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 WarnS(
"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)
700 poly
p=(poly)tmpW.
data;
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(%d.) arg.(%s) is not a proc(but %s(%d)), nesting=%d",
1226 if (b && (h->rtyp==
IDHDL) && (h->e==
NULL))
1232 if(
pi->data.s.body==
NULL )
1249 pi,
pi->data.s.body_lineno-(iiCurrArgs==
NULL) );
1258 if (iiCurrArgs!=
NULL)
1260 if (err==0)
Warn(
"too many arguments for %s",
IDID(iiCurrProc));
1282 if (iiCurrArgs==
NULL)
1284 if (strcmp(p->
name,
"#")==0)
1293 if (strcmp(p->
name,
"#")==0)
1295 is_default_list=
TRUE;
1303 if (is_default_list)
1361 if (keepring)
IDRING(h)->ref--;
1373 Warn(
"'%s': no such identifier\n", v->
name);
1376 package frompack=v->req_packhdl;
1391 if (h==frompack->idroot)
1393 frompack->idroot=h->
next;
1397 idhdl hh=frompack->idroot;
1398 while ((hh!=
NULL) && (hh->
next!=h))
1408 h->
next=rootpack->idroot;
1544 WarnS(
"package not found\n");
1578 r->block0 = (
int *)
omAlloc0(3 *
sizeof(
int *));
1579 r->block1 = (
int *)
omAlloc0(3 *
sizeof(
int *));
1598 if (h!=
NULL)
return h;
1600 if (h!=
NULL)
return h;
1607 if (h!=
NULL)
return h;
1615 if (h!=
NULL)
return h;
1634 L->
m[0].
data=(
void *)(
long)r->cf->ch;
1640 for(i=0; i<r->N; i++)
1646 L->
m[1].
data=(
void *)LL;
1663 if (r->block1[i]-r->block0[i] >=0 )
1665 j=r->block1[
i]-r->block0[
i];
1668 if ((r->wvhdl!=
NULL) && (r->wvhdl[i]!=
NULL))
1670 for(;j>=0; j--) (*iv)[
j]=r->wvhdl[
i][
j];
1672 else switch (r->order[i])
1679 for(;j>=0; j--) (*iv)[
j]=1;
1689 LLL->
m[1].
data=(
void *)iv;
1690 LL->
m[
i].
data=(
void *)LLL;
1693 L->
m[2].
data=(
void *)LL;
1703 pSetCoeff0(q->m[0],(number)(r->qideal->m[0]));
1704 L->
m[3].
data=(
void *)q;
1723 L->
m[0].
data=(
void *)0;
1733 L->
m[1].
data=(
void *)LL;
1757 L->
m[0].
data=(
void *)0;
1767 L->
m[1].
data=(
void *)LL;
1801 LL->
m[1].
data=(
void *) C->modExponent;
1803 L->
m[1].
data=(
void *)LL;
1828 LL->
m[0].
data=
nlMapGMP((number) R->cf->modBase, R->cf, R->cf);
1830 LL->
m[1].
data=(
void *) R->cf->modExponent;
1832 L->
m[1].
data=(
void *)LL;
1846 WerrorS(
"ring with polynomial data must be the base ring or compatible");
1859 else if ( C->extRing!=
NULL )
1869 Lc->
m[0].
data=(
void*)(
long)C->m_nfCharQ;
1876 Lc->
m[1].
data=(
void*)Lv;
1887 Loo->
m[1].
data=(
void *)iv;
1890 Lo->
m[0].
data=(
void*)Loo;
1893 Lc->
m[2].
data=(
void*)Lo;
1899 res->
data=(
void*)Lc;
1904 res->
data=(
void *)(
long)C->ch;
1925 WerrorS(
"ring with polynomial data must be the base ring or compatible");
1943 L->
m[0].
data=(
char*)r->cf; r->cf->ref++;
1949 for(i=0; i<r->N; i++)
1952 LL->m[
i].data=(
void *)
omStrDup(r->names[i]);
1955 L->
m[1].
data=(
void *)LL;
1975 assume( r->block0[i] == r->block1[i] );
1976 const int s = r->block0[
i];
1977 assume( -2 < s && s < 2);
1982 else if (r->block1[i]-r->block0[i] >=0 )
1984 int bl=j=r->block1[
i]-r->block0[
i];
1992 j+=r->wvhdl[
i][bl+1];
1995 if ((r->wvhdl!=
NULL) && (r->wvhdl[i]!=
NULL))
1997 for(;j>=0; j--) (*iv)[
j]=r->wvhdl[
i][j+(j>bl)];
1999 else switch (r->order[i])
2006 for(;j>=0; j--) (*iv)[
j]=1;
2016 LLL->
m[1].
data=(
void *)iv;
2017 LL->m[
i].data=(
void *)LLL;
2020 L->
m[2].
data=(
void *)LL;
2024 if (r->qideal==
NULL)
2029 #ifdef HAVE_PLURAL // NC! in rDecompose 2050 || (r->qideal !=
NULL)
2057 WerrorS(
"ring with polynomial data must be the base ring or compatible");
2082 else if ( r->cf->extRing!=
NULL )
2092 Lc->
m[0].
data=(
void*)(
long)r->cf->m_nfCharQ;
2099 Lc->
m[1].
data=(
void*)Lv;
2110 Loo->
m[1].
data=(
void *)iv;
2113 Lo->
m[0].
data=(
void*)Loo;
2116 Lc->
m[2].
data=(
void*)Lo;
2122 L->
m[0].
data=(
void*)Lc;
2127 L->
m[0].
data=(
void *)(
long)r->cf->ch;
2134 for(i=0; i<r->N; i++)
2140 L->
m[1].
data=(
void *)LL;
2161 assume( r->block0[i] == r->block1[i] );
2162 const int s = r->block0[
i];
2168 else if (r->block1[i]-r->block0[i] >=0 )
2170 int bl=j=r->block1[
i]-r->block0[
i];
2178 j+=r->wvhdl[
i][bl+1];
2181 if ((r->wvhdl!=
NULL) && (r->wvhdl[i]!=
NULL))
2183 for(;j>=0; j--) (*iv)[
j]=r->wvhdl[
i][j+(j>bl)];
2185 else switch (r->order[i])
2192 for(;j>=0; j--) (*iv)[
j]=1;
2202 LLL->
m[1].
data=(
void *)iv;
2203 LL->
m[
i].
data=(
void *)LLL;
2206 L->
m[2].
data=(
void *)LL;
2210 if (r->qideal==
NULL)
2215 #ifdef HAVE_PLURAL // NC! in rDecompose 2234 WerrorS(
"invalid coeff. field description, expecting 0");
2242 WerrorS(
"invalid coeff. field description, expecting precision list");
2252 WerrorS(
"invalid coeff. field description list");
2255 int r1=(int)(
long)LL->
m[0].
data;
2256 int r2=(int)(
long)LL->
m[1].
data;
2278 R->cf->float_len=
si_min(r1,32767);
2279 R->cf->float_len2=
si_min(r2,32767);
2288 WerrorS(
"invalid coeff. field description, expecting parameter name");
2305 unsigned int modExponent = 1;
2309 mpz_init_set_ui(modBase,0);
2320 number tmp= (number) LL->
m[0].
data;
2327 mpz_init_set_ui(modBase,(
unsigned long) LL->
m[0].
data);
2331 mpz_init_set_ui(modBase,0);
2335 modExponent = (
unsigned long) LL->
m[1].
data;
2343 if ((mpz_cmp_ui(modBase, 1) == 0) && (
mpz_sgn1(modBase) < 0))
2345 WerrorS(
"Wrong ground ring specification (module is 1)");
2348 if (modExponent < 1)
2350 WerrorS(
"Wrong ground ring specification (exponent smaller than 1)");
2359 else if (modExponent > 1)
2362 if ((mpz_cmp_ui(modBase, 2) == 0) && (modExponent <= 8*
sizeof(
unsigned long)))
2373 info.
exp= modExponent;
2384 info.
exp= modExponent;
2398 for(i=0;i<R->N-1;i++)
2400 for(j=i+1;j<R->N;j++)
2402 if (strcmp(R->names[i],R->names[j])==0)
2405 Warn(
"name conflict var(%d) and var(%d): `%s`, rename to `@%s`",i+1,j+1,R->names[i],R->names[i]);
2407 R->names[
j]=(
char *)
omAlloc(2+strlen(R->names[i]));
2408 sprintf(R->names[j],
"@%s",R->names[i]);
2414 for(i=0;i<
rPar(R); i++)
2420 Warn(
"name conflict par(%d) and var(%d): `%s`, renaming the VARIABLE to `@@(%d)`",i+1,j+1,R->names[j],i+1);
2426 sprintf(R->names[j],
"@@(%d)",i+1);
2452 poly
p=(poly)v->
m[i].
Data();
2458 Werror(
"var name %d must be a string or a ring variable",i+1);
2464 Werror(
"var name %d must be `string`",i+1);
2471 WerrorS(
"variable must be given as `list`");
2487 for (
int j=0;
j < n-1;
j++)
2494 &&(strcmp((
char*)vv->
m[0].
Data(),
"L")==0))
2496 number nn=(number)vv->
m[1].
Data();
2503 Werror(
"illegal argument for pseudo ordering L: %d",vv->
m[1].
Typ());
2510 if (bitmask!=0) n--;
2514 R->block0=(
int *)
omAlloc0(n*
sizeof(
int));
2515 R->block1=(
int *)
omAlloc0(n*
sizeof(
int));
2518 for (j_in_R= n-2; j_in_R>=0; j_in_R--)
2521 for(j_in_R=0,j_in_L=0;j_in_R<n-1;j_in_R++,j_in_L++)
2526 WerrorS(
"ordering must be list of lists");
2533 if (strcmp((
char*)vv->
m[0].
