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 1.55 2008-06-10 14:35:40 motsak Exp $ |
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10 | *******************************************************************/ |
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11 | |
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12 | #define OM_CHECK 4 |
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13 | #define OM_TRACK 5 |
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14 | |
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15 | #include "mod2.h" |
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16 | |
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17 | #ifdef HAVE_PLURAL |
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18 | #define PLURAL_INTERNAL_DECLARATIONS |
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19 | |
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20 | #include "febase.h" |
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21 | #include "ring.h" |
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22 | #include "polys.h" |
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23 | #include "numbers.h" |
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24 | #include "ideals.h" |
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25 | #include "matpol.h" |
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26 | #include "kbuckets.h" |
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27 | #include "kstd1.h" |
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28 | #include "sbuckets.h" |
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29 | #include "prCopy.h" |
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30 | #include "p_Mult_q.h" |
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31 | |
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32 | #include "pInline1.h" |
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33 | |
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34 | #include "gring.h" |
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35 | #include "sca.h" |
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36 | |
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37 | |
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38 | #define MYTEST 0 |
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39 | #define OUTPUT 0 |
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40 | |
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41 | |
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42 | // dirty tricks: |
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43 | #include "p_MemAdd.h" |
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44 | |
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45 | bool bUseExtensions = true; |
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46 | |
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47 | /* global nc_macros : */ |
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48 | |
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49 | #define freeT(A,v) omