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My Project
UNKNOWN_GIT_VERSION
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Go to the source code of this file.
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poly | p_Farey (poly p, number N, const ring r) |
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poly | p_ChineseRemainder (poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R) |
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void | p_Setm_General (poly p, const ring r) |
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void | p_Setm_Syz (poly p, ring r, int *Components, long *ShiftedComponents) |
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void | p_Setm_Dummy (poly p, const ring r) |
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void | p_Setm_TotalDegree (poly p, const ring r) |
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void | p_Setm_WFirstTotalDegree (poly p, const ring r) |
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p_SetmProc | p_GetSetmProc (const ring r) |
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long | p_Deg (poly a, const ring r) |
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long | p_WFirstTotalDegree (poly p, const ring r) |
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long | p_WTotaldegree (poly p, const ring r) |
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long | p_DegW (poly p, const short *w, const ring R) |
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int | p_Weight (int i, const ring r) |
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long | p_WDegree (poly p, const ring r) |
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long | pLDeg0 (poly p, int *l, const ring r) |
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long | pLDeg0c (poly p, int *l, const ring r) |
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long | pLDegb (poly p, int *l, const ring r) |
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long | pLDeg1 (poly p, int *l, const ring r) |
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long | pLDeg1c (poly p, int *l, const ring r) |
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long | pLDeg1_Deg (poly p, int *l, const ring r) |
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long | pLDeg1c_Deg (poly p, int *l, const ring r) |
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long | pLDeg1_Totaldegree (poly p, int *l, const ring r) |
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long | pLDeg1c_Totaldegree (poly p, int *l, const ring r) |
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long | pLDeg1_WFirstTotalDegree (poly p, int *l, const ring r) |
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long | pLDeg1c_WFirstTotalDegree (poly p, int *l, const ring r) |
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static unsigned long | p_GetMaxExpL2 (unsigned long l1, unsigned long l2, const ring r, unsigned long number_of_exp) |
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static unsigned long | p_GetMaxExpL2 (unsigned long l1, unsigned long l2, const ring r) |
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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, next == NULL, ord is not set More...
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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 More...
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BOOLEAN | p_OneComp (poly p, const ring r) |
| return TRUE if all monoms have the same component More...
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int | p_IsPurePower (const poly p, const ring r) |
| return i, if head depends only on var(i) More...
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int | p_IsUnivariate (poly p, const ring r) |
| return i, if poly depends only on var(i) More...
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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) More...
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poly | p_ISet (long i, const ring r) |
| returns the poly representing the integer i More...
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poly | p_One (const ring r) |
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void | p_Split (poly p, poly *h) |
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BOOLEAN | p_HasNotCF (poly p1, poly p2, const ring r) |
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const char * | p_Read (const char *st, poly &rc, const ring r) |
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poly | p_mInit (const char *st, BOOLEAN &ok, const ring r) |
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poly | p_NSet (number n, const ring r) |
| returns the poly representing the number n, destroys n More...
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poly | p_MDivide (poly a, poly b, const ring r) |
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poly | p_Div_nn (poly p, const number n, const ring r) |
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poly | p_Div_mm (poly p, const poly m, const ring r) |
| divide polynomial by monomial More...
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poly | p_DivideM (poly a, poly b, const ring r) |
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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), i.e., LT(f)*c*m = LT(g), for some coefficient c and some monomial m; does not take components into account More...
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void | p_Lcm (const poly a, const poly b, poly m, const ring r) |
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poly | p_Lcm (const poly a, const poly b, const ring r) |
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poly | p_LcmRat (const poly a, const poly b, const long lCompM, const ring r) |
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void | p_LmDeleteAndNextRat (poly *p, int ishift, ring r) |
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poly | p_GetCoeffRat (poly p, int ishift, ring r) |
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void | p_ContentRat (poly &ph, const ring r) |
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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 divisor != NULL; p may be NULL; assumes a global monomial ordering in r; performs polynomial division of p by divisor: More...
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poly | p_Diff (poly a, int k, const ring r) |
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static poly | p_DiffOpM (poly a, poly b, BOOLEAN multiply, const ring r) |
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poly | p_DiffOp (poly a, poly b, BOOLEAN multiply, const ring r) |
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poly | p_Sub (poly p1, poly p2, const ring r) |
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static poly | p_MonPower (poly p, int exp, const ring r) |
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static void | p_MonMult (poly p, poly q, const ring r) |
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static poly | p_MonMultC (poly p, poly q, const ring rr) |
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static number * | pnBin (int exp, const ring r) |
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static void | pnFreeBin (number *bin, int exp, const coeffs r) |
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static poly | p_TwoMonPower (poly p, int exp, const ring r) |
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static poly | p_Pow (poly p, int i, const ring r) |
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static poly | p_Pow_charp (poly p, int i, const ring r) |
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poly | p_Power (poly p, int i, const ring r) |
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void | p_Content (poly ph, const ring r) |
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void | p_ContentForGB (poly ph, const ring r) |
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void | p_SimpleContent (poly ph, int smax, const ring r) |
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number | p_InitContent (poly ph, const ring r) |
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poly | p_Cleardenom (poly p, const ring r) |
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void | p_Cleardenom_n (poly ph, const ring r, number &c) |
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void | p_ProjectiveUnique (poly ph, const ring r) |
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int | p_Size (poly p, const ring r) |
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poly | p_Homogen (poly p, int varnum, const ring r) |
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BOOLEAN | p_IsHomogeneous (poly p, const ring r) |
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BOOLEAN | p_VectorHasUnitB (poly p, int *k, const ring r) |
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void | p_VectorHasUnit (poly p, int *k, int *len, const ring r) |
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poly | p_TakeOutComp1 (poly *p, int k, const ring r) |
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poly | p_TakeOutComp (poly *p, int k, const ring r) |
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void | p_TakeOutComp (poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
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void | p_DeleteComp (poly *p, int k, const ring r) |
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poly | p_Vec2Poly (poly v, int k, const ring r) |
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void | p_Vec2Array (poly v, poly *p, int len, const ring r) |
| vector to already allocated array (len>=p_MaxComp(v,r)) More...
