24 #define TRANSEXT_PRIVATES 170 p->exp[o->
data.dp.place]=ord;
181 int *
w=o->
data.wp.weights;
183 for(
int i=a;
i<=e;
i++) ord+=((
unsigned long)
p_GetExp(p,
i,r))*((
unsigned long)w[
i-a]);
187 for(
int i=a;
i<=e;
i++)
197 p->exp[o->
data.wp.place]=ord;
203 const short a=o->
data.am.start;
204 const short e=o->
data.am.end;
205 const int *
w=o->
data.am.weights;
207 for(
short i=a;
i<=e;
i++, w++)
212 for(
short i=a;
i<=e;
i++)
224 const short len_gen= o->
data.am.len_gen;
226 if ((c > 0) && (c <= len_gen))
229 assume( w[0] == len_gen );
233 p->exp[o->
data.am.place] = ord;
240 a=o->
data.wp64.start;
244 for(
int i=a;
i<=e;
i++)
251 if(ei!=0 && ai/ei!=wi)
255 Print(
"ai %lld, wi %lld\n",ai,wi);
257 Print(
"ai %ld, wi %ld\n",ai,wi);
265 Print(
"ai %lld, ord %lld\n",ai,ord);
267 Print(
"ai %ld, ord %ld\n",ai,ord);
272 long a_0=(long)(ord&mask);
273 long a_1=(long)(ord >>31 );
279 p->exp[o->
data.wp64.place]=a_1;
280 p->exp[o->
data.wp64.place+1]=a_0;
293 int pl=o->
data.cp.place;
294 for(
int i=a;
i<=e;
i++) { p->exp[pl]=
p_GetExp(p,
i,r); pl++; }
302 o->
data.syzcomp.Components);
304 o->
data.syzcomp.ShiftedComponents);
305 if (ShiftedComponents !=
NULL)
308 assume(c == 0 || Components[c] != 0);
309 sc = ShiftedComponents[Components[c]];
310 assume(c == 0 || sc != 0);
312 p->exp[o->
data.syzcomp.place]=sc;
318 const short place = o->
data.syz.place;
319 const int limit = o->
data.syz.limit;
321 if (c > (
unsigned long)limit)
322 p->exp[place] = o->
data.syz.curr_index;
325 assume( (1 <= c) && (c <= (
unsigned long)limit) );
326 p->exp[place]= o->
data.syz.syz_index[c];
342 Print(
"p_Setm_General: ro_isTemp ord: pos: %d, p: ", pos);
p_wrp(p, r);
351 const int*
const pVarOffset = o->
data.isTemp.pVarOffset;
356 for(
int i = 1;
i <= r->N;
i++ )
358 const int vo = pVarOffset[
i];
368 for(
int i = 1;
i <= r->N;
i++ )
370 const int vo = pVarOffset[
i];
390 Print(
"p_Setm_General: ro_is ord: pos: %d, p: ", pos);
p_wrp(p, r);
399 const ideal F = o->
data.is.F;
400 const int limit = o->
data.is.limit;
402 const int start = o->
data.is.start;
404 if( F !=
NULL && c > limit )
408 Print(
"p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit);
409 PrintS(
"preComputed Values: ");
428 const poly
pp = F->m[c];
437 Print(
"Respective F[c - %d: %d] pp: ", limit, c);
442 const int end = o->
data.is.end;
450 Print(
"p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]);
456 for(
int i = start;
i <= end;
i++)
457 p->exp[
i] += pp->exp[
i];
460 if (r->NegWeightL_Offset !=
NULL)
462 for (
int i=r->NegWeightL_Size-1;
i>=0;
i--)
464 const int _i = r->NegWeightL_Offset[
i];
465 if( start <= _i && _i <= end )
472 const int*
const pVarOffset = o->
data.is.pVarOffset;
476 for(
int i = 1;
i <= r->N;
i++ )
478 const int vo = pVarOffset[
i];
492 const int*
const pVarOffset = o->
data.is.pVarOffset;
497 const int vo = pVarOffset[0];
503 Print(
"ELSE p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]);
516 if (pos == r->OrdSize)
return;
521 void p_Setm_Syz(poly
p, ring r,
int* Components,
long* ShiftedComponents)
557 if (r->typ[0].ord_typ ==
ro_dp &&
558 r->typ[0].data.dp.start == 1 &&
559 r->typ[0].data.dp.end == r->N &&
560 r->typ[0].data.dp.place == r->pOrdIndex)
562 if (r->typ[0].ord_typ ==
ro_wp &&
563 r->typ[0].data.wp.start == 1 &&
