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Go to the source code of this file.
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#define | pIfThen(cond, check) do {if (cond) {check;}} while (0) |
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#define | p_Test(p, r) _p_Test(p, r, PDEBUG) |
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#define | p_LmTest(p, r) _p_LmTest(p, r, PDEBUG) |
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#define | pp_Test(p, lmRing, tailRing) _pp_Test(p, lmRing, tailRing, PDEBUG) |
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#define | p_SetmComp p_Setm |
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#define | __p_Mult_nn(p, n, r) r->p_Procs->p_Mult_nn(p, n, r) |
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#define | __pp_Mult_nn(p, n, r) r->p_Procs->pp_Mult_nn(p, n, r) |
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#define | _p_LmCmpAction(p, q, r, actionE, actionG, actionS) |
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#define | pDivAssume(x) do {} while (0) |
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#define | p_LmCmpAction(p, q, r, actionE, actionG, actionS) _p_LmCmpAction(p, q, r, actionE, actionG, actionS) |
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#define | p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r) |
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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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unsigned long | p_GetShortExpVector (const poly a, 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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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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poly | p_One (const ring r) |
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int | p_MinDeg (poly p, intvec *w, const ring R) |
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long | p_DegW (poly p, const short *w, const ring R) |
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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_NSet (number n, const ring r) |
| returns the poly representing the number n, destroys n More...
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void | p_Vec2Polys (poly v, poly **p, int *len, 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) |
| julia: vector to already allocated array (len=p_MaxComp(v,r)) More...
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void | p_ShallowDelete (poly *p, const ring r) |
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poly | p_Sub (poly a, poly b, const ring r) |
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poly | p_Power (poly p, int i, const ring r) |
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BOOLEAN | pIsMonomOf (poly p, poly m) |
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BOOLEAN | pHaveCommonMonoms (poly p, poly q) |
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BOOLEAN | p_LmCheckIsFromRing (poly p, ring r) |
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BOOLEAN | p_LmCheckPolyRing (poly p, ring r) |
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BOOLEAN | p_CheckIsFromRing (poly p, ring r) |
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BOOLEAN | p_CheckPolyRing (poly p, ring r) |
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BOOLEAN | p_CheckRing (ring r) |
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BOOLEAN | _p_Test (poly p, ring r, int level) |
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BOOLEAN | _p_LmTest (poly p, ring r, int level) |
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BOOLEAN | _pp_Test (poly p, ring lmRing, ring tailRing, int level) |
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static unsigned | pLength (poly a) |
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poly | p_Last (const poly a, int &l, const ring r) |
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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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void | p_ProjectiveUnique (poly p, const ring r) |
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void | p_ContentForGB (poly p, const ring r) |
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void | p_Content (poly p, const ring r) |
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void | p_SimpleContent (poly p, int s, 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 p, const ring r, number &c) |
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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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static void | p_Setm (poly p, const ring r) |
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p_SetmProc | p_GetSetmProc (const ring r) |
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poly | p_Subst (poly p, int n, poly e, const ring r) |
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static unsigned long | p_SetComp (poly p, unsigned long c, ring r) |
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static void | p_SetCompP (poly p, int i, ring r) |
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static void | p_SetCompP (poly p, int i, ring lmRing, ring tailRing) |
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static long | p_MaxComp (poly p, ring lmRing, ring tailRing) |
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static long | p_MaxComp (poly p, ring lmRing) |
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static long | p_MinComp (poly p, ring lmRing, ring tailRing) |
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static long | p_MinComp (poly p, ring lmRing) |
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static poly | pReverse (poly p) |
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void | pEnlargeSet (poly **p, int length, int increment) |
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void | p_String0 (poly p, ring lmRing, ring tailRing) |
| print p according to ShortOut in lmRing & tailRing More...
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char * | p_String (poly p, ring lmRing, ring tailRing) |
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void | p_Write (poly p, ring lmRing, ring tailRing) |
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void | p_Write0 (poly p, ring lmRing, ring tailRing) |
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void | p_wrp (poly p, ring lmRing, ring tailRing) |
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void | p_String0Short (const poly p, ring lmRing, ring tailRing) |
| print p in a short way, if possible More...
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void | p_String0Long (const poly p, ring lmRing, ring tailRing) |
| print p in a long way More...
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static long | p_FDeg (const poly p, const ring r) |
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static long | p_LDeg (const poly p, int *l, const ring r) |
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long | p_WFirstTotalDegree (poly p, ring r) |
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long | p_WTotaldegree (poly p, 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, ring r) |
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long | pLDeg0c (poly p, int *l, ring r) |
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long | pLDegb (poly p, int *l, ring r) |
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long | pLDeg1 (poly p, int *l, ring r) |
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long | pLDeg1c (poly p, int *l, ring r) |
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long | pLDeg1_Deg (poly p, int *l, ring r) |
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long | pLDeg1c_Deg (poly p, int *l, ring r) |
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long | pLDeg1_Totaldegree (poly p, int *l, ring r) |
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long | pLDeg1c_Totaldegree (poly p, int *l, ring r) |
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long | pLDeg1_WFirstTotalDegree (poly p, int *l, ring r) |
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long | pLDeg1c_WFirstTotalDegree (poly p, int *l, ring r) |
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BOOLEAN | p_EqualPolys (poly p1, poly p2, const ring r) |
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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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long | p_Deg (poly a, const ring r) |
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static number | p_SetCoeff (poly p, number n, ring r) |
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static long | p_GetOrder (poly p, ring r) |
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static unsigned long | p_AddComp (poly p, unsigned long v, ring r) |
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static unsigned long | p_SubComp (poly p, unsigned long v, ring r) |
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static long | p_GetExp (const poly p, const unsigned long iBitmask, const int VarOffset) |
| get a single variable exponent @Note: the integer VarOffset encodes: More...
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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 More...
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static long | p_GetExp (const poly p, const ring r, const int VarOffset) |
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static long | p_SetExp (poly p, const long e, const ring r, const int VarOffset) |
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static long | p_GetExp (const poly p, const int v, const ring r) |
| get v^th exponent for a monomial More...
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static long | p_SetExp (poly p, const int v, const long e, const ring r) |
| set v^th exponent for a monomial More...
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static long | p_IncrExp (poly p, int v, ring r) |
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static long | p_DecrExp (poly p, int v, ring r) |
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static long | p_AddExp (poly p, int v, long ee, ring r) |
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static long | p_SubExp (poly p, int v, long ee, ring r) |
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static long | p_MultExp (poly p, int v, long ee, ring r) |
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static long | p_GetExpSum (poly p1, poly p2, int i, ring r) |
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static long | p_GetExpDiff (poly p1, poly p2, int i, ring r) |
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static int | p_Comp_k_n (poly a, poly b, int k, ring r) |
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static poly | p_New (const ring, omBin bin) |
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static poly | p_New (ring r) |
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static void | p_LmFree (poly p, ring) |
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static void | p_LmFree (poly *p, ring) |
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static poly | p_LmFreeAndNext (poly p, ring) |
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static void | p_LmDelete (poly p, const ring r) |
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static void | p_LmDelete (poly *p, const ring r) |
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static poly | p_LmDeleteAndNext (poly p, const ring r) |
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unsigned long | p_GetMaxExpL (poly p, const ring r, unsigned long l_max=0) |
| return the maximal exponent of p in form of the maximal long var More...
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poly | p_GetMaxExpP (poly p, 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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static unsigned long | p_GetMaxExp (const unsigned long l, const ring r) |
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static unsigned long | p_GetMaxExp (const poly p, const ring r) |
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static unsigned long | p_GetTotalDegree (const unsigned long l, const ring r, const int number_of_exps) |
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static poly | p_Copy_noCheck (poly p, const ring r) |
| returns a copy of p (without any additional testing) More...
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static poly | p_Copy (poly p, const ring r) |
| returns a copy of p More...
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static poly | p_Head (poly p, const ring r) |
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static poly | p_Copy (poly p, const ring lmRing, const ring tailRing) |
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static void | p_Delete (poly *p, const ring r) |
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static void | p_Delete (poly *p, const ring lmRing, const ring tailRing) |
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static poly | p_ShallowCopyDelete (poly p, const ring r, omBin bin) |
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static poly | p_Add_q (poly p, poly q, const ring r) |
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static poly | p_Add_q (poly p, poly q, int &lp, int lq, const ring r) |
| like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q) More...
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static poly | p_Mult_nn (poly p, number n, const ring r) |
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static poly | p_Mult_nn (poly p, number n, const ring lmRing, const ring tailRing) |
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static poly | pp_Mult_nn (poly p, number n, const ring r) |
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static BOOLEAN | p_LmIsConstantComp (const poly p, const ring r) |
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static BOOLEAN | p_LmIsConstant (const poly p, const ring r) |
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static poly | pp_Mult_mm (poly p, poly m, const ring r) |
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static poly | p_Mult_mm (poly p, poly m, const ring r) |
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static poly | p_Minus_mm_Mult_qq (poly p, const poly m, const poly q, int &lp, int lq, const poly spNoether, const ring r) |
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static poly | p_Minus_mm_Mult_qq (poly p, const poly m, const poly q, const ring r) |
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static poly | pp_Mult_Coeff_mm_DivSelect (poly p, const poly m, const ring r) |
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static poly | pp_Mult_Coeff_mm_DivSelect (poly p, int &lp, const poly m, const ring r) |
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static poly | p_Neg (poly p, const ring r) |
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poly | _p_Mult_q (poly p, poly q, const int copy, const ring r) |
| Returns: p * q, Destroys: if !copy then p, q Assumes: pLength(p) >= 2 pLength(q) >=2. More...
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static poly | p_Mult_q (poly p, poly q, const ring r) |
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static poly | pp_Mult_qq (poly p, poly q, const ring r) |
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static poly | p_Plus_mm_Mult_qq (poly p, poly m, poly q, int &lp, int lq, const ring r) |
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static poly | p_Plus_mm_Mult_qq (poly p, poly m, poly q, const ring r) |
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static poly | p_Merge_q (poly p, poly q, const ring r) |
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static poly | p_SortAdd (poly p, const ring r, BOOLEAN revert=FALSE) |
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static poly | p_SortMerge (poly p, const ring r, BOOLEAN revert=FALSE) |
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static char * | p_String (poly p, ring p_ring) |
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static void | p_String0 (poly p, ring p_ring) |
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static void | p_Write (poly p, ring p_ring) |
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static void | p_Write0 (poly p, ring p_ring) |
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static void | p_wrp (poly p, ring p_ring) |
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static void | p_MemAdd_NegWeightAdjust (poly p, const ring r) |
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static void | p_MemSub_NegWeightAdjust (poly p, const ring r) |
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static void | p_ExpVectorCopy (poly d_p, poly s_p, const ring r) |
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static poly | p_Init (const ring r, omBin bin) |
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static poly | p_Init (const ring r) |
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static poly | p_LmInit (poly p, const ring r) |
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static poly | p_LmInit (poly s_p, const ring s_r, const ring d_r, omBin d_bin) |
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static poly | p_LmInit (poly s_p, const ring s_r, const ring d_r) |
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static poly | p_GetExp_k_n (poly p, int l, int k, const ring r) |
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static poly | p_LmShallowCopyDelete (poly p, const ring r) |
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static void | p_ExpVectorAdd (poly p1, poly p2, const ring r) |
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static void | p_ExpVectorSum (poly pr, poly p1, poly p2, const ring r) |
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static void | p_ExpVectorSub (poly p1, poly p2, const ring r) |
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static void | p_ExpVectorAddSub (poly p1, poly p2, poly p3, const ring r) |
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static void | p_ExpVectorDiff (poly pr, poly p1, poly p2, const ring r) |
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static BOOLEAN | p_ExpVectorEqual (poly p1, poly p2, const ring r) |
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static long | p_Totaldegree (poly p, const ring r) |
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static void | p_GetExpV (poly p, int *ev, const ring r) |
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static void | p_GetExpVL (poly p, int64 *ev, const ring r) |
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static void | p_SetExpV (poly p, int *ev, const ring r) |
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static void | p_SetExpVL (poly p, int64 *ev, const ring r) |
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static int | p_LmCmp (poly p, poly q, const ring r) |
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static int | p_LtCmp (poly p, poly q, const ring r) |
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static int | p_LtCmpNoAbs (poly p, poly q, const ring r) |
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static int | p_LtCmpOrdSgnDiffM (poly p, poly q, const ring r) |
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static int | p_LtCmpOrdSgnDiffP (poly p, poly q, const ring r) |
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static int | p_LtCmpOrdSgnEqM (poly p, poly q, const ring r) |
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static int | p_LtCmpOrdSgnEqP (poly p, poly q, const ring r) |
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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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static int | p_Cmp (poly p1, poly p2, ring r) |
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static int | p_CmpPolys (poly p1, poly p2, ring r) |
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static BOOLEAN | _p_LmDivisibleByNoComp (poly a, poly b, const ring r) |
| return: FALSE, if there exists i, such that a->exp[i] > b->exp[i] TRUE, otherwise (1) Consider long vars, instead of single exponents (2) Clearly, if la > lb, then FALSE (3) Suppose la <= lb, and consider first bits of single exponents in l: if TRUE, then value of these bits is la ^ lb if FALSE, then la-lb causes an "overflow" into one of those bits, i.e., la ^ lb != la - lb More...
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static BOOLEAN | _p_LmDivisibleByNoComp (poly a, const ring r_a, poly b, const ring r_b) |
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static BOOLEAN | _p_LmDivisibleByNoCompPart (poly a, const ring r_a, poly b, const ring r_b, const int start, const int end) |
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static BOOLEAN | _p_LmDivisibleByPart (poly a, const ring r_a, poly b, const ring r_b, const int start, const int end) |
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static BOOLEAN | p_LmDivisibleByPart (poly a, poly b, const ring r, const int start, const int end) |
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static BOOLEAN | _p_LmDivisibleBy (poly a, poly b, const ring r) |
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static BOOLEAN | _p_LmDivisibleBy (poly a, const ring r_a, poly b, const ring r_b) |
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static BOOLEAN | p_LmDivisibleByNoComp (poly a, poly b, const ring r) |
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static BOOLEAN | p_LmDivisibleByNoComp (poly a, const ring ra, poly b, const ring rb) |
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static BOOLEAN | p_LmDivisibleBy (poly a, poly b, const ring r) |
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static BOOLEAN | p_DivisibleBy (poly a, poly b, const ring r) |
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static BOOLEAN | p_DivisibleBy (poly a, const ring r_a, poly b, const ring r_b) |
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static BOOLEAN | p_LmDivisibleBy (poly a, const ring r_a, poly b, const ring r_b) |
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static BOOLEAN | p_LmShortDivisibleBy (poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r) |
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static BOOLEAN | p_LmShortDivisibleByNoComp (poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r) |
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static BOOLEAN | p_LmShortDivisibleBy (poly a, unsigned long sev_a, const ring r_a, poly b, unsigned long not_sev_b, const ring r_b) |
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static BOOLEAN | p_IsConstantComp (const poly p, const ring r) |
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static BOOLEAN | p_IsConstant (const poly p, const ring r) |
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static BOOLEAN | p_IsOne (const poly p, const ring R) |
| either poly(1) or gen(k)?! More...
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static BOOLEAN | p_IsConstantPoly (const poly p, const ring r) |
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static BOOLEAN | p_IsUnit (const poly p, const ring r) |
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static BOOLEAN | p_LmExpVectorAddIsOk (const poly p1, const poly p2, const ring r) |
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void | p_Split (poly p, poly *r) |
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BOOLEAN | p_HasNotCF (poly p1, poly p2, const ring r) |
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poly | p_mInit (const char *s, BOOLEAN &ok, const ring r) |
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const char * | p_Read (const char *s, poly &p, const ring r) |
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poly | p_MDivide (poly a, poly b, const ring r) |
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poly | p_DivideM (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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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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poly | p_GetCoeffRat (poly p, int ishift, ring r) |
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void | p_LmDeleteAndNextRat (poly *p, int ishift, ring r) |
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void | p_ContentRat (poly &ph, const ring r) |
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poly | p_Diff (poly a, int k, const ring r) |
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poly | p_DiffOp (poly a, poly b, BOOLEAN multiply, const ring r) |
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int | p_Weight (int c, 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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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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void | p_TakeOutComp (poly *p, long comp, poly *q, int *lq, const ring r) |
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poly | p_TakeOutComp (poly *p, int k, const ring r) |
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void | p_DeleteComp (poly *p, int k, const ring r) |
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void | pSetDegProcs (ring r, pFDegProc new_FDeg, pLDegProc new_lDeg=NULL) |
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void | pRestoreDegProcs (ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
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void | p_SetModDeg (intvec *w, ring r) |
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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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poly | n_PermNumber (const number z, const int *par_perm, const int OldPar, 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=NULL, int OldPar=0, BOOLEAN use_mult=FALSE) |
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poly | p_Series (int n, poly p, poly u, intvec *w, const ring R) |
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int | p_Var (poly mi, 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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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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poly | p_Div_mm (poly p, const poly m, const ring r) |
| divide polynomial by monomial More...
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◆ __p_Mult_nn
#define __p_Mult_nn |
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| r->p_Procs->p_Mult_nn(p, n, r) |
◆ __pp_Mult_nn
#define __pp_Mult_nn |
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| r->p_Procs->pp_Mult_nn(p, n, r) |
◆ _p_LmCmpAction
#define _p_LmCmpAction |
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actionE, |
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actionS |
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Value:
actionE, actionG, actionS)
Definition at line 1213 of file p_polys.h.
◆ p_LmCmpAction
#define p_LmCmpAction |
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| _p_LmCmpAction(p, q, r, actionE, actionG, actionS) |
◆ p_LmEqual
◆ p_LmTest
◆ p_SetmComp
◆ p_Test
◆ pDivAssume
◆ pIfThen
◆ pp_Test
◆ _p_LmDivisibleBy() [1/2]
◆ _p_LmDivisibleBy() [2/2]
static BOOLEAN _p_LmDivisibleBy |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ _p_LmDivisibleByNoComp() [1/2]
static BOOLEAN _p_LmDivisibleByNoComp |
( |
poly |
a, |
|
|
const ring |
r_a, |
|
|
poly |
b, |
|
|
const ring |
r_b |
|
) |
| |
|
inlinestatic |
◆ _p_LmDivisibleByNoComp() [2/2]
static BOOLEAN _p_LmDivisibleByNoComp |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
return: FALSE, if there exists i, such that a->exp[i] > b->exp[i] TRUE, otherwise (1) Consider long vars, instead of single exponents (2) Clearly, if la > lb, then FALSE (3) Suppose la <= lb, and consider first bits of single exponents in l: if TRUE, then value of these bits is la ^ lb if FALSE, then la-lb causes an "overflow" into one of those bits, i.e., la ^ lb != la - lb
Definition at line 1691 of file p_polys.h.
1693 int i=r->VarL_Size - 1;
1694 unsigned long divmask = r->divmask;
1695 unsigned long la, lb;
1697 if (r->VarL_LowIndex >= 0)
1699 i += r->VarL_LowIndex;
1705 (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
1712 while (
i>=r->VarL_LowIndex);
1718 la = a->exp[r->VarL_Offset[
i]];
1719 lb =
b->exp[r->VarL_Offset[
i]];
1721 (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
◆ _p_LmDivisibleByNoCompPart()
◆ _p_LmDivisibleByPart()
◆ _p_LmTest()
BOOLEAN _p_LmTest |
( |
poly |
p, |
|
|
ring |
r, |
|
|
int |
level |
|
) |
| |
◆ _p_Mult_q()
poly _p_Mult_q |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const int |
copy, |
|
|
const ring |
r |
|
) |
| |
Returns: p * q, Destroys: if !copy then p, q Assumes: pLength(p) >= 2 pLength(q) >=2.
Definition at line 273 of file p_Mult_q.cc.
◆ _p_Test()
BOOLEAN _p_Test |
( |
poly |
p, |
|
|
ring |
r, |
|
|
int |
level |
|
) |
| |
Definition at line 212 of file pDebug.cc.
266 long c1, cc1, ccc1, ec1;
270 if (o->
data.syzcomp.Components!=
NULL)
272 cc1 = o->
data.syzcomp.Components[c1];
273 ccc1 = o->
data.syzcomp.ShiftedComponents[cc1];
275 else { cc1=0; ccc1=0; }
278 ec1 =
p->exp[o->
data.syzcomp.place];
310 for (
i=r->N;
i>0;
i--)
◆ _pp_Test()
BOOLEAN _pp_Test |
( |
poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing, |
|
|
int |
level |
|
) |
| |
◆ 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_Add_q() [1/2]
static poly p_Add_q |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 893 of file p_polys.h.
896 if (q==
NULL)
return p;
897 if (
p==
NULL)
return q;
899 return r->p_Procs->p_Add_q(
p, q, shorter, r);
◆ p_Add_q() [2/2]
static poly p_Add_q |
( |
poly |
p, |
|
|
poly |
q, |
|
|
int & |
lp, |
|
|
int |
lq, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q)
Definition at line 903 of file p_polys.h.
906 if (q==
NULL)
return p;
907 if (
p==
NULL) { lp=
lq;
return q; }
909 poly
res = r->p_Procs->p_Add_q(
p, q, shorter, r);
◆ p_AddComp()
static unsigned long p_AddComp |
( |
poly |
p, |
|
|
unsigned long |
v, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_AddExp()
static long p_AddExp |
( |
poly |
p, |
|
|
int |
v, |
|
|
long |
ee, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_CheckIsFromRing()
BOOLEAN p_CheckIsFromRing |
( |
poly |
p, |
|
|
ring |
r |
|
) |
| |
◆ p_CheckPolyRing()
BOOLEAN p_CheckPolyRing |
( |
poly |
p, |
|
|
ring |
r |
|
) |
| |
◆ p_CheckRing()
◆ p_ChineseRemainder()
poly p_ChineseRemainder |
( |
poly * |
xx, |
|
|
number * |
x, |
|
|
number * |
q, |
|
|
int |
rl, |
|
|
CFArray & |
inv_cache, |
|
|
const ring |
R |
|
) |
| |
◆ p_Cleardenom()
poly p_Cleardenom |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
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 |
p, |
|
|
const ring |
r, |
|
|
number & |
c |
|
) |
| |
Definition at line 2891 of file p_polys.cc.
2900 #if CLEARENUMERATORS
2953 #if CLEARENUMERATORS
◆ p_Cmp()
static int p_Cmp |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_CmpPolys()
static int p_CmpPolys |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_Comp_k_n()
static int p_Comp_k_n |
( |
poly |
a, |
|
|
poly |
b, |
|
|
int |
k, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ 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 |
p, |
|
|
const ring |
r |
|
) |
| |
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 |
p, |
|
|
const ring |
r |
|
) |
| |
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, |
|
|
const ring |
r |
|
) |
| |
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_Copy() [1/2]
static poly p_Copy |
( |
poly |
p, |
|
|
const ring |
lmRing, |
|
|
const ring |
tailRing |
|
) |
| |
|
inlinestatic |
Definition at line 840 of file p_polys.h.
845 if (tailRing == lmRing)
◆ p_Copy() [2/2]
static poly p_Copy |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
returns a copy of p
Definition at line 813 of file p_polys.h.
◆ p_Copy_noCheck()
static poly p_Copy_noCheck |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
returns a copy of p (without any additional testing)
Definition at line 803 of file p_polys.h.
809 return r->p_Procs->p_Copy(
p, r);
◆ p_DecrExp()
static long p_DecrExp |
( |
poly |
p, |
|
|
int |
v, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_Deg()
long p_Deg |
( |
poly |
a, |
|
|
const ring |
r |
|
) |
| |
◆ p_DegW()
long p_DegW |
( |
poly |
p, |
|
|
const short * |
w, |
|
|
const ring |
R |
|
) |
| |
◆ p_Delete() [1/2]
static void p_Delete |
( |
poly * |
p, |
|
|
const ring |
lmRing, |
|
|
const ring |
tailRing |
|
) |
| |
|
inlinestatic |
Definition at line 865 of file p_polys.h.
871 if (tailRing == lmRing)
◆ p_Delete() [2/2]
static void p_Delete |
( |
poly * |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_DeleteComp()
void p_DeleteComp |
( |
poly * |
p, |
|
|
int |
k, |
|
|
const ring |
r |
|
) |
| |
◆ p_Diff()
poly p_Diff |
( |
poly |
a, |
|
|
int |
k, |
|
|
const ring |
r |
|
) |
| |
◆ p_DiffOp()
poly p_DiffOp |
( |
poly |
a, |
|
|
poly |
b, |
|
|
BOOLEAN |
multiply, |
|
|
const ring |
r |
|
) |
| |
◆ p_Div_mm()
poly p_Div_mm |
( |
poly |
p, |
|
|
const poly |
m, |
|
|
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, |
|
|
const number |
n, |
|
|
const ring |
r |
|
) |
| |
◆ p_DivideM()
poly p_DivideM |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
◆ p_DivisibleBy() [1/2]
◆ p_DivisibleBy() [2/2]
static BOOLEAN p_DivisibleBy |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_DivisibleByRingCase()
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
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_ExpVectorAdd()
static void p_ExpVectorAdd |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_ExpVectorAddSub()
static void p_ExpVectorAddSub |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
poly |
p3, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_ExpVectorCopy()
static void p_ExpVectorCopy |
( |
poly |
d_p, |
|
|
poly |
s_p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1250 of file p_polys.h.
1254 memcpy(d_p->exp, s_p->exp, r->ExpL_Size*
sizeof(
long));
◆ p_ExpVectorDiff()
static void p_ExpVectorDiff |
( |
poly |
pr, |
|
|
poly |
p1, |
|
|
poly |
p2, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_ExpVectorEqual()
static BOOLEAN p_ExpVectorEqual |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1426 of file p_polys.h.
1431 unsigned i = r->ExpL_Size;
1432 unsigned long *ep = p1->exp;
1433 unsigned long *eq = p2->exp;
1438 if (ep[
i] != eq[
i])
return FALSE;
◆ p_ExpVectorSub()
static void p_ExpVectorSub |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_ExpVectorSum()
static void p_ExpVectorSum |
( |
poly |
pr, |
|
|
poly |
p1, |
|
|
poly |
p2, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_Farey()
poly p_Farey |
( |
poly |
p, |
|
|
number |
N, |
|
|
const ring |
r |
|
) |
| |
◆ p_FDeg()
Definition at line 381 of file p_polys.h.
381 {
return r->pFDeg(
p,r); }
◆ p_GcdMon()
poly p_GcdMon |
( |
poly |
f, |
|
|
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_GetExp() [1/3]
get v^th exponent for a monomial
Definition at line 573 of file p_polys.h.
578 return p_GetExp(
p, r->bitmask, r->VarOffset[
v]);
◆ p_GetExp() [2/3]
◆ p_GetExp() [3/3]
static long p_GetExp |
( |
const poly |
p, |
|
|
const unsigned long |
iBitmask, |
|
|
const int |
VarOffset |
|
) |
| |
|
inlinestatic |
get a single variable exponent @Note: the integer VarOffset encodes:
- the position of a variable in the exponent vector p->exp (lower 24 bits)
- number of bits to shift to the right in the upper 8 bits (which takes at most 6 bits for 64 bit) Thus VarOffset always has 2 zero higher bits!
Definition at line 470 of file p_polys.h.
472 pAssume2((VarOffset >> (24 + 6)) == 0);
474 int pos=(VarOffset & 0xffffff);
475 int bitpos=(VarOffset >> 24);
476 unsigned long exp=(
p->exp[pos] >> bitmask) & iBitmask;
480 ((
p->exp[(VarOffset & 0xffffff)] >> (VarOffset >> 24))
◆ p_GetExp_k_n()
static poly p_GetExp_k_n |
( |
poly |
p, |
|
|
int |
l, |
|
|
int |
k, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1309 of file p_polys.h.
1316 memcpy(np->exp,
p->exp, r->ExpL_Size*
sizeof(
long));
◆ p_GetExpDiff()
static long p_GetExpDiff |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
int |
i, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_GetExpSum()
static long p_GetExpSum |
( |
poly |
p1, |
|
|
poly |
p2, |
|
|
int |
i, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_GetExpV()
static void p_GetExpV |
( |
poly |
p, |
|
|
int * |
ev, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1457 of file p_polys.h.
1460 for (
unsigned j = r->N;
j!=0;
j--)
◆ p_GetExpVL()
static void p_GetExpVL |
( |
poly |
p, |
|
|
int64 * |
ev, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1466 of file p_polys.h.
1469 for (
unsigned j = r->N;
j!=0;
j--)
◆ p_GetMaxExp() [1/2]
static unsigned long p_GetMaxExp |
( |
const poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_GetMaxExp() [2/2]
static unsigned long p_GetMaxExp |
( |
const unsigned long |
l, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 748 of file p_polys.h.
750 unsigned long bitmask = r->bitmask;
751 unsigned long max = (
l & bitmask);
752 unsigned long j = r->ExpPerLong - 1;
756 unsigned long i = r->BitsPerExp;
760 e = ((
l >>
i) & bitmask);
761 if ((
unsigned long) e >
max)
◆ p_GetMaxExpL()
unsigned long p_GetMaxExpL |
( |
poly |
p, |
|
|
const ring |
r, |
|
|
unsigned long |
l_max = 0 |
|
) |
| |
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_GetMaxExpP()
poly p_GetMaxExpP |
( |
poly |
p, |
|
|
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_GetOrder()
static long p_GetOrder |
( |
poly |
p, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 422 of file p_polys.h.
425 if (r->typ==
NULL)
return ((
p)->
exp[r->pOrdIndex]);
429 switch(r->typ[
i].ord_typ)
442 return ((
p)->
exp[r->pOrdIndex]);
◆ 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 |
a, |
|
|
const ring |
r |
|
) |
| |
Definition at line 4679 of file p_polys.cc.
4682 unsigned long ev = 0;
4696 for (;
j<=r->N;
j++)
◆ p_GetShortExpVector() [2/2]
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_GetTotalDegree()
static unsigned long p_GetTotalDegree |
( |
const unsigned long |
l, |
|
|
const ring |
r, |
|
|
const int |
number_of_exps |
|
) |
| |
|
inlinestatic |
Definition at line 777 of file p_polys.h.
779 const unsigned long bitmask = r->bitmask;
780 unsigned long sum = (
l & bitmask);
781 unsigned long j = number_of_exps - 1;
785 unsigned long i = r->BitsPerExp;
788 sum += ((
l >>
i) & bitmask);
◆ 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_Head()
static poly p_Head |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 826 of file p_polys.h.
833 memcpy(np->exp,
p->exp, r->ExpL_Size*
sizeof(
long));
◆ p_Homogen()
poly p_Homogen |
( |
poly |
p, |
|
|
int |
varnum, |
|
|
const ring |
r |
|
) |
| |
◆ p_IncrExp()
static long p_IncrExp |
( |
poly |
p, |
|
|
int |
v, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_Init() [1/2]
static poly p_Init |
( |
const ring |
r | ) |
|
|
inlinestatic |
◆ p_Init() [2/2]
◆ 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_IsConstant()
◆ p_IsConstantComp()
◆ p_IsConstantPoly()
◆ 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_IsOne()
either poly(1) or gen(k)?!
Definition at line 1937 of file p_polys.h.
◆ p_IsPurePower()
return i, if head depends only on var(i)
Definition at line 1218 of file p_polys.cc.
◆ p_IsUnit()
◆ 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 |
a, |
|
|
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_LDeg()
static long p_LDeg |
( |
const poly |
p, |
|
|
int * |
l, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 382 of file p_polys.h.
382 {
return r->pLDeg(
p,
l,r); }
◆ p_LmCheckIsFromRing()
BOOLEAN p_LmCheckIsFromRing |
( |
poly |
p, |
|
|
ring |
r |
|
) |
| |
Definition at line 71 of file pDebug.cc.
75 #if (OM_TRACK > 0) && defined(OM_TRACK_CUSTOM)
76 void* custom = omGetCustomOfAddr(
p);
85 "monomial not from specified ring",
p,r);
◆ p_LmCheckPolyRing()
BOOLEAN p_LmCheckPolyRing |
( |
poly |
p, |
|
|
ring |
r |
|
) |
| |
◆ p_LmCmp()
static int p_LmCmp |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1498 of file p_polys.h.
1503 const unsigned long* _s1 = ((
unsigned long*)
p->exp);
1504 const unsigned long* _s2 = ((
unsigned long*) q->exp);
1507 const unsigned long _l = r->CmpL_Size;
1511 LengthGeneral_OrdGeneral_LoopTop:
1517 if (_i == _l)
return 0;
1518 goto LengthGeneral_OrdGeneral_LoopTop;
1520 const long* _ordsgn = (
long*) r->ordsgn;
1526 return -(_ordsgn[_i]);
1530 if (_ordsgn[_i] == 1)
return 1;
1533 if (_ordsgn[_i] == 1)
return -1;
◆ p_LmDelete() [1/2]
static void p_LmDelete |
( |
poly * |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LmDelete() [2/2]
static void p_LmDelete |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LmDeleteAndNext()
static poly p_LmDeleteAndNext |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LmDeleteAndNextRat()
void p_LmDeleteAndNextRat |
( |
poly * |
p, |
|
|
int |
ishift, |
|
|
ring |
r |
|
) |
| |
◆ p_LmDivisibleBy() [1/2]
◆ p_LmDivisibleBy() [2/2]
static BOOLEAN p_LmDivisibleBy |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LmDivisibleByNoComp() [1/2]
static BOOLEAN p_LmDivisibleByNoComp |
( |
poly |
a, |
|
|
const ring |
ra, |
|
|
poly |
b, |
|
|
const ring |
rb |
|
) |
| |
|
inlinestatic |
◆ p_LmDivisibleByNoComp() [2/2]
static BOOLEAN p_LmDivisibleByNoComp |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LmDivisibleByPart()
◆ p_LmExpVectorAddIsOk()
Definition at line 1964 of file p_polys.h.
1969 unsigned long l1, l2, divmask = r->divmask;
1972 for (
i=0;
i<r->VarL_Size;
i++)
1974 l1 = p1->exp[r->VarL_Offset[
i]];
1975 l2 = p2->exp[r->VarL_Offset[
i]];
1977 if ( (l1 > ULONG_MAX - l2) ||
1978 (((l1 & divmask) ^ (l2 & divmask)) != ((l1 + l2) & divmask)))
◆ p_LmFree() [1/2]
static void p_LmFree |
( |
poly * |
p, |
|
|
ring |
|
|
) |
| |
|
inlinestatic |
◆ p_LmFree() [2/2]
static void p_LmFree |
( |
poly |
p, |
|
|
ring |
|
|
) |
| |
|
inlinestatic |
◆ p_LmFreeAndNext()
static poly p_LmFreeAndNext |
( |
poly |
p, |
|
|
ring |
|
|
) |
| |
|
inlinestatic |
◆ p_LmInit() [1/3]
static poly p_LmInit |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1272 of file p_polys.h.
1278 memcpy(np->exp,
p->exp, r->ExpL_Size*
sizeof(
long));
◆ p_LmInit() [2/3]
static poly p_LmInit |
( |
poly |
s_p, |
|
|
const ring |
s_r, |
|
|
const ring |
d_r |
|
) |
| |
|
inlinestatic |
◆ p_LmInit() [3/3]
static poly p_LmInit |
( |
poly |
s_p, |
|
|
const ring |
s_r, |
|
|
const ring |
d_r, |
|
|
omBin |
d_bin |
|
) |
| |
|
inlinestatic |
Definition at line 1283 of file p_polys.h.
1288 poly d_p =
p_Init(d_r, d_bin);
1289 for (
unsigned i=d_r->N;
i!=0;
i--)
◆ p_LmIsConstant()
◆ p_LmIsConstantComp()
Definition at line 963 of file p_polys.h.
966 int i = r->VarL_Size - 1;
970 if (
p->exp[r->VarL_Offset[
i]] != 0)
◆ p_LmShallowCopyDelete()
static poly p_LmShallowCopyDelete |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1330 of file p_polys.h.
1334 poly new_p =
p_New(r);
1335 memcpy(new_p->exp,
p->exp, r->ExpL_Size*
sizeof(
long));
◆ p_LmShortDivisibleBy() [1/2]
static BOOLEAN p_LmShortDivisibleBy |
( |
poly |
a, |
|
|
unsigned long |
sev_a, |
|
|
const ring |
r_a, |
|
|
poly |
b, |
|
|
unsigned long |
not_sev_b, |
|
|
const ring |
r_b |
|
) |
| |
|
inlinestatic |
Definition at line 1895 of file p_polys.h.
1904 if (sev_a & not_sev_b)
◆ p_LmShortDivisibleBy() [2/2]
static BOOLEAN p_LmShortDivisibleBy |
( |
poly |
a, |
|
|
unsigned long |
sev_a, |
|
|
poly |
b, |
|
|
unsigned long |
not_sev_b, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1855 of file p_polys.h.
1864 if (sev_a & not_sev_b)
◆ p_LmShortDivisibleByNoComp()
static BOOLEAN p_LmShortDivisibleByNoComp |
( |
poly |
a, |
|
|
unsigned long |
sev_a, |
|
|
poly |
b, |
|
|
unsigned long |
not_sev_b, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1875 of file p_polys.h.
1884 if (sev_a & not_sev_b)
◆ 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_LtCmp()
static int p_LtCmp |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LtCmpNoAbs()
static int p_LtCmpNoAbs |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LtCmpOrdSgnDiffM()
static int p_LtCmpOrdSgnDiffM |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LtCmpOrdSgnDiffP()
static int p_LtCmpOrdSgnDiffP |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LtCmpOrdSgnEqM()
static int p_LtCmpOrdSgnEqM |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_LtCmpOrdSgnEqP()
static int p_LtCmpOrdSgnEqP |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_MaxComp() [1/2]
static long p_MaxComp |
( |
poly |
p, |
|
|
ring |
lmRing |
|
) |
| |
|
inlinestatic |
◆ p_MaxComp() [2/2]
static long p_MaxComp |
( |
poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
|
inlinestatic |
◆ p_MDivide()
poly p_MDivide |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
◆ p_MemAdd_NegWeightAdjust()
static void p_MemAdd_NegWeightAdjust |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1229 of file p_polys.h.
1231 if (r->NegWeightL_Offset !=
NULL)
1233 for (
int i=r->NegWeightL_Size-1;
i>=0;
i--)
◆ p_MemSub_NegWeightAdjust()
static void p_MemSub_NegWeightAdjust |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1239 of file p_polys.h.
1241 if (r->NegWeightL_Offset !=
NULL)
1243 for (
int i=r->NegWeightL_Size-1;
i>=0;
i--)
◆ p_Merge_q()
static poly p_Merge_q |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1149 of file p_polys.h.
1152 return r->p_Procs->p_Merge_q(
p, q, r);
◆ p_MinComp() [1/2]
static long p_MinComp |
( |
poly |
p, |
|
|
ring |
lmRing |
|
) |
| |
|
inlinestatic |
◆ p_MinComp() [2/2]
static long p_MinComp |
( |
poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
|
inlinestatic |
◆ p_MinDeg()
◆ p_mInit()
Definition at line 1412 of file p_polys.cc.
1418 if ((
s!=st)&&isdigit(st[0]))
◆ p_Minus_mm_Mult_qq() [1/2]
static poly p_Minus_mm_Mult_qq |
( |
poly |
p, |
|
|
const poly |
m, |
|
|
const poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1018 of file p_polys.h.
1022 return r->p_Procs->p_Minus_mm_Mult_qq(
p,
m, q, shorter,
NULL, r);
◆ p_Minus_mm_Mult_qq() [2/2]
static poly p_Minus_mm_Mult_qq |
( |
poly |
p, |
|
|
const poly |
m, |
|
|
const poly |
q, |
|
|
int & |
lp, |
|
|
int |
lq, |
|
|
const poly |
spNoether, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1007 of file p_polys.h.
1011 const poly
res = r->p_Procs->p_Minus_mm_Mult_qq(
p,
m, q, shorter, spNoether, r);
◆ p_Mult_mm()
static poly p_Mult_mm |
( |
poly |
p, |
|
|
poly |
m, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 998 of file p_polys.h.
1004 return r->p_Procs->p_Mult_mm(
p,
m, r);
◆ p_Mult_nn() [1/2]
static poly p_Mult_nn |
( |
poly |
p, |
|
|
number |
n, |
|
|
const ring |
lmRing, |
|
|
const ring |
tailRing |
|
) |
| |
|
inlinestatic |
Definition at line 930 of file p_polys.h.
935 if (lmRing == tailRing)
940 p = lmRing->p_Procs->p_Mult_nn(
p, n, lmRing);
943 pNext(
p) = tailRing->p_Procs->p_Mult_nn(pnext, n, tailRing);
◆ p_Mult_nn() [2/2]
static poly p_Mult_nn |
( |
poly |
p, |
|
|
number |
n, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 915 of file p_polys.h.
926 return r->p_Procs->p_Mult_nn(
p, n, r);
◆ p_Mult_q()
static poly p_Mult_q |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1051 of file p_polys.h.
1068 q = r->p_Procs->p_mm_Mult(q,
p, r);
1075 p = r->p_Procs->p_Mult_mm(
p, q, r);
◆ p_MultExp()
static long p_MultExp |
( |
poly |
p, |
|
|
int |
v, |
|
|
long |
ee, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_Neg()
static poly p_Neg |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1044 of file p_polys.h.
1046 return r->p_Procs->p_Neg(
p, r);
◆ p_New() [1/2]
◆ p_New() [2/2]
static poly p_New |
( |
ring |
r | ) |
|
|
inlinestatic |
◆ 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_Plus_mm_Mult_qq() [1/2]
static poly p_Plus_mm_Mult_qq |
( |
poly |
p, |
|
|
poly |
m, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_Plus_mm_Mult_qq() [2/2]
static poly p_Plus_mm_Mult_qq |
( |
poly |
p, |
|
|
poly |
m, |
|
|
poly |
q, |
|
|
int & |
lp, |
|
|
int |
lq, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1120 of file p_polys.h.
1132 number n_neg =
n_Copy(n_old, r->cf);
1135 res = r->p_Procs->p_Minus_mm_Mult_qq(
p,
m, q, shorter,
NULL, r);
1136 lp = (lp +
lq) - shorter;
◆ 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_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 |
p, |
|
|
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_SetCoeff()
static number p_SetCoeff |
( |
poly |
p, |
|
|
number |
n, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_SetComp()
static unsigned long p_SetComp |
( |
poly |
p, |
|
|
unsigned long |
c, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_SetCompP() [1/2]
static void p_SetCompP |
( |
poly |
p, |
|
|
int |
i, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
|
inlinestatic |
◆ p_SetCompP() [2/2]
static void p_SetCompP |
( |
poly |
p, |
|
|
int |
i, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_SetExp() [1/3]
set v^th exponent for a monomial
Definition at line 583 of file p_polys.h.
588 return p_SetExp(
p, e, r->bitmask, r->VarOffset[
v]);
◆ p_SetExp() [2/3]
static long p_SetExp |
( |
poly |
p, |
|
|
const long |
e, |
|
|
const ring |
r, |
|
|
const int |
VarOffset |
|
) |
| |
|
inlinestatic |
◆ p_SetExp() [3/3]
static unsigned long p_SetExp |
( |
poly |
p, |
|
|
const unsigned long |
e, |
|
|
const unsigned long |
iBitmask, |
|
|
const int |
VarOffset |
|
) |
| |
|
inlinestatic |
set a single variable exponent @Note: VarOffset encodes the position in p->exp
- See also
- p_GetExp
Definition at line 489 of file p_polys.h.
493 pAssume2((VarOffset >> (24 + 6)) == 0);
496 REGISTER int shift = VarOffset >> 24;
497 unsigned long ee = e << shift ;
501 p->exp[
offset] &= ~( iBitmask << shift );
◆ p_SetExpV()
static void p_SetExpV |
( |
poly |
p, |
|
|
int * |
ev, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1472 of file p_polys.h.
1475 for (
unsigned j = r->N;
j!=0;
j--)
◆ p_SetExpVL()
static void p_SetExpVL |
( |
poly |
p, |
|
|
int64 * |
ev, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1482 of file p_polys.h.
1485 for (
unsigned j = r->N;
j!=0;
j--)
◆ p_Setm()
static void p_Setm |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_SetModDeg()
void p_SetModDeg |
( |
intvec * |
w, |
|
|
ring |
r |
|
) |
| |
◆ p_ShallowCopyDelete()
static poly p_ShallowCopyDelete |
( |
poly |
p, |
|
|
const ring |
r, |
|
|
omBin |
bin |
|
) |
| |
|
inlinestatic |
Definition at line 885 of file p_polys.h.
889 return r->p_Procs->p_ShallowCopyDelete(
p, r, bin);
◆ p_ShallowDelete()
void p_ShallowDelete |
( |
poly * |
p, |
|
|
const 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 |
p, |
|
|
int |
s, |
|
|
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_SortAdd()
◆ p_SortMerge()
◆ p_Split()
void p_Split |
( |
poly |
p, |
|
|
poly * |
r |
|
) |
| |
◆ p_String() [1/2]
char* p_String |
( |
poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
◆ p_String() [2/2]
static char* p_String |
( |
poly |
p, |
|
|
ring |
p_ring |
|
) |
| |
|
inlinestatic |
◆ p_String0() [1/2]
void p_String0 |
( |
poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
print p according to ShortOut in lmRing & tailRing
Definition at line 134 of file polys0.cc.
