 else if( l->
nr > 5 )
4227 int mu = (int)(
long)(l->
m[0].
Data( ));
4228 int pg = (int)(
long)(l->
m[1].
Data( ));
4229 int n = (int)(
long)(l->
m[2].
Data( ));
4240 if( n != num->
length( ) )
4244 else if( n != den->
length( ) )
4248 else if( n != mul->
length( ) )
4268 for( i=0; i<n; i++ )
4270 if( (*num)[
i] <= 0 )
4274 if( (*den)[
i] <= 0 )
4278 if( (*mul)[
i] <= 0 )
4290 for( i=0, j=n-1; i<=
j; i++,j-- )
4293 (*den)[
i] != (*den)[
j] ||
4294 (*mul)[
i] != (*mul)[
j] )
4304 for( i=0, j=1; i<n/2; i++,j++ )
4306 if( (*num)[
i]*(*den)[
j] >= (*num)[
j]*(*den)[
i] )
4316 for( mu=0, i=0; i<n; i++ )
4321 if( mu != (
int)(long)(l->
m[0].
Data( )) )
4330 for( pg=0, i=0; i<n; i++ )
4332 if( (*num)[
i]<=(*den)[
i] )
4338 if( pg != (
int)(long)(l->
m[1].
Data( )) )
4367 WerrorS(
"first argument is not a spectrum:" );
4372 WerrorS(
"second argument is not a spectrum:" );
4405 int k = (int)(
long)second->
Data( );
4409 WerrorS(
"first argument is not a spectrum" );
4414 WerrorS(
"second argument should be positive" );
4451 WerrorS(
"first argument is not a spectrum" );
4456 WerrorS(
"second argument is not a spectrum" );
4480 memset(&tmp,0,
sizeof(tmp));
4499 WerrorS(
"Ground field not implemented!");
4519 LP->
m= (int)(
long)(v->
Data());
4525 LP->
n= (int)(
long)(v->
Data());
4531 LP->
m1= (int)(
long)(v->
Data());
4537 LP->
m2= (int)(
long)(v->
Data());
4543 LP->
m3= (int)(
long)(v->
Data());
4545 #ifdef mprDEBUG_PROT 4546 Print(
"m (constraints) %d\n",LP->
m);
4547 Print(
"n (columns) %d\n",LP->
n);
4571 lres->
m[4].
data=(
void*)(
long)LP->
m;
4574 lres->
m[5].
data=(
void*)(
long)LP->
n;
4576 res->
data= (
void*)lres;
4583 ideal gls = (ideal)(arg1->
Data());
4584 int imtype= (int)(
long)arg2->
Data();
4609 int howclean= (int)(
long)arg3->
Data();
4616 WerrorS(
"Ground field not implemented!");
4623 unsigned long int ii = (
unsigned long int)arg2->
Data();
4629 WerrorS(
"Input polynomial is constant!");
4655 if ( (vpos != i) && (
pGetExp( piter, i ) != 0) )
4657 WerrorS(
"The input polynomial must be univariate!");
4665 number * pcoeffs= (number *)
omAlloc( (deg+1) *
sizeof( number ) );
4667 for ( i= deg; i >= 0; i-- )
4681 #ifdef mprDEBUG_PROT 4682 for (i=deg; i >= 0; i--)
4690 roots->
solver( howclean );
4697 rlist->
Init( elem );
4701 for ( j= 0; j < elem; j++ )
4710 for ( j= 0; j < elem; j++ )
4714 rlist->
m[
j].