564 r->typ[0].data.wp.end == r->N &&
565 r->typ[0].data.wp.place == r->pOrdIndex &&
566 r->typ[0].data.wp.weights == r->firstwv)
591 for (i=1; i<= r->firstBlockEnds; i++)
593 sum +=
p_GetExp(p, i, r)*r->firstwv[i-1];
610 for (i=0;r->order[
i]!=0;i++)
617 for (k=b0 ;k<=b1 ;k++)
619 j+=
p_GetExp(p,k,r)*r->wvhdl[
i][k - b0 ]*r->OrdSgn;
626 for (k=b0 ;k<=b1 ;k++)
628 j+=
p_GetExp(p,k,r)*r->wvhdl[
i][k - b0 ];
635 for (k=b0 ;k<=b1 ;k++)
637 j+=
p_GetExp(p,k,r)*r->wvhdl[
i][k - b0 ];
648 for (k=b0 ;k<=b1 ;k++)
656 for (k=0;k<=(b1 - b0 );k++)
697 if ((r->firstwv==
NULL) || (i>r->firstBlockEnds))
701 return r->firstwv[i-1];
711 for(i=1;i<=r->firstBlockEnds;i++)
712 j+=
p_GetExp(p, i, r)*r->firstwv[i-1];
714 for (;i<=
rVar(r);i++)
752 return r->pFDeg(p, r);
805 long o = r->pFDeg(p, r);
881 if ((t=r->pFDeg(p, r))>max) max=t;
891 if ((t=r->pFDeg(p, r))>max) max=t;
1096 static inline unsigned long 1098 unsigned long number_of_exp)
1100 const unsigned long bitmask = r->bitmask;
1101 unsigned long ml1 = l1 & bitmask;
1102 unsigned long ml2 = l2 & bitmask;
1103 unsigned long max = (ml1 > ml2 ? ml1 : ml2);
1104 unsigned long j = number_of_exp - 1;
1108 unsigned long mask = bitmask << r->BitsPerExp;
1113 max |= ((ml1 > ml2 ? ml1 : ml2) & mask);
1116 mask = mask << r->BitsPerExp;
1122 static inline unsigned long 1136 unsigned long l_p, l_max;
1137 unsigned long divmask = r->divmask;
1141 offset = r->VarL_Offset[0];
1143 l_max = max->exp[
offset];
1146 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1149 for (i=1; i<r->VarL_Size; i++)
1151 offset = r->VarL_Offset[
i];
1153 l_max = max->exp[
offset];
1156 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1167 unsigned long l_p, divmask = r->divmask;
1172 l_p = p->exp[r->VarL_Offset[0]];
1174 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1176 for (i=1; i<r->VarL_Size; i++)
1178 l_p = p->exp[r->VarL_Offset[
i]];
1181 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1247 if((k!=-1)&&(k!=i))
return 0;
1264 for(i=r->N; i>0; i--)
1360 const char *
p_Read(
const char *st, poly &rc,
const ring r)
1373 while (*s!=
'\0') s++;
1385 const char *s_save=
s;
1387 if (((
unsigned long)i) > r->bitmask/2)
1418 for(
unsigned int k = iFirstAltVar;
k <= iLastAltVar;
k++)
1438 if ((s!=st)&&isdigit(st[0]))
1480 for(i=(
int)r->N; i; i--)
1569 WerrorS(
"not implemented for letterplace rings");
1620 for(
int i = (
int)
rVar(r);
i>0;
i--)
1623 if (exponent < 0)
return FALSE;
1630 void p_Lcm(
const poly a,
const poly
b, poly
m,
const ring r)
1632 for (
int i=r->N;
i; --
i)
1639 poly
p_Lcm(
const poly a,
const poly
b,
const ring r)
1647 #ifdef HAVE_RATGRING 1652 poly
p_LcmRat(
const poly a,
const poly
b,
const long lCompM,
const ring r)
1660 for (
int i = r->real_var_end;
i>=r->real_var_start;
i--)
1727 poly *C = (poly *)
omAlloc0((len+1)*
sizeof(poly));
1728 poly *LM = (poly *)
omAlloc0((len+1)*
sizeof(poly));
1729 int *
D = (
int *)
omAlloc0((len+1)*
sizeof(int));
1730 int *L = (
int *)
omAlloc0((len+1)*
sizeof(int));
1736 int HasConstantCoef = 0;
1737 int is = r->real_var_start - 1;
1743 mintdeg =
si_min(mintdeg,D[k]);
1745 minlen =
si_min(minlen,L[k]);
1749 HasConstantCoef = 1;
1759 int mindeglen = len;
1771 if (D[i] == mintdeg)
1773 if (L[i] < mindeglen)
1780 d =
p_Copy(C[pmindeglen], r);