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void | p_Vec2Polys (poly v, poly **p, int *len, const ring r) |
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void | pSetDegProcs (ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
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void | pRestoreDegProcs (ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
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static long | pModDeg (poly p, ring r) |
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void | p_SetModDeg (intvec *w, ring r) |
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void | pEnlargeSet (poly **p, int l, int increment) |
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void | p_Norm (poly p1, const ring r) |
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void | p_Normalize (poly p, const ring r) |
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static void | p_SplitAndReversePoly (poly p, int n, poly *non_zero, poly *zero, const ring r) |
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static poly | p_Subst1 (poly p, int n, const ring r) |
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static poly | p_Subst2 (poly p, int n, number e, const ring r) |
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static poly | p_Subst0 (poly p, int n, const ring r) |
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poly | p_Subst (poly p, int n, poly e, const ring r) |
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poly | n_PermNumber (const number z, const int *par_perm, const int, const ring src, const ring dst) |
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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) |
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poly | pp_Jet (poly p, int m, const ring R) |
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poly | p_Jet (poly p, int m, const ring R) |
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poly | pp_JetW (poly p, int m, short *w, const ring R) |
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poly | p_JetW (poly p, int m, short *w, const ring R) |
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int | p_MinDeg (poly p, intvec *w, const ring R) |
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static poly | p_Invers (int n, poly u, intvec *w, const ring R) |
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poly | p_Series (int n, poly p, poly u, intvec *w, const ring R) |
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BOOLEAN | p_EqualPolys (poly p1, poly p2, const ring r) |
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static BOOLEAN | p_ExpVectorEqual (poly p1, poly p2, const ring r1, const ring r2) |
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BOOLEAN | p_EqualPolys (poly p1, poly p2, const ring r1, const ring r2) |
| same as the usual p_EqualPolys for polys belonging to equal rings More...
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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 More...
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poly | p_Last (const poly p, int &l, const ring r) |
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int | p_Var (poly m, const ring r) |
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int | p_LowVar (poly p, const ring r) |
| the minimal index of used variables - 1 More...
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void | p_Shift (poly *p, int i, const ring r) |
| shifts components of the vector p by i More...
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static unsigned long | GetBitFields (const long e, const unsigned int s, const unsigned int n) |
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unsigned long | p_GetShortExpVector (const poly p, const ring r) |
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unsigned long | p_GetShortExpVector (const poly p, const poly pp, const ring r) |
| p_GetShortExpVector of p * pp More...
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int | p_Compare (const poly a, const poly b, const ring R) |
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poly | p_GcdMon (poly f, poly g, const ring r) |
| polynomial gcd for f=mon More...
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◆ CLEARENUMERATORS
#define CLEARENUMERATORS 1 |
◆ LINKAGE
◆ MYTEST
◆ n_Delete__T
#define n_Delete__T |
( |
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n, |
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r |
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) |
| do {} while (0) |
◆ p_Delete__T
◆ Sy_bit_L
#define Sy_bit_L |
( |
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x | ) |
(((unsigned long)1L)<<(x)) |
◆ TRANSEXT_PRIVATES
#define TRANSEXT_PRIVATES |
◆ GetBitFields()
static unsigned long GetBitFields |
( |
const long |
e, |
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const unsigned int |
s, |
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const unsigned int |
n |
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) |
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inlinestatic |
Definition at line 4646 of file p_polys.cc.
4649 #define Sy_bit_L(x) (((unsigned long)1L)<<(x))
4651 unsigned long ev = 0L;
◆ n_PermNumber()
Definition at line 3924 of file p_polys.cc.
3927 PrintS(
"\nSource Ring: \n");
3932 number zz =
n_Copy(z, src->cf);
3937 PrintS(
"\nDestination Ring: \n");
3949 const coeffs srcCf = src->cf;
3957 const ring srcExtRing = srcCf->extRing;
3960 const coeffs dstCf = dst->cf;
3972 zz =
NUM((fraction)z);
3976 if( !DENIS1((fraction)z) )
3979 WarnS(
"Not defined: Cannot map a rational fraction and make a polynomial out of it! Ignoring the denominator.");
3985 WerrorS(
"Number permutation is not implemented for this data yet!");
3997 if ((par_perm ==
NULL) && (
rPar(dst) != 0 &&
rVar (srcExtRing) > 0))
4000 perm=(
int *)
omAlloc0((
rVar(srcExtRing)+1)*
sizeof(int));
4011 && (!DENIS1((fraction)z))
4014 number n=nMap(
pGetCoeff(DEN((fraction)z)),srcExtRing->cf, dstCf);
◆ p_ChineseRemainder()
poly p_ChineseRemainder |
( |
poly * |
xx, |
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number * |
x, |
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number * |
q, |
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int |
rl, |
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CFArray & |
inv_cache, |
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const ring |
R |
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) |
| |
◆ p_Cleardenom()
poly p_Cleardenom |
( |
poly |
p, |
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const ring |
r |
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) |
| |
Definition at line 2782 of file p_polys.cc.
2789 #if CLEARENUMERATORS
2832 #if 0 && CLEARENUMERATORS
2876 #ifdef HAVE_RATGRING
◆ p_Cleardenom_n()
void p_Cleardenom_n |
( |
poly |
ph, |
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const ring |
r, |
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number & |
c |
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) |
| |
Definition at line 2891 of file p_polys.cc.
2900 #if CLEARENUMERATORS
2953 #if CLEARENUMERATORS
◆ p_Compare()
◆ p_ComparePolys()
returns TRUE if p1 is a skalar multiple of p2 assume p1 != NULL and p2 != NULL
Definition at line 4474 of file p_polys.cc.
4494 while ((p1 !=
NULL) )
◆ p_Content()
void p_Content |
( |
poly |
ph, |
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const ring |
r |
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) |
| |
Definition at line 2238 of file p_polys.cc.
2240 if (ph==
NULL)
return;
2246 if (
cf->cfSubringGcd==
ndGcd)
return;
2251 goto content_finish;
2263 goto content_finish;
◆ p_ContentForGB()
void p_ContentForGB |
( |
poly |
ph, |
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const ring |
r |
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) |
| |
Definition at line 2283 of file p_polys.cc.
2291 #if CLEARENUMERATORS
2344 #if CLEARENUMERATORS
2409 h =
n_Init(1, r->cf->extRing->cf);
◆ p_ContentRat()
void p_ContentRat |
( |
poly & |
ph, |
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const ring |
r |
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) |
| |
Definition at line 1691 of file p_polys.cc.