Data(),
"L")==0)
2541 WerrorS(
"ordering name must be a (string,intvec)(1)");
2546 if (j_in_R==0) R->block0[0]=1;
2563 if (jj<0) R->block0[j_in_R]=1;
2564 else R->block0[j_in_R]=R->block1[jj]+1;
2576 R->block1[j_in_R]=
si_max(R->block0[j_in_R],R->block0[j_in_R]+iv_len-1);
2577 if (R->block1[j_in_R]>R->N)
2579 if (R->block0[j_in_R]>R->N)
2581 Werror(
"not enough variables for ordering %d (%s)",j_in_R,
rSimpleOrdStr(R->order[j_in_R]));
2584 R->block1[j_in_R]=R->N;
2585 iv_len=R->block1[j_in_R]-R->block0[j_in_R]+1;
2590 switch (R->order[j_in_R])
2599 R->wvhdl[j_in_R] =(
int *)
omAlloc(iv_len*
sizeof(
int));
2600 for (i=0; i<iv_len;i++)
2602 R->wvhdl[j_in_R][
i]=(*iv)[
i];
2606 R->wvhdl[j_in_R] =(
int *)
omAlloc((iv->
length()+1)*
sizeof(
int));
2607 for (i=0; i<iv_len;i++)
2609 R->wvhdl[j_in_R][
i]=(*iv)[
i];
2611 R->wvhdl[j_in_R][
i]=iv->
length() - iv_len;
2613 for (; i<iv->
length(); i++)
2615 R->wvhdl[j_in_R][i+1]=(*iv)[
i];
2619 R->wvhdl[j_in_R] =(
int *)
omAlloc((iv->
length())*
sizeof(
int));
2620 for (i=0; i<iv->
length();i++) R->wvhdl[j_in_R][i]=(*iv)[
i];
2621 R->block1[j_in_R]=
si_max(R->block0[j_in_R],R->block0[j_in_R]+(
int)
sqrt((
double)(iv->
length()-1)));
2622 if (R->block1[j_in_R]>R->N)
2624 WerrorS(
"ordering matrix too big");
2642 R->block1[j_in_R]=R->block0[j_in_R]=0;
2646 R->block1[j_in_R]=R->block0[j_in_R]=(*iv)[0];
2652 R->block1[j_in_R] = R->block0[j_in_R] = 0;
2655 const int s = (*iv)[0];
2656 assume( -2 < s && s < 2 );
2657 R->block1[j_in_R] = R->block0[j_in_R] =
s;
2666 WerrorS(
"ring order not implemented");
2674 WerrorS(
"ordering name must be a (string,intvec)");
2683 if (R->block1[j_in_R] != R->N)
2694 R->block0[j_in_R] <= R->N)
2696 R->block1[j_in_R] = R->N;
2700 Werror(
"ordering incomplete: size (%d) should be %d",R->block1[j_in_R],R->N);
2704 if (R->block0[j_in_R]>R->N)
2706 Werror(
"not enough variables (%d) for ordering block %d, scanned so far:",R->N,j_in_R+1);
2707 for(
int ii=0;ii<=j_in_R;ii++)
2708 Werror(
"ord[%d]: %s from v%d to v%d",ii+1,
rSimpleOrdStr(R->order[ii]),R->block0[ii],R->block1[ii]);
2723 R->block0=(
int*)
omRealloc0Size(R->block0,n*
sizeof(
int),(n+1)*
sizeof(
int));
2724 R->block1=(
int*)
omRealloc0Size(R->block1,n*
sizeof(
int),(n+1)*
sizeof(
int));
2736 WerrorS(
"ordering must be given as `list`");
2739 if (bitmask!=0) R->bitmask=bitmask*2;
2771 int ch = (int)(
long)L->
m[0].
Data();
2781 Warn(
"%d is invalid characteristic of ground field. %d is used.", ch, l);
2804 int ch = (int)(
long)LL->
m[0].
Data();
2805 while ((ch!=
fftable[is_gf_char]) && (
fftable[is_gf_char])) is_gf_char++;
2806 if (
fftable[is_gf_char]==0) is_gf_char=-1;
2827 WerrorS(
"could not create the specified coefficient field");
2831 if( extRing->qideal !=
NULL )
2835 extParam.
r = extRing;
2842 extParam.
r = extRing;
2852 WerrorS(
"coefficient field must be described by `int` or `list`");
2858 WerrorS(
"could not create coefficient field described by the input!");
2870 if (bitmask!=0x7fff) R->bitmask=bitmask*2;
2877 ideal q=(ideal)L->
m[3].
Data();
2883 WerrorS(
"coefficient fields must be equal if q-ideal !=0");
2890 int par_perm_size=0;
2909 par_perm_size=
rPar(orig_ring);
2919 WerrorS(
"coefficient fields must be equal if q-ideal !=0");
2923 perm=(
int *)
omAlloc0((orig_ring->N+1)*
sizeof(int));
2924 if (par_perm_size!=0)
2925 par_perm=(
int *)
omAlloc0(par_perm_size*
sizeof(
int));
2929 maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
2938 else if (par_perm_size!=0)
2943 for(i=
IDELEMS(q)-1; i>=0; i--)
2946 par_perm,par_perm_size);
2948 pTest(dest_id->m[i]);
2964 WerrorS(
"q-ideal must be given as `ideal`");
2992 while (i>=0) {
omfree(R->names[i]); i--; }
3013 ideal
id=(ideal)a->
Data();
3016 for (i=1; i<=
IDELEMS(
id); i++)
3023 res->
data=(
char *)result;
3033 int n=(int)(
long)b->
Data();
3034 int d=(int)(
long)c->
Data();
3041 if ((d>n) || (d<1) || (n<1))
3046 int *choise = (
int*)
omAlloc(d*
sizeof(
int));
3050 temp=(ideal)id->
Data();
3063 if (choise[l-1]<=
IDELEMS(temp))
3065 p =
pCopy(temp->m[choise[l-1]-1]);
3066 if (sign == -1) p =
pNeg(p);
3078 res->
data=(
char *)result;
3093 int add_row_shift=0;
3099 add_row_shift = ww->
min_in();
3100 (*weights) -= add_row_shift;
3113 memset(&tmp,0,
sizeof(tmp));
3129 if ((fullres==
NULL) && (minres==
NULL))
3156 for (
int i=length-1;
i>=0;
i--)
3168 for (
int i=length-1;
i>=0;
i--)
3241 ideal F=(ideal)id->
Data();
3247 res->
data=(
char *)iv;
3251 double wNsqr = (double)2.0 / (
double)n;
3253 x = (
int * )
omAlloc(2 * (n + 1) *
sizeof(int));
3255 for (i = n; i!=0; i--)
3256 (*iv)[i-1] = x[i + n + 1];
3274 res->
data=(
void *)b;
3292 #ifdef HAVE_SPECTRUM 3300 spec.
mu = (int)(
long)(l->
m[0].