1852 int divisorLE =
p_GetExp(divisor, 1, r);
1860 int e =
p_GetExp(p, 1, r) - divisorLE;
1915 for(i=
rVar(r);i>0;i--)
1965 poly
p_Sub(poly p1, poly p2,
const ring r)
1987 for (i=
rVar(r); i!=0; i--)
2045 bin = (number *)
omAlloc0(h*
sizeof(number));
2054 y =
n_Mult(x,bin[e-1],r->cf);
2066 int e,
h = (exp >> 1) + 1;
2086 poly tail,
b,
res,
h;
2088 number *bin =
pnBin(exp,r);
2099 al = (exp + 1) *
sizeof(poly);
2102 for (e=1; e<
exp; e++)
2108 for (e=exp-1; e>eh; e--)
2117 for (e=eh; e!=0; e--)
2184 if ( (i > 0) && ((
unsigned long ) i > (r->bitmask))
2185 #ifdef HAVE_SHIFTBBA
2190 Werror(
"exponent %d is too large, max. is %ld",i,r->bitmask);
2234 int char_p=
rChar(r);
2235 if ((char_p>0) && (i>char_p)
2241 while (rest>=char_p)
2255 return p_Pow(p,i,r);
2256 if ((char_p==0) || (i<=char_p))
2258 return p_Pow(p,i,r);
2272 if (ph==
NULL)
return;
2278 if (cf->cfSubringGcd==
ndGcd)
return;
2283 goto content_finish;
2295 goto content_finish;
2313 #define CLEARENUMERATORS 1 2323 #if CLEARENUMERATORS 2376 #if CLEARENUMERATORS 2441 h =
n_Init(1, r->cf->extRing->cf);
2458 if(!
n_IsOne(h,r->cf->extRing->cf))
2523 #if 1 // currently only used by Singular/janet 2527 if (ph==
NULL)
return;
2538 if (
n_Size(d,r->cf)<=smax)
2546 if (smax==1) smax=2;
2605 d=
nlAdd(n1,t,r->cf);
2607 d=
nlSub(n1,t,r->cf);
2616 d=
nlAdd(n2,t,r->cf);
2618 d=
nlSub(n2,t,r->cf);
2625 d=
nlGcd(n1,n2,r->cf);
2641 if (s<s2)
return n_Copy(d,r->cf);
2642 else return n_Copy(d2,r->cf);
2798 #if CLEARENUMERATORS 2841 #if 0 && CLEARENUMERATORS 2885 #ifdef HAVE_RATGRING 2909 #if CLEARENUMERATORS 2962 #if CLEARENUMERATORS 3062 number t=
n_Mult(c,h,r->cf);
3150 fraction
f = (fraction) h;
3151 number n=
p_GetCoeff (NUM (f),C->extRing->cf);
3161 if (!
n_IsOne (n, C->extRing->cf))
3165 nMap=
n_SetMap (C->extRing->cf, C);
3166 number ninv= nMap (n,C->extRing->cf, C);
3179 number p_GetAllDenom(poly ph,
const ring r)
3181 number d=
n_Init(1,r->cf);
3189 number dd=
n_Mult(d,h,r->cf);
3203 if (r->cf->has_simple_Alloc)
3231 if ((varnum < 1) || (varnum >
rVar(r)))
3280 if (d(qp,r) != o)
return FALSE;
3332 if ((*len == 0) || (j<*len))
3432 pNext(qq) = pNext_q;
3508 if (*p==
NULL)
return;
3557 for(
int i=len-1;
i>=0;
i--) p[
i]=
NULL;
3562 if (k>len) {
Werror(
"wrong rank:%d, should be %d",len,k); }
3567 pNext(h)=p[k-1];p[k-1]=
h;
3571 for(
int i=len-1;
i>=0;
i--)
3588 if (*len==0) *len=1;
3589 *p=(poly*)
omAlloc((*len)*
sizeof(poly));
3600 r->pFDeg = new_FDeg;
3602 if (new_lDeg ==
NULL)
3603 new_lDeg = r->pLDegOrig;
3605 r->pLDeg = new_lDeg;
3612 r->pFDeg = old_FDeg;
3613 r->pLDeg = old_lDeg;
3628 if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1];
3638 pOldFDeg = r->pFDeg;
3639 pOldLDeg = r->pLDeg;
3640 pOldLexOrder = r->pLexOrder;
3642 r->pLexOrder =
TRUE;
3662 if (increment==0)
return;
3663 h=(poly*)
omAlloc0(increment*
sizeof(poly));
3667 h=(poly*)
omReallocSize((poly*)*
p,l*
sizeof(poly),(l+increment)*
sizeof(poly));
3670 memset(&(h[l]),0,increment*
sizeof(poly));
3789 while (non_zero !=
NULL)
3797 result =
p_Add_q(result,qq,r);
3813 poly zero, non_zero;
3818 while (non_zero !=
NULL)
3838 result =
p_Add_q(result,qq,r);
3909 for(i=
rVar(r);i>0;i--)
3910 me[i]+=exponent*ee[i];
3933 poly
n_PermNumber(
const number z,
const int *par_perm,
const int ,
const ring src,
const ring dst)
