25 #define TRANSEXT_PRIVATES 181 p->exp[o->
data.dp.place]=ord;
192 int *
w=o->
data.wp.weights;
194 for(
int i=a;
i<=e;
i++) ord+=((
unsigned long)
p_GetExp(p,
i,r))*((
unsigned long)w[
i-
a]);
198 for(
int i=a;
i<=e;
i++)
208 p->exp[o->
data.wp.place]=ord;
214 const short a=o->
data.am.start;
215 const short e=o->
data.am.end;
216 const int *
w=o->
data.am.weights;
218 for(
short i=a;
i<=e;
i++, w++)
223 for(
short i=a;
i<=e;
i++)
235 const short len_gen= o->
data.am.len_gen;
237 if ((c > 0) && (c <= len_gen))
240 assume( w[0] == len_gen );
244 p->exp[o->
data.am.place] = ord;
251 a=o->
data.wp64.start;
255 for(
int i=a;
i<=e;
i++)
262 if(ei!=0 && ai/ei!=wi)
266 Print(
"ai %lld, wi %lld\n",ai,wi);
268 Print(
"ai %ld, wi %ld\n",ai,wi);
276 Print(
"ai %lld, ord %lld\n",ai,ord);
278 Print(
"ai %ld, ord %ld\n",ai,ord);
283 long a_0=(long)(ord&mask);
284 long a_1=(long)(ord >>31 );
290 p->exp[o->
data.wp64.place]=a_1;
291 p->exp[o->
data.wp64.place+1]=a_0;
304 int pl=o->
data.cp.place;
305 for(
int i=a;
i<=e;
i++) { p->exp[pl]=
p_GetExp(p,
i,r); pl++; }
313 o->
data.syzcomp.Components);
315 o->
data.syzcomp.ShiftedComponents);
316 if (ShiftedComponents !=
NULL)
319 assume(c == 0 || Components[c] != 0);
320 sc = ShiftedComponents[Components[c]];
321 assume(c == 0 || sc != 0);
323 p->exp[o->
data.syzcomp.place]=sc;
329 const short place = o->
data.syz.place;
330 const int limit = o->
data.syz.limit;
332 if (c > (
unsigned long)limit)
333 p->exp[place] = o->
data.syz.curr_index;
336 assume( (1 <= c) && (c <= (
unsigned long)limit) );
337 p->exp[place]= o->
data.syz.syz_index[c];
353 Print(
"p_Setm_General: ro_isTemp ord: pos: %d, p: ", pos);
p_wrp(p, r);
362 const int*
const pVarOffset = o->
data.isTemp.pVarOffset;
367 for(
int i = 1;
i <= r->N;
i++ )
369 const int vo = pVarOffset[
i];
379 for(
int i = 1;
i <= r->N;
i++ )
381 const int vo = pVarOffset[
i];
401 Print(
"p_Setm_General: ro_is ord: pos: %d, p: ", pos);
p_wrp(p, r);
410 const ideal F = o->
data.is.F;
411 const int limit = o->
data.is.limit;
413 const int start = o->
data.is.start;
415 if( F !=
NULL && c > limit )
419 Print(
"p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit);
420 PrintS(
"preComputed Values: ");
448 Print(
"Respective F[c - %d: %d] pp: ", limit, c);
453 const int end = o->
data.is.end;
460 Print(
"p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]);
465 for(
int i = start;
i <= end;
i++)
466 p->exp[
i] += pp->exp[
i];
469 if (r->NegWeightL_Offset !=
NULL)
471 for (
int i=r->NegWeightL_Size-1;
i>=0;
i--)
473 const int _i = r->NegWeightL_Offset[
i];
474 if( start <= _i && _i <= end )
481 const int*
const pVarOffset = o->
data.is.pVarOffset;
485 for(
int i = 1;
i <= r->N;
i++ )
487 const int vo = pVarOffset[
i];
501 const int*
const pVarOffset = o->
data.is.pVarOffset;
506 const int vo = pVarOffset[0];
512 Print(
"ELSE p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]);
525 if (pos == r->OrdSize)
return;
566 if (r->typ[0].ord_typ ==
ro_dp &&
567 r->typ[0].data.dp.start == 1 &&
568 r->typ[0].data.dp.end == r->N &&
569 r->typ[0].data.dp.place == r->pOrdIndex)
571 if (r->typ[0].ord_typ ==
ro_wp &&
572 r->typ[0].data.wp.start == 1 &&
573 r->typ[0].data.wp.end == r->N &&
574 r->typ[0].data.wp.place == r->pOrdIndex &&
575 r->typ[0].data.wp.weights == r->firstwv)
600 for (i=1; i<= r->firstBlockEnds; i++)
602 sum +=
p_GetExp(p, i, r)*r->firstwv[i-1];
619 for (i=0;r->order[
i]!=0;i++)
626 for (k=b0 ;k<=b1 ;k++)