1699 poly *C = (poly *)
omAlloc0((len+1)*
sizeof(poly));
1700 poly *LM = (poly *)
omAlloc0((len+1)*
sizeof(poly));
1701 int *
D = (
int *)
omAlloc0((len+1)*
sizeof(int));
1702 int *L = (
int *)
omAlloc0((len+1)*
sizeof(int));
1708 int HasConstantCoef = 0;
1709 int is = r->real_var_start - 1;
1721 HasConstantCoef = 1;
1731 int mindeglen = len;
1743 if (
D[
i] == mintdeg)
1745 if (L[
i] < mindeglen)
1752 d =
p_Copy(C[pmindeglen], r);
◆ p_Deg()
long p_Deg |
( |
poly |
a, |
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const ring |
r |
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) |
| |
◆ p_DegW()
long p_DegW |
( |
poly |
p, |
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const short * |
w, |
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const ring |
R |
|
) |
| |
◆ p_DeleteComp()
void p_DeleteComp |
( |
poly * |
p, |
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int |
k, |
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const ring |
r |
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) |
| |
◆ p_Diff()
poly p_Diff |
( |
poly |
a, |
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int |
k, |
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const ring |
r |
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) |
| |
◆ p_DiffOp()
poly p_DiffOp |
( |
poly |
a, |
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poly |
b, |
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BOOLEAN |
multiply, |
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const ring |
r |
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) |
| |
◆ p_DiffOpM()
static poly p_DiffOpM |
( |
poly |
a, |
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poly |
b, |
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BOOLEAN |
multiply, |
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|
const ring |
r |
|
) |
| |
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static |
◆ p_Div_mm()
poly p_Div_mm |
( |
poly |
p, |
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const poly |
m, |
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const ring |
r |
|
) |
| |
divide polynomial by monomial
Definition at line 1500 of file p_polys.cc.
◆ p_Div_nn()
poly p_Div_nn |
( |
poly |
p, |
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const number |
n, |
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const ring |
r |
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) |
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◆ p_DivideM()
poly p_DivideM |
( |
poly |
a, |
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poly |
b, |
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const ring |
r |
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) |
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◆ p_DivisibleByRingCase()
BOOLEAN p_DivisibleByRingCase |
( |
poly |
f, |
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poly |
g, |
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const ring |
r |
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) |
| |
divisibility check over ground ring (which may contain zero divisors); TRUE iff LT(f) divides LT(g), i.e., LT(f)*c*m = LT(g), for some coefficient c and some monomial m; does not take components into account
Definition at line 1589 of file p_polys.cc.
1592 for(
int i = (
int)
rVar(r);
i>0;
i--)
◆ p_EqualPolys() [1/2]
◆ p_EqualPolys() [2/2]
same as the usual p_EqualPolys for polys belonging to equal rings
Definition at line 4448 of file p_polys.cc.
4451 assume( r1->cf == r2->cf );
4453 while ((p1 !=
NULL) && (p2 !=
NULL))
◆ p_ExpVectorEqual()
Definition at line 4424 of file p_polys.cc.
4431 int i = r1->ExpL_Size;
4433 assume( r1->ExpL_Size == r2->ExpL_Size );
4435 unsigned long *ep = p1->exp;
4436 unsigned long *eq = p2->exp;
4441 if (ep[
i] != eq[
i])
return FALSE;
◆ p_Farey()
poly p_Farey |
( |
poly |
p, |
|
|
number |
N, |
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const ring |
r |
|
) |
| |
◆ p_GcdMon()
poly p_GcdMon |
( |
poly |
f, |
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poly |
g, |
|
|
const ring |
r |
|
) |
| |
polynomial gcd for f=mon
Definition at line 4838 of file p_polys.cc.
4845 int *mf=(
int*)
omAlloc((r->N+1)*
sizeof(int));
4847 int *mh=(
int*)
omAlloc((r->N+1)*
sizeof(int));
4861 for(
unsigned j=r->N;
j!=0;
j--)
4863 if (mh[
j]<mf[
j]) mf[
j]=mh[
j];
4864 if (mf[
j]>0) const_mon=
FALSE;
4866 if (one_coeff && const_mon)
break;
◆ p_GetCoeffRat()
poly p_GetCoeffRat |
( |
poly |
p, |
|
|
int |
ishift, |
|
|
ring |
r |
|
) |
| |
◆ p_GetMaxExpL()
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
Definition at line 1167 of file p_polys.cc.
1169 unsigned long l_p, divmask = r->divmask;
1174 l_p =
p->exp[r->VarL_Offset[0]];
1176 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1178 for (
i=1;
i<r->VarL_Size;
i++)
1180 l_p =
p->exp[r->VarL_Offset[
i]];
1183 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
◆ p_GetMaxExpL2() [1/2]
static unsigned long p_GetMaxExpL2 |
( |
unsigned long |
l1, |
|
|
unsigned long |
l2, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_GetMaxExpL2() [2/2]
static unsigned long p_GetMaxExpL2 |
( |
unsigned long |
l1, |
|
|
unsigned long |
l2, |
|
|
const ring |
r, |
|
|
unsigned long |
number_of_exp |
|
) |
| |
|
inlinestatic |
Definition at line 1099 of file p_polys.cc.
1102 const unsigned long bitmask = r->bitmask;
1103 unsigned long ml1 = l1 & bitmask;
1104 unsigned long ml2 = l2 & bitmask;
1105 unsigned long max = (ml1 > ml2 ? ml1 : ml2);
1106 unsigned long j = number_of_exp - 1;
1110 unsigned long mask = bitmask << r->BitsPerExp;
1115 max |= ((ml1 > ml2 ? ml1 : ml2) & mask);
1118 mask = mask << r->BitsPerExp;
◆ p_GetMaxExpP()
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, next == NULL, ord is not set
Definition at line 1130 of file p_polys.cc.
1138 unsigned long l_p, l_max;
1139 unsigned long divmask = r->divmask;
1143 offset = r->VarL_Offset[0];
1148 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
1151 for (
i=1;
i<r->VarL_Size;
i++)
1158 (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
◆ p_GetSetmProc()
Definition at line 552 of file p_polys.cc.
559 if (r->typ[0].ord_typ ==
ro_dp &&
560 r->typ[0].data.dp.start == 1 &&
561 r->typ[0].data.dp.end == r->N &&
562 r->typ[0].data.dp.place == r->pOrdIndex)
564 if (r->typ[0].ord_typ ==
ro_wp &&
565 r->typ[0].data.wp.start == 1 &&
566 r->typ[0].data.wp.end == r->N &&
567 r->typ[0].data.wp.place == r->pOrdIndex &&
568 r->typ[0].data.wp.weights == r->firstwv)
◆ p_GetShortExpVector() [1/2]
unsigned long p_GetShortExpVector |
( |
const poly |
p, |
|
|
const poly |
pp, |
|
|
const ring |
r |
|
) |
| |
p_GetShortExpVector of p * pp
Definition at line 4731 of file p_polys.cc.