3936 PrintS(
"\nSource Ring: \n");
3941 number zz =
n_Copy(z, src->cf);
3946 PrintS(
"\nDestination Ring: \n");
3958 const coeffs srcCf = src->cf;
3966 const ring srcExtRing = srcCf->extRing;
3969 const coeffs dstCf = dst->cf;
3981 zz = NUM((fraction)z);
3985 if( !DENIS1((fraction)z) )
3988 WarnS(
"Not defined: Cannot map a rational fraction and make a polynomial out of it! Ignoring the denominator.");
3994 WerrorS(
"Number permutation is not implemented for this data yet!");
4006 if ((par_perm ==
NULL) && (
rPar(dst) != 0 &&
rVar (srcExtRing) > 0))
4009 perm=(
int *)
omAlloc0((
rVar(srcExtRing)+1)*
sizeof(int));
4019 && (!DENIS1((fraction)z))
4022 number n=nMap(
pGetCoeff(DEN((fraction)z)),srcExtRing->cf, dstCf);
4036 poly
p_PermPoly (poly
p,
const int * perm,
const ring oldRing,
const ring dst,
4043 const int OldpVariables =
rVar(oldRing);
4045 poly result_last =
NULL;
4051 poly tmp_mm=
p_One(dst);
4061 number n = nMap(
p_GetCoeff(p, oldRing), oldRing->cf, dst->cf);
4090 int mapped_to_par = 0;
4091 for(
int i = 1;
i <= OldpVariables;
i++)
4121 n_Power(ee, e, &eee, dst->cf);
4122 ee =
n_Mult(c, eee, dst->cf);
4128 const int par = -perm[
i];
4132 const coeffs C = dst->cf;
4134 const ring
R = C->extRing;
4142 pcn = NUM((fraction)c);
4203 if (result_last==
NULL)
4209 pNext(result_last)=qq;
4412 p=
p_JetW(
p_Mult_q(p,
p_Invers(n-
p_MinDeg(p,w,R),u,w,R),R),n,ww,R);
4420 while ((p1 !=
NULL) && (p2 !=
NULL))
4439 int i = r1->ExpL_Size;
4441 assume( r1->ExpL_Size == r2->ExpL_Size );
4443 unsigned long *ep = p1->exp;
4444 unsigned long *eq = p2->exp;
4449 if (ep[i] != eq[i])
return FALSE;
4459 assume( r1->cf == r2->cf );
4461 while ((p1 !=
NULL) && (p2 !=
NULL))
4502 while ((p1 !=
NULL) )
4564 if (m==
NULL)
return 0;
4567 for (i=
rVar(r); i>0; i--)
4590 if (p ==
NULL)
return -1;
4597 while ((l < (
rVar(r))) && (lex == 0))
4614 poly qp1 = *
p,qp2 = *
p;
4618 BOOLEAN toPoly= ((j == -
i) && (j ==
k));
4639 qp2->next = qp1->next;
4655 const unsigned int s,
const unsigned int n)
4657 #define Sy_bit_L(x) (((unsigned long)1L)<<(x)) 4659 unsigned long ev = 0L;
4664 if (e > (
long) i) ev |=
Sy_bit_L(s+i);
4690 unsigned long ev = 0;
4704 for (;
j<=r->N;
j++)
4744 unsigned long ev = 0;
4748 unsigned long i = 0L;
4759 for (; j<=r->N; j++)
4802 #define p_Delete__T p_ShallowDelete 4804 #define n_Delete__T(n, r) do {} while (0) 4815 if ((r==0)&&(a!=
NULL))
4853 int *mf=(
int*)
omAlloc((r->N+1)*
sizeof(int));
4855 int *mh=(
int*)
omAlloc((r->N+1)*
sizeof(int));
4869 for(
unsigned j=r->N;
j!=0;
j--)
4871 if (mh[
j]<mf[
j]) mf[
j]=mh[
j];
4872 if (mf[j]>0) const_mon=
FALSE;
4874 if (one_coeff && const_mon)
break;
#define p_LmCheckPolyRing2(p, r)
int status int void size_t count
static FORCE_INLINE number n_Sub(number a, number b, const coeffs r)
return the difference of 'a' and 'b', i.e., a-b
BOOLEAN p_VectorHasUnitB(poly p, int *k, const ring r)
#define __p_GetComp(p, r)
void p_SetModDeg(intvec *w, ring r)
for idElimination, like a, except pFDeg, pWeigths ignore it
unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max)
return the maximal exponent of p in form of the maximal long var
static FORCE_INLINE number n_GetNumerator(number &n, const coeffs r)
return the numerator of n (if elements of r are by nature not fractional, result is n) ...
