[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /*************************************************************** |
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| 5 | * File: gring.cc |
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| 6 | * Purpose: noncommutative kernel procedures |
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| 7 | * Author: levandov (Viktor Levandovsky) |
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| 8 | * Created: 8/00 - 11/00 |
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[341696] | 9 | * Version: $Id$ |
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[35aab3] | 10 | *******************************************************************/ |
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[52e2f6] | 11 | |
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[022ef5] | 12 | #define MYTEST 0 |
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| 13 | #define OUTPUT 0 |
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| 14 | |
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| 15 | #if MYTEST |
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[52e2f6] | 16 | #define OM_CHECK 4 |
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| 17 | #define OM_TRACK 5 |
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[022ef5] | 18 | #endif |
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[52e2f6] | 19 | |
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[599326] | 20 | #include <kernel/mod2.h> |
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[86016d] | 21 | |
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[f2f460] | 22 | #ifdef HAVE_PLURAL |
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[5a9e7b] | 23 | #define PLURAL_INTERNAL_DECLARATIONS |
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| 24 | |
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[599326] | 25 | #include <kernel/febase.h> |
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| 26 | #include <kernel/options.h> |
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| 27 | #include <kernel/ring.h> |
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| 28 | #include <kernel/polys.h> |
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| 29 | #include <kernel/numbers.h> |
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| 30 | #include <kernel/ideals.h> |
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| 31 | #include <kernel/matpol.h> |
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| 32 | #include <kernel/kbuckets.h> |
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| 33 | #include <kernel/kstd1.h> |
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| 34 | #include <kernel/sbuckets.h> |
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| 35 | #include <kernel/prCopy.h> |
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| 36 | #include <kernel/p_Mult_q.h> |
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| 37 | #include <kernel/pInline1.h> |
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[b1a5c1] | 38 | |
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[6bde67] | 39 | // dirty tricks: |
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[599326] | 40 | #include <kernel/p_MemAdd.h> |
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[6bde67] | 41 | |
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[599326] | 42 | #include <kernel/gring.h> |
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| 43 | #include <kernel/sca.h> |
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[6bde67] | 44 | #include <summator.h> |
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[5a9e7b] | 45 | |
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[599326] | 46 | #include <kernel/ncSAMult.h> // for CMultiplier etc classes |
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| 47 | #include <kernel/ncSAFormula.h> // for CFormulaPowerMultiplier and enum Enum_ncSAType |
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[1495df4] | 48 | |
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[43cbc0] | 49 | #ifdef HAVE_RATGRING |
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[599326] | 50 | #include <kernel/ratgring.h> |
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[43cbc0] | 51 | #endif |
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| 52 | |
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[52e2f6] | 53 | |
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[57bfa2] | 54 | |
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[8f63e4c] | 55 | int iNCExtensions = 0x00001; // only SCA can be used by default |
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[57bfa2] | 56 | |
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| 57 | |
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| 58 | int& getNCExtensions() |
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| 59 | { |
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| 60 | return (iNCExtensions); |
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| 61 | } |
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| 62 | |
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| 63 | int setNCExtensions(int iMask) |
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| 64 | { |
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| 65 | const int iOld = getNCExtensions(); |
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| 66 | getNCExtensions() = iMask; |
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| 67 | return (iOld); |
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| 68 | } |
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| 69 | |
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| 70 | |
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| 71 | bool ncExtensions(int iMask) // = 0x0FFFF |
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| 72 | { |
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| 73 | return ((getNCExtensions() & iMask) == iMask); |
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| 74 | } |
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| 75 | |
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| 76 | |
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| 77 | |
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| 78 | |
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[efcd6fc] | 79 | static const bool bNoPluralMultiplication = false; // use only formula shortcuts in my OOP Multiplier |
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| 80 | |
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| 81 | // the following make sense only if bNoPluralMultiplication is false: |
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| 82 | static const bool bNoFormula = true; // don't use any formula shortcuts |
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| 83 | static const bool bNoCache = false; // only formula whenever possible, only make sanse if bNoFormula is false! |
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| 84 | |
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| 85 | |
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[f2a4f3f] | 86 | // false, true, false == old "good" Plural |
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| 87 | // false, false ==>> Plural + Cache + Direct Formula - not much |
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| 88 | // false, false, true ==>> Plural Mult + Direct Formula (no ~cache) |
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| 89 | // true, *, * == new OOP multiplication! |
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| 90 | |
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[06879b7] | 91 | |
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[35aab3] | 92 | /* global nc_macros : */ |
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[5a9e7b] | 93 | |
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[35aab3] | 94 | #define freeT(A,v) omFreeSize((ADDRESS)A,(v+1)*sizeof(int)) |
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| 95 | #define freeN(A,k) omFreeSize((ADDRESS)A,k*sizeof(number)) |
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| 96 | |
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| 97 | |
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[86016d] | 98 | // some forward declarations: |
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| 99 | |
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| 100 | |
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[5accf0] | 101 | // polynomial multiplication functions for p_Procs : |
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[86016d] | 102 | poly gnc_pp_Mult_mm(const poly p, const poly m, const ring r, poly &last); |
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| 103 | poly gnc_p_Mult_mm(poly p, const poly m, const ring r); |
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| 104 | poly gnc_mm_Mult_p(const poly m, poly p, const ring r); |
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| 105 | poly gnc_mm_Mult_pp(const poly m, const poly p, const ring r); |
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| 106 | |
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| 107 | |
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| 108 | // set pProcs for r and global variable p_Procs as for general non-commutative algebras. |
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| 109 | void gnc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs); |
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| 110 | |
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| 111 | /* syzygies : */ |
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| 112 | poly gnc_CreateSpolyOld(const poly p1, const poly p2/*, poly spNoether*/, const ring r); |
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| 113 | poly gnc_ReduceSpolyOld(const poly p1, poly p2/*, poly spNoether*/, const ring r); |
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| 114 | |
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| 115 | poly gnc_CreateSpolyNew(const poly p1, const poly p2/*, poly spNoether*/, const ring r); |
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| 116 | poly gnc_ReduceSpolyNew(const poly p1, poly p2/*, poly spNoether*/, const ring r); |
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| 117 | |
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| 118 | |
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| 119 | |
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| 120 | void gnc_kBucketPolyRedNew(kBucket_pt b, poly p, number *c); |
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| 121 | void gnc_kBucketPolyRed_ZNew(kBucket_pt b, poly p, number *c); |
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| 122 | |
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| 123 | void gnc_kBucketPolyRedOld(kBucket_pt b, poly p, number *c); |
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| 124 | void gnc_kBucketPolyRed_ZOld(kBucket_pt b, poly p, number *c); |
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| 125 | |
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| 126 | |
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| 127 | // poly gnc_ReduceSpolyNew(poly p1, poly p2, poly spNoether, const ring r); |
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| 128 | // void gnc_ReduceSpolyTail(poly p1, poly q, poly q2, poly spNoether, const ring r); |
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| 129 | |
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[5accf0] | 130 | // void nc_kBucketPolyRed(kBucket_pt b, poly p); |
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[86016d] | 131 | |
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| 132 | ideal gnc_gr_mora(const ideal, const ideal, const intvec *, const intvec *, kStrategy); // Not yet! |
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| 133 | ideal gnc_gr_bba (const ideal F, const ideal Q, const intvec *, const intvec *, kStrategy strat); |
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| 134 | |
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| 135 | |
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[022ef5] | 136 | void nc_CleanUp(nc_struct* p); // just free memory! |
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| 137 | void nc_rCleanUp(ring r); // smaller than kill: just free mem |
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| 138 | |
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| 139 | |
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[86016d] | 140 | #if 0 |
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| 141 | // deprecated functions: |
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| 142 | // poly gnc_p_Minus_mm_Mult_qq_ign(poly p, const poly m, poly q, int & d1, poly d2, const ring ri, poly &d3); |
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| 143 | // poly gnc_p_Minus_mm_Mult_qq(poly p, const poly m, poly q, const ring r); |
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| 144 | // poly nc_p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, int lq, const ring r); |
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| 145 | // poly nc_p_Plus_mm_Mult_qq (poly p, const poly m, const poly q, int &lp, int lq, const ring r); |
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| 146 | #endif |
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| 147 | |
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| 148 | |
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[35aab3] | 149 | |
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[52e2f6] | 150 | /*2 |
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| 151 | * returns the LCM of the head terms of a and b |
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[151000] | 152 | * without coefficient!!! |
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[52e2f6] | 153 | */ |
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| 154 | poly p_Lcm(const poly a, const poly b, const long lCompM, const ring r) |
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| 155 | { |
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[b902246] | 156 | poly m = // p_One( r); |
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[b1a5c1] | 157 | p_Init(r); |
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[52e2f6] | 158 | |
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| 159 | const int pVariables = r->N; |
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| 160 | |
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[b1a5c1] | 161 | for (int i = pVariables; i!=0; i--) |
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[52e2f6] | 162 | { |
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| 163 | const int lExpA = p_GetExp (a, i, r); |
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| 164 | const int lExpB = p_GetExp (b, i, r); |
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| 165 | |
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| 166 | p_SetExp (m, i, si_max(lExpA, lExpB), r); |
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| 167 | } |
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| 168 | |
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| 169 | p_SetComp (m, lCompM, r); |
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| 170 | |
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| 171 | p_Setm(m,r); |
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| 172 | |
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| 173 | #ifdef PDEBUG |
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[151000] | 174 | // p_Test(m,r); |
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[52e2f6] | 175 | #endif |
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| 176 | |
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[b1a5c1] | 177 | n_New(&(p_GetCoeff(m, r)), r); |
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[151000] | 178 | |
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[52e2f6] | 179 | return(m); |
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| 180 | }; |
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| 181 | |
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| 182 | poly p_Lcm(const poly a, const poly b, const ring r) |
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| 183 | { |
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| 184 | #ifdef PDEBUG |
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| 185 | p_Test(a, r); |
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| 186 | p_Test(b, r); |
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| 187 | #endif |
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| 188 | |
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| 189 | const long lCompP1 = p_GetComp(a, r); |
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| 190 | const long lCompP2 = p_GetComp(b, r); |
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| 191 | |
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| 192 | const poly m = p_Lcm(a, b, si_max(lCompP1, lCompP2), r); |
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[b1a5c1] | 193 | |
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[52e2f6] | 194 | #ifdef PDEBUG |
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[151000] | 195 | // p_Test(m,r); |
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[52e2f6] | 196 | #endif |
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| 197 | return(m); |
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| 198 | }; |
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| 199 | |
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| 200 | |
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| 201 | |
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[86016d] | 202 | /////////////////////////////////////////////////////////////////////////////// |
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[5a9e7b] | 203 | poly nc_p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, |
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| 204 | const int, const poly, const ring r) |
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[35aab3] | 205 | { |
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[5a9e7b] | 206 | poly mc = p_Neg( p_Copy(m, r), r ); |
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[d5f9aea] | 207 | poly mmc = nc_mm_Mult_pp( mc, q, r ); |
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[5a9e7b] | 208 | p_Delete(&mc, r); |
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| 209 | |
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| 210 | p = p_Add_q(p, mmc, r); |
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| 211 | |
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| 212 | lp = pLength(p); // ring independent! |
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| 213 | |
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| 214 | return(p); |
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[35aab3] | 215 | } |
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| 216 | |
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[5a9e7b] | 217 | // returns p + m*q destroys p, const: q, m |
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| 218 | poly nc_p_Plus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, |
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| 219 | const int, const ring r) |
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[35aab3] | 220 | { |
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[d5f9aea] | 221 | p = p_Add_q(p, nc_mm_Mult_pp( m, q, r ), r); |
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[5a9e7b] | 222 | |
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| 223 | lp = pLength(p); |
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| 224 | |
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[35aab3] | 225 | return(p); |
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| 226 | } |
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| 227 | |
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[5a9e7b] | 228 | #if 0 |
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| 229 | poly gnc_p_Minus_mm_Mult_qq_ign(poly p, const poly m, poly q, int & d1, poly d2, const ring r, poly &d3) |
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[9306b5d] | 230 | { |
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[5a9e7b] | 231 | poly t; |
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| 232 | int i; |
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| 233 | |
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| 234 | return gnc_p_Minus_mm_Mult_qq(p, m, q, d1, i, t, r); |
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[9306b5d] | 235 | } |
