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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9 | * Version: $Id: gring.cc,v 1.68 2008-07-26 14:28:03 motsak Exp $ |
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10 | *******************************************************************/ |
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11 | |
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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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16 | #define OM_CHECK 4 |
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17 | #define OM_TRACK 5 |
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18 | #endif |
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19 | |
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20 | #include "mod2.h" |
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21 | |
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22 | #ifdef HAVE_PLURAL |
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23 | #define PLURAL_INTERNAL_DECLARATIONS |
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24 | |
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25 | #include "febase.h" |
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26 | #include "ring.h" |
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27 | #include "polys.h" |
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28 | #include "numbers.h" |
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29 | #include "ideals.h" |
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30 | #include "matpol.h" |
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31 | #include "kbuckets.h" |
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32 | #include "kstd1.h" |
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33 | #include "sbuckets.h" |
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34 | #include "prCopy.h" |
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35 | #include "p_Mult_q.h" |
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36 | #include "pInline1.h" |
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37 | |
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38 | // dirty tricks: |
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39 | #include "p_MemAdd.h" |
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40 | |
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41 | #include "gring.h" |
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42 | #include "sca.h" |
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43 | #include <summator.h> |
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44 | |
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45 | #include <ncSAMult.h> // for CMultiplier etc classes |
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46 | #include <ncSAFormula.h> // for CFormulaPowerMultiplier and enum Enum_ncSAType |
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47 | |
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48 | |
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49 | static const bool bNoPluralMultiplication = false; // use only formula shortcuts in my OOP Multiplier |
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50 | |
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51 | // the following make sense only if bNoPluralMultiplication is false: |
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52 | static const bool bNoFormula = true; // don't use any formula shortcuts |
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53 | static const bool bNoCache = false; // only formula whenever possible, only make sanse if bNoFormula is false! |
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54 | |
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55 | |
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56 | // false, true, false == old "good" Plural |
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57 | // false, false ==>> Plural + Cache + Direct Formula - not much |
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58 | // false, false, true ==>> Plural Mult + Direct Formula (no ~cache) |
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59 | // true, *, * == new OOP multiplication! |
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60 | |
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61 | bool bUseExtensions = true; |
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62 | |
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63 | /* global nc_macros : */ |
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64 | |
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65 | #define freeT(A,v) omFreeSize((ADDRESS)A,(v+1)*sizeof(int)) |
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66 | #define freeN(A,k) omFreeSize((ADDRESS)A,k*sizeof(number)) |
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67 | |
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68 | |
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69 | // some forward declarations: |
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70 | |
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71 | |
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72 | // polynomial multiplication functions for p_Procs : |
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73 | poly gnc_pp_Mult_mm(const poly p, const poly m, const ring r, poly &last); |
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74 | poly gnc_p_Mult_mm(poly p, const poly m, const ring r); |
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75 | poly gnc_mm_Mult_p(const poly m, poly p, const ring r); |
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76 | poly gnc_mm_Mult_pp(const poly m, const poly p, const ring r); |
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77 | |
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78 | |
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79 | // set pProcs for r and global variable p_Procs as for general non-commutative algebras. |
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80 | void gnc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs); |
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81 | |
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82 | /* syzygies : */ |
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83 | poly gnc_CreateSpolyOld(const poly p1, const poly p2/*, poly spNoether*/, const ring r); |
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84 | poly gnc_ReduceSpolyOld(const poly p1, poly p2/*, poly spNoether*/, const ring r); |
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85 | |
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86 | poly gnc_CreateSpolyNew(const poly p1, const poly p2/*, poly spNoether*/, const ring r); |
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87 | poly gnc_ReduceSpolyNew(const poly p1, poly p2/*, poly spNoether*/, const ring r); |
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88 | |
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89 | |
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90 | |
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91 | void gnc_kBucketPolyRedNew(kBucket_pt b, poly p, number *c); |
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92 | void gnc_kBucketPolyRed_ZNew(kBucket_pt b, poly p, number *c); |
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93 | |
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94 | void gnc_kBucketPolyRedOld(kBucket_pt b, poly p, number *c); |
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95 | void gnc_kBucketPolyRed_ZOld(kBucket_pt b, poly p, number *c); |
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96 | |
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97 | |
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98 | // poly gnc_ReduceSpolyNew(poly p1, poly p2, poly spNoether, const ring r); |
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99 | // void gnc_ReduceSpolyTail(poly p1, poly q, poly q2, poly spNoether, const ring r); |
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100 | |
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101 | // void nc_kBucketPolyRed(kBucket_pt b, poly p); |
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102 | |
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103 | ideal gnc_gr_mora(const ideal, const ideal, const intvec *, const intvec *, kStrategy); // Not yet! |
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104 | ideal gnc_gr_bba (const ideal F, const ideal Q, const intvec *, const intvec *, kStrategy strat); |
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105 | |
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106 | |
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107 | void nc_CleanUp(nc_struct* p); // just free memory! |
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108 | void nc_rCleanUp(ring r); // smaller than kill: just free mem |
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109 | |
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110 | |
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111 | #if 0 |
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112 | // deprecated functions: |
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113 | // 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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114 | // poly gnc_p_Minus_mm_Mult_qq(poly p, const poly m, poly q, const ring r); |
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115 | // 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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116 | // 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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117 | #endif |
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118 | |
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119 | |
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120 | |
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121 | /*2 |
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122 | * returns the LCM of the head terms of a and b |
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123 | * without coefficient!!! |
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124 | */ |
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125 | poly p_Lcm(const poly a, const poly b, const long lCompM, const ring r) |
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126 | { |
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127 | poly m = // p_One( r); |
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128 | p_Init(r); |
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129 | |
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130 | const int pVariables = r->N; |
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131 | |
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132 | for (int i = pVariables; i!=0; i--) |
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133 | { |
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134 | const int lExpA = p_GetExp (a, i, r); |
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135 | const int lExpB = p_GetExp (b, i, r); |
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136 | |
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137 | p_SetExp (m, i, si_max(lExpA, lExpB), r); |
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138 | } |
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139 | |
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140 | p_SetComp (m, lCompM, r); |
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141 | |
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142 | p_Setm(m,r); |
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143 | |
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144 | #ifdef PDEBUG |
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145 | // p_Test(m,r); |
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146 | #endif |
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147 | |
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148 | n_New(&(p_GetCoeff(m, r)), r); |
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149 | |
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150 | return(m); |
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151 | }; |
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152 | |
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153 | poly p_Lcm(const poly a, const poly b, const ring r) |
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154 | { |
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155 | #ifdef PDEBUG |
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156 | p_Test(a, r); |
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157 | p_Test(b, r); |
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158 | #endif |
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159 | |
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160 | const long lCompP1 = p_GetComp(a, r); |
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161 | const long lCompP2 = p_GetComp(b, r); |
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162 | |
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163 | const poly m = p_Lcm(a, b, si_max(lCompP1, lCompP2), r); |
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164 | |
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165 | #ifdef PDEBUG |
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166 | // p_Test(m,r); |
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167 | #endif |
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168 | return(m); |
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169 | }; |
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170 | |
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171 | |
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172 | |
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173 | /////////////////////////////////////////////////////////////////////////////// |
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174 | poly nc_p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, |
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175 | const int, const poly, const ring r) |
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176 | { |
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177 | poly mc = p_Neg( p_Copy(m, r), r ); |
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178 | poly mmc = nc_mm_Mult_pp( mc, q, r ); |
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179 | p_Delete(&mc, r); |
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180 | |
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181 | p = p_Add_q(p, mmc, r); |
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182 | |
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183 | lp = pLength(p); // ring independent! |
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184 | |
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185 | return(p); |
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186 | } |
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187 | |
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188 | // returns p + m*q destroys p, const: q, m |
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189 | poly nc_p_Plus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, |
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190 | const int, const ring r) |
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191 | { |
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192 | p = p_Add_q(p, nc_mm_Mult_pp( m, q, r ), r); |
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193 | |
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194 | lp = pLength(p); |
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195 | |
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196 | return(p); |
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197 | } |
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198 | |
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199 | #if 0 |
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200 | 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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201 | { |
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202 | poly t; |
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203 | int i; |
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204 | |
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205 | return gnc_p_Minus_mm_Mult_qq(p, m, q, d1, i, t, r); |
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206 | } |
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207 | #endif |
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208 | |
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209 | |
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210 | //----------- auxiliary routines-------------------------- |
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211 | poly _gnc_p_Mult_q(poly p, poly q, const int copy, const ring r) // not used anymore! |
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212 | /* destroy p,q unless copy=1 */ |
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213 | { |
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214 | poly res=NULL; |
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215 | poly ghost=NULL; |
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216 | poly qq,pp; |
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217 | if (copy) |
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218 | { |
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219 | qq=p_Copy(q,r); |
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220 | pp=p_Copy(p,r); |
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221 | } |
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222 | else |
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223 | { |
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224 | qq=q; |
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225 | pp=p; |
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226 | } |
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227 | while (qq!=NULL) |
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228 | { |
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229 | res=p_Add_q(res, pp_Mult_mm(pp, qq, r), r); // p_Head(qq, r)? |
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230 | qq=p_LmDeleteAndNext(qq,r); |
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231 | } |
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232 | p_Delete(&pp,r); |
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233 | return(res); |