Data( ));
3301 spec.
pg = (int)(
long)(l->
m[1].
Data( ));
3302 spec.
n = (int)(
long)(l->
m[2].
Data( ));
3310 for(
int i=0;
i<spec.
n;
i++ )
3313 spec.
w[
i] = (*mul)[
i];
3344 for(
int i=0;
i<spec.
n;
i++ )
3348 (*mult)[
i] = spec.
w[
i];
3358 L->
m[0].
data = (
void*)(
long)spec.
mu;
3359 L->
m[1].
data = (
void*)(
long)spec.
pg;
3360 L->
m[2].
data = (
void*)(
long)spec.
n;
3361 L->
m[3].
data = (
void*)num;
3362 L->
m[4].
data = (
void*)den;
3363 L->
m[5].
data = (
void*)mult;
3411 WerrorS(
"the list is too short" );
3414 WerrorS(
"the list is too long" );
3418 WerrorS(
"first element of the list should be int" );
3421 WerrorS(
"second element of the list should be int" );
3424 WerrorS(
"third element of the list should be int" );
3427 WerrorS(
"fourth element of the list should be intvec" );
3430 WerrorS(
"fifth element of the list should be intvec" );
3433 WerrorS(
"sixth element of the list should be intvec" );
3437 WerrorS(
"first element of the list should be positive" );
3440 WerrorS(
"wrong number of numerators" );
3443 WerrorS(
"wrong number of denominators" );
3446 WerrorS(
"wrong number of multiplicities" );
3450 WerrorS(
"the Milnor number should be positive" );
3453 WerrorS(
"the geometrical genus should be nonnegative" );
3456 WerrorS(
"all numerators should be positive" );
3459 WerrorS(
"all denominators should be positive" );
3462 WerrorS(
"all multiplicities should be positive" );
3466 WerrorS(
"it is not symmetric" );
3469 WerrorS(
"it is not monotonous" );
3473 WerrorS(
"the Milnor number is wrong" );
3476 WerrorS(
"the geometrical genus is wrong" );
3480 WerrorS(
"unspecific error" );
3516 ( fast==2 ? 2 : 1 ) );
3526 ( fast==0 || (*node)->weight<=smax ) )
3538 if( search->
nf!=(poly)
NULL )
3548 cmp =
pCmp( (*node)->mon,f );
3571 (*node)->nf = search->
nf;
3575 while( cmp<0 && f!=(poly)NULL );
3577 search = search->
next;
3588 if( (*node)->weight<=(
Rational)1 ) pg++;
3589 if( (*node)->weight==smax ) z++;
3590 if( (*node)->weight>weight_prev ) n++;
3592 weight_prev = (*node)->weight;
3593 node = &((*node)->next);
3605 if( search->
nf!=(poly)
NULL )
3615 cmp =
pCmp( (*node)->mon,f );
3628 while( cmp<0 && f!=(poly)
NULL );
3630 search = search->
next;
3644 n = ( z > 0 ? 2*n - 1 : 2*n );
3659 ( fast==0 || search->
weight<=smax );
3660 search=search->
next )
3685 for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3688 (*den) [n2] = (*den)[n1];
3689 (*mult)[n2] = (*mult)[n1];
3697 if( fast==0 || fast==1 )
3701 for(
int n1=0, n2=n-1 ; n1<n2 && symmetric==
TRUE; n1++, n2-- )
3703 if( (*mult)[n1]!=(*mult)[n2] ||
3704 (*den) [n1]!= (*den)[n2] ||
3711 if( symmetric==
FALSE )
3721 (*L)->m[0].data = (
void*)(
long)
mu;
3738 (*L)->m[0].data = (
void*)(
long)
mu;
3739 (*L)->m[1].data = (
void*)(
long)pg;
3740 (*L)->m[2].data = (
void*)(
long)n;
3741 (*L)->m[3].data = (
void*)nom;
3742 (*L)->m[4].data = (
void*)den;
3743 (*L)->m[5].data = (
void*)mult;
3752 #ifdef SPECTRUM_DEBUG 3753 #ifdef SPECTRUM_PRINT 3754 #ifdef SPECTRUM_IOSTREAM 3755 cout <<
"spectrumCompute\n";
3756 if( fast==0 ) cout <<
" no optimization" << endl;
3757 if( fast==1 ) cout <<
" weight optimization" << endl;
3758 if( fast==2 ) cout <<
" symmetry optimization" << endl;
3760 fputs(
"spectrumCompute\n",stdout );
3761 if( fast==0 ) fputs(
" no optimization\n", stdout );
3762 if( fast==1 ) fputs(
" weight optimization\n", stdout );
3763 if( fast==2 ) fputs(
" symmetry optimization\n", stdout );
3807 #ifdef SPECTRUM_DEBUG 3808 #ifdef SPECTRUM_PRINT 3809 #ifdef SPECTRUM_IOSTREAM 3810 cout <<
"\n computing the Jacobi ideal...\n";
3812 fputs(
"\n computing the Jacobi ideal...\n",stdout );
3821 #ifdef SPECTRUM_DEBUG 3822 #ifdef SPECTRUM_PRINT 3823 #ifdef SPECTRUM_IOSTREAM 3826 fputs(
" ", stdout );