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[5a9e7b] | 236 | #endif |
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| 237 | |
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| 238 | |
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[35aab3] | 239 | //----------- auxiliary routines-------------------------- |
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[6bde67] | 240 | poly _gnc_p_Mult_q(poly p, poly q, const int copy, const ring r) // not used anymore! |
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[35aab3] | 241 | /* destroy p,q unless copy=1 */ |
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| 242 | { |
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| 243 | poly res=NULL; |
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| 244 | poly ghost=NULL; |
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| 245 | poly qq,pp; |
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| 246 | if (copy) |
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| 247 | { |
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| 248 | qq=p_Copy(q,r); |
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| 249 | pp=p_Copy(p,r); |
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| 250 | } |
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| 251 | else |
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| 252 | { |
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| 253 | qq=q; |
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| 254 | pp=p; |
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| 255 | } |
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| 256 | while (qq!=NULL) |
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| 257 | { |
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[5a9e7b] | 258 | res=p_Add_q(res, pp_Mult_mm(pp, qq, r), r); // p_Head(qq, r)? |
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[35aab3] | 259 | qq=p_LmDeleteAndNext(qq,r); |
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| 260 | } |
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| 261 | p_Delete(&pp,r); |
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| 262 | return(res); |
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| 263 | } |
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| 264 | |
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[5a9e7b] | 265 | // return pPolyP * pPolyQ; destroy or reuse pPolyP and pPolyQ |
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| 266 | poly _nc_p_Mult_q(poly pPolyP, poly pPolyQ, const ring rRing) |
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| 267 | { |
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| 268 | assume( rIsPluralRing(rRing) ); |
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[6bde67] | 269 | #ifdef PDEBUG |
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| 270 | p_Test(pPolyP, rRing); |
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| 271 | p_Test(pPolyQ, rRing); |
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| 272 | #endif |
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| 273 | #ifdef RDEBUG |
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| 274 | rTest(rRing); |
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| 275 | #endif |
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[26d633] | 276 | |
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[6bde67] | 277 | int lp, lq; |
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[5a9e7b] | 278 | |
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[6bde67] | 279 | pqLength(pPolyP, pPolyQ, lp, lq, MIN_LENGTH_BUCKET); |
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[5a9e7b] | 280 | |
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[6bde67] | 281 | bool bUsePolynomial = TEST_OPT_NOT_BUCKETS || (si_max(lp, lq) < MIN_LENGTH_BUCKET); // ??? |
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[5a9e7b] | 282 | |
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[6bde67] | 283 | CPolynomialSummator sum(rRing, bUsePolynomial); |
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[26d633] | 284 | |
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[6bde67] | 285 | if (lq <= lp) // ? |
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| 286 | { |
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| 287 | // always length(q) times "p * q[j]" |
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| 288 | for( ; pPolyQ!=NULL; pPolyQ = p_LmDeleteAndNext( pPolyQ, rRing ) ) |
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| 289 | sum += pp_Mult_mm( pPolyP, pPolyQ, rRing); |
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[5a9e7b] | 290 | |
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[6bde67] | 291 | p_Delete( &pPolyP, rRing ); |
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| 292 | } else |
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| 293 | { |
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| 294 | // always length(p) times "p[i] * q" |
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| 295 | for( ; pPolyP!=NULL; pPolyP = p_LmDeleteAndNext( pPolyP, rRing ) ) |
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| 296 | sum += nc_mm_Mult_pp( pPolyP, pPolyQ, rRing); |
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[5a9e7b] | 297 | |
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[6bde67] | 298 | p_Delete( &pPolyQ, rRing ); |
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| 299 | } |
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[5a9e7b] | 300 | |
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[6bde67] | 301 | return(sum); |
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| 302 | } |
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[5a9e7b] | 303 | |
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| 304 | // return pPolyP * pPolyQ; preserve pPolyP and pPolyQ |
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| 305 | poly _nc_pp_Mult_qq(const poly pPolyP, const poly pPolyQ, const ring rRing) |
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| 306 | { |
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| 307 | assume( rIsPluralRing(rRing) ); |
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[6bde67] | 308 | #ifdef PDEBUG |
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| 309 | p_Test(pPolyP, rRing); |
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| 310 | p_Test(pPolyQ, rRing); |
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| 311 | #endif |
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| 312 | #ifdef RDEBUG |
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| 313 | rTest(rRing); |
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| 314 | #endif |
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[5a9e7b] | 315 | |
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[6bde67] | 316 | int lp, lq; |
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[5a9e7b] | 317 | |
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[6bde67] | 318 | pqLength(pPolyP, pPolyQ, lp, lq, MIN_LENGTH_BUCKET); |
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[5a9e7b] | 319 | |
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[6bde67] | 320 | bool bUsePolynomial = TEST_OPT_NOT_BUCKETS || (si_max(lp, lq) < MIN_LENGTH_BUCKET); // ??? |
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| 321 | |
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| 322 | CPolynomialSummator sum(rRing, bUsePolynomial); |
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[5a9e7b] | 323 | |
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[6bde67] | 324 | if (lq <= lp) // ? |
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| 325 | { |
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| 326 | // always length(q) times "p * q[j]" |
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| 327 | for( poly q = pPolyQ; q !=NULL; q = pNext(q) ) |
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| 328 | sum += pp_Mult_mm(pPolyP, q, rRing); |
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| 329 | } else |
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| 330 | { |
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| 331 | // always length(p) times "p[i] * q" |
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| 332 | for( poly p = pPolyP; p !=NULL; p = pNext(p) ) |
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| 333 | sum += nc_mm_Mult_pp( p, pPolyQ, rRing); |
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| 334 | } |
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[26d633] | 335 | |
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[6bde67] | 336 | return(sum); |
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[5a9e7b] | 337 | } |
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| 338 | |
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| 339 | |
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| 340 | |
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| 341 | poly gnc_mm_Mult_nn (int *F, int *G, const ring r); |
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| 342 | poly gnc_mm_Mult_uu (int *F,int jG,int bG, const ring r); |
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| 343 | |
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| 344 | /* #define nc_uu_Mult_ww nc_uu_Mult_ww_vert */ |
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| 345 | poly gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r); |
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| 346 | /* poly nc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r); */ |
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| 347 | /* poly nc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r); */ |
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| 348 | /* poly nc_uu_Mult_ww_hvdiag (int i, int a, int j, int b, const ring r); */ |
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| 349 | /* not written yet */ |
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| 350 | |
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| 351 | |
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| 352 | poly gnc_p_Mult_mm_Common(poly p, const poly m, int side, const ring r) |
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[35aab3] | 353 | /* p is poly, m is mono with coeff, destroys p */ |
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| 354 | /* if side==1, computes p_Mult_mm; otherwise, mm_Mult_p */ |
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| 355 | { |
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| 356 | if ((p==NULL) || (m==NULL)) return NULL; |
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| 357 | /* if (pNext(p)==NULL) return(nc_mm_Mult_nn(p,pCopy(m),r)); */ |
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| 358 | /* excluded - the cycle will do it anyway - OK. */ |
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| 359 | if (p_IsConstant(m,r)) return(p_Mult_nn(p,p_GetCoeff(m,r),r)); |
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| 360 | |
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| 361 | #ifdef PDEBUG |
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| 362 | p_Test(p,r); |
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| 363 | p_Test(m,r); |
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| 364 | #endif |
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| 365 | poly v=NULL; |
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| 366 | int rN=r->N; |
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| 367 | int *P=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 368 | int *M=(int *)omAlloc0((rN+1)*sizeof(int)); |
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| 369 | /* coefficients: */ |
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| 370 | number cP,cM,cOut; |
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| 371 | p_GetExpV(m, M, r); |
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| 372 | cM=p_GetCoeff(m,r); |
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| 373 | /* components:*/ |
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| 374 | const int expM=p_GetComp(m,r); |
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| 375 | int expP=0; |
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| 376 | int expOut=0; |
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| 377 | /* bucket constraints: */ |
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| 378 | int UseBuckets=1; |
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| 379 | if (pLength(p)< MIN_LENGTH_BUCKET || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
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[6bde67] | 380 | |
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| 381 | CPolynomialSummator sum(r, UseBuckets == 0); |
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[35aab3] | 382 | |
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| 383 | while (p!=NULL) |
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| 384 | { |
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| 385 | #ifdef PDEBUG |
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| 386 | p_Test(p,r); |
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| 387 | #endif |
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| 388 | expP=p_GetComp(p,r); |
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| 389 | if (expP==0) |
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| 390 | { |
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| 391 | expOut=expM; |
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| 392 | } |
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| 393 | else |
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| 394 | { |
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| 395 | if (expM==0) |
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| 396 | { |
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| 397 | expOut=expP; |
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| 398 | #ifdef PDEBUG |
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[b1a5c1] | 399 | if (side) |
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[35aab3] | 400 | { |
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[b1a5c1] | 401 | Print("gnc_p_Mult_mm: Multiplication in the left module from the right"); |
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| 402 | } |
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[b87f029] | 403 | #endif |
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[35aab3] | 404 | } |
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| 405 | else |
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| 406 | { |
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| 407 | /* REPORT_ERROR */ |
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[ea68ed] | 408 | #ifdef PDEBUG |
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[b1a5c1] | 409 | const char* s; |
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| 410 | if (side==1) s="gnc_p_Mult_mm"; |
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| 411 | else s="gnc_mm_Mult_p"; |
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| 412 | Print("%s: exponent mismatch %d and %d\n",s,expP,expM); |
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[ea68ed] | 413 | #endif |
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[35aab3] | 414 | expOut=0; |
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| 415 | } |
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| 416 | } |
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| 417 | p_GetExpV(p,P,r); |
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| 418 | cP=p_GetCoeff(p,r); |
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| 419 | cOut=n_Mult(cP,cM,r); |
---|
| 420 | if (side==1) |
---|
| 421 | { |
---|
[5a9e7b] | 422 | v = gnc_mm_Mult_nn(P, M, r); |
---|
[35aab3] | 423 | } |
---|
| 424 | else |
---|
| 425 | { |
---|
[5a9e7b] | 426 | v = gnc_mm_Mult_nn(M, P, r); |
---|
[35aab3] | 427 | } |
---|
| 428 | v = p_Mult_nn(v,cOut,r); |
---|
[f524fd] | 429 | n_Delete(&cOut,r); |
---|
[35aab3] | 430 | p_SetCompP(v,expOut,r); |
---|
[6bde67] | 431 | |
---|
| 432 | sum += v; |
---|
| 433 | |
---|
[fb82895] | 434 | p_LmDelete(&p,r); |
---|
[35aab3] | 435 | } |
---|
| 436 | freeT(P,rN); |
---|
| 437 | freeT(M,rN); |
---|
[6bde67] | 438 | |
---|
| 439 | return(sum); |
---|
[35aab3] | 440 | } |
---|
| 441 | |
---|
[5a9e7b] | 442 | /* poly functions defined in p_Procs : */ |
---|
| 443 | poly gnc_pp_Mult_mm(const poly p, const poly m, const ring r, poly &last) |
---|
| 444 | { |
---|
| 445 | return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 1, r) ); |
---|
| 446 | } |
---|
| 447 | |
---|
| 448 | poly gnc_p_Mult_mm(poly p, const poly m, const ring r) |
---|
| 449 | { |
---|
| 450 | return( gnc_p_Mult_mm_Common(p, m, 1, r) ); |
---|
| 451 | } |
---|
| 452 | |
---|
| 453 | poly gnc_mm_Mult_p(const poly m, poly p, const ring r) |
---|
| 454 | { |
---|
| 455 | return( gnc_p_Mult_mm_Common(p, m, 0, r) ); |
---|
| 456 | } |
---|
| 457 | |
---|
| 458 | poly gnc_mm_Mult_pp(const poly m, const poly p, const ring r) |
---|
| 459 | { |
---|
| 460 | return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 0, r) ); |
---|
| 461 | } |
---|
| 462 | |
---|
| 463 | |
---|
| 464 | |
---|
| 465 | poly gnc_mm_Mult_nn(int *F0, int *G0, const ring r) |
---|
[35aab3] | 466 | /* destroys nothing, no coeffs and exps */ |
---|
| 467 | { |
---|
| 468 | poly out=NULL; |
---|
| 469 | int i,j; |
---|
| 470 | int iF,jG,iG; |
---|
| 471 | int rN=r->N; |
---|
| 472 | int ExpSize=(((rN+1)*sizeof(int)+sizeof(long)-1)/sizeof(long))*sizeof(long); |
---|
| 473 | |
---|
| 474 | int *F=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 475 | int *G=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 476 | |
---|
| 477 | memcpy(F, F0,(rN+1)*sizeof(int)); |
---|
| 478 | // pExpVectorCopy(F,F0); |
---|
| 479 | memcpy(G, G0,(rN+1)*sizeof(int)); |
---|
| 480 | // pExpVectorCopy(G,G0); |
---|
| 481 | F[0]=0; /* important for p_MemAdd */ |
---|
| 482 | G[0]=0; |
---|
| 483 | |
---|
| 484 | iF=rN; |
---|
| 485 | while ((F[iF]==0)&&(iF>=1)) iF--; /* last exp_num of F */ |
---|
| 486 | if (iF==0) /* F0 is zero vector */ |
---|
| 487 | { |
---|
| 488 | out=pOne(); |
---|
| 489 | p_SetExpV(out,G0,r); |
---|
| 490 | p_Setm(out,r); |
---|
| 491 | freeT(F,rN); |
---|
| 492 | freeT(G,rN); |
---|
| 493 | return(out); |
---|
| 494 | } |
---|
| 495 | jG=1; |
---|
| 496 | while ((G[jG]==0)&&(jG<rN)) jG++; /* first exp_num of G */ |
---|
| 497 | iG=rN; |
---|
| 498 | while ((G[iG]==0)&&(iG>1)) iG--; /* last exp_num of G */ |
---|
| 499 | |
---|
| 500 | out=pOne(); |
---|
| 501 | |
---|
| 502 | if (iF<=jG) |
---|
| 503 | /* i.e. no mixed exp_num , MERGE case */ |
---|
| 504 | { |
---|
| 505 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
---|
| 506 | p_SetExpV(out,F,r); |
---|
| 507 | p_Setm(out,r); |
---|
| 508 | // omFreeSize((ADDRESS)F,ExpSize); |
---|
| 509 | freeT(F,rN); |
---|
| 510 | freeT(G,rN); |
---|
| 511 | return(out); |
---|
| 512 | } |
---|
| 513 | |
---|
| 514 | number cff=n_Init(1,r); |
---|
| 515 | number tmp_num=NULL; |
---|
| 516 | int cpower=0; |
---|
| 517 | |
---|
[86016d] | 518 | if (ncRingType(r)==nc_skew) |
---|
[35aab3] | 519 | { |
---|
[52e2f6] | 520 | if (r->GetNC()->IsSkewConstant==1) |
---|
[35aab3] | 521 | { |
---|
| 522 | int tpower=0; |
---|
| 523 | for(j=jG; j<=iG; j++) |
---|
| 524 | { |
---|
| 525 | if (G[j]!=0) |
---|
| 526 | { |
---|
| 527 | cpower = 0; |
---|
| 528 | for(i=j+1; i<=iF; i++) |
---|
| 529 | { |
---|
| 530 | cpower = cpower + F[i]; |
---|
| 531 | } |
---|
[f2a4f3f] | 532 | cpower = cpower*G[j]; // bug! here may happen an arithmetic overflow!!! |
---|
[35aab3] | 533 | tpower = tpower + cpower; |
---|
| 534 | } |
---|
| 535 | } |
---|
[52e2f6] | 536 | cff = n_Copy(p_GetCoeff(MATELEM(r->GetNC()->COM,1,2),r),r); |
---|
[35aab3] | 537 | nPower(cff,tpower,&tmp_num); |
---|
| 538 | n_Delete(&cff,r); |
---|
| 539 | cff = tmp_num; |
---|
| 540 | } |
---|
| 541 | else /* skew commutative with nonequal coeffs */ |
---|
| 542 | { |
---|
| 543 | number totcff=n_Init(1,r); |
---|
| 544 | for(j=jG; j<=iG; j++) |
---|
| 545 | { |
---|
| 546 | if (G[j]!=0) |
---|
| 547 | { |
---|
| 548 | cpower = 0; |
---|
| 549 | for(i=j+1; i<=iF; i++) |
---|
| 550 | { |
---|
| 551 | if (F[i]!=0) |
---|
| 552 | { |
---|
[f2a4f3f] | 553 | cpower = F[i]*G[j]; // bug! overflow danger!!! |
---|
[52e2f6] | 554 | cff = n_Copy(p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r),r); |
---|
[35aab3] | 555 | nPower(cff,cpower,&tmp_num); |
---|
| 556 | cff = nMult(totcff,tmp_num); |
---|
[b1a5c1] | 557 | nDelete(&totcff); |
---|
[35aab3] | 558 | nDelete(&tmp_num); |
---|
| 559 | totcff = n_Copy(cff,r); |
---|
| 560 | n_Delete(&cff,r); |
---|
| 561 | } |
---|
| 562 | } /* end 2nd for */ |
---|
| 563 | } |
---|
| 564 | } |
---|
| 565 | cff=totcff; |
---|
| 566 | } |
---|
| 567 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
---|
| 568 | p_SetExpV(out,F,r); |
---|
| 569 | p_Setm(out,r); |
---|
| 570 | p_SetCoeff(out,cff,r); |
---|
| 571 | // p_MemAdd_NegWeightAdjust(p, r); ??? do we need this? |
---|
| 572 | freeT(F,rN); |
---|
| 573 | freeT(G,rN); |
---|
| 574 | return(out); |
---|
| 575 | } /* end nc_skew */ |
---|
[b87f029] | 576 | |
---|
[35aab3] | 577 | /* now we have to destroy out! */ |
---|
[b87f029] | 578 | p_Delete(&out,r); |
---|
| 579 | out = NULL; |
---|
[35aab3] | 580 | |
---|
| 581 | if (iG==jG) |
---|
| 582 | /* g is univariate monomial */ |
---|
| 583 | { |
---|
[52e2f6] | 584 | /* if (ri->GetNC()->type==nc_skew) -- postpone to TU */ |
---|
[5a9e7b] | 585 | out = gnc_mm_Mult_uu(F,jG,G[jG],r); |
---|
[35aab3] | 586 | freeT(F,rN); |
---|
| 587 | freeT(G,rN); |
---|
| 588 | return(out); |
---|
| 589 | } |
---|
| 590 | |
---|
| 591 | number n1=n_Init(1,r); |
---|
| 592 | int *Prv=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 593 | int *Nxt=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 594 | |
---|
| 595 | int *log=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 596 | int cnt=0; int cnf=0; |
---|
| 597 | |
---|
| 598 | /* splitting F wrt jG */ |
---|
| 599 | for (i=1;i<=jG;i++) |
---|
| 600 | { |
---|
| 601 | Prv[i]=F[i]; Nxt[i]=0; /* mult at the very end */ |
---|
| 602 | if (F[i]!=0) cnf++; |
---|
| 603 | } |
---|
| 604 | |
---|
| 605 | if (cnf==0) freeT(Prv,rN); |
---|
| 606 | |
---|
| 607 | for (i=jG+1;i<=rN;i++) |
---|
| 608 | { |
---|
| 609 | Nxt[i]=F[i]; |
---|
| 610 | /* if (cnf!=0) Prv[i]=0; */ |
---|
| 611 | if (F[i]!=0) |
---|
| 612 | { |
---|
| 613 | cnt++; |
---|
| 614 | } /* effective part for F */ |
---|
| 615 | } |
---|
| 616 | freeT(F,rN); |
---|
| 617 | cnt=0; |
---|
| 618 | |
---|
| 619 | for (i=1;i<=rN;i++) |
---|
| 620 | { |
---|
| 621 | if (G[i]!=0) |
---|
| 622 | { |
---|
| 623 | cnt++; |
---|
| 624 | log[cnt]=i; |
---|
| 625 | } /* lG for G */ |
---|
| 626 | } |
---|
| 627 | |
---|
| 628 | /* ---------------------- A C T I O N ------------------------ */ |
---|
| 629 | poly D=NULL; |
---|
| 630 | poly Rout=NULL; |
---|
| 631 | number *c=(number *)omAlloc0((rN+1)*sizeof(number)); |
---|
| 632 | c[0]=n_Init(1,r); |
---|
| 633 | |
---|
| 634 | int *Op=Nxt; |
---|
| 635 | int *On=G; |
---|
| 636 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 637 | |
---|
| 638 | for (i=jG;i<=rN;i++) U[i]=Nxt[i]+G[i]; /* make leadterm */ |
---|
| 639 | Nxt=NULL; |
---|
| 640 | G=NULL; |
---|
| 641 | cnt=1; |
---|
| 642 | int t=0; |
---|
| 643 | poly w=NULL; |
---|
| 644 | poly Pn=pOne(); |
---|
| 645 | p_SetExpV(Pn,On,r); |
---|
| 646 | p_Setm(Pn,r); |
---|
| 647 | |
---|
| 648 | while (On[iG]!=0) |
---|
| 649 | { |
---|
| 650 | t=log[cnt]; |
---|
| 651 | |
---|
[5a9e7b] | 652 | w=gnc_mm_Mult_uu(Op,t,On[t],r); |
---|
[35aab3] | 653 | c[cnt]=n_Mult(c[cnt-1],p_GetCoeff(w,r),r); |
---|
| 654 | D = pNext(w); /* getting coef and rest D */ |
---|
[fb82895] | 655 | p_LmDelete(&w,r); |
---|
[35aab3] | 656 | w=NULL; |
---|
| 657 | |
---|
| 658 | Op[t] += On[t]; /* update exp_vectors */ |
---|
| 659 | On[t] = 0; |
---|
| 660 | |
---|
| 661 | if (t!=iG) /* not the last step */ |
---|
| 662 | { |
---|
| 663 | p_SetExpV(Pn,On,r); |
---|
| 664 | p_Setm(Pn,r); |
---|
| 665 | #ifdef PDEBUG |
---|
| 666 | p_Test(Pn,r); |
---|
| 667 | #endif |
---|
| 668 | |
---|
| 669 | // if (pNext(D)==0) |
---|
| 670 | // is D a monomial? could be postponed higher |
---|
| 671 | // { |
---|
| 672 | // Rout=nc_mm_Mult_nn(D,Pn,r); |
---|
| 673 | // } |
---|
| 674 | // else |
---|
| 675 | // { |
---|
[5a9e7b] | 676 | Rout=gnc_p_Mult_mm(D,Pn,r); |
---|
[35aab3] | 677 | // } |
---|
| 678 | } |
---|
| 679 | else |
---|
| 680 | { |
---|
| 681 | Rout=D; |
---|
| 682 | D=NULL; |
---|
| 683 | } |
---|
| 684 | |
---|
| 685 | if (Rout!=NULL) |
---|
| 686 | { |
---|
| 687 | Rout=p_Mult_nn(Rout,c[cnt-1],r); /* Rest is ready */ |
---|
| 688 | out=p_Add_q(out,Rout,r); |
---|
| 689 | Rout=NULL; |
---|
| 690 | } |
---|
| 691 | cnt++; |
---|
| 692 | } |
---|
| 693 | freeT(On,rN); |
---|
| 694 | freeT(Op,rN); |
---|
| 695 | p_Delete(&Pn,r); |
---|
| 696 | omFreeSize((ADDRESS)log,(rN+1)*sizeof(int)); |
---|
| 697 | |
---|
| 698 | /* leadterm and Prv-part */ |
---|
| 699 | |
---|
| 700 | Rout=pOne(); |
---|
| 701 | /* U is lead.monomial */ |
---|
| 702 | U[0]=0; |
---|
| 703 | p_SetExpV(Rout,U,r); |
---|
| 704 | p_Setm(Rout,r); /* use again this name Rout */ |
---|
| 705 | #ifdef PDEBUG |
---|
| 706 | p_Test(Rout,r); |
---|
| 707 | #endif |
---|
| 708 | p_SetCoeff(Rout,c[cnt-1],r); |
---|
| 709 | out=p_Add_q(out,Rout,r); |
---|
| 710 | freeT(U,rN); |
---|
| 711 | freeN(c,rN+1); |
---|
| 712 | if (cnf!=0) /* Prv is non-zero vector */ |
---|
| 713 | { |
---|
| 714 | Rout=pOne(); |
---|
| 715 | Prv[0]=0; |
---|
| 716 | p_SetExpV(Rout,Prv,r); |
---|
| 717 | p_Setm(Rout,r); |
---|
| 718 | #ifdef PDEBUG |
---|
| 719 | p_Test(Rout,r); |
---|
| 720 | #endif |
---|
[5a9e7b] | 721 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
[35aab3] | 722 | freeT(Prv,rN); |
---|
| 723 | p_Delete(&Rout,r); |
---|
| 724 | } |
---|
| 725 | return (out); |
---|
| 726 | } |
---|
| 727 | |
---|
| 728 | |
---|
[5a9e7b] | 729 | poly gnc_mm_Mult_uu(int *F,int jG,int bG, const ring r) |
---|
[35aab3] | 730 | /* f=mono(F),g=(x_iG)^bG */ |
---|
| 731 | { |
---|
| 732 | poly out=NULL; |
---|
| 733 | int i; |
---|
| 734 | number num=NULL; |
---|
| 735 | |
---|
| 736 | int rN=r->N; |
---|
| 737 | int iF=r->N; |
---|
| 738 | while ((F[iF]==0)&&(iF>0)) iF-- ; /* last exponent_num of F */ |
---|
| 739 | |
---|
| 740 | if (iF==0) /* F==zero vector in other words */ |
---|
| 741 | { |
---|
| 742 | out=pOne(); |
---|
| 743 | p_SetExp(out,jG,bG,r); |
---|
| 744 | p_Setm(out,r); |
---|
| 745 | return(out); |
---|
| 746 | } |
---|
| 747 | |
---|
| 748 | int jF=1; |
---|
| 749 | while ((F[jF]==0)&&(jF<=rN)) jF++; /* first exp of F */ |
---|
| 750 | |
---|
| 751 | if (iF<=jG) /* i.e. no mixed exp_num */ |
---|
| 752 | { |
---|
| 753 | out=pOne(); |
---|
| 754 | F[jG]=F[jG]+bG; |
---|
| 755 | p_SetExpV(out,F,r); |
---|
| 756 | p_Setm(out,r); |
---|
| 757 | return(out); |
---|
| 758 | } |
---|
| 759 | |
---|
| 760 | if (iF==jF) /* uni times uni */ |
---|
| 761 | { |
---|
[5a9e7b] | 762 | out=gnc_uu_Mult_ww(iF,F[iF],jG,bG,r); |
---|
[35aab3] | 763 | return(out); |
---|
| 764 | } |
---|
| 765 | |
---|
| 766 | /* Now: F is mono with >=2 exponents, jG<iF */ |
---|
| 767 | /* check the quasi-commutative case */ |
---|
[52e2f6] | 768 | // matrix LCOM=r->GetNC()->COM; |
---|
[35aab3] | 769 | // number rescoef=n_Init(1,r); |
---|
| 770 | // number tmpcoef=n_Init(1,r); |
---|
| 771 | // int tmpint; |
---|
| 772 | // i=iF; |
---|
| 773 | // while (i>=jG+1) |
---|
| 774 | // /* all the non-zero exponents */ |
---|
| 775 | // { |
---|
| 776 | // if (MATELEM(LCOM,jG,i)!=NULL) |
---|
| 777 | // { |
---|
| 778 | // tmpcoef=pGetCoeff(MATELEM(LCOM,jG,i)); |
---|
| 779 | // tmpint=(int)F[i]; |
---|
| 780 | // nPower(tmpcoef,F[i],&tmpcoef); |
---|
| 781 | // rescoef=nMult(rescoef,tmpcoef); |
---|
| 782 | // i--; |
---|
| 783 | // } |
---|
| 784 | // else |
---|
| 785 | // { |
---|
| 786 | // if (F[i]!=0) break; |
---|
| 787 | // } |
---|
| 788 | // } |
---|
| 789 | // if (iF==i) |
---|
| 790 | // /* no action took place*/ |
---|
| 791 | // { |
---|
| 792 | |
---|
| 793 | // } |
---|
| 794 | // else /* power the result up to bG */ |
---|
| 795 | // { |
---|
| 796 | // nPower(rescoef,bG,&rescoef); |
---|
| 797 | // /* + cleanup, post-processing */ |
---|
| 798 | // } |
---|
| 799 | |
---|
| 800 | int *Prv=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
| 801 | int *Nxt=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
| 802 | int *lF=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
[26d633] | 803 | |
---|
[35aab3] | 804 | int cnt=0; int cnf=0; |
---|
| 805 | /* splitting F wrt jG */ |
---|
| 806 | for (i=1;i<=jG;i++) /* mult at the very end */ |
---|
| 807 | { |
---|
| 808 | Prv[i]=F[i]; Nxt[i]=0; |
---|
| 809 | if (F[i]!=0) cnf++; |
---|
| 810 | } |
---|
[26d633] | 811 | |
---|
[f2a4f3f] | 812 | if (cnf==0) |
---|
| 813 | { |
---|
| 814 | freeT(Prv,rN); Prv = NULL; |
---|
| 815 | } |
---|
[26d633] | 816 | |
---|
[35aab3] | 817 | for (i=jG+1;i<=rN;i++) |
---|
| 818 | { |
---|
| 819 | Nxt[i]=F[i]; |
---|
| 820 | if (cnf!=0) { Prv[i]=0;} |
---|
| 821 | if (F[i]!=0) |
---|
| 822 | { |
---|
| 823 | cnt++; |
---|
| 824 | lF[cnt]=i; |
---|
| 825 | } /* eff_part,lF_for_F */ |
---|
| 826 | } |
---|
| 827 | |
---|
| 828 | if (cnt==1) /* Nxt consists of 1 nonzero el-t only */ |
---|
| 829 | { |
---|
| 830 | int q=lF[1]; |
---|
| 831 | poly Rout=pOne(); |
---|
[5a9e7b] | 832 | out=gnc_uu_Mult_ww(q,Nxt[q],jG,bG,r); |
---|
[f2a4f3f] | 833 | |
---|
| 834 | freeT(Nxt,rN); Nxt = NULL; |
---|
[35aab3] | 835 | |
---|
| 836 | if (cnf!=0) |
---|
| 837 | { |
---|
| 838 | Prv[0]=0; |
---|
| 839 | p_SetExpV(Rout,Prv,r); |
---|
| 840 | p_Setm(Rout,r); |
---|
[f2a4f3f] | 841 | |
---|
[35aab3] | 842 | #ifdef PDEBUG |
---|
| 843 | p_Test(Rout,r); |
---|
| 844 | #endif |
---|
[26d633] | 845 | |
---|
[35aab3] | 846 | freeT(Prv,rN); |
---|
[f2a4f3f] | 847 | Prv = NULL; |
---|
[26d633] | 848 | |
---|
[5a9e7b] | 849 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
[35aab3] | 850 | } |
---|
| 851 | |
---|
[f2a4f3f] | 852 | freeT(lF,rN); |
---|
| 853 | lF = NULL; |
---|
[26d633] | 854 | |
---|
[35aab3] | 855 | p_Delete(&Rout,r); |
---|
[f2a4f3f] | 856 | |
---|
| 857 | assume(Nxt == NULL); |
---|
| 858 | assume(lF == NULL); |
---|
| 859 | assume(Prv == NULL); |
---|
[26d633] | 860 | |
---|
[35aab3] | 861 | return (out); |
---|
| 862 | } |
---|
| 863 | /* -------------------- MAIN ACTION --------------------- */ |
---|
| 864 | |
---|
| 865 | poly D=NULL; |
---|
| 866 | poly Rout=NULL; |
---|
| 867 | number *c=(number *)omAlloc0((cnt+2)*sizeof(number)); |
---|
| 868 | c[cnt+1]=n_Init(1,r); |
---|
| 869 | i=cnt+2; /* later in freeN */ |
---|
| 870 | int *Op=Nxt; |
---|
[f2a4f3f] | 871 | |
---|
[35aab3] | 872 | int *On=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 873 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 874 | |
---|
| 875 | |
---|
| 876 | // pExpVectorCopy(U,Nxt); |
---|
| 877 | memcpy(U, Nxt,(rN+1)*sizeof(int)); |
---|
| 878 | U[jG] = U[jG] + bG; |
---|
| 879 | |
---|
| 880 | /* Op=Nxt and initial On=(0); */ |
---|
| 881 | Nxt=NULL; |
---|
| 882 | |
---|
| 883 | poly Pp; |
---|
| 884 | poly Pn; |
---|
| 885 | int t=0; |
---|
| 886 | int first=lF[1]; |
---|
| 887 | int nlast=lF[cnt]; |
---|
| 888 | int kk=0; |
---|
| 889 | /* cnt--; */ |
---|
| 890 | /* now lF[cnt] should be <=iF-1 */ |
---|
| 891 | |
---|
| 892 | while (Op[first]!=0) |
---|
| 893 | { |
---|
| 894 | t=lF[cnt]; /* cnt as it was computed */ |
---|
| 895 | |
---|
[5a9e7b] | 896 | poly w=gnc_uu_Mult_ww(t,Op[t],jG,bG,r); |
---|
[35aab3] | 897 | c[cnt]=n_Copy(p_GetCoeff(w,r),r); |
---|
| 898 | D = pNext(w); /* getting coef and rest D */ |
---|
[fb82895] | 899 | p_LmDelete(&w,r); |
---|
[35aab3] | 900 | w=NULL; |
---|
| 901 | |
---|
| 902 | Op[t]= 0; |
---|
| 903 | Pp=pOne(); |
---|
| 904 | p_SetExpV(Pp,Op,r); |
---|
| 905 | p_Setm(Pp,r); |
---|
| 906 | |
---|
| 907 | if (t<nlast) |
---|
| 908 | { |
---|
| 909 | kk=lF[cnt+1]; |
---|
| 910 | On[kk]=F[kk]; |
---|
| 911 | |
---|
| 912 | Pn=pOne(); |
---|
| 913 | p_SetExpV(Pn,On,r); |
---|
| 914 | p_Setm(Pn,r); |
---|
| 915 | |
---|
| 916 | if (t!=first) /* typical expr */ |
---|
| 917 | { |
---|
[5a9e7b] | 918 | w=gnc_p_Mult_mm(D,Pn,r); |
---|
| 919 | Rout=gnc_mm_Mult_p(Pp,w,r); |
---|
[35aab3] | 920 | w=NULL; |
---|
| 921 | } |
---|
| 922 | else /* last step */ |
---|
| 923 | { |
---|
| 924 | On[t]=0; |
---|
| 925 | p_SetExpV(Pn,On,r); |
---|
| 926 | p_Setm(Pn,r); |
---|
[5a9e7b] | 927 | Rout=gnc_p_Mult_mm(D,Pn,r); |
---|
[35aab3] | 928 | } |
---|
| 929 | #ifdef PDEBUG |
---|
| 930 | p_Test(Pp,r); |
---|
| 931 | #endif |
---|
| 932 | p_Delete(&Pn,r); |
---|
| 933 | } |
---|
| 934 | else /* first step */ |
---|
| 935 | { |
---|
[5a9e7b] | 936 | Rout=gnc_mm_Mult_p(Pp,D,r); |
---|
[35aab3] | 937 | } |
---|
| 938 | #ifdef PDEBUG |
---|
| 939 | p_Test(Pp,r); |
---|
| 940 | #endif |
---|
| 941 | p_Delete(&Pp,r); |
---|
| 942 | num=n_Mult(c[cnt+1],c[cnt],r); |
---|
| 943 | n_Delete(&c[cnt],r); |
---|
| 944 | c[cnt]=num; |
---|
| 945 | Rout=p_Mult_nn(Rout,c[cnt+1],r); /* Rest is ready */ |
---|
| 946 | out=p_Add_q(out,Rout,r); |
---|
| 947 | Pp=NULL; |
---|
| 948 | cnt--; |
---|
| 949 | } |
---|
| 950 | /* only to feel safe:*/ |
---|
| 951 | Pn=Pp=NULL; |
---|
| 952 | freeT(On,rN); |
---|
| 953 | freeT(Op,rN); |
---|
| 954 | |
---|
| 955 | /* leadterm and Prv-part with coef 1 */ |
---|
| 956 | /* U[0]=exp; */ |
---|
| 957 | /* U[jG]=U[jG]+bG; */ |
---|
| 958 | /* make leadterm */ |
---|
| 959 | /* ??????????? we have done it already :-0 */ |
---|
[f2a4f3f] | 960 | |
---|
[35aab3] | 961 | Rout=pOne(); |
---|
| 962 | p_SetExpV(Rout,U,r); |
---|
| 963 | p_Setm(Rout,r); /* use again this name */ |
---|
| 964 | p_SetCoeff(Rout,c[cnt+1],r); /* last computed coef */ |
---|
[f2a4f3f] | 965 | |
---|
[35aab3] | 966 | out=p_Add_q(out,Rout,r); |
---|
[f2a4f3f] | 967 | |
---|
[35aab3] | 968 | Rout=NULL; |
---|
[f2a4f3f] | 969 | |
---|
| 970 | freeT(U, rN); |
---|
| 971 | freeN(c, i); |
---|
| 972 | freeT(lF, rN); |
---|
[35aab3] | 973 | |
---|
| 974 | if (cnf!=0) |
---|
| 975 | { |
---|
| 976 | Rout=pOne(); |
---|
| 977 | p_SetExpV(Rout,Prv,r); |
---|
| 978 | p_Setm(Rout,r); |
---|
[f2a4f3f] | 979 | freeT(Prv, rN); |
---|
[5a9e7b] | 980 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
[35aab3] | 981 | p_Delete(&Rout,r); |
---|
| 982 | } |
---|
[26d633] | 983 | |
---|
[35aab3] | 984 | return (out); |
---|
| 985 | } |
---|
| 986 | |
---|
[5a9e7b] | 987 | poly gnc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r) |
---|
[35aab3] | 988 | { |
---|
| 989 | int k,m; |
---|
| 990 | int rN=r->N; |
---|
[e0cb6c] | 991 | const int cMTindex = UPMATELEM(j,i,rN); |
---|
| 992 | matrix cMT=r->GetNC()->MT[cMTindex]; /* cMT=current MT */ |
---|
[35aab3] | 993 | |
---|
| 994 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r); |
---|
| 995 | /* var(j); */ |
---|
| 996 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); |
---|
| 997 | /*var(i); for convenience */ |
---|
| 998 | #ifdef PDEBUG |
---|
| 999 | p_Test(x,r); |
---|
| 1000 | p_Test(y,r); |
---|
| 1001 | #endif |
---|
| 1002 | poly t=NULL; |
---|
| 1003 | /* ------------ Main Cycles ----------------------------*/ |
---|
| 1004 | |
---|
| 1005 | for (k=2;k<=a;k++) |
---|
| 1006 | { |
---|
[807ee2] | 1007 | t = MATELEM(cMT,k,1); |
---|
[35aab3] | 1008 | |
---|
| 1009 | if (t==NULL) /* not computed yet */ |
---|
| 1010 | { |
---|
| 1011 | t = nc_p_CopyGet(MATELEM(cMT,k-1,1),r); |
---|
| 1012 | // t=p_Copy(MATELEM(cMT,k-1,1),r); |
---|
[5a9e7b] | 1013 | t = gnc_mm_Mult_p(y,t,r); |
---|
[e0cb6c] | 1014 | cMT=r->GetNC()->MT[cMTindex]; // since multiplication can change the MT table... |
---|
| 1015 | assume( t != NULL ); |
---|
| 1016 | #ifdef PDEBUG |
---|
| 1017 | p_Test(t,r); |
---|
| 1018 | #endif |
---|
[35aab3] | 1019 | MATELEM(cMT,k,1) = nc_p_CopyPut(t,r); |
---|
| 1020 | // omCheckAddr(cMT->m); |
---|
| 1021 | p_Delete(&t,r); |
---|
| 1022 | } |
---|
| 1023 | t=NULL; |
---|
| 1024 | } |
---|
| 1025 | |
---|
| 1026 | for (m=2;m<=b;m++) |
---|
| 1027 | { |
---|
[807ee2] | 1028 | t = MATELEM(cMT,a,m); |
---|
[35aab3] | 1029 | // t=MATELEM(cMT,a,m); |
---|
| 1030 | if (t==NULL) //not computed yet |
---|
| 1031 | { |
---|
| 1032 | t = nc_p_CopyGet(MATELEM(cMT,a,m-1),r); |
---|
[e0cb6c] | 1033 | assume( t != NULL ); |
---|
[35aab3] | 1034 | // t=p_Copy(MATELEM(cMT,a,m-1),r); |
---|
[5a9e7b] | 1035 | t = gnc_p_Mult_mm(t,x,r); |
---|
[e0cb6c] | 1036 | cMT=r->GetNC()->MT[cMTindex]; // since multiplication can change the MT table... |
---|
| 1037 | #ifdef PDEBUG |
---|
| 1038 | p_Test(t,r); |
---|
| 1039 | #endif |
---|
[35aab3] | 1040 | MATELEM(cMT,a,m) = nc_p_CopyPut(t,r); |
---|
| 1041 | // MATELEM(cMT,a,m) = t; |
---|
| 1042 | // omCheckAddr(cMT->m); |
---|
| 1043 | p_Delete(&t,r); |
---|
| 1044 | } |
---|
| 1045 | t=NULL; |
---|
| 1046 | } |
---|
| 1047 | p_Delete(&x,r); |
---|
| 1048 | p_Delete(&y,r); |
---|
[e0cb6c] | 1049 | t=MATELEM(cMT,a,b); |
---|
| 1050 | assume( t != NULL ); |
---|
| 1051 | |
---|
| 1052 | t= nc_p_CopyGet(t,r); |
---|
| 1053 | #ifdef PDEBUG |
---|
| 1054 | p_Test(t,r); |
---|
| 1055 | #endif |
---|
[35aab3] | 1056 | // return(p_Copy(t,r)); |
---|
| 1057 | /* since the last computed element was cMT[a,b] */ |
---|
| 1058 | return(t); |
---|
| 1059 | } |
---|
| 1060 | |
---|
[a7fbdd] | 1061 | |
---|
[efcd6fc] | 1062 | static inline poly gnc_uu_Mult_ww_formula (int i, int a, int j, int b, const ring r) |
---|
[a7fbdd] | 1063 | { |
---|
[efcd6fc] | 1064 | if(bNoFormula) |
---|
| 1065 | return gnc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
[26d633] | 1066 | |
---|
[a7fbdd] | 1067 | CFormulaPowerMultiplier* FormulaMultiplier = GetFormulaPowerMultiplier(r); |
---|
| 1068 | Enum_ncSAType PairType = _ncSA_notImplemented; |
---|
[26d633] | 1069 | |
---|
[a7fbdd] | 1070 | if( FormulaMultiplier != NULL ) |
---|
| 1071 | PairType = FormulaMultiplier->GetPair(j, i); |
---|
[26d633] | 1072 | |
---|
[a7fbdd] | 1073 | |
---|
| 1074 | if( PairType == _ncSA_notImplemented ) |
---|
| 1075 | return gnc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
| 1076 | |
---|
[26d633] | 1077 | |
---|
[a7fbdd] | 1078 | // return FormulaMultiplier->Multiply(j, i, b, a); |
---|
| 1079 | poly t = CFormulaPowerMultiplier::Multiply( PairType, j, i, b, a, r); |
---|
[26d633] | 1080 | |
---|
[a7fbdd] | 1081 | int rN=r->N; |
---|
| 1082 | matrix cMT = r->GetNC()->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
| 1083 | |
---|
| 1084 | |
---|
| 1085 | MATELEM(cMT, a, b) = nc_p_CopyPut(t,r); |
---|
[26d633] | 1086 | |
---|
[a7fbdd] | 1087 | // t=MATELEM(cMT,a,b); |
---|
| 1088 | // t= nc_p_CopyGet(MATELEM(cMT,a,b),r); |
---|
| 1089 | // return(p_Copy(t,r)); |
---|
| 1090 | /* since the last computed element was cMT[a,b] */ |
---|
| 1091 | return(t); |
---|
| 1092 | } |
---|
| 1093 | |
---|
| 1094 | |
---|
[5a9e7b] | 1095 | poly gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r) |
---|
[35aab3] | 1096 | /* (x_i)^a times (x_j)^b */ |
---|
| 1097 | /* x_i = y, x_j = x ! */ |
---|
| 1098 | { |
---|
| 1099 | /* Check zero exceptions, (q-)commutativity and is there something to do? */ |
---|
| 1100 | assume(a!=0); |
---|
| 1101 | assume(b!=0); |
---|
| 1102 | poly out=pOne(); |
---|
| 1103 | if (i<=j) |
---|
| 1104 | { |
---|
| 1105 | p_SetExp(out,i,a,r); |
---|
| 1106 | p_AddExp(out,j,b,r); |
---|
| 1107 | p_Setm(out,r); |
---|
| 1108 | return(out); |
---|
| 1109 | }/* zero exeptions and usual case */ |
---|
| 1110 | /* if ((a==0)||(b==0)||(i<=j)) return(out); */ |
---|
| 1111 | |
---|
[52e2f6] | 1112 | if (MATELEM(r->GetNC()->COM,j,i)!=NULL) |
---|
[35aab3] | 1113 | /* commutative or quasicommutative case */ |
---|
| 1114 | { |
---|
| 1115 | p_SetExp(out,i,a,r); |
---|
| 1116 | p_AddExp(out,j,b,r); |
---|
| 1117 | p_Setm(out,r); |
---|
[52e2f6] | 1118 | if (r->cf->nIsOne(p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r))) /* commutative case */ |
---|
[35aab3] | 1119 | { |
---|
| 1120 | return(out); |
---|
| 1121 | } |
---|
| 1122 | else |
---|
| 1123 | { |
---|
[52e2f6] | 1124 | number tmp_number=p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r); /* quasicommutative case */ |
---|
[a7fbdd] | 1125 | nPower(tmp_number,a*b,&tmp_number); // BUG! ;-( |
---|
[35aab3] | 1126 | p_SetCoeff(out,tmp_number,r); |
---|
| 1127 | return(out); |
---|
| 1128 | } |
---|
| 1129 | }/* end_of commutative or quasicommutative case */ |
---|
| 1130 | p_Delete(&out,r); |
---|
| 1131 | |
---|
[a7fbdd] | 1132 | |
---|
[b902246] | 1133 | if(bNoCache && !bNoFormula) // don't use cache whenever possible! |
---|
[efcd6fc] | 1134 | { // without cache!? |
---|
| 1135 | CFormulaPowerMultiplier* FormulaMultiplier = GetFormulaPowerMultiplier(r); |
---|
| 1136 | Enum_ncSAType PairType = _ncSA_notImplemented; |
---|
| 1137 | |
---|
| 1138 | if( FormulaMultiplier != NULL ) |
---|
| 1139 | PairType = FormulaMultiplier->GetPair(j, i); |
---|
| 1140 | |
---|
| 1141 | if( PairType != _ncSA_notImplemented ) |
---|
| 1142 | // // return FormulaMultiplier->Multiply(j, i, b, a); |
---|
| 1143 | return CFormulaPowerMultiplier::Multiply( PairType, j, i, b, a, r); |
---|
| 1144 | } |
---|
| 1145 | |
---|
[26d633] | 1146 | |
---|
[35aab3] | 1147 | /* we are here if i>j and variables do not commute or quasicommute */ |
---|
| 1148 | /* in fact, now a>=1 and b>=1; and j<i */ |
---|
| 1149 | /* now check whether the polynomial is already computed */ |
---|
| 1150 | int rN=r->N; |
---|
| 1151 | int vik = UPMATELEM(j,i,rN); |
---|
[52e2f6] | 1152 | int cMTsize=r->GetNC()->MTsize[vik]; |
---|
[35aab3] | 1153 | int newcMTsize=0; |
---|
[4bbe3b] | 1154 | newcMTsize=si_max(a,b); |
---|
[35aab3] | 1155 | |
---|
| 1156 | if (newcMTsize<=cMTsize) |
---|
| 1157 | { |
---|
[52e2f6] | 1158 | out = nc_p_CopyGet(MATELEM(r->GetNC()->MT[vik],a,b),r); |
---|
[35aab3] | 1159 | if (out !=NULL) return (out); |
---|
| 1160 | } |
---|
| 1161 | int k,m; |
---|
| 1162 | if (newcMTsize > cMTsize) |
---|
| 1163 | { |
---|
| 1164 | int inM=(((newcMTsize+6)/7)*7); |
---|
| 1165 | assume (inM>=newcMTsize); |
---|
| 1166 | newcMTsize = inM; |
---|
| 1167 | // matrix tmp = (matrix)omAlloc0(inM*inM*sizeof(poly)); |
---|
| 1168 | matrix tmp = mpNew(newcMTsize,newcMTsize); |
---|
| 1169 | |
---|
| 1170 | for (k=1;k<=cMTsize;k++) |
---|
| 1171 | { |
---|
| 1172 | for (m=1;m<=cMTsize;m++) |
---|
| 1173 | { |
---|
[03cecc2] | 1174 | out = MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m); |
---|
[35aab3] | 1175 | if ( out != NULL ) |
---|
| 1176 | { |
---|
[52e2f6] | 1177 | MATELEM(tmp,k,m) = out;/*MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m)*/ |
---|
[35aab3] | 1178 | // omCheckAddr(tmp->m); |
---|
[52e2f6] | 1179 | MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m)=NULL; |
---|
| 1180 | // omCheckAddr(r->GetNC()->MT[UPMATELEM(j,i,rN)]->m); |
---|
[b902246] | 1181 | out=NULL; |
---|
[35aab3] | 1182 | } |
---|
| 1183 | } |
---|
| 1184 | } |
---|
[52e2f6] | 1185 | id_Delete((ideal *)&(r->GetNC()->MT[UPMATELEM(j,i,rN)]),r); |
---|
| 1186 | r->GetNC()->MT[UPMATELEM(j,i,rN)] = tmp; |
---|
[35aab3] | 1187 | tmp=NULL; |
---|
[52e2f6] | 1188 | r->GetNC()->MTsize[UPMATELEM(j,i,rN)] = newcMTsize; |
---|
[35aab3] | 1189 | } |
---|
| 1190 | /* The update of multiplication matrix is finished */ |
---|
[a7fbdd] | 1191 | |
---|
| 1192 | |
---|
| 1193 | return gnc_uu_Mult_ww_formula(i, a, j, b, r); |
---|
| 1194 | |
---|
| 1195 | out = gnc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
| 1196 | // out = nc_uu_Mult_ww_horvert(i, a, j, b, r); |
---|
| 1197 | return(out); |
---|
[35aab3] | 1198 | } |
---|
| 1199 | |
---|
[5a9e7b] | 1200 | poly gnc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r) |
---|
[35aab3] | 1201 | |
---|
| 1202 | { |
---|
| 1203 | int k,m; |
---|
| 1204 | int rN=r->N; |
---|
[52e2f6] | 1205 | matrix cMT=r->GetNC()->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
[35aab3] | 1206 | |
---|
| 1207 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r);/* var(j); */ |
---|
| 1208 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); /*var(i); for convenience */ |
---|
| 1209 | #ifdef PDEBUG |
---|
| 1210 | p_Test(x,r); |
---|
| 1211 | p_Test(y,r); |
---|
| 1212 | #endif |
---|
| 1213 | |
---|
| 1214 | poly t=NULL; |
---|
| 1215 | |
---|
| 1216 | int toXY; |
---|
| 1217 | int toYX; |
---|
| 1218 | |
---|
| 1219 | if (a==1) /* y*x^b, b>=2 */ |
---|
| 1220 | { |
---|
| 1221 | toXY=b-1; |
---|
| 1222 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=2)) toXY--; |
---|
| 1223 | for (m=toXY+1;m<=b;m++) |
---|
| 1224 | { |
---|
| 1225 | t=MATELEM(cMT,1,m); |
---|
| 1226 | if (t==NULL) /* remove after debug */ |
---|
| 1227 | { |
---|
| 1228 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
[5a9e7b] | 1229 | t = gnc_p_Mult_mm(t,x,r); |
---|
[35aab3] | 1230 | MATELEM(cMT,1,m) = t; |
---|
| 1231 | /* omCheckAddr(cMT->m); */ |
---|
| 1232 | } |
---|
| 1233 | else |
---|
| 1234 | { |
---|
| 1235 | /* Error, should never get there */ |
---|
| 1236 | WarnS("Error: a=1; MATELEM!=0"); |
---|
| 1237 | } |
---|
| 1238 | t=NULL; |
---|
| 1239 | } |
---|
| 1240 | return(p_Copy(MATELEM(cMT,1,b),r)); |
---|
| 1241 | } |
---|
| 1242 | |
---|
| 1243 | if (b==1) /* y^a*x, a>=2 */ |
---|
| 1244 | { |
---|
| 1245 | toYX=a-1; |
---|
| 1246 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=2)) toYX--; |
---|
| 1247 | for (m=toYX+1;m<=a;m++) |
---|
| 1248 | { |
---|
| 1249 | t=MATELEM(cMT,m,1); |
---|
| 1250 | if (t==NULL) /* remove after debug */ |
---|
| 1251 | { |
---|
| 1252 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
[5a9e7b] | 1253 | t = gnc_mm_Mult_p(y,t,r); |
---|
[35aab3] | 1254 | MATELEM(cMT,m,1) = t; |
---|
| 1255 | /* omCheckAddr(cMT->m); */ |
---|
| 1256 | } |
---|
| 1257 | else |
---|
| 1258 | { |
---|
| 1259 | /* Error, should never get there */ |
---|
| 1260 | WarnS("Error: b=1, MATELEM!=0"); |
---|
| 1261 | } |
---|
| 1262 | t=NULL; |
---|
| 1263 | } |
---|
| 1264 | return(p_Copy(MATELEM(cMT,a,1),r)); |
---|
| 1265 | } |
---|
| 1266 | |
---|
| 1267 | /* ------------ Main Cycles ----------------------------*/ |
---|
| 1268 | /* a>1, b>1 */ |
---|
| 1269 | |
---|
| 1270 | int dXY=0; int dYX=0; |
---|
| 1271 | /* dXY = distance for computing x-mult, then y-mult */ |
---|
| 1272 | /* dYX = distance for computing y-mult, then x-mult */ |
---|
| 1273 | int toX=a-1; int toY=b-1; /* toX = to axe X, toY = to axe Y */ |
---|
| 1274 | toXY=b-1; toYX=a-1; |
---|
| 1275 | /* if toX==0, toXY = dist. to computed y * x^toXY */ |
---|
| 1276 | /* if toY==0, toYX = dist. to computed y^toYX * x */ |
---|
| 1277 | while ( (MATELEM(cMT,toX,b)==NULL) && (toX>=1)) toX--; |
---|
| 1278 | if (toX==0) /* the whole column is not computed yet */ |
---|
| 1279 | { |
---|
| 1280 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=1)) toXY--; |
---|
| 1281 | /* toXY >=1 */ |
---|
| 1282 | dXY=b-1-toXY; |
---|
| 1283 | } |
---|
| 1284 | dXY=dXY+a-toX; /* the distance to nearest computed y^toX x^b */ |
---|
| 1285 | |
---|
| 1286 | while ( (MATELEM(cMT,a,toY)==NULL) && (toY>=1)) toY--; |
---|
| 1287 | if (toY==0) /* the whole row is not computed yet */ |
---|
| 1288 | { |
---|
| 1289 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=1)) toYX--; |
---|
| 1290 | /* toYX >=1 */ |
---|
| 1291 | dYX=a-1-toYX; |
---|
| 1292 | } |
---|
| 1293 | dYX=dYX+b-toY; /* the distance to nearest computed y^a x^toY */ |
---|
| 1294 | |
---|
| 1295 | if (dYX>=dXY) |
---|
| 1296 | { |
---|
| 1297 | /* first x, then y */ |
---|
| 1298 | if (toX==0) /* start with the row*/ |
---|
| 1299 | { |
---|
| 1300 | for (m=toXY+1;m<=b;m++) |
---|
| 1301 | { |
---|
| 1302 | t=MATELEM(cMT,1,m); |
---|
| 1303 | if (t==NULL) /* remove after debug */ |
---|
| 1304 | { |
---|
| 1305 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
[5a9e7b] | 1306 | t = gnc_p_Mult_mm(t,x,r); |
---|
[35aab3] | 1307 | MATELEM(cMT,1,m) = t; |
---|
| 1308 | /* omCheckAddr(cMT->m); */ |
---|
| 1309 | } |
---|
| 1310 | else |
---|
| 1311 | { |
---|
| 1312 | /* Error, should never get there */ |
---|
| 1313 | WarnS("dYX>=dXY,toXY; MATELEM==0"); |
---|
| 1314 | } |
---|
| 1315 | t=NULL; |
---|
| 1316 | } |
---|
| 1317 | toX=1; /* y*x^b is computed */ |
---|
| 1318 | } |
---|
| 1319 | /* Now toX>=1 */ |
---|
| 1320 | for (k=toX+1;k<=a;k++) |
---|
| 1321 | { |
---|
| 1322 | t=MATELEM(cMT,k,b); |
---|
| 1323 | if (t==NULL) /* remove after debug */ |
---|
| 1324 | { |
---|
| 1325 | t = p_Copy(MATELEM(cMT,k-1,b),r); |
---|
[5a9e7b] | 1326 | t = gnc_mm_Mult_p(y,t,r); |
---|
[35aab3] | 1327 | MATELEM(cMT,k,b) = t; |
---|
| 1328 | /* omCheckAddr(cMT->m); */ |
---|
| 1329 | } |
---|
| 1330 | else |
---|
| 1331 | { |
---|
| 1332 | /* Error, should never get there */ |
---|
| 1333 | WarnS("dYX>=dXY,toX; MATELEM==0"); |
---|
| 1334 | } |
---|
| 1335 | t=NULL; |
---|
| 1336 | } |
---|
| 1337 | } /* endif (dYX>=dXY) */ |
---|
| 1338 | |
---|
| 1339 | |
---|
| 1340 | if (dYX<dXY) |
---|
| 1341 | { |
---|
| 1342 | /* first y, then x */ |
---|
| 1343 | if (toY==0) /* start with the column*/ |
---|
| 1344 | { |
---|
| 1345 | for (m=toYX+1;m<=a;m++) |
---|
| 1346 | { |
---|
| 1347 | t=MATELEM(cMT,m,1); |
---|
| 1348 | if (t==NULL) /* remove after debug */ |
---|
| 1349 | { |
---|
| 1350 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
[5a9e7b] | 1351 | t = gnc_mm_Mult_p(y,t,r); |
---|
[35aab3] | 1352 | MATELEM(cMT,m,1) = t; |
---|
| 1353 | /* omCheckAddr(cMT->m); */ |
---|
| 1354 | } |
---|
| 1355 | else |
---|
| 1356 | { |
---|
| 1357 | /* Error, should never get there */ |
---|
| 1358 | WarnS("dYX<dXY,toYX; MATELEM==0"); |
---|
| 1359 | } |
---|
| 1360 | t=NULL; |
---|
| 1361 | } |
---|
| 1362 | toY=1; /* y^a*x is computed */ |
---|
| 1363 | } |
---|
| 1364 | /* Now toY>=1 */ |
---|
| 1365 | for (k=toY+1;k<=b;k++) |
---|
| 1366 | { |
---|
| 1367 | t=MATELEM(cMT,a,k); |
---|
| 1368 | if (t==NULL) /* remove after debug */ |
---|
| 1369 | { |
---|
| 1370 | t = p_Copy(MATELEM(cMT,a,k-1),r); |
---|
[5a9e7b] | 1371 | t = gnc_p_Mult_mm(t,x,r); |
---|
[35aab3] | 1372 | MATELEM(cMT,a,k) = t; |
---|
| 1373 | /* omCheckAddr(cMT->m); */ |
---|
| 1374 | } |
---|
| 1375 | else |
---|
| 1376 | { |
---|
| 1377 | /* Error, should never get there */ |
---|
| 1378 | WarnS("dYX<dXY,toY; MATELEM==0"); |
---|
| 1379 | } |
---|
| 1380 | t=NULL; |
---|
| 1381 | } |
---|
| 1382 | } /* endif (dYX<dXY) */ |
---|
| 1383 | |
---|
| 1384 | p_Delete(&x,r); |
---|
| 1385 | p_Delete(&y,r); |
---|
| 1386 | t=p_Copy(MATELEM(cMT,a,b),r); |
---|
| 1387 | return(t); /* since the last computed element was cMT[a,b] */ |
---|
| 1388 | } |
---|
| 1389 | |
---|
| 1390 | |
---|
| 1391 | /* ----------------------------- Syzygies ---------------------- */ |
---|
| 1392 | |
---|
| 1393 | /*2 |
---|
| 1394 | * reduction of p2 with p1 |
---|
| 1395 | * do not destroy p1, but p2 |
---|
| 1396 | * p1 divides p2 -> for use in NF algorithm |
---|
| 1397 | */ |
---|
[5a9e7b] | 1398 | poly gnc_ReduceSpolyOld(const poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
[35aab3] | 1399 | { |
---|
[52e2f6] | 1400 | assume(p_LmDivisibleBy(p1, p2, r)); |
---|
| 1401 | |
---|
[b1a5c1] | 1402 | #ifdef PDEBUG |
---|
[35aab3] | 1403 | if (p_GetComp(p1,r)!=p_GetComp(p2,r) |
---|
| 1404 | && (p_GetComp(p1,r)!=0) |
---|
| 1405 | && (p_GetComp(p2,r)!=0)) |
---|
| 1406 | { |
---|
[b1a5c1] | 1407 | dReportError("nc_ReduceSpolyOld: different components"); |
---|
[35aab3] | 1408 | return(NULL); |
---|
| 1409 | } |
---|
[b1a5c1] | 1410 | #endif |
---|
[6b5dd2] | 1411 | poly m = pOne(); |
---|
[35aab3] | 1412 | p_ExpVectorDiff(m,p2,p1,r); |
---|
[ec547b3] | 1413 | //p_Setm(m,r); |
---|
[35aab3] | 1414 | #ifdef PDEBUG |
---|
| 1415 | p_Test(m,r); |
---|
| 1416 | #endif |
---|
| 1417 | /* pSetComp(m,r)=0? */ |
---|
[86016d] | 1418 | poly N = nc_mm_Mult_p(m, p_Head(p1,r), r); |
---|
[6b5dd2] | 1419 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
| 1420 | number cF = n_Copy( p_GetCoeff(p2, r),r); |
---|
[4bbe3b] | 1421 | /* GCD stuff */ |
---|
[6b5dd2] | 1422 | number cG = nGcd(C, cF, r); |
---|
| 1423 | if ( !nEqual(cG, n_Init(1,r) ) ) |
---|
[4bbe3b] | 1424 | { |
---|
[6b5dd2] | 1425 | cF = nDiv(cF, cG); |
---|
| 1426 | C = nDiv(C, cG); |
---|
[4bbe3b] | 1427 | } |
---|
[6b5dd2] | 1428 | p2 = p_Mult_nn(p2, C, r); |
---|
[d5f9aea] | 1429 | poly out = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
[6b5dd2] | 1430 | N = p_Add_q(N, out, r); |
---|
| 1431 | p_Test(p2,r); |
---|
| 1432 | p_Test(N,r); |
---|
| 1433 | number MinusOne = n_Init(-1,r); |
---|
[35aab3] | 1434 | if (!n_Equal(cF,MinusOne,r)) |
---|
| 1435 | { |
---|
[6b5dd2] | 1436 | cF = n_Neg(cF,r); |
---|
| 1437 | N = p_Mult_nn(N, cF, r); |
---|
| 1438 | p_Test(N,r); |
---|
[35aab3] | 1439 | } |
---|
[6b5dd2] | 1440 | out = p_Add_q(p2,N,r); |
---|
| 1441 | p_Test(out,r); |
---|
[a0d9be] | 1442 | if ( out!=NULL ) p_Content(out,r); |
---|
[35aab3] | 1443 | p_Delete(&m,r); |
---|
| 1444 | n_Delete(&cF,r); |
---|
| 1445 | n_Delete(&C,r); |
---|
| 1446 | n_Delete(&MinusOne,r); |
---|
| 1447 | return(out); |
---|
| 1448 | |
---|
[5a9e7b] | 1449 | } |
---|
[35aab3] | 1450 | |
---|
[5a9e7b] | 1451 | poly gnc_ReduceSpolyNew(const poly p1, poly p2, const ring r) |
---|
[35aab3] | 1452 | { |
---|
[52e2f6] | 1453 | assume(p_LmDivisibleBy(p1, p2, r)); |
---|
| 1454 | |
---|
[5a9e7b] | 1455 | const long lCompP1 = p_GetComp(p1,r); |
---|
| 1456 | const long lCompP2 = p_GetComp(p2,r); |
---|
| 1457 | |
---|
| 1458 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
| 1459 | { |
---|
| 1460 | #ifdef PDEBUG |
---|
| 1461 | Werror("gnc_ReduceSpolyNew: different non-zero components!"); |
---|
| 1462 | #endif |
---|
| 1463 | return(NULL); |
---|
| 1464 | } |
---|
| 1465 | |
---|
| 1466 | poly m = pOne(); |
---|
| 1467 | p_ExpVectorDiff(m, p2, p1, r); |
---|
| 1468 | //p_Setm(m,r); |
---|
| 1469 | #ifdef PDEBUG |
---|
| 1470 | p_Test(m,r); |
---|
| 1471 | #endif |
---|
| 1472 | |
---|
| 1473 | /* pSetComp(m,r)=0? */ |
---|
[86016d] | 1474 | poly N = nc_mm_Mult_p(m, p_Head(p1,r), r); |
---|
[5a9e7b] | 1475 | |
---|
| 1476 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
| 1477 | number cF = n_Copy( p_GetCoeff(p2, r), r); |
---|
| 1478 | |
---|
| 1479 | /* GCD stuff */ |
---|
| 1480 | number cG = nGcd(C, cF, r); |
---|
| 1481 | |
---|
| 1482 | if (!n_IsOne(cG, r)) |
---|
| 1483 | { |
---|
[ae7706] | 1484 | number n_tmp; |
---|
| 1485 | n_tmp = n_Div(cF, cG, r); n_Delete(&cF,r); cF=n_tmp; |
---|
| 1486 | n_tmp = n_Div(C, cG, r); n_Delete(&C,r); C=n_tmp; |
---|
[5a9e7b] | 1487 | } |
---|
| 1488 | |
---|
| 1489 | p2 = p_Mult_nn(p2, C, r); // p2 !!! |
---|
| 1490 | p_Test(p2,r); |
---|
| 1491 | n_Delete(&C,r); |
---|
| 1492 | |
---|
[d5f9aea] | 1493 | poly out = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
[5a9e7b] | 1494 | p_Delete(&m,r); |
---|
| 1495 | |
---|
| 1496 | N = p_Add_q(N, out, r); |
---|
| 1497 | p_Test(N,r); |
---|
| 1498 | |
---|
| 1499 | if (!n_IsMOne(cF,r)) // ??? |
---|
| 1500 | { |
---|
| 1501 | cF = n_Neg(cF,r); |
---|
| 1502 | N = p_Mult_nn(N, cF, r); |
---|
| 1503 | p_Test(N,r); |
---|
| 1504 | } |
---|
[ae7706] | 1505 | n_Delete(&cF,r); |
---|
[5a9e7b] | 1506 | |
---|
| 1507 | out = p_Add_q(p2,N,r); // delete N, p2 |
---|
| 1508 | p_Test(out,r); |
---|
[a0d9be] | 1509 | if ( out!=NULL ) p_Content(out,r); |
---|
[5a9e7b] | 1510 | return(out); |
---|
[35aab3] | 1511 | } |
---|
| 1512 | |
---|
[5a9e7b] | 1513 | |
---|
[35aab3] | 1514 | /*4 |
---|
| 1515 | * creates the S-polynomial of p1 and p2 |
---|
| 1516 | * do not destroy p1 and p2 |
---|
| 1517 | */ |
---|
[5a9e7b] | 1518 | poly gnc_CreateSpolyOld(poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
[35aab3] | 1519 | { |
---|
[b1a5c1] | 1520 | #ifdef PDEBUG |
---|
[35aab3] | 1521 | if ((p_GetComp(p1,r)!=p_GetComp(p2,r)) |
---|
| 1522 | && (p_GetComp(p1,r)!=0) |
---|
| 1523 | && (p_GetComp(p2,r)!=0)) |
---|
| 1524 | { |
---|
[b1a5c1] | 1525 | dReportError("gnc_CreateSpolyOld : different components!"); |
---|
[35aab3] | 1526 | return(NULL); |
---|
| 1527 | } |
---|
[b1a5c1] | 1528 | #endif |
---|
[86016d] | 1529 | if ((ncRingType(r)==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
[35aab3] | 1530 | { |
---|
| 1531 | return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
| 1532 | } |
---|
| 1533 | poly pL=pOne(); |
---|
| 1534 | poly m1=pOne(); |
---|
| 1535 | poly m2=pOne(); |
---|
| 1536 | pLcm(p1,p2,pL); |
---|
| 1537 | p_Setm(pL,r); |
---|
| 1538 | #ifdef PDEBUG |
---|
| 1539 | p_Test(pL,r); |
---|
| 1540 | #endif |
---|
| 1541 | p_ExpVectorDiff(m1,pL,p1,r); |
---|
| 1542 | //p_SetComp(m1,0,r); |
---|
[ec547b3] | 1543 | //p_Setm(m1,r); |
---|
[35aab3] | 1544 | #ifdef PDEBUG |
---|
| 1545 | p_Test(m1,r); |
---|
| 1546 | #endif |
---|
| 1547 | p_ExpVectorDiff(m2,pL,p2,r); |
---|
| 1548 | //p_SetComp(m2,0,r); |
---|
[ec547b3] | 1549 | //p_Setm(m2,r); |
---|
[35aab3] | 1550 | #ifdef PDEBUG |
---|
| 1551 | p_Test(m2,r); |
---|
| 1552 | #endif |
---|
| 1553 | p_Delete(&pL,r); |
---|
| 1554 | /* zero exponents ! */ |
---|
[86016d] | 1555 | poly M1 = nc_mm_Mult_p(m1,p_Head(p1,r),r); |
---|
[4bbe3b] | 1556 | number C1 = n_Copy(p_GetCoeff(M1,r),r); |
---|
[86016d] | 1557 | poly M2 = nc_mm_Mult_p(m2,p_Head(p2,r),r); |
---|
[4bbe3b] | 1558 | number C2 = n_Copy(p_GetCoeff(M2,r),r); |
---|
| 1559 | /* GCD stuff */ |
---|
| 1560 | number C = nGcd(C1,C2,r); |
---|
| 1561 | if (!nEqual(C,n_Init(1,r))) |
---|
| 1562 | { |
---|
| 1563 | C1=nDiv(C1,C); |
---|
| 1564 | C2=nDiv(C2,C); |
---|
| 1565 | } |
---|
[35aab3] | 1566 | M1=p_Mult_nn(M1,C2,r); |
---|
| 1567 | p_SetCoeff(m1,C2,r); |
---|
| 1568 | number MinusOne=n_Init(-1,r); |
---|
| 1569 | if (n_Equal(C1,MinusOne,r)) |
---|
| 1570 | { |
---|
| 1571 | M2=p_Add_q(M1,M2,r); |
---|
| 1572 | } |
---|
| 1573 | else |
---|
| 1574 | { |
---|
| 1575 | C1=n_Neg(C1,r); |
---|
| 1576 | M2=p_Mult_nn(M2,C1,r); |
---|
| 1577 | M2=p_Add_q(M1,M2,r); |
---|
| 1578 | p_SetCoeff(m2,C1,r); |
---|
| 1579 | } |
---|
| 1580 | /* M1 is killed, M2=res = C2 M1 - C1 M2 */ |
---|
| 1581 | poly tmp=p_Copy(p1,r); |
---|
| 1582 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
[86016d] | 1583 | M1=nc_mm_Mult_p(m1,tmp,r); |
---|
[35aab3] | 1584 | tmp=p_Copy(p2,r); |
---|
| 1585 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
| 1586 | M2=p_Add_q(M2,M1,r); |
---|
[86016d] | 1587 | M1=nc_mm_Mult_p(m2,tmp,r); |
---|
[35aab3] | 1588 | M2=p_Add_q(M2,M1,r); |
---|
| 1589 | p_Delete(&m1,r); |
---|
| 1590 | p_Delete(&m2,r); |
---|
| 1591 | // n_Delete(&C1,r); |
---|
| 1592 | // n_Delete(&C2,r); |
---|
| 1593 | n_Delete(&MinusOne,r); |
---|
| 1594 | #ifdef PDEBUG |
---|
| 1595 | p_Test(M2,r); |
---|
| 1596 | #endif |
---|
[a0d9be] | 1597 | if (M2!=NULL) M2=p_Cleardenom(M2,r); |
---|
| 1598 | //if (M2!=NULL) p_Content(M2); // done by pCleardenom |
---|
[35aab3] | 1599 | return(M2); |
---|
| 1600 | } |
---|
| 1601 | |
---|
[5a9e7b] | 1602 | poly gnc_CreateSpolyNew(poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
| 1603 | { |
---|
[52e2f6] | 1604 | assume(r == currRing); |
---|
| 1605 | |
---|
| 1606 | #ifdef PDEBUG |
---|
| 1607 | pTest(p1); |
---|
| 1608 | pTest(p2); |
---|
| 1609 | #if MYTEST |
---|
| 1610 | Print("p1: "); pWrite(p1); |
---|
| 1611 | Print("p2: "); pWrite(p2); |
---|
| 1612 | #endif |
---|
| 1613 | #endif |
---|
[b1a5c1] | 1614 | |
---|
[5a9e7b] | 1615 | const long lCompP1 = p_GetComp(p1,r); |
---|
| 1616 | const long lCompP2 = p_GetComp(p2,r); |
---|
| 1617 | |
---|
| 1618 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
| 1619 | { |
---|
| 1620 | #ifdef PDEBUG |
---|
| 1621 | Werror("gnc_CreateSpolyNew: different non-zero components!"); |
---|
[e915737] | 1622 | assume(0); |
---|
[5a9e7b] | 1623 | #endif |
---|
| 1624 | return(NULL); |
---|
| 1625 | } |
---|
| 1626 | |
---|
[52e2f6] | 1627 | #ifdef PDEBUG |
---|
| 1628 | if (lCompP1!=lCompP2) |
---|
| 1629 | { |
---|
| 1630 | WarnS("gnc_CreateSpolyNew: vector & poly in SPoly!"); |
---|
| 1631 | } |
---|
| 1632 | #endif |
---|
[b1a5c1] | 1633 | |
---|
| 1634 | |
---|
[52e2f6] | 1635 | // if ((r->GetNC()->type==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
[5a9e7b] | 1636 | // { |
---|
| 1637 | // return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
| 1638 | // } |
---|
| 1639 | |
---|
[b902246] | 1640 | // poly pL=p_One( r); |
---|
[5a9e7b] | 1641 | |
---|
[b902246] | 1642 | poly m1=p_One( r); |
---|
| 1643 | poly m2=p_One( r); |
---|
[5a9e7b] | 1644 | |
---|
[52e2f6] | 1645 | poly pL = p_Lcm(p1,p2,r); // pL = lcm( lm(p1), lm(p2) ) |
---|
[5a9e7b] | 1646 | |
---|
| 1647 | |
---|
| 1648 | #ifdef PDEBUG |
---|
[151000] | 1649 | // p_Test(pL,r); |
---|
[5a9e7b] | 1650 | #endif |
---|
| 1651 | |
---|
[52e2f6] | 1652 | p_ExpVectorDiff(m1, pL, p1, r); // m1 = pL / lm(p1) |
---|
[5a9e7b] | 1653 | //p_SetComp(m1,0,r); |
---|
| 1654 | //p_Setm(m1,r); |
---|
[52e2f6] | 1655 | |
---|
[5a9e7b] | 1656 | #ifdef PDEBUG |
---|
| 1657 | p_Test(m1,r); |
---|
| 1658 | #endif |
---|
[52e2f6] | 1659 | // assume(p_GetComp(m1,r) == 0); |
---|
[5a9e7b] | 1660 | |
---|
[52e2f6] | 1661 | p_ExpVectorDiff(m2, pL, p2, r); // m2 = pL / lm(p2) |
---|
[5a9e7b] | 1662 | |
---|
| 1663 | //p_SetComp(m2,0,r); |
---|
| 1664 | //p_Setm(m2,r); |
---|
| 1665 | #ifdef PDEBUG |
---|
| 1666 | p_Test(m2,r); |
---|
| 1667 | #endif |
---|
| 1668 | |
---|
[52e2f6] | 1669 | #ifdef PDEBUG |
---|
| 1670 | #if MYTEST |
---|
| 1671 | Print("m1: "); pWrite(m1); |
---|
| 1672 | Print("m2: "); pWrite(m2); |
---|
| 1673 | #endif |
---|
| 1674 | #endif |
---|
| 1675 | |
---|
[b1a5c1] | 1676 | |
---|
[52e2f6] | 1677 | // assume(p_GetComp(m2,r) == 0); |
---|
| 1678 | |
---|
| 1679 | #ifdef PDEBUG |
---|
[b1a5c1] | 1680 | #if 0 |
---|
[52e2f6] | 1681 | if( (p_GetComp(m2,r) != 0) || (p_GetComp(m1,r) != 0) ) |
---|
| 1682 | { |
---|
| 1683 | WarnS("gnc_CreateSpolyNew: wrong monomials!"); |
---|
[b1a5c1] | 1684 | |
---|
| 1685 | |
---|
[52e2f6] | 1686 | #ifdef RDEBUG |
---|
| 1687 | PrintS("m1 = "); p_Write(m1, r); |
---|
[3664c9a] | 1688 | p_DebugPrint(m1, r); |
---|
[b1a5c1] | 1689 | |
---|
[52e2f6] | 1690 | PrintS("m2 = "); p_Write(m2, r); |
---|
[3664c9a] | 1691 | p_DebugPrint(m2, r); |
---|
[52e2f6] | 1692 | |
---|
| 1693 | PrintS("p1 = "); p_Write(p1, r); |
---|
[3664c9a] | 1694 | p_DebugPrint(p1, r); |
---|