data=(
void *)dummy;
4728 res->
data= (
void*)rlist;
4737 p= (ideal)arg1->
Data();
4738 w= (ideal)arg2->
Data();
4749 int tdg= (int)(
long)arg3->
Data();
4756 WerrorS(
"Last input parameter must be > 0!");
4764 if ( m != (
int)
pow((
double)tdg+1,(
double)n) )
4766 Werror(
"Size of second input ideal must be equal to %d!",
4767 (
int)
pow((
double)tdg+1,(
double)n));
4774 WerrorS(
"Ground field not implemented!");
4779 number *pevpoint= (number *)
omAlloc( n *
sizeof( number ) );
4780 for ( i= 0; i < n; i++ )
4789 WerrorS(
"Elements of first input ideal must not be equal to -1, 0, 1!");
4798 WerrorS(
"Elements of first input ideal must be numbers!");
4801 pevpoint[
i]=
nCopy( tmp );
4805 number *wresults= (number *)
omAlloc( m *
sizeof( number ) );
4806 for ( i= 0; i <
m; i++ )
4815 WerrorS(
"Elements of second input ideal must be numbers!");
4830 res->
data= (
void*)rpoly;
4845 else gls= (ideal)(v->
Data());
4851 else imtype= (int)(
long)v->
Data();
4856 ideal test_id=
idInit(1,1);
4858 for(j=
IDELEMS(gls)-1;j>=0;j--)
4860 if (gls->m[j]!=
NULL)
4862 test_id->m[0]=gls->m[
j];
4866 WerrorS(
"Newton polytope not of expected dimension");
4880 unsigned long int ii=(
unsigned long int)v->
Data();
4888 else howclean= (int)(
long)v->
Data();
4917 WerrorS(
"Error occurred during matrix setup!");
4925 #ifdef mprDEBUG_PROT 4930 WerrorS(
"Unsuitable input ideal: Minor of resultant matrix is singular!");
4936 if ( interpolate_det )
4942 if ( interpolate_det )
4947 #ifdef mprDEBUG_PROT 4949 for (i=0; i < c; i++)
pWrite(iproots[i]->getPoly());
4951 for (i=0; i < c; i++)
pWrite(muiproots[i]->getPoly());
4955 arranger=
new rootArranger( iproots, muiproots, howclean );
4966 WerrorS(
"Solver was unable to find any roots!");
4972 for (i=0; i <
count; i++)
delete iproots[i];
4975 for (i=0; i <
count; i++)
delete muiproots[i];
4982 res->
data= (
void *)listofroots;
4994 int count=
self->roots[0]->getAnzRoots();
4995 int elem=
self->roots[0]->getAnzElems();
4999 if ( self->found_roots )
5001 listofroots->
Init( count );
5003 for (i=0; i <
count; i++)
5006 onepoint->
Init(elem);
5007 for ( j= 0; j < elem; j++ )
5023 listofroots->
m[
i].
data=(
void *)onepoint;
5031 listofroots->
Init( 0 );
5045 if (rg==
NULL)
return;
5065 Warn(
"deleting denom_list for ring change to %s",
IDID(h));
5077 if ((rg!=
NULL) && (rg->idroot==
NULL))
5105 if((*iv)[
i]>=0) { neg=
FALSE;
break; }
5110 (*iv)[
i]= - (*iv)[
i];
5119 if((*iv)[
i]>=0) { neg=
FALSE;
break; }
5124 (*iv)[
i]= -(*iv)[
i];
5133 if((*iv)[
i]!=1) { all_one=
FALSE;
break; }
5139 (*iv2)[2]=iv->
length()-2;
5151 if((*iv)[
i]!=1) { all_one=
FALSE;
break; }
5157 (*iv2)[2]=iv->
length()-2;
5191 (*iv)[2] += (*iv2)[2];
5198 if (!change) h=h->
next;
5206 int last = 0, o=0, n = 1,
i=0, typ = 1,
j;
5218 R->bitmask=(*iv)[2];
5231 WerrorS(
"invalid combination of orderings");
5239 WerrorS(
"more than one ordering c/C specified");
5245 R->block0=(
int *)
omAlloc0(n*
sizeof(
int));
5246 R->block1=(
int *)
omAlloc0(n*
sizeof(
int));
5249 int *weights=(
int*)
omAlloc0((R->N+1)*
sizeof(int));
5252 for (
j=0;
j < n-1;
j++)
5283 R->block0[n] = last+1;
5286 R->wvhdl[n][
i-2] = (*iv)[
i];
5288 if (weights[last]==0) weights[
last]=(*iv)[
i]*typ;
5290 R->block1[n] =
si_min(last,R->N);
5301 R->block0[n] = last+1;
5302 if (iv->
length() == 3) last+=(*iv)[2];
5303 else last += (*iv)[0];
5304 R->block1[n] =
si_min(last,R->N);
5308 if (weights[
i]==0) weights[
i]=typ;
5320 const int s = (*iv)[2];
5330 const int s = (*iv)[2];
5332 if( 1 < s || s < -1 )
return TRUE;
5348 R->block0[n] = last+1;
5353 R->wvhdl[n][
i-2]=(*iv)[
i];
5355 if (weights[last]==0) weights[
last]=(*iv)[
i]*typ;
5357 last=R->block0[n]-1;
5362 R->block0[n] = last+1;
5365 if (R->block1[n]- R->block0[n]+2>=iv->
length())
5366 WarnS(
"missing module weights");
5367 for (
i=2;
i<=(R->block1[n]-R->block0[n]+2);
i++)
5369 R->wvhdl[n][
i-2]=(*iv)[
i];
5371 if (weights[last]==0) weights[
last]=(*iv)[
i]*typ;
5373 R->wvhdl[n][
i-2]=iv->
length() -3 -(R->block1[n]- R->block0[n]);
5376 R->wvhdl[n][
i-1]=(*iv)[
i];
5378 last=R->block0[n]-1;
5383 R->block0[n] = last+1;
5391 if (weights[last]==0) weights[
last]=(*iv)[
i]*typ;
5393 last=R->block0[n]-1;
5399 if (Mtyp==0)
return TRUE;
5400 if (Mtyp==-1) typ = -1;
5404 R->wvhdl[n][
i-2]=(*iv)[
i];
5406 R->block0[n] = last+1;
5408 R->block1[n] =
si_min(last,R->N);
5409 for(
i=R->block1[n];
i>=R->block0[n];
i--)
5411 if (weights[
i]==0) weights[
i]=typ;
5421 Werror(
"Internal Error: Unknown ordering %d", (*iv)[1]);
5428 Werror(
"mismatch of number of vars (%d) and ordering (>=%d vars)",
5436 for(
i=1;
i<=R->N;
i++)
5437 {
if (weights[
i]<0) { R->OrdSgn=-1;
break; }}
5451 if (R->block1[n] != R->N)
5462 R->block0[n] <= R->N)
5464 R->block1[n] = R->N;
5468 Werror(
"mismatch of number of vars (%d) and ordering (%d vars)",
5487 *p = (
char*)sl->
name;
5555 WerrorS(
"parameter expected");
5561 extParam.
r =
rDefault( cf, pars, names);
5562 for(
int i=pars-1;
i>=0;
i--)
5574 int ch = (int)(
long)pn->
Data();
5585 if ((ch<2)||(ch!=ch2))
5587 Warn(
"%d is invalid as characteristic of the ground field. 32003 is used.", ch);
5602 if ((ch!=0) && (ch!=
IsPrime(ch)) && (pars == 1))
5614 if ((ch!=0) && (ch!=
IsPrime(ch)))
5616 WerrorS(
"too many parameters");
5624 WerrorS(
"parameter expected");
5630 extParam.
r =
rDefault( ch, pars, names);
5631 for(
int i=pars-1;
i>=0;
i--)
5644 && ((strcmp(pn->
name,
"real")==0) || (strcmp(pn->
name,
"complex")==0)))
5647 BOOLEAN complex_flag=(strcmp(pn->
name,
"complex")==0);
5650 float_len=(int)(
long)pnn->
Data();
5651 float_len2=float_len;
5655 float_len2=(int)(
long)pnn->
Data();
5674 if (param.
float_len < SHORT_REAL_LENGTH)
5690 else if ((pn->
name !=
NULL) && (strcmp(pn->
name,
"integer") == 0))
5694 unsigned int modExponent = 1;
5695 mpz_init_set_si(modBase, 0);
5702 mpz_set_ui(modBase, (
int)(
long) pnn->
Data());
5706 modExponent = (long) pnn->
Data();
5711 mpz_mul_ui(modBase, modBase, (
int)(
long) pnn->
Data());
5724 if ((mpz_cmp_ui(modBase, 1) == 0) && (mpz_cmp_ui(modBase, 0) < 0))
5726 WerrorS(
"Wrong ground ring specification (module is 1)");
5729 if (modExponent < 1)
5731 WerrorS(
"Wrong ground ring specification (exponent smaller than 1");
5736 if (modExponent > 1 && cf ==
NULL)
5738 if ((mpz_cmp_ui(modBase, 2) == 0) && (modExponent <= 8*
sizeof(
unsigned long)))
5747 if (mpz_cmp_ui(modBase,0)==0)
5749 WerrorS(
"modulus must not be 0 or parameter not allowed");
5755 info.
exp= modExponent;
5760 else if (cf ==
NULL)
5762 if (mpz_cmp_ui(modBase,0)==0)
5764 WerrorS(
"modulus must not be 0 or parameter not allowed");
5770 info.
exp= modExponent;
5781 extParam.
r = (ring)pn->
Data();
5793 WerrorS(
"Wrong or unknown ground field specification");
5799 Print(
"pn[%p]: type: %d [%s]: %p, name: %s", (
void*)p, p->
Typ(),
Tok2Cmdname(p->Typ()), p->Data(), (p->name ==
NULL?
"NULL" : p->name) );
5821 WerrorS(
"Invalid ground field specification");
5837 Werror(
"too many ring variables(%d), max is %d",l,MAX_SHORT);
5845 WerrorS(
"name of ring variable expected");
5898 int *perm=(
int *)
omAlloc0((org_ring->N+1)*
sizeof(int));
5906 Werror(
"too many ring variables(%d), max is %d",l,MAX_SHORT);
5915 WerrorS(
"name of ring variable expected");
5925 for(;
i<org_ring->N;
i++)
5927 if (strcmp(org_ring->names[
i],R->names[
j])==0)
5935 Werror(
"variable %d (%s) not in basering",
j+1,R->names[
j]);
5948 for(
j=R->block0[
i];j<=R->block1[
i];
j++)
5952 if (min_var==-1) min_var=perm[
j];
5960 R->block0[
i]=min_var;
5961 R->block1[
i]=max_var;
5962 if (R->wvhdl[
i]!=
NULL)
5965 R->wvhdl[
i]=(
int*)
omAlloc0((max_var-min_var+1)*
sizeof(int));
5966 for(
j=org_ring->block0[
i];j<=org_ring->block1[
i];
j++)
5970 R->wvhdl[
i][perm[
j]-R->block0[
i]]=
5971 org_ring->wvhdl[
i][
j-org_ring->block0[
i]];
5997 R->order[
j-1]=R->order[
j];
5998 R->block0[
j-1]=R->block0[
j];
5999 R->block1[
j-1]=R->block1[
j];
6001 R->wvhdl[
j-1]=R->wvhdl[
j];
6009 while (R->order[n]==0) n--;
6012 if (R->block1[n] != R->N)
6023 R->block0[n] <= R->N)
6025 R->block1[n] = R->N;
6029 Werror(
"mismatch of number of vars (%d) and ordering (%d vars) in block %d",
6030 R->N,R->block1[n],n);
6036 R->OrdSgn = org_ring->OrdSgn;
6059 if ((r->ref<=0)&&(r->order!=
NULL))
6069 if (j==0)
WarnS(
"killing the basering for level 0");
6074 while (r->idroot!=
NULL)
6077 killhdl2(r->idroot,&(r->idroot),r);
6172 resid=(ideal)(res.
data);
6225 ideal I=(ideal)u->
Data();
6228 for(i=I->nrows*I->ncols-1;i>=0;i--)
6240 switch (p->language)
6248 if(p->libname!=
NULL)
6249 Print(
",%s", p->libname);
6262 memset(&tmp_in,0,
sizeof(tmp_in));
6264 tmp_in.
data=(
void*)(
long)(*aa)[
i];
6268 bo=
jjPROC(&tmp_out,proc,&tmp_in);
6272 Werror(
"apply fails at index %d",
i+1);
6275 if (
i==0) { memcpy(res,&tmp_out,
sizeof(tmp_out)); }
6280 memcpy(curr,&tmp_out,
sizeof(tmp_out));
6302 for(
int i=0;
i<=aa->
nr;
i++)
6304 memset(&tmp_in,0,
sizeof(tmp_in));
6305 tmp_in.
Copy(&(aa->
m[
i]));
6309 bo=
jjPROC(&tmp_out,proc,&tmp_in);
6314 Werror(
"apply fails at index %d",
i+1);
6317 if (
i==0) { memcpy(res,&tmp_out,
sizeof(tmp_out)); }
6322 memcpy(curr,&tmp_out,
sizeof(tmp_out));
6329 memset(res,0,
sizeof(
sleftv));
6345 WerrorS(
"first argument to `apply` must allow an index");
6355 char assume_yylinebuf[80];
6357 int lev=(long)a->
Data();
6364 if (bo) {
WerrorS(
"syntax error in ASSUME");
return TRUE;}
6378 char *ss=(
char*)
omAlloc(strlen(a)+strlen(s)+30);
6380 int end_s=strlen(s);
6381 while ((end_s>0) && ((s[end_s]<=
' ')||(s[end_s]==
';'))) end_s--;
6383 char *
name=(
char *)
omAlloc(strlen(a)+strlen(s)+30);
6384 sprintf(name,
"%s->%s",a,s);
6386 int start_s=end_s-1;
6387 while ((start_s>=0) && (s[start_s]!=
';')) start_s--;
6390 sprintf(ss,
"parameter def %s;return(%s);\n",a,s);
6395 sprintf(ss,
"parameter def %s;%s;return(%s);\n",a,s,s+start_s+1);
6397 memset(r,0,
sizeof(*r));
6417 memset(&tmp,0,
sizeof(tmp));
6435 memset(&n,0,
sizeof(n));
6453 sprintf(buf,
"wrong length of parameters(%d), expected ",t);
6455 sprintf(buf,
"par. %d is of type `%s`, expected ",nr,
Tok2Cmdname(t));
6456 for(
int i=1;
i<=T[0];
i++)
6461 if (i<T[0]) strcat(buf,
",");
6470 if (type_list[0]==0)
return TRUE;
6473 if (report)
WerrorS(
"no arguments expected");
6478 if (l!=(
int)type_list[0])
6483 for(
int i=1;
i<=
l;
i++,args=args->
next)
6485 short t=type_list[
i];
6489 || (t!=args->Typ()))
BOOLEAN rHasLocalOrMixedOrdering(const ring r)
int status int void size_t count
BOOLEAN jjCHARSERIES(leftv res, leftv u)
for idElimination, like a, except pFDeg, pWeigths ignore it
CanonicalForm map(const CanonicalForm &primElem, const Variable &alpha, const CanonicalForm &F, const Variable &beta)
map from to such that is mapped onto
complex root finder for univariate polynomials based on laguers algorithm
#define omRealloc0Size(addr, o_size, size)
static FORCE_INLINE char const ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
#define idMaxIdeal(D)
initialise the maximal ideal (at 0)
const CanonicalForm int s
int iiTestConvert(int inputType, int outputType)
idhdl ggetid(const char *n)
char *(* fe_fgets_stdin)(const char *pr, char *s, int size)
unsigned char * proc[NUM_PROC]
#define omCheckAddrSize(addr, size)
Class used for (list of) interpreter objects.
void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
static FORCE_INLINE BOOLEAN nCoeff_is_numeric(const coeffs r)
resolvente syReorder(resolvente res, int length, syStrategy syzstr, BOOLEAN toCopy=TRUE, resolvente totake=NULL)
number * interpolateDense(const number *q)
Solves the Vandermode linear system {i=1}^{n} x_i^k-1 w_i = q_k, k=1,..,n.
matrix mapToMatrix(matrix m)
ring rSubring(ring org_ring, sleftv *rv)
Base class for solving 0-dim poly systems using u-resultant.
only used if HAVE_RINGS is defined
void mu(int **points, int sizePoints)
void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
#define SHORT_REAL_LENGTH
vandermonde system solver for interpolating polynomials from their values
resolvente liFindRes(lists L, int *len, int *typ0, intvec ***weights)
#define idDelete(H)
delete an ideal
static BOOLEAN rField_is_Zp_a(const ring r)
static BOOLEAN rSleftvList2StringArray(leftv sl, char **p)
static BOOLEAN rComposeVar(const lists L, ring R)
ring rCompose(const lists L, const BOOLEAN check_comp)
only used if HAVE_RINGS is defined
BOOLEAN mpKoszul(leftv res, leftv c, leftv b, leftv id)
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
BOOLEAN iiExprArith1(leftv res, leftv a, int op)
static int si_min(const int a, const int b)
BOOLEAN jjVARIABLES_P(leftv res, leftv u)
idhdl rSimpleFindHdl(ring r, idhdl root, idhdl n)
Linear Programming / Linear Optimization using Simplex - Algorithm.
Compatiblity layer for legacy polynomial operations (over currRing)
BOOLEAN rSleftvOrdering2Ordering(sleftv *ord, ring R)
BOOLEAN iiConvert(int inputType, int outputType, int index, leftv input, leftv output, const struct sConvertTypes *dConvertTypes)
int exprlist_length(leftv v)
BOOLEAN semicProc3(leftv res, leftv u, leftv v, leftv w)
void syMinimizeResolvente(resolvente res, int length, int first)
static int rPar(const ring r)
(r->cf->P)
spectrum spectrumFromList(lists l)
BOOLEAN jjPROC(leftv res, leftv u, leftv v)
lists syConvRes(syStrategy syzstr, BOOLEAN toDel, int add_row_shift)
BOOLEAN jjRESULTANT(leftv res, leftv u, leftv v, leftv w)
static BOOLEAN rField_is_R(const ring r)
void list_error(semicState state)
static FORCE_INLINE void nSetChar(const coeffs r)
initialisations after each ring change
resMatrixBase * accessResMat()
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_Z(const coeffs r)
#define omFreeSize(addr, size)
procinfo * iiInitSingularProcinfo(procinfov pi, const char *libname, const char *procname, int, long pos, BOOLEAN pstatic)
BOOLEAN jjBETTI2(leftv res, leftv u, leftv v)
static short rVar(const ring r)
#define rVar(r) (r->N)
intvec * ivCopy(const intvec *o)
static int * multiplicity
poly singclap_resultant(poly f, poly g, poly x, const ring r)
void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge, ring tailRing)
intvec * id_QHomWeight(ideal id, const ring r)
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...
#define pCmp(p1, p2)
pCmp: args may be NULL returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2))) ...
BOOLEAN spectrumProc(leftv result, leftv first)
static BOOLEAN rField_is_Q_a(const ring r)
BOOLEAN jjVARIABLES_ID(leftv res, leftv u)
denominator_list DENOMINATOR_LIST
uResultant::resMatType determineMType(int imtype)
ideal kStd(ideal F, ideal Q, tHomog h, intvec **w, intvec *hilb, int syzComp, int newIdeal, intvec *vw, s_poly_proc_t sp)
BOOLEAN maApplyFetch(int what, map theMap, leftv res, leftv w, ring preimage_r, int *perm, int *par_perm, int P, nMapFunc nMap)
BOOLEAN iiAssignCR(leftv r, leftv arg)
static long p_Totaldegree(poly p, const ring r)
poly iiHighCorner(ideal I, int ak)
bool solver(const int polishmode=PM_NONE)
BOOLEAN spmulProc(leftv result, leftv first, leftv second)
BOOLEAN hasConstTerm(poly h, const ring r)
void WerrorS(const char *s)
static BOOLEAN rField_is_GF(const ring r)
static char const ** rParameter(const ring r)
(r->cf->parameter)
char * lString(lists l, BOOLEAN typed, int dim)
ring rAssure_HasComp(const ring r)
ideal loNewtonPolytope(const ideal id)
void killlocals_rec(idhdl *root, int v, ring r)
syStrategy syConvList(lists li)
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy ...
void hRadical(scfmon rad, int *Nrad, int Nvar)
static FORCE_INLINE BOOLEAN nCoeff_is_long_C(const coeffs r)
rootContainer ** specializeInU(BOOLEAN matchUp=false, const number subDetVal=NULL)
int hasOne(ideal J, const ring r)
static void list1(const char *s, idhdl h, BOOLEAN c, BOOLEAN fullname)
poly numvec2poly(const number *q)
void rComposeC(lists L, ring R)
static void jjINT_S_TO_ID(int n, int *e, leftv res)
BOOLEAN iiBranchTo(leftv res, leftv args)
void Print(leftv store=NULL, int spaces=0)
Called by type_cmd (e.g. "r;") or as default in jPRINT.
static FORCE_INLINE BOOLEAN nCoeff_is_Ring(const coeffs r)
Creation data needed for finite fields.
BOOLEAN iiExport(leftv v, int toLev)
idhdl rDefault(const char *s)
static BOOLEAN idIsZeroDim(ideal i)
idhdl get(const char *s, int lev)
real floating point (GMP) numbers
BOOLEAN iiApplyBIGINTMAT(leftv, leftv, int, leftv)
BOOLEAN iiParameter(leftv p)
short float_len2
additional char-flags, rInit
#define pGetVariables(p, e)
void rDecomposeRing_41(leftv h, const coeffs C)
#define nPrint(a)
only for debug, over any initalized currRing
lists getList(spectrum &spec)
int iiRegularity(lists L)
void rDecomposeCF(leftv h, const ring r, const ring R)
void hDelete(scfmon ev, int ev_length)
BOOLEAN iiTestAssume(leftv a, leftv b)
semicState list_is_spectrum(lists l)
BOOLEAN kWeight(leftv res, leftv id)
#define omReallocSize(addr, o_size, size)
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
#define pGetExp(p, i)
Exponent.
single prescision (6,6) real numbers
void killhdl2(idhdl h, idhdl *ih, ring r)
idhdl enterid(const char *s, int lev, int t, idhdl *root, BOOLEAN init, BOOLEAN search)
BOOLEAN hasLinearTerm(poly h, const ring r)
static int rBlocks(ring r)
BOOLEAN syBetti1(leftv res, leftv u)
spectrumState spectrumStateFromList(spectrumPolyList &speclist, lists *L, int fast)
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...
short float_len
additional char-flags, rInit
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)
Coefficient rings, fields and other domains suitable for Singular polynomials.
BOOLEAN killlocals_list(int v, lists L)
static BOOLEAN rComposeOrder(const lists L, const BOOLEAN check_comp, ring R)
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
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 ...
void hKill(monf xmem, int Nvar)
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...
for(int i=0;i< R->ExpL_Size;i++) Print("%09lx "
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...
BOOLEAN mapFromMatrix(matrix m)
void list_cmd(int typ, const char *what, const char *prefix, BOOLEAN iterate, BOOLEAN fullname)
void computeNF(ideal stdJ, poly hc, poly wc, spectrumPolyList *NF, const ring r)
only used if HAVE_RINGS is defined
static long pTotaldegree(poly p)
static leftv rOptimizeOrdAsSleftv(leftv ord)
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
int search(const CFArray &A, const CanonicalForm &F, int i, int j)
search for F in A between index i and j
The main handler for Singular numbers which are suitable for Singular polynomials.
static BOOLEAN iiNoKeepRing
void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
double(* wFunctional)(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
int status int void * buf
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
void hPure(scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
const ExtensionInfo & info
< [in] sqrfree poly
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
static void rDecomposeC(leftv h, const ring R)
BOOLEAN hasAxis(ideal J, int k, const ring r)
complex floating point (GMP) numbers
static FORCE_INLINE char * nCoeffName(const coeffs cf)
const char * rSimpleOrdStr(int ord)
int mult_spectrumh(spectrum &)
gmp_float sqrt(const gmp_float &a)
static resolvente iiCopyRes(resolvente r, int l)
BOOLEAN nuUResSolve(leftv res, leftv args)
solve a multipolynomial system using the u-resultant Input ideal must be 0-dimensional and (currRing-...
static void iiReportTypes(int nr, int t, const short *T)
BOOLEAN rCheckIV(const intvec *iv)
void atSet(idhdl root, char *name, void *data, int typ)
const unsigned short fftable[]
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
#define pIsConstant(p)
like above, except that Comp might be != 0
struct for passing initialization parameters to naInitChar
only used if HAVE_RINGS is defined
BOOLEAN iiApplyLIST(leftv res, leftv a, int op, leftv proc)
void spectrumPrintError(spectrumState state)
void fillContainer(number *_coeffs, number *_ievpoint, const int _var, const int _tdg, const rootType _rt, const int _anz)
const char * iiTwoOps(int t)
static int si_max(const int a, const int b)
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
virtual ideal getMatrix()
ring rInit(leftv pn, leftv rv, leftv ord)
Induced (Schreyer) ordering.
void PrintS(const char *s)
matrix singclap_irrCharSeries(ideal I, const ring r)
static BOOLEAN rField_is_Q(const ring r)
lists rDecompose(const ring r)
BOOLEAN iiApplyIDEAL(leftv, leftv, int, leftv)
BOOLEAN spectrumfProc(leftv result, leftv first)
char name(const Variable &v)
void nlGMP(number &i, mpz_t n, const coeffs r)
gmp_complex * getRoot(const int i)
idhdl rFindHdl(ring r, idhdl n)
static unsigned pLength(poly a)
BOOLEAN loSimplex(leftv res, leftv args)
Implementation of the Simplex Algorithm.
static FORCE_INLINE BOOLEAN nCoeff_is_GF(const coeffs r)
BOOLEAN slWrite(si_link l, leftv v)
BOOLEAN rEqual(ring r1, ring r2, BOOLEAN qr)
returns TRUE, if r1 equals r2 FALSE, otherwise Equality is determined componentwise, if qr == 1, then qrideal equality is tested, as well
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
lists scIndIndset(ideal S, BOOLEAN all, ideal Q)
spectrumState spectrumCompute(poly h, lists *L, int fast)
mprState mprIdealCheck(const ideal theIdeal, const char *name, uResultant::resMatType mtype, BOOLEAN rmatrix=false)
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
void iiMakeResolv(resolvente r, int length, int rlen, char *name, int typ0, intvec **weights)
rootContainer ** interpolateDenseSP(BOOLEAN matchUp=false, const number subDetVal=NULL)
static void rRenameVars(ring R)
static void rDecomposeC_41(leftv h, const coeffs C)
static BOOLEAN rField_is_long_C(const ring r)
void rSetSyzComp(int k, const ring r)
void rChangeCurrRing(ring r)
static BOOLEAN rField_is_Zp(const ring r)
void hLexR(scfmon rad, int Nrad, varset var, int Nvar)
INLINE_THIS void Init(int l=0)
matrix mpNew(int r, int c)
create a r x c zero-matrix
BOOLEAN syBetti2(leftv res, leftv u, leftv w)
int iiDeclCommand(leftv sy, leftv name, int lev, int t, idhdl *root, BOOLEAN isring, BOOLEAN init_b)
void paPrint(const char *n, package p)
BOOLEAN iiCheckRing(int i)
ideal idInit(int idsize, int rank)
initialise an ideal / module
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...