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234 | } |
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235 | |
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236 | // return pPolyP * pPolyQ; destroy or reuse pPolyP and pPolyQ |
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237 | poly _nc_p_Mult_q(poly pPolyP, poly pPolyQ, const ring rRing) |
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238 | { |
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239 | assume( rIsPluralRing(rRing) ); |
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240 | #ifdef PDEBUG |
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241 | p_Test(pPolyP, rRing); |
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242 | p_Test(pPolyQ, rRing); |
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243 | #endif |
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244 | #ifdef RDEBUG |
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245 | rTest(rRing); |
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246 | #endif |
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247 | |
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248 | int lp, lq; |
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249 | |
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250 | pqLength(pPolyP, pPolyQ, lp, lq, MIN_LENGTH_BUCKET); |
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251 | |
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252 | bool bUsePolynomial = TEST_OPT_NOT_BUCKETS || (si_max(lp, lq) < MIN_LENGTH_BUCKET); // ??? |
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253 | |
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254 | CPolynomialSummator sum(rRing, bUsePolynomial); |
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255 | |
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256 | if (lq <= lp) // ? |
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257 | { |
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258 | // always length(q) times "p * q[j]" |
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259 | for( ; pPolyQ!=NULL; pPolyQ = p_LmDeleteAndNext( pPolyQ, rRing ) ) |
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260 | sum += pp_Mult_mm( pPolyP, pPolyQ, rRing); |
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261 | |
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262 | p_Delete( &pPolyP, rRing ); |
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263 | } else |
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264 | { |
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265 | // always length(p) times "p[i] * q" |
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266 | for( ; pPolyP!=NULL; pPolyP = p_LmDeleteAndNext( pPolyP, rRing ) ) |
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267 | sum += nc_mm_Mult_pp( pPolyP, pPolyQ, rRing); |
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268 | |
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269 | p_Delete( &pPolyQ, rRing ); |
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270 | } |
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271 | |
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272 | return(sum); |
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273 | } |
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274 | |
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275 | // return pPolyP * pPolyQ; preserve pPolyP and pPolyQ |
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276 | poly _nc_pp_Mult_qq(const poly pPolyP, const poly pPolyQ, const ring rRing) |
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277 | { |
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278 | assume( rIsPluralRing(rRing) ); |
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279 | #ifdef PDEBUG |
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280 | p_Test(pPolyP, rRing); |
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281 | p_Test(pPolyQ, rRing); |
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282 | #endif |
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283 | #ifdef RDEBUG |
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284 | rTest(rRing); |
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285 | #endif |
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286 | |
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287 | int lp, lq; |
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288 | |
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289 | pqLength(pPolyP, pPolyQ, lp, lq, MIN_LENGTH_BUCKET); |
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290 | |
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291 | bool bUsePolynomial = TEST_OPT_NOT_BUCKETS || (si_max(lp, lq) < MIN_LENGTH_BUCKET); // ??? |
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292 | |
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293 | CPolynomialSummator sum(rRing, bUsePolynomial); |
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294 | |
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295 | if (lq <= lp) // ? |
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296 | { |
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297 | // always length(q) times "p * q[j]" |
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298 | for( poly q = pPolyQ; q !=NULL; q = pNext(q) ) |
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299 | sum += pp_Mult_mm(pPolyP, q, rRing); |
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300 | } else |
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301 | { |
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302 | // always length(p) times "p[i] * q" |
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303 | for( poly p = pPolyP; p !=NULL; p = pNext(p) ) |
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304 | sum += nc_mm_Mult_pp( p, pPolyQ, rRing); |
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305 | } |
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306 | |
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307 | return(sum); |
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308 | } |
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309 | |
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310 | |
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311 | |
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312 | poly gnc_mm_Mult_nn (int *F, int *G, const ring r); |
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313 | poly gnc_mm_Mult_uu (int *F,int jG,int bG, const ring r); |
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314 | |
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315 | /* #define nc_uu_Mult_ww nc_uu_Mult_ww_vert */ |
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316 | poly gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r); |
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317 | /* poly nc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r); */ |
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318 | /* poly nc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r); */ |
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319 | /* poly nc_uu_Mult_ww_hvdiag (int i, int a, int j, int b, const ring r); */ |
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320 | /* not written yet */ |
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321 | |
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322 | |
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323 | poly gnc_p_Mult_mm_Common(poly p, const poly m, int side, const ring r) |
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324 | /* p is poly, m is mono with coeff, destroys p */ |
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325 | /* if side==1, computes p_Mult_mm; otherwise, mm_Mult_p */ |
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326 | { |
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327 | if ((p==NULL) || (m==NULL)) return NULL; |
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328 | /* if (pNext(p)==NULL) return(nc_mm_Mult_nn(p,pCopy(m),r)); */ |
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329 | /* excluded - the cycle will do it anyway - OK. */ |
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330 | if (p_IsConstant(m,r)) return(p_Mult_nn(p,p_GetCoeff(m,r),r)); |
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331 | |
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332 | #ifdef PDEBUG |
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333 | p_Test(p,r); |
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334 | p_Test(m,r); |
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335 | #endif |
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336 | poly v=NULL; |
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337 | int rN=r->N; |
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338 | int *P=(int *)omAlloc0((rN+1)*sizeof(int)); |
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339 | int *M=(int *)omAlloc0((rN+1)*sizeof(int)); |
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340 | /* coefficients: */ |
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341 | number cP,cM,cOut; |
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342 | p_GetExpV(m, M, r); |
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343 | cM=p_GetCoeff(m,r); |
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344 | /* components:*/ |
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345 | const int expM=p_GetComp(m,r); |
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346 | int expP=0; |
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347 | int expOut=0; |
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348 | /* bucket constraints: */ |
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349 | int UseBuckets=1; |
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350 | if (pLength(p)< MIN_LENGTH_BUCKET || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
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351 | |
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352 | CPolynomialSummator sum(r, UseBuckets == 0); |
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353 | |
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354 | while (p!=NULL) |
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355 | { |
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356 | #ifdef PDEBUG |
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357 | p_Test(p,r); |
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358 | #endif |
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359 | expP=p_GetComp(p,r); |
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360 | if (expP==0) |
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361 | { |
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362 | expOut=expM; |
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363 | } |
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364 | else |
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365 | { |
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366 | if (expM==0) |
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367 | { |
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368 | expOut=expP; |
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369 | #ifdef PDEBUG |
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370 | if (side) |
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371 | { |
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372 | Print("gnc_p_Mult_mm: Multiplication in the left module from the right"); |
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373 | } |
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374 | #endif |
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375 | } |
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376 | else |
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377 | { |
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378 | /* REPORT_ERROR */ |
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379 | #ifdef PDEBUG |
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380 | const char* s; |
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381 | if (side==1) s="gnc_p_Mult_mm"; |
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382 | else s="gnc_mm_Mult_p"; |
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383 | Print("%s: exponent mismatch %d and %d\n",s,expP,expM); |
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384 | #endif |
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385 | expOut=0; |
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386 | } |
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387 | } |
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388 | p_GetExpV(p,P,r); |
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389 | cP=p_GetCoeff(p,r); |
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390 | cOut=n_Mult(cP,cM,r); |
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391 | if (side==1) |
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392 | { |
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393 | v = gnc_mm_Mult_nn(P, M, r); |
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394 | } |
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395 | else |
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396 | { |
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397 | v = gnc_mm_Mult_nn(M, P, r); |
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398 | } |
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399 | v = p_Mult_nn(v,cOut,r); |
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400 | p_SetCompP(v,expOut,r); |
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401 | |
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402 | sum += v; |
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403 | |
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404 | p_DeleteLm(&p,r); |
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405 | } |
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406 | freeT(P,rN); |
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407 | freeT(M,rN); |
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408 | |
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409 | return(sum); |
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410 | } |
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411 | |
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412 | /* poly functions defined in p_Procs : */ |
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413 | poly gnc_pp_Mult_mm(const poly p, const poly m, const ring r, poly &last) |
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414 | { |
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415 | return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 1, r) ); |
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416 | } |
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417 | |
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418 | poly gnc_p_Mult_mm(poly p, const poly m, const ring r) |
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419 | { |
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420 | return( gnc_p_Mult_mm_Common(p, m, 1, r) ); |
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421 | } |
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422 | |
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423 | poly gnc_mm_Mult_p(const poly m, poly p, const ring r) |
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424 | { |
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425 | return( gnc_p_Mult_mm_Common(p, m, 0, r) ); |
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426 | } |
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427 | |
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428 | poly gnc_mm_Mult_pp(const poly m, const poly p, const ring r) |
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429 | { |
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430 | return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 0, r) ); |
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431 | } |
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432 | |
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433 | |
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434 | |
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435 | poly gnc_mm_Mult_nn(int *F0, int *G0, const ring r) |
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436 | /* destroys nothing, no coeffs and exps */ |
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437 | { |
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438 | poly out=NULL; |
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439 | int i,j; |
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440 | int iF,jG,iG; |
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441 | int rN=r->N; |
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442 | int ExpSize=(((rN+1)*sizeof(int)+sizeof(long)-1)/sizeof(long))*sizeof(long); |
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443 | |
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444 | int *F=(int *)omAlloc0((rN+1)*sizeof(int)); |
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445 | int *G=(int *)omAlloc0((rN+1)*sizeof(int)); |
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446 | |
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447 | memcpy(F, F0,(rN+1)*sizeof(int)); |
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448 | // pExpVectorCopy(F,F0); |
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449 | memcpy(G, G0,(rN+1)*sizeof(int)); |
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450 | // pExpVectorCopy(G,G0); |
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451 | F[0]=0; /* important for p_MemAdd */ |
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452 | G[0]=0; |
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453 | |
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454 | iF=rN; |
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455 | while ((F[iF]==0)&&(iF>=1)) iF--; /* last exp_num of F */ |
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456 | if (iF==0) /* F0 is zero vector */ |
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457 | { |
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458 | out=pOne(); |
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459 | p_SetExpV(out,G0,r); |
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460 | p_Setm(out,r); |
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461 | freeT(F,rN); |
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462 | freeT(G,rN); |