static FORCE_INLINE number n_GetUnit(number n, const coeffs r)
in Z: 1 in Z/kZ (where k is not a prime): largest divisor of n (taken in Z) that is co-prime with k i...
LINLINE number nlSub(number la, number li, const coeffs r)
static unsigned long p_AddComp(poly p, unsigned long v, ring r)
static FORCE_INLINE number n_Gcd(number a, number b, const coeffs r)
in Z: return the gcd of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ...
void p_Setm_General(poly p, const ring r)
const CanonicalForm int s
poly p_Diff(poly a, int k, const ring r)
static poly p_MonPower(poly p, int exp, const ring r)
const char * eati(const char *s, int *i)
const CanonicalForm int const CFList const Variable & y
int p_GetVariables(poly p, int *e, const ring r)
set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 return #(e[i]>0) ...
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
static FORCE_INLINE BOOLEAN n_IsUnit(number n, const coeffs r)
TRUE iff n has a multiplicative inverse in the given coeff field/ring r.
static FORCE_INLINE const char * n_Read(const char *s, number *a, const coeffs r)
!!! Recommendation: This method is too cryptic to be part of the user- !!! interface. As defined here, it is merely a helper !!! method for parsing number input strings.
#define POLY_NEGWEIGHT_OFFSET
long pLDeg1(poly p, int *l, const ring r)
static int p_Cmp(poly p1, poly p2, ring r)
static poly p_LmDeleteAndNext(poly p, const ring r)
number ndGcd(number, number, const coeffs r)
static BOOLEAN rField_is_Zp_a(const ring r)
long pLDeg1c_Totaldegree(poly p, int *l, const ring r)
poly p_Div_mm(poly p, const poly m, const ring r)
divide polynomial by monomial
BOOLEAN p_ComparePolys(poly p1, poly p2, const ring r)
returns TRUE if p1 is a skalar multiple of p2 assume p1 != NULL and p2 != NULL
p_SetmProc p_GetSetmProc(const ring r)
gmp_float exp(const gmp_float &a)
BOOLEAN nlGreaterZero(number za, const coeffs r)
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
static int si_min(const int a, const int b)
long pLDeg1c(poly p, int *l, const ring r)
static BOOLEAN pOldLexOrder
poly p_Homogen(poly p, int varnum, const ring r)
void p_Split(poly p, poly *h)
void p_VectorHasUnit(poly p, int *k, int *len, const ring r)
short * iv2array(intvec *iv, const ring R)
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
BOOLEAN p_IsHomogeneous(poly p, const ring r)
static int rPar(const ring r)
(r->cf->P)
static poly p_Mult_mm(poly p, poly m, const ring r)
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
static long p_IncrExp(poly p, int v, ring r)
void p_Setm_WFirstTotalDegree(poly p, const ring r)
int p_MinDeg(poly p, intvec *w, const ring R)
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
poly p_GcdMon(poly f, poly g, const ring r)
polynomial gcd for f=mon
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
static BOOLEAN rIsSyzIndexRing(const ring r)
static int _componentsExternal
static poly p_DiffOpM(poly a, poly b, BOOLEAN multiply, const ring r)
static int rGetCurrSyzLimit(const ring r)
static BOOLEAN rIsRatGRing(const ring r)
#define TEST_OPT_CONTENTSB
long p_WDegree(poly p, const ring r)
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
static long pModDeg(poly p, ring r)
static void p_GetExpV(poly p, int *ev, const ring r)
#define omFreeSize(addr, size)
LINLINE number nlAdd(number la, number li, const coeffs r)
static poly p_Subst1(poly p, int n, const ring r)
void nlInpGcd(number &a, number b, const coeffs r)
static short rVar(const ring r)
#define rVar(r) (r->N)
long pLDeg0c(poly p, int *l, const ring r)
void sBucketDestroyAdd(sBucket_pt bucket, poly *p, int *length)
poly p_Div_nn(poly p, const number n, const ring r)
void p_Lcm(const poly a, const poly b, poly m, const ring r)
static BOOLEAN rField_is_Q_a(const ring r)
number nlGcd(number a, number b, const coeffs r)
void p_ContentForGB(poly ph, const ring r)
static void p_MonMult(poly p, poly q, const ring r)
static long p_Totaldegree(poly p, const ring r)
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
poly p_Subst(poly p, int n, poly e, const ring r)
void WerrorS(const char *s)
void p_Setm_TotalDegree(poly p, const ring r)
static FORCE_INLINE number n_NormalizeHelper(number a, number b, const coeffs r)
assume that r is a quotient field (otherwise, return 1) for arguments (a1/a2,b1/b2) return (lcm(a1...