[52e2f6] | 1695 | |
---|
| 1696 | PrintS("p2 = "); p_Write(p2, r); |
---|
[3664c9a] | 1697 | p_DebugPrint(p2, r); |
---|
[52e2f6] | 1698 | |
---|
| 1699 | PrintS("pL = "); p_Write(pL, r); |
---|
[3664c9a] | 1700 | p_DebugPrint(pL, r); |
---|
[52e2f6] | 1701 | #endif |
---|
[b1a5c1] | 1702 | |
---|
[52e2f6] | 1703 | } |
---|
[b1a5c1] | 1704 | |
---|
[52e2f6] | 1705 | #endif |
---|
| 1706 | #endif |
---|
[b1a5c1] | 1707 | |
---|
[5a9e7b] | 1708 | p_Delete(&pL,r); |
---|
| 1709 | |
---|
| 1710 | /* zero exponents !? */ |
---|
[86016d] | 1711 | poly M1 = nc_mm_Mult_p(m1,p_Head(p1,r),r); // M1 = m1 * lt(p1) |
---|
| 1712 | poly M2 = nc_mm_Mult_p(m2,p_Head(p2,r),r); // M2 = m2 * lt(p2) |
---|
[5a9e7b] | 1713 | |
---|
[52e2f6] | 1714 | #ifdef PDEBUG |
---|
| 1715 | p_Test(M1,r); |
---|
| 1716 | p_Test(M2,r); |
---|
| 1717 | |
---|
| 1718 | #if MYTEST |
---|
| 1719 | Print("M1: "); pWrite(M1); |
---|
| 1720 | Print("M2: "); pWrite(M2); |
---|
| 1721 | #endif |
---|
| 1722 | #endif |
---|
[b1a5c1] | 1723 | |
---|
[5a9e7b] | 1724 | if(M1 == NULL || M2 == NULL) |
---|
| 1725 | { |
---|
[84d05f8] | 1726 | #ifdef PDEBUG |
---|
[5a9e7b] | 1727 | Print("\np1 = "); |
---|
| 1728 | p_Write(p1, r); |
---|
| 1729 | |
---|
| 1730 | Print("m1 = "); |
---|
| 1731 | p_Write(m1, r); |
---|
| 1732 | |
---|
| 1733 | Print("p2 = "); |
---|
| 1734 | p_Write(p2, r); |
---|
| 1735 | |
---|
| 1736 | Print("m2 = "); |
---|
| 1737 | p_Write(m2, r); |
---|
| 1738 | |
---|
| 1739 | Werror("ERROR in nc_CreateSpoly: result of multiplication is Zero!\n"); |
---|
| 1740 | #endif |
---|
[84d05f8] | 1741 | return(NULL); |
---|
| 1742 | } |
---|
[5a9e7b] | 1743 | |
---|
| 1744 | number C1 = n_Copy(p_GetCoeff(M1,r),r); // C1 = lc(M1) |
---|
| 1745 | number C2 = n_Copy(p_GetCoeff(M2,r),r); // C2 = lc(M2) |
---|
| 1746 | |
---|
| 1747 | /* GCD stuff */ |
---|
| 1748 | number C = nGcd(C1, C2, r); // C = gcd(C1, C2) |
---|
| 1749 | |
---|
| 1750 | if (!n_IsOne(C, r)) // if C != 1 |
---|
| 1751 | { |
---|
| 1752 | C1=n_Div(C1, C, r); // C1 = C1 / C |
---|
| 1753 | C2=n_Div(C2, C, r); // C2 = C2 / C |
---|
| 1754 | } |
---|
| 1755 | |
---|
| 1756 | n_Delete(&C,r); // destroy the number C |
---|
| 1757 | |
---|
| 1758 | C1=n_Neg(C1,r); |
---|
| 1759 | |
---|
| 1760 | // number MinusOne=n_Init(-1,r); |
---|
| 1761 | // if (n_Equal(C1,MinusOne,r)) // lc(M1) / gcd( lc(M1), lc(M2)) == -1 ???? |
---|
| 1762 | // { |
---|
| 1763 | // M2=p_Add_q(M1,M2,r); // ????? |
---|
| 1764 | // } |
---|
| 1765 | // else |
---|
| 1766 | // { |
---|
| 1767 | M1=p_Mult_nn(M1,C2,r); // M1 = (C2*lc(p1)) * (lcm(lm(p1),lm(p2)) / lm(p1)) * lm(p1) |
---|
[52e2f6] | 1768 | |
---|
| 1769 | #ifdef PDEBUG |
---|
| 1770 | p_Test(M1,r); |
---|
| 1771 | #endif |
---|
| 1772 | |
---|
[5a9e7b] | 1773 | M2=p_Mult_nn(M2,C1,r); // M2 =(-C1*lc(p2)) * (lcm(lm(p1),lm(p2)) / lm(p2)) * lm(p2) |
---|
[52e2f6] | 1774 | |
---|
| 1775 | |
---|
[b1a5c1] | 1776 | |
---|
[52e2f6] | 1777 | #ifdef PDEBUG |
---|
| 1778 | p_Test(M2,r); |
---|
| 1779 | |
---|
| 1780 | #if MYTEST |
---|
| 1781 | Print("M1: "); pWrite(M1); |
---|
| 1782 | Print("M2: "); pWrite(M2); |
---|
| 1783 | #endif |
---|
| 1784 | #endif |
---|
| 1785 | |
---|
| 1786 | |
---|
[5a9e7b] | 1787 | M2=p_Add_q(M1,M2,r); // M1 is killed, M2 = spoly(lt(p1), lt(p2)) = C2*M1 - C1*M2 |
---|
[52e2f6] | 1788 | |
---|
| 1789 | #ifdef PDEBUG |
---|
| 1790 | p_Test(M2,r); |
---|
| 1791 | |
---|
| 1792 | #if MYTEST |
---|
| 1793 | Print("M2: "); pWrite(M2); |
---|
| 1794 | #endif |
---|
| 1795 | |
---|
| 1796 | #endif |
---|
| 1797 | |
---|
| 1798 | // M2 == 0 for supercommutative algebras! |
---|
[5a9e7b] | 1799 | // } |
---|
| 1800 | // n_Delete(&MinusOne,r); |
---|
| 1801 | |
---|
| 1802 | p_SetCoeff(m1,C2,r); // lc(m1) = C2!!! |
---|
| 1803 | p_SetCoeff(m2,C1,r); // lc(m2) = C1!!! |
---|
| 1804 | |
---|
[52e2f6] | 1805 | #ifdef PDEBUG |
---|
| 1806 | p_Test(m1,r); |
---|
| 1807 | p_Test(m2,r); |
---|
| 1808 | #endif |
---|
| 1809 | |
---|
| 1810 | // poly tmp = p_Copy(p1,r); // tmp = p1 |
---|
| 1811 | // tmp=p_LmDeleteAndNext(tmp,r); // tmp = tail(p1) |
---|
| 1812 | //#ifdef PDEBUG |
---|
| 1813 | // p_Test(tmp,r); |
---|
| 1814 | //#endif |
---|
[b1a5c1] | 1815 | |
---|
[52e2f6] | 1816 | M1 = nc_mm_Mult_pp(m1, pNext(p1), r); // M1 = m1 * tail(p1), delete tmp // ??? |
---|
| 1817 | |
---|
| 1818 | #ifdef PDEBUG |
---|
| 1819 | p_Test(M1,r); |
---|
| 1820 | |
---|
| 1821 | #if MYTEST |
---|
| 1822 | Print("M1: "); pWrite(M1); |
---|
| 1823 | #endif |
---|
[5a9e7b] | 1824 | |
---|
[52e2f6] | 1825 | #endif |
---|
[b1a5c1] | 1826 | |
---|
[5a9e7b] | 1827 | M2=p_Add_q(M2,M1,r); // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1), delete M1 |
---|
[52e2f6] | 1828 | #ifdef PDEBUG |
---|
| 1829 | p_Test(M2,r); |
---|
| 1830 | |
---|
| 1831 | #if MYTEST |
---|
| 1832 | Print("M2: "); pWrite(M2); |
---|
| 1833 | #endif |
---|
| 1834 | |
---|
| 1835 | #endif |
---|
| 1836 | |
---|
| 1837 | // tmp=p_Copy(p2,r); // tmp = p2 |
---|
| 1838 | // tmp=p_LmDeleteAndNext(tmp,r); // tmp = tail(p2) |
---|
| 1839 | |
---|
| 1840 | //#ifdef PDEBUG |
---|
| 1841 | // p_Test(tmp,r); |
---|
| 1842 | //#endif |
---|
| 1843 | |
---|
| 1844 | M1 = nc_mm_Mult_pp(m2, pNext(p2), r); // M1 = m2 * tail(p2), detele tmp |
---|
[b1a5c1] | 1845 | |
---|
[52e2f6] | 1846 | #ifdef PDEBUG |
---|
| 1847 | p_Test(M1,r); |
---|
| 1848 | |
---|
| 1849 | #if MYTEST |
---|
| 1850 | Print("M1: "); pWrite(M1); |
---|
| 1851 | #endif |
---|
| 1852 | |
---|
| 1853 | #endif |
---|
| 1854 | |
---|
| 1855 | M2 = p_Add_q(M2,M1,r); // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1) + m2*tail(p2) |
---|
| 1856 | |
---|
| 1857 | #ifdef PDEBUG |
---|
| 1858 | p_Test(M2,r); |
---|
| 1859 | |
---|
| 1860 | #if MYTEST |
---|
| 1861 | Print("M2: "); pWrite(M2); |
---|
| 1862 | #endif |
---|
[b1a5c1] | 1863 | |
---|
[52e2f6] | 1864 | #endif |
---|
[5a9e7b] | 1865 | // delete M1 |
---|
| 1866 | |
---|
| 1867 | p_Delete(&m1,r); // => n_Delete(&C1,r); |
---|
| 1868 | p_Delete(&m2,r); // => n_Delete(&C2,r); |
---|
| 1869 | |
---|
| 1870 | #ifdef PDEBUG |
---|
| 1871 | p_Test(M2,r); |
---|
| 1872 | #endif |
---|
| 1873 | |
---|
[a0d9be] | 1874 | if (M2!=NULL) p_Cleardenom(M2,r); |
---|
| 1875 | // if (M2!=NULL) p_Content(M2); |
---|
[5a9e7b] | 1876 | |
---|
| 1877 | return(M2); |
---|
| 1878 | } |
---|
| 1879 | |
---|
| 1880 | |
---|
| 1881 | |
---|
| 1882 | |
---|
| 1883 | #if 0 |
---|
[35aab3] | 1884 | /*5 |
---|
| 1885 | * reduction of tail(q) with p1 |
---|
| 1886 | * lead(p1) divides lead(pNext(q2)) and pNext(q2) is reduced |
---|
| 1887 | * do not destroy p1, but tail(q) |
---|
| 1888 | */ |
---|
[5a9e7b] | 1889 | void gnc_ReduceSpolyTail(poly p1, poly q, poly q2, poly spNoether, const ring r) |
---|
[35aab3] | 1890 | { |
---|
| 1891 | poly a1=p_Head(p1,r); |
---|
| 1892 | poly Q=pNext(q2); |
---|
| 1893 | number cQ=p_GetCoeff(Q,r); |
---|
| 1894 | poly m=pOne(); |
---|
| 1895 | p_ExpVectorDiff(m,Q,p1,r); |
---|
| 1896 | // p_SetComp(m,0,r); |
---|
[ec547b3] | 1897 | //p_Setm(m,r); |
---|
[35aab3] | 1898 | #ifdef PDEBUG |
---|
| 1899 | p_Test(m,r); |
---|
| 1900 | #endif |
---|
| 1901 | /* pSetComp(m,r)=0? */ |
---|
[d5f9aea] | 1902 | poly M = nc_mm_Mult_pp(m, p1,r); |
---|
[35aab3] | 1903 | number C=p_GetCoeff(M,r); |
---|
[86016d] | 1904 | M=p_Add_q(M,nc_mm_Mult_p(m,p_LmDeleteAndNext(p_Copy(p1,r),r),r),r); // _pp? |
---|
[35aab3] | 1905 | q=p_Mult_nn(q,C,r); |
---|
| 1906 | number MinusOne=n_Init(-1,r); |
---|
| 1907 | if (!n_Equal(cQ,MinusOne,r)) |
---|
| 1908 | { |
---|
| 1909 | cQ=nNeg(cQ); |
---|
| 1910 | M=p_Mult_nn(M,cQ,r); |
---|
| 1911 | } |
---|
| 1912 | Q=p_Add_q(Q,M,r); |
---|
| 1913 | pNext(q2)=Q; |
---|
| 1914 | |
---|
| 1915 | p_Delete(&m,r); |
---|
| 1916 | n_Delete(&C,r); |
---|
| 1917 | n_Delete(&cQ,r); |
---|
| 1918 | n_Delete(&MinusOne,r); |
---|
| 1919 | /* return(q); */ |
---|
| 1920 | } |
---|
[5a9e7b] | 1921 | #endif |
---|
| 1922 | |
---|
[35aab3] | 1923 | |
---|
| 1924 | /*6 |
---|
| 1925 | * creates the commutative lcm(lm(p1),lm(p2)) |
---|
| 1926 | * do not destroy p1 and p2 |
---|
| 1927 | */ |
---|
[4bbe3b] | 1928 | poly nc_CreateShortSpoly(poly p1, poly p2, const ring r) |
---|
[35aab3] | 1929 | { |
---|
[52e2f6] | 1930 | #ifdef PDEBUG |
---|
| 1931 | p_Test(p1, r); |
---|
| 1932 | p_Test(p2, r); |
---|
| 1933 | #endif |
---|
| 1934 | |
---|
| 1935 | const long lCompP1 = p_GetComp(p1,r); |
---|
| 1936 | const long lCompP2 = p_GetComp(p2,r); |
---|
| 1937 | |
---|
| 1938 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
[35aab3] | 1939 | { |
---|
[ea68ed] | 1940 | #ifdef PDEBUG |
---|
[151000] | 1941 | Werror("nc_CreateShortSpoly: wrong module components!"); // !!!! |
---|
[ea68ed] | 1942 | #endif |
---|
[35aab3] | 1943 | return(NULL); |
---|
| 1944 | } |
---|
[b1a5c1] | 1945 | |
---|
[26d633] | 1946 | poly m; |
---|
[43cbc0] | 1947 | if ( ! rIsRatGRing(currRing)) |
---|
| 1948 | { |
---|
| 1949 | m = p_Lcm(p1, p2, si_max(lCompP1, lCompP2), r); |
---|
| 1950 | } |
---|
[26d633] | 1951 | #ifdef HAVE_RATGRING |
---|
[43cbc0] | 1952 | else |
---|
| 1953 | { |
---|
| 1954 | /* rational version */ |
---|
| 1955 | m = p_LcmRat(p1, p2, si_max(lCompP1, lCompP2), r); |
---|
| 1956 | } |
---|
[26d633] | 1957 | #endif |
---|
[52e2f6] | 1958 | |
---|
[151000] | 1959 | // n_Delete(&p_GetCoeff(m, r), r); |
---|
| 1960 | // pSetCoeff0(m, NULL); |
---|
[52e2f6] | 1961 | |
---|
[35aab3] | 1962 | #ifdef PDEBUG |
---|
[151000] | 1963 | // p_Test(m,r); |
---|
[35aab3] | 1964 | #endif |
---|
[b1a5c1] | 1965 | |
---|
[35aab3] | 1966 | return(m); |
---|
| 1967 | } |
---|
| 1968 | |
---|
[5a9e7b] | 1969 | void gnc_kBucketPolyRedOld(kBucket_pt b, poly p, number *c) |
---|
[35aab3] | 1970 | { |
---|
[a81a22] | 1971 | // b will not be multiplied by any constant in this impl. |
---|
[35aab3] | 1972 | // ==> *c=1 |
---|
[0a8ee5] | 1973 | if (c!=NULL) *c=nInit(1); |
---|
[35aab3] | 1974 | poly m=pOne(); |
---|
| 1975 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
[ec547b3] | 1976 | //pSetm(m); |
---|
[35aab3] | 1977 | #ifdef PDEBUG |
---|
| 1978 | pTest(m); |
---|
| 1979 | #endif |
---|
[d5f9aea] | 1980 | poly pp= nc_mm_Mult_pp(m,p,currRing); |
---|
[875d68] | 1981 | assume(pp!=NULL); |
---|
[35aab3] | 1982 | pDelete(&m); |
---|
[5f4ae4] | 1983 | number n=pGetCoeff(pp); |
---|
[35aab3] | 1984 | number nn; |
---|
[0a8ee5] | 1985 | if (!n_IsMOne(n,currRing)) |
---|
[35aab3] | 1986 | { |
---|
| 1987 | nn=nNeg(nInvers(n)); |
---|
[5f4ae4] | 1988 | n=nMult(nn,pGetCoeff(kBucketGetLm(b))); |
---|
| 1989 | nDelete(&nn); |
---|
| 1990 | pp=p_Mult_nn(pp,n,currRing); |
---|
| 1991 | nDelete(&n); |
---|
| 1992 | } |
---|
| 1993 | else |
---|
| 1994 | { |
---|
| 1995 | pp=p_Mult_nn(pp,pGetCoeff(kBucketGetLm(b)),currRing); |
---|
[35aab3] | 1996 | } |
---|
| 1997 | int l=pLength(pp); |
---|
| 1998 | kBucket_Add_q(b,pp,&l); |
---|
| 1999 | } |
---|
| 2000 | |
---|
[5a9e7b] | 2001 | void gnc_kBucketPolyRedNew(kBucket_pt b, poly p, number *c) |
---|
| 2002 | { |
---|
| 2003 | #ifdef PDEBUG |
---|
| 2004 | // Print(">*"); |
---|
| 2005 | #endif |
---|
| 2006 | |
---|
| 2007 | #ifdef KDEBUG |
---|
| 2008 | if( !kbTest(b) )Werror("nc_kBucketPolyRed: broken bucket!"); |
---|
| 2009 | #endif |
---|
| 2010 | |
---|
| 2011 | #ifdef PDEBUG |
---|
| 2012 | pTest(p); |
---|
[52e2f6] | 2013 | #if MYTEST |
---|
| 2014 | Print("p: "); pWrite(p); |
---|
| 2015 | #endif |
---|
[5a9e7b] | 2016 | #endif |
---|
| 2017 | |
---|
| 2018 | // b will not be multiplied by any constant in this impl. |
---|
| 2019 | // ==> *c=1 |
---|
[0a8ee5] | 2020 | if (c!=NULL) *c=nInit(1); |
---|
[5a9e7b] | 2021 | poly m = pOne(); |
---|
| 2022 | const poly pLmB = kBucketGetLm(b); // no new copy! |
---|
| 2023 | |
---|
[52e2f6] | 2024 | assume( pLmB != NULL ); |
---|
[b1a5c1] | 2025 | |
---|
[5a9e7b] | 2026 | #ifdef PDEBUG |
---|
| 2027 | pTest(pLmB); |
---|
[52e2f6] | 2028 | |
---|
| 2029 | #if MYTEST |
---|
| 2030 | Print("pLmB: "); pWrite(pLmB); |
---|
| 2031 | #endif |
---|
[5a9e7b] | 2032 | #endif |
---|
| 2033 | |
---|
| 2034 | pExpVectorDiff(m, pLmB, p); |
---|
| 2035 | //pSetm(m); |
---|
| 2036 | |
---|
| 2037 | #ifdef PDEBUG |
---|
| 2038 | pTest(m); |
---|
[52e2f6] | 2039 | #if MYTEST |
---|
| 2040 | Print("m: "); pWrite(m); |
---|
| 2041 | #endif |
---|
[5a9e7b] | 2042 | #endif |
---|
| 2043 | |
---|
[52e2f6] | 2044 | poly pp = nc_mm_Mult_pp(m, p, currRing); |
---|
[5a9e7b] | 2045 | pDelete(&m); |
---|
| 2046 | |
---|
[52e2f6] | 2047 | assume( pp != NULL ); |
---|
| 2048 | const number n = pGetCoeff(pp); // bug! |
---|
[5a9e7b] | 2049 | |
---|
| 2050 | if (!n_IsMOne(n,currRing) ) // does this improve performance??!? also see below... // TODO: check later on. |
---|
[0a8ee5] | 2051 | // if n == -1 => nn = 1 and -1/n |
---|
[5a9e7b] | 2052 | { |
---|
[0a8ee5] | 2053 | number nn=nNeg(nInvers(n)); |
---|
| 2054 | number t = nMult(nn,pGetCoeff(pLmB)); |
---|
| 2055 | nDelete(&nn); |
---|
| 2056 | pp = p_Mult_nn(pp,t,currRing); |
---|
| 2057 | nDelete(&t); |
---|
| 2058 | } |
---|
| 2059 | else |
---|
| 2060 | { |
---|
| 2061 | pp = p_Mult_nn(pp,pGetCoeff(pLmB),currRing); |
---|
[5a9e7b] | 2062 | } |
---|
| 2063 | |
---|
| 2064 | int l = pLength(pp); |
---|
| 2065 | |
---|
| 2066 | #ifdef PDEBUG |
---|
| 2067 | pTest(pp); |
---|
| 2068 | // Print("PP: "); pWrite(pp); |
---|
| 2069 | #endif |
---|
| 2070 | |
---|
| 2071 | kBucket_Add_q(b,pp,&l); |
---|
| 2072 | |
---|
| 2073 | |
---|
| 2074 | #ifdef PDEBUG |
---|
| 2075 | // Print("*>"); |
---|
| 2076 | #endif |
---|
| 2077 | } |
---|
| 2078 | |
---|
| 2079 | |
---|
| 2080 | void gnc_kBucketPolyRed_ZOld(kBucket_pt b, poly p, number *c) |
---|
[a81a22] | 2081 | { |
---|
| 2082 | // b is multiplied by a constant in this impl. |
---|
[0a8ee5] | 2083 | number ctmp; |
---|
[a81a22] | 2084 | poly m=pOne(); |
---|
| 2085 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
| 2086 | //pSetm(m); |
---|
| 2087 | #ifdef PDEBUG |
---|
| 2088 | pTest(m); |
---|
| 2089 | #endif |
---|
[0a8ee5] | 2090 | if(p_IsConstant(m,currRing)) |
---|
| 2091 | { |
---|
[45d41f] | 2092 | pDelete(&m); |
---|
[0a8ee5] | 2093 | ctmp = kBucketPolyRed(b,p,pLength(p),NULL); |
---|
[45d41f] | 2094 | } |
---|
[0a8ee5] | 2095 | else |
---|
| 2096 | { |
---|
| 2097 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
| 2098 | number c2,cc; |
---|
[a0d9be] | 2099 | p_Cleardenom_n(pp,currRing,c2); |
---|
[0a8ee5] | 2100 | pDelete(&m); |
---|
| 2101 | ctmp = kBucketPolyRed(b,pp,pLength(pp),NULL); |
---|
| 2102 | //cc=*c; |
---|
| 2103 | //*c=nMult(*c,c2); |
---|
| 2104 | nDelete(&c2); |
---|
| 2105 | //nDelete(&cc); |
---|
| 2106 | pDelete(&pp); |
---|
| 2107 | } |
---|
| 2108 | if (c!=NULL) *c=ctmp; |
---|
| 2109 | else nDelete(&ctmp); |
---|
[a81a22] | 2110 | } |
---|
| 2111 | |
---|
[5a9e7b] | 2112 | void gnc_kBucketPolyRed_ZNew(kBucket_pt b, poly p, number *c) |
---|
| 2113 | { |
---|
| 2114 | // b is multiplied by a constant in this impl. |
---|
[0a8ee5] | 2115 | number ctmp; |
---|
[5a9e7b] | 2116 | poly m=pOne(); |
---|
| 2117 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
| 2118 | //pSetm(m); |
---|
| 2119 | #ifdef PDEBUG |
---|
| 2120 | pTest(m); |
---|
| 2121 | #endif |
---|
| 2122 | |
---|
| 2123 | if(p_IsConstant(m,currRing)) |
---|
| 2124 | { |
---|
| 2125 | pDelete(&m); |
---|
[0a8ee5] | 2126 | ctmp = kBucketPolyRed(b,p,pLength(p),NULL); |
---|
[5a9e7b] | 2127 | } |
---|
[0a8ee5] | 2128 | else |
---|
| 2129 | { |
---|
| 2130 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
| 2131 | number c2,cc; |
---|
[a0d9be] | 2132 | p_Cleardenom_n(pp,currRing,c2); |
---|
[0a8ee5] | 2133 | pDelete(&m); |
---|
| 2134 | ctmp = kBucketPolyRed(b,pp,pLength(pp),NULL); |
---|
| 2135 | //cc=*c; |
---|
| 2136 | //*c=nMult(*c,c2); |
---|
| 2137 | nDelete(&c2); |
---|
| 2138 | //nDelete(&cc); |
---|
| 2139 | pDelete(&pp); |
---|
| 2140 | } |
---|
| 2141 | if (c!=NULL) *c=ctmp; |
---|
| 2142 | else nDelete(&ctmp); |
---|
[5a9e7b] | 2143 | } |
---|
| 2144 | |
---|
| 2145 | |
---|
| 2146 | inline void nc_PolyPolyRedOld(poly &b, poly p, number *c) |
---|
[35aab3] | 2147 | // reduces b with p, do not delete both |
---|
| 2148 | { |
---|
| 2149 | // b will not by multiplied by any constant in this impl. |
---|
| 2150 | // ==> *c=1 |
---|
[5f4ae4] | 2151 | if (c!=NULL) *c=nInit(1); |
---|
[35aab3] | 2152 | poly m=pOne(); |
---|
| 2153 | pExpVectorDiff(m,pHead(b),p); |
---|
[ec547b3] | 2154 | //pSetm(m); |
---|
[35aab3] | 2155 | #ifdef PDEBUG |
---|
| 2156 | pTest(m); |
---|
| 2157 | #endif |
---|
[d5f9aea] | 2158 | poly pp=nc_mm_Mult_pp(m,p,currRing); |
---|
[875d68] | 2159 | assume(pp!=NULL); |
---|
[18ff4c] | 2160 | |
---|
[35aab3] | 2161 | pDelete(&m); |
---|
[5f4ae4] | 2162 | number n=pGetCoeff(pp); |
---|
[35aab3] | 2163 | number nn; |
---|
[5f4ae4] | 2164 | if (!nIsMOne(n)) |
---|
[35aab3] | 2165 | { |
---|
| 2166 | nn=nNeg(nInvers(n)); |
---|
[5f4ae4] | 2167 | n=nMult(nn,pGetCoeff(b)); |
---|
| 2168 | nDelete(&nn); |
---|
| 2169 | pp=p_Mult_nn(pp,n,currRing); |
---|
| 2170 | nDelete(&n); |
---|
| 2171 | } |
---|
| 2172 | else |
---|
| 2173 | { |
---|
| 2174 | pp=p_Mult_nn(pp,pGetCoeff(b),currRing); |
---|
[35aab3] | 2175 | } |
---|
| 2176 | b=p_Add_q(b,pp,currRing); |
---|
| 2177 | } |
---|
| 2178 | |
---|
[5a9e7b] | 2179 | |
---|
| 2180 | inline void nc_PolyPolyRedNew(poly &b, poly p, number *c) |
---|
| 2181 | // reduces b with p, do not delete both |
---|
| 2182 | { |
---|
[875d68] | 2183 | #ifdef PDEBUG |
---|
| 2184 | pTest(b); |
---|
| 2185 | pTest(p); |
---|
| 2186 | #endif |
---|
| 2187 | |
---|
| 2188 | #if MYTEST |
---|
| 2189 | PrintS("nc_PolyPolyRedNew("); |
---|
| 2190 | pWrite0(b); |
---|
| 2191 | PrintS(", "); |
---|
| 2192 | pWrite0(p); |
---|
[18ff4c] | 2193 | PrintS(", *c): "); |
---|
| 2194 | #endif |
---|
| 2195 | |
---|
[5a9e7b] | 2196 | // b will not by multiplied by any constant in this impl. |
---|
| 2197 | // ==> *c=1 |
---|
[0a8ee5] | 2198 | if (c!=NULL) *c=nInit(1); |
---|
[5a9e7b] | 2199 | |
---|
[875d68] | 2200 | poly pp = NULL; |
---|
| 2201 | |
---|
| 2202 | // there is a problem when p is a square(=>0!) |
---|
| 2203 | |
---|
| 2204 | while((b != NULL) && (pp == NULL)) |
---|
| 2205 | { |
---|
| 2206 | |
---|
| 2207 | // poly pLmB = pHead(b); |
---|
[18ff4c] | 2208 | poly m = pOne(); |
---|
[875d68] | 2209 | pExpVectorDiff(m, b, p); |
---|
| 2210 | // pDelete(&pLmB); |
---|
[5a9e7b] | 2211 | //pSetm(m); |
---|
[18ff4c] | 2212 | |
---|
[5a9e7b] | 2213 | #ifdef PDEBUG |
---|
[875d68] | 2214 | pTest(m); |
---|
| 2215 | pTest(b); |
---|
[5a9e7b] | 2216 | #endif |
---|
[875d68] | 2217 | |
---|
[18ff4c] | 2218 | pp = nc_mm_Mult_pp(m, p, currRing); |
---|
[875d68] | 2219 | |
---|
| 2220 | #if MYTEST |
---|
[18ff4c] | 2221 | PrintS("\n{b': "); |
---|
[875d68] | 2222 | pWrite0(b); |
---|
[18ff4c] | 2223 | PrintS(", m: "); |
---|
[875d68] | 2224 | pWrite0(m); |
---|
[18ff4c] | 2225 | PrintS(", pp: "); |
---|
| 2226 | pWrite0(pp); |
---|
[875d68] | 2227 | PrintS(" }\n"); |
---|
[18ff4c] | 2228 | #endif |
---|
[875d68] | 2229 | |
---|
| 2230 | pDelete(&m); // one m for all tries! |
---|
| 2231 | |
---|
| 2232 | // assume( pp != NULL ); |
---|
[18ff4c] | 2233 | |
---|
[875d68] | 2234 | if( pp == NULL ) |
---|
| 2235 | { |
---|
| 2236 | b = p_LmDeleteAndNext(b, currRing); |
---|
| 2237 | |
---|
| 2238 | if( !p_DivisibleBy(p, b, currRing) ) |
---|
[18ff4c] | 2239 | return; |
---|
| 2240 | |
---|
[875d68] | 2241 | } |
---|
| 2242 | } |
---|
| 2243 | |
---|
| 2244 | #if MYTEST |
---|
[18ff4c] | 2245 | PrintS("{b': "); |
---|
[875d68] | 2246 | pWrite0(b); |
---|
[18ff4c] | 2247 | PrintS(", pp: "); |
---|
| 2248 | pWrite0(pp); |
---|
[875d68] | 2249 | PrintS(" }\n"); |
---|
[18ff4c] | 2250 | #endif |
---|
[875d68] | 2251 | |
---|
| 2252 | |
---|
| 2253 | if(b == NULL) return; |
---|
| 2254 | |
---|
| 2255 | |
---|
| 2256 | assume(pp != NULL); |
---|
[5a9e7b] | 2257 | |
---|
| 2258 | const number n = pGetCoeff(pp); // no new copy |
---|
| 2259 | |
---|
| 2260 | number nn; |
---|
| 2261 | |
---|
| 2262 | if (!n_IsMOne(n, currRing)) // TODO: as above. |
---|
| 2263 | { |
---|
[5f4ae4] | 2264 | nn=nNeg(nInvers(n)); |
---|
| 2265 | number t = nMult(nn, pGetCoeff(b)); |
---|
| 2266 | nDelete(&nn); |
---|
| 2267 | pp=p_Mult_nn(pp, t, currRing); |
---|
| 2268 | nDelete(&t); |
---|
| 2269 | } |
---|
| 2270 | else |
---|
| 2271 | { |
---|
| 2272 | pp=p_Mult_nn(pp, pGetCoeff(b), currRing); |
---|
[5a9e7b] | 2273 | } |
---|
| 2274 | |
---|
| 2275 | |
---|
| 2276 | b=p_Add_q(b,pp,currRing); |
---|
| 2277 | |
---|
| 2278 | } |
---|
| 2279 | |
---|
| 2280 | void nc_PolyPolyRed(poly &b, poly p, number *c) |
---|
| 2281 | { |
---|
[8fbdb2] | 2282 | #if 0 |
---|
[5a9e7b] | 2283 | nc_PolyPolyRedOld(b, p, c); |
---|
[8fbdb2] | 2284 | #else |
---|
| 2285 | nc_PolyPolyRedNew(b, p, c); |
---|
| 2286 | #endif |
---|
[5a9e7b] | 2287 | } |
---|
| 2288 | |
---|
| 2289 | |
---|
| 2290 | poly nc_mm_Bracket_nn(poly m1, poly m2); |
---|
| 2291 | |
---|
[69262fa] | 2292 | poly nc_p_Bracket_qq(poly p, const poly q) |
---|
[35aab3] | 2293 | /* returns [p,q], destroys p */ |
---|
| 2294 | { |
---|
[69262fa] | 2295 | assume(p != NULL && q!= NULL); |
---|
[b1a5c1] | 2296 | |
---|
[35aab3] | 2297 | if (!rIsPluralRing(currRing)) return(NULL); |
---|
| 2298 | if (pComparePolys(p,q)) return(NULL); |
---|
| 2299 | /* Components !? */ |
---|
| 2300 | poly Q=NULL; |
---|
| 2301 | number coef=NULL; |
---|
| 2302 | poly res=NULL; |
---|
| 2303 | poly pres=NULL; |
---|
| 2304 | int UseBuckets=1; |
---|
| 2305 | if ((pLength(p)< MIN_LENGTH_BUCKET/2) && (pLength(q)< MIN_LENGTH_BUCKET/2) || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
---|
[6bde67] | 2306 | |
---|
| 2307 | |
---|
| 2308 | CPolynomialSummator sum(currRing, UseBuckets == 0); |
---|
[26d633] | 2309 | |
---|
[35aab3] | 2310 | while (p!=NULL) |
---|
| 2311 | { |
---|
| 2312 | Q=q; |
---|
| 2313 | while(Q!=NULL) |
---|
| 2314 | { |
---|
| 2315 | pres=nc_mm_Bracket_nn(p,Q); /* since no coeffs are taken into account there */ |
---|
| 2316 | if (pres!=NULL) |
---|
| 2317 | { |
---|
[f56364] | 2318 | coef = nMult(pGetCoeff(p),pGetCoeff(Q)); |
---|
| 2319 | pres = p_Mult_nn(pres,coef,currRing); |
---|
[6bde67] | 2320 | |
---|
| 2321 | sum += pres; |
---|
[35aab3] | 2322 | nDelete(&coef); |
---|
| 2323 | } |
---|
| 2324 | pIter(Q); |
---|
| 2325 | } |
---|
| 2326 | p=pLmDeleteAndNext(p); |
---|
| 2327 | } |
---|
[6bde67] | 2328 | return(sum); |
---|
[35aab3] | 2329 | } |
---|
| 2330 | |
---|
| 2331 | poly nc_mm_Bracket_nn(poly m1, poly m2) |
---|
| 2332 | /*returns [m1,m2] for two monoms, destroys nothing */ |
---|
| 2333 | /* without coeffs */ |
---|
| 2334 | { |
---|
| 2335 | if (pLmIsConstant(m1) || pLmIsConstant(m1)) return(NULL); |
---|
| 2336 | if (pLmCmp(m1,m2)==0) return(NULL); |
---|
| 2337 | int rN=currRing->N; |
---|
| 2338 | int *M1=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 2339 | int *M2=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 2340 | int *PREFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 2341 | int *SUFFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 2342 | pGetExpV(m1,M1); |
---|
| 2343 | pGetExpV(m2,M2); |
---|
| 2344 | poly res=NULL; |
---|
| 2345 | poly ares=NULL; |
---|
| 2346 | poly bres=NULL; |
---|
| 2347 | poly prefix=NULL; |
---|
| 2348 | poly suffix=NULL; |
---|
| 2349 | int nMin,nMax; |
---|
| 2350 | number nTmp=NULL; |
---|
| 2351 | int i,j,k; |
---|
| 2352 | for (i=1;i<=rN;i++) |
---|
| 2353 | { |
---|
| 2354 | if (M2[i]!=0) |
---|
| 2355 | { |
---|
| 2356 | ares=NULL; |
---|
| 2357 | for (j=1;j<=rN;j++) |
---|
| 2358 | { |
---|
| 2359 | if (M1[j]!=0) |
---|
| 2360 | { |
---|
| 2361 | bres=NULL; |
---|
| 2362 | /* compute [ x_j^M1[j],x_i^M2[i] ] */ |
---|
| 2363 | if (i<j) {nMax=j; nMin=i;} else {nMax=i; nMin=j;} |
---|
[52e2f6] | 2364 | if ( (i==j) || ((MATELEM(currRing->GetNC()->COM,nMin,nMax)!=NULL) && nIsOne(pGetCoeff(MATELEM(currRing->GetNC()->C,nMin,nMax))) )) /* not (the same exp. or commuting exps)*/ |
---|
[35aab3] | 2365 | { bres=NULL; } |
---|
| 2366 | else |
---|
| 2367 | { |
---|
[5a9e7b] | 2368 | if (i<j) { bres=gnc_uu_Mult_ww(j,M1[j],i,M2[i],currRing); } |
---|
| 2369 | else bres=gnc_uu_Mult_ww(i,M2[i],j,M1[j],currRing); |
---|
[35aab3] | 2370 | if (nIsOne(pGetCoeff(bres))) |
---|
| 2371 | { |
---|
| 2372 | bres=pLmDeleteAndNext(bres); |
---|
| 2373 | } |
---|
| 2374 | else |
---|
| 2375 | { |
---|
| 2376 | nTmp=nSub(pGetCoeff(bres),nInit(1)); |
---|
| 2377 | pSetCoeff(bres,nTmp); /* only lc ! */ |
---|
| 2378 | } |
---|
| 2379 | #ifdef PDEBUG |
---|
| 2380 | pTest(bres); |
---|
| 2381 | #endif |
---|
| 2382 | if (i>j) bres=p_Neg(bres, currRing); |
---|
| 2383 | } |
---|
| 2384 | if (bres!=NULL) |
---|
| 2385 | { |
---|
| 2386 | /* now mult (prefix, bres, suffix) */ |
---|
| 2387 | memcpy(SUFFIX, M1,(rN+1)*sizeof(int)); |
---|
| 2388 | memcpy(PREFIX, M1,(rN+1)*sizeof(int)); |
---|
| 2389 | for (k=1;k<=j;k++) SUFFIX[k]=0; |
---|
| 2390 | for (k=j;k<=rN;k++) PREFIX[k]=0; |
---|
| 2391 | SUFFIX[0]=0; |
---|
| 2392 | PREFIX[0]=0; |
---|
| 2393 | prefix=pOne(); |
---|
| 2394 | suffix=pOne(); |
---|
| 2395 | pSetExpV(prefix,PREFIX); |
---|
| 2396 | pSetm(prefix); |
---|
| 2397 | pSetExpV(suffix,SUFFIX); |
---|
| 2398 | pSetm(suffix); |
---|
[5a9e7b] | 2399 | if (!pLmIsConstant(prefix)) bres = gnc_mm_Mult_p(prefix, bres,currRing); |
---|
| 2400 | if (!pLmIsConstant(suffix)) bres = gnc_p_Mult_mm(bres, suffix,currRing); |
---|
[35aab3] | 2401 | ares=p_Add_q(ares, bres,currRing); |
---|
| 2402 | /* What to give free? */ |
---|
[5a9e7b] | 2403 | /* Do we have to free PREFIX/SUFFIX? it seems so */ |
---|
[35aab3] | 2404 | pDelete(&prefix); |
---|
| 2405 | pDelete(&suffix); |
---|
| 2406 | } |
---|
| 2407 | } |
---|
| 2408 | } |
---|
| 2409 | if (ares!=NULL) |
---|
| 2410 | { |
---|
| 2411 | /* now mult (prefix, bres, suffix) */ |
---|
| 2412 | memcpy(SUFFIX, M2,(rN+1)*sizeof(int)); |
---|
| 2413 | memcpy(PREFIX, M2,(rN+1)*sizeof(int)); |
---|
| 2414 | for (k=1;k<=i;k++) SUFFIX[k]=0; |
---|
| 2415 | for (k=i;k<=rN;k++) PREFIX[k]=0; |
---|
| 2416 | SUFFIX[0]=0; |
---|
| 2417 | PREFIX[0]=0; |
---|
| 2418 | prefix=pOne(); |
---|
| 2419 | suffix=pOne(); |
---|
| 2420 | pSetExpV(prefix,PREFIX); |
---|
| 2421 | pSetm(prefix); |
---|
| 2422 | pSetExpV(suffix,SUFFIX); |
---|
| 2423 | pSetm(suffix); |
---|
| 2424 | bres=ares; |
---|
[5a9e7b] | 2425 | if (!pLmIsConstant(prefix)) bres = gnc_mm_Mult_p(prefix, bres,currRing); |
---|
| 2426 | if (!pLmIsConstant(suffix)) bres = gnc_p_Mult_mm(bres, suffix,currRing); |
---|
[35aab3] | 2427 | res=p_Add_q(res, bres,currRing); |
---|
| 2428 | pDelete(&prefix); |
---|
| 2429 | pDelete(&suffix); |
---|
| 2430 | } |
---|
| 2431 | } |
---|
| 2432 | } |
---|
| 2433 | freeT(M1, rN); |
---|
| 2434 | freeT(M2, rN); |
---|
| 2435 | freeT(PREFIX, rN); |
---|
| 2436 | freeT(SUFFIX, rN); |
---|
[f56364] | 2437 | pTest(res); |
---|
[35aab3] | 2438 | return(res); |
---|
| 2439 | } |
---|
| 2440 | |
---|
[728288] | 2441 | ideal twostd(ideal I) // works in currRing only! |
---|
[35aab3] | 2442 | { |
---|
[728288] | 2443 | ideal J = kStd(I, currQuotient, testHomog, NULL, NULL, 0, 0, NULL); // in currRing!!! |
---|
| 2444 | idSkipZeroes(J); // ring independent! |
---|
| 2445 | |
---|
| 2446 | const int rN = currRing->N; |
---|
[f4b74e2] | 2447 | |
---|
[35aab3] | 2448 | loop |
---|
| 2449 | { |
---|
[728288] | 2450 | ideal K = NULL; |
---|
| 2451 | const int s = idElem(J); // ring independent |
---|
[5accf0] | 2452 | |
---|
[728288] | 2453 | for(int i = 0; i < s; i++) |
---|
[35aab3] | 2454 | { |
---|
[728288] | 2455 | const poly p = J->m[i]; |
---|
[f4b74e2] | 2456 | |
---|
[728288] | 2457 | #ifdef PDEBUG |
---|
| 2458 | p_Test(p, currRing); |
---|
| 2459 | #if 0 |
---|
| 2460 | Print("p: "); // ! |
---|
| 2461 | p_Write(p, currRing); |
---|
| 2462 | #endif |
---|
| 2463 | #endif |
---|
[f4b74e2] | 2464 | |
---|
[728288] | 2465 | for (int j = 1; j <= rN; j++) // for all j = 1..N |
---|
[35aab3] | 2466 | { |
---|
[b902246] | 2467 | poly varj = p_One( currRing); |
---|
[b1a5c1] | 2468 | p_SetExp(varj, j, 1, currRing); |
---|
[728288] | 2469 | p_Setm(varj, currRing); |
---|
| 2470 | |
---|
| 2471 | poly q = pp_Mult_mm(p, varj, currRing); // q = J[i] * var(j), |
---|
| 2472 | |
---|
| 2473 | #ifdef PDEBUG |
---|
| 2474 | p_Test(varj, currRing); |
---|
| 2475 | p_Test(p, currRing); |
---|
| 2476 | p_Test(q, currRing); |
---|
| 2477 | #if 0 |
---|
| 2478 | Print("Reducing p: "); // ! |
---|
| 2479 | p_Write(p, currRing); |
---|
| 2480 | Print("With q: "); // ! |
---|
| 2481 | p_Write(q, currRing); |
---|
| 2482 | #endif |
---|
| 2483 | #endif |
---|
| 2484 | |
---|
| 2485 | p_Delete(&varj, currRing); |
---|
| 2486 | |
---|
| 2487 | if (q != NULL) |
---|
| 2488 | { |
---|
[b1a5c1] | 2489 | #ifdef PDEBUG |
---|
[728288] | 2490 | #if 0 |
---|
| 2491 | Print("Reducing q[j = %d]: ", j); // ! |
---|
| 2492 | p_Write(q, currRing); |
---|
| 2493 | |
---|
| 2494 | Print("With p:"); |
---|
[f4b74e2] | 2495 | p_Write(p, currRing); |
---|
| 2496 | |
---|
[728288] | 2497 | #endif |
---|
| 2498 | #endif |
---|
| 2499 | |
---|
| 2500 | // bug: lm(p) may not divide lm(p * var(i)) in a SCA! |
---|
| 2501 | if( p_LmDivisibleBy(p, q, currRing) ) |
---|
| 2502 | q = nc_ReduceSpoly(p, q, currRing); |
---|
| 2503 | |
---|
| 2504 | |
---|
| 2505 | #ifdef PDEBUG |
---|
| 2506 | p_Test(q, currRing); |
---|
| 2507 | #if 0 |
---|
| 2508 | Print("reductum q/p: "); |
---|
[f4b74e2] | 2509 | p_Write(q, currRing); |
---|
[5accf0] | 2510 | |
---|
[728288] | 2511 | // Print("With J!\n"); |
---|
| 2512 | #endif |
---|
| 2513 | #endif |
---|
[b1a5c1] | 2514 | |
---|
[728288] | 2515 | // if( q != NULL) |
---|
| 2516 | q = kNF(J, currQuotient, q, 0, KSTD_NF_NONORM); // in currRing!!! |
---|
| 2517 | |
---|
| 2518 | #ifdef PDEBUG |
---|
| 2519 | p_Test(q, currRing); |
---|
| 2520 | #if 0 |
---|
| 2521 | Print("NF(J/currQuotient)=> q: "); // ! |
---|
| 2522 | p_Write(q, currRing); |
---|
| 2523 | #endif |
---|
| 2524 | #endif |
---|
| 2525 | if (q!=NULL) |
---|
[35aab3] | 2526 | { |
---|
[728288] | 2527 | if (p_IsConstant(q, currRing)) // => return (1)! |
---|
| 2528 | { |
---|
| 2529 | p_Delete(&q, currRing); |
---|
| 2530 | id_Delete(&J, currRing); |
---|
| 2531 | |
---|
| 2532 | if (K != NULL) |
---|
| 2533 | id_Delete(&K, currRing); |
---|
| 2534 | |
---|
| 2535 | ideal Q = idInit(1,1); // ring independent! |
---|
[b902246] | 2536 | Q->m[0] = p_One(currRing); |
---|
[728288] | 2537 | |
---|
| 2538 | return(Q); |
---|
| 2539 | } |
---|
| 2540 | |
---|
| 2541 | // flag = false; |
---|
| 2542 | |
---|
| 2543 | // K += q: |
---|
| 2544 | |
---|
| 2545 | ideal Q = idInit(1,1); // ring independent |
---|
| 2546 | Q->m[0]=q; |
---|
| 2547 | |
---|
| 2548 | if( K == NULL ) |
---|
| 2549 | K = Q; |
---|
| 2550 | else |
---|
| 2551 | { |
---|
| 2552 | ideal id_tmp = idSimpleAdd(K, Q); // in currRing |
---|
| 2553 | id_Delete(&K, currRing); |
---|
| 2554 | id_Delete(&Q, currRing); |
---|
| 2555 | K = id_tmp; // K += Q |
---|
| 2556 | } |
---|
[35aab3] | 2557 | } |
---|
[5accf0] | 2558 | |
---|
[728288] | 2559 | |
---|
| 2560 | } // if q != NULL |
---|
| 2561 | } // for all variables |
---|
| 2562 | |
---|
[35aab3] | 2563 | } |
---|
[b1a5c1] | 2564 | |
---|
[728288] | 2565 | if (K == NULL) // nothing new: i.e. all elements are two-sided |
---|
[35aab3] | 2566 | return(J); |
---|
| 2567 | /* now we update GrBasis J with K */ |
---|
[8e165ec] | 2568 | // iSize=IDELEMS(J); |
---|
[728288] | 2569 | #ifdef PDEBUG |
---|
| 2570 | idTest(J); // in currRing! |
---|
| 2571 | #if 0 |
---|
[f4b74e2] | 2572 | Print("J:"); |
---|
| 2573 | idPrint(J); |
---|
| 2574 | PrintLn(); |
---|
[728288] | 2575 | #endif // debug |
---|
| 2576 | #endif |
---|
[f4b74e2] | 2577 | |
---|
| 2578 | |
---|
| 2579 | |
---|
[728288] | 2580 | #ifdef PDEBUG |
---|
| 2581 | idTest(K); // in currRing! |
---|
| 2582 | #if 0 |
---|
[f4b74e2] | 2583 | Print("+K:"); |
---|
| 2584 | idPrint(K); |
---|
| 2585 | PrintLn(); |
---|
[728288] | 2586 | #endif // debug |
---|
| 2587 | #endif |
---|
[f4b74e2] | 2588 | |
---|
| 2589 | |
---|
[728288] | 2590 | int iSize = idElem(J); // ring independent |
---|
[5accf0] | 2591 | |
---|
[b1a5c1] | 2592 | // J += K: |
---|
[728288] | 2593 | ideal id_tmp = idSimpleAdd(J,K); // in currRing |
---|
| 2594 | id_Delete(&K, currRing); id_Delete(&J, currRing); |
---|
[f4b74e2] | 2595 | |
---|
[728288] | 2596 | #if 1 |
---|
| 2597 | BITSET save_test=test; |
---|
| 2598 | test|=Sy_bit(OPT_SB_1); // ring independent |
---|
| 2599 | J = kStd(id_tmp, currQuotient, testHomog, NULL, NULL, 0, iSize); // J = J + K, J - std // in currRing! |
---|
[f4b74e2] | 2600 | test = save_test; |
---|
[728288] | 2601 | #else |
---|
| 2602 | J=kStd(id_tmp, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
| 2603 | #endif |
---|
[5accf0] | 2604 | |
---|
[728288] | 2605 | id_Delete(&id_tmp, currRing); |
---|
| 2606 | idSkipZeroes(J); // ring independent |
---|
[5accf0] | 2607 | |
---|
[728288] | 2608 | #ifdef PDEBUG |
---|
| 2609 | idTest(J); // in currRing! |
---|
| 2610 | #if 0 |
---|
[f4b74e2] | 2611 | Print("J:"); |
---|
| 2612 | idPrint(J); |
---|
| 2613 | PrintLn(); |
---|
[728288] | 2614 | #endif // debug |
---|
| 2615 | #endif |
---|
| 2616 | } // loop |
---|
[35aab3] | 2617 | } |
---|
| 2618 | |
---|
[728288] | 2619 | |
---|
[35aab3] | 2620 | matrix nc_PrintMat(int a, int b, ring r, int metric) |
---|
| 2621 | /* returns matrix with the info on noncomm multiplication */ |
---|
| 2622 | { |
---|
| 2623 | |
---|
| 2624 | if ( (a==b) || !rIsPluralRing(r) ) return(NULL); |
---|
| 2625 | int i; |
---|
| 2626 | int j; |
---|
| 2627 | if (a>b) {j=b; i=a;} |
---|
| 2628 | else {j=a; i=b;} |
---|
| 2629 | /* i<j */ |
---|
| 2630 | int rN=r->N; |
---|
[52e2f6] | 2631 | int size=r->GetNC()->MTsize[UPMATELEM(i,j,rN)]; |
---|
| 2632 | matrix M = r->GetNC()->MT[UPMATELEM(i,j,rN)]; |
---|
[35aab3] | 2633 | /* return(M); */ |
---|
| 2634 | int sizeofres; |
---|
| 2635 | if (metric==0) |
---|
| 2636 | { |
---|
| 2637 | sizeofres=sizeof(int); |
---|
| 2638 | } |
---|
| 2639 | if (metric==1) |
---|
| 2640 | { |
---|
| 2641 | sizeofres=sizeof(number); |
---|
| 2642 | } |
---|
| 2643 | matrix res=mpNew(size,size); |
---|
| 2644 | int s; |
---|
| 2645 | int t; |
---|
| 2646 | int length; |
---|
| 2647 | long totdeg; |
---|
| 2648 | poly p; |
---|
| 2649 | for(s=1;s<=size;s++) |
---|
| 2650 | { |
---|
| 2651 | for(t=1;t<=size;t++) |
---|
| 2652 | { |
---|
| 2653 | p=MATELEM(M,s,t); |
---|
| 2654 | if (p==NULL) |
---|
| 2655 | { |
---|
| 2656 | MATELEM(res,s,t)=0; |
---|
| 2657 | } |
---|
| 2658 | else |
---|
| 2659 | { |
---|
| 2660 | length = pLength(p); |
---|
| 2661 | if (metric==0) /* length */ |
---|
| 2662 | { |
---|
| 2663 | MATELEM(res,s,t)= p_ISet(length,r); |
---|
| 2664 | } |
---|
| 2665 | else if (metric==1) /* sum of deg divided by the length */ |
---|
| 2666 | { |
---|
| 2667 | totdeg=0; |
---|
| 2668 | while (p!=NULL) |
---|
| 2669 | { |
---|
| 2670 | totdeg=totdeg+pDeg(p,r); |
---|
| 2671 | pIter(p); |
---|
| 2672 | } |
---|
| 2673 | number ntd = nInit(totdeg); |
---|
| 2674 | number nln = nInit(length); |
---|
| 2675 | number nres=nDiv(ntd,nln); |
---|
| 2676 | nDelete(&ntd); |
---|
| 2677 | nDelete(&nln); |
---|
| 2678 | MATELEM(res,s,t)=p_NSet(nres,r); |
---|
| 2679 | } |
---|
| 2680 | } |
---|
| 2681 | } |
---|
| 2682 | } |
---|
| 2683 | return(res); |
---|
| 2684 | } |
---|
| 2685 | |
---|
[022ef5] | 2686 | inline void nc_CleanUp(nc_struct* p) |
---|
| 2687 | { |
---|
| 2688 | assume(p != NULL); |
---|
| 2689 | omFreeSize((ADDRESS)p,sizeof(nc_struct)); |
---|
| 2690 | } |
---|
| 2691 | |
---|
| 2692 | inline void nc_CleanUp(ring r) |
---|
| 2693 | { |
---|
| 2694 | /* small CleanUp of r->GetNC() */ |
---|
| 2695 | assume(r != NULL); |
---|
| 2696 | nc_CleanUp(r->GetNC()); |
---|
| 2697 | r->GetNC() = NULL; |
---|
| 2698 | } |
---|
| 2699 | |
---|
| 2700 | void nc_rKill(ring r) |
---|
[52e2f6] | 2701 | // kills the nc extension of ring r |
---|
[35aab3] | 2702 | { |
---|
[a7fbdd] | 2703 | if( r->GetNC()->GetGlobalMultiplier() != NULL ) |
---|
[1495df4] | 2704 | { |
---|
| 2705 | delete r->GetNC()->GetGlobalMultiplier(); |
---|
| 2706 | r->GetNC()->GetGlobalMultiplier() = NULL; |
---|
| 2707 | } |
---|
| 2708 | |
---|
[a7fbdd] | 2709 | if( r->GetNC()->GetFormulaPowerMultiplier() != NULL ) |
---|
| 2710 | { |
---|
| 2711 | delete r->GetNC()->GetFormulaPowerMultiplier(); |
---|
| 2712 | r->GetNC()->GetFormulaPowerMultiplier() = NULL; |
---|
| 2713 | } |
---|
[26d633] | 2714 | |
---|
| 2715 | |
---|
[35aab3] | 2716 | int i,j; |
---|
| 2717 | int rN=r->N; |
---|
[e90187] | 2718 | if ( rN > 1 ) |
---|
[35aab3] | 2719 | { |
---|
[e90187] | 2720 | for(i=1;i<rN;i++) |
---|
[35aab3] | 2721 | { |
---|
[e90187] | 2722 | for(j=i+1;j<=rN;j++) |
---|
| 2723 | { |
---|
[26b68f] | 2724 | id_Delete((ideal *)&(r->GetNC()->MT[UPMATELEM(i,j,rN)]),r); |
---|
[e90187] | 2725 | } |
---|
[35aab3] | 2726 | } |
---|
[52e2f6] | 2727 | omFreeSize((ADDRESS)r->GetNC()->MT,rN*(rN-1)/2*sizeof(matrix)); |
---|
| 2728 | omFreeSize((ADDRESS)r->GetNC()->MTsize,rN*(rN-1)/2*sizeof(int)); |
---|
[26b68f] | 2729 | id_Delete((ideal *)&(r->GetNC()->COM),r); |
---|
[35aab3] | 2730 | } |
---|
[26b68f] | 2731 | id_Delete((ideal *)&(r->GetNC()->C),r); |
---|
| 2732 | id_Delete((ideal *)&(r->GetNC()->D),r); |
---|
[5accf0] | 2733 | |
---|
[52e2f6] | 2734 | if( rIsSCA(r) && (r->GetNC()->SCAQuotient() != NULL) ) |
---|
[86016d] | 2735 | { |
---|
[26b68f] | 2736 | id_Delete(&r->GetNC()->SCAQuotient(), r); // Custom SCA destructor!!! |
---|
[86016d] | 2737 | } |
---|
| 2738 | |
---|
[5accf0] | 2739 | |
---|
[022ef5] | 2740 | nc_CleanUp(r); |
---|
[35aab3] | 2741 | } |
---|
| 2742 | |
---|
[52e2f6] | 2743 | |
---|
[022ef5] | 2744 | //////////////////////////////////////////////////////////////////////////////////////////////// |
---|
[52e2f6] | 2745 | |
---|
[022ef5] | 2746 | |
---|
[262fc3] | 2747 | poly nc_p_CopyGet(poly a, const ring r) |
---|
| 2748 | /* for use in getting the mult. matrix elements*/ |
---|
[e5fc4d4] | 2749 | /* ring r must be a currRing! */ |
---|
[52e2f6] | 2750 | /* for consistency, copies a poly from the comm. r->GetNC()->basering */ |
---|
[e5fc4d4] | 2751 | /* to its image in NC ring */ |
---|
[35aab3] | 2752 | { |
---|
[e5fc4d4] | 2753 | if (r != currRing) |
---|
| 2754 | { |
---|
| 2755 | #ifdef PDEBUF |
---|
| 2756 | Werror("nc_p_CopyGet call not in currRing"); |
---|
| 2757 | #endif |
---|
| 2758 | return(NULL); |
---|
| 2759 | } |
---|
[26b68f] | 2760 | return(p_Copy(a,r)); |
---|
[35aab3] | 2761 | } |
---|
| 2762 | |
---|
[262fc3] | 2763 | poly nc_p_CopyPut(poly a, const ring r) |
---|
| 2764 | /* for use in defining the mult. matrix elements*/ |
---|
[e5fc4d4] | 2765 | /* ring r must be a currRing! */ |
---|
| 2766 | /* for consistency, puts a polynomial from the NC ring */ |
---|
[52e2f6] | 2767 | /* to its presentation in the comm. r->GetNC()->basering */ |
---|
[35aab3] | 2768 | { |
---|
[e5fc4d4] | 2769 | if (r != currRing) |
---|
| 2770 | { |
---|
| 2771 | #ifdef PDEBUF |
---|
| 2772 | Werror("nc_p_CopyGet call not in currRing"); |
---|
| 2773 | #endif |
---|
| 2774 | return(NULL); |
---|
| 2775 | } |
---|
[875d68] | 2776 | |
---|
[26b68f] | 2777 | return(p_Copy(a,r)); |
---|
[35aab3] | 2778 | } |
---|
| 2779 | |
---|
[e5fc4d4] | 2780 | BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r) |
---|
[ea68ed] | 2781 | /* returns TRUE if there were errors */ |
---|
| 2782 | /* checks whether product of vars from PolyVar defines */ |
---|
[35aab3] | 2783 | /* an admissible subalgebra of r */ |
---|
[e5fc4d4] | 2784 | /* r is indeed currRing and assumed to be noncomm. */ |
---|
[35aab3] | 2785 | { |
---|
[ea68ed] | 2786 | ring save = currRing; |
---|
| 2787 | int WeChangeRing = 0; |
---|
| 2788 | if (currRing != r) |
---|
| 2789 | { |
---|
| 2790 | rChangeCurrRing(r); |
---|
| 2791 | WeChangeRing = 1; |
---|
| 2792 | } |
---|
[35aab3] | 2793 | int rN=r->N; |
---|
| 2794 | int *ExpVar=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
| 2795 | int *ExpTmp=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
| 2796 | p_GetExpV(PolyVar, ExpVar, r); |
---|
| 2797 | int i; int j; int k; |
---|
| 2798 | poly test=NULL; |
---|
| 2799 | int OK=1; |
---|
[ea68ed] | 2800 | for (i=1; i<rN; i++) |
---|
[35aab3] | 2801 | { |
---|
| 2802 | if (ExpVar[i]==0) /* i.e. not in PolyVar */ |
---|
[b87f029] | 2803 | { |
---|
[ea68ed] | 2804 | for (j=i+1; j<=rN; j++) |
---|
[35aab3] | 2805 | { |
---|
[807ee2] | 2806 | if (ExpVar[j]==0) |
---|
| 2807 | { |
---|
| 2808 | test = MATELEM(r->GetNC()->D,i,j); |
---|
| 2809 | while (test!=NULL) |
---|
| 2810 | { |
---|
[35aab3] | 2811 | p_GetExpV(test, ExpTmp, r); |
---|
[807ee2] | 2812 | OK=1; |
---|
| 2813 | for (k=1;k<=rN;k++) |
---|
[35aab3] | 2814 | { |
---|
[807ee2] | 2815 | if (ExpTmp[k]!=0) |
---|
| 2816 | { |
---|
| 2817 | if (ExpVar[k]!=0) OK=0; |
---|
| 2818 | } |
---|
| 2819 | } |
---|
| 2820 | if (!OK) |
---|
| 2821 | { |
---|
| 2822 | if ( WeChangeRing ) |
---|
| 2823 | rChangeCurrRing(save); |
---|
| 2824 | return(TRUE); |
---|
[35aab3] | 2825 | } |
---|
[807ee2] | 2826 | pIter(test); |
---|
[35aab3] | 2827 | } |
---|
[807ee2] | 2828 | } |
---|
[35aab3] | 2829 | } |
---|
| 2830 | } |
---|
| 2831 | } |
---|
| 2832 | freeT(ExpVar,rN); |
---|
| 2833 | freeT(ExpTmp,rN); |
---|
[ea68ed] | 2834 | if ( WeChangeRing ) |
---|
| 2835 | rChangeCurrRing(save); |
---|
| 2836 | return(FALSE); |
---|
| 2837 | } |
---|
| 2838 | |
---|
[52e2f6] | 2839 | |
---|
| 2840 | BOOLEAN gnc_CheckOrdCondition(matrix D, ring r) |
---|
[ea68ed] | 2841 | /* returns TRUE if there were errors */ |
---|
| 2842 | /* checks whether the current ordering */ |
---|
[52e2f6] | 2843 | /* is admissible for r and D == r->GetNC()->D */ |
---|