4736 unsigned long ev = 0;
4740 unsigned long i = 0L;
4751 for (;
j<=r->N;
j++)
◆ p_GetShortExpVector() [2/2]
unsigned long p_GetShortExpVector |
( |
const poly |
p, |
|
|
const ring |
r |
|
) |
| |
Definition at line 4679 of file p_polys.cc.
4682 unsigned long ev = 0;
4696 for (;
j<=r->N;
j++)
◆ p_GetVariables()
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)
Definition at line 1259 of file p_polys.cc.
1266 for(
i=r->N;
i>0;
i--)
◆ p_HasNotCF()
◆ p_Homogen()
poly p_Homogen |
( |
poly |
p, |
|
|
int |
varnum, |
|
|
const ring |
r |
|
) |
| |
◆ p_InitContent()
number p_InitContent |
( |
poly |
ph, |
|
|
const ring |
r |
|
) |
| |
Definition at line 2549 of file p_polys.cc.
2573 d=
nlAdd(n1,t,r->cf);
2575 d=
nlSub(n1,t,r->cf);
2584 d=
nlAdd(n2,t,r->cf);
2586 d=
nlSub(n2,t,r->cf);
2593 d=
nlGcd(n1,n2,r->cf);
2616 if (s2==-1)
return n_Copy(d,r->cf);
◆ p_Invers()
static poly p_Invers |
( |
int |
n, |
|
|
poly |
u, |
|
|
intvec * |
w, |
|
|
const ring |
R |
|
) |
| |
|
static |
◆ p_ISet()
poly p_ISet |
( |
long |
i, |
|
|
const ring |
r |
|
) |
| |
returns the poly representing the integer i
Definition at line 1289 of file p_polys.cc.
◆ p_IsHomogeneous()
◆ p_IsPurePower()
return i, if head depends only on var(i)
Definition at line 1218 of file p_polys.cc.
◆ p_IsUnivariate()
int p_IsUnivariate |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
return i, if poly depends only on var(i)
Definition at line 1239 of file p_polys.cc.
1249 if((
k!=-1)&&(
k!=
i))
return 0;
◆ p_Jet()
poly p_Jet |
( |
poly |
p, |
|
|
int |
m, |
|
|
const ring |
R |
|
) |
| |
◆ p_JetW()
poly p_JetW |
( |
poly |
p, |
|
|
int |
m, |
|
|
short * |
w, |
|
|
const ring |
R |
|
) |
| |
◆ p_Last()
poly p_Last |
( |
const poly |
p, |
|
|
int & |
l, |
|
|
const ring |
r |
|
) |
| |
◆ p_Lcm() [1/2]
◆ p_Lcm() [2/2]
◆ p_LcmRat()
Definition at line 1624 of file p_polys.cc.
1632 for (
int i = r->real_var_end;
i>=r->real_var_start;
i--)
◆ p_LmDeleteAndNextRat()
void p_LmDeleteAndNextRat |
( |
poly * |
p, |
|
|
int |
ishift, |
|
|
ring |
r |
|
) |
| |
◆ p_LowVar()
int p_LowVar |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
the minimal index of used variables - 1
Definition at line 4578 of file p_polys.cc.
4582 if (
p ==
NULL)
return -1;
4589 while ((
l < (
rVar(r))) && (lex == 0))
◆ p_MDivide()
poly p_MDivide |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
◆ p_MinDeg()
◆ p_mInit()
Definition at line 1412 of file p_polys.cc.
1418 if ((
s!=st)&&isdigit(st[0]))
◆ p_MonMult()
static void p_MonMult |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
static |
◆ p_MonMultC()
static poly p_MonMultC |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
rr |
|
) |
| |
|
static |
◆ p_MonPower()
static poly p_MonPower |
( |
poly |
p, |
|
|
int |
exp, |
|
|
const ring |
r |
|
) |
| |
|
static |
◆ p_Norm()
void p_Norm |
( |
poly |
p1, |
|
|
const ring |
r |
|
) |
| |
◆ p_Normalize()
void p_Normalize |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
◆ p_NSet()
poly p_NSet |
( |
number |
n, |
|
|
const ring |
r |
|
) |
| |
returns the poly representing the number n, destroys n
Definition at line 1435 of file p_polys.cc.
◆ p_One()
poly p_One |
( |
const ring |
r | ) |
|
◆ p_OneComp()
return TRUE if all monoms have the same component
Definition at line 1200 of file p_polys.cc.
◆ p_PermPoly()
Definition at line 4028 of file p_polys.cc.
4035 const int OldpVariables =
rVar(oldRing);
4037 poly result_last =
NULL;
4043 poly tmp_mm=
p_One(dst);
4053 number n = nMap(
p_GetCoeff(
p, oldRing), oldRing->cf, dst->cf);
4082 int mapped_to_par = 0;
4083 for(
int i = 1;
i <= OldpVariables;
i++)
4113 n_Power(ee, e, &eee, dst->cf);
4114 ee =
n_Mult(c, eee, dst->cf);
4120 const int par = -perm[
i];
4124 const coeffs C = dst->cf;
4126 const ring
R = C->extRing;
4134 pcn =
NUM((fraction)c);
4195 if (result_last==
NULL)
4201 pNext(result_last)=qq;
◆ p_PolyDiv()
assumes that p and divisor are univariate polynomials in r, mentioning the same variable; assumes divisor != NULL; p may be NULL; assumes a global monomial ordering in r; performs polynomial division of p by divisor:
- afterwards p contains the remainder of the division, i.e., p_before = result * divisor + p_afterwards;
- if needResult == TRUE, then the method computes and returns 'result', otherwise NULL is returned (This parametrization can be used when one is only interested in the remainder of the division. In this case, the method will be slightly faster.) leaves divisor unmodified
Definition at line 1817 of file p_polys.cc.
1824 int divisorLE =
p_GetExp(divisor, 1, r);
◆ p_Pow()
static poly p_Pow |
( |
poly |
p, |
|
|
int |
i, |
|
|
const ring |
r |
|
) |
| |
|
static |
◆ p_Pow_charp()
static poly p_Pow_charp |
( |
poly |
p, |
|
|
int |
i, |
|
|
const ring |
r |
|
) |
| |
|
static |
◆ p_Power()
poly p_Power |
( |
poly |
p, |
|
|
int |
i, |
|
|
const ring |
r |
|
) |
| |
Definition at line 2144 of file p_polys.cc.