const Variable & v
< [in] a sqrfree bivariate poly
BOOLEAN kQHWeight(leftv res, leftv v)
static BOOLEAN iiInternalExport(leftv v, int toLev)
void * atGet(idhdl root, const char *name, int t, void *defaultReturnValue)
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)
void rComposeRing(lists L, ring R)
void mult(unsigned long *result, unsigned long *a, unsigned long *b, unsigned long p, int dega, int degb)
#define BREAK_LINE_LENGTH
static BOOLEAN rField_is_Ring(const ring r)
void rDecomposeRing(leftv h, const ring R)
intvec * syBettiOfComputation(syStrategy syzstr, BOOLEAN minim=TRUE, int *row_shift=NULL, intvec *weights=NULL)
BOOLEAN iiDefaultParameter(leftv p)
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
struct for passing initialization parameters to naInitChar
void wCall(poly *s, int sl, int *x, double wNsqr, const ring R)
BOOLEAN semicProc(leftv res, leftv u, leftv v)
void rDelete(ring r)
unconditionally deletes fields in r
BOOLEAN nuMPResMat(leftv res, leftv arg1, leftv arg2)
returns module representing the multipolynomial resultant matrix Arguments 2: ideal i...
const char * Tok2Cmdname(int tok)
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic ...
BOOLEAN iiWRITE(leftv, leftv v)
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 jjBETTI(leftv res, leftv u)
coeffs basecoeffs() const
static BOOLEAN rField_is_Ring_Z(const ring r)
void pNorm(poly p, const ring R=currRing)
static BOOLEAN rField_is_long_R(const ring r)
lists liMakeResolv(resolvente r, int length, int reallen, int typ0, intvec **weights, int add_row_shift)
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
int rTypeOfMatrixOrder(const intvec *order)
int iiOpsTwoChar(const char *s)
BOOLEAN jjMINRES(leftv res, leftv v)
void CleanUp(ring r=currRing)
void Clean(ring r=currRing)
const char * par_name
parameter name
ideal idrCopyR(ideal id, ring src_r, ring dest_r)
lists rDecompose_list_cf(const ring r)
static int rInternalChar(const ring r)
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
void newBuffer(char *s, feBufferTypes t, procinfo *pi, int lineno)
rRingOrder_t rOrderName(char *ordername)
BOOLEAN iiApplyINTVEC(leftv res, leftv a, int op, leftv proc)
number nlMapGMP(number from, const coeffs src, const coeffs dst)
BOOLEAN iiARROW(leftv r, char *a, char *s)
BOOLEAN ringIsLocal(const ring r)
BOOLEAN spaddProc(leftv result, leftv first, leftv second)
int idGetNumberOfChoise(int t, int d, int begin, int end, int *choise)
char * complexToStr(gmp_complex &c, const unsigned int oprec, const coeffs src)
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
leftv iiMap(map theMap, const char *what)
idhdl packFindHdl(package r)
#define omCheckAddr(addr)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
void iiCheckPack(package &p)
ideal singclap_factorize(poly f, intvec **v, int with_exps, const ring r)
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...
virtual IStateType initState() const
#define omFreeBin(addr, bin)
BOOLEAN rDecompose_CF(leftv res, const coeffs C)
Rational pow(const Rational &a, int e)
char * iiGetLibProcBuffer(procinfo *pi, int part)
#define IMATELEM(M, I, J)
static poly p_Init(const ring r, omBin bin)
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
BOOLEAN jjBETTI2_ID(leftv res, leftv u, leftv v)
void syKillEmptyEntres(resolvente res, int length)
BOOLEAN iiApply(leftv res, leftv a, int op, leftv proc)
int mult_spectrum(spectrum &)
lists listOfRoots(rootArranger *self, const unsigned int oprec)
static BOOLEAN rField_is_numeric(const ring r)
BOOLEAN lRingDependend(lists L)
scfmon hInit(ideal S, ideal Q, int *Nexist, ring tailRing)
void copy_deep(spectrum &spec, lists l)
void delete_node(spectrumPolyNode **)
void Werror(const char *fmt,...)
virtual number getSubDet()
ideal kGroebner(ideal F, ideal Q)
void syKillComputation(syStrategy syzstr, ring r=currRing)
const char * lastreserved
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 void killlocals0(int v, idhdl *localhdl, const ring r)
double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
BOOLEAN loNewtonP(leftv res, leftv arg1)
compute Newton Polytopes of input polynomials
#define pCopy(p)
return a copy of the poly
#define MATELEM(mat, i, j)
poly computeWC(const newtonPolygon &np, Rational max_weight, const ring r)
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
syStrategy syForceMin(lists li)
int IsCmd(const char *n, int &tok)
void hSupp(scfmon stc, int Nstc, varset var, int *Nvar)
BOOLEAN iiAssign(leftv l, leftv r, BOOLEAN toplevel)
BOOLEAN mpJacobi(leftv res, leftv a)