628 j+=
p_GetExp(p,k,r)*r->wvhdl[
i][k - b0 ]*r->OrdSgn;
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++)
672 for (k=b0 ;k<=b1 ;k++)
674 j+=
p_GetExp(p,k, r)*r->wvhdl[
i][ k- b0 ];
681 Print(
"missing order %d in p_WTotaldegree\n",r->order[i]);
706 if ((r->firstwv==
NULL) || (i>r->firstBlockEnds))
710 return r->firstwv[i-1];
720 for(i=1;i<=r->firstBlockEnds;i++)
721 j+=
p_GetExp(p, i, r)*r->firstwv[i-1];
723 for (;i<=
rVar(r);i++)
761 return r->pFDeg(p, r);
814 long o = r->pFDeg(p, r);
890 if ((t=r->pFDeg(p, r))>max) max=t;
900 if ((t=r->pFDeg(p, r))>max) max=t;
1105 static inline unsigned long 1107 unsigned long number_of_exp)
1109 const unsigned long bitmask = r->bitmask;
1110 unsigned long ml1 = l1 & bitmask;
1111 unsigned long ml2 = l2 & bitmask;
1112 unsigned long max = (ml1 > ml2 ? ml1 : ml2);
1113 unsigned long j = number_of_exp - 1;
1117 unsigned long mask = bitmask << r->BitsPerExp;
1122 max |= ((ml1 > ml2 ? ml1 : ml2) & mask);
1125 mask = mask << r->BitsPerExp;
1131 static inline unsigned long 1145 unsigned long l_p, l_max;
1146 unsigned long divmask = r->divmask;
1150 offset = r->VarL_Offset[0];
1152 l_max = max->exp[
offset];
1155 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1158 for (i=1; i<r->VarL_Size; i++)
1160 offset = r->VarL_Offset[
i];
1162 l_max = max->exp[
offset];
1165 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1176 unsigned long l_p, divmask = r->divmask;
1181 l_p = p->exp[r->VarL_Offset[0]];
1183 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1185 for (i=1; i<r->VarL_Size; i++)
1187 l_p = p->exp[r->VarL_Offset[
i]];
1190 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1229 if (p ==
NULL)
return 0;
1262 if((k!=-1)&&(k!=i))
return 0;
1279 for(i=r->N; i>0; i--)
1366 while (*s!=
'\0') s++;
1378 const char *s_save=
s;
1380 if (((
unsigned long)i) > r->bitmask/2)
1411 for(
unsigned int k = iFirstAltVar;
k <= iLastAltVar;
k++)
1431 if ((s!=st)&&isdigit(st[0]))
1473 for(i=(
int)r->N; i; i--)
1517 for(i=(
int)r->N; i; i--)
1562 for(
int i = (
int)
rVar(r);
i>0;
i--)
1565 if (exponent < 0)
return FALSE;
1583 #ifdef HAVE_RATGRING 1596 for (
int i = r->real_var_end;
i>=r->real_var_start;
i--)
1665 int *
D = (
int *)
omAlloc0((len+1)*
sizeof(int));
1666 int *L = (
int *)
omAlloc0((len+1)*
sizeof(int));
1672 int HasConstantCoef = 0;
1673 int is = r->real_var_start - 1;
1679 mintdeg =
si_min(mintdeg,D[k]);
1681 minlen =
si_min(minlen,L[k]);
1685 HasConstantCoef = 1;
1695 int mindeglen = len;
1707 if (D[i] == mintdeg)
1709 if (L[i] < mindeglen)
1716 d =
p_Copy(C[pmindeglen], r);
1788 int divisorLE =
p_GetExp(divisor, 1, r);
1796 int e =
p_GetExp(p, 1, r) - divisorLE;
1851 for(i=
rVar(r);i>0;i--)
1923 for (i=
rVar(r); i!=0; i--)
1981 bin = (number *)
omAlloc0(h*
sizeof(number));
1990 y =
n_Mult(x,bin[e-1],r->cf);
2002 int e,
h = (exp >> 1) + 1;
2024 number *bin =
pnBin(exp,r);
2035 al = (exp + 1) *
sizeof(
poly);
2038 for (e=1; e<
exp; e++)
2044 for (e=exp-1; e>eh; e--)
2053 for (e=eh; e!=0; e--)
2120 if ( (i > 0) && ((
unsigned long ) i > (r->bitmask)))
2122 Werror(
"exponent %d is too large, max. is %ld",i,r->bitmask);
2166 int char_p=
rChar(r);
2167 if ((char_p>0) && (i>char_p)
2173 while (rest>=char_p)
2189 return p_Pow(p,i,r);
2190 if ((char_p==0) || (i<=char_p))
2192 return p_Pow(p,i,r);
2205 #define CLEARENUMERATORS 1 2214 #if CLEARENUMERATORS 2268 #if CLEARENUMERATORS 2333 h =
n_Init(1, r->cf->extRing->cf);
2350 if(!