2156 if ( (
i > 0) && ((
unsigned long )
i > (r->bitmask)))
2158 Werror(
"exponent %d is too large, max. is %ld",
i,r->bitmask);
2202 int char_p=
rChar(r);
2203 if ((char_p>0) && (
i>char_p)
2209 while (rest>=char_p)
2224 if ((char_p==0) || (
i<=char_p))
◆ p_ProjectiveUnique()
void p_ProjectiveUnique |
( |
poly |
ph, |
|
|
const ring |
r |
|
) |
| |
Definition at line 3080 of file p_polys.cc.
3141 fraction
f = (fraction)
h;
3152 if (!
n_IsOne (n, C->extRing->cf))
3156 nMap=
n_SetMap (C->extRing->cf, C);
3157 number ninv= nMap (n,C->extRing->cf, C);
◆ p_Read()
Definition at line 1340 of file p_polys.cc.
1353 while (*
s!=
'\0')
s++;
1365 const char *s_save=
s;
1367 if (((
unsigned long)
i) > r->bitmask/2)
1398 for(
unsigned int k = iFirstAltVar;
k <= iLastAltVar;
k++)
◆ p_Series()
poly p_Series |
( |
int |
n, |
|
|
poly |
p, |
|
|
poly |
u, |
|
|
intvec * |
w, |
|
|
const ring |
R |
|
) |
| |
Definition at line 4396 of file p_polys.cc.
4404 p=
p_JetW(
p_Mult_q(
p,
p_Invers(n-
p_MinDeg(
p,
w,
R),u,
w,
R),
R),n,ww,
R);
◆ p_Setm_Dummy()
void p_Setm_Dummy |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
◆ p_Setm_General()
void p_Setm_General |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
!!!????? where?????
Definition at line 154 of file p_polys.cc.
172 p->exp[o->
data.dp.place]=ord;
183 int *
w=o->
data.wp.weights;
185 for(
int i=a;
i<=e;
i++) ord+=((
unsigned long)
p_GetExp(
p,
i,r))*((
unsigned long)
w[
i-a]);
189 for(
int i=a;
i<=e;
i++)
199 p->exp[o->
data.wp.place]=ord;
205 const short a=o->
data.am.start;
206 const short e=o->
data.am.end;
207 const int *
w=o->
data.am.weights;
209 for(
short i=a;
i<=e;
i++,
w++)
214 for(
short i=a;
i<=e;
i++)
226 const short len_gen= o->
data.am.len_gen;
228 if ((c > 0) && (c <= len_gen))
235 p->exp[o->
data.am.place] = ord;
242 a=o->
data.wp64.start;
246 for(
int i=a;
i<=e;
i++)
253 if(ei!=0 && ai/ei!=wi)
257 Print(
"ai %lld, wi %lld\n",ai,wi);
259 Print(
"ai %ld, wi %ld\n",ai,wi);
267 Print(
"ai %lld, ord %lld\n",ai,ord);
269 Print(
"ai %ld, ord %ld\n",ai,ord);
274 long a_0=(long)(ord&mask);
275 long a_1=(long)(ord >>31 );
281 p->exp[o->
data.wp64.place]=a_1;
282 p->exp[o->
data.wp64.place+1]=a_0;
295 int pl=o->
data.cp.place;
304 o->
data.syzcomp.Components);
306 o->
data.syzcomp.ShiftedComponents);
307 if (ShiftedComponents !=
NULL)
310 assume(c == 0 || Components[c] != 0);
311 sc = ShiftedComponents[Components[c]];
312 assume(c == 0 || sc != 0);
314 p->exp[o->
data.syzcomp.place]=sc;
320 const short place = o->
data.syz.place;
321 const int limit = o->
data.syz.limit;
323 if (c > (
unsigned long)limit)
324 p->exp[place] = o->
data.syz.curr_index;
327 assume( (1 <= c) && (c <= (
unsigned long)limit) );
328 p->exp[place]= o->
data.syz.syz_index[c];
344 Print(
"p_Setm_General: ro_isTemp ord: pos: %d, p: ", pos);
p_wrp(
p, r);
353 const int*
const pVarOffset = o->
data.isTemp.pVarOffset;
358 for(
int i = 1;
i <= r->N;
i++ )
360 const int vo = pVarOffset[
i];
370 for(
int i = 1;
i <= r->N;
i++ )
372 const int vo = pVarOffset[
i];
392 Print(
"p_Setm_General: ro_is ord: pos: %d, p: ", pos);
p_wrp(
p, r);
401 const ideal F = o->
data.is.F;
402 const int limit = o->
data.is.limit;
404 const int start = o->
data.is.start;
406 if( F !=
NULL && c > limit )
410 Print(
"p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit);
411 PrintS(
"preComputed Values: ");
430 const poly
pp = F->m[c];
439 Print(
"Respective F[c - %d: %d] pp: ", limit, c);
444 const int end = o->
data.is.end;
452 Print(
"p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start,
p->exp[start]);
458 for(
int i = start;
i <= end;
i++)
459 p->exp[
i] +=
pp->exp[
i];
462 if (r->NegWeightL_Offset !=
NULL)
464 for (
int i=r->NegWeightL_Size-1;
i>=0;
i--)
466 const int _i = r->NegWeightL_Offset[
i];
467 if( start <= _i && _i <= end )
474 const int*
const pVarOffset = o->
data.is.pVarOffset;
478 for(
int i = 1;
i <= r->N;
i++ )
480 const int vo = pVarOffset[
i];
494 const int*
const pVarOffset = o->
data.is.pVarOffset;
499 const int vo = pVarOffset[0];
505 Print(
"ELSE p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo,
p->exp[vo]);
518 if (pos == r->OrdSize)
return;
◆ p_Setm_Syz()
void p_Setm_Syz |
( |
poly |
p, |
|
|
ring |
r, |
|
|
int * |
Components, |
|
|
long * |
ShiftedComponents |
|
) |
| |
◆ p_Setm_TotalDegree()
void p_Setm_TotalDegree |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
◆ p_Setm_WFirstTotalDegree()
void p_Setm_WFirstTotalDegree |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
◆ p_SetModDeg()
void p_SetModDeg |
( |
intvec * |
w, |
|
|
ring |
r |
|
) |
| |
◆ p_Shift()
void p_Shift |
( |
poly * |
p, |
|
|
int |
i, |
|
|
const ring |
r |
|
) |
| |
shifts components of the vector p by i
Definition at line 4604 of file p_polys.cc.
4606 poly qp1 = *
p,qp2 = *
p;
4631 qp2->next = qp1->next;
◆ p_SimpleContent()
void p_SimpleContent |
( |
poly |
ph, |
|
|
int |
smax, |
|
|
const ring |
r |
|
) |
| |
Definition at line 2492 of file p_polys.cc.