145 if ((
p_GetComp(
p, lmRing) == 0) || (!lmRing->VectorOut))
177 if (
p ==
NULL)
break;
◆ p_String0() [2/2]
static void p_String0 |
( |
poly |
p, |
|
|
ring |
p_ring |
|
) |
| |
|
inlinestatic |
◆ p_String0Long()
void p_String0Long |
( |
const poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
print p in a long way
print p in a long way
Definition at line 114 of file polys0.cc.
124 lmRing->ShortOut =
FALSE;
125 tailRing->ShortOut =
FALSE;
129 lmRing->ShortOut = bLMShortOut;
130 tailRing->ShortOut = bTAILShortOut;
◆ p_String0Short()
void p_String0Short |
( |
const poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
print p in a short way, if possible
print p in a short way, if possible
Definition at line 95 of file polys0.cc.
109 lmRing->ShortOut = bLMShortOut;
110 tailRing->ShortOut = bTAILShortOut;
◆ p_Sub()
poly p_Sub |
( |
poly |
a, |
|
|
poly |
b, |
|
|
const ring |
r |
|
) |
| |
◆ p_SubComp()
static unsigned long p_SubComp |
( |
poly |
p, |
|
|
unsigned long |
v, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_SubExp()
static long p_SubExp |
( |
poly |
p, |
|
|
int |
v, |
|
|
long |
ee, |
|
|
ring |
r |
|
) |
| |
|
inlinestatic |
◆ p_Subst()
poly p_Subst |
( |
poly |
p, |
|
|
int |
n, |
|
|
poly |
e, |
|
|
const ring |
r |
|
) |
| |
◆ p_TakeOutComp() [1/2]
poly p_TakeOutComp |
( |
poly * |
p, |
|
|
int |
k, |
|
|
const ring |
r |
|
) |
| |
◆ p_TakeOutComp() [2/2]
void p_TakeOutComp |
( |
poly * |
p, |
|
|
long |
comp, |
|
|
poly * |
q, |
|
|
int * |
lq, |
|
|
const ring |
r |
|
) |
| |
◆ p_TakeOutComp1()
poly p_TakeOutComp1 |
( |
poly * |
p, |
|
|
int |
k, |
|
|
const ring |
r |
|
) |
| |
◆ p_Totaldegree()
static long p_Totaldegree |
( |
poly |
p, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1444 of file p_polys.h.
1450 for (
unsigned i=r->VarL_Size-1;
i!=0;
i--)
◆ p_Var()
int p_Var |
( |
poly |
mi, |
|
|
const ring |
r |
|
) |
| |
◆ p_Vec2Array()
void p_Vec2Array |
( |
poly |
v, |
|
|
poly * |
p, |
|
|
int |
len, |
|
|
const ring |
r |
|
) |
| |
julia: 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 |
c, |
|
|
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, |
|
|
ring |
r |
|
) |
| |
Definition at line 588 of file p_polys.cc.
593 for (
i=1;
i<= r->firstBlockEnds;
i++)
◆ p_Write() [1/2]
void p_Write |
( |
poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
◆ p_Write() [2/2]
static void p_Write |
( |
poly |
p, |
|
|
ring |
p_ring |
|
) |
| |
|
inlinestatic |
◆ p_Write0() [1/2]
void p_Write0 |
( |
poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
◆ p_Write0() [2/2]
static void p_Write0 |
( |
poly |
p, |
|
|
ring |
p_ring |
|
) |
| |
|
inlinestatic |
◆ p_wrp() [1/2]
void p_wrp |
( |
poly |
p, |
|
|
ring |
lmRing, |
|
|
ring |
tailRing |
|
) |
| |
◆ p_wrp() [2/2]
static void p_wrp |
( |
poly |
p, |
|
|
ring |
p_ring |
|
) |
| |
|
inlinestatic |
◆ 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 |
length, |
|
|
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));
◆ pHaveCommonMonoms()
BOOLEAN pHaveCommonMonoms |
( |
poly |
p, |
|
|
poly |
q |
|
) |
| |
◆ pIsMonomOf()
BOOLEAN pIsMonomOf |
( |
poly |
p, |
|
|
poly |
m |
|
) |
| |
◆ pLDeg0()
long pLDeg0 |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg0c()
long pLDeg0c |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg1()
long pLDeg1 |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg1_Deg()
long pLDeg1_Deg |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg1_Totaldegree()
long pLDeg1_Totaldegree |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg1_WFirstTotalDegree()
long pLDeg1_WFirstTotalDegree |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg1c()
long pLDeg1c |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg1c_Deg()
long pLDeg1c_Deg |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg1c_Totaldegree()
long pLDeg1c_Totaldegree |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDeg1c_WFirstTotalDegree()
long pLDeg1c_WFirstTotalDegree |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
◆ pLDegb()
long pLDegb |
( |
poly |
p, |
|
|
int * |
l, |
|
|
ring |
r |
|
) |
| |
Definition at line 803 of file p_polys.cc.
807 long o = r->pFDeg(
p, r);
◆ pLength()
static unsigned pLength |
( |
poly |
a | ) |
|
|
inlinestatic |
◆ pp_Jet()
poly pp_Jet |
( |
poly |
p, |
|
|
int |
m, |
|
|
const ring |
R |
|
) |
| |
◆ pp_JetW()
poly pp_JetW |
( |
poly |
p, |
|
|
int |
m, |
|
|
short * |
w, |
|
|
const ring |
R |
|
) |
| |
◆ pp_Mult_Coeff_mm_DivSelect() [1/2]
static poly pp_Mult_Coeff_mm_DivSelect |
( |
poly |
p, |
|
|
const poly |
m, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1027 of file p_polys.h.
1030 return r->p_Procs->pp_Mult_Coeff_mm_DivSelect(
p,
m, shorter, r);
◆ pp_Mult_Coeff_mm_DivSelect() [2/2]
static poly pp_Mult_Coeff_mm_DivSelect |
( |
poly |
p, |
|
|
int & |
lp, |
|
|
const poly |
m, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1035 of file p_polys.h.
1038 poly
pp = r->p_Procs->pp_Mult_Coeff_mm_DivSelect(
p,
m, shorter, r);
◆ pp_Mult_mm()
static poly pp_Mult_mm |
( |
poly |
p, |
|
|
poly |
m, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 988 of file p_polys.h.
994 return r->p_Procs->pp_Mult_mm(
p,
m, r);
◆ pp_Mult_nn()
static poly pp_Mult_nn |
( |
poly |
p, |
|
|
number |
n, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 949 of file p_polys.h.
957 return r->p_Procs->pp_Mult_nn(
p, n, r);
◆ pp_Mult_qq()
static poly pp_Mult_qq |
( |
poly |
p, |
|
|
poly |
q, |
|
|
const ring |
r |
|
) |
| |
|
inlinestatic |
Definition at line 1088 of file p_polys.h.
1094 return r->p_Procs->pp_mm_Mult(q,
p, r);
1099 return r->p_Procs->pp_Mult_mm(
p, q, r);
◆ pRestoreDegProcs()
Definition at line 3600 of file p_polys.cc.
3603 r->pFDeg = old_FDeg;
3604 r->pLDeg = old_lDeg;
◆ pReverse()
static poly pReverse |
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poly |
p | ) |
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inlinestatic |
◆ 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;
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
#define _pPolyAssume2(cond, p, r)
static poly p_Pow_charp(poly p, int i, const ring r)
static int si_min(const int a, const int b)
static poly _p_Mult_q_Normal(poly p, poly q, const int copy, 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
static BOOLEAN _p_LmDivisibleByNoCompPart(poly a, const ring r_a, poly b, const ring r_b, const int start, const int end)
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 )
#define p_MemCmp_LengthGeneral_OrdGeneral(s1, s2, length, ordsgn, actionE, actionG, actionS)
#define pIfThen1(cond, check)
static void writemon(poly p, int ko, const ring r)
static BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r)
return: FALSE, if there exists i, such that a->exp[i] > b->exp[i] TRUE, otherwise (1) Consider long v...