poly p_TakeOutComp1(poly *p, int k, const ring r)
static BOOLEAN rField_is_GF(const ring r)
void p_Norm(poly p1, const ring r)
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
void p_SimpleContent(poly ph, int smax, const ring r)
static long p_MultExp(poly p, int v, long ee, ring r)
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy ...
long pLDeg1_Deg(poly p, int *l, const ring r)
static BOOLEAN rIsLPRing(const ring r)
poly singclap_pdivide(poly f, poly g, const ring r)
static poly p_TwoMonPower(poly p, int exp, const ring r)
static number p_SetCoeff(poly p, number n, ring r)
poly p_Sub(poly p1, poly p2, const ring r)
long(* pLDegProc)(poly p, int *length, ring r)
static void p_LmFree(poly p, ring)
static void p_SetExpV(poly p, int *ev, const ring r)
static poly p_Copy(poly p, const ring r)
returns a copy of p
static FORCE_INLINE BOOLEAN nCoeff_is_Q_a(const coeffs r)
long totaldegreeWecart_IV(poly p, ring r, const short *w)
long pLDeg1c_Deg(poly p, int *l, const ring r)
static BOOLEAN rField_has_simple_inverse(const ring r)
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
static FORCE_INLINE number n_Param(const int iParameter, const coeffs r)
return the (iParameter^th) parameter as a NEW number NOTE: parameter numbering: 1..n_NumberOfParameters(...)
void p_Cleardenom_n(poly ph, const ring r, number &c)
int p_IsUnivariate(poly p, const ring r)
return i, if poly depends only on var(i)
poly pp_JetW(poly p, int m, short *w, const ring R)
static poly p_SortAdd(poly p, const ring r, BOOLEAN revert=FALSE)
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
BOOLEAN p_CheckPolyRing(poly p, ring r)
int p_Weight(int i, const ring r)
#define omReallocSize(addr, o_size, size)
const char * p_Read(const char *st, poly &rc, const ring r)
void p_ContentRat(poly &ph, const ring r)
static FORCE_INLINE void n_ClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
Computes the content and (inplace) divides it out on a collection of numbers number c is the content ...
static poly p_Head(poly p, const ring r)
long p_DegW(poly p, const short *w, const ring R)
void p_Setm_Syz(poly p, ring r, int *Components, long *ShiftedComponents)
int r_IsRingVar(const char *n, char **names, int N)
long p_Deg(poly a, const ring r)
poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r)
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)
void p_Vec2Array(poly v, poly *p, int len, const ring r)
vector to already allocated array (len>=p_MaxComp(v,r))
int p_Size(poly p, const ring r)
static int p_Comp_k_n(poly a, poly b, int k, ring r)
poly p_Farey(poly p, number N, const ring r)
#define TEST_OPT_INTSTRATEGY
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
static void p_SetCompP(poly p, int i, ring r)
const CanonicalForm CFMap CFMap & N
Concrete implementation of enumerators over polynomials.
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent : the integer VarOffset encodes:
static int max(int a, int b)
This is a polynomial enumerator for simple iteration over coefficients of polynomials.
void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg)
number ntInit(long i, const coeffs cf)
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
static BOOLEAN p_IsConstant(const poly p, const ring r)
The main handler for Singular numbers which are suitable for Singular polynomials.
void p_LmDeleteAndNextRat(poly *p, int ishift, ring r)
static poly p_MonMultC(poly p, poly q, const ring rr)
long p_WFirstTotalDegree(poly p, const ring r)
for(int i=0;i<=n;i++) degsf[i]
static poly p_Subst0(poly p, int n, const ring r)
void p_Vec2Polys(poly v, poly **p, int *len, const ring r)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
static FORCE_INLINE BOOLEAN n_DivBy(number a, number b, const coeffs r)
test whether 'a' is divisible 'b'; for r encoding a field: TRUE iff 'b' does not represent zero in Z:...