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463 | return(out); |
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464 | } |
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465 | jG=1; |
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466 | while ((G[jG]==0)&&(jG<rN)) jG++; /* first exp_num of G */ |
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467 | iG=rN; |
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468 | while ((G[iG]==0)&&(iG>1)) iG--; /* last exp_num of G */ |
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469 | |
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470 | out=pOne(); |
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471 | |
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472 | if (iF<=jG) |
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473 | /* i.e. no mixed exp_num , MERGE case */ |
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474 | { |
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475 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
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476 | p_SetExpV(out,F,r); |
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477 | p_Setm(out,r); |
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478 | // omFreeSize((ADDRESS)F,ExpSize); |
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479 | freeT(F,rN); |
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480 | freeT(G,rN); |
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481 | return(out); |
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482 | } |
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483 | |
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484 | number cff=n_Init(1,r); |
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485 | number tmp_num=NULL; |
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486 | int cpower=0; |
---|
487 | |
---|
488 | if (ncRingType(r)==nc_skew) |
---|
489 | { |
---|
490 | if (r->GetNC()->IsSkewConstant==1) |
---|
491 | { |
---|
492 | int tpower=0; |
---|
493 | for(j=jG; j<=iG; j++) |
---|
494 | { |
---|
495 | if (G[j]!=0) |
---|
496 | { |
---|
497 | cpower = 0; |
---|
498 | for(i=j+1; i<=iF; i++) |
---|
499 | { |
---|
500 | cpower = cpower + F[i]; |
---|
501 | } |
---|
502 | cpower = cpower*G[j]; // bug! here may happen an arithmetic overflow!!! |
---|
503 | tpower = tpower + cpower; |
---|
504 | } |
---|
505 | } |
---|
506 | cff = n_Copy(p_GetCoeff(MATELEM(r->GetNC()->COM,1,2),r),r); |
---|
507 | nPower(cff,tpower,&tmp_num); |
---|
508 | n_Delete(&cff,r); |
---|
509 | cff = tmp_num; |
---|
510 | } |
---|
511 | else /* skew commutative with nonequal coeffs */ |
---|
512 | { |
---|
513 | number totcff=n_Init(1,r); |
---|
514 | for(j=jG; j<=iG; j++) |
---|
515 | { |
---|
516 | if (G[j]!=0) |
---|
517 | { |
---|
518 | cpower = 0; |
---|
519 | for(i=j+1; i<=iF; i++) |
---|
520 | { |
---|
521 | if (F[i]!=0) |
---|
522 | { |
---|
523 | cpower = F[i]*G[j]; // bug! overflow danger!!! |
---|
524 | cff = n_Copy(p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r),r); |
---|
525 | nPower(cff,cpower,&tmp_num); |
---|
526 | cff = nMult(totcff,tmp_num); |
---|
527 | nDelete(&totcff); |
---|
528 | nDelete(&tmp_num); |
---|
529 | totcff = n_Copy(cff,r); |
---|
530 | n_Delete(&cff,r); |
---|
531 | } |
---|
532 | } /* end 2nd for */ |
---|
533 | } |
---|
534 | } |
---|
535 | cff=totcff; |
---|
536 | } |
---|
537 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
---|
538 | p_SetExpV(out,F,r); |
---|
539 | p_Setm(out,r); |
---|
540 | p_SetCoeff(out,cff,r); |
---|
541 | // p_MemAdd_NegWeightAdjust(p, r); ??? do we need this? |
---|
542 | freeT(F,rN); |
---|
543 | freeT(G,rN); |
---|
544 | return(out); |
---|
545 | } /* end nc_skew */ |
---|
546 | |
---|
547 | /* now we have to destroy out! */ |
---|
548 | p_Delete(&out,r); |
---|
549 | out = NULL; |
---|
550 | |
---|
551 | if (iG==jG) |
---|
552 | /* g is univariate monomial */ |
---|
553 | { |
---|
554 | /* if (ri->GetNC()->type==nc_skew) -- postpone to TU */ |
---|
555 | out = gnc_mm_Mult_uu(F,jG,G[jG],r); |
---|
556 | freeT(F,rN); |
---|
557 | freeT(G,rN); |
---|
558 | return(out); |
---|
559 | } |
---|
560 | |
---|
561 | number n1=n_Init(1,r); |
---|
562 | int *Prv=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
563 | int *Nxt=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
564 | |
---|
565 | int *log=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
566 | int cnt=0; int cnf=0; |
---|
567 | |
---|
568 | /* splitting F wrt jG */ |
---|
569 | for (i=1;i<=jG;i++) |
---|
570 | { |
---|
571 | Prv[i]=F[i]; Nxt[i]=0; /* mult at the very end */ |
---|
572 | if (F[i]!=0) cnf++; |
---|
573 | } |
---|
574 | |
---|
575 | if (cnf==0) freeT(Prv,rN); |
---|
576 | |
---|
577 | for (i=jG+1;i<=rN;i++) |
---|
578 | { |
---|
579 | Nxt[i]=F[i]; |
---|
580 | /* if (cnf!=0) Prv[i]=0; */ |
---|
581 | if (F[i]!=0) |
---|
582 | { |
---|
583 | cnt++; |
---|
584 | } /* effective part for F */ |
---|
585 | } |
---|
586 | freeT(F,rN); |
---|
587 | cnt=0; |
---|
588 | |
---|
589 | for (i=1;i<=rN;i++) |
---|
590 | { |
---|
591 | if (G[i]!=0) |
---|
592 | { |
---|
593 | cnt++; |
---|
594 | log[cnt]=i; |
---|
595 | } /* lG for G */ |
---|
596 | } |
---|
597 | |
---|
598 | /* ---------------------- A C T I O N ------------------------ */ |
---|
599 | poly D=NULL; |
---|
600 | poly Rout=NULL; |
---|
601 | number *c=(number *)omAlloc0((rN+1)*sizeof(number)); |
---|
602 | c[0]=n_Init(1,r); |
---|
603 | |
---|
604 | int *Op=Nxt; |
---|
605 | int *On=G; |
---|
606 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
607 | |
---|
608 | for (i=jG;i<=rN;i++) U[i]=Nxt[i]+G[i]; /* make leadterm */ |
---|
609 | Nxt=NULL; |
---|
610 | G=NULL; |
---|
611 | cnt=1; |
---|
612 | int t=0; |
---|
613 | poly w=NULL; |
---|
614 | poly Pn=pOne(); |
---|
615 | p_SetExpV(Pn,On,r); |
---|
616 | p_Setm(Pn,r); |
---|
617 | |
---|
618 | while (On[iG]!=0) |
---|
619 | { |
---|
620 | t=log[cnt]; |
---|
621 | |
---|
622 | w=gnc_mm_Mult_uu(Op,t,On[t],r); |
---|
623 | c[cnt]=n_Mult(c[cnt-1],p_GetCoeff(w,r),r); |
---|
624 | D = pNext(w); /* getting coef and rest D */ |
---|
625 | p_DeleteLm(&w,r); |
---|
626 | w=NULL; |
---|
627 | |
---|
628 | Op[t] += On[t]; /* update exp_vectors */ |
---|
629 | On[t] = 0; |
---|
630 | |
---|
631 | if (t!=iG) /* not the last step */ |
---|
632 | { |
---|
633 | p_SetExpV(Pn,On,r); |
---|
634 | p_Setm(Pn,r); |
---|
635 | #ifdef PDEBUG |
---|
636 | p_Test(Pn,r); |
---|
637 | #endif |
---|
638 | |
---|
639 | // if (pNext(D)==0) |
---|
640 | // is D a monomial? could be postponed higher |
---|
641 | // { |
---|
642 | // Rout=nc_mm_Mult_nn(D,Pn,r); |
---|
643 | // } |
---|
644 | // else |
---|
645 | // { |
---|
646 | Rout=gnc_p_Mult_mm(D,Pn,r); |
---|
647 | // } |
---|
648 | } |
---|
649 | else |
---|
650 | { |
---|
651 | Rout=D; |
---|
652 | D=NULL; |
---|
653 | } |
---|
654 | |
---|
655 | if (Rout!=NULL) |
---|
656 | { |
---|
657 | Rout=p_Mult_nn(Rout,c[cnt-1],r); /* Rest is ready */ |
---|
658 | out=p_Add_q(out,Rout,r); |
---|
659 | Rout=NULL; |
---|
660 | } |
---|
661 | cnt++; |
---|
662 | } |
---|
663 | freeT(On,rN); |
---|
664 | freeT(Op,rN); |
---|
665 | p_Delete(&Pn,r); |
---|
666 | omFreeSize((ADDRESS)log,(rN+1)*sizeof(int)); |
---|
667 | |
---|
668 | /* leadterm and Prv-part */ |
---|
669 | |
---|
670 | Rout=pOne(); |
---|
671 | /* U is lead.monomial */ |
---|
672 | U[0]=0; |
---|
673 | p_SetExpV(Rout,U,r); |
---|
674 | p_Setm(Rout,r); /* use again this name Rout */ |
---|
675 | #ifdef PDEBUG |
---|
676 | p_Test(Rout,r); |
---|
677 | #endif |
---|
678 | p_SetCoeff(Rout,c[cnt-1],r); |
---|
679 | out=p_Add_q(out,Rout,r); |
---|
680 | freeT(U,rN); |
---|
681 | freeN(c,rN+1); |
---|
682 | if (cnf!=0) /* Prv is non-zero vector */ |
---|
683 | { |
---|
684 | Rout=pOne(); |
---|
685 | Prv[0]=0; |
---|
686 | p_SetExpV(Rout,Prv,r); |
---|
687 | p_Setm(Rout,r); |
---|
688 | #ifdef PDEBUG |
---|
689 | p_Test(Rout,r); |
---|
690 | #endif |
---|
691 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
692 | freeT(Prv,rN); |
---|
693 | p_Delete(&Rout,r); |
---|
694 | } |
---|
695 | return (out); |
---|
696 | } |
---|
697 | |
---|
698 | |
---|
699 | poly gnc_mm_Mult_uu(int *F,int jG,int bG, const ring r) |
---|
700 | /* f=mono(F),g=(x_iG)^bG */ |
---|
701 | { |
---|
702 | poly out=NULL; |
---|
703 | int i; |
---|
704 | number num=NULL; |
---|
705 | |
---|
706 | int rN=r->N; |
---|
707 | int iF=r->N; |
---|
708 | while ((F[iF]==0)&&(iF>0)) iF-- ; /* last exponent_num of F */ |
---|
709 | |
---|
710 | if (iF==0) /* F==zero vector in other words */ |
---|
711 | { |
---|
712 | out=pOne(); |
---|
713 | p_SetExp(out,jG,bG,r); |
---|
714 | p_Setm(out,r); |
---|
715 | return(out); |
---|
716 | } |
---|
717 | |
---|
718 | int jF=1; |
---|
719 | while ((F[jF]==0)&&(jF<=rN)) jF++; /* first exp of F */ |
---|
720 | |
---|
721 | if (iF<=jG) /* i.e. no mixed exp_num */ |
---|
722 | { |
---|
723 | out=pOne(); |
---|
724 | F[jG]=F[jG]+bG; |
---|
725 | p_SetExpV(out,F,r); |
---|
726 | p_Setm(out,r); |
---|
727 | return(out); |
---|
728 | } |
---|
729 | |
---|
730 | if (iF==jF) /* uni times uni */ |
---|
731 | { |
---|
732 | out=gnc_uu_Mult_ww(iF,F[iF],jG,bG,r); |
---|
733 | return(out); |
---|
734 | } |
---|
735 | |
---|
736 | /* Now: F is mono with >=2 exponents, jG<iF */ |
---|
737 | /* check the quasi-commutative case */ |
---|
738 | // matrix LCOM=r->GetNC()->COM; |
---|
739 | // number rescoef=n_Init(1,r); |
---|
740 | // number tmpcoef=n_Init(1,r); |
---|
741 | // int tmpint; |
---|
742 | // i=iF; |
---|
743 | // while (i>=jG+1) |
---|
744 | // /* all the non-zero exponents */ |
---|
745 | // { |
---|
746 | // if (MATELEM(LCOM,jG,i)!=NULL) |
---|
747 | // { |
---|
748 | // tmpcoef=pGetCoeff(MATELEM(LCOM,jG,i)); |
---|
749 | // tmpint=(int)F[i]; |
---|
750 | // nPower(tmpcoef,F[i],&tmpcoef); |
---|
751 | // rescoef=nMult(rescoef,tmpcoef); |
---|
752 | // i--; |
---|
753 | // } |
---|
754 | // else |
---|
755 | // { |
---|
756 | // if (F[i]!=0) break; |
---|
757 | // } |
---|
758 | // } |
---|
759 | // if (iF==i) |
---|
760 | // /* no action took place*/ |
---|
761 | // { |
---|
762 | |
---|
763 | // } |
---|
764 | // else /* power the result up to bG */ |
---|
765 | // { |
---|
766 | // nPower(rescoef,bG,&rescoef); |
---|
767 | // /* + cleanup, post-processing */ |
---|
768 | // } |
---|
769 | |
---|
770 | int *Prv=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
771 | int *Nxt=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
772 | int *lF=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
773 | |
---|
774 | int cnt=0; int cnf=0; |
---|
775 | /* splitting F wrt jG */ |
---|
776 | for (i=1;i<=jG;i++) /* mult at the very end */ |
---|
777 | { |
---|
778 | Prv[i]=F[i]; Nxt[i]=0; |
---|
779 | if (F[i]!=0) cnf++; |
---|
780 | } |
---|
781 | |
---|
782 | if (cnf==0) |
---|
783 | { |
---|
784 | freeT(Prv,rN); Prv = NULL; |
---|
785 | } |
---|
786 | |
---|
787 | for (i=jG+1;i<=rN;i++) |
---|
788 | { |
---|
789 | Nxt[i]=F[i]; |
---|
790 | if (cnf!=0) { Prv[i]=0;} |
---|
791 | if (F[i]!=0) |
---|
792 | { |
---|
793 | cnt++; |
---|
794 | lF[cnt]=i; |
---|
795 | } /* eff_part,lF_for_F */ |
---|
796 | } |
---|
797 | |
---|
798 | if (cnt==1) /* Nxt consists of 1 nonzero el-t only */ |
---|
799 | { |
---|
800 | int q=lF[1]; |
---|
801 | poly Rout=pOne(); |
---|
802 | out=gnc_uu_Mult_ww(q,Nxt[q],jG,bG,r); |
---|
803 | |
---|
804 | freeT(Nxt,rN); Nxt = NULL; |
---|
805 | |
---|
806 | if (cnf!=0) |
---|
807 | { |
---|
808 | Prv[0]=0; |
---|
809 | p_SetExpV(Rout,Prv,r); |
---|
810 | p_Setm(Rout,r); |
---|
811 | |
---|
812 | #ifdef PDEBUG |
---|
813 | p_Test(Rout,r); |
---|
814 | #endif |
---|
815 | |
---|
816 | freeT(Prv,rN); |
---|
817 | Prv = NULL; |
---|
818 | |
---|
819 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
820 | } |
---|
821 | |
---|
822 | freeT(lF,rN); |
---|
823 | lF = NULL; |
---|
824 | |
---|
825 | p_Delete(&Rout,r); |
---|
826 | |
---|
827 | assume(Nxt == NULL); |
---|
828 | assume(lF == NULL); |
---|
829 | assume(Prv == NULL); |
---|
830 | |
---|
831 | return (out); |
---|
832 | } |
---|
833 | /* -------------------- MAIN ACTION --------------------- */ |
---|
834 | |
---|
835 | poly D=NULL; |
---|
836 | poly Rout=NULL; |
---|
837 | number *c=(number *)omAlloc0((cnt+2)*sizeof(number)); |
---|
838 | c[cnt+1]=n_Init(1,r); |
---|
839 | i=cnt+2; /* later in freeN */ |
---|
840 | int *Op=Nxt; |
---|
841 | |
---|
842 | int *On=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
843 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
844 | |
---|
845 | |
---|
846 | // pExpVectorCopy(U,Nxt); |
---|
847 | memcpy(U, Nxt,(rN+1)*sizeof(int)); |
---|
848 | U[jG] = U[jG] + bG; |
---|
849 | |
---|
850 | /* Op=Nxt and initial On=(0); */ |
---|
851 | Nxt=NULL; |
---|
852 | |
---|
853 | poly Pp; |
---|
854 | poly Pn; |
---|
855 | int t=0; |
---|
856 | int first=lF[1]; |
---|
857 | int nlast=lF[cnt]; |
---|
858 | int kk=0; |
---|
859 | /* cnt--; */ |
---|
860 | /* now lF[cnt] should be <=iF-1 */ |
---|
861 | |
---|
862 | while (Op[first]!=0) |
---|
863 | { |
---|
864 | t=lF[cnt]; /* cnt as it was computed */ |
---|
865 | |
---|
866 | poly w=gnc_uu_Mult_ww(t,Op[t],jG,bG,r); |
---|
867 | c[cnt]=n_Copy(p_GetCoeff(w,r),r); |
---|
868 | D = pNext(w); /* getting coef and rest D */ |
---|
869 | p_DeleteLm(&w,r); |
---|
870 | w=NULL; |
---|
871 | |
---|
872 | Op[t]= 0; |
---|
873 | Pp=pOne(); |
---|
874 | p_SetExpV(Pp,Op,r); |
---|
875 | p_Setm(Pp,r); |
---|
876 | |
---|
877 | if (t<nlast) |
---|
878 | { |
---|
879 | kk=lF[cnt+1]; |
---|
880 | On[kk]=F[kk]; |
---|
881 | |
---|
882 | Pn=pOne(); |
---|
883 | p_SetExpV(Pn,On,r); |
---|
884 | p_Setm(Pn,r); |
---|
885 | |
---|
886 | if (t!=first) /* typical expr */ |
---|
887 | { |
---|
888 | w=gnc_p_Mult_mm(D,Pn,r); |
---|
889 | Rout=gnc_mm_Mult_p(Pp,w,r); |
---|
890 | w=NULL; |
---|
891 | } |
---|
892 | else /* last step */ |
---|
893 | { |
---|
894 | On[t]=0; |
---|
895 | p_SetExpV(Pn,On,r); |
---|
896 | p_Setm(Pn,r); |
---|
897 | Rout=gnc_p_Mult_mm(D,Pn,r); |
---|
898 | } |
---|
899 | #ifdef PDEBUG |
---|
900 | p_Test(Pp,r); |
---|
901 | #endif |
---|
902 | p_Delete(&Pn,r); |
---|
903 | } |
---|
904 | else /* first step */ |
---|
905 | { |
---|
906 | Rout=gnc_mm_Mult_p(Pp,D,r); |
---|
907 | } |
---|
908 | #ifdef PDEBUG |
---|
909 | p_Test(Pp,r); |
---|
910 | #endif |
---|
911 | p_Delete(&Pp,r); |
---|
912 | num=n_Mult(c[cnt+1],c[cnt],r); |
---|
913 | n_Delete(&c[cnt],r); |
---|
914 | c[cnt]=num; |
---|
915 | Rout=p_Mult_nn(Rout,c[cnt+1],r); /* Rest is ready */ |
---|
916 | out=p_Add_q(out,Rout,r); |
---|
917 | Pp=NULL; |
---|
918 | cnt--; |
---|
919 | } |
---|
920 | /* only to feel safe:*/ |
---|
921 | Pn=Pp=NULL; |
---|
922 | freeT(On,rN); |
---|
923 | freeT(Op,rN); |
---|
924 | |
---|
925 | /* leadterm and Prv-part with coef 1 */ |
---|
926 | /* U[0]=exp; */ |
---|
927 | /* U[jG]=U[jG]+bG; */ |
---|
928 | /* make leadterm */ |
---|
929 | /* ??????????? we have done it already :-0 */ |
---|
930 | |
---|
931 | Rout=pOne(); |
---|
932 | p_SetExpV(Rout,U,r); |
---|
933 | p_Setm(Rout,r); /* use again this name */ |
---|
934 | p_SetCoeff(Rout,c[cnt+1],r); /* last computed coef */ |
---|
935 | |
---|
936 | out=p_Add_q(out,Rout,r); |
---|
937 | |
---|
938 | Rout=NULL; |
---|
939 | |
---|
940 | freeT(U, rN); |
---|
941 | freeN(c, i); |
---|
942 | freeT(lF, rN); |
---|
943 | |
---|
944 | if (cnf!=0) |
---|
945 | { |
---|
946 | Rout=pOne(); |
---|
947 | p_SetExpV(Rout,Prv,r); |
---|
948 | p_Setm(Rout,r); |
---|
949 | freeT(Prv, rN); |
---|
950 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
951 | p_Delete(&Rout,r); |
---|
952 | } |
---|
953 | |
---|
954 | return (out); |
---|
955 | } |
---|
956 | |
---|
957 | poly gnc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r) |
---|
958 | { |
---|
959 | int k,m; |
---|
960 | int rN=r->N; |
---|
961 | matrix cMT=r->GetNC()->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
962 | |
---|
963 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r); |
---|
964 | /* var(j); */ |
---|
965 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); |
---|
966 | /*var(i); for convenience */ |
---|
967 | #ifdef PDEBUG |
---|
968 | p_Test(x,r); |
---|
969 | p_Test(y,r); |
---|
970 | #endif |
---|
971 | poly t=NULL; |
---|
972 | /* ------------ Main Cycles ----------------------------*/ |
---|
973 | |
---|
974 | for (k=2;k<=a;k++) |
---|
975 | { |
---|
976 | t = nc_p_CopyGet(MATELEM(cMT,k,1),r); |
---|
977 | |
---|
978 | if (t==NULL) /* not computed yet */ |
---|
979 | { |
---|
980 | t = nc_p_CopyGet(MATELEM(cMT,k-1,1),r); |
---|
981 | // t=p_Copy(MATELEM(cMT,k-1,1),r); |
---|
982 | t = gnc_mm_Mult_p(y,t,r); |
---|
983 | MATELEM(cMT,k,1) = nc_p_CopyPut(t,r); |
---|
984 | // omCheckAddr(cMT->m); |
---|
985 | p_Delete(&t,r); |
---|
986 | } |
---|
987 | t=NULL; |
---|
988 | } |
---|
989 | |
---|
990 | for (m=2;m<=b;m++) |
---|
991 | { |
---|
992 | t = nc_p_CopyGet(MATELEM(cMT,a,m),r); |
---|
993 | // t=MATELEM(cMT,a,m); |
---|
994 | if (t==NULL) //not computed yet |
---|
995 | { |
---|
996 | t = nc_p_CopyGet(MATELEM(cMT,a,m-1),r); |
---|
997 | // t=p_Copy(MATELEM(cMT,a,m-1),r); |
---|
998 | t = gnc_p_Mult_mm(t,x,r); |
---|
999 | MATELEM(cMT,a,m) = nc_p_CopyPut(t,r); |
---|
1000 | // MATELEM(cMT,a,m) = t; |
---|
1001 | // omCheckAddr(cMT->m); |
---|
1002 | p_Delete(&t,r); |
---|
1003 | } |
---|
1004 | t=NULL; |
---|
1005 | } |
---|
1006 | p_Delete(&x,r); |
---|
1007 | p_Delete(&y,r); |
---|
1008 | // t=MATELEM(cMT,a,b); |
---|
1009 | t= nc_p_CopyGet(MATELEM(cMT,a,b),r); |
---|
1010 | // return(p_Copy(t,r)); |
---|
1011 | /* since the last computed element was cMT[a,b] */ |
---|
1012 | return(t); |
---|
1013 | } |
---|
1014 | |
---|
1015 | |
---|
1016 | static inline poly gnc_uu_Mult_ww_formula (int i, int a, int j, int b, const ring r) |
---|
1017 | { |
---|
1018 | if(bNoFormula) |
---|
1019 | return gnc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
1020 | |
---|
1021 | CFormulaPowerMultiplier* FormulaMultiplier = GetFormulaPowerMultiplier(r); |
---|
1022 | Enum_ncSAType PairType = _ncSA_notImplemented; |
---|
1023 | |
---|
1024 | if( FormulaMultiplier != NULL ) |
---|
1025 | PairType = FormulaMultiplier->GetPair(j, i); |
---|
1026 | |
---|
1027 | |
---|
1028 | if( PairType == _ncSA_notImplemented ) |
---|
1029 | return gnc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
1030 | |
---|
1031 | |
---|
1032 | // return FormulaMultiplier->Multiply(j, i, b, a); |
---|
1033 | poly t = CFormulaPowerMultiplier::Multiply( PairType, j, i, b, a, r); |
---|
1034 | |
---|
1035 | int rN=r->N; |
---|
1036 | matrix cMT = r->GetNC()->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
1037 | |
---|
1038 | |
---|
1039 | MATELEM(cMT, a, b) = nc_p_CopyPut(t,r); |
---|
1040 | |
---|
1041 | // t=MATELEM(cMT,a,b); |
---|
1042 | // t= nc_p_CopyGet(MATELEM(cMT,a,b),r); |