3837 #ifdef SPECTRUM_DEBUG 3838 #ifdef SPECTRUM_PRINT 3839 #ifdef SPECTRUM_IOSTREAM 3841 cout <<
" computing a standard basis..." << endl;
3843 fputs(
"\n", stdout );
3844 fputs(
" computing a standard basis...\n", stdout );
3852 #ifdef SPECTRUM_DEBUG 3853 #ifdef SPECTRUM_PRINT 3854 for( i=0; i<
IDELEMS(stdJ); i++ )
3856 #ifdef SPECTRUM_IOSTREAM 3859 fputs(
" ",stdout );
3904 #ifdef SPECTRUM_DEBUG 3905 #ifdef SPECTRUM_PRINT 3906 #ifdef SPECTRUM_IOSTREAM 3907 cout <<
"\n computing the highest corner...\n";
3909 fputs(
"\n computing the highest corner...\n", stdout );
3914 poly hc = (poly)NULL;
3918 if( hc!=(poly)NULL )
3933 #ifdef SPECTRUM_DEBUG 3934 #ifdef SPECTRUM_PRINT 3935 #ifdef SPECTRUM_IOSTREAM 3938 fputs(
" ", stdout );
3948 #ifdef SPECTRUM_DEBUG 3949 #ifdef SPECTRUM_PRINT 3950 #ifdef SPECTRUM_IOSTREAM 3951 cout <<
"\n computing the newton polygon...\n";
3953 fputs(
"\n computing the newton polygon...\n", stdout );
3960 #ifdef SPECTRUM_DEBUG 3961 #ifdef SPECTRUM_PRINT 3970 #ifdef SPECTRUM_DEBUG 3971 #ifdef SPECTRUM_PRINT 3972 #ifdef SPECTRUM_IOSTREAM 3973 cout <<
"\n computing the weight corner...\n";
3975 fputs(
"\n computing the weight corner...\n", stdout );
3980 poly wc = ( fast==0 ?
pCopy( hc ) :
3985 #ifdef SPECTRUM_DEBUG 3986 #ifdef SPECTRUM_PRINT 3987 #ifdef SPECTRUM_IOSTREAM 3990 fputs(
" ", stdout );
4000 #ifdef SPECTRUM_DEBUG 4001 #ifdef SPECTRUM_PRINT 4002 #ifdef SPECTRUM_IOSTREAM 4003 cout <<
"\n computing NF...\n" << endl;
4005 fputs(
"\n computing NF...\n", stdout );
4014 #ifdef SPECTRUM_DEBUG 4015 #ifdef SPECTRUM_PRINT 4017 #ifdef SPECTRUM_IOSTREAM 4020 fputs(
"\n", stdout );
4045 WerrorS(
"polynomial is zero" );
4048 WerrorS(
"polynomial has constant term" );
4051 WerrorS(
"not a singularity" );
4054 WerrorS(
"the singularity is not isolated" );
4057 WerrorS(
"highest corner cannot be computed" );
4060 WerrorS(
"principal part is degenerate" );
4066 WerrorS(
"unknown error occurred" );
4083 WerrorS(
"only works for local orderings" );
4091 WerrorS(
"does not work in quotient rings" );
4104 result->
data = (
char*)L;
4137 WerrorS(
"only works for local orderings" );
4142 WerrorS(
"does not work in quotient rings" );
4155 result->
data = (
char*)L;
4201 else if( l->
nr > 5 )
4239 int mu = (int)(
long)(l->
m[0].
Data( ));
4240 int pg = (int)(
long)(l->
m[1].
Data( ));
4241 int n = (int)(
long)(l->
m[2].
Data( ));
4252 if( n != num->
length( ) )
4256 else if( n != den->
length( ) )
4260 else if( n != mul->
length( ) )
4280 for( i=0; i<n; i++ )
4282 if( (*num)[
i] <= 0 )
4286 if( (*den)[
i] <= 0 )
4290 if( (*mul)[
i] <= 0 )
4302 for( i=0, j=n-1; i<=
j; i++,j-- )
4305 (*den)[
i] != (*den)[
j] ||
4306 (*mul)[
i] != (*mul)[
j] )
4316 for( i=0, j=1; i<n/2; i++,j++ )
4318 if( (*num)[
i]*(*den)[
j] >= (*num)[
j]*(*den)[
i] )
4328 for( mu=0, i=0; i<n; i++ )
4333 if( mu != (
int)(long)(l->
m[0].
Data( )) )
4342 for( pg=0, i=0; i<n; i++ )
4344 if( (*num)[
i]<=(*den)[
i] )
4350 if( pg != (
int)(long)(l->
m[1].
Data( )) )
4379 WerrorS(
"first argument is not a spectrum:" );
4384 WerrorS(
"second argument is not a spectrum:" );
4417 int k = (int)(
long)second->
Data( );
4421 WerrorS(
"first argument is not a spectrum" );
4426 WerrorS(
"second argument should be positive" );
4463 WerrorS(
"first argument is not a spectrum" );
4468 WerrorS(
"second argument is not a spectrum" );
4492 memset(&tmp,0,
sizeof(tmp));
4511 WerrorS(
"Ground field not implemented!");
4531 LP->
m= (int)(
long)(v->
Data());
4537 LP->
n= (int)(
long)(v->
Data());
4543 LP->
m1= (int)(
long)(v->
Data());
4549 LP->
m2= (int)(
long)(v->
Data());
4555 LP->
m3= (int)(
long)(v->
Data());
4557 #ifdef mprDEBUG_PROT 4558 Print(
"m (constraints) %d\n",LP->
m);
4559 Print(
"n (columns) %d\n",LP->
n);
4583 lres->
m[4].
data=(
void*)(
long)LP->
m;
4586 lres->
m[5].