long pLDeg0(poly p, int *l, const ring r)
static FORCE_INLINE number n_ChineseRemainderSym(number *a, number *b, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs r)
sBucket_pt sBucketCreate(const ring r)
static FORCE_INLINE void n_Write(number n, const coeffs r, const BOOLEAN bShortOut=TRUE)
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
poly p_Jet(poly p, int m, const ring R)
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
poly singclap_gcd(poly f, poly g, const ring r)
polynomial gcd via singclap_gcd_r resp. idSyzygies destroys f and g
void p_Setm_Dummy(poly p, const ring r)
static int p_LmCmp(poly p, poly q, const ring r)
static FORCE_INLINE number n_Invers(number a, const coeffs r)
return the multiplicative inverse of 'a'; raise an error if 'a' is not invertible ...
BOOLEAN rSamePolyRep(ring r1, ring r2)
returns TRUE, if r1 and r2 represents the monomials in the same way FALSE, otherwise this is an analo...
static FORCE_INLINE number n_InpNeg(number n, const coeffs r)
in-place negation of n MUST BE USED: n = n_InpNeg(n) (no copy is returned)
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.
static number * pnBin(int exp, const ring r)
poly p_GetCoeffRat(poly p, int ishift, ring r)
int p_Compare(const poly a, const poly b, const ring R)
Induced (Schreyer) ordering.
void PrintS(const char *s)
static void p_ExpVectorSub(poly p1, poly p2, const ring r)
void(* p_SetmProc)(poly p, const ring r)
static BOOLEAN rField_is_Q(const ring r)
int p_LowVar(poly p, const ring r)
the minimal index of used variables - 1
#define p_LmCheckPolyRing1(p, r)
static long p_MinComp(poly p, ring lmRing, ring tailRing)
static void p_ExpVectorAdd(poly p1, poly p2, const ring r)
BOOLEAN rOrd_SetCompRequiresSetm(const ring r)
return TRUE if p_SetComp requires p_Setm
static poly p_LmFreeAndNext(poly p, ring)
void rWrite(ring r, BOOLEAN details)
static unsigned pLength(poly a)
void p_Content(poly ph, const ring r)
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
static FORCE_INLINE BOOLEAN nCoeff_is_GF(const coeffs r)
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
static poly p_Pow(poly p, int i, const ring r)
poly p_JetW(poly p, int m, short *w, const ring R)
poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r)
assumes that p and divisor are univariate polynomials in r, mentioning the same variable; assumes div...
static short scaFirstAltVar(ring r)
static poly pReverse(poly p)
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
number p_InitContent(poly ph, const ring r)
poly p_Series(int n, poly p, poly u, intvec *w, const ring R)
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
static unsigned long p_SubComp(poly p, unsigned long v, ring r)
void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg)
static long p_GetOrder(poly p, ring r)
static BOOLEAN rField_is_Zp(const ring r)
static FORCE_INLINE number n_Farey(number a, number b, const coeffs r)
BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r)
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
void p_Normalize(poly p, const ring r)
#define rRing_has_Comp(r)
static void p_Delete(poly *p, const ring r)
void nlNormalize(number &x, const coeffs r)
poly p_mInit(const char *st, BOOLEAN &ok, const ring r)
unsigned long p_GetShortExpVector(const poly p, const ring r)
#define p_LmEqual(p1, p2, r)
const Variable & v
< [in] a sqrfree bivariate poly
static unsigned long GetBitFields(const long e, const unsigned int s, const unsigned int n)
BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r)
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent : VarOffset encodes the position in p->exp
poly p_DivideM(poly a, poly b, const ring r)
BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r)
divisibility check over ground ring (which may contain zero divisors); TRUE iff LT(f) divides LT(g)...
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
static FORCE_INLINE void n_Power(number a, int b, number *res, const coeffs r)
fill res with the power a^b
#define __p_Mult_nn(p, n, r)
static pLDegProc pOldLDeg
long pLDegb(poly p, int *l, const ring r)
static BOOLEAN rField_is_Ring(const ring r)
void pEnlargeSet(poly **p, int l, int increment)
long pLDeg1_Totaldegree(poly p, int *l, const ring r)
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
BOOLEAN p_LmCheckPolyRing(poly p, ring r)
poly n_PermNumber(const number z, const int *par_perm, const int, const ring src, const ring dst)
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic ...