---|
1043 | // return(p_Copy(t,r)); |
---|
1044 | /* since the last computed element was cMT[a,b] */ |
---|
1045 | return(t); |
---|
1046 | } |
---|
1047 | |
---|
1048 | |
---|
1049 | poly gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r) |
---|
1050 | /* (x_i)^a times (x_j)^b */ |
---|
1051 | /* x_i = y, x_j = x ! */ |
---|
1052 | { |
---|
1053 | /* Check zero exceptions, (q-)commutativity and is there something to do? */ |
---|
1054 | assume(a!=0); |
---|
1055 | assume(b!=0); |
---|
1056 | poly out=pOne(); |
---|
1057 | if (i<=j) |
---|
1058 | { |
---|
1059 | p_SetExp(out,i,a,r); |
---|
1060 | p_AddExp(out,j,b,r); |
---|
1061 | p_Setm(out,r); |
---|
1062 | return(out); |
---|
1063 | }/* zero exeptions and usual case */ |
---|
1064 | /* if ((a==0)||(b==0)||(i<=j)) return(out); */ |
---|
1065 | |
---|
1066 | if (MATELEM(r->GetNC()->COM,j,i)!=NULL) |
---|
1067 | /* commutative or quasicommutative case */ |
---|
1068 | { |
---|
1069 | p_SetExp(out,i,a,r); |
---|
1070 | p_AddExp(out,j,b,r); |
---|
1071 | p_Setm(out,r); |
---|
1072 | if (r->cf->nIsOne(p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r))) /* commutative case */ |
---|
1073 | { |
---|
1074 | return(out); |
---|
1075 | } |
---|
1076 | else |
---|
1077 | { |
---|
1078 | number tmp_number=p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r); /* quasicommutative case */ |
---|
1079 | nPower(tmp_number,a*b,&tmp_number); // BUG! ;-( |
---|
1080 | p_SetCoeff(out,tmp_number,r); |
---|
1081 | return(out); |
---|
1082 | } |
---|
1083 | }/* end_of commutative or quasicommutative case */ |
---|
1084 | p_Delete(&out,r); |
---|
1085 | |
---|
1086 | |
---|
1087 | if(bNoCache && !bNoFormula) // don't use cache whenever possible! |
---|
1088 | { // without cache!? |
---|
1089 | CFormulaPowerMultiplier* FormulaMultiplier = GetFormulaPowerMultiplier(r); |
---|
1090 | Enum_ncSAType PairType = _ncSA_notImplemented; |
---|
1091 | |
---|
1092 | if( FormulaMultiplier != NULL ) |
---|
1093 | PairType = FormulaMultiplier->GetPair(j, i); |
---|
1094 | |
---|
1095 | if( PairType != _ncSA_notImplemented ) |
---|
1096 | // // return FormulaMultiplier->Multiply(j, i, b, a); |
---|
1097 | return CFormulaPowerMultiplier::Multiply( PairType, j, i, b, a, r); |
---|
1098 | } |
---|
1099 | |
---|
1100 | |
---|
1101 | /* we are here if i>j and variables do not commute or quasicommute */ |
---|
1102 | /* in fact, now a>=1 and b>=1; and j<i */ |
---|
1103 | /* now check whether the polynomial is already computed */ |
---|
1104 | int rN=r->N; |
---|
1105 | int vik = UPMATELEM(j,i,rN); |
---|
1106 | int cMTsize=r->GetNC()->MTsize[vik]; |
---|
1107 | int newcMTsize=0; |
---|
1108 | newcMTsize=si_max(a,b); |
---|
1109 | |
---|
1110 | if (newcMTsize<=cMTsize) |
---|
1111 | { |
---|
1112 | out = nc_p_CopyGet(MATELEM(r->GetNC()->MT[vik],a,b),r); |
---|
1113 | if (out !=NULL) return (out); |
---|
1114 | } |
---|
1115 | int k,m; |
---|
1116 | if (newcMTsize > cMTsize) |
---|
1117 | { |
---|
1118 | int inM=(((newcMTsize+6)/7)*7); |
---|
1119 | assume (inM>=newcMTsize); |
---|
1120 | newcMTsize = inM; |
---|
1121 | // matrix tmp = (matrix)omAlloc0(inM*inM*sizeof(poly)); |
---|
1122 | matrix tmp = mpNew(newcMTsize,newcMTsize); |
---|
1123 | |
---|
1124 | for (k=1;k<=cMTsize;k++) |
---|
1125 | { |
---|
1126 | for (m=1;m<=cMTsize;m++) |
---|
1127 | { |
---|
1128 | out = MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m); |
---|
1129 | if ( out != NULL ) |
---|
1130 | { |
---|
1131 | MATELEM(tmp,k,m) = out;/*MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m)*/ |
---|
1132 | // omCheckAddr(tmp->m); |
---|
1133 | MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m)=NULL; |
---|
1134 | // omCheckAddr(r->GetNC()->MT[UPMATELEM(j,i,rN)]->m); |
---|
1135 | out=NULL; |
---|
1136 | } |
---|
1137 | } |
---|
1138 | } |
---|
1139 | id_Delete((ideal *)&(r->GetNC()->MT[UPMATELEM(j,i,rN)]),r); |
---|
1140 | r->GetNC()->MT[UPMATELEM(j,i,rN)] = tmp; |
---|
1141 | tmp=NULL; |
---|
1142 | r->GetNC()->MTsize[UPMATELEM(j,i,rN)] = newcMTsize; |
---|
1143 | } |
---|
1144 | /* The update of multiplication matrix is finished */ |
---|
1145 | |
---|
1146 | |
---|
1147 | return gnc_uu_Mult_ww_formula(i, a, j, b, r); |
---|
1148 | |
---|
1149 | out = gnc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
1150 | // out = nc_uu_Mult_ww_horvert(i, a, j, b, r); |
---|
1151 | return(out); |
---|
1152 | } |
---|
1153 | |
---|
1154 | poly gnc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r) |
---|
1155 | |
---|
1156 | { |
---|
1157 | int k,m; |
---|
1158 | int rN=r->N; |
---|
1159 | matrix cMT=r->GetNC()->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
1160 | |
---|
1161 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r);/* var(j); */ |
---|
1162 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); /*var(i); for convenience */ |
---|
1163 | #ifdef PDEBUG |
---|
1164 | p_Test(x,r); |
---|
1165 | p_Test(y,r); |
---|
1166 | #endif |
---|
1167 | |
---|
1168 | poly t=NULL; |
---|
1169 | |
---|
1170 | int toXY; |
---|
1171 | int toYX; |
---|
1172 | |
---|
1173 | if (a==1) /* y*x^b, b>=2 */ |
---|
1174 | { |
---|
1175 | toXY=b-1; |
---|
1176 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=2)) toXY--; |
---|
1177 | for (m=toXY+1;m<=b;m++) |
---|
1178 | { |
---|
1179 | t=MATELEM(cMT,1,m); |
---|
1180 | if (t==NULL) /* remove after debug */ |
---|
1181 | { |
---|
1182 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
1183 | t = gnc_p_Mult_mm(t,x,r); |
---|
1184 | MATELEM(cMT,1,m) = t; |
---|
1185 | /* omCheckAddr(cMT->m); */ |
---|
1186 | } |
---|
1187 | else |
---|
1188 | { |
---|
1189 | /* Error, should never get there */ |
---|
1190 | WarnS("Error: a=1; MATELEM!=0"); |
---|
1191 | } |
---|
1192 | t=NULL; |
---|
1193 | } |
---|
1194 | return(p_Copy(MATELEM(cMT,1,b),r)); |
---|
1195 | } |
---|
1196 | |
---|
1197 | if (b==1) /* y^a*x, a>=2 */ |
---|
1198 | { |
---|
1199 | toYX=a-1; |
---|
1200 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=2)) toYX--; |
---|
1201 | for (m=toYX+1;m<=a;m++) |
---|
1202 | { |
---|
1203 | t=MATELEM(cMT,m,1); |
---|
1204 | if (t==NULL) /* remove after debug */ |
---|
1205 | { |
---|
1206 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
1207 | t = gnc_mm_Mult_p(y,t,r); |
---|
1208 | MATELEM(cMT,m,1) = t; |
---|
1209 | /* omCheckAddr(cMT->m); */ |
---|
1210 | } |
---|
1211 | else |
---|
1212 | { |
---|
1213 | /* Error, should never get there */ |
---|
1214 | WarnS("Error: b=1, MATELEM!=0"); |
---|
1215 | } |
---|
1216 | t=NULL; |
---|
1217 | } |
---|
1218 | return(p_Copy(MATELEM(cMT,a,1),r)); |
---|
1219 | } |
---|
1220 | |
---|
1221 | /* ------------ Main Cycles ----------------------------*/ |
---|
1222 | /* a>1, b>1 */ |
---|
1223 | |
---|
1224 | int dXY=0; int dYX=0; |
---|
1225 | /* dXY = distance for computing x-mult, then y-mult */ |
---|
1226 | /* dYX = distance for computing y-mult, then x-mult */ |
---|
1227 | int toX=a-1; int toY=b-1; /* toX = to axe X, toY = to axe Y */ |
---|
1228 | toXY=b-1; toYX=a-1; |
---|
1229 | /* if toX==0, toXY = dist. to computed y * x^toXY */ |
---|
1230 | /* if toY==0, toYX = dist. to computed y^toYX * x */ |
---|
1231 | while ( (MATELEM(cMT,toX,b)==NULL) && (toX>=1)) toX--; |
---|
1232 | if (toX==0) /* the whole column is not computed yet */ |
---|
1233 | { |
---|
1234 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=1)) toXY--; |
---|
1235 | /* toXY >=1 */ |
---|
1236 | dXY=b-1-toXY; |
---|
1237 | } |
---|
1238 | dXY=dXY+a-toX; /* the distance to nearest computed y^toX x^b */ |
---|
1239 | |
---|
1240 | while ( (MATELEM(cMT,a,toY)==NULL) && (toY>=1)) toY--; |
---|
1241 | if (toY==0) /* the whole row is not computed yet */ |
---|
1242 | { |
---|
1243 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=1)) toYX--; |
---|
1244 | /* toYX >=1 */ |
---|
1245 | dYX=a-1-toYX; |
---|
1246 | } |
---|
1247 | dYX=dYX+b-toY; /* the distance to nearest computed y^a x^toY */ |
---|
1248 | |
---|
1249 | if (dYX>=dXY) |
---|
1250 | { |
---|
1251 | /* first x, then y */ |
---|
1252 | if (toX==0) /* start with the row*/ |
---|
1253 | { |
---|
1254 | for (m=toXY+1;m<=b;m++) |
---|
1255 | { |
---|
1256 | t=MATELEM(cMT,1,m); |
---|
1257 | if (t==NULL) /* remove after debug */ |
---|
1258 | { |
---|
1259 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
1260 | t = gnc_p_Mult_mm(t,x,r); |
---|
1261 | MATELEM(cMT,1,m) = t; |
---|
1262 | /* omCheckAddr(cMT->m); */ |
---|
1263 | } |
---|
1264 | else |
---|
1265 | { |
---|
1266 | /* Error, should never get there */ |
---|
1267 | WarnS("dYX>=dXY,toXY; MATELEM==0"); |
---|
1268 | } |
---|
1269 | t=NULL; |
---|
1270 | } |
---|
1271 | toX=1; /* y*x^b is computed */ |
---|
1272 | } |
---|
1273 | /* Now toX>=1 */ |
---|
1274 | for (k=toX+1;k<=a;k++) |
---|
1275 | { |
---|
1276 | t=MATELEM(cMT,k,b); |
---|
1277 | if (t==NULL) /* remove after debug */ |
---|
1278 | { |
---|
1279 | t = p_Copy(MATELEM(cMT,k-1,b),r); |
---|
1280 | t = gnc_mm_Mult_p(y,t,r); |
---|
1281 | MATELEM(cMT,k,b) = t; |
---|
1282 | /* omCheckAddr(cMT->m); */ |
---|
1283 | } |
---|
1284 | else |
---|
1285 | { |
---|
1286 | /* Error, should never get there */ |
---|
1287 | WarnS("dYX>=dXY,toX; MATELEM==0"); |
---|
1288 | } |
---|
1289 | t=NULL; |
---|
1290 | } |
---|
1291 | } /* endif (dYX>=dXY) */ |
---|
1292 | |
---|
1293 | |
---|
1294 | if (dYX<dXY) |
---|
1295 | { |
---|
1296 | /* first y, then x */ |
---|
1297 | if (toY==0) /* start with the column*/ |
---|
1298 | { |
---|
1299 | for (m=toYX+1;m<=a;m++) |
---|
1300 | { |
---|
1301 | t=MATELEM(cMT,m,1); |
---|
1302 | if (t==NULL) /* remove after debug */ |
---|
1303 | { |
---|
1304 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
1305 | t = gnc_mm_Mult_p(y,t,r); |
---|
1306 | MATELEM(cMT,m,1) = t; |
---|
1307 | /* omCheckAddr(cMT->m); */ |
---|
1308 | } |
---|
1309 | else |
---|
1310 | { |
---|
1311 | /* Error, should never get there */ |
---|
1312 | WarnS("dYX<dXY,toYX; MATELEM==0"); |
---|
1313 | } |
---|
1314 | t=NULL; |
---|
1315 | } |
---|
1316 | toY=1; /* y^a*x is computed */ |
---|
1317 | } |
---|
1318 | /* Now toY>=1 */ |
---|
1319 | for (k=toY+1;k<=b;k++) |
---|
1320 | { |
---|
1321 | t=MATELEM(cMT,a,k); |
---|
1322 | if (t==NULL) /* remove after debug */ |
---|
1323 | { |
---|
1324 | t = p_Copy(MATELEM(cMT,a,k-1),r); |
---|
1325 | t = gnc_p_Mult_mm(t,x,r); |
---|
1326 | MATELEM(cMT,a,k) = t; |
---|
1327 | /* omCheckAddr(cMT->m); */ |
---|
1328 | } |
---|
1329 | else |
---|
1330 | { |
---|
1331 | /* Error, should never get there */ |
---|
1332 | WarnS("dYX<dXY,toY; MATELEM==0"); |
---|
1333 | } |
---|
1334 | t=NULL; |
---|
1335 | } |
---|
1336 | } /* endif (dYX<dXY) */ |
---|
1337 | |
---|
1338 | p_Delete(&x,r); |
---|
1339 | p_Delete(&y,r); |
---|
1340 | t=p_Copy(MATELEM(cMT,a,b),r); |
---|
1341 | return(t); /* since the last computed element was cMT[a,b] */ |
---|
1342 | } |
---|
1343 | |
---|
1344 | |
---|
1345 | /* ----------------------------- Syzygies ---------------------- */ |
---|
1346 | |
---|
1347 | /*2 |
---|
1348 | * reduction of p2 with p1 |
---|
1349 | * do not destroy p1, but p2 |
---|
1350 | * p1 divides p2 -> for use in NF algorithm |
---|
1351 | */ |
---|
1352 | poly gnc_ReduceSpolyOld(const poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1353 | { |
---|
1354 | assume(p_LmDivisibleBy(p1, p2, r)); |
---|
1355 | |
---|
1356 | #ifdef PDEBUG |
---|
1357 | if (p_GetComp(p1,r)!=p_GetComp(p2,r) |
---|
1358 | && (p_GetComp(p1,r)!=0) |
---|
1359 | && (p_GetComp(p2,r)!=0)) |
---|
1360 | { |
---|
1361 | dReportError("nc_ReduceSpolyOld: different components"); |
---|
1362 | return(NULL); |
---|
1363 | } |
---|
1364 | #endif |
---|
1365 | poly m = pOne(); |
---|
1366 | p_ExpVectorDiff(m,p2,p1,r); |
---|
1367 | //p_Setm(m,r); |
---|
1368 | #ifdef PDEBUG |
---|
1369 | p_Test(m,r); |
---|
1370 | #endif |
---|
1371 | /* pSetComp(m,r)=0? */ |
---|
1372 | poly N = nc_mm_Mult_p(m, p_Head(p1,r), r); |
---|
1373 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
1374 | number cF = n_Copy( p_GetCoeff(p2, r),r); |
---|
1375 | /* GCD stuff */ |
---|
1376 | number cG = nGcd(C, cF, r); |
---|
1377 | if ( !nEqual(cG, n_Init(1,r) ) ) |
---|
1378 | { |
---|
1379 | cF = nDiv(cF, cG); |
---|
1380 | C = nDiv(C, cG); |
---|
1381 | } |
---|
1382 | p2 = p_Mult_nn(p2, C, r); |
---|
1383 | poly out = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
1384 | N = p_Add_q(N, out, r); |
---|
1385 | p_Test(p2,r); |
---|
1386 | p_Test(N,r); |
---|
1387 | number MinusOne = n_Init(-1,r); |
---|
1388 | if (!n_Equal(cF,MinusOne,r)) |
---|
1389 | { |
---|
1390 | cF = n_Neg(cF,r); |
---|
1391 | N = p_Mult_nn(N, cF, r); |
---|
1392 | p_Test(N,r); |
---|
1393 | } |
---|
1394 | out = p_Add_q(p2,N,r); |
---|
1395 | p_Test(out,r); |
---|
1396 | if ( out!=NULL ) pContent(out); |
---|
1397 | p_Delete(&m,r); |
---|
1398 | n_Delete(&cF,r); |
---|
1399 | n_Delete(&C,r); |
---|
1400 | n_Delete(&MinusOne,r); |
---|
1401 | return(out); |
---|
1402 | |
---|
1403 | } |
---|
1404 | |
---|
1405 | poly gnc_ReduceSpolyNew(const poly p1, poly p2, const ring r) |
---|
1406 | { |
---|
1407 | assume(p_LmDivisibleBy(p1, p2, r)); |
---|
1408 | |
---|
1409 | const long lCompP1 = p_GetComp(p1,r); |
---|
1410 | const long lCompP2 = p_GetComp(p2,r); |
---|
1411 | |
---|
1412 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
1413 | { |
---|
1414 | #ifdef PDEBUG |
---|
1415 | Werror("gnc_ReduceSpolyNew: different non-zero components!"); |
---|
1416 | #endif |
---|
1417 | return(NULL); |
---|
1418 | } |
---|
1419 | |
---|
1420 | poly m = pOne(); |
---|
1421 | p_ExpVectorDiff(m, p2, p1, r); |
---|
1422 | //p_Setm(m,r); |
---|
1423 | #ifdef PDEBUG |
---|
1424 | p_Test(m,r); |
---|
1425 | #endif |
---|
1426 | |
---|
1427 | /* pSetComp(m,r)=0? */ |
---|
1428 | poly N = nc_mm_Mult_p(m, p_Head(p1,r), r); |
---|
1429 | |
---|
1430 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
1431 | number cF = n_Copy( p_GetCoeff(p2, r), r); |
---|
1432 | |
---|
1433 | /* GCD stuff */ |
---|
1434 | number cG = nGcd(C, cF, r); |
---|
1435 | |
---|
1436 | if (!n_IsOne(cG, r)) |
---|
1437 | { |
---|
1438 | cF = n_Div(cF, cG, r); |
---|
1439 | C = n_Div(C, cG, r); |
---|
1440 | } |
---|
1441 | |
---|
1442 | p2 = p_Mult_nn(p2, C, r); // p2 !!! |
---|
1443 | p_Test(p2,r); |
---|
1444 | n_Delete(&C,r); |
---|
1445 | |
---|
1446 | poly out = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
1447 | p_Delete(&m,r); |
---|
1448 | |
---|
1449 | N = p_Add_q(N, out, r); |
---|
1450 | p_Test(N,r); |
---|
1451 | |
---|
1452 | if (!n_IsMOne(cF,r)) // ??? |
---|
1453 | { |
---|
1454 | cF = n_Neg(cF,r); |
---|
1455 | N = p_Mult_nn(N, cF, r); |
---|
1456 | p_Test(N,r); |
---|
1457 | } |
---|
1458 | |
---|
1459 | out = p_Add_q(p2,N,r); // delete N, p2 |
---|
1460 | p_Test(out,r); |
---|
1461 | if ( out!=NULL ) pContent(out); |
---|
1462 | n_Delete(&cF,r); |
---|
1463 | return(out); |
---|
1464 | } |
---|
1465 | |
---|
1466 | |
---|
1467 | /*4 |
---|
1468 | * creates the S-polynomial of p1 and p2 |
---|
1469 | * do not destroy p1 and p2 |
---|
1470 | */ |
---|
1471 | poly gnc_CreateSpolyOld(poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1472 | { |
---|
1473 | #ifdef PDEBUG |
---|
1474 | if ((p_GetComp(p1,r)!=p_GetComp(p2,r)) |
---|
1475 | && (p_GetComp(p1,r)!=0) |
---|
1476 | && (p_GetComp(p2,r)!=0)) |
---|
1477 | { |
---|
1478 | dReportError("gnc_CreateSpolyOld : different components!"); |
---|
1479 | return(NULL); |
---|
1480 | } |
---|
1481 | #endif |
---|
1482 | if ((ncRingType(r)==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
1483 | { |
---|
1484 | return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
1485 | } |
---|
1486 | poly pL=pOne(); |
---|
1487 | poly m1=pOne(); |
---|
1488 | poly m2=pOne(); |
---|
1489 | pLcm(p1,p2,pL); |
---|
1490 | p_Setm(pL,r); |
---|
1491 | #ifdef PDEBUG |
---|
1492 | p_Test(pL,r); |
---|
1493 | #endif |
---|
1494 | p_ExpVectorDiff(m1,pL,p1,r); |
---|
1495 | //p_SetComp(m1,0,r); |
---|
1496 | //p_Setm(m1,r); |
---|
1497 | #ifdef PDEBUG |
---|
1498 | p_Test(m1,r); |
---|
1499 | #endif |
---|
1500 | p_ExpVectorDiff(m2,pL,p2,r); |
---|
1501 | //p_SetComp(m2,0,r); |
---|
1502 | //p_Setm(m2,r); |
---|
1503 | #ifdef PDEBUG |
---|
1504 | p_Test(m2,r); |
---|
1505 | #endif |
---|
1506 | p_Delete(&pL,r); |
---|
1507 | /* zero exponents ! */ |
---|
1508 | poly M1 = nc_mm_Mult_p(m1,p_Head(p1,r),r); |
---|
1509 | number C1 = n_Copy(p_GetCoeff(M1,r),r); |
---|
1510 | poly M2 = nc_mm_Mult_p(m2,p_Head(p2,r),r); |
---|
1511 | number C2 = n_Copy(p_GetCoeff(M2,r),r); |
---|
1512 | /* GCD stuff */ |
---|
1513 | number C = nGcd(C1,C2,r); |
---|
1514 | if (!nEqual(C,n_Init(1,r))) |
---|
1515 | { |
---|
1516 | C1=nDiv(C1,C); |
---|
1517 | C2=nDiv(C2,C); |
---|
1518 | } |
---|
1519 | M1=p_Mult_nn(M1,C2,r); |
---|
1520 | p_SetCoeff(m1,C2,r); |
---|
1521 | number MinusOne=n_Init(-1,r); |
---|
1522 | if (n_Equal(C1,MinusOne,r)) |
---|
1523 | { |
---|
1524 | M2=p_Add_q(M1,M2,r); |
---|
1525 | } |
---|
1526 | else |
---|
1527 | { |
---|
1528 | C1=n_Neg(C1,r); |
---|
1529 | M2=p_Mult_nn(M2,C1,r); |
---|
1530 | M2=p_Add_q(M1,M2,r); |
---|
1531 | p_SetCoeff(m2,C1,r); |
---|
1532 | } |
---|
1533 | /* M1 is killed, M2=res = C2 M1 - C1 M2 */ |
---|
1534 | poly tmp=p_Copy(p1,r); |
---|
1535 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
1536 | M1=nc_mm_Mult_p(m1,tmp,r); |
---|
1537 | tmp=p_Copy(p2,r); |
---|
1538 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
1539 | M2=p_Add_q(M2,M1,r); |
---|
1540 | M1=nc_mm_Mult_p(m2,tmp,r); |
---|
1541 | M2=p_Add_q(M2,M1,r); |
---|
1542 | p_Delete(&m1,r); |
---|
1543 | p_Delete(&m2,r); |
---|
1544 | // n_Delete(&C1,r); |
---|
1545 | // n_Delete(&C2,r); |
---|
1546 | n_Delete(&MinusOne,r); |
---|
1547 | #ifdef PDEBUG |
---|
1548 | p_Test(M2,r); |
---|
1549 | #endif |
---|
1550 | if (M2!=NULL) pCleardenom(M2); |
---|
1551 | if (M2!=NULL) pContent(M2); |
---|
1552 | return(M2); |
---|
1553 | } |
---|
1554 | |
---|
1555 | poly gnc_CreateSpolyNew(poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1556 | { |
---|
1557 | assume(r == currRing); |
---|
1558 | |
---|
1559 | #ifdef PDEBUG |
---|
1560 | pTest(p1); |
---|
1561 | pTest(p2); |
---|
1562 | #if MYTEST |
---|
1563 | Print("p1: "); pWrite(p1); |
---|
1564 | Print("p2: "); pWrite(p2); |
---|
1565 | #endif |
---|
1566 | #endif |
---|
1567 | |
---|
1568 | const long lCompP1 = p_GetComp(p1,r); |
---|
1569 | const long lCompP2 = p_GetComp(p2,r); |
---|
1570 | |
---|
1571 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
1572 | { |
---|
1573 | #ifdef PDEBUG |
---|
1574 | Werror("gnc_CreateSpolyNew: different non-zero components!"); |
---|
1575 | #endif |
---|
1576 | return(NULL); |
---|
1577 | } |
---|
1578 | |
---|
1579 | #ifdef PDEBUG |
---|
1580 | if (lCompP1!=lCompP2) |
---|
1581 | { |
---|
1582 | WarnS("gnc_CreateSpolyNew: vector & poly in SPoly!"); |
---|
1583 | } |
---|
1584 | #endif |
---|
1585 | |
---|
1586 | |
---|
1587 | // if ((r->GetNC()->type==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
1588 | // { |
---|
1589 | // return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
1590 | // } |
---|
1591 | |
---|
1592 | // poly pL=p_One( r); |
---|
1593 | |
---|
1594 | poly m1=p_One( r); |
---|
1595 | poly m2=p_One( r); |
---|
1596 | |
---|
1597 | poly pL = p_Lcm(p1,p2,r); // pL = lcm( lm(p1), lm(p2) ) |
---|
1598 | |
---|
1599 | |
---|
1600 | #ifdef PDEBUG |
---|
1601 | // p_Test(pL,r); |
---|
1602 | #endif |
---|
1603 | |
---|
1604 | p_ExpVectorDiff(m1, pL, p1, r); // m1 = pL / lm(p1) |
---|
1605 | //p_SetComp(m1,0,r); |
---|
1606 | //p_Setm(m1,r); |
---|
1607 | |
---|
1608 | #ifdef PDEBUG |
---|
1609 | p_Test(m1,r); |
---|
1610 | #endif |
---|
1611 | // assume(p_GetComp(m1,r) == 0); |
---|
1612 | |
---|
1613 | p_ExpVectorDiff(m2, pL, p2, r); // m2 = pL / lm(p2) |
---|
1614 | |
---|
1615 | //p_SetComp(m2,0,r); |
---|
1616 | //p_Setm(m2,r); |
---|
1617 | #ifdef PDEBUG |
---|
1618 | p_Test(m2,r); |
---|
1619 | #endif |
---|
1620 | |
---|
1621 | #ifdef PDEBUG |
---|
1622 | #if MYTEST |
---|
1623 | Print("m1: "); pWrite(m1); |
---|
1624 | Print("m2: "); pWrite(m2); |
---|
1625 | #endif |
---|
1626 | #endif |
---|
1627 | |
---|
1628 | |
---|
1629 | // assume(p_GetComp(m2,r) == 0); |
---|
1630 | |
---|
1631 | #ifdef PDEBUG |
---|
1632 | #if 0 |
---|
1633 | if( (p_GetComp(m2,r) != 0) || (p_GetComp(m1,r) != 0) ) |
---|
1634 | { |
---|
1635 | WarnS("gnc_CreateSpolyNew: wrong monomials!"); |
---|
1636 | |
---|
1637 | |
---|
1638 | #ifdef RDEBUG |
---|
1639 | PrintS("m1 = "); p_Write(m1, r); |
---|
1640 | p_DebugPrint(m1, r); |
---|
1641 | |
---|
1642 | PrintS("m2 = "); p_Write(m2, r); |
---|
1643 | p_DebugPrint(m2, r); |
---|
1644 | |
---|
1645 | PrintS("p1 = "); p_Write(p1, r); |
---|
1646 | p_DebugPrint(p1, r); |
---|
1647 | |
---|
1648 | PrintS("p2 = "); p_Write(p2, r); |
---|
1649 | p_DebugPrint(p2, r); |
---|
1650 | |
---|
1651 | PrintS("pL = "); p_Write(pL, r); |
---|
1652 | p_DebugPrint(pL, r); |
---|
1653 | #endif |
---|
1654 | |
---|
1655 | } |
---|
1656 | |
---|
1657 | #endif |
---|
1658 | #endif |
---|
1659 | |
---|
1660 | p_Delete(&pL,r); |
---|
1661 | |
---|
1662 | /* zero exponents !? */ |
---|
1663 | poly M1 = nc_mm_Mult_p(m1,p_Head(p1,r),r); // M1 = m1 * lt(p1) |
---|
1664 | poly M2 = nc_mm_Mult_p(m2,p_Head(p2,r),r); // M2 = m2 * lt(p2) |
---|
1665 | |
---|
1666 | #ifdef PDEBUG |
---|
1667 | p_Test(M1,r); |
---|
1668 | p_Test(M2,r); |
---|
1669 | |
---|
1670 | #if MYTEST |
---|
1671 | Print("M1: "); pWrite(M1); |
---|
1672 | Print("M2: "); pWrite(M2); |
---|
1673 | #endif |
---|
1674 | #endif |
---|
1675 | |
---|
1676 | if(M1 == NULL || M2 == NULL) |
---|
1677 | { |
---|
1678 | #ifdef PDEBUG |
---|
1679 | Print("\np1 = "); |
---|
1680 | p_Write(p1, r); |
---|
1681 | |
---|
1682 | Print("m1 = "); |
---|
1683 | p_Write(m1, r); |
---|
1684 | |
---|
1685 | Print("p2 = "); |
---|
1686 | p_Write(p2, r); |
---|
1687 | |
---|
1688 | Print("m2 = "); |
---|
1689 | p_Write(m2, r); |
---|
1690 | |
---|
1691 | Werror("ERROR in nc_CreateSpoly: result of multiplication is Zero!\n"); |
---|
1692 | #endif |
---|
1693 | return(NULL); |
---|
1694 | } |
---|
1695 | |
---|
1696 | number C1 = n_Copy(p_GetCoeff(M1,r),r); // C1 = lc(M1) |
---|
1697 | number C2 = n_Copy(p_GetCoeff(M2,r),r); // C2 = lc(M2) |
---|
1698 | |
---|
1699 | /* GCD stuff */ |
---|
1700 | number C = nGcd(C1, C2, r); // C = gcd(C1, C2) |
---|
1701 | |
---|
1702 | if (!n_IsOne(C, r)) // if C != 1 |
---|
1703 | { |
---|
1704 | C1=n_Div(C1, C, r); // C1 = C1 / C |
---|
1705 | C2=n_Div(C2, C, r); // C2 = C2 / C |
---|
1706 | } |
---|
1707 | |
---|
1708 | n_Delete(&C,r); // destroy the number C |
---|
1709 | |
---|
1710 | C1=n_Neg(C1,r); |
---|
1711 | |
---|
1712 | // number MinusOne=n_Init(-1,r); |
---|
1713 | // if (n_Equal(C1,MinusOne,r)) // lc(M1) / gcd( lc(M1), lc(M2)) == -1 ???? |
---|
1714 | // { |
---|
1715 | // M2=p_Add_q(M1,M2,r); // ????? |
---|
1716 | // } |
---|
1717 | // else |
---|
1718 | // { |
---|
1719 | M1=p_Mult_nn(M1,C2,r); // M1 = (C2*lc(p1)) * (lcm(lm(p1),lm(p2)) / lm(p1)) * lm(p1) |
---|
1720 | |
---|
1721 | #ifdef PDEBUG |
---|
1722 | p_Test(M1,r); |
---|
1723 | #endif |
---|
1724 | |
---|
1725 | M2=p_Mult_nn(M2,C1,r); // M2 =(-C1*lc(p2)) * (lcm(lm(p1),lm(p2)) / lm(p2)) * lm(p2) |
---|
1726 | |
---|
1727 | |
---|
1728 | |
---|
1729 | #ifdef PDEBUG |
---|
1730 | p_Test(M2,r); |
---|
1731 | |
---|
1732 | #if MYTEST |
---|
1733 | Print("M1: "); pWrite(M1); |
---|
1734 | Print("M2: "); pWrite(M2); |
---|
1735 | #endif |
---|
1736 | #endif |
---|
1737 | |
---|
1738 | |
---|
1739 | M2=p_Add_q(M1,M2,r); // M1 is killed, M2 = spoly(lt(p1), lt(p2)) = C2*M1 - C1*M2 |
---|
1740 | |
---|
1741 | #ifdef PDEBUG |
---|
1742 | p_Test(M2,r); |
---|
1743 | |
---|
1744 | #if MYTEST |
---|
1745 | Print("M2: "); pWrite(M2); |
---|
1746 | #endif |
---|
1747 | |
---|
1748 | #endif |
---|
1749 | |
---|
1750 | // M2 == 0 for supercommutative algebras! |
---|
1751 | // } |
---|
1752 | // n_Delete(&MinusOne,r); |
---|
1753 | |
---|
1754 | p_SetCoeff(m1,C2,r); // lc(m1) = C2!!! |
---|
1755 | p_SetCoeff(m2,C1,r); // lc(m2) = C1!!! |
---|
1756 | |
---|
1757 | #ifdef PDEBUG |
---|
1758 | p_Test(m1,r); |
---|
1759 | p_Test(m2,r); |
---|
1760 | #endif |
---|
1761 | |
---|
1762 | // poly tmp = p_Copy(p1,r); // tmp = p1 |
---|
1763 | // tmp=p_LmDeleteAndNext(tmp,r); // tmp = tail(p1) |
---|
1764 | //#ifdef PDEBUG |
---|
1765 | // p_Test(tmp,r); |
---|
1766 | //#endif |
---|
1767 | |
---|
1768 | M1 = nc_mm_Mult_pp(m1, pNext(p1), r); // M1 = m1 * tail(p1), delete tmp // ??? |
---|
1769 | |
---|
1770 | #ifdef PDEBUG |
---|
1771 | p_Test(M1,r); |
---|
1772 | |
---|
1773 | #if MYTEST |
---|
1774 | Print("M1: "); pWrite(M1); |
---|
1775 | #endif |
---|
1776 | |
---|
1777 | #endif |
---|
1778 | |
---|
1779 | M2=p_Add_q(M2,M1,r); // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1), delete M1 |
---|
1780 | #ifdef PDEBUG |
---|
1781 | p_Test(M2,r); |
---|
1782 | |
---|
1783 | #if MYTEST |
---|
1784 | Print("M2: "); pWrite(M2); |
---|
1785 | #endif |
---|
1786 | |
---|
1787 | #endif |
---|
1788 | |
---|
1789 | // tmp=p_Copy(p2,r); // tmp = p2 |
---|
1790 | // tmp=p_LmDeleteAndNext(tmp,r); // tmp = tail(p2) |
---|
1791 | |
---|
1792 | //#ifdef PDEBUG |
---|
1793 | // p_Test(tmp,r); |
---|
1794 | //#endif |
---|
1795 | |
---|
1796 | M1 = nc_mm_Mult_pp(m2, pNext(p2), r); // M1 = m2 * tail(p2), detele tmp |
---|
1797 | |
---|
1798 | #ifdef PDEBUG |
---|
1799 | p_Test(M1,r); |
---|
1800 | |
---|
1801 | #if MYTEST |
---|
1802 | Print("M1: "); pWrite(M1); |
---|
1803 | #endif |
---|
1804 | |
---|
1805 | #endif |
---|
1806 | |
---|
1807 | M2 = p_Add_q(M2,M1,r); // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1) + m2*tail(p2) |
---|
1808 | |
---|
1809 | #ifdef PDEBUG |
---|
1810 | p_Test(M2,r); |
---|
1811 | |
---|
1812 | #if MYTEST |
---|
1813 | Print("M2: "); pWrite(M2); |
---|
1814 | #endif |
---|
1815 | |
---|
1816 | #endif |
---|
1817 | // delete M1 |
---|
1818 | |
---|
1819 | p_Delete(&m1,r); // => n_Delete(&C1,r); |
---|
1820 | p_Delete(&m2,r); // => n_Delete(&C2,r); |
---|
1821 | |
---|
1822 | #ifdef PDEBUG |
---|
1823 | p_Test(M2,r); |
---|
1824 | #endif |
---|
1825 | |
---|
1826 | if (M2!=NULL) pCleardenom(M2); //? |
---|
1827 | // if (M2!=NULL) pContent(M2); |
---|
1828 | |
---|
1829 | return(M2); |
---|
1830 | } |
---|
1831 | |
---|
1832 | |
---|
1833 | |
---|
1834 | |
---|
1835 | #if 0 |
---|
1836 | /*5 |
---|
1837 | * reduction of tail(q) with p1 |
---|
1838 | * lead(p1) divides lead(pNext(q2)) and pNext(q2) is reduced |
---|
1839 | * do not destroy p1, but tail(q) |
---|
1840 | */ |
---|
1841 | void gnc_ReduceSpolyTail(poly p1, poly q, poly q2, poly spNoether, const ring r) |
---|
1842 | { |
---|
1843 | poly a1=p_Head(p1,r); |
---|
1844 | poly Q=pNext(q2); |
---|
1845 | number cQ=p_GetCoeff(Q,r); |
---|
1846 | poly m=pOne(); |
---|
1847 | p_ExpVectorDiff(m,Q,p1,r); |
---|
1848 | // p_SetComp(m,0,r); |
---|
1849 | //p_Setm(m,r); |
---|
1850 | #ifdef PDEBUG |
---|
1851 | p_Test(m,r); |
---|
1852 | #endif |
---|
1853 | /* pSetComp(m,r)=0? */ |
---|
1854 | poly M = nc_mm_Mult_pp(m, p1,r); |
---|
1855 | number C=p_GetCoeff(M,r); |
---|
1856 | M=p_Add_q(M,nc_mm_Mult_p(m,p_LmDeleteAndNext(p_Copy(p1,r),r),r),r); // _pp? |
---|
1857 | q=p_Mult_nn(q,C,r); |
---|
1858 | number MinusOne=n_Init(-1,r); |
---|
1859 | if (!n_Equal(cQ,MinusOne,r)) |
---|
1860 | { |
---|
1861 | cQ=nNeg(cQ); |
---|
1862 | M=p_Mult_nn(M,cQ,r); |
---|
1863 | } |
---|
1864 | Q=p_Add_q(Q,M,r); |
---|
1865 | pNext(q2)=Q; |
---|
1866 | |
---|
1867 | p_Delete(&m,r); |
---|
1868 | n_Delete(&C,r); |
---|
1869 | n_Delete(&cQ,r); |
---|
1870 | n_Delete(&MinusOne,r); |
---|
1871 | /* return(q); */ |
---|
1872 | } |
---|
1873 | #endif |
---|
1874 | |
---|
1875 | |
---|
1876 | /*6 |
---|
1877 | * creates the commutative lcm(lm(p1),lm(p2)) |
---|
1878 | * do not destroy p1 and p2 |
---|
1879 | */ |
---|
1880 | poly nc_CreateShortSpoly(poly p1, poly p2, const ring r) |
---|
1881 | { |
---|
1882 | #ifdef PDEBUG |
---|
1883 | p_Test(p1, r); |
---|
1884 | p_Test(p2, r); |
---|
1885 | #endif |
---|
1886 | |
---|
1887 | const long lCompP1 = p_GetComp(p1,r); |
---|
1888 | const long lCompP2 = p_GetComp(p2,r); |
---|
1889 | |
---|
1890 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
1891 | { |
---|
1892 | #ifdef PDEBUG |
---|
1893 | Werror("nc_CreateShortSpoly: wrong module components!"); // !!!! |
---|
1894 | #endif |
---|
1895 | return(NULL); |
---|
1896 | } |
---|
1897 | |
---|
1898 | poly m = p_Lcm(p1, p2, si_max(lCompP1, lCompP2), r); |
---|
1899 | |
---|
1900 | // n_Delete(&p_GetCoeff(m, r), r); |
---|
1901 | // pSetCoeff0(m, NULL); |
---|
1902 | |
---|
1903 | #ifdef PDEBUG |
---|
1904 | // p_Test(m,r); |
---|
1905 | #endif |
---|
1906 | |
---|
1907 | return(m); |
---|
1908 | } |
---|
1909 | |
---|
1910 | void gnc_kBucketPolyRedOld(kBucket_pt b, poly p, number *c) |
---|
1911 | { |
---|
1912 | // b will not be multiplied by any constant in this impl. |
---|
1913 | // ==> *c=1 |
---|
1914 | *c=nInit(1); |
---|
1915 | poly m=pOne(); |
---|
1916 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
1917 | //pSetm(m); |
---|
1918 | #ifdef PDEBUG |
---|
1919 | pTest(m); |
---|
1920 | #endif |
---|
1921 | poly pp= nc_mm_Mult_pp(m,p,currRing); |
---|
1922 | assume(pp!=NULL); |
---|
1923 | pDelete(&m); |
---|
1924 | number n=nCopy(pGetCoeff(pp)); |
---|
1925 | number MinusOne=nInit(-1); |
---|
1926 | number nn; |
---|
1927 | if (!nEqual(n,MinusOne)) |
---|
1928 | { |
---|
1929 | nn=nNeg(nInvers(n)); |
---|
1930 | } |
---|
1931 | else nn=nInit(1); |
---|
1932 | nDelete(&n); |
---|
1933 | n=nMult(nn,pGetCoeff(kBucketGetLm(b))); |
---|
1934 | nDelete(&nn); |
---|
1935 | pp=p_Mult_nn(pp,n,currRing); |
---|
1936 | nDelete(&n); |
---|
1937 | nDelete(&MinusOne); |
---|
1938 | int l=pLength(pp); |
---|
1939 | kBucket_Add_q(b,pp,&l); |
---|
1940 | } |
---|
1941 | |
---|
1942 | void gnc_kBucketPolyRedNew(kBucket_pt b, poly p, number *c) |
---|
1943 | { |
---|
1944 | #ifdef PDEBUG |
---|
1945 | // Print(">*"); |
---|
1946 | #endif |
---|
1947 | |
---|
1948 | #ifdef KDEBUG |
---|
1949 | if( !kbTest(b) )Werror("nc_kBucketPolyRed: broken bucket!"); |
---|
1950 | #endif |
---|
1951 | |
---|
1952 | #ifdef PDEBUG |
---|
1953 | pTest(p); |
---|
1954 | #if MYTEST |
---|
1955 | Print("p: "); pWrite(p); |
---|
1956 | #endif |
---|
1957 | #endif |
---|
1958 | |
---|
1959 | // b will not be multiplied by any constant in this impl. |
---|
1960 | // ==> *c=1 |
---|
1961 | *c=nInit(1); |
---|
1962 | poly m = pOne(); |
---|
1963 | const poly pLmB = kBucketGetLm(b); // no new copy! |
---|
1964 | |
---|
1965 | assume( pLmB != NULL ); |
---|
1966 | |
---|
1967 | #ifdef PDEBUG |
---|
1968 | pTest(pLmB); |
---|
1969 | |
---|
1970 | #if MYTEST |
---|
1971 | Print("pLmB: "); pWrite(pLmB); |
---|
1972 | #endif |
---|
1973 | #endif |
---|
1974 | |
---|
1975 | pExpVectorDiff(m, pLmB, p); |
---|
1976 | //pSetm(m); |
---|
1977 | |
---|
1978 | #ifdef PDEBUG |
---|
1979 | pTest(m); |
---|
1980 | #if MYTEST |
---|
1981 | Print("m: "); pWrite(m); |
---|
1982 | #endif |
---|
1983 | #endif |
---|
1984 | |
---|
1985 | poly pp = nc_mm_Mult_pp(m, p, currRing); |
---|
1986 | pDelete(&m); |
---|
1987 | |
---|
1988 | assume( pp != NULL ); |
---|
1989 | const number n = pGetCoeff(pp); // bug! |
---|
1990 | number nn; |
---|
1991 | |
---|
1992 | if (!n_IsMOne(n,currRing) ) // does this improve performance??!? also see below... // TODO: check later on. |
---|
1993 | { |
---|
1994 | nn=nNeg(nInvers(nCopy(n))); |
---|
1995 | } |
---|
1996 | else nn=nInit(1); // if n == -1 => nn = 1 and -1/n otherwise |
---|
1997 | |
---|
1998 | number t = nMult(nn,pGetCoeff(pLmB)); |
---|
1999 | nDelete(&nn); |
---|
2000 | |
---|
2001 | pp = p_Mult_nn(pp,t,currRing); |
---|
2002 | nDelete(&t); |
---|
2003 | |
---|
2004 | int l = pLength(pp); |
---|
2005 | |
---|
2006 | #ifdef PDEBUG |
---|
2007 | pTest(pp); |
---|
2008 | // Print("PP: "); pWrite(pp); |
---|
2009 | #endif |
---|
2010 | |
---|
2011 | kBucket_Add_q(b,pp,&l); |
---|
2012 | |
---|
2013 | |
---|
2014 | #ifdef PDEBUG |
---|
2015 | // Print("*>"); |
---|
2016 | #endif |
---|
2017 | } |
---|
2018 | |
---|
2019 | |
---|
2020 | void gnc_kBucketPolyRed_ZOld(kBucket_pt b, poly p, number *c) |
---|
2021 | { |
---|
2022 | // b is multiplied by a constant in this impl. |
---|
2023 | poly m=pOne(); |
---|
2024 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
2025 | //pSetm(m); |
---|
2026 | #ifdef PDEBUG |
---|
2027 | pTest(m); |
---|
2028 | #endif |
---|
2029 | if(p_IsConstant(m,currRing)){ |
---|
2030 | pDelete(&m); |
---|
2031 | *c = kBucketPolyRed(b,p,pLength(p),NULL); |
---|
2032 | return; |
---|
2033 | } |
---|
2034 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
2035 | number c2,cc; |
---|
2036 | pCleardenom_n(pp,c2); |
---|
2037 | pDelete(&m); |
---|
2038 | *c = kBucketPolyRed(b,pp,pLength(pp),NULL); |
---|
2039 | //cc=*c; |
---|
2040 | //*c=nMult(*c,c2); |
---|
2041 | nDelete(&c2); |
---|
2042 | //nDelete(&cc); |
---|
2043 | pDelete(&pp); |
---|
2044 | |
---|
2045 | } |
---|
2046 | |
---|
2047 | void gnc_kBucketPolyRed_ZNew(kBucket_pt b, poly p, number *c) |
---|
2048 | { |
---|
2049 | // b is multiplied by a constant in this impl. |
---|
2050 | poly m=pOne(); |
---|
2051 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
2052 | //pSetm(m); |
---|
2053 | #ifdef PDEBUG |
---|
2054 | pTest(m); |
---|
2055 | #endif |
---|
2056 | |
---|
2057 | if(p_IsConstant(m,currRing)) |
---|
2058 | { |
---|
2059 | pDelete(&m); |
---|
2060 | *c = kBucketPolyRed(b,p,pLength(p),NULL); |
---|
2061 | return; |
---|
2062 | } |
---|
2063 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
2064 | number c2,cc; |
---|
2065 | pCleardenom_n(pp,c2); |
---|
2066 | pDelete(&m); |
---|
2067 | *c = kBucketPolyRed(b,pp,pLength(pp),NULL); |
---|
2068 | //cc=*c; |
---|
2069 | //*c=nMult(*c,c2); |
---|
2070 | nDelete(&c2); |
---|
2071 | //nDelete(&cc); |
---|
2072 | pDelete(&pp); |
---|
2073 | |
---|
2074 | } |
---|
2075 | |
---|
2076 | |
---|
2077 | inline void nc_PolyPolyRedOld(poly &b, poly p, number *c) |
---|
2078 | // reduces b with p, do not delete both |
---|
2079 | { |
---|
2080 | // b will not by multiplied by any constant in this impl. |
---|
2081 | // ==> *c=1 |
---|
2082 | *c=nInit(1); |
---|
2083 | poly m=pOne(); |
---|
2084 | pExpVectorDiff(m,pHead(b),p); |
---|
2085 | //pSetm(m); |
---|
2086 | #ifdef PDEBUG |
---|
2087 | pTest(m); |
---|
2088 | #endif |
---|
2089 | poly pp=nc_mm_Mult_pp(m,p,currRing); |
---|
2090 | assume(pp!=NULL); |
---|
2091 | |
---|
2092 | pDelete(&m); |
---|
2093 | number n=nCopy(pGetCoeff(pp)); |
---|
2094 | number MinusOne=nInit(-1); |
---|
2095 | number nn; |
---|
2096 | if (!nEqual(n,MinusOne)) |
---|
2097 | { |
---|
2098 | nn=nNeg(nInvers(n)); |
---|
2099 | } |
---|
2100 | else nn=nInit(1); |
---|
2101 | nDelete(&n); |
---|
2102 | n=nMult(nn,pGetCoeff(b)); |
---|
2103 | nDelete(&nn); |
---|
2104 | pp=p_Mult_nn(pp,n,currRing); |
---|
2105 | nDelete(&n); |
---|
2106 | nDelete(&MinusOne); |
---|
2107 | b=p_Add_q(b,pp,currRing); |
---|
2108 | } |
---|
2109 | |
---|
2110 | |
---|
2111 | inline void nc_PolyPolyRedNew(poly &b, poly p, number *c) |
---|
2112 | // reduces b with p, do not delete both |
---|
2113 | { |
---|
2114 | #ifdef PDEBUG |
---|
2115 | pTest(b); |
---|
2116 | pTest(p); |
---|
2117 | #endif |
---|
2118 | |
---|
2119 | #if MYTEST |
---|
2120 | PrintS("nc_PolyPolyRedNew("); |
---|
2121 | pWrite0(b); |
---|
2122 | PrintS(", "); |
---|
2123 | pWrite0(p); |
---|
2124 | PrintS(", *c): "); |
---|
2125 | #endif |
---|
2126 | |
---|
2127 | // b will not by multiplied by any constant in this impl. |
---|
2128 | // ==> *c=1 |
---|
2129 | *c=nInit(1); |
---|
2130 | |
---|
2131 | poly pp = NULL; |
---|
2132 | |
---|
2133 | // there is a problem when p is a square(=>0!) |
---|
2134 | |
---|
2135 | while((b != NULL) && (pp == NULL)) |
---|
2136 | { |
---|
2137 | |
---|
2138 | // poly pLmB = pHead(b); |
---|
2139 | poly m = pOne(); |
---|
2140 | pExpVectorDiff(m, b, p); |
---|
2141 | // pDelete(&pLmB); |
---|
2142 | //pSetm(m); |
---|
2143 | |
---|
2144 | #ifdef PDEBUG |
---|
2145 | pTest(m); |
---|
2146 | pTest(b); |
---|
2147 | #endif |
---|
2148 | |
---|
2149 | pp = nc_mm_Mult_pp(m, p, currRing); |
---|
2150 | |
---|
2151 | #if MYTEST |
---|
2152 | PrintS("\n{b': "); |
---|
2153 | pWrite0(b); |
---|
2154 | PrintS(", m: "); |
---|
2155 | pWrite0(m); |
---|
2156 | PrintS(", pp: "); |
---|
2157 | pWrite0(pp); |
---|
2158 | PrintS(" }\n"); |
---|
2159 | #endif |
---|
2160 | |
---|
2161 | pDelete(&m); // one m for all tries! |
---|
2162 | |
---|
2163 | // assume( pp != NULL ); |
---|
2164 | |
---|
2165 | if( pp == NULL ) |
---|
2166 | { |
---|
2167 | b = p_LmDeleteAndNext(b, currRing); |
---|
2168 | |
---|
2169 | if( !p_DivisibleBy(p, b, currRing) ) |
---|
2170 | return; |
---|
2171 | |
---|
2172 | } |
---|
2173 | } |
---|
2174 | |
---|
2175 | #if MYTEST |
---|
2176 | PrintS("{b': "); |
---|
2177 | pWrite0(b); |
---|
2178 | PrintS(", pp: "); |
---|
2179 | pWrite0(pp); |
---|
2180 | PrintS(" }\n"); |
---|
2181 | #endif |
---|
2182 | |
---|
2183 | |
---|
2184 | if(b == NULL) return; |
---|
2185 | |
---|
2186 | |
---|
2187 | assume(pp != NULL); |
---|
2188 | |
---|
2189 | const number n = pGetCoeff(pp); // no new copy |
---|
2190 | |
---|
2191 | number nn; |
---|
2192 | |
---|
2193 | if (!n_IsMOne(n, currRing)) // TODO: as above. |
---|
2194 | { |
---|
2195 | nn=nNeg(nInvers(nCopy(n))); |
---|
2196 | } |
---|
2197 | else nn=nInit(1); |
---|
2198 | |
---|
2199 | number t = nMult(nn, pGetCoeff(b)); |
---|
2200 | nDelete(&nn); |
---|
2201 | |
---|
2202 | pp=p_Mult_nn(pp, t, currRing); |
---|
2203 | nDelete(&t); |
---|
2204 | |
---|