data=(
void*)(
long)LP->
n;
4588 res->
data= (
void*)lres;
4595 ideal gls = (ideal)(arg1->
Data());
4596 int imtype= (int)(
long)arg2->
Data();
4620 gls= (poly)(arg1->
Data());
4621 int howclean= (int)(
long)arg3->
Data();
4628 WerrorS(
"Ground field not implemented!");
4635 unsigned long int ii = (
unsigned long int)arg2->
Data();
4641 WerrorS(
"Input polynomial is constant!");
4667 if ( (vpos != i) && (
pGetExp( piter, i ) != 0) )
4669 WerrorS(
"The input polynomial must be univariate!");
4677 number * pcoeffs= (number *)
omAlloc( (deg+1) *
sizeof( number ) );
4679 for ( i= deg; i >= 0; i-- )
4693 #ifdef mprDEBUG_PROT 4694 for (i=deg; i >= 0; i--)
4702 roots->
solver( howclean );
4709 rlist->
Init( elem );
4713 for ( j= 0; j < elem; j++ )
4722 for ( j= 0; j < elem; j++ )
4726 rlist->
m[
j].
data=(
void *)dummy;
4740 res->
data= (
void*)rlist;
4749 p= (ideal)arg1->
Data();
4750 w= (ideal)arg2->
Data();
4761 int tdg= (int)(
long)arg3->
Data();
4768 WerrorS(
"Last input parameter must be > 0!");
4776 if ( m != (
int)
pow((
double)tdg+1,(
double)n) )
4778 Werror(
"Size of second input ideal must be equal to %d!",
4779 (
int)
pow((
double)tdg+1,(
double)n));
4786 WerrorS(
"Ground field not implemented!");
4791 number *pevpoint= (number *)
omAlloc( n *
sizeof( number ) );
4792 for ( i= 0; i < n; i++ )
4801 WerrorS(
"Elements of first input ideal must not be equal to -1, 0, 1!");
4810 WerrorS(
"Elements of first input ideal must be numbers!");
4813 pevpoint[
i]=
nCopy( tmp );
4817 number *wresults= (number *)
omAlloc( m *
sizeof( number ) );
4818 for ( i= 0; i <
m; i++ )
4827 WerrorS(
"Elements of second input ideal must be numbers!");
4842 res->
data= (
void*)rpoly;
4857 else gls= (ideal)(v->
Data());
4863 else imtype= (int)(
long)v->
Data();
4868 ideal test_id=
idInit(1,1);
4870 for(j=
IDELEMS(gls)-1;j>=0;j--)
4872 if (gls->m[j]!=
NULL)
4874 test_id->m[0]=gls->m[
j];
4878 WerrorS(
"Newton polytope not of expected dimension");
4892 unsigned long int ii=(
unsigned long int)v->
Data();
4900 else howclean= (int)(
long)v->
Data();
4929 WerrorS(
"Error occurred during matrix setup!");
4937 #ifdef mprDEBUG_PROT 4942 WerrorS(
"Unsuitable input ideal: Minor of resultant matrix is singular!");
4948 if ( interpolate_det )
4954 if ( interpolate_det )
4959 #ifdef mprDEBUG_PROT 4961 for (i=0; i < c; i++)
pWrite(iproots[i]->getPoly());
4963 for (i=0; i < c; i++)
pWrite(muiproots[i]->getPoly());
4967 arranger=
new rootArranger( iproots, muiproots, howclean );
4978 WerrorS(
"Solver was unable to find any roots!");
4984 for (i=0; i <
count; i++)
delete iproots[i];
4987 for (i=0; i <
count; i++)
delete muiproots[i];
4994 res->
data= (
void *)listofroots;
5006 int count=
self->roots[0]->getAnzRoots();
5007 int elem=
self->roots[0]->getAnzElems();
5011 if ( self->found_roots )
5013 listofroots->
Init( count );
5015 for (i=0; i <
count; i++)
5018 onepoint->
Init(elem);
5019 for ( j= 0; j < elem; j++ )
5035 listofroots->
m[
i].