[ea68ed] | 2844 | /* to be executed in a currRing */ |
---|
| 2845 | { |
---|
[b87f029] | 2846 | /* analyze D: an upper triangular matrix of polys */ |
---|
[ea68ed] | 2847 | /* check the ordering condition for D */ |
---|
| 2848 | ring save = currRing; |
---|
| 2849 | int WeChangeRing = 0; |
---|
[e5fc4d4] | 2850 | if (r != currRing) |
---|
[ea68ed] | 2851 | { |
---|
| 2852 | rChangeCurrRing(r); |
---|
| 2853 | WeChangeRing = 1; |
---|
| 2854 | } |
---|
| 2855 | poly p,q; |
---|
| 2856 | int i,j; |
---|
[e5fc4d4] | 2857 | int report = 0; |
---|
[ea68ed] | 2858 | for(i=1; i<r->N; i++) |
---|
| 2859 | { |
---|
| 2860 | for(j=i+1; j<=r->N; j++) |
---|
[b87f029] | 2861 | { |
---|
[ea68ed] | 2862 | p = nc_p_CopyGet(MATELEM(D,i,j),r); |
---|
| 2863 | if ( p != NULL) |
---|
| 2864 | { |
---|
[b902246] | 2865 | q = p_One(r); // replaces pOne(); |
---|
[5a9e7b] | 2866 | p_SetExp(q,i,1,r); |
---|
| 2867 | p_SetExp(q,j,1,r); |
---|
| 2868 | p_Setm(q,r); |
---|
| 2869 | if (p_LmCmp(q,p,r) != 1) /* i.e. lm(p)==xy < lm(q)==D_ij */ |
---|
| 2870 | { |
---|
[5accf0] | 2871 | Werror("Bad ordering at %d,%d\n",i,j); |
---|
[8eda39] | 2872 | #if 0 /*Singularg should not differ from Singular except in error case*/ |
---|
[5a9e7b] | 2873 | p_Write(p,r); |
---|
| 2874 | p_Write(q,r); |
---|
[ea68ed] | 2875 | #endif |
---|
[5a9e7b] | 2876 | report = 1; |
---|
| 2877 | } |
---|
| 2878 | p_Delete(&q,r); |
---|
| 2879 | p_Delete(&p,r); |
---|
| 2880 | p = NULL; |
---|
[ea68ed] | 2881 | } |
---|
| 2882 | } |
---|
| 2883 | } |
---|
| 2884 | if ( WeChangeRing ) |
---|
| 2885 | rChangeCurrRing(save); |
---|
[e5fc4d4] | 2886 | return(report); |
---|
[35aab3] | 2887 | } |
---|
| 2888 | |
---|
| 2889 | |
---|
[e5a4ba] | 2890 | |
---|
| 2891 | /// returns TRUE if there were errors |
---|
| 2892 | /// analyze inputs, check them for consistency |
---|
| 2893 | /// detects nc_type, DO NOT initialize multiplication but call for it at the end |
---|
| 2894 | /// checks the ordering condition and evtl. NDC |
---|
| 2895 | /// NOTE: all the data belong to the curr, |
---|
| 2896 | /// we change r which may be the same ring, and must have the same representation! |
---|
| 2897 | BOOLEAN nc_CallPlural(matrix CCC, matrix DDD, |
---|
[52e2f6] | 2898 | poly CCN, poly DDN, |
---|
[b1a5c1] | 2899 | ring r, |
---|
[52e2f6] | 2900 | bool bSetupQuotient, bool bCopyInput, bool bBeQuiet, |
---|
[e5a4ba] | 2901 | ring curr, bool dummy_ring /*=false*/) |
---|
[6c0f53] | 2902 | { |
---|
[e5a4ba] | 2903 | assume( r != NULL ); |
---|
| 2904 | assume( curr != NULL ); |
---|
| 2905 | |
---|
| 2906 | if( !bSetupQuotient) |
---|
| 2907 | assume( (r->qideal == NULL) ); // The basering must NOT be a qring!?? |
---|
[26b68f] | 2908 | |
---|
[e5a4ba] | 2909 | assume( rSamePolyRep(r, curr) || bCopyInput ); // wrong assumption? |
---|
[875d68] | 2910 | |
---|
[18ff4c] | 2911 | |
---|
[52e2f6] | 2912 | if( r->N == 1 ) // clearly commutative!!! |
---|
| 2913 | { |
---|
| 2914 | assume( |
---|
| 2915 | ( (CCC != NULL) && (MATCOLS(CCC) == 1) && (MATROWS(CCC) == 1) && (MATELEM(CCC,1,1) == NULL) ) || |
---|
| 2916 | ( (CCN == NULL) ) |
---|
| 2917 | ); |
---|
[b1a5c1] | 2918 | |
---|
[52e2f6] | 2919 | assume( |
---|
| 2920 | ( (DDD != NULL) && (MATCOLS(DDD) == 1) && (MATROWS(DDD) == 1) && (MATELEM(DDD,1,1) == NULL) ) || |
---|
| 2921 | ( (DDN == NULL) ) |
---|
| 2922 | ); |
---|
[5eb716] | 2923 | if(!dummy_ring) |
---|
| 2924 | { |
---|
| 2925 | WarnS("commutative ring with 1 variable"); |
---|
| 2926 | return FALSE; |
---|
| 2927 | } |
---|
[52e2f6] | 2928 | } |
---|
| 2929 | |
---|
| 2930 | // there must be: |
---|
| 2931 | assume( (CCC != NULL) != (CCN != NULL) ); // exactly one data about coeffs (C). |
---|
| 2932 | assume( !((DDD != NULL) && (DDN != NULL)) ); // at most one data about tails (D). |
---|
[b1a5c1] | 2933 | |
---|
[52e2f6] | 2934 | ring save = currRing; |
---|
[875d68] | 2935 | |
---|
[52e2f6] | 2936 | if( save != curr ) |
---|
| 2937 | rChangeCurrRing(curr); |
---|
[875d68] | 2938 | |
---|
[52e2f6] | 2939 | #if OUTPUT |
---|
| 2940 | if( CCC != NULL ) |
---|
[6c0f53] | 2941 | { |
---|
[b1a5c1] | 2942 | PrintS("nc_CallPlural(), Input data, CCC: \n"); |
---|
[52e2f6] | 2943 | iiWriteMatrix(CCC, "C", 2, 4); |
---|
[6c0f53] | 2944 | } |
---|
[52e2f6] | 2945 | if( DDD != NULL ) |
---|
| 2946 | { |
---|
[b1a5c1] | 2947 | PrintS("nc_CallPlural(), Input data, DDD: \n"); |
---|
[52e2f6] | 2948 | iiWriteMatrix(DDD, "D", 2, 4); |
---|
| 2949 | } |
---|
| 2950 | #endif |
---|
[18ff4c] | 2951 | |
---|
[b1a5c1] | 2952 | |
---|
[52e2f6] | 2953 | #ifndef NDEBUG |
---|
| 2954 | idTest((ideal)CCC); |
---|
| 2955 | idTest((ideal)DDD); |
---|
| 2956 | pTest(CCN); |
---|
| 2957 | pTest(DDN); |
---|
| 2958 | #endif |
---|
[18ff4c] | 2959 | |
---|
[52e2f6] | 2960 | if( (!bBeQuiet) && (r->GetNC() != NULL) ) |
---|
| 2961 | WarnS("going to redefine the algebra structure"); |
---|
[b1a5c1] | 2962 | |
---|
[52e2f6] | 2963 | if( currRing != r ) |
---|
| 2964 | rChangeCurrRing(r); |
---|
[f12e32] | 2965 | |
---|
[52e2f6] | 2966 | matrix CC = NULL; |
---|
| 2967 | poly CN = NULL; |
---|
| 2968 | matrix C; bool bCnew = false; |
---|
[18ff4c] | 2969 | |
---|
[52e2f6] | 2970 | matrix DD = NULL; |
---|
| 2971 | poly DN = NULL; |
---|
| 2972 | matrix D; bool bDnew = false; |
---|
| 2973 | |
---|
| 2974 | number nN, pN, qN; |
---|
| 2975 | |
---|
| 2976 | bool IsSkewConstant = false, tmpIsSkewConstant; |
---|
| 2977 | int i, j; |
---|
[f12e32] | 2978 | |
---|
[52e2f6] | 2979 | nc_type nctype = nc_undef; |
---|
[b1a5c1] | 2980 | |
---|
[52e2f6] | 2981 | ////////////////////////////////////////////////////////////////// |
---|
| 2982 | // check the correctness of arguments, without any real chagnes!!! |
---|
| 2983 | |
---|
[b1a5c1] | 2984 | |
---|
[52e2f6] | 2985 | |
---|
| 2986 | // check C |
---|
[f12e32] | 2987 | if ((CCC != NULL) && ( (MATCOLS(CCC)==1) || MATROWS(CCC)==1 ) ) |
---|
| 2988 | { |
---|
| 2989 | CN = MATELEM(CCC,1,1); |
---|
| 2990 | } |
---|
[b87f029] | 2991 | else |
---|
[f12e32] | 2992 | { |
---|
| 2993 | if ((CCC != NULL) && ( (MATCOLS(CCC)!=r->N) || (MATROWS(CCC)!=r->N) )) |
---|
| 2994 | { |
---|
[52e2f6] | 2995 | Werror("Square %d x %d matrix expected", r->N, r->N); |
---|
| 2996 | |
---|
| 2997 | if( currRing != save ) |
---|
| 2998 | rChangeCurrRing(save); |
---|
[f12e32] | 2999 | return TRUE; |
---|
| 3000 | } |
---|
| 3001 | } |
---|
[875d68] | 3002 | if (( CCC != NULL) && (CC == NULL)) CC = CCC; // mpCopy(CCC); // bug!? |
---|
[f12e32] | 3003 | if (( CCN != NULL) && (CN == NULL)) CN = CCN; |
---|
| 3004 | |
---|
[52e2f6] | 3005 | // check D |
---|
[f12e32] | 3006 | if ((DDD != NULL) && ( (MATCOLS(DDD)==1) || MATROWS(DDD)==1 ) ) |
---|
| 3007 | { |
---|
| 3008 | DN = MATELEM(DDD,1,1); |
---|
| 3009 | } |
---|
[b87f029] | 3010 | else |
---|
[f12e32] | 3011 | { |
---|
| 3012 | if ((DDD != NULL) && ( (MATCOLS(DDD)!=r->N) || (MATROWS(DDD)!=r->N) )) |
---|
| 3013 | { |
---|
| 3014 | Werror("Square %d x %d matrix expected",r->N,r->N); |
---|
[52e2f6] | 3015 | |
---|
| 3016 | if( currRing != save ) |
---|
| 3017 | rChangeCurrRing(save); |
---|
[f12e32] | 3018 | return TRUE; |
---|
| 3019 | } |
---|
| 3020 | } |
---|
[52e2f6] | 3021 | |
---|
[875d68] | 3022 | if (( DDD != NULL) && (DD == NULL)) DD = DDD; // mpCopy(DDD); // ??? |
---|
[f12e32] | 3023 | if (( DDN != NULL) && (DN == NULL)) DN = DDN; |
---|
| 3024 | |
---|
[52e2f6] | 3025 | // further checks and some analysis: |
---|
| 3026 | // all data in 'curr'! |
---|
[6c0f53] | 3027 | if (CN != NULL) /* create matrix C = CN * Id */ |
---|
| 3028 | { |
---|
[52e2f6] | 3029 | nN = p_GetCoeff(CN, curr); |
---|
| 3030 | if (n_IsZero(nN, curr)) |
---|
[6c0f53] | 3031 | { |
---|
| 3032 | Werror("Incorrect input : zero coefficients are not allowed"); |
---|
[52e2f6] | 3033 | |
---|
| 3034 | if( currRing != save ) |
---|
| 3035 | rChangeCurrRing(save); |
---|
[6c0f53] | 3036 | return TRUE; |
---|
| 3037 | } |
---|
[52e2f6] | 3038 | |
---|
| 3039 | if (n_IsOne(nN, curr)) |
---|
| 3040 | nctype = nc_lie; |
---|
[b87f029] | 3041 | else |
---|
[52e2f6] | 3042 | nctype = nc_general; |
---|
| 3043 | |
---|
| 3044 | IsSkewConstant = true; |
---|
| 3045 | |
---|
[875d68] | 3046 | C = mpNew(r->N,r->N); // ring independent! |
---|
[52e2f6] | 3047 | bCnew = true; |
---|
| 3048 | |
---|
[6c0f53] | 3049 | for(i=1; i<r->N; i++) |
---|
| 3050 | for(j=i+1; j<=r->N; j++) |
---|
[52e2f6] | 3051 | MATELEM(C,i,j) = prCopyR_NoSort(CN, curr, r); // nc_p_CopyPut(CN, r); // copy CN from curr into r |
---|
[e5a4ba] | 3052 | |
---|
| 3053 | #ifndef NDEBUG |
---|
| 3054 | idTest((ideal)C); |
---|
| 3055 | #endif |
---|
| 3056 | |
---|
[52e2f6] | 3057 | } else |
---|
[f12e32] | 3058 | if ( (CN == NULL) && (CC != NULL) ) /* copy matrix C */ |
---|
[6c0f53] | 3059 | { |
---|
| 3060 | /* analyze C */ |
---|
[52e2f6] | 3061 | |
---|
| 3062 | pN = NULL; /* check the consistency later */ |
---|
| 3063 | |
---|
| 3064 | if( r->N > 1 ) |
---|
| 3065 | if ( MATELEM(CC,1,2) != NULL ) |
---|
| 3066 | pN = p_GetCoeff(MATELEM(CC,1,2), curr); |
---|
| 3067 | |
---|
| 3068 | tmpIsSkewConstant = true; |
---|
| 3069 | |
---|
[6c0f53] | 3070 | for(i=1; i<r->N; i++) |
---|
| 3071 | for(j=i+1; j<=r->N; j++) |
---|
[b87f029] | 3072 | { |
---|
[52e2f6] | 3073 | if (MATELEM(CC,i,j) == NULL) |
---|
[875d68] | 3074 | qN = NULL; |
---|
| 3075 | else |
---|
[52e2f6] | 3076 | qN = p_GetCoeff(MATELEM(CC,i,j),curr); |
---|
[18ff4c] | 3077 | |
---|
[875d68] | 3078 | if ( qN == NULL ) /* check the consistency: Cij!=0 */ |
---|
[52e2f6] | 3079 | // find also illegal pN |
---|
[875d68] | 3080 | { |
---|
| 3081 | Werror("Incorrect input : matrix of coefficients contains zeros in the upper triangle"); |
---|
[52e2f6] | 3082 | |
---|
| 3083 | if( currRing != save ) |
---|
| 3084 | rChangeCurrRing(save); |
---|
[875d68] | 3085 | return TRUE; |
---|
| 3086 | } |
---|
[52e2f6] | 3087 | |
---|
| 3088 | if (!n_Equal(pN, qN, curr)) tmpIsSkewConstant = false; |
---|
[6c0f53] | 3089 | } |
---|
[52e2f6] | 3090 | |
---|
| 3091 | if( bCopyInput ) |
---|
[6c0f53] | 3092 | { |
---|
[52e2f6] | 3093 | C = mpCopy(CC, curr, r); // Copy C into r!!!??? |
---|
[e5a4ba] | 3094 | #ifndef NDEBUG |
---|
| 3095 | idTest((ideal)C); |
---|
| 3096 | #endif |
---|
[52e2f6] | 3097 | bCnew = true; |
---|
[6c0f53] | 3098 | } |
---|
[b87f029] | 3099 | else |
---|
[52e2f6] | 3100 | C = CC; |
---|
| 3101 | |
---|
| 3102 | IsSkewConstant = tmpIsSkewConstant; |
---|
| 3103 | |
---|
| 3104 | if ( tmpIsSkewConstant && n_IsOne(pN, curr) ) |
---|
| 3105 | nctype = nc_lie; |
---|
| 3106 | else |
---|
| 3107 | nctype = nc_general; |
---|
[6c0f53] | 3108 | } |
---|
| 3109 | |
---|
| 3110 | /* initialition of the matrix D */ |
---|
[52e2f6] | 3111 | if ( DD == NULL ) /* we treat DN only (it could also be NULL) */ |
---|
[6c0f53] | 3112 | { |
---|
[52e2f6] | 3113 | D = mpNew(r->N,r->N); bDnew = true; |
---|
| 3114 | |
---|
[6c0f53] | 3115 | if (DN == NULL) |
---|
| 3116 | { |
---|
[52e2f6] | 3117 | if ( (nctype == nc_lie) || (nctype == nc_undef) ) |
---|
| 3118 | nctype = nc_comm; /* it was nc_skew earlier */ |
---|
[6c0f53] | 3119 | else /* nc_general, nc_skew */ |
---|
[52e2f6] | 3120 | nctype = nc_skew; |
---|
[6c0f53] | 3121 | } |
---|
| 3122 | else /* DN != NULL */ |
---|
| 3123 | for(i=1; i<r->N; i++) |
---|
[875d68] | 3124 | for(j=i+1; j<=r->N; j++) |
---|
[52e2f6] | 3125 | MATELEM(D,i,j) = prCopyR_NoSort(DN, curr, r); // project DN into r->GetNC()->basering! |
---|
[e5a4ba] | 3126 | #ifndef NDEBUG |
---|
| 3127 | idTest((ideal)D); |
---|
| 3128 | #endif |
---|
[6c0f53] | 3129 | } |
---|
| 3130 | else /* DD != NULL */ |
---|
[b87f029] | 3131 | { |
---|
[52e2f6] | 3132 | bool b = true; // DD == null ? |
---|
[b1a5c1] | 3133 | |
---|
[52e2f6] | 3134 | for(int i = 1; (i < r->N) && b; i++) |
---|
| 3135 | for(int j = i+1; (j <= r->N) && b; j++) |
---|
| 3136 | if (MATELEM(DD, i, j) != NULL) |
---|
| 3137 | { |
---|
| 3138 | b = false; |
---|
| 3139 | break; |
---|
| 3140 | } |
---|
| 3141 | |
---|
| 3142 | if (b) // D == NULL!!! |
---|
| 3143 | { |
---|
| 3144 | if ( (nctype == nc_lie) || (nctype == nc_undef) ) |
---|
| 3145 | nctype = nc_comm; /* it was nc_skew earlier */ |
---|
| 3146 | else /* nc_general, nc_skew */ |
---|
| 3147 | nctype = nc_skew; |
---|
| 3148 | } |
---|
[b1a5c1] | 3149 | |
---|
[52e2f6] | 3150 | if( bCopyInput ) |
---|
| 3151 | { |
---|
| 3152 | D = mpCopy(DD, curr, r); // Copy DD into r!!! |
---|
[e5a4ba] | 3153 | #ifndef NDEBUG |
---|
| 3154 | idTest((ideal)D); |
---|
| 3155 | #endif |
---|
[52e2f6] | 3156 | bDnew = true; |
---|
| 3157 | } |
---|
| 3158 | else |
---|
| 3159 | D = DD; |
---|
[6c0f53] | 3160 | } |
---|
[ea68ed] | 3161 | |
---|
[52e2f6] | 3162 | assume( C != NULL ); |
---|
| 3163 | assume( D != NULL ); |
---|
[b1a5c1] | 3164 | |
---|
[52e2f6] | 3165 | #if OUTPUT |
---|
| 3166 | PrintS("nc_CallPlural(), Computed data, C: \n"); |
---|
| 3167 | iiWriteMatrix(C, "C", 2, 4); |
---|
| 3168 | |
---|
| 3169 | PrintS("nc_CallPlural(), Computed data, D: \n"); |
---|
| 3170 | iiWriteMatrix(D, "D", 2, 4); |
---|
| 3171 | |
---|
| 3172 | Print("\nTemporary: type = %d, IsSkewConstant = %d\n", nctype, IsSkewConstant); |
---|
| 3173 | #endif |
---|
| 3174 | |
---|
| 3175 | |
---|
| 3176 | // check the ordering condition for D (both matrix and poly cases): |
---|
| 3177 | if ( gnc_CheckOrdCondition(D, r) ) |
---|
[6c0f53] | 3178 | { |
---|
[52e2f6] | 3179 | if( bCnew ) mpDelete( &C, r ); |
---|
| 3180 | if( bDnew ) mpDelete( &D, r ); |
---|
| 3181 | |
---|
[ea68ed] | 3182 | Werror("Matrix of polynomials violates the ordering condition"); |
---|
[52e2f6] | 3183 | |
---|
| 3184 | if( currRing != save ) |
---|
| 3185 | rChangeCurrRing(save); |
---|
[6c0f53] | 3186 | return TRUE; |
---|
| 3187 | } |
---|
[18ff4c] | 3188 | |
---|
[52e2f6] | 3189 | // okay now we are ready for this!!! |
---|
| 3190 | |
---|
| 3191 | // create new non-commutative structure |
---|
| 3192 | nc_struct *nc_new = (nc_struct *)omAlloc0(sizeof(nc_struct)); |
---|
| 3193 | |
---|
[cf315c] | 3194 | ncRingType(nc_new, nctype); |
---|
[52e2f6] | 3195 | |
---|
| 3196 | nc_new->C = C; // if C and D were given by matrices at the beginning they are in r |
---|
| 3197 | nc_new->D = D; // otherwise they should be in r->GetNC()->basering(polynomial * Id_{N}) |
---|
| 3198 | |
---|
| 3199 | nc_new->IsSkewConstant = (IsSkewConstant?1:0); |
---|
| 3200 | |
---|
| 3201 | // Setup new NC structure!!! |
---|
| 3202 | if (r->GetNC() != NULL) |
---|
[022ef5] | 3203 | nc_rKill(r); |
---|
[52e2f6] | 3204 | |
---|
| 3205 | r->GetNC() = nc_new; |
---|
[18ff4c] | 3206 | |
---|
[52e2f6] | 3207 | if( currRing != save ) |
---|
| 3208 | rChangeCurrRing(save); |
---|
| 3209 | |
---|
| 3210 | return gnc_InitMultiplication(r, bSetupQuotient); |
---|
[6c0f53] | 3211 | } |
---|
| 3212 | |
---|
[022ef5] | 3213 | ////////////////////////////////////////////////////////////////////////////// |
---|
| 3214 | |
---|
| 3215 | bool nc_rCopy(ring res, const ring r, bool bSetupQuotient) |
---|
| 3216 | { |
---|
[26d633] | 3217 | if (nc_CallPlural(r->GetNC()->C, r->GetNC()->D, NULL, NULL, res, bSetupQuotient, true, true, r)) |
---|
[022ef5] | 3218 | { |
---|
| 3219 | WarnS("Error occured while coping/setuping the NC structure!"); // No reaction!??? |
---|
| 3220 | return true; // error |
---|
| 3221 | } |
---|
| 3222 | |
---|
| 3223 | return false; |
---|
| 3224 | } |
---|
| 3225 | |
---|
[86016d] | 3226 | ////////////////////////////////////////////////////////////////////////////// |
---|
[52e2f6] | 3227 | BOOLEAN gnc_InitMultiplication(ring r, bool bSetupQuotient) |
---|
[6c0f53] | 3228 | { |
---|
| 3229 | /* returns TRUE if there were errors */ |
---|
[8e165ec] | 3230 | /* initialize the multiplication: */ |
---|
[52e2f6] | 3231 | /* r->GetNC()->MTsize, r->GetNC()->MT, r->GetNC()->COM, */ |
---|
| 3232 | /* and r->GetNC()->IsSkewConstant for the skew case */ |
---|
[262fc3] | 3233 | if (rVar(r)==1) |
---|
[e90187] | 3234 | { |
---|
[86016d] | 3235 | ncRingType(r, nc_comm); |
---|
[52e2f6] | 3236 | r->GetNC()->IsSkewConstant=1; |
---|
[e90187] | 3237 | return FALSE; |
---|
| 3238 | } |
---|
[52e2f6] | 3239 | |
---|
[3c8a31] | 3240 | ring save = currRing; |
---|
[52e2f6] | 3241 | |
---|
[3c8a31] | 3242 | int WeChangeRing = 0; |
---|
| 3243 | if (currRing!=r) |
---|
| 3244 | { |
---|
| 3245 | rChangeCurrRing(r); |
---|
| 3246 | WeChangeRing = 1; |
---|
| 3247 | } |
---|
[26b68f] | 3248 | assume( (currRing == r) |
---|
| 3249 | && (currRing->GetNC()!=NULL) ); // otherwise we cannot work with all these matrices! |
---|
[5a9e7b] | 3250 | |
---|
[6c0f53] | 3251 | int i,j; |
---|
[52e2f6] | 3252 | r->GetNC()->MT = (matrix *)omAlloc0((r->N*(r->N-1))/2*sizeof(matrix)); |
---|
| 3253 | r->GetNC()->MTsize = (int *)omAlloc0((r->N*(r->N-1))/2*sizeof(int)); |
---|
| 3254 | idTest(((ideal)r->GetNC()->C)); |
---|
| 3255 | matrix COM = mpCopy(r->GetNC()->C); |
---|
[b147507] | 3256 | poly p,q; |
---|
[6c0f53] | 3257 | short DefMTsize=7; |
---|
| 3258 | int IsNonComm=0; |
---|
| 3259 | int tmpIsSkewConstant; |
---|
[b87f029] | 3260 | |
---|
[6c0f53] | 3261 | for(i=1; i<r->N; i++) |
---|
| 3262 | { |
---|
| 3263 | for(j=i+1; j<=r->N; j++) |
---|
| 3264 | { |
---|
[52e2f6] | 3265 | if ( MATELEM(r->GetNC()->D,i,j) == NULL ) /* quasicommutative case */ |
---|
[6c0f53] | 3266 | { |
---|
[e19002] | 3267 | /* 1x1 mult.matrix */ |
---|
[52e2f6] | 3268 | r->GetNC()->MTsize[UPMATELEM(i,j,r->N)] = 1; |
---|
| 3269 | r->GetNC()->MT[UPMATELEM(i,j,r->N)] = mpNew(1,1); |
---|
[6c0f53] | 3270 | } |
---|
| 3271 | else /* pure noncommutative case */ |
---|
| 3272 | { |
---|
[e19002] | 3273 | /* TODO check the special multiplication properties */ |
---|
| 3274 | IsNonComm = 1; |
---|
| 3275 | p_Delete(&(MATELEM(COM,i,j)),r); |
---|
| 3276 | //MATELEM(COM,i,j) = NULL; // done by p_Delete |
---|
[52e2f6] | 3277 | r->GetNC()->MTsize[UPMATELEM(i,j,r->N)] = DefMTsize; /* default sizes */ |
---|
| 3278 | r->GetNC()->MT[UPMATELEM(i,j,r->N)] = mpNew(DefMTsize, DefMTsize); |
---|
[6c0f53] | 3279 | } |
---|
| 3280 | /* set MT[i,j,1,1] to c_i_j*x_i*x_j + D_i_j */ |
---|
[b902246] | 3281 | p = p_One(r); /* instead of p = pOne(); */ |
---|
[52e2f6] | 3282 | if (MATELEM(r->GetNC()->C,i,j)!=NULL) |
---|
| 3283 | p_SetCoeff(p,n_Copy(pGetCoeff(MATELEM(r->GetNC()->C,i,j)),r),r); |
---|
[6c0f53] | 3284 | p_SetExp(p,i,1,r); |
---|
| 3285 | p_SetExp(p,j,1,r); |
---|
| 3286 | p_Setm(p,r); |
---|
[26b68f] | 3287 | p_Test(MATELEM(r->GetNC()->D,i,j),r); |
---|
[52e2f6] | 3288 | q = nc_p_CopyGet(MATELEM(r->GetNC()->D,i,j),r); |
---|
[b147507] | 3289 | p = p_Add_q(p,q,r); |
---|
[52e2f6] | 3290 | MATELEM(r->GetNC()->MT[UPMATELEM(i,j,r->N)],1,1) = nc_p_CopyPut(p,r); |
---|
[3c8a31] | 3291 | p_Delete(&p,r); |
---|
[8c8c80] | 3292 | // p = NULL;// done by p_Delete |
---|
[6c0f53] | 3293 | } |
---|
| 3294 | } |
---|
[86016d] | 3295 | if (ncRingType(r)==nc_undef) |
---|
[6c0f53] | 3296 | { |
---|
| 3297 | if (IsNonComm==1) |
---|
| 3298 | { |
---|
| 3299 | // assume(pN!=NULL); |
---|
[52e2f6] | 3300 | // if ((tmpIsSkewConstant==1) && (nIsOne(pGetCoeff(pN)))) r->GetNC()->type=nc_lie; |
---|
| 3301 | // else r->GetNC()->type=nc_general; |
---|
[6c0f53] | 3302 | } |
---|
[b87f029] | 3303 | if (IsNonComm==0) |
---|
[6c0f53] | 3304 | { |
---|
[86016d] | 3305 | ncRingType(r, nc_skew); /* TODO: check whether it is commutative */ |
---|
[52e2f6] | 3306 | r->GetNC()->IsSkewConstant=tmpIsSkewConstant; |
---|
[6c0f53] | 3307 | } |
---|
| 3308 | } |
---|
[52e2f6] | 3309 | r->GetNC()->COM=COM; |
---|
[5a9e7b] | 3310 | |
---|
[52e2f6] | 3311 | nc_p_ProcsSet(r, r->p_Procs); |
---|
[5a9e7b] | 3312 | |
---|
[52e2f6] | 3313 | if(bSetupQuotient) // Test me!!! |
---|
[3c8a31] | 3314 | { |
---|
[b1a5c1] | 3315 | nc_SetupQuotient(r); |
---|
[3c8a31] | 3316 | } |
---|
[52e2f6] | 3317 | |
---|
[a7fbdd] | 3318 | |
---|
[b902246] | 3319 | // ??? |
---|
[efcd6fc] | 3320 | if( bNoPluralMultiplication ) |
---|
[b902246] | 3321 | ncInitSpecialPairMultiplication(r); |
---|
[efcd6fc] | 3322 | |
---|
| 3323 | |
---|
[b902246] | 3324 | if(!rIsSCA(r) && !bNoFormula) |
---|
| 3325 | ncInitSpecialPowersMultiplication(r); |
---|
[26d633] | 3326 | |
---|
| 3327 | |
---|
[52e2f6] | 3328 | if (save != currRing) |
---|
| 3329 | rChangeCurrRing(save); |
---|
| 3330 | |
---|
[6c0f53] | 3331 | return FALSE; |
---|
| 3332 | } |
---|
| 3333 | |
---|
[86016d] | 3334 | void gnc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs) |
---|
[5a9e7b] | 3335 | { |
---|
| 3336 | // "commutative" |
---|
[52e2f6] | 3337 | p_Procs->p_Mult_mm = rGR->p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
| 3338 | p_Procs->pp_Mult_mm = rGR->p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
| 3339 | p_Procs->p_Minus_mm_Mult_qq = rGR->p_Procs->p_Minus_mm_Mult_qq = NULL; |
---|
| 3340 | // gnc_p_Minus_mm_Mult_qq_ign; // should not be used!!!??? |
---|
[5a9e7b] | 3341 | |
---|
| 3342 | |
---|
| 3343 | |
---|