2205 | b=p_Add_q(b,pp,currRing); |
---|
2206 | |
---|
2207 | } |
---|
2208 | |
---|
2209 | void nc_PolyPolyRed(poly &b, poly p, number *c) |
---|
2210 | { |
---|
2211 | #if 0 |
---|
2212 | nc_PolyPolyRedOld(b, p, c); |
---|
2213 | #else |
---|
2214 | nc_PolyPolyRedNew(b, p, c); |
---|
2215 | #endif |
---|
2216 | } |
---|
2217 | |
---|
2218 | |
---|
2219 | poly nc_mm_Bracket_nn(poly m1, poly m2); |
---|
2220 | |
---|
2221 | poly nc_p_Bracket_qq(poly p, poly q) |
---|
2222 | /* returns [p,q], destroys p */ |
---|
2223 | { |
---|
2224 | |
---|
2225 | if (!rIsPluralRing(currRing)) return(NULL); |
---|
2226 | if (pComparePolys(p,q)) return(NULL); |
---|
2227 | /* Components !? */ |
---|
2228 | poly Q=NULL; |
---|
2229 | number coef=NULL; |
---|
2230 | poly res=NULL; |
---|
2231 | poly pres=NULL; |
---|
2232 | int UseBuckets=1; |
---|
2233 | if ((pLength(p)< MIN_LENGTH_BUCKET/2) && (pLength(q)< MIN_LENGTH_BUCKET/2) || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
---|
2234 | |
---|
2235 | |
---|
2236 | CPolynomialSummator sum(currRing, UseBuckets == 0); |
---|
2237 | |
---|
2238 | while (p!=NULL) |
---|
2239 | { |
---|
2240 | Q=q; |
---|
2241 | while(Q!=NULL) |
---|
2242 | { |
---|
2243 | pres=nc_mm_Bracket_nn(p,Q); /* since no coeffs are taken into account there */ |
---|
2244 | if (pres!=NULL) |
---|
2245 | { |
---|
2246 | coef = nMult(pGetCoeff(p),pGetCoeff(Q)); |
---|
2247 | pres = p_Mult_nn(pres,coef,currRing); |
---|
2248 | |
---|
2249 | sum += pres; |
---|
2250 | nDelete(&coef); |
---|
2251 | } |
---|
2252 | pIter(Q); |
---|
2253 | } |
---|
2254 | p=pLmDeleteAndNext(p); |
---|
2255 | } |
---|
2256 | return(sum); |
---|
2257 | } |
---|
2258 | |
---|
2259 | poly nc_mm_Bracket_nn(poly m1, poly m2) |
---|
2260 | /*returns [m1,m2] for two monoms, destroys nothing */ |
---|
2261 | /* without coeffs */ |
---|
2262 | { |
---|
2263 | if (pLmIsConstant(m1) || pLmIsConstant(m1)) return(NULL); |
---|
2264 | if (pLmCmp(m1,m2)==0) return(NULL); |
---|
2265 | int rN=currRing->N; |
---|
2266 | int *M1=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2267 | int *M2=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2268 | int *PREFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2269 | int *SUFFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2270 | pGetExpV(m1,M1); |
---|
2271 | pGetExpV(m2,M2); |
---|
2272 | poly res=NULL; |
---|
2273 | poly ares=NULL; |
---|
2274 | poly bres=NULL; |
---|
2275 | poly prefix=NULL; |
---|
2276 | poly suffix=NULL; |
---|
2277 | int nMin,nMax; |
---|
2278 | number nTmp=NULL; |
---|
2279 | int i,j,k; |
---|
2280 | for (i=1;i<=rN;i++) |
---|
2281 | { |
---|
2282 | if (M2[i]!=0) |
---|
2283 | { |
---|
2284 | ares=NULL; |
---|
2285 | for (j=1;j<=rN;j++) |
---|
2286 | { |
---|
2287 | if (M1[j]!=0) |
---|
2288 | { |
---|
2289 | bres=NULL; |
---|
2290 | /* compute [ x_j^M1[j],x_i^M2[i] ] */ |
---|
2291 | if (i<j) {nMax=j; nMin=i;} else {nMax=i; nMin=j;} |
---|
2292 | 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)*/ |
---|
2293 | { bres=NULL; } |
---|
2294 | else |
---|
2295 | { |
---|
2296 | if (i<j) { bres=gnc_uu_Mult_ww(j,M1[j],i,M2[i],currRing); } |
---|
2297 | else bres=gnc_uu_Mult_ww(i,M2[i],j,M1[j],currRing); |
---|
2298 | if (nIsOne(pGetCoeff(bres))) |
---|
2299 | { |
---|
2300 | bres=pLmDeleteAndNext(bres); |
---|
2301 | } |
---|
2302 | else |
---|
2303 | { |
---|
2304 | nTmp=nSub(pGetCoeff(bres),nInit(1)); |
---|
2305 | pSetCoeff(bres,nTmp); /* only lc ! */ |
---|
2306 | } |
---|
2307 | #ifdef PDEBUG |
---|
2308 | pTest(bres); |
---|
2309 | #endif |
---|
2310 | if (i>j) bres=p_Neg(bres, currRing); |
---|
2311 | } |
---|
2312 | if (bres!=NULL) |
---|
2313 | { |
---|
2314 | /* now mult (prefix, bres, suffix) */ |
---|
2315 | memcpy(SUFFIX, M1,(rN+1)*sizeof(int)); |
---|
2316 | memcpy(PREFIX, M1,(rN+1)*sizeof(int)); |
---|
2317 | for (k=1;k<=j;k++) SUFFIX[k]=0; |
---|
2318 | for (k=j;k<=rN;k++) PREFIX[k]=0; |
---|
2319 | SUFFIX[0]=0; |
---|
2320 | PREFIX[0]=0; |
---|
2321 | prefix=pOne(); |
---|
2322 | suffix=pOne(); |
---|
2323 | pSetExpV(prefix,PREFIX); |
---|
2324 | pSetm(prefix); |
---|
2325 | pSetExpV(suffix,SUFFIX); |
---|
2326 | pSetm(suffix); |
---|
2327 | if (!pLmIsConstant(prefix)) bres = gnc_mm_Mult_p(prefix, bres,currRing); |
---|
2328 | if (!pLmIsConstant(suffix)) bres = gnc_p_Mult_mm(bres, suffix,currRing); |
---|
2329 | ares=p_Add_q(ares, bres,currRing); |
---|
2330 | /* What to give free? */ |
---|
2331 | /* Do we have to free PREFIX/SUFFIX? it seems so */ |
---|
2332 | pDelete(&prefix); |
---|
2333 | pDelete(&suffix); |
---|
2334 | } |
---|
2335 | } |
---|
2336 | } |
---|
2337 | if (ares!=NULL) |
---|
2338 | { |
---|
2339 | /* now mult (prefix, bres, suffix) */ |
---|
2340 | memcpy(SUFFIX, M2,(rN+1)*sizeof(int)); |
---|
2341 | memcpy(PREFIX, M2,(rN+1)*sizeof(int)); |
---|
2342 | for (k=1;k<=i;k++) SUFFIX[k]=0; |
---|
2343 | for (k=i;k<=rN;k++) PREFIX[k]=0; |
---|
2344 | SUFFIX[0]=0; |
---|
2345 | PREFIX[0]=0; |
---|
2346 | prefix=pOne(); |
---|
2347 | suffix=pOne(); |
---|
2348 | pSetExpV(prefix,PREFIX); |
---|
2349 | pSetm(prefix); |
---|
2350 | pSetExpV(suffix,SUFFIX); |
---|
2351 | pSetm(suffix); |
---|
2352 | bres=ares; |
---|
2353 | if (!pLmIsConstant(prefix)) bres = gnc_mm_Mult_p(prefix, bres,currRing); |
---|
2354 | if (!pLmIsConstant(suffix)) bres = gnc_p_Mult_mm(bres, suffix,currRing); |
---|
2355 | res=p_Add_q(res, bres,currRing); |
---|
2356 | pDelete(&prefix); |
---|
2357 | pDelete(&suffix); |
---|
2358 | } |
---|
2359 | } |
---|
2360 | } |
---|
2361 | freeT(M1, rN); |
---|
2362 | freeT(M2, rN); |
---|
2363 | freeT(PREFIX, rN); |
---|
2364 | freeT(SUFFIX, rN); |
---|
2365 | pTest(res); |
---|
2366 | return(res); |
---|
2367 | } |
---|
2368 | |
---|
2369 | ideal twostd(ideal I) // works in currRing only! |
---|
2370 | { |
---|
2371 | ideal J = kStd(I, currQuotient, testHomog, NULL, NULL, 0, 0, NULL); // in currRing!!! |
---|
2372 | idSkipZeroes(J); // ring independent! |
---|
2373 | |
---|
2374 | const int rN = currRing->N; |
---|
2375 | |
---|
2376 | loop |
---|
2377 | { |
---|
2378 | ideal K = NULL; |
---|
2379 | const int s = idElem(J); // ring independent |
---|
2380 | |
---|
2381 | for(int i = 0; i < s; i++) |
---|
2382 | { |
---|
2383 | const poly p = J->m[i]; |
---|
2384 | |
---|
2385 | #ifdef PDEBUG |
---|
2386 | p_Test(p, currRing); |
---|
2387 | #if 0 |
---|
2388 | Print("p: "); // ! |
---|
2389 | p_Write(p, currRing); |
---|
2390 | #endif |
---|
2391 | #endif |
---|
2392 | |
---|
2393 | for (int j = 1; j <= rN; j++) // for all j = 1..N |
---|
2394 | { |
---|
2395 | poly varj = p_One( currRing); |
---|
2396 | p_SetExp(varj, j, 1, currRing); |
---|
2397 | p_Setm(varj, currRing); |
---|
2398 | |
---|
2399 | poly q = pp_Mult_mm(p, varj, currRing); // q = J[i] * var(j), |
---|
2400 | |
---|
2401 | #ifdef PDEBUG |
---|
2402 | p_Test(varj, currRing); |
---|
2403 | p_Test(p, currRing); |
---|
2404 | p_Test(q, currRing); |
---|
2405 | #if 0 |
---|
2406 | Print("Reducing p: "); // ! |
---|
2407 | p_Write(p, currRing); |
---|
2408 | Print("With q: "); // ! |
---|
2409 | p_Write(q, currRing); |
---|
2410 | #endif |
---|
2411 | #endif |
---|
2412 | |
---|
2413 | p_Delete(&varj, currRing); |
---|
2414 | |
---|
2415 | if (q != NULL) |
---|
2416 | { |
---|
2417 | #ifdef PDEBUG |
---|
2418 | #if 0 |
---|
2419 | Print("Reducing q[j = %d]: ", j); // ! |
---|
2420 | p_Write(q, currRing); |
---|
2421 | |
---|
2422 | Print("With p:"); |
---|
2423 | p_Write(p, currRing); |
---|
2424 | |
---|
2425 | #endif |
---|
2426 | #endif |
---|
2427 | |
---|
2428 | // bug: lm(p) may not divide lm(p * var(i)) in a SCA! |
---|
2429 | if( p_LmDivisibleBy(p, q, currRing) ) |
---|
2430 | q = nc_ReduceSpoly(p, q, currRing); |
---|
2431 | |
---|
2432 | |
---|
2433 | #ifdef PDEBUG |
---|
2434 | p_Test(q, currRing); |
---|
2435 | #if 0 |
---|
2436 | Print("reductum q/p: "); |
---|
2437 | p_Write(q, currRing); |
---|
2438 | |
---|
2439 | // Print("With J!\n"); |
---|
2440 | #endif |
---|
2441 | #endif |
---|
2442 | |
---|
2443 | // if( q != NULL) |
---|
2444 | q = kNF(J, currQuotient, q, 0, KSTD_NF_NONORM); // in currRing!!! |
---|
2445 | |
---|
2446 | #ifdef PDEBUG |
---|
2447 | p_Test(q, currRing); |
---|
2448 | #if 0 |
---|
2449 | Print("NF(J/currQuotient)=> q: "); // ! |
---|
2450 | p_Write(q, currRing); |
---|
2451 | #endif |
---|
2452 | #endif |
---|
2453 | if (q!=NULL) |
---|
2454 | { |
---|
2455 | if (p_IsConstant(q, currRing)) // => return (1)! |
---|
2456 | { |
---|
2457 | p_Delete(&q, currRing); |
---|
2458 | id_Delete(&J, currRing); |
---|
2459 | |
---|
2460 | if (K != NULL) |
---|
2461 | id_Delete(&K, currRing); |
---|
2462 | |
---|
2463 | ideal Q = idInit(1,1); // ring independent! |
---|
2464 | Q->m[0] = p_One(currRing); |
---|
2465 | |
---|
2466 | return(Q); |
---|
2467 | } |
---|
2468 | |
---|
2469 | // flag = false; |
---|
2470 | |
---|
2471 | // K += q: |
---|
2472 | |
---|
2473 | ideal Q = idInit(1,1); // ring independent |
---|
2474 | Q->m[0]=q; |
---|
2475 | |
---|
2476 | if( K == NULL ) |
---|
2477 | K = Q; |
---|
2478 | else |
---|
2479 | { |
---|
2480 | ideal id_tmp = idSimpleAdd(K, Q); // in currRing |
---|
2481 | id_Delete(&K, currRing); |
---|
2482 | id_Delete(&Q, currRing); |
---|
2483 | K = id_tmp; // K += Q |
---|
2484 | } |
---|
2485 | } |
---|
2486 | |
---|
2487 | |
---|
2488 | } // if q != NULL |
---|
2489 | } // for all variables |
---|
2490 | |
---|
2491 | } |
---|
2492 | |
---|
2493 | if (K == NULL) // nothing new: i.e. all elements are two-sided |
---|
2494 | return(J); |
---|
2495 | /* now we update GrBasis J with K */ |
---|
2496 | // iSize=IDELEMS(J); |
---|
2497 | #ifdef PDEBUG |
---|
2498 | idTest(J); // in currRing! |
---|
2499 | #if 0 |
---|
2500 | Print("J:"); |
---|
2501 | idPrint(J); |
---|
2502 | PrintLn(); |
---|
2503 | #endif // debug |
---|
2504 | #endif |
---|
2505 | |
---|
2506 | |
---|
2507 | |
---|
2508 | #ifdef PDEBUG |
---|
2509 | idTest(K); // in currRing! |
---|
2510 | #if 0 |
---|
2511 | Print("+K:"); |
---|
2512 | idPrint(K); |
---|
2513 | PrintLn(); |
---|
2514 | #endif // debug |
---|
2515 | #endif |
---|
2516 | |
---|
2517 | |
---|
2518 | int iSize = idElem(J); // ring independent |
---|
2519 | |
---|
2520 | // J += K: |
---|
2521 | ideal id_tmp = idSimpleAdd(J,K); // in currRing |
---|
2522 | id_Delete(&K, currRing); id_Delete(&J, currRing); |
---|
2523 | |
---|
2524 | #if 1 |
---|
2525 | BITSET save_test=test; |
---|
2526 | test|=Sy_bit(OPT_SB_1); // ring independent |
---|
2527 | J = kStd(id_tmp, currQuotient, testHomog, NULL, NULL, 0, iSize); // J = J + K, J - std // in currRing! |
---|
2528 | test = save_test; |
---|
2529 | #else |
---|
2530 | J=kStd(id_tmp, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
2531 | #endif |
---|
2532 | |
---|
2533 | id_Delete(&id_tmp, currRing); |
---|
2534 | idSkipZeroes(J); // ring independent |
---|
2535 | |
---|
2536 | #ifdef PDEBUG |
---|
2537 | idTest(J); // in currRing! |
---|
2538 | #if 0 |
---|
2539 | Print("J:"); |
---|
2540 | idPrint(J); |
---|
2541 | PrintLn(); |
---|
2542 | #endif // debug |
---|
2543 | #endif |
---|
2544 | } // loop |
---|
2545 | } |
---|
2546 | |
---|
2547 | |
---|
2548 | matrix nc_PrintMat(int a, int b, ring r, int metric) |
---|
2549 | /* returns matrix with the info on noncomm multiplication */ |
---|
2550 | { |
---|
2551 | |
---|
2552 | if ( (a==b) || !rIsPluralRing(r) ) return(NULL); |
---|
2553 | int i; |
---|
2554 | int j; |
---|
2555 | if (a>b) {j=b; i=a;} |
---|
2556 | else {j=a; i=b;} |
---|
2557 | /* i<j */ |
---|
2558 | int rN=r->N; |
---|
2559 | int size=r->GetNC()->MTsize[UPMATELEM(i,j,rN)]; |
---|
2560 | matrix M = r->GetNC()->MT[UPMATELEM(i,j,rN)]; |
---|
2561 | /* return(M); */ |
---|
2562 | int sizeofres; |
---|
2563 | if (metric==0) |
---|
2564 | { |
---|
2565 | sizeofres=sizeof(int); |
---|
2566 | } |
---|
2567 | if (metric==1) |
---|
2568 | { |
---|
2569 | sizeofres=sizeof(number); |
---|
2570 | } |
---|
2571 | matrix res=mpNew(size,size); |
---|
2572 | int s; |
---|
2573 | int t; |
---|
2574 | int length; |
---|
2575 | long totdeg; |
---|
2576 | poly p; |
---|
2577 | for(s=1;s<=size;s++) |
---|
2578 | { |
---|
2579 | for(t=1;t<=size;t++) |
---|
2580 | { |
---|
2581 | p=MATELEM(M,s,t); |
---|
2582 | if (p==NULL) |
---|
2583 | { |
---|
2584 | MATELEM(res,s,t)=0; |
---|
2585 | } |
---|
2586 | else |
---|
2587 | { |
---|
2588 | length = pLength(p); |
---|
2589 | if (metric==0) /* length */ |
---|
2590 | { |
---|
2591 | MATELEM(res,s,t)= p_ISet(length,r); |
---|
2592 | } |
---|
2593 | else if (metric==1) /* sum of deg divided by the length */ |
---|
2594 | { |
---|
2595 | totdeg=0; |
---|
2596 | while (p!=NULL) |
---|
2597 | { |
---|
2598 | totdeg=totdeg+pDeg(p,r); |
---|
2599 | pIter(p); |
---|
2600 | } |
---|
2601 | number ntd = nInit(totdeg); |
---|
2602 | number nln = nInit(length); |
---|
2603 | number nres=nDiv(ntd,nln); |
---|
2604 | nDelete(&ntd); |
---|
2605 | nDelete(&nln); |
---|
2606 | MATELEM(res,s,t)=p_NSet(nres,r); |
---|
2607 | } |
---|
2608 | } |
---|
2609 | } |
---|
2610 | } |
---|
2611 | return(res); |
---|
2612 | } |
---|
2613 | |
---|
2614 | inline void nc_CleanUp(nc_struct* p) |
---|
2615 | { |
---|
2616 | assume(p != NULL); |
---|
2617 | omFreeSize((ADDRESS)p,sizeof(nc_struct)); |
---|
2618 | } |
---|
2619 | |
---|
2620 | inline void nc_CleanUp(ring r) |
---|
2621 | { |
---|
2622 | /* small CleanUp of r->GetNC() */ |
---|
2623 | assume(r != NULL); |
---|
2624 | nc_CleanUp(r->GetNC()); |
---|
2625 | r->GetNC() = NULL; |
---|
2626 | } |
---|
2627 | |
---|
2628 | void nc_rKill(ring r) |
---|
2629 | // kills the nc extension of ring r |
---|
2630 | { |
---|
2631 | if (r->GetNC()->ref >= 1) /* in use by somebody else */ |
---|
2632 | { |
---|
2633 | r->GetNC()->ref--; |
---|
2634 | r->GetNC() = NULL; // don't cleanup, just dereference |
---|
2635 | return; |
---|
2636 | } |
---|
2637 | /* otherwise kill the previous nc data */ |
---|
2638 | |
---|
2639 | assume( r->GetNC()->ref == 0 ); |
---|
2640 | |
---|
2641 | if( r->GetNC()->GetGlobalMultiplier() != NULL ) |
---|
2642 | { |
---|
2643 | delete r->GetNC()->GetGlobalMultiplier(); |
---|
2644 | r->GetNC()->GetGlobalMultiplier() = NULL; |
---|
2645 | } |
---|
2646 | |
---|
2647 | if( r->GetNC()->GetFormulaPowerMultiplier() != NULL ) |
---|
2648 | { |
---|
2649 | delete r->GetNC()->GetFormulaPowerMultiplier(); |
---|
2650 | r->GetNC()->GetFormulaPowerMultiplier() = NULL; |
---|
2651 | } |
---|
2652 | |
---|
2653 | |
---|
2654 | int i,j; |
---|
2655 | int rN=r->N; |
---|
2656 | if ( rN > 1 ) |
---|
2657 | { |
---|
2658 | for(i=1;i<rN;i++) |
---|
2659 | { |
---|
2660 | for(j=i+1;j<=rN;j++) |
---|
2661 | { |
---|
2662 | id_Delete((ideal *)&(r->GetNC()->MT[UPMATELEM(i,j,rN)]),r->GetNC()->basering); |
---|
2663 | } |
---|
2664 | } |
---|
2665 | omFreeSize((ADDRESS)r->GetNC()->MT,rN*(rN-1)/2*sizeof(matrix)); |
---|
2666 | omFreeSize((ADDRESS)r->GetNC()->MTsize,rN*(rN-1)/2*sizeof(int)); |
---|
2667 | id_Delete((ideal *)&(r->GetNC()->COM),r->GetNC()->basering); |
---|
2668 | } |
---|
2669 | id_Delete((ideal *)&(r->GetNC()->C),r->GetNC()->basering); |
---|
2670 | id_Delete((ideal *)&(r->GetNC()->D),r->GetNC()->basering); |
---|
2671 | |
---|
2672 | if( rIsSCA(r) && (r->GetNC()->SCAQuotient() != NULL) ) |
---|
2673 | { |
---|
2674 | id_Delete(&r->GetNC()->SCAQuotient(), r->GetNC()->basering); // Custom SCA destructor!!! |
---|
2675 | } |
---|
2676 | |
---|
2677 | r->GetNC()->basering->ref--; |
---|
2678 | |
---|
2679 | if ((r->GetNC()->basering->ref<=0)&&(r->GetNC()->basering->GetNC()==NULL)) |
---|
2680 | { |
---|
2681 | WarnS("Killing a base ring!"); |
---|
2682 | // rWrite(r->GetNC()->basering); |
---|
2683 | rKill(r->GetNC()->basering); |
---|
2684 | } |
---|
2685 | |
---|
2686 | nc_CleanUp(r); |
---|
2687 | } |
---|
2688 | |
---|
2689 | |
---|
2690 | //////////////////////////////////////////////////////////////////////////////////////////////// |
---|
2691 | |
---|
2692 | // share the same nc-structure with a new copy ``res'' of ``r''. |
---|
2693 | // used by rCopy only. |
---|
2694 | // additionally inits multipication on ``res''! |
---|
2695 | // NOTE: update nc structure on res: share NC structure of r with res since they are the same!!! |
---|
2696 | // i.e. no data copy!!! Multiplications will be setuped as well! |
---|
2697 | inline |
---|
2698 | void nc_rCopy0(ring res, const ring r) |
---|
2699 | { |
---|
2700 | assume(rIsPluralRing(r)); |
---|
2701 | assume( res != r ); |
---|
2702 | |
---|
2703 | res->GetNC() = r->GetNC(); |
---|
2704 | res->GetNC()->ref++; |
---|
2705 | nc_p_ProcsSet(res, res->p_Procs); |
---|
2706 | } |
---|
2707 | |
---|
2708 | |
---|
2709 | |
---|
2710 | |
---|
2711 | inline void nc_rClean0(ring r) // inverse to nc_rCopy0! ps: no real deletion! |
---|
2712 | { |
---|
2713 | assume(rIsPluralRing(r)); |
---|
2714 | |
---|
2715 | r->GetNC()->ref--; |
---|
2716 | r->GetNC() = NULL; |
---|
2717 | // p_ProcsSet(res, r->p_Procs); // ??? |
---|
2718 | } |
---|
2719 | |
---|
2720 | poly nc_p_CopyGet(poly a, const ring r) |
---|
2721 | /* for use in getting the mult. matrix elements*/ |
---|
2722 | /* ring r must be a currRing! */ |
---|
2723 | /* for consistency, copies a poly from the comm. r->GetNC()->basering */ |
---|
2724 | /* to its image in NC ring */ |
---|
2725 | { |
---|
2726 | if (r != currRing) |
---|
2727 | { |
---|
2728 | #ifdef PDEBUF |
---|
2729 | Werror("nc_p_CopyGet call not in currRing"); |
---|
2730 | #endif |
---|
2731 | return(NULL); |
---|
2732 | } |
---|
2733 | if (!rIsPluralRing(r)) return(p_Copy(a,r)); |
---|
2734 | if (r==r->GetNC()->basering) return(p_Copy(a,r)); |
---|
2735 | else |
---|
2736 | { |
---|
2737 | return(prCopyR_NoSort(a,r->GetNC()->basering,r)); |
---|
2738 | } |
---|
2739 | } |
---|
2740 | |
---|
2741 | poly nc_p_CopyPut(poly a, const ring r) |
---|
2742 | /* for use in defining the mult. matrix elements*/ |
---|
2743 | /* ring r must be a currRing! */ |
---|
2744 | /* for consistency, puts a polynomial from the NC ring */ |
---|
2745 | /* to its presentation in the comm. r->GetNC()->basering */ |
---|
2746 | { |
---|
2747 | if (r != currRing) |
---|
2748 | { |
---|
2749 | #ifdef PDEBUF |
---|
2750 | Werror("nc_p_CopyGet call not in currRing"); |
---|
2751 | #endif |
---|
2752 | return(NULL); |
---|
2753 | } |
---|
2754 | |
---|
2755 | if (!rIsPluralRing(r)) return(p_Copy(a,r)); |
---|
2756 | if (r==r->GetNC()->basering) return(p_Copy(a,r)); |
---|
2757 | else |
---|
2758 | { |
---|
2759 | return(prCopyR_NoSort(a,r,r->GetNC()->basering)); |
---|
2760 | } |
---|
2761 | } |
---|
2762 | |
---|
2763 | BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r) |
---|
2764 | /* returns TRUE if there were errors */ |
---|
2765 | /* checks whether product of vars from PolyVar defines */ |
---|
2766 | /* an admissible subalgebra of r */ |
---|