data=(
void *)onepoint;
5043 listofroots->
Init( 0 );
5057 if (rg==
NULL)
return;
5082 Warn(
"deleting denom_list for ring change to %s",
IDID(h));
5096 if ((rg!=
NULL) && (rg->idroot==
NULL))
5124 if((*iv)[
i]>=0) { neg=
FALSE;
break; }
5129 (*iv)[
i]= - (*iv)[
i];
5138 if((*iv)[
i]>=0) { neg=
FALSE;
break; }
5143 (*iv)[
i]= -(*iv)[
i];
5152 if((*iv)[
i]!=1) { all_one=
FALSE;
break; }
5158 (*iv2)[2]=iv->
length()-2;
5170 if((*iv)[
i]!=1) { all_one=
FALSE;
break; }
5176 (*iv2)[2]=iv->
length()-2;
5210 (*iv)[2] += (*iv2)[2];
5217 if (!change) h=h->
next;
5225 int last = 0, o=0, n = 1,
i=0, typ = 1,
j;
5237 R->bitmask=(*iv)[2]*2+1;
5250 WerrorS(
"invalid combination of orderings");
5258 WerrorS(
"more than one ordering c/C specified");
5264 R->block0=(
int *)
omAlloc0(n*
sizeof(
int));
5265 R->block1=(
int *)
omAlloc0(n*
sizeof(
int));
5268 int *weights=(
int*)
omAlloc0((R->N+1)*
sizeof(int));
5271 for (
j=0;
j < n-1;
j++)
5302 R->block0[n] = last+1;
5305 R->wvhdl[n][
i-2] = (*iv)[
i];
5307 if (weights[last]==0) weights[
last]=(*iv)[
i]*typ;
5309 R->block1[n] =
si_min(last,R->N);
5320 R->block0[n] = last+1;
5321 if (iv->
length() == 3) last+=(*iv)[2];
5322 else last += (*iv)[0];
5323 R->block1[n] =
si_min(last,R->N);
5327 if (weights[
i]==0) weights[
i]=typ;
5339 const int s = (*iv)[2];
5349 const int s = (*iv)[2];
5351 if( 1 < s || s < -1 )
return TRUE;
5367 R->block0[n] = last+1;
5372 R->wvhdl[n][
i-2]=(*iv)[
i];
5374 if (weights[last]==0) weights[
last]=(*iv)[
i]*typ;
5376 last=R->block0[n]-1;
5381 R->block0[n] = last+1;
5384 if (R->block1[n]- R->block0[n]+2>=iv->
length())
5385 WarnS(
"missing module weights");
5386 for (
i=2;
i<=(R->block1[n]-R->block0[n]+2);
i++)
5388 R->wvhdl[n][
i-2]=(*iv)[
i];
5390 if (weights[last]==0) weights[
last]=(*iv)[
i]*typ;
5392 R->wvhdl[n][
i-2]=iv->
length() -3 -(R->block1[n]- R->block0[n]);
5395 R->wvhdl[n][
i-1]=(*iv)[
i];
5397 last=R->block0[n]-1;
5402 R->block0[n] = last+1;
5410 if (weights[last]==0) weights[
last]=(*iv)[
i]*typ;
5412 last=R->block0[n]-1;
5418 if (Mtyp==0)
return TRUE;
5419 if (Mtyp==-1) typ = -1;
5423 R->wvhdl[n][
i-2]=(*iv)[
i];
5425 R->block0[n] = last+1;
5427 R->block1[n] =
si_min(last,R->N);
5428 for(
i=R->block1[n];
i>=R->block0[n];
i--)
5430 if (weights[
i]==0) weights[
i]=typ;
5440 Werror(
"Internal Error: Unknown ordering %d", (*iv)[1]);
5447 Werror(
"mismatch of number of vars (%d) and ordering (>=%d vars)",
5455 for(
i=1;
i<=R->N;
i++)
5456 {
if (weights[
i]<0) { R->OrdSgn=-1;
break; }}
5470 if (R->block1[n] != R->N)
5481 R->block0[n] <= R->N)
5483 R->block1[n] = R->N;
5487 Werror(
"mismatch of number of vars (%d) and ordering (%d vars)",
5506 *p = (
char*)sl->
name;
5574 WerrorS(
"parameter expected");
5580 extParam.
r =
rDefault( cf, pars, names);
5581 for(
int i=pars-1;
i>=0;
i--)
5593 int ch = (int)(
long)pn->
Data();
5604 if ((ch<2)||(ch!=ch2))
5606 Warn(
"%d is invalid as characteristic of the ground field. 32003 is used.", ch);
5621 if ((ch!=0) && (ch!=
IsPrime(ch)) && (pars == 1))
5633 if ((ch!=0) && (ch!=
IsPrime(ch)))
5635 WerrorS(
"too many parameters");
5643 WerrorS(
"parameter expected");
5649 extParam.
r =
rDefault( ch, pars, names);
5650 for(
int i=pars-1;
i>=0;
i--)
5663 && ((strcmp(pn->
name,
"real")==0) || (strcmp(pn->
name,
"complex")==0)))
5666 BOOLEAN complex_flag=(strcmp(pn->
name,
"complex")==0);
5669 float_len=(int)(
long)pnn->
Data();
5670 float_len2=float_len;
5674 float_len2=(int)(
long)pnn->
Data();
5693 if (param.
float_len < SHORT_REAL_LENGTH)
5709 else if ((pn->
name !=
NULL) && (strcmp(pn->
name,
"integer") == 0))
5713 unsigned int modExponent = 1;
5714 mpz_init_set_si(modBase, 0);
5721 mpz_set_ui(modBase, (
int)(
long) pnn->
Data());
5725 modExponent = (long) pnn->
Data();
5730 mpz_mul_ui(modBase, modBase, (
int)(
long) pnn->
Data());
5743 if ((mpz_cmp_ui(modBase, 1) == 0) && (
mpz_sgn1(modBase) < 0))
5745 WerrorS(
"Wrong ground ring specification (module is 1)");
5748 if (modExponent < 1)
5750 WerrorS(
"Wrong ground ring specification (exponent smaller than 1");
5755 if (modExponent > 1 && cf ==
NULL)
5757 if ((mpz_cmp_ui(modBase, 2) == 0) && (modExponent <= 8*
sizeof(
unsigned long)))
5768 WerrorS(
"modulus must not be 0 or parameter not allowed");
5774 info.
exp= modExponent;
5779 else if (cf ==
NULL)
5783 WerrorS(
"modulus must not be 0 or parameter not allowed");
5789 info.
exp= modExponent;
5800 extParam.
r = (ring)pn->
Data();
5812 WerrorS(
"Wrong or unknown ground field specification");
5818 Print(
"pn[%p]: type: %d [%s]: %p, name: %s", (
void*)p, p->
Typ(),
Tok2Cmdname(p->Typ()), p->Data(), (p->name ==
NULL?