2495 if (ph==
NULL)
return;
2506 if (
n_Size(d,r->cf)<=smax)
2514 if (smax==1) smax=2;
◆ p_Size()
int p_Size |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
Definition at line 3191 of file p_polys.cc.
3194 if (r->cf->has_simple_Alloc)
◆ p_Split()
void p_Split |
( |
poly |
p, |
|
|
poly * |
h |
|
) |
| |
◆ p_SplitAndReversePoly()
static void p_SplitAndReversePoly |
( |
poly |
p, |
|
|
int |
n, |
|
|
poly * |
non_zero, |
|
|
poly * |
zero, |
|
|
const ring |
r |
|
) |
| |
|
static |
◆ p_Sub()
poly p_Sub |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
const ring |
r |
|
) |
| |
◆ p_Subst()
poly p_Subst |
( |
poly |
p, |
|
|
int |
n, |
|
|
poly |
e, |
|
|
const ring |
r |
|
) |
| |
◆ p_Subst0()
static poly p_Subst0 |
( |
poly |
p, |
|
|
int |
n, |
|
|
const ring |
r |
|
) |
| |
|
static |
◆ p_Subst1()
static poly p_Subst1 |
( |
poly |
p, |
|
|
int |
n, |
|
|
const ring |
r |
|
) |
| |
|
static |
◆ p_Subst2()
static poly p_Subst2 |
( |
poly |
p, |
|
|
int |
n, |
|
|
number |
e, |
|
|
const ring |
r |
|
) |
| |
|
static |
Definition at line 3799 of file p_polys.cc.
3804 poly zero, non_zero;
3809 while (non_zero !=
NULL)
◆ p_TakeOutComp() [1/2]
poly p_TakeOutComp |
( |
poly * |
p, |
|
|
int |
k, |
|
|
const ring |
r |
|
) |
| |
◆ p_TakeOutComp() [2/2]
void p_TakeOutComp |
( |
poly * |
r_p, |
|
|
long |
comp, |
|
|
poly * |
r_q, |
|
|
int * |
lq, |
|
|
const ring |
r |
|
) |
| |
◆ p_TakeOutComp1()
poly p_TakeOutComp1 |
( |
poly * |
p, |
|
|
int |
k, |
|
|
const ring |
r |
|
) |
| |
◆ p_TwoMonPower()
static poly p_TwoMonPower |
( |
poly |
p, |
|
|
int |
exp, |
|
|
const ring |
r |
|
) |
| |
|
static |
Definition at line 2053 of file p_polys.cc.
2058 poly tail,
b,
res,
h;
2071 al = (
exp + 1) *
sizeof(poly);
2074 for (e=1; e<
exp; e++)
2080 for (e=
exp-1; e>eh; e--)
2089 for (e=eh; e!=0; e--)
◆ p_Var()
int p_Var |
( |
poly |
m, |
|
|
const ring |
r |
|
) |
| |
◆ p_Vec2Array()
void p_Vec2Array |
( |
poly |
v, |
|
|
poly * |
p, |
|
|
int |
len, |
|
|
const ring |
r |
|
) |
| |
vector to already allocated array (len>=p_MaxComp(v,r))
julia: vector to already allocated array (len=p_MaxComp(v,r))
Definition at line 3543 of file p_polys.cc.
3553 if (
k>len) {
Werror(
"wrong rank:%d, should be %d",len,
k); }
3562 for(
int i=len-1;
i>=0;
i--)
◆ p_Vec2Poly()
poly p_Vec2Poly |
( |
poly |
v, |
|
|
int |
k, |
|
|
const ring |
r |
|
) |
| |
◆ p_Vec2Polys()
void p_Vec2Polys |
( |
poly |
v, |
|
|
poly ** |
p, |
|
|
int * |
len, |
|
|
const ring |
r |
|
) |
| |
Definition at line 3573 of file p_polys.cc.
3579 if (*len==0) *len=1;
3580 *
p=(poly*)
omAlloc0((*len)*
sizeof(poly));
◆ p_VectorHasUnit()
void p_VectorHasUnit |
( |
poly |
p, |
|
|
int * |
k, |
|
|
int * |
len, |
|
|
const ring |
r |
|
) |
| |
Definition at line 3302 of file p_polys.cc.
3323 if ((*len == 0) || (
j<*len))
◆ p_VectorHasUnitB()
◆ p_WDegree()
long p_WDegree |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
Definition at line 706 of file p_polys.cc.
713 for(
i=1;
i<=r->firstBlockEnds;
i++)
◆ p_Weight()
int p_Weight |
( |
int |
i, |
|
|
const ring |
r |
|
) |
| |
Definition at line 697 of file p_polys.cc.
699 if ((r->firstwv==
NULL) || (
i>r->firstBlockEnds))
703 return r->firstwv[
i-1];
◆ p_WFirstTotalDegree()
long p_WFirstTotalDegree |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
Definition at line 588 of file p_polys.cc.
593 for (
i=1;
i<= r->firstBlockEnds;
i++)
◆ p_WTotaldegree()
long p_WTotaldegree |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
Definition at line 605 of file p_polys.cc.
612 for (
i=0;r->order[
i]!=0;
i++)
619 for (
k=b0 ;
k<=b1 ;
k++)
628 for (
k=b0 ;
k<=b1 ;
k++)
637 for (
k=b0 ;
k<=b1 ;
k++)
650 for (
k=b0 ;
k<=b1 ;
k++)
658 for (
k=0;
k<=(b1 - b0 );
k++)
◆ pEnlargeSet()
void pEnlargeSet |
( |
poly ** |
p, |
|
|
int |
l, |
|
|
int |
increment |
|
) |
| |
Definition at line 3647 of file p_polys.cc.