[86016d] | 3344 | // non-commutaitve multiplication by monomial from the left |
---|
[52e2f6] | 3345 | rGR->GetNC()->p_Procs.mm_Mult_p = gnc_mm_Mult_p; |
---|
| 3346 | rGR->GetNC()->p_Procs.mm_Mult_pp = gnc_mm_Mult_pp; |
---|
[5a9e7b] | 3347 | |
---|
[52e2f6] | 3348 | rGR->GetNC()->p_Procs.GB = gnc_gr_bba; // bba even for local case! |
---|
[5a9e7b] | 3349 | |
---|
[52e2f6] | 3350 | // rGR->GetNC()->p_Procs.GlobalGB = gnc_gr_bba; |
---|
| 3351 | // rGR->GetNC()->p_Procs.LocalGB = gnc_gr_mora; |
---|
[5a9e7b] | 3352 | |
---|
| 3353 | |
---|
| 3354 | #if 0 |
---|
| 3355 | // Previous Plural's implementation... |
---|
[52e2f6] | 3356 | rGR->GetNC()->p_Procs.SPoly = gnc_CreateSpolyOld; |
---|
| 3357 | rGR->GetNC()->p_Procs.ReduceSPoly = gnc_ReduceSpolyOld; |
---|
[5a9e7b] | 3358 | |
---|
[52e2f6] | 3359 | rGR->GetNC()->p_Procs.BucketPolyRed = gnc_kBucketPolyRedOld; |
---|
| 3360 | rGR->GetNC()->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZOld; |
---|
[5a9e7b] | 3361 | #else |
---|
[86016d] | 3362 | // A bit cleaned up and somewhat rewritten functions... |
---|
[52e2f6] | 3363 | rGR->GetNC()->p_Procs.SPoly = gnc_CreateSpolyNew; |
---|
[b1a5c1] | 3364 | rGR->GetNC()->p_Procs.ReduceSPoly = gnc_ReduceSpolyNew; |
---|
[5a9e7b] | 3365 | |
---|
[52e2f6] | 3366 | rGR->GetNC()->p_Procs.BucketPolyRed = gnc_kBucketPolyRedNew; |
---|
| 3367 | rGR->GetNC()->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZNew; |
---|
[5a9e7b] | 3368 | #endif |
---|
| 3369 | |
---|
| 3370 | |
---|
| 3371 | |
---|
| 3372 | |
---|
| 3373 | #if 0 |
---|
[86016d] | 3374 | // Old Stuff |
---|
[5a9e7b] | 3375 | p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
| 3376 | _p_procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
| 3377 | |
---|
| 3378 | p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
| 3379 | _p_procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
| 3380 | |
---|
| 3381 | p_Procs->p_Minus_mm_Mult_qq = NULL; // gnc_p_Minus_mm_Mult_qq_ign; |
---|
| 3382 | _p_procs->p_Minus_mm_Mult_qq= NULL; // gnc_p_Minus_mm_Mult_qq_ign; |
---|
| 3383 | |
---|
[52e2f6] | 3384 | r->GetNC()->mmMultP() = gnc_mm_Mult_p; |
---|
| 3385 | r->GetNC()->mmMultPP() = gnc_mm_Mult_pp; |
---|
[5a9e7b] | 3386 | |
---|
[52e2f6] | 3387 | r->GetNC()->GB() = gnc_gr_bba; |
---|
[5a9e7b] | 3388 | |
---|
[52e2f6] | 3389 | r->GetNC()->SPoly() = gnc_CreateSpoly; |
---|
| 3390 | r->GetNC()->ReduceSPoly() = gnc_ReduceSpoly; |
---|
[5a9e7b] | 3391 | |
---|
| 3392 | #endif |
---|
| 3393 | } |
---|
| 3394 | |
---|
| 3395 | |
---|
[86016d] | 3396 | // set pProcs table for rGR and global variable p_Procs |
---|
| 3397 | void nc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs) |
---|
| 3398 | { |
---|
| 3399 | assume(rIsPluralRing(rGR)); |
---|
| 3400 | assume(p_Procs!=NULL); |
---|
| 3401 | |
---|
| 3402 | gnc_p_ProcsSet(rGR, p_Procs); |
---|
| 3403 | |
---|
[57bfa2] | 3404 | if(rIsSCA(rGR) && ncExtensions(SCAMASK) ) |
---|
[86016d] | 3405 | { |
---|
| 3406 | sca_p_ProcsSet(rGR, p_Procs); |
---|
| 3407 | } |
---|
| 3408 | } |
---|
| 3409 | |
---|
| 3410 | |
---|
| 3411 | |
---|
[68349d] | 3412 | /* substitute the n-th variable by e in p |
---|
| 3413 | * destroy p |
---|
| 3414 | * e is not a constant |
---|
| 3415 | */ |
---|
| 3416 | poly nc_pSubst(poly p, int n, poly e) |
---|
| 3417 | { |
---|
| 3418 | int rN=currRing->N; |
---|
| 3419 | int *PRE = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 3420 | int *SUF = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
| 3421 | int i,j,pow; |
---|
[6a33fd] | 3422 | number C; |
---|
[68349d] | 3423 | poly suf,pre; |
---|
| 3424 | poly res = NULL; |
---|
| 3425 | poly out = NULL; |
---|
| 3426 | while ( p!= NULL ) |
---|
| 3427 | { |
---|
[6a33fd] | 3428 | C = pGetCoeff(p); |
---|
[68349d] | 3429 | pGetExpV(p, PRE); /* faster splitting? */ |
---|
| 3430 | pow = PRE[n]; PRE[n]=0; |
---|
| 3431 | res = NULL; |
---|
| 3432 | if (pow!=0) |
---|
| 3433 | { |
---|
| 3434 | for (i=n+1; i<=rN; i++) |
---|
| 3435 | { |
---|
[5a9e7b] | 3436 | SUF[i] = PRE[i]; |
---|
| 3437 | PRE[i] = 0; |
---|
[68349d] | 3438 | } |
---|
| 3439 | res = pPower(pCopy(e),pow); |
---|
| 3440 | /* multiply with prefix */ |
---|
| 3441 | pre = pOne(); |
---|
| 3442 | pSetExpV(pre,PRE); |
---|
| 3443 | pSetm(pre); |
---|
[86016d] | 3444 | res = nc_mm_Mult_p(pre,res,currRing); |
---|
[68349d] | 3445 | /* multiply with suffix */ |
---|
| 3446 | suf = pOne(); |
---|
| 3447 | pSetExpV(suf,SUF); |
---|
| 3448 | pSetm(suf); |
---|
[5a9e7b] | 3449 | res = p_Mult_mm(res,suf,currRing); |
---|
[6a33fd] | 3450 | res = p_Mult_nn(res,C,currRing); |
---|
[ea68ed] | 3451 | pSetComp(res,PRE[0]); |
---|
[68349d] | 3452 | } |
---|
| 3453 | else /* pow==0 */ |
---|
| 3454 | { |
---|
| 3455 | res = pHead(p); |
---|
| 3456 | } |
---|
| 3457 | p = pLmDeleteAndNext(p); |
---|
| 3458 | out = pAdd(out,res); |
---|
| 3459 | } |
---|
| 3460 | freeT(PRE,rN); |
---|
| 3461 | freeT(SUF,rN); |
---|
| 3462 | return(out); |
---|
| 3463 | } |
---|
| 3464 | |
---|
[8e165ec] | 3465 | static ideal idPrepareStd(ideal T, ideal s, int k) |
---|
| 3466 | { |
---|
| 3467 | /* T is a left SB, without zeros, s is a list with zeros */ |
---|
| 3468 | #ifdef PDEBUG |
---|
| 3469 | if (IDELEMS(s)!=IDELEMS(T)) |
---|
| 3470 | { |
---|
| 3471 | Print("ideals of diff. size!!!"); |
---|
| 3472 | } |
---|
| 3473 | #endif |
---|
| 3474 | ideal t = idCopy(T); |
---|
| 3475 | int j,rs=idRankFreeModule(s),rt=idRankFreeModule(t); |
---|
| 3476 | poly p,q; |
---|
| 3477 | |
---|
| 3478 | ideal res = idInit(2*idElem(t),1+idElem(t)); |
---|
| 3479 | if (rs == 0) |
---|
| 3480 | { |
---|
| 3481 | for (j=0; j<IDELEMS(t); j++) |
---|
| 3482 | { |
---|
| 3483 | if (s->m[j]!=NULL) pSetCompP(s->m[j],1); |
---|
| 3484 | if (t->m[j]!=NULL) pSetCompP(t->m[j],1); |
---|
| 3485 | } |
---|
| 3486 | k = si_max(k,1); |
---|
| 3487 | } |
---|
| 3488 | for (j=0; j<IDELEMS(t); j++) |
---|
| 3489 | { |
---|
| 3490 | if (s->m[j]!=NULL) |
---|
| 3491 | { |
---|
| 3492 | p = s->m[j]; |
---|
| 3493 | q = pOne(); |
---|
| 3494 | pSetComp(q,k+1+j); |
---|
| 3495 | pSetmComp(q); |
---|
[b87f029] | 3496 | #if 0 |
---|
[8e165ec] | 3497 | while (pNext(p)) pIter(p); |
---|
| 3498 | pNext(p) = q; |
---|
| 3499 | #else |
---|
| 3500 | p = pAdd(p,q); |
---|
| 3501 | s->m[j] = p; |
---|
| 3502 | #ifdef PDEBUG |
---|
| 3503 | pTest(p); |
---|
| 3504 | #endif |
---|
| 3505 | #endif |
---|
| 3506 | } |
---|
| 3507 | } |
---|
| 3508 | res = idSimpleAdd(t,s); |
---|
| 3509 | idDelete(&t); |
---|
| 3510 | res->rank = 1+idElem(T); |
---|
| 3511 | return(res); |
---|
| 3512 | } |
---|
| 3513 | |
---|
| 3514 | ideal Approx_Step(ideal L) |
---|
| 3515 | { |
---|
| 3516 | int N=currRing->N; |
---|
| 3517 | int i,j; // k=syzcomp |
---|
[9f73706] | 3518 | int flag, flagcnt=0, syzcnt=0; |
---|
[8e165ec] | 3519 | int syzcomp = 0; |
---|
| 3520 | int k=1; /* for ideals not modules */ |
---|
| 3521 | ideal I = kStd(L, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
| 3522 | idSkipZeroes(I); |
---|
| 3523 | ideal s_I; |
---|
| 3524 | int idI = idElem(I); |
---|
| 3525 | ideal trickyQuotient,s_trickyQuotient; |
---|
| 3526 | if (currQuotient !=NULL) |
---|
| 3527 | { |
---|
| 3528 | trickyQuotient = idSimpleAdd(currQuotient,I); |
---|
| 3529 | } |
---|
| 3530 | else |
---|
| 3531 | trickyQuotient = I; |
---|
| 3532 | idSkipZeroes(trickyQuotient); |
---|
| 3533 | poly *var = (poly *)omAlloc0((N+1)*sizeof(poly)); |
---|
| 3534 | // poly *W = (poly *)omAlloc0((2*N+1)*sizeof(poly)); |
---|
| 3535 | resolvente S = (resolvente)omAlloc0((N+1)*sizeof(ideal)); |
---|
| 3536 | ideal SI, res; |
---|
| 3537 | matrix MI; |
---|
| 3538 | poly x=pOne(); |
---|
| 3539 | var[0]=x; |
---|
| 3540 | ideal h2, h3, s_h2, s_h3; |
---|
| 3541 | poly p,q,qq; |
---|
| 3542 | /* init vars */ |
---|
| 3543 | for (i=1; i<=N; i++ ) |
---|
| 3544 | { |
---|
| 3545 | x = pOne(); |
---|
| 3546 | pSetExp(x,i,1); |
---|
| 3547 | pSetm(x); |
---|
| 3548 | var[i]=pCopy(x); |
---|
| 3549 | } |
---|
| 3550 | /* init NF's */ |
---|
| 3551 | for (i=1; i<=N; i++ ) |
---|
| 3552 | { |
---|
| 3553 | h2 = idInit(idI,1); |
---|
| 3554 | flag = 0; |
---|
| 3555 | for (j=0; j< idI; j++ ) |
---|
| 3556 | { |
---|
[5a9e7b] | 3557 | q = pp_Mult_mm(I->m[j],var[i],currRing); |
---|
[8e165ec] | 3558 | q = kNF(I,currQuotient,q,0,0); |
---|
| 3559 | if (q!=0) |
---|
| 3560 | { |
---|
[5a9e7b] | 3561 | h2->m[j]=pCopy(q); |
---|
| 3562 | // pShift(&(h2->m[flag]),1); |
---|
| 3563 | flag++; |
---|
| 3564 | pDelete(&q); |
---|
[8e165ec] | 3565 | } |
---|
| 3566 | else |
---|
[5a9e7b] | 3567 | h2->m[j]=0; |
---|
[8e165ec] | 3568 | } |
---|
| 3569 | /* W[1..idElems(I)] */ |
---|
| 3570 | if (flag >0) |
---|
| 3571 | { |
---|
| 3572 | /* compute syzygies with values in I*/ |
---|
| 3573 | // idSkipZeroes(h2); |
---|
| 3574 | // h2 = idSimpleAdd(h2,I); |
---|
| 3575 | // h2->rank=flag+idI+1; |
---|
| 3576 | idTest(h2); |
---|
[f44fb9] | 3577 | //idShow(h2); |
---|
[8e165ec] | 3578 | ring orig_ring=currRing; |
---|
| 3579 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 3580 | syzcomp = 1; |
---|
| 3581 | rSetSyzComp(syzcomp); |
---|
| 3582 | if (orig_ring != syz_ring) |
---|
| 3583 | { |
---|
[b1a5c1] | 3584 | s_h2=idrCopyR_NoSort(h2,orig_ring); |
---|
| 3585 | // s_trickyQuotient=idrCopyR_NoSort(trickyQuotient,orig_ring); |
---|
| 3586 | // rDebugPrint(syz_ring); |
---|
| 3587 | s_I=idrCopyR_NoSort(I,orig_ring); |
---|
[8e165ec] | 3588 | } |
---|
| 3589 | else |
---|
| 3590 | { |
---|
[b1a5c1] | 3591 | s_h2 = h2; |
---|
| 3592 | s_I = I; |
---|
| 3593 | // s_trickyQuotient=trickyQuotient; |
---|
[8e165ec] | 3594 | } |
---|
| 3595 | idTest(s_h2); |
---|
| 3596 | // idTest(s_trickyQuotient); |
---|
| 3597 | Print(".proceeding with the variable %d\n",i); |
---|
| 3598 | s_h3 = idPrepareStd(s_I, s_h2, 1); |
---|
| 3599 | BITSET save_test=test; |
---|
| 3600 | test|=Sy_bit(OPT_SB_1); |
---|
| 3601 | idTest(s_h3); |
---|
| 3602 | idDelete(&s_h2); |
---|
| 3603 | s_h2=idCopy(s_h3); |
---|
| 3604 | idDelete(&s_h3); |
---|
| 3605 | Print("...computing Syz"); |
---|
[c315ad] | 3606 | s_h3 = kStd(s_h2, currQuotient,(tHomog)FALSE,NULL,NULL,syzcomp,idI); |
---|
[8e165ec] | 3607 | test=save_test; |
---|
[f44fb9] | 3608 | //idShow(s_h3); |
---|
[8e165ec] | 3609 | if (orig_ring != syz_ring) |
---|
| 3610 | { |
---|
[b1a5c1] | 3611 | idDelete(&s_h2); |
---|
| 3612 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
| 3613 | { |
---|
| 3614 | if (s_h3->m[j] != NULL) |
---|
| 3615 | { |
---|
| 3616 | if (p_MinComp(s_h3->m[j],syz_ring) > syzcomp) /* i.e. it is a syzygy */ |
---|
| 3617 | pShift(&s_h3->m[j], -syzcomp); |
---|
| 3618 | else |
---|
| 3619 | pDelete(&s_h3->m[j]); |
---|
| 3620 | } |
---|
| 3621 | } |
---|
| 3622 | idSkipZeroes(s_h3); |
---|
| 3623 | s_h3->rank -= syzcomp; |
---|
| 3624 | rChangeCurrRing(orig_ring); |
---|
| 3625 | // s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
| 3626 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
| 3627 | rKill(syz_ring); |
---|
[8e165ec] | 3628 | } |
---|
| 3629 | idTest(s_h3); |
---|
[c315ad] | 3630 | S[syzcnt]=kStd(s_h3,currQuotient,(tHomog)FALSE,NULL,NULL); |
---|
[8e165ec] | 3631 | syzcnt++; |
---|
| 3632 | idDelete(&s_h3); |
---|
| 3633 | } /* end if flag >0 */ |
---|
[b87f029] | 3634 | else |
---|
[8e165ec] | 3635 | { |
---|
| 3636 | flagcnt++; |
---|
| 3637 | } |
---|
| 3638 | } |
---|
[b87f029] | 3639 | if (flagcnt == N) |
---|
[8e165ec] | 3640 | { |
---|
| 3641 | Print("the input is a two--sided ideal"); |
---|
| 3642 | return(I); |
---|
| 3643 | } |
---|
| 3644 | if (syzcnt >0) |
---|
| 3645 | { |
---|
| 3646 | Print("..computing Intersect of %d modules\n",syzcnt); |
---|
| 3647 | if (syzcnt == 1) |
---|
| 3648 | SI = S[0]; |
---|
| 3649 | else |
---|
| 3650 | SI = idMultSect(S, syzcnt); |
---|
[f44fb9] | 3651 | //idShow(SI); |
---|
[8e165ec] | 3652 | MI = idModule2Matrix(SI); |
---|
| 3653 | res= idInit(MATCOLS(MI),1); |
---|
| 3654 | for (i=1; i<= MATCOLS(MI); i++) |
---|
[b87f029] | 3655 | { |
---|
[8e165ec] | 3656 | p = NULL; |
---|
| 3657 | for (j=0; j< idElem(I); j++) |
---|
[b87f029] | 3658 | { |
---|
[b1a5c1] | 3659 | q = pCopy(MATELEM(MI,j+1,i)); |
---|
| 3660 | if (q!=NULL) |
---|
| 3661 | { |
---|
| 3662 | q = pMult(q,pCopy(I->m[j])); |
---|
| 3663 | p = pAdd(p,q); |
---|
| 3664 | } |
---|
[8e165ec] | 3665 | } |
---|
| 3666 | res->m[i-1]=p; |
---|
| 3667 | } |
---|
| 3668 | Print("final std"); |
---|
| 3669 | res = kStd(res, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
| 3670 | idSkipZeroes(res); |
---|
| 3671 | return(res); |
---|
| 3672 | } |
---|
| 3673 | else |
---|
| 3674 | { |
---|
| 3675 | Print("No syzygies"); |
---|
| 3676 | return(I); |
---|
| 3677 | } |
---|
| 3678 | } |
---|
| 3679 | |
---|
| 3680 | |
---|
[52e2f6] | 3681 | // creates a commutative nc extension; "converts" comm.ring to a Plural ring |
---|
[8e165ec] | 3682 | ring nc_rCreateNCcomm(ring r) |
---|
| 3683 | { |
---|
| 3684 | if (rIsPluralRing(r)) return r; |
---|
[5accf0] | 3685 | |
---|
[52e2f6] | 3686 | matrix C = mpNew(r->N,r->N); // ring-independent!?! |
---|
[8e165ec] | 3687 | matrix D = mpNew(r->N,r->N); |
---|
[52e2f6] | 3688 | |
---|
| 3689 | for(int i=1; i<r->N; i++) |
---|
| 3690 | for(int j=i+1; j<=r->N; j++) |
---|
[b902246] | 3691 | MATELEM(C,i,j) = p_One( r); |
---|
[52e2f6] | 3692 | |
---|
[5eb716] | 3693 | if (nc_CallPlural(C, D, NULL, NULL, r, false, true, false, currRing, TRUE)) // TODO: what about quotient ideal? |
---|
[52e2f6] | 3694 | WarnS("Error initializing multiplication!"); // No reaction!??? |
---|
[b1a5c1] | 3695 | |
---|
[8e165ec] | 3696 | return r; |
---|
| 3697 | } |
---|
| 3698 | |
---|
[6b5dd2] | 3699 | poly p_CopyEmbed(poly p, ring srcRing, int shift, int par_shift) |
---|
| 3700 | /* NOT USED ANYMORE: replaced by maFindPerm in ring.cc */ |
---|
| 3701 | /* for use with embeddings: currRing is a sum of smaller rings */ |
---|
| 3702 | /* and srcRing is one of such smaller rings */ |
---|
[8e165ec] | 3703 | /* shift defines the position of a subring in srcRing */ |
---|
[6b5dd2] | 3704 | /* par_shift defines the position of a subfield in basefield of CurrRing */ |
---|
[8e165ec] | 3705 | { |
---|
| 3706 | if (currRing == srcRing) |
---|
| 3707 | { |
---|
| 3708 | return(p_Copy(p,currRing)); |
---|
| 3709 | } |
---|
| 3710 | nMapFunc nMap=nSetMap(srcRing); |
---|
| 3711 | poly q; |
---|
[6b5dd2] | 3712 | // if ( nMap == nCopy) |
---|
| 3713 | // { |
---|
| 3714 | // q = prCopyR(p,srcRing); |
---|
| 3715 | // } |
---|
| 3716 | // else |
---|
[8e165ec] | 3717 | { |
---|
| 3718 | int *perm = (int *)omAlloc0((srcRing->N+1)*sizeof(int)); |
---|
[6b5dd2] | 3719 | int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
[8e165ec] | 3720 | // int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
| 3721 | int i; |
---|
| 3722 | // if (srcRing->P > 0) |
---|
| 3723 | // { |
---|
| 3724 | // for (i=0; i<srcRing->P; i++) |
---|
[5a9e7b] | 3725 | // par_perm[i]=-i; |
---|
[8e165ec] | 3726 | // } |
---|
| 3727 | if ((shift<0) || (shift > currRing->N)) |
---|
| 3728 | { |
---|
| 3729 | Werror("bad shifts in p_CopyEmbed"); |
---|
| 3730 | return(0); |
---|
| 3731 | } |
---|
[6b5dd2] | 3732 | for (i=1; i<= srcRing->N; i++) |
---|
| 3733 | { |
---|
| 3734 | perm[i] = shift+i; |
---|
| 3735 | } |
---|
[8e165ec] | 3736 | q = pPermPoly(p,perm,srcRing,nMap,par_perm,srcRing->P); |
---|
| 3737 | } |
---|
| 3738 | return(q); |
---|
| 3739 | } |
---|
| 3740 | |
---|
[b39bc1f] | 3741 | poly pOppose(ring Rop, poly p) |
---|
| 3742 | /* opposes a vector p from Rop to currRing */ |
---|
[71ac89a] | 3743 | { |
---|
| 3744 | /* the simplest case:*/ |
---|
[b39bc1f] | 3745 | if ( Rop == currRing ) return(pCopy(p)); |
---|
| 3746 | /* check Rop == rOpposite(currRing) */ |
---|
| 3747 | if ( !rIsLikeOpposite(currRing, Rop) ) |
---|
| 3748 | { |
---|
| 3749 | WarnS("an opposite ring should be used"); |
---|
| 3750 | return NULL; |
---|
| 3751 | } |
---|
| 3752 | /* nMapFunc nMap = nSetMap(Rop);*/ |
---|
| 3753 | /* since we know that basefields coinside! */ |
---|
[71ac89a] | 3754 | int *perm=(int *)omAlloc0((Rop->N+1)*sizeof(int)); |
---|
[b39bc1f] | 3755 | if (!p_IsConstantPoly(p, Rop)) |
---|
[71ac89a] | 3756 | { |
---|
[b39bc1f] | 3757 | /* we know perm exactly */ |
---|
| 3758 | int i; |
---|
| 3759 | for(i=1; i<=Rop->N; i++) |
---|
| 3760 | { |
---|
| 3761 | perm[i] = Rop->N+1-i; |
---|
| 3762 | } |
---|
[71ac89a] | 3763 | } |
---|
[b39bc1f] | 3764 | poly res = pPermPoly(p, perm, Rop, nCopy); |
---|
[71ac89a] | 3765 | omFreeSize((ADDRESS)perm,(Rop->N+1)*sizeof(int)); |
---|
| 3766 | return res; |
---|
| 3767 | } |
---|
| 3768 | |
---|
[b39bc1f] | 3769 | ideal idOppose(ring Rop, ideal I) |
---|
| 3770 | /* opposes a module I from Rop to currRing */ |
---|
| 3771 | { |
---|
| 3772 | /* the simplest case:*/ |
---|
| 3773 | if ( Rop == currRing ) return idCopy(I); |
---|
| 3774 | /* check Rop == rOpposite(currRing) */ |
---|
| 3775 | if (!rIsLikeOpposite(currRing, Rop)) |
---|
| 3776 | { |
---|
| 3777 | WarnS("an opposite ring should be used"); |
---|
| 3778 | return NULL; |
---|
| 3779 | } |
---|
| 3780 | int i; |
---|
| 3781 | ideal idOp = idInit(I->ncols, I->rank); |
---|
| 3782 | for (i=0; i< (I->ncols)*(I->nrows); i++) |
---|
[b87f029] | 3783 | { |
---|
| 3784 | idOp->m[i] = pOppose(Rop,I->m[i]); |
---|
[b39bc1f] | 3785 | } |
---|
| 3786 | idTest(idOp); |
---|
| 3787 | return idOp; |
---|
| 3788 | } |
---|
| 3789 | |
---|
| 3790 | BOOLEAN rIsLikeOpposite(ring rBase, ring rCandidate) |
---|
| 3791 | /* checks whether rings rBase and rCandidate */ |
---|
| 3792 | /* could be opposite to each other */ |
---|
| 3793 | /* returns TRUE if it is so */ |
---|
| 3794 | { |
---|
| 3795 | /* the same basefield */ |
---|
| 3796 | int diagnose = TRUE; |
---|
| 3797 | ring save = currRing; |
---|
| 3798 | rChangeCurrRing(rBase); |
---|
| 3799 | nMapFunc nMap = nSetMap(rCandidate); |
---|
| 3800 | if (nMap != nCopy) diagnose = FALSE; |
---|
| 3801 | rChangeCurrRing(save); |
---|
| 3802 | /* same number of variables */ |
---|
| 3803 | if (rBase->N != rCandidate->N) diagnose = FALSE; |
---|
| 3804 | /* nc and comm ring */ |
---|
| 3805 | if ( rIsPluralRing(rBase) != rIsPluralRing(rCandidate) ) diagnose = FALSE; |
---|
[e270ea] | 3806 | /* both are qrings */ |
---|
| 3807 | /* NO CHECK, since it is used in building opposite qring */ |
---|
| 3808 | /* if ( ((rBase->qideal != NULL) && (rCandidate->qideal == NULL)) */ |
---|
| 3809 | /* || ((rBase->qideal == NULL) && (rCandidate->qideal != NULL)) ) */ |
---|
| 3810 | /* diagnose = FALSE; */ |
---|
[b39bc1f] | 3811 | /* TODO: varnames are e->E etc */ |
---|
| 3812 | return diagnose; |
---|
| 3813 | } |
---|
[71ac89a] | 3814 | |
---|
[86016d] | 3815 | |
---|
| 3816 | |
---|
[022ef5] | 3817 | bool nc_SetupQuotient(ring rGR, const ring rG, bool bCopy) |
---|
[86016d] | 3818 | { |
---|
[022ef5] | 3819 | if( rGR->qideal == NULL ) |
---|
[e024c6c] | 3820 | return false; // no quotient = no work! done!? What about factors of SCA? |
---|
[022ef5] | 3821 | |
---|
| 3822 | bool ret = true; |
---|
[5accf0] | 3823 | // currently only super-commutative extension deals with factors. |
---|
[022ef5] | 3824 | |
---|
[57bfa2] | 3825 | if( ncExtensions(SCAMASK) ) |
---|
[022ef5] | 3826 | { |
---|
| 3827 | bool sca_ret = sca_SetupQuotient(rGR, rG, bCopy); |
---|
[b1a5c1] | 3828 | |
---|
[022ef5] | 3829 | if(sca_ret) // yes it was dealt with! |
---|
| 3830 | ret = false; |
---|
| 3831 | } |
---|
| 3832 | |
---|
| 3833 | if( bCopy ) |
---|
| 3834 | { |
---|
| 3835 | assume(rIsPluralRing(rGR) == rIsPluralRing(rG)); |
---|
| 3836 | assume((rGR->qideal==NULL) == (rG->qideal==NULL)); |
---|
| 3837 | assume(rIsSCA(rGR) == rIsSCA(rG)); |
---|
| 3838 | assume(ncRingType(rGR) == ncRingType(rG)); |
---|
| 3839 | } |
---|
| 3840 | |
---|
| 3841 | return ret; |
---|
[86016d] | 3842 | } |
---|
| 3843 | |
---|
| 3844 | |
---|
[ea68ed] | 3845 | |
---|
| 3846 | // int Commutative_Context(ring r, leftv expression) |
---|
| 3847 | // /* returns 1 if expression consists */ |
---|
| 3848 | // /* of commutative elements */ |
---|
| 3849 | // { |
---|
| 3850 | // /* crucial: poly -> ideal, module, matrix */ |
---|
| 3851 | // } |
---|
| 3852 | |
---|
| 3853 | // int Comm_Context_Poly(ring r, poly p) |
---|
| 3854 | // { |
---|
[52e2f6] | 3855 | // poly COMM=r->GetNC()->COMM; |
---|
[ea68ed] | 3856 | // poly pp=pOne(); |
---|
| 3857 | // memset(pp->exp,0,r->ExpL_Size*sizeof(long)); |
---|
| 3858 | // while (p!=NULL) |
---|
| 3859 | // { |
---|
| 3860 | // for (i=0;i<=r->ExpL_Size;i++) |
---|
| 3861 | // { |
---|
[b87f029] | 3862 | // if ((p->exp[i]) && (pp->exp[i])) return(FALSE); |
---|
[ea68ed] | 3863 | // /* nonzero exponent of non-comm variable */ |
---|
| 3864 | // } |
---|
| 3865 | // pIter(p); |
---|
| 3866 | // } |
---|
| 3867 | // return(TRUE); |
---|
| 3868 | // } |
---|
[32c4523] | 3869 | #endif |
---|