#define p_MemDiff_LengthGeneral(r, s1, s2, length)
static unsigned long p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps)
void StringAppendS(const char *st)
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:
#define p_MemSum_LengthGeneral(r, s1, s2, length)
void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg)
static poly _p_Mult_q_Normal_ZeroDiv(poly p, poly q, const int copy, const ring r)
static poly p_DebugInit(poly p, ring src_ring, ring dest_ring)
static poly p_MonPower(poly p, int exp, const ring r)
void p_Normalize(poly p, const ring r)
BOOLEAN pDebugLmShortDivisibleByNoComp(poly p1, unsigned long sev_1, ring r_1, poly p2, unsigned long not_sev_2, ring r_2)
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 ...
void p_Write0(poly p, ring lmRing, ring tailRing)
BOOLEAN rOrd_SetCompRequiresSetm(const ring r)
return TRUE if p_SetComp requires p_Setm
static BOOLEAN rCanShortOut(const ring r)
BOOLEAN p_CheckIsFromRing(poly p, ring r)
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
static pLDegProc pOldLDeg
void sBucketDestroyAdd(sBucket_pt bucket, poly *p, int *length)
void sBucket_Add_m(sBucket_pt bucket, poly p)
unsigned long p_GetShortExpVector(const poly a, const ring r)
unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max=0)
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)
BOOLEAN p_DebugLmDivisibleByNoComp(poly a, poly b, ring r)
#define p_SetRingOfLm(p, r)
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)
#define MIN_LENGTH_BUCKET
#define p_MemSub_LengthGeneral(r, s, length)
char * p_String(poly p, ring lmRing, ring tailRing)
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 poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, 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)
BOOLEAN pqLength(poly p, poly q, int &lp, int &lq, const int min)
#define TEST_OPT_CONTENTSB
#define __p_GetComp(p, r)
static void p_MemAdd_NegWeightAdjust(poly p, const ring r)
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
#define p_MemAdd_LengthGeneral(r, s, length)
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_Greater(number a, number b, const coeffs r)
ordered fields: TRUE iff 'a' is larger than 'b'; in Z/pZ: TRUE iff la > lb, where la and lb are the l...
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 BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring 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)
BOOLEAN _p_LmTest(poly p, ring r, int level)
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
BOOLEAN p_LmCheckIsFromRing(poly p, ring r)
static short rVar(const ring r)
#define rVar(r) (r->N)
static long p_MinComp(poly p, ring lmRing, ring tailRing)
#define p_MemAddSub_LengthGeneral(r, s, t, length)
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)
#define omIsBinPageAddr(addr)
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
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)
#define pPolyAssumeReturnMsg(cond, msg)
#define _pPolyAssumeReturnMsg(cond, msg, p, r)
static FORCE_INLINE void n_Write(number n, const coeffs r, const BOOLEAN bShortOut=TRUE)
#define TEST_OPT_NOT_BUCKETS
void PrintS(const char *s)
size_t omSizeWOfAddr(void *addr)
poly sBucketSortAdd(poly p, const ring r)
Sorts p with bucketSort: p may have equal monomials.
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)
char * p_String(poly p, ring lmRing, ring tailRing)
omError_t omTestBinAddrSize(void *addr, size_t size, int check_level)
#define omFreeBinAddr(addr)
static int p_Comp_k_n(poly a, poly b, int k, ring r)
static short scaFirstAltVar(ring r)
BOOLEAN dPolyReportError(poly p, ring r, const char *fmt,...)
static poly _p_Mult_q_Bucket(poly p, const int lp, poly q, const int lq, const int copy, const ring r)
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)
#define pFalseReturn(cond)
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)
void p_Write0(poly p, ring lmRing, ring tailRing)
#define pAssumeReturn(cond)
static int max(int a, int b)
number ndGcd(number, number, const coeffs r)
static void p_LmDelete(poly p, const ring r)
static poly p_New(const ring, omBin bin)
number nlGcd(number a, number b, const coeffs r)
The main handler for Singular numbers which are suitable for Singular polynomials.
#define omTypeAlloc0Bin(type, addr, bin)
void p_String0(poly p, ring lmRing, ring tailRing)
print p according to ShortOut in lmRing & tailRing
poly nc_p_Plus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, const int, const ring r)
static int p_LtCmp(poly p, poly q, const ring r)
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
#define omTypeAllocBin(type, addr, bin)
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
poly sBucketSortMerge(poly p, const ring r)
Sorts p with bucketSort: assumes all monomials of p are different.
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)
void p_Setm_WFirstTotalDegree(poly p, const ring r)
static BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r)
#define __pp_Mult_nn(p, n, r)
poly _nc_p_Mult_q(poly p, poly q, const ring r)
general NC-multiplication with destruction
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...
void p_Setm_General(poly p, const ring r)
static FORCE_INLINE number n_Farey(number a, number b, const coeffs r)
poly singclap_pmult(poly f, poly g, const ring r)
BOOLEAN p_CheckRing(ring 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
BOOLEAN pIsMonomOf(poly p, poly m)
#define p_LmCheckPolyRing2(p, r)
BOOLEAN p_CheckRing(ring r)
static void p_LmFree(poly p, ring)
void p_ContentForGB(poly ph, const ring r)
number ntInit(long i, const coeffs cf)
long p_Deg(poly a, const ring r)
static BOOLEAN rIsNCRing(const ring r)
void nlInpGcd(number &a, number b, const coeffs r)
static void p_Delete(poly *p, const ring r)
poly _nc_pp_Mult_qq(const poly p, const poly q, const ring r)
general NC-multiplication without destruction
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
static void p_MemSub_NegWeightAdjust(poly p, const ring r)
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
void rWrite(ring r, BOOLEAN details)
void StringSetS(const char *st)
#define omTestList(ptr, level)
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)
#define _pPolyAssumeReturn(cond, p, r)
@ ringorder_IS
Induced (Schreyer) ordering.
#define omSizeWOfBin(bin_ptr)
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 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)
#define MIN_LENGTH_FACTORY
poly _p_Mult_q(poly p, poly q, const int copy, const ring r)
Returns: p * q, Destroys: if !copy then p, q Assumes: pLength(p) >= 2 pLength(q) >=2.
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 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)
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)
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
static unsigned long p_GetMaxExp(const unsigned long l, const ring r)
CanonicalForm ndConvSingNFactoryN(number, BOOLEAN, const coeffs)
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
CFArray copy(const CFList &list)
write elements of list into an array
void p_String0(poly p, ring lmRing, ring tailRing)
print p according to ShortOut in lmRing & tailRing
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 BOOLEAN rShortOut(const ring r)
static BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, 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.
BOOLEAN _p_Test(poly p, ring r, int level)
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 poly p_Mult_nn(poly p, number n, const ring r)
BOOLEAN pDebugLmShortDivisibleBy(poly p1, unsigned long sev_1, ring r_1, poly p2, unsigned long not_sev_2, ring r_2)
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 FORCE_INLINE BOOLEAN nCoeff_is_Domain(const coeffs r)
returns TRUE, if r is a field or r has no zero divisors (i.e is a domain)
static BOOLEAN p_LmIsConstant(const poly p, const ring r)
static BOOLEAN rField_is_Q(const ring r)
#define omReallocSize(addr, o_size, size)
int p_Weight(int i, const ring r)