2767 | /* r is indeed currRing and assumed to be noncomm. */ |
---|
2768 | { |
---|
2769 | ring save = currRing; |
---|
2770 | int WeChangeRing = 0; |
---|
2771 | if (currRing != r) |
---|
2772 | { |
---|
2773 | rChangeCurrRing(r); |
---|
2774 | WeChangeRing = 1; |
---|
2775 | } |
---|
2776 | int rN=r->N; |
---|
2777 | int *ExpVar=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
2778 | int *ExpTmp=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
2779 | p_GetExpV(PolyVar, ExpVar, r); |
---|
2780 | int i; int j; int k; |
---|
2781 | poly test=NULL; |
---|
2782 | int OK=1; |
---|
2783 | for (i=1; i<rN; i++) |
---|
2784 | { |
---|
2785 | if (ExpVar[i]==0) /* i.e. not in PolyVar */ |
---|
2786 | { |
---|
2787 | for (j=i+1; j<=rN; j++) |
---|
2788 | { |
---|
2789 | if (ExpVar[j]==0) |
---|
2790 | { |
---|
2791 | test = nc_p_CopyGet(MATELEM(r->GetNC()->D,i,j),r); |
---|
2792 | while (test!=NULL) |
---|
2793 | { |
---|
2794 | p_GetExpV(test, ExpTmp, r); |
---|
2795 | OK=1; |
---|
2796 | for (k=1;k<=rN;k++) |
---|
2797 | { |
---|
2798 | if (ExpTmp[k]!=0) |
---|
2799 | { |
---|
2800 | if (ExpVar[k]!=0) OK=0; |
---|
2801 | } |
---|
2802 | } |
---|
2803 | if (!OK) return(TRUE); |
---|
2804 | pIter(test); |
---|
2805 | } |
---|
2806 | } |
---|
2807 | } |
---|
2808 | } |
---|
2809 | } |
---|
2810 | p_Delete(&test,r); |
---|
2811 | freeT(ExpVar,rN); |
---|
2812 | freeT(ExpTmp,rN); |
---|
2813 | if ( WeChangeRing ) |
---|
2814 | rChangeCurrRing(save); |
---|
2815 | return(FALSE); |
---|
2816 | } |
---|
2817 | |
---|
2818 | |
---|
2819 | BOOLEAN gnc_CheckOrdCondition(matrix D, ring r) |
---|
2820 | /* returns TRUE if there were errors */ |
---|
2821 | /* checks whether the current ordering */ |
---|
2822 | /* is admissible for r and D == r->GetNC()->D */ |
---|
2823 | /* to be executed in a currRing */ |
---|
2824 | { |
---|
2825 | /* analyze D: an upper triangular matrix of polys */ |
---|
2826 | /* check the ordering condition for D */ |
---|
2827 | ring save = currRing; |
---|
2828 | int WeChangeRing = 0; |
---|
2829 | if (r != currRing) |
---|
2830 | { |
---|
2831 | rChangeCurrRing(r); |
---|
2832 | WeChangeRing = 1; |
---|
2833 | } |
---|
2834 | poly p,q; |
---|
2835 | int i,j; |
---|
2836 | int report = 0; |
---|
2837 | for(i=1; i<r->N; i++) |
---|
2838 | { |
---|
2839 | for(j=i+1; j<=r->N; j++) |
---|
2840 | { |
---|
2841 | p = nc_p_CopyGet(MATELEM(D,i,j),r); |
---|
2842 | if ( p != NULL) |
---|
2843 | { |
---|
2844 | q = p_One(r); // replaces pOne(); |
---|
2845 | p_SetExp(q,i,1,r); |
---|
2846 | p_SetExp(q,j,1,r); |
---|
2847 | p_Setm(q,r); |
---|
2848 | if (p_LmCmp(q,p,r) != 1) /* i.e. lm(p)==xy < lm(q)==D_ij */ |
---|
2849 | { |
---|
2850 | Werror("Bad ordering at %d,%d\n",i,j); |
---|
2851 | #ifdef PDEBUG |
---|
2852 | p_Write(p,r); |
---|
2853 | p_Write(q,r); |
---|
2854 | #endif |
---|
2855 | report = 1; |
---|
2856 | } |
---|
2857 | p_Delete(&q,r); |
---|
2858 | p_Delete(&p,r); |
---|
2859 | p = NULL; |
---|
2860 | } |
---|
2861 | } |
---|
2862 | } |
---|
2863 | if ( WeChangeRing ) |
---|
2864 | rChangeCurrRing(save); |
---|
2865 | return(report); |
---|
2866 | } |
---|
2867 | |
---|
2868 | |
---|
2869 | BOOLEAN nc_CallPlural( |
---|
2870 | matrix CCC, matrix DDD, |
---|
2871 | poly CCN, poly DDN, |
---|
2872 | ring r, |
---|
2873 | bool bSetupQuotient, bool bCopyInput, bool bBeQuiet, |
---|
2874 | ring curr) |
---|
2875 | /* returns TRUE if there were errors */ |
---|
2876 | /* analyze inputs, check them for consistency */ |
---|
2877 | /* detects nc_type, DO NOT initialize multiplication but call for it at the end*/ |
---|
2878 | /* checks the ordering condition and evtl. NDC */ |
---|
2879 | // NOTE: all the data belong to the curr, |
---|
2880 | // we change r which may be the same ring, and must have the same representation! |
---|
2881 | { |
---|
2882 | // assume( curr != r ); |
---|
2883 | assume( rSamePolyRep(r, curr) ); |
---|
2884 | |
---|
2885 | |
---|
2886 | if( r->N == 1 ) // clearly commutative!!! |
---|
2887 | { |
---|
2888 | assume( |
---|
2889 | ( (CCC != NULL) && (MATCOLS(CCC) == 1) && (MATROWS(CCC) == 1) && (MATELEM(CCC,1,1) == NULL) ) || |
---|
2890 | ( (CCN == NULL) ) |
---|
2891 | ); |
---|
2892 | |
---|
2893 | assume( |
---|
2894 | ( (DDD != NULL) && (MATCOLS(DDD) == 1) && (MATROWS(DDD) == 1) && (MATELEM(DDD,1,1) == NULL) ) || |
---|
2895 | ( (DDN == NULL) ) |
---|
2896 | ); |
---|
2897 | |
---|
2898 | |
---|
2899 | } |
---|
2900 | |
---|
2901 | |
---|
2902 | // there must be: |
---|
2903 | assume( (CCC != NULL) != (CCN != NULL) ); // exactly one data about coeffs (C). |
---|
2904 | assume( !((DDD != NULL) && (DDN != NULL)) ); // at most one data about tails (D). |
---|
2905 | |
---|
2906 | ring save = currRing; |
---|
2907 | |
---|
2908 | if( save != curr ) |
---|
2909 | rChangeCurrRing(curr); |
---|
2910 | |
---|
2911 | #if OUTPUT |
---|
2912 | if( CCC != NULL ) |
---|
2913 | { |
---|
2914 | PrintS("nc_CallPlural(), Input data, CCC: \n"); |
---|
2915 | iiWriteMatrix(CCC, "C", 2, 4); |
---|
2916 | } |
---|
2917 | if( DDD != NULL ) |
---|
2918 | { |
---|
2919 | PrintS("nc_CallPlural(), Input data, DDD: \n"); |
---|
2920 | iiWriteMatrix(DDD, "D", 2, 4); |
---|
2921 | } |
---|
2922 | #endif |
---|
2923 | |
---|
2924 | |
---|
2925 | #ifndef NDEBUG |
---|
2926 | idTest((ideal)CCC); |
---|
2927 | idTest((ideal)DDD); |
---|
2928 | pTest(CCN); |
---|
2929 | pTest(DDN); |
---|
2930 | #endif |
---|
2931 | |
---|
2932 | if( (!bBeQuiet) && (r->GetNC() != NULL) ) |
---|
2933 | WarnS("going to redefine the algebra structure"); |
---|
2934 | |
---|
2935 | if( currRing != r ) |
---|
2936 | rChangeCurrRing(r); |
---|
2937 | |
---|
2938 | #ifndef NDEBUG |
---|
2939 | idTest((ideal)CCC); |
---|
2940 | idTest((ideal)DDD); |
---|
2941 | pTest(CCN); |
---|
2942 | pTest(DDN); |
---|
2943 | #endif |
---|
2944 | |
---|
2945 | matrix CC = NULL; |
---|
2946 | poly CN = NULL; |
---|
2947 | matrix C; bool bCnew = false; |
---|
2948 | |
---|
2949 | matrix DD = NULL; |
---|
2950 | poly DN = NULL; |
---|
2951 | matrix D; bool bDnew = false; |
---|
2952 | |
---|
2953 | number nN, pN, qN; |
---|
2954 | |
---|
2955 | bool IsSkewConstant = false, tmpIsSkewConstant; |
---|
2956 | int i, j; |
---|
2957 | |
---|
2958 | nc_type nctype = nc_undef; |
---|
2959 | |
---|
2960 | ////////////////////////////////////////////////////////////////// |
---|
2961 | // check the correctness of arguments, without any real chagnes!!! |
---|
2962 | |
---|
2963 | |
---|
2964 | |
---|
2965 | // check C |
---|
2966 | if ((CCC != NULL) && ( (MATCOLS(CCC)==1) || MATROWS(CCC)==1 ) ) |
---|
2967 | { |
---|
2968 | CN = MATELEM(CCC,1,1); |
---|
2969 | } |
---|
2970 | else |
---|
2971 | { |
---|
2972 | if ((CCC != NULL) && ( (MATCOLS(CCC)!=r->N) || (MATROWS(CCC)!=r->N) )) |
---|
2973 | { |
---|
2974 | Werror("Square %d x %d matrix expected", r->N, r->N); |
---|
2975 | |
---|
2976 | if( currRing != save ) |
---|
2977 | rChangeCurrRing(save); |
---|
2978 | return TRUE; |
---|
2979 | } |
---|
2980 | } |
---|
2981 | if (( CCC != NULL) && (CC == NULL)) CC = CCC; // mpCopy(CCC); // bug!? |
---|
2982 | if (( CCN != NULL) && (CN == NULL)) CN = CCN; |
---|
2983 | |
---|
2984 | // check D |
---|
2985 | if ((DDD != NULL) && ( (MATCOLS(DDD)==1) || MATROWS(DDD)==1 ) ) |
---|
2986 | { |
---|
2987 | DN = MATELEM(DDD,1,1); |
---|
2988 | } |
---|
2989 | else |
---|
2990 | { |
---|
2991 | if ((DDD != NULL) && ( (MATCOLS(DDD)!=r->N) || (MATROWS(DDD)!=r->N) )) |
---|
2992 | { |
---|
2993 | Werror("Square %d x %d matrix expected",r->N,r->N); |
---|
2994 | |
---|
2995 | if( currRing != save ) |
---|
2996 | rChangeCurrRing(save); |
---|
2997 | return TRUE; |
---|
2998 | } |
---|
2999 | } |
---|
3000 | |
---|
3001 | if (( DDD != NULL) && (DD == NULL)) DD = DDD; // mpCopy(DDD); // ??? |
---|
3002 | if (( DDN != NULL) && (DN == NULL)) DN = DDN; |
---|
3003 | |
---|
3004 | // further checks and some analysis: |
---|
3005 | // all data in 'curr'! |
---|
3006 | if (CN != NULL) /* create matrix C = CN * Id */ |
---|
3007 | { |
---|
3008 | nN = p_GetCoeff(CN, curr); |
---|
3009 | if (n_IsZero(nN, curr)) |
---|
3010 | { |
---|
3011 | Werror("Incorrect input : zero coefficients are not allowed"); |
---|
3012 | |
---|
3013 | if( currRing != save ) |
---|
3014 | rChangeCurrRing(save); |
---|
3015 | return TRUE; |
---|
3016 | } |
---|
3017 | |
---|
3018 | if (n_IsOne(nN, curr)) |
---|
3019 | nctype = nc_lie; |
---|
3020 | else |
---|
3021 | nctype = nc_general; |
---|
3022 | |
---|
3023 | IsSkewConstant = true; |
---|
3024 | |
---|
3025 | C = mpNew(r->N,r->N); // ring independent! |
---|
3026 | bCnew = true; |
---|
3027 | |
---|
3028 | for(i=1; i<r->N; i++) |
---|
3029 | for(j=i+1; j<=r->N; j++) |
---|
3030 | MATELEM(C,i,j) = prCopyR_NoSort(CN, curr, r); // nc_p_CopyPut(CN, r); // copy CN from curr into r |
---|
3031 | } else |
---|
3032 | if ( (CN == NULL) && (CC != NULL) ) /* copy matrix C */ |
---|
3033 | { |
---|
3034 | /* analyze C */ |
---|
3035 | |
---|
3036 | pN = NULL; /* check the consistency later */ |
---|
3037 | |
---|
3038 | if( r->N > 1 ) |
---|
3039 | if ( MATELEM(CC,1,2) != NULL ) |
---|
3040 | pN = p_GetCoeff(MATELEM(CC,1,2), curr); |
---|
3041 | |
---|
3042 | tmpIsSkewConstant = true; |
---|
3043 | |
---|
3044 | for(i=1; i<r->N; i++) |
---|
3045 | for(j=i+1; j<=r->N; j++) |
---|
3046 | { |
---|
3047 | if (MATELEM(CC,i,j) == NULL) |
---|
3048 | qN = NULL; |
---|
3049 | else |
---|
3050 | qN = p_GetCoeff(MATELEM(CC,i,j),curr); |
---|
3051 | |
---|
3052 | if ( qN == NULL ) /* check the consistency: Cij!=0 */ |
---|
3053 | // find also illegal pN |
---|
3054 | { |
---|
3055 | Werror("Incorrect input : matrix of coefficients contains zeros in the upper triangle"); |
---|
3056 | |
---|
3057 | if( currRing != save ) |
---|
3058 | rChangeCurrRing(save); |
---|
3059 | return TRUE; |
---|
3060 | } |
---|
3061 | |
---|
3062 | if (!n_Equal(pN, qN, curr)) tmpIsSkewConstant = false; |
---|
3063 | } |
---|
3064 | |
---|
3065 | if( bCopyInput ) |
---|
3066 | { |
---|
3067 | C = mpCopy(CC, curr, r); // Copy C into r!!!??? |
---|
3068 | bCnew = true; |
---|
3069 | } |
---|
3070 | else |
---|
3071 | C = CC; |
---|
3072 | |
---|
3073 | IsSkewConstant = tmpIsSkewConstant; |
---|
3074 | |
---|
3075 | if ( tmpIsSkewConstant && n_IsOne(pN, curr) ) |
---|
3076 | nctype = nc_lie; |
---|
3077 | else |
---|
3078 | nctype = nc_general; |
---|
3079 | } |
---|
3080 | |
---|
3081 | /* initialition of the matrix D */ |
---|
3082 | if ( DD == NULL ) /* we treat DN only (it could also be NULL) */ |
---|
3083 | { |
---|
3084 | D = mpNew(r->N,r->N); bDnew = true; |
---|
3085 | |
---|
3086 | if (DN == NULL) |
---|
3087 | { |
---|
3088 | if ( (nctype == nc_lie) || (nctype == nc_undef) ) |
---|
3089 | nctype = nc_comm; /* it was nc_skew earlier */ |
---|
3090 | else /* nc_general, nc_skew */ |
---|
3091 | nctype = nc_skew; |
---|
3092 | } |
---|
3093 | else /* DN != NULL */ |
---|
3094 | for(i=1; i<r->N; i++) |
---|
3095 | for(j=i+1; j<=r->N; j++) |
---|
3096 | MATELEM(D,i,j) = prCopyR_NoSort(DN, curr, r); // project DN into r->GetNC()->basering! |
---|
3097 | } |
---|
3098 | else /* DD != NULL */ |
---|
3099 | { |
---|
3100 | bool b = true; // DD == null ? |
---|
3101 | |
---|
3102 | for(int i = 1; (i < r->N) && b; i++) |
---|
3103 | for(int j = i+1; (j <= r->N) && b; j++) |
---|
3104 | if (MATELEM(DD, i, j) != NULL) |
---|
3105 | { |
---|
3106 | b = false; |
---|
3107 | break; |
---|
3108 | } |
---|
3109 | |
---|
3110 | if (b) // D == NULL!!! |
---|
3111 | { |
---|
3112 | if ( (nctype == nc_lie) || (nctype == nc_undef) ) |
---|
3113 | nctype = nc_comm; /* it was nc_skew earlier */ |
---|
3114 | else /* nc_general, nc_skew */ |
---|
3115 | nctype = nc_skew; |
---|
3116 | } |
---|
3117 | |
---|
3118 | if( bCopyInput ) |
---|
3119 | { |
---|
3120 | D = mpCopy(DD, curr, r); // Copy DD into r!!! |
---|
3121 | bDnew = true; |
---|
3122 | } |
---|
3123 | else |
---|
3124 | D = DD; |
---|
3125 | |
---|
3126 | } |
---|
3127 | |
---|
3128 | assume( C != NULL ); |
---|
3129 | assume( D != NULL ); |
---|
3130 | |
---|
3131 | #if OUTPUT |
---|
3132 | PrintS("nc_CallPlural(), Computed data, C: \n"); |
---|
3133 | iiWriteMatrix(C, "C", 2, 4); |
---|
3134 | |
---|
3135 | PrintS("nc_CallPlural(), Computed data, D: \n"); |
---|
3136 | iiWriteMatrix(D, "D", 2, 4); |
---|
3137 | |
---|
3138 | Print("\nTemporary: type = %d, IsSkewConstant = %d\n", nctype, IsSkewConstant); |
---|
3139 | #endif |
---|
3140 | |
---|
3141 | |
---|
3142 | |
---|
3143 | |
---|
3144 | // check the ordering condition for D (both matrix and poly cases): |
---|
3145 | if ( gnc_CheckOrdCondition(D, r) ) |
---|
3146 | { |
---|
3147 | if( bCnew ) mpDelete( &C, r ); |
---|
3148 | if( bDnew ) mpDelete( &D, r ); |
---|
3149 | |
---|
3150 | Werror("Matrix of polynomials violates the ordering condition"); |
---|
3151 | |
---|
3152 | if( currRing != save ) |
---|
3153 | rChangeCurrRing(save); |
---|
3154 | return TRUE; |
---|
3155 | } |
---|
3156 | |
---|
3157 | // okay now we are ready for this!!! |
---|
3158 | |
---|
3159 | // create new non-commutative structure |
---|
3160 | nc_struct *nc_new = (nc_struct *)omAlloc0(sizeof(nc_struct)); |
---|
3161 | |
---|
3162 | ncRingType(nc_new, nctype); |
---|
3163 | |
---|
3164 | nc_new->C = C; // if C and D were given by matrices at the beginning they are in r |
---|
3165 | nc_new->D = D; // otherwise they should be in r->GetNC()->basering(polynomial * Id_{N}) |
---|
3166 | |
---|
3167 | nc_new->IsSkewConstant = (IsSkewConstant?1:0); |
---|
3168 | |
---|
3169 | nc_new->ref = 1; |
---|
3170 | nc_new->basering = r; // !? |
---|
3171 | |
---|
3172 | // Setup new NC structure!!! |
---|
3173 | if (r->GetNC() != NULL) |
---|
3174 | nc_rKill(r); |
---|
3175 | |
---|
3176 | r->ref++; // ? |
---|
3177 | r->GetNC() = nc_new; |
---|
3178 | |
---|
3179 | if( currRing != save ) |
---|
3180 | rChangeCurrRing(save); |
---|
3181 | |
---|
3182 | return gnc_InitMultiplication(r, bSetupQuotient); |
---|
3183 | } |
---|
3184 | |
---|
3185 | ////////////////////////////////////////////////////////////////////////////// |
---|
3186 | |
---|
3187 | bool nc_rCopy(ring res, const ring r, bool bSetupQuotient) |
---|
3188 | { |
---|
3189 | if (nc_CallPlural(r->GetNC()->C, r->GetNC()->D, NULL, NULL, res, bSetupQuotient, true, true, r)) |
---|
3190 | { |
---|
3191 | WarnS("Error occured while coping/setuping the NC structure!"); // No reaction!??? |
---|
3192 | return true; // error |
---|
3193 | } |
---|
3194 | |
---|
3195 | return false; |
---|
3196 | } |
---|
3197 | |
---|
3198 | ////////////////////////////////////////////////////////////////////////////// |
---|
3199 | BOOLEAN gnc_InitMultiplication(ring r, bool bSetupQuotient) |
---|
3200 | { |
---|
3201 | /* returns TRUE if there were errors */ |
---|
3202 | /* initialize the multiplication: */ |
---|
3203 | /* r->GetNC()->MTsize, r->GetNC()->MT, r->GetNC()->COM, */ |
---|
3204 | /* and r->GetNC()->IsSkewConstant for the skew case */ |
---|
3205 | if (rVar(r)==1) |
---|
3206 | { |
---|
3207 | ncRingType(r, nc_comm); |
---|
3208 | r->GetNC()->IsSkewConstant=1; |
---|
3209 | return FALSE; |
---|
3210 | } |
---|
3211 | |
---|
3212 | ring save = currRing; |
---|
3213 | |
---|
3214 | int WeChangeRing = 0; |
---|
3215 | if (currRing!=r) |
---|
3216 | { |
---|
3217 | rChangeCurrRing(r); |
---|
3218 | WeChangeRing = 1; |
---|
3219 | } |
---|
3220 | assume( (currRing == r->GetNC()->basering) |
---|
3221 | || ((currRing->GetNC()!=NULL) && (currRing->GetNC()->basering==r->GetNC()->basering)) ); // otherwise we cannot work with all these matrices! |
---|
3222 | |
---|
3223 | int i,j; |
---|
3224 | r->GetNC()->MT = (matrix *)omAlloc0((r->N*(r->N-1))/2*sizeof(matrix)); |
---|
3225 | r->GetNC()->MTsize = (int *)omAlloc0((r->N*(r->N-1))/2*sizeof(int)); |
---|
3226 | idTest(((ideal)r->GetNC()->C)); |
---|
3227 | matrix COM = mpCopy(r->GetNC()->C); |
---|
3228 | poly p,q; |
---|
3229 | short DefMTsize=7; |
---|
3230 | int IsNonComm=0; |
---|
3231 | int tmpIsSkewConstant; |
---|
3232 | |
---|
3233 | for(i=1; i<r->N; i++) |
---|
3234 | { |
---|
3235 | for(j=i+1; j<=r->N; j++) |
---|
3236 | { |
---|
3237 | if ( MATELEM(r->GetNC()->D,i,j) == NULL ) /* quasicommutative case */ |
---|
3238 | { |
---|
3239 | /* 1x1 mult.matrix */ |
---|
3240 | r->GetNC()->MTsize[UPMATELEM(i,j,r->N)] = 1; |
---|
3241 | r->GetNC()->MT[UPMATELEM(i,j,r->N)] = mpNew(1,1); |
---|
3242 | } |
---|
3243 | else /* pure noncommutative case */ |
---|
3244 | { |
---|
3245 | /* TODO check the special multiplication properties */ |
---|
3246 | IsNonComm = 1; |
---|
3247 | p_Delete(&(MATELEM(COM,i,j)),r); |
---|
3248 | //MATELEM(COM,i,j) = NULL; // done by p_Delete |
---|
3249 | r->GetNC()->MTsize[UPMATELEM(i,j,r->N)] = DefMTsize; /* default sizes */ |
---|
3250 | r->GetNC()->MT[UPMATELEM(i,j,r->N)] = mpNew(DefMTsize, DefMTsize); |
---|
3251 | } |
---|
3252 | /* set MT[i,j,1,1] to c_i_j*x_i*x_j + D_i_j */ |
---|
3253 | p = p_One(r); /* instead of p = pOne(); */ |
---|
3254 | if (MATELEM(r->GetNC()->C,i,j)!=NULL) |
---|
3255 | p_SetCoeff(p,n_Copy(pGetCoeff(MATELEM(r->GetNC()->C,i,j)),r),r); |
---|
3256 | p_SetExp(p,i,1,r); |
---|
3257 | p_SetExp(p,j,1,r); |
---|
3258 | p_Setm(p,r); |
---|
3259 | p_Test(MATELEM(r->GetNC()->D,i,j),r->GetNC()->basering); |
---|
3260 | q = nc_p_CopyGet(MATELEM(r->GetNC()->D,i,j),r); |
---|
3261 | p = p_Add_q(p,q,r); |
---|
3262 | MATELEM(r->GetNC()->MT[UPMATELEM(i,j,r->N)],1,1) = nc_p_CopyPut(p,r); |
---|
3263 | p_Delete(&p,r); |
---|
3264 | // p = NULL;// done by p_Delete |
---|
3265 | } |
---|
3266 | } |
---|
3267 | if (ncRingType(r)==nc_undef) |
---|
3268 | { |
---|
3269 | if (IsNonComm==1) |
---|
3270 | { |
---|
3271 | // assume(pN!=NULL); |
---|
3272 | // if ((tmpIsSkewConstant==1) && (nIsOne(pGetCoeff(pN)))) r->GetNC()->type=nc_lie; |
---|
3273 | // else r->GetNC()->type=nc_general; |
---|
3274 | } |
---|
3275 | if (IsNonComm==0) |
---|
3276 | { |
---|
3277 | ncRingType(r, nc_skew); /* TODO: check whether it is commutative */ |
---|
3278 | r->GetNC()->IsSkewConstant=tmpIsSkewConstant; |
---|
3279 | } |
---|
3280 | } |
---|
3281 | r->GetNC()->COM=COM; |
---|
3282 | |
---|
3283 | nc_p_ProcsSet(r, r->p_Procs); |
---|
3284 | |
---|
3285 | if(bSetupQuotient) // Test me!!! |
---|
3286 | { |
---|
3287 | nc_SetupQuotient(r); |
---|
3288 | } |
---|
3289 | |
---|
3290 | |
---|
3291 | // ??? |
---|
3292 | if( bNoPluralMultiplication ) |
---|
3293 | ncInitSpecialPairMultiplication(r); |
---|
3294 | |
---|
3295 | |
---|
3296 | if(!rIsSCA(r) && !bNoFormula) |
---|
3297 | ncInitSpecialPowersMultiplication(r); |
---|
3298 | |
---|
3299 | |
---|
3300 | if (save != currRing) |
---|
3301 | rChangeCurrRing(save); |
---|
3302 | |
---|
3303 | return FALSE; |
---|
3304 | } |
---|
3305 | |
---|
3306 | void gnc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs) |
---|
3307 | { |
---|
3308 | // "commutative" |
---|