n_IsOne(h,r->cf->extRing->cf))
2415 #if 1 // currently only used by Singular/janet 2419 if (ph==
NULL)
return;
2430 if (
n_Size(d,r->cf)<=smax)
2439 if (smax==1) smax=2;
2498 d=
nlAdd(n1,t,r->cf);
2500 d=
nlSub(n1,t,r->cf);
2509 d=
nlAdd(n2,t,r->cf);
2511 d=
nlSub(n2,t,r->cf);
2518 d=
nlGcd(n1,n2,r->cf);
2541 if (s2==-1)
return n_Copy(d,r->cf);
2714 #if CLEARENUMERATORS 2764 #if 0 && CLEARENUMERATORS 2822 #ifdef HAVE_RATGRING 2846 #if CLEARENUMERATORS 2892 #if CLEARENUMERATORS 2992 number t=
n_Mult(c,h,r->cf);
3082 fraction
f = (fraction) h;
3083 number n=
p_GetCoeff (NUM (f),C->extRing->cf);
3093 if (!
n_IsOne (n, C->extRing->cf))
3097 nMap=
n_SetMap (C->extRing->cf, C);
3098 number ninv= nMap (n,C->extRing->cf, C);
3111 number p_GetAllDenom(
poly ph,
const ring r)
3113 number d=
n_Init(1,r->cf);
3121 number dd=
n_Mult(d,h,r->cf);
3135 if (r->cf->has_simple_Alloc)
3163 if ((varnum < 1) || (varnum >
rVar(r)))
3212 if (d(qp,r) != o)
return FALSE;
3266 if ((*len == 0) || (j<*len))
3366 pNext(qq) = pNext_q;
3442 if (*p==
NULL)
return;
3476 if (*len==0) *len=1;
3483 (*p)[k-1]=
p_Add_q((*p)[k-1],h,r);
3495 r->pFDeg = new_FDeg;
3497 if (new_lDeg ==
NULL)
3498 new_lDeg = r->pLDegOrig;
3500 r->pLDeg = new_lDeg;
3507 r->pFDeg = old_FDeg;
3508 r->pLDeg = old_lDeg;
3523 if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1];
3533 pOldFDeg = r->pFDeg;
3534 pOldLDeg = r->pLDeg;
3535 pOldLexOrder = r->pLexOrder;
3537 r->pLexOrder =
TRUE;
3557 if (increment==0)
return;
3567 memset(&(h[l]),0,increment*
sizeof(
poly));
3689 while (non_zero !=
NULL)
3697 result =
p_Add_q(result,qq,r);
3713 poly zero, non_zero;
3718 while (non_zero !=
NULL)
3738 result =
p_Add_q(result,qq,r);
3809 for(i=
rVar(r);i>0;i--)
3810 me[i]+=exponent*ee[i];
3833 poly n_PermNumber(
const number z,
const int *par_perm,
const int ,
const ring src,
const ring dst)
3836 PrintS(
"\nSource Ring: \n");
3841 number zz =
n_Copy(z, src->cf);
3846 PrintS(
"\nDestination Ring: \n");
3858 const coeffs srcCf = src->cf;
3866 const ring srcExtRing = srcCf->extRing;
3869 const coeffs dstCf = dst->cf;
3881 zz = NUM((fraction)z);
3885 if( !DENIS1((fraction)z) )
3888 WarnS(
"Not defined: Cannot map a rational fraction and make a polynomial out of it! Ignoring the denumerator.");
3894 Werror(
"Number permutation is not implemented for this data yet!");
3906 if ((par_perm ==
NULL) && (
rPar(dst) != 0 &&
rVar (srcExtRing) > 0))
3909 perm=(
int *)
omAlloc0((
rVar(srcExtRing)+1)*
sizeof(int));
3920 && (!DENIS1((fraction)z))
3923 number n=nMap(
pGetCoeff(DEN((fraction)z)),srcExtRing->cf, dstCf);
3944 const int OldpVariables =
rVar(oldRing);
3961 number n = nMap(
p_GetCoeff(p, oldRing), oldRing->cf, dst->cf);
3990 int mapped_to_par = 0;
3991 for(
int i = 1;
i <= OldpVariables;
i++)
4021 n_Power(ee, e, &eee, dst->cf);
4022 ee =
n_Mult(c, eee, dst->cf);
4028 const int par = -perm[
i];
4032 const coeffs C = dst->cf;
4034 const ring
R = C->extRing;
4042 pcn = NUM((fraction)c);
4103 if (result_last==
NULL)
4109 pNext(result_last)=qq;
4284 p=
p_JetW(
p_Mult_q(p,
p_Invers(n-
p_MinDeg(p,w,R),u,w,R),R),n,ww,R);
4320 while ((p1 !=
NULL) && (p2 !=
NULL))
4339 int i = r1->ExpL_Size;
4341 assume( r1->ExpL_Size == r2->ExpL_Size );
4343 unsigned long *ep = p1->exp;
4344 unsigned long *eq = p2->exp;
4349 if (ep[i] != eq[i])
return FALSE;
4359 assume( r1->cf == r2->cf );
4361 while ((p1 !=
NULL) && (p2 !=
NULL))
4402 while ((p1 !=
NULL) )
4464 if (m==
NULL)
return 0;
4467 for (i=
rVar(r); i>0; i--)
4490 if (p ==
NULL)
return -1;
4497 while ((l < (
rVar(r))) && (lex == 0))
4520 if ((
p_GetComp(qp1,r)+i > 0) || ((j == -i) && (j ==
k)))
4538 qp2->next = qp1->next;
4554 const unsigned int s,
const unsigned int n)
4556 #define Sy_bit_L(x) (((unsigned long)1L)<<(x)) 4558 unsigned long ev = 0L;
4563 if (e > (
long) i) ev |=
Sy_bit_L(s+i);
4589 unsigned long ev = 0;
4603 for (;
j<=r->N;
j++)
4643 unsigned long ev = 0;
4647 unsigned long i = 0L;
4658 for (; j<=r->N; j++)
4701 #define p_Delete__T p_ShallowDelete 4703 #define n_Delete__T(n, r) do {} while (0) #define p_LmCheckPolyRing2(p, r)
int status int void size_t count
BOOLEAN p_VectorHasUnitB(poly p, int *k, const ring 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 poly p_LmDeleteAndNext(poly p, const ring r)
static BOOLEAN rField_is_Zp_a(const ring r)
long pLDeg1c_Totaldegree(poly p, int *l, const ring r)
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)
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)
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)
poly singclap_gcd(poly f, poly g, const ring r)
destroys f and g
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)
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;
void sBucket_Add_p(sBucket_pt bucket, poly p, int length)
adds poly p to bucket destroys p!
poly p_Subst(poly p, int n, poly e, const ring r)
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)
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 int pLength(poly a)
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)
static long p_SubExp(poly p, int v, long ee, ring 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)
int p_Size(poly p, const ring r)
poly p_Invers(int n, poly u, intvec *w, 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.
for(int i=0;i< R->ExpL_Size;i++) Print("%09lx "
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)
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)
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)
static number p_InitContent(poly ph, const ring r)
poly p_GetCoeffRat(poly p, int ishift, ring r)
Induced (Schreyer) ordering.
void PrintS(const char *s)
static poly p_Mult_nn(poly p, number n, 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)
poly p_Divide(poly a, poly b, const ring r)
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)
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.
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)
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
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)
long pLDeg1c_WFirstTotalDegree(poly p, int *l, 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)
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)
poly p_TakeOutComp(poly *p, int k, 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)