"NULL" : p->name) );
5840 WerrorS(
"Invalid ground field specification");
5856 Werror(
"too many ring variables(%d), max is %d",l,MAX_SHORT);
5864 WerrorS(
"name of ring variable expected");
5917 int *perm=(
int *)
omAlloc0((org_ring->N+1)*
sizeof(int));
5925 Werror(
"too many ring variables(%d), max is %d",l,MAX_SHORT);
5934 WerrorS(
"name of ring variable expected");
5944 for(;
i<org_ring->N;
i++)
5946 if (strcmp(org_ring->names[
i],R->names[
j])==0)
5954 Werror(
"variable %d (%s) not in basering",
j+1,R->names[
j]);
5967 for(
j=R->block0[
i];j<=R->block1[
i];
j++)
5971 if (min_var==-1) min_var=perm[
j];
5979 R->block0[
i]=min_var;
5980 R->block1[
i]=max_var;
5981 if (R->wvhdl[
i]!=
NULL)
5984 R->wvhdl[
i]=(
int*)
omAlloc0((max_var-min_var+1)*
sizeof(int));
5985 for(
j=org_ring->block0[
i];j<=org_ring->block1[
i];
j++)
5989 R->wvhdl[
i][perm[
j]-R->block0[
i]]=
5990 org_ring->wvhdl[
i][
j-org_ring->block0[
i]];
6016 R->order[
j-1]=R->order[
j];
6017 R->block0[
j-1]=R->block0[
j];
6018 R->block1[
j-1]=R->block1[
j];
6020 R->wvhdl[
j-1]=R->wvhdl[
j];
6028 while (R->order[n]==0) n--;
6031 if (R->block1[n] != R->N)
6042 R->block0[n] <= R->N)
6044 R->block1[n] = R->N;
6048 Werror(
"mismatch of number of vars (%d) and ordering (%d vars) in block %d",
6049 R->N,R->block1[n],n);
6055 R->OrdSgn = org_ring->OrdSgn;
6078 if ((r->ref<=0)&&(r->order!=
NULL))
6088 if (j==0)
WarnS(
"killing the basering for level 0");
6093 while (r->idroot!=
NULL)
6096 killhdl2(r->idroot,&(r->idroot),r);
6143 Warn(
"deleting denom_list for ring change from %s",
IDID(h));
6208 resid=(ideal)(res.
data);
6261 ideal I=(ideal)u->
Data();
6264 for(i=I->nrows*I->ncols-1;i>=0;i--)
6276 switch (p->language)
6285 if(p->libname!=
NULL)
6286 Print(
",%s", p->libname);
6299 memset(&tmp_in,0,
sizeof(tmp_in));
6301 tmp_in.
data=(
void*)(
long)(*aa)[
i];
6305 bo=
jjPROC(&tmp_out,proc,&tmp_in);
6309 Werror(
"apply fails at index %d",
i+1);
6312 if (
i==0) { memcpy(res,&tmp_out,
sizeof(tmp_out)); }
6317 memcpy(curr,&tmp_out,
sizeof(tmp_out));
6339 for(
int i=0;
i<=aa->
nr;
i++)
6341 memset(&tmp_in,0,
sizeof(tmp_in));
6342 tmp_in.
Copy(&(aa->
m[
i]));
6346 bo=
jjPROC(&tmp_out,proc,&tmp_in);
6351 Werror(
"apply fails at index %d",
i+1);
6354 if (
i==0) { memcpy(res,&tmp_out,
sizeof(tmp_out)); }
6359 memcpy(curr,&tmp_out,
sizeof(tmp_out));
6366 memset(res,0,
sizeof(
sleftv));
6382 WerrorS(
"first argument to `apply` must allow an index");
6392 char assume_yylinebuf[80];
6394 int lev=(long)a->
Data();
6401 if (bo) {
WerrorS(
"syntax error in ASSUME");
return TRUE;}
6415 char *ss=(
char*)
omAlloc(strlen(a)+strlen(s)+30);
6417 int end_s=strlen(s);
6418 while ((end_s>0) && ((s[end_s]<=
' ')||(s[end_s]==
';'))) end_s--;
6420 char *
name=(
char *)
omAlloc(strlen(a)+strlen(s)+30);
6421 sprintf(name,
"%s->%s",a,s);
6423 int start_s=end_s-1;
6424 while ((start_s>=0) && (s[start_s]!=
';')) start_s--;
6427 sprintf(ss,
"parameter def %s;return(%s);\n",a,s);
6432 sprintf(ss,
"parameter def %s;%s;return(%s);\n",a,s,s+start_s+1);
6434 memset(r,0,
sizeof(*r));
6454 memset(&tmp,0,
sizeof(tmp));
6472 memset(&n,0,
sizeof(n));
6490 sprintf(buf,
"wrong length of parameters(%d), expected ",t);
6492 sprintf(buf,
"par. %d is of type `%s`, expected ",nr,
Tok2Cmdname(t));
6493 for(
int i=1;
i<=T[0];
i++)
6498 if (i<T[0]) strcat(buf,
",");
6508 if (type_list[0]==0)
return TRUE;
6511 if (l!=(
int)type_list[0])
6516 for(
int i=1;
i<=
l;
i++,args=args->
next)
6518 short t=type_list[
i];
6522 || (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)
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)
ring rCompose(const lists L, const BOOLEAN check_comp, const long bitmask)
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)
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)
#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...
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.
BOOLEAN iiBranchTo(leftv, leftv args)
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)
for(int i=0;i<=n;i++) degsf[i]
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)
#define __pp_Mult_nn(p, n, r)
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)
#define __p_Mult_nn(p, n, 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)
static BOOLEAN length(leftv result, leftv arg)
int iiOpsTwoChar(const char *s)
BOOLEAN jjMINRES(leftv res, leftv v)
void CleanUp(ring r=currRing)
void Clean(ring r=currRing)
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
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)