LINLINE void nlDelete(number *a, const coeffs r)
poly p_Last(const poly p, int &l, const ring r)
static FORCE_INLINE number n_Div(number a, number b, const coeffs r)
return the quotient of 'a' and 'b', i.e., a/b; raises an error if 'b' is not invertible in r exceptio...
long(* pFDegProc)(poly p, ring r)
static poly p_Pow_charp(poly p, int i, const ring r)
static pFDegProc pOldFDeg
static short scaLastAltVar(ring r)
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
static FORCE_INLINE number n_GetDenom(number &n, const coeffs r)
return the denominator of n (if elements of r are by nature not fractional, result is 1) ...
static bool rIsSCA(const ring r)
static FORCE_INLINE BOOLEAN n_Equal(number a, number b, const coeffs r)
TRUE iff 'a' and 'b' represent the same number; they may have different representations.
static poly p_LmInit(poly p, const ring r)
static FORCE_INLINE number n_ExactDiv(number a, number b, const coeffs r)
assume that there is a canonical subring in cf and we know that division is possible for these a and ...
static void p_Setm(poly p, const ring r)
poly p_DiffOp(poly a, poly b, BOOLEAN multiply, const ring r)
static long p_AddExp(poly p, int v, long ee, ring r)
long pLDeg1_WFirstTotalDegree(poly p, int *l, const ring r)
static poly p_GetExp_k_n(poly p, int l, int k, const ring r)
static FORCE_INLINE number n_SubringGcd(number a, number b, const coeffs r)
poly p_MDivide(poly a, poly b, const ring r)
long pLDeg1c_WFirstTotalDegree(poly p, int *l, const ring r)
poly p_Vec2Poly(poly v, int k, const ring r)
int dReportError(const char *fmt,...)
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
static long * _componentsShifted
static unsigned long p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, unsigned long number_of_exp)
static poly p_Neg(poly p, const ring r)
static void p_LmDelete(poly p, const ring r)
static poly p_Invers(int n, poly u, intvec *w, const ring R)
int exponent(const CanonicalForm &f, int q)
int exponent ( const CanonicalForm & f, int q )
static poly p_Subst2(poly p, int n, number e, const ring r)
long p_WTotaldegree(poly p, const ring r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
void p_wrp(poly p, ring lmRing, ring tailRing)
poly pp_Jet(poly p, int m, const ring R)
poly nc_pSubst(poly p, int n, poly e, const ring r)
substitute the n-th variable by e in p destroy p e is not a constant
void p_Write(poly p, ring lmRing, ring tailRing)
static FORCE_INLINE BOOLEAN n_GreaterZero(number n, const coeffs r)
ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2), where m is the long representing n in C: TRUE iff (Im(n) != 0 and Im(n) >= 0) or (Im(n) == 0 and Re(n) >= 0) in K(a)/<p(a)>: TRUE iff (n != 0 and (LC(n) > 0 or deg(n) > 0)) in K(t_1, ..., t_n): TRUE iff (LC(numerator(n) is a constant and > 0) or (LC(numerator(n) is not a constant) in Z/2^kZ: TRUE iff 0 < n <= 2^(k-1) in Z/mZ: TRUE iff the internal mpz is greater than zero in Z: TRUE iff n > 0
static void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r)
static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r)
static BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r1, const ring r2)
static long p_DecrExp(poly p, int v, ring r)
static poly p_Add_q(poly p, poly q, const ring r)
static BOOLEAN rField_has_Units(const ring r)
void sBucket_Add_m(sBucket_pt bucket, poly p)
poly p_TakeOutComp(poly *p, int k, const ring r)
static BOOLEAN rIsNCRing(const ring r)
static poly p_Init(const ring r, omBin bin)
poly p_Cleardenom(poly p, const ring r)
int p_Var(poly m, const ring r)
static FORCE_INLINE int n_Size(number n, const coeffs r)
return a non-negative measure for the complexity of n; return 0 only when n represents zero; (used fo...
void p_ProjectiveUnique(poly ph, const ring r)
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
static poly p_Mult_q(poly p, poly q, const ring r)
poly p_Power(poly p, int i, const ring r)
void Werror(const char *fmt,...)
void p_DeleteComp(poly *p, int k, const ring r)
static FORCE_INLINE void n_ClearDenominators(ICoeffsEnumerator &numberCollectionEnumerator, number &d, const coeffs r)
(inplace) Clears denominators on a collection of numbers number d is the LCM of all the coefficient d...
static long p_MaxComp(poly p, ring lmRing, ring tailRing)
BOOLEAN p_OneComp(poly p, const ring r)
return TRUE if all monoms have the same component
poly p_GetMaxExpP(poly p, const ring r)
return monomial r such that GetExp(r,i) is maximum of all monomials in p; coeff == 0...
static void pnFreeBin(number *bin, int exp, const coeffs r)