3309 | p_Procs->p_Mult_mm = rGR->p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
3310 | p_Procs->pp_Mult_mm = rGR->p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
3311 | p_Procs->p_Minus_mm_Mult_qq = rGR->p_Procs->p_Minus_mm_Mult_qq = NULL; |
---|
3312 | // gnc_p_Minus_mm_Mult_qq_ign; // should not be used!!!??? |
---|
3313 | |
---|
3314 | |
---|
3315 | |
---|
3316 | // non-commutaitve multiplication by monomial from the left |
---|
3317 | rGR->GetNC()->p_Procs.mm_Mult_p = gnc_mm_Mult_p; |
---|
3318 | rGR->GetNC()->p_Procs.mm_Mult_pp = gnc_mm_Mult_pp; |
---|
3319 | |
---|
3320 | rGR->GetNC()->p_Procs.GB = gnc_gr_bba; // bba even for local case! |
---|
3321 | |
---|
3322 | // rGR->GetNC()->p_Procs.GlobalGB = gnc_gr_bba; |
---|
3323 | // rGR->GetNC()->p_Procs.LocalGB = gnc_gr_mora; |
---|
3324 | |
---|
3325 | |
---|
3326 | #if 0 |
---|
3327 | // Previous Plural's implementation... |
---|
3328 | rGR->GetNC()->p_Procs.SPoly = gnc_CreateSpolyOld; |
---|
3329 | rGR->GetNC()->p_Procs.ReduceSPoly = gnc_ReduceSpolyOld; |
---|
3330 | |
---|
3331 | rGR->GetNC()->p_Procs.BucketPolyRed = gnc_kBucketPolyRedOld; |
---|
3332 | rGR->GetNC()->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZOld; |
---|
3333 | #else |
---|
3334 | // A bit cleaned up and somewhat rewritten functions... |
---|
3335 | rGR->GetNC()->p_Procs.SPoly = gnc_CreateSpolyNew; |
---|
3336 | rGR->GetNC()->p_Procs.ReduceSPoly = gnc_ReduceSpolyNew; |
---|
3337 | |
---|
3338 | rGR->GetNC()->p_Procs.BucketPolyRed = gnc_kBucketPolyRedNew; |
---|
3339 | rGR->GetNC()->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZNew; |
---|
3340 | #endif |
---|
3341 | |
---|
3342 | |
---|
3343 | |
---|
3344 | |
---|
3345 | #if 0 |
---|
3346 | // Old Stuff |
---|
3347 | p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
3348 | _p_procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
3349 | |
---|
3350 | p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
3351 | _p_procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
3352 | |
---|
3353 | p_Procs->p_Minus_mm_Mult_qq = NULL; // gnc_p_Minus_mm_Mult_qq_ign; |
---|
3354 | _p_procs->p_Minus_mm_Mult_qq= NULL; // gnc_p_Minus_mm_Mult_qq_ign; |
---|
3355 | |
---|
3356 | r->GetNC()->mmMultP() = gnc_mm_Mult_p; |
---|
3357 | r->GetNC()->mmMultPP() = gnc_mm_Mult_pp; |
---|
3358 | |
---|
3359 | r->GetNC()->GB() = gnc_gr_bba; |
---|
3360 | |
---|
3361 | r->GetNC()->SPoly() = gnc_CreateSpoly; |
---|
3362 | r->GetNC()->ReduceSPoly() = gnc_ReduceSpoly; |
---|
3363 | |
---|
3364 | #endif |
---|
3365 | } |
---|
3366 | |
---|
3367 | |
---|
3368 | // set pProcs table for rGR and global variable p_Procs |
---|
3369 | void nc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs) |
---|
3370 | { |
---|
3371 | assume(rIsPluralRing(rGR)); |
---|
3372 | assume(p_Procs!=NULL); |
---|
3373 | |
---|
3374 | gnc_p_ProcsSet(rGR, p_Procs); |
---|
3375 | |
---|
3376 | if(rIsSCA(rGR) && bUseExtensions) |
---|
3377 | { |
---|
3378 | sca_p_ProcsSet(rGR, p_Procs); |
---|
3379 | } |
---|
3380 | } |
---|
3381 | |
---|
3382 | |
---|
3383 | |
---|
3384 | /* substitute the n-th variable by e in p |
---|
3385 | * destroy p |
---|
3386 | * e is not a constant |
---|
3387 | */ |
---|
3388 | poly nc_pSubst(poly p, int n, poly e) |
---|
3389 | { |
---|
3390 | int rN=currRing->N; |
---|
3391 | int *PRE = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
3392 | int *SUF = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
3393 | int i,j,pow; |
---|
3394 | number C; |
---|
3395 | poly suf,pre; |
---|
3396 | poly res = NULL; |
---|
3397 | poly out = NULL; |
---|
3398 | while ( p!= NULL ) |
---|
3399 | { |
---|
3400 | C = pGetCoeff(p); |
---|
3401 | pGetExpV(p, PRE); /* faster splitting? */ |
---|
3402 | pow = PRE[n]; PRE[n]=0; |
---|
3403 | res = NULL; |
---|
3404 | if (pow!=0) |
---|
3405 | { |
---|
3406 | for (i=n+1; i<=rN; i++) |
---|
3407 | { |
---|
3408 | SUF[i] = PRE[i]; |
---|
3409 | PRE[i] = 0; |
---|
3410 | } |
---|
3411 | res = pPower(pCopy(e),pow); |
---|
3412 | /* multiply with prefix */ |
---|
3413 | pre = pOne(); |
---|
3414 | pSetExpV(pre,PRE); |
---|
3415 | pSetm(pre); |
---|
3416 | res = nc_mm_Mult_p(pre,res,currRing); |
---|
3417 | /* multiply with suffix */ |
---|
3418 | suf = pOne(); |
---|
3419 | pSetExpV(suf,SUF); |
---|
3420 | pSetm(suf); |
---|
3421 | res = p_Mult_mm(res,suf,currRing); |
---|
3422 | res = p_Mult_nn(res,C,currRing); |
---|
3423 | pSetComp(res,PRE[0]); |
---|
3424 | } |
---|
3425 | else /* pow==0 */ |
---|
3426 | { |
---|
3427 | res = pHead(p); |
---|
3428 | } |
---|
3429 | p = pLmDeleteAndNext(p); |
---|
3430 | out = pAdd(out,res); |
---|
3431 | } |
---|
3432 | freeT(PRE,rN); |
---|
3433 | freeT(SUF,rN); |
---|
3434 | return(out); |
---|
3435 | } |
---|
3436 | |
---|
3437 | static ideal idPrepareStd(ideal T, ideal s, int k) |
---|
3438 | { |
---|
3439 | /* T is a left SB, without zeros, s is a list with zeros */ |
---|
3440 | #ifdef PDEBUG |
---|
3441 | if (IDELEMS(s)!=IDELEMS(T)) |
---|
3442 | { |
---|
3443 | Print("ideals of diff. size!!!"); |
---|
3444 | } |
---|
3445 | #endif |
---|
3446 | ideal t = idCopy(T); |
---|
3447 | int j,rs=idRankFreeModule(s),rt=idRankFreeModule(t); |
---|
3448 | poly p,q; |
---|
3449 | |
---|
3450 | ideal res = idInit(2*idElem(t),1+idElem(t)); |
---|
3451 | if (rs == 0) |
---|
3452 | { |
---|
3453 | for (j=0; j<IDELEMS(t); j++) |
---|
3454 | { |
---|
3455 | if (s->m[j]!=NULL) pSetCompP(s->m[j],1); |
---|
3456 | if (t->m[j]!=NULL) pSetCompP(t->m[j],1); |
---|
3457 | } |
---|
3458 | k = si_max(k,1); |
---|
3459 | } |
---|
3460 | for (j=0; j<IDELEMS(t); j++) |
---|
3461 | { |
---|
3462 | if (s->m[j]!=NULL) |
---|
3463 | { |
---|
3464 | p = s->m[j]; |
---|
3465 | q = pOne(); |
---|
3466 | pSetComp(q,k+1+j); |
---|
3467 | pSetmComp(q); |
---|
3468 | #if 0 |
---|
3469 | while (pNext(p)) pIter(p); |
---|
3470 | pNext(p) = q; |
---|
3471 | #else |
---|
3472 | p = pAdd(p,q); |
---|
3473 | s->m[j] = p; |
---|
3474 | #ifdef PDEBUG |
---|
3475 | pTest(p); |
---|
3476 | #endif |
---|
3477 | #endif |
---|
3478 | } |
---|
3479 | } |
---|
3480 | res = idSimpleAdd(t,s); |
---|
3481 | idDelete(&t); |
---|
3482 | res->rank = 1+idElem(T); |
---|
3483 | return(res); |
---|
3484 | } |
---|
3485 | |
---|
3486 | ideal Approx_Step(ideal L) |
---|
3487 | { |
---|
3488 | int N=currRing->N; |
---|
3489 | int i,j; // k=syzcomp |
---|
3490 | int flag, flagcnt=0, syzcnt=0; |
---|
3491 | int syzcomp = 0; |
---|
3492 | int k=1; /* for ideals not modules */ |
---|
3493 | ideal I = kStd(L, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
3494 | idSkipZeroes(I); |
---|
3495 | ideal s_I; |
---|
3496 | int idI = idElem(I); |
---|
3497 | ideal trickyQuotient,s_trickyQuotient; |
---|
3498 | if (currQuotient !=NULL) |
---|
3499 | { |
---|
3500 | trickyQuotient = idSimpleAdd(currQuotient,I); |
---|
3501 | } |
---|
3502 | else |
---|
3503 | trickyQuotient = I; |
---|
3504 | idSkipZeroes(trickyQuotient); |
---|
3505 | poly *var = (poly *)omAlloc0((N+1)*sizeof(poly)); |
---|
3506 | // poly *W = (poly *)omAlloc0((2*N+1)*sizeof(poly)); |
---|
3507 | resolvente S = (resolvente)omAlloc0((N+1)*sizeof(ideal)); |
---|
3508 | ideal SI, res; |
---|
3509 | matrix MI; |
---|
3510 | poly x=pOne(); |
---|
3511 | var[0]=x; |
---|
3512 | ideal h2, h3, s_h2, s_h3; |
---|
3513 | poly p,q,qq; |
---|
3514 | /* init vars */ |
---|
3515 | for (i=1; i<=N; i++ ) |
---|
3516 | { |
---|
3517 | x = pOne(); |
---|
3518 | pSetExp(x,i,1); |
---|
3519 | pSetm(x); |
---|
3520 | var[i]=pCopy(x); |
---|
3521 | } |
---|
3522 | /* init NF's */ |
---|
3523 | for (i=1; i<=N; i++ ) |
---|
3524 | { |
---|
3525 | h2 = idInit(idI,1); |
---|
3526 | flag = 0; |
---|
3527 | for (j=0; j< idI; j++ ) |
---|
3528 | { |
---|
3529 | q = pp_Mult_mm(I->m[j],var[i],currRing); |
---|
3530 | q = kNF(I,currQuotient,q,0,0); |
---|
3531 | if (q!=0) |
---|
3532 | { |
---|
3533 | h2->m[j]=pCopy(q); |
---|
3534 | // pShift(&(h2->m[flag]),1); |
---|
3535 | flag++; |
---|
3536 | pDelete(&q); |
---|
3537 | } |
---|
3538 | else |
---|
3539 | h2->m[j]=0; |
---|
3540 | } |
---|
3541 | /* W[1..idElems(I)] */ |
---|
3542 | if (flag >0) |
---|
3543 | { |
---|
3544 | /* compute syzygies with values in I*/ |
---|
3545 | // idSkipZeroes(h2); |
---|
3546 | // h2 = idSimpleAdd(h2,I); |
---|
3547 | // h2->rank=flag+idI+1; |
---|
3548 | idTest(h2); |
---|
3549 | idShow(h2); |
---|
3550 | ring orig_ring=currRing; |
---|
3551 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
3552 | syzcomp = 1; |
---|
3553 | rSetSyzComp(syzcomp); |
---|
3554 | if (orig_ring != syz_ring) |
---|
3555 | { |
---|
3556 | s_h2=idrCopyR_NoSort(h2,orig_ring); |
---|
3557 | // s_trickyQuotient=idrCopyR_NoSort(trickyQuotient,orig_ring); |
---|
3558 | // rDebugPrint(syz_ring); |
---|
3559 | s_I=idrCopyR_NoSort(I,orig_ring); |
---|
3560 | } |
---|
3561 | else |
---|
3562 | { |
---|
3563 | s_h2 = h2; |
---|
3564 | s_I = I; |
---|
3565 | // s_trickyQuotient=trickyQuotient; |
---|
3566 | } |
---|
3567 | idTest(s_h2); |
---|
3568 | // idTest(s_trickyQuotient); |
---|
3569 | Print(".proceeding with the variable %d\n",i); |
---|
3570 | s_h3 = idPrepareStd(s_I, s_h2, 1); |
---|
3571 | BITSET save_test=test; |
---|
3572 | test|=Sy_bit(OPT_SB_1); |
---|
3573 | idTest(s_h3); |
---|
3574 | idDelete(&s_h2); |
---|
3575 | s_h2=idCopy(s_h3); |
---|
3576 | idDelete(&s_h3); |
---|
3577 | Print("...computing Syz"); |
---|
3578 | s_h3 = kStd(s_h2, currQuotient,(tHomog)FALSE,NULL,NULL,syzcomp,idI); |
---|
3579 | test=save_test; |
---|
3580 | idShow(s_h3); |
---|
3581 | if (orig_ring != syz_ring) |
---|
3582 | { |
---|
3583 | idDelete(&s_h2); |
---|
3584 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
3585 | { |
---|
3586 | if (s_h3->m[j] != NULL) |
---|
3587 | { |
---|
3588 | if (p_MinComp(s_h3->m[j],syz_ring) > syzcomp) /* i.e. it is a syzygy */ |
---|
3589 | pShift(&s_h3->m[j], -syzcomp); |
---|
3590 | else |
---|
3591 | pDelete(&s_h3->m[j]); |
---|
3592 | } |
---|
3593 | } |
---|
3594 | idSkipZeroes(s_h3); |
---|
3595 | s_h3->rank -= syzcomp; |
---|
3596 | rChangeCurrRing(orig_ring); |
---|
3597 | // s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
3598 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
3599 | rKill(syz_ring); |
---|
3600 | } |
---|
3601 | idTest(s_h3); |
---|
3602 | S[syzcnt]=kStd(s_h3,currQuotient,(tHomog)FALSE,NULL,NULL); |
---|
3603 | syzcnt++; |
---|
3604 | idDelete(&s_h3); |
---|
3605 | } /* end if flag >0 */ |
---|
3606 | else |
---|
3607 | { |
---|
3608 | flagcnt++; |
---|
3609 | } |
---|
3610 | } |
---|
3611 | if (flagcnt == N) |
---|
3612 | { |
---|
3613 | Print("the input is a two--sided ideal"); |
---|
3614 | return(I); |
---|
3615 | } |
---|
3616 | if (syzcnt >0) |
---|
3617 | { |
---|
3618 | Print("..computing Intersect of %d modules\n",syzcnt); |
---|
3619 | if (syzcnt == 1) |
---|
3620 | SI = S[0]; |
---|
3621 | else |
---|
3622 | SI = idMultSect(S, syzcnt); |
---|
3623 | idShow(SI); |
---|
3624 | MI = idModule2Matrix(SI); |
---|
3625 | res= idInit(MATCOLS(MI),1); |
---|
3626 | for (i=1; i<= MATCOLS(MI); i++) |
---|
3627 | { |
---|
3628 | p = NULL; |
---|
3629 | for (j=0; j< idElem(I); j++) |
---|
3630 | { |
---|
3631 | q = pCopy(MATELEM(MI,j+1,i)); |
---|
3632 | if (q!=NULL) |
---|
3633 | { |
---|
3634 | q = pMult(q,pCopy(I->m[j])); |
---|
3635 | p = pAdd(p,q); |
---|
3636 | } |
---|
3637 | } |
---|
3638 | res->m[i-1]=p; |
---|
3639 | } |
---|
3640 | Print("final std"); |
---|
3641 | res = kStd(res, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
3642 | idSkipZeroes(res); |
---|
3643 | return(res); |
---|
3644 | } |
---|
3645 | else |
---|
3646 | { |
---|
3647 | Print("No syzygies"); |
---|
3648 | return(I); |
---|
3649 | } |
---|
3650 | } |
---|
3651 | |
---|
3652 | |
---|
3653 | // creates a commutative nc extension; "converts" comm.ring to a Plural ring |
---|
3654 | ring nc_rCreateNCcomm(ring r) |
---|
3655 | { |
---|
3656 | if (rIsPluralRing(r)) return r; |
---|
3657 | |
---|
3658 | matrix C = mpNew(r->N,r->N); // ring-independent!?! |
---|
3659 | matrix D = mpNew(r->N,r->N); |
---|
3660 | |
---|
3661 | for(int i=1; i<r->N; i++) |
---|
3662 | for(int j=i+1; j<=r->N; j++) |
---|
3663 | MATELEM(C,i,j) = p_One( r); |
---|
3664 | |
---|
3665 | if (nc_CallPlural(C, D, NULL, NULL, r)) // TODO: what about quotient ideal? |
---|
3666 | WarnS("Error initializing multiplication!"); // No reaction!??? |
---|
3667 | |
---|
3668 | return r; |
---|
3669 | } |
---|
3670 | |
---|
3671 | poly p_CopyEmbed(poly p, ring srcRing, int shift, int par_shift) |
---|
3672 | /* NOT USED ANYMORE: replaced by maFindPerm in ring.cc */ |
---|
3673 | /* for use with embeddings: currRing is a sum of smaller rings */ |
---|
3674 | /* and srcRing is one of such smaller rings */ |
---|
3675 | /* shift defines the position of a subring in srcRing */ |
---|
3676 | /* par_shift defines the position of a subfield in basefield of CurrRing */ |
---|
3677 | { |
---|
3678 | if (currRing == srcRing) |
---|
3679 | { |
---|
3680 | return(p_Copy(p,currRing)); |
---|
3681 | } |
---|
3682 | nMapFunc nMap=nSetMap(srcRing); |
---|
3683 | poly q; |
---|
3684 | // if ( nMap == nCopy) |
---|
3685 | // { |
---|
3686 | // q = prCopyR(p,srcRing); |
---|
3687 | // } |
---|
3688 | // else |
---|
3689 | { |
---|
3690 | int *perm = (int *)omAlloc0((srcRing->N+1)*sizeof(int)); |
---|
3691 | int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
3692 | // int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
3693 | int i; |
---|
3694 | // if (srcRing->P > 0) |
---|
3695 | // { |
---|
3696 | // for (i=0; i<srcRing->P; i++) |
---|
3697 | // par_perm[i]=-i; |
---|
3698 | // } |
---|
3699 | if ((shift<0) || (shift > currRing->N)) |
---|
3700 | { |
---|
3701 | Werror("bad shifts in p_CopyEmbed"); |
---|
3702 | return(0); |
---|
3703 | } |
---|
3704 | for (i=1; i<= srcRing->N; i++) |
---|
3705 | { |
---|
3706 | perm[i] = shift+i; |
---|
3707 | } |
---|
3708 | q = pPermPoly(p,perm,srcRing,nMap,par_perm,srcRing->P); |
---|
3709 | } |
---|
3710 | return(q); |
---|
3711 | } |
---|
3712 | |
---|
3713 | poly pOppose(ring Rop, poly p) |
---|
3714 | /* opposes a vector p from Rop to currRing */ |
---|
3715 | { |
---|
3716 | /* the simplest case:*/ |
---|
3717 | if ( Rop == currRing ) return(pCopy(p)); |
---|
3718 | /* check Rop == rOpposite(currRing) */ |
---|
3719 | if ( !rIsLikeOpposite(currRing, Rop) ) |
---|
3720 | { |
---|
3721 | WarnS("an opposite ring should be used"); |
---|
3722 | return NULL; |
---|
3723 | } |
---|
3724 | /* nMapFunc nMap = nSetMap(Rop);*/ |
---|
3725 | /* since we know that basefields coinside! */ |
---|
3726 | int *perm=(int *)omAlloc0((Rop->N+1)*sizeof(int)); |
---|
3727 | if (!p_IsConstantPoly(p, Rop)) |
---|
3728 | { |
---|
3729 | /* we know perm exactly */ |
---|
3730 | int i; |
---|
3731 | for(i=1; i<=Rop->N; i++) |
---|
3732 | { |
---|
3733 | perm[i] = Rop->N+1-i; |
---|
3734 | } |
---|
3735 | } |
---|
3736 | poly res = pPermPoly(p, perm, Rop, nCopy); |
---|
3737 | omFreeSize((ADDRESS)perm,(Rop->N+1)*sizeof(int)); |
---|
3738 | return res; |
---|
3739 | } |
---|
3740 | |
---|
3741 | ideal idOppose(ring Rop, ideal I) |
---|
3742 | /* opposes a module I from Rop to currRing */ |
---|
3743 | { |
---|
3744 | /* the simplest case:*/ |
---|
3745 | if ( Rop == currRing ) return idCopy(I); |
---|
3746 | /* check Rop == rOpposite(currRing) */ |
---|
3747 | if (!rIsLikeOpposite(currRing, Rop)) |
---|
3748 | { |
---|
3749 | WarnS("an opposite ring should be used"); |
---|
3750 | return NULL; |
---|
3751 | } |
---|
3752 | int i; |
---|
3753 | ideal idOp = idInit(I->ncols, I->rank); |
---|
3754 | for (i=0; i< (I->ncols)*(I->nrows); i++) |
---|
3755 | { |
---|
3756 | idOp->m[i] = pOppose(Rop,I->m[i]); |
---|
3757 | } |
---|
3758 | idTest(idOp); |
---|
3759 | return idOp; |
---|
3760 | } |
---|
3761 | |
---|
3762 | BOOLEAN rIsLikeOpposite(ring rBase, ring rCandidate) |
---|
3763 | /* checks whether rings rBase and rCandidate */ |
---|
3764 | /* could be opposite to each other */ |
---|
3765 | /* returns TRUE if it is so */ |
---|
3766 | { |
---|
3767 | /* the same basefield */ |
---|
3768 | int diagnose = TRUE; |
---|
3769 | ring save = currRing; |
---|
3770 | rChangeCurrRing(rBase); |
---|
3771 | nMapFunc nMap = nSetMap(rCandidate); |
---|
3772 | if (nMap != nCopy) diagnose = FALSE; |
---|
3773 | rChangeCurrRing(save); |
---|
3774 | /* same number of variables */ |
---|
3775 | if (rBase->N != rCandidate->N) diagnose = FALSE; |
---|
3776 | /* nc and comm ring */ |
---|
3777 | if ( rIsPluralRing(rBase) != rIsPluralRing(rCandidate) ) diagnose = FALSE; |
---|
3778 | /* both are qrings */ |
---|
3779 | /* NO CHECK, since it is used in building opposite qring */ |
---|
3780 | /* if ( ((rBase->qideal != NULL) && (rCandidate->qideal == NULL)) */ |
---|
3781 | /* || ((rBase->qideal == NULL) && (rCandidate->qideal != NULL)) ) */ |
---|
3782 | /* diagnose = FALSE; */ |
---|
3783 | /* TODO: varnames are e->E etc */ |
---|
3784 | return diagnose; |
---|
3785 | } |
---|
3786 | |
---|
3787 | |
---|
3788 | |
---|
3789 | bool nc_SetupQuotient(ring rGR, const ring rG, bool bCopy) |
---|
3790 | { |
---|
3791 | if( rGR->qideal == NULL ) |
---|
3792 | return false; // no quotient = no work! done!? |
---|
3793 | |
---|
3794 | bool ret = true; |
---|
3795 | // currently only super-commutative extension deals with factors. |
---|
3796 | |
---|
3797 | if( bUseExtensions ) |
---|
3798 | { |
---|
3799 | bool sca_ret = sca_SetupQuotient(rGR, rG, bCopy); |
---|
3800 | |
---|
3801 | if(sca_ret) // yes it was dealt with! |
---|
3802 | ret = false; |
---|
3803 | } |
---|
3804 | |
---|
3805 | if( bCopy ) |
---|
3806 | { |
---|
3807 | assume(rIsPluralRing(rGR) == rIsPluralRing(rG)); |
---|
3808 | assume((rGR->qideal==NULL) == (rG->qideal==NULL)); |
---|
3809 | assume(rIsSCA(rGR) == rIsSCA(rG)); |
---|
3810 | assume(ncRingType(rGR) == ncRingType(rG)); |
---|
3811 | } |
---|
3812 | |
---|
3813 | return ret; |
---|
3814 | } |
---|
3815 | |
---|
3816 | |
---|
3817 | |
---|
3818 | // int Commutative_Context(ring r, leftv expression) |
---|
3819 | // /* returns 1 if expression consists */ |
---|
3820 | // /* of commutative elements */ |
---|
3821 | // { |
---|
3822 | // /* crucial: poly -> ideal, module, matrix */ |
---|
3823 | // } |
---|
3824 | |
---|
3825 | // int Comm_Context_Poly(ring r, poly p) |
---|
3826 | // { |
---|
3827 | // poly COMM=r->GetNC()->COMM; |
---|
3828 | // poly pp=pOne(); |
---|
3829 | // memset(pp->exp,0,r->ExpL_Size*sizeof(long)); |
---|
3830 | // while (p!=NULL) |
---|
3831 | // { |
---|
3832 | // for (i=0;i<=r->ExpL_Size;i++) |
---|
3833 | // { |
---|
3834 | // if ((p->exp[i]) && (pp->exp[i])) return(FALSE); |
---|
3835 | // /* nonzero exponent of non-comm variable */ |
---|
3836 | // } |
---|
3837 | // pIter(p); |
---|
3838 | // } |
---|
3839 | // return(TRUE); |
---|
3840 | // } |
---|
3841 | #endif |
---|