3653 if (increment==0)
return;
3654 h=(poly*)
omAlloc0(increment*
sizeof(poly));
3661 memset(&(
h[
l]),0,increment*
sizeof(poly));
◆ pLDeg0()
long pLDeg0 |
( |
poly |
p, |
|
|
int * |
l, |
|
|
const ring |
r |
|
) |
| |
◆ pLDeg0c()
long pLDeg0c |
( |
poly |
p, |
|
|
int * |
l, |
|
|
const ring |
r |
|
) |
| |
◆ pLDeg1()
long pLDeg1 |
( |
poly |
p, |
|
|
int * |
l, |
|
|
const ring |
r |
|
) |
| |
◆ pLDeg1_Deg()
long pLDeg1_Deg |
( |
poly |
p, |
|
|
int * |
l, |
|
|
const ring |
r |
|
) |
| |
◆ pLDeg1_Totaldegree()
long pLDeg1_Totaldegree |
( |
poly |
p, |
|
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int * |
l, |
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const ring |
r |
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) |
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◆ pLDeg1_WFirstTotalDegree()
long pLDeg1_WFirstTotalDegree |
( |
poly |
p, |
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int * |
l, |
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const ring |
r |
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) |
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◆ pLDeg1c()
long pLDeg1c |
( |
poly |
p, |
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int * |
l, |
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const ring |
r |
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) |
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◆ pLDeg1c_Deg()
long pLDeg1c_Deg |
( |
poly |
p, |
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int * |
l, |
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const ring |
r |
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◆ pLDeg1c_Totaldegree()
long pLDeg1c_Totaldegree |
( |
poly |
p, |
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int * |
l, |
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const ring |
r |
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) |
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◆ pLDeg1c_WFirstTotalDegree()
long pLDeg1c_WFirstTotalDegree |
( |
poly |
p, |
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int * |
l, |
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const ring |
r |
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) |
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◆ pLDegb()
long pLDegb |
( |
poly |
p, |
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int * |
l, |
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const ring |
r |
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) |
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Definition at line 803 of file p_polys.cc.
807 long o = r->pFDeg(
p, r);
◆ pModDeg()
static long pModDeg |
( |
poly |
p, |
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ring |
r |
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) |
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static |
Definition at line 3615 of file p_polys.cc.
3619 if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1];
◆ pnBin()
static number* pnBin |
( |
int |
exp, |
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const ring |
r |
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) |
| |
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static |
◆ pnFreeBin()
static void pnFreeBin |
( |
number * |
bin, |
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int |
exp, |
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const coeffs |
r |
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) |
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static |
◆ pp_Jet()
poly pp_Jet |
( |
poly |
p, |
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int |
m, |
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const ring |
R |
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) |
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◆ pp_JetW()
poly pp_JetW |
( |
poly |
p, |
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int |
m, |
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short * |
w, |
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const ring |
R |
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◆ pRestoreDegProcs()
Definition at line 3600 of file p_polys.cc.
3603 r->pFDeg = old_FDeg;
3604 r->pLDeg = old_lDeg;
◆ pSetDegProcs()
Definition at line 3588 of file p_polys.cc.
3591 r->pFDeg = new_FDeg;
3593 if (new_lDeg ==
NULL)
3594 new_lDeg = r->pLDegOrig;
3596 r->pLDeg = new_lDeg;
◆ _components
◆ _componentsExternal
int _componentsExternal = 0 |
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static |
◆ _componentsShifted
long* _componentsShifted = NULL |
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static |
◆ pOldFDeg
◆ pOldLDeg
◆ pOldLexOrder
◆ pSetm_error
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
static poly p_Pow_charp(poly p, int i, const ring r)
static int si_min(const int a, const int b)
poly singclap_gcd(poly f, poly g, const ring r)
polynomial gcd via singclap_gcd_r resp. idSyzygies destroys f and g
int dReportError(const char *fmt,...)
static unsigned long p_SubComp(poly p, unsigned long v, ring r)
static poly p_LmFreeAndNext(poly p, ring)
int exponent(const CanonicalForm &f, int q)
int exponent ( const CanonicalForm & f, int q )
static poly p_LmDeleteAndNext(poly p, const ring r)
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg)
static poly p_MonPower(poly p, int exp, const ring r)
void p_Normalize(poly p, const ring r)
static poly p_Invers(int n, poly u, intvec *w, 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 ...
BOOLEAN rOrd_SetCompRequiresSetm(const ring r)
return TRUE if p_SetComp requires p_Setm
const CanonicalForm int const CFList const Variable & y
static pLDegProc pOldLDeg
void sBucketDestroyAdd(sBucket_pt bucket, poly *p, int *length)
void sBucket_Add_m(sBucket_pt bucket, poly p)
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)
long(* pFDegProc)(poly p, ring r)
static poly p_Head(poly p, const ring r)
static poly p_Mult_mm(poly p, poly m, const ring r)
static poly p_Neg(poly p, const ring r)
static poly p_LmInit(poly p, const ring r)
static void p_SetCompP(poly p, int i, ring r)
static number * pnBin(int exp, const ring r)
static poly p_TwoMonPower(poly p, int exp, const ring r)
short * iv2array(intvec *iv, const ring R)
poly singclap_pdivide(poly f, poly g, const ring r)
long totaldegreeWecart_IV(poly p, ring r, const short *w)
#define TEST_OPT_CONTENTSB
#define __p_GetComp(p, r)
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
number p_InitContent(poly ph, const ring r)
void p_wrp(poly p, ring lmRing, ring tailRing)
static unsigned long p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, unsigned long number_of_exp)
const CanonicalForm CFMap CFMap & N
static BOOLEAN rField_is_Zp_a(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 number n_Param(const int iParameter, const coeffs r)
return the (iParameter^th) parameter as a NEW number NOTE: parameter numbering: 1....
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
#define POLY_NEGWEIGHT_OFFSET
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...
static BOOLEAN rField_has_Units(const ring r)
#define __p_Mult_nn(p, n, r)
void p_Lcm(const poly a, const poly b, poly m, const ring r)
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
LINLINE number nlSub(number la, number li, const coeffs r)
static void p_ExpVectorSub(poly p1, poly p2, 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,...
#define p_LmEqual(p1, p2, r)
This is a polynomial enumerator for simple iteration over coefficients of polynomials.
void p_Setm_Dummy(poly p, 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 @Note: VarOffset encodes the position in p->exp
BOOLEAN p_LmCheckPolyRing(poly p, ring r)
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
static int rGetCurrSyzLimit(const ring r)
static unsigned pLength(poly a)
poly n_PermNumber(const number z, const int *par_perm, const int, const ring src, const ring dst)
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
int r_IsRingVar(const char *n, char **names, int N)
static void p_SetExpV(poly p, int *ev, const ring r)
void p_LmDeleteAndNextRat(poly *p, int ishift, ring r)
for(int i=0;i<=n;i++) degsf[i]
long p_WFirstTotalDegree(poly p, const ring r)
static poly p_Copy(poly p, const ring r)
returns a copy of p
poly p_Power(poly p, int i, const ring r)
static pFDegProc pOldFDeg
static short rVar(const ring r)
#define rVar(r) (r->N)
static long p_MinComp(poly p, ring lmRing, ring tailRing)
static void p_ExpVectorAdd(poly p1, poly p2, const ring r)
static long p_GetOrder(poly p, ring r)
#define TEST_OPT_INTSTRATEGY
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)
poly p_Sub(poly p1, poly p2, const ring r)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
static BOOLEAN rField_is_Q_a(const ring r)
static poly p_SortAdd(poly p, const ring r, BOOLEAN revert=FALSE)
static FORCE_INLINE void n_Write(number n, const coeffs r, const BOOLEAN bShortOut=TRUE)
void PrintS(const char *s)
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....
#define omFreeSize(addr, size)
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
static int p_Cmp(poly p1, poly p2, ring r)
static int p_Comp_k_n(poly a, poly b, int k, ring r)
static short scaFirstAltVar(ring r)
static poly p_MonMultC(poly p, poly q, const ring rr)
static BOOLEAN rField_is_Ring(const ring r)
poly p_Div_nn(poly p, const number n, const ring r)
static poly p_Subst2(poly p, int n, number e, const ring r)
sBucket_pt sBucketCreate(const ring r)
void p_ContentRat(poly &ph, const ring r)
poly p_JetW(poly p, int m, short *w, const ring R)
static BOOLEAN rIsRatGRing(const ring r)
static FORCE_INLINE BOOLEAN nCoeff_is_Q_a(const coeffs r)
static int max(int a, int b)
number ndGcd(number, number, const coeffs r)
static void p_LmDelete(poly p, const ring r)
number nlGcd(number a, number b, const coeffs r)
The main handler for Singular numbers which are suitable for Singular polynomials.
void nlNormalize(number &x, const coeffs r)
void p_Write(poly p, ring lmRing, ring tailRing)
poly p_Cleardenom(poly p, const ring r)
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
static int rPar(const ring r)
(r->cf->P)
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
const char * p_Read(const char *st, poly &rc, const ring r)
static void p_GetExpV(poly p, int *ev, const ring r)
static poly p_Init(const ring r, omBin bin)
static int p_LmCmp(poly p, poly q, const ring r)
int p_MinDeg(poly p, intvec *w, const ring R)
static void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r)
void p_Setm_WFirstTotalDegree(poly p, const ring r)
static void pnFreeBin(number *bin, int exp, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
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)
BOOLEAN nlGreaterZero(number za, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
static poly p_Subst1(poly p, int n, const ring r)
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
static long p_MultExp(poly p, int v, long ee, ring r)
void p_Setm_General(poly p, const ring r)
static FORCE_INLINE number n_Farey(number a, number b, const coeffs r)
gmp_float exp(const gmp_float &a)
static FORCE_INLINE number n_Sub(number a, number b, const coeffs r)
return the difference of 'a' and 'b', i.e., a-b
#define p_LmCheckPolyRing2(p, r)
static void p_LmFree(poly p, ring)
void p_ContentForGB(poly ph, const ring r)
number ntInit(long i, const coeffs cf)
static BOOLEAN rIsNCRing(const ring r)
long p_Deg(poly a, const ring r)
void nlInpGcd(number &a, number b, const coeffs r)
static void p_Delete(poly *p, const ring r)
static poly p_Add_q(poly p, poly q, const ring r)
static BOOLEAN rField_is_GF(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 FORCE_INLINE number n_Invers(number a, const coeffs r)
return the multiplicative inverse of 'a'; raise an error if 'a' is not invertible
void rWrite(ring r, BOOLEAN details)
static int si_max(const int a, const int b)
static unsigned long p_AddComp(poly p, unsigned long v, 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...
void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg)
LINLINE number nlAdd(number la, number li, const coeffs r)
BOOLEAN p_CheckPolyRing(poly p, ring r)
#define rRing_has_Comp(r)
@ ringorder_IS
Induced (Schreyer) ordering.
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
void Werror(const char *fmt,...)
static BOOLEAN pOldLexOrder
static short scaLastAltVar(ring r)
static number p_SetCoeff(poly p, number n, ring r)
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),...
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
static int _componentsExternal
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 WerrorS(const char *s)
static poly p_Pow(poly p, int i, const ring r)
static BOOLEAN rField_has_simple_inverse(const ring r)
static poly p_DiffOpM(poly a, poly b, BOOLEAN multiply, const ring r)
static long p_AddExp(poly p, int v, long ee, ring r)
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:...
static FORCE_INLINE number n_ChineseRemainderSym(number *a, number *b, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs r)
const char * eati(const char *s, int *i)
#define p_LmCheckPolyRing1(p, r)
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
static long * _componentsShifted
static FORCE_INLINE number n_SubringGcd(number a, number b, const coeffs r)
poly p_GetCoeffRat(poly p, int ishift, ring r)
static FORCE_INLINE void n_Power(number a, int b, number *res, const coeffs r)
fill res with the power a^b
static void p_Setm(poly p, const ring r)
static unsigned long GetBitFields(const long e, const unsigned int s, const unsigned int n)
static poly p_GetExp_k_n(poly p, int l, int k, const ring r)
static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r)
const Variable & v
< [in] a sqrfree bivariate poly
static long p_IncrExp(poly p, int v, ring r)
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 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 long p_Totaldegree(poly p, const ring r)
static BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r1, const ring r2)
static BOOLEAN p_IsConstant(const poly p, const ring r)
static void p_MonMult(poly p, poly q, const ring r)
void p_Vec2Array(poly v, poly *p, int len, const ring r)
vector to already allocated array (len>=p_MaxComp(v,r))
@ ringorder_aa
for idElimination, like a, except pFDeg, pWeigths ignore it
const CanonicalForm int s
int status int void size_t count
static BOOLEAN rIsSyzIndexRing(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...
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
void p_Setm_TotalDegree(poly p, const ring r)
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
static poly p_Mult_q(poly p, poly q, const ring r)
@ ringorder_rs
opposite of ls
@ ringorder_a64
for int64 weights
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
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...
static bool rIsSCA(const ring r)
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
LINLINE void nlDelete(number *a, const coeffs r)
static BOOLEAN rField_is_Zp(const ring r)
static poly p_Subst0(poly p, int n, const ring r)
static long p_MaxComp(poly p, ring lmRing, ring tailRing)
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 poly pReverse(poly p)
static long p_DecrExp(poly p, int v, 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
static long pModDeg(poly p, ring r)
@ n_algExt
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic
static BOOLEAN rField_is_Q(const ring r)
#define omReallocSize(addr, o_size, size)
int p_Weight(int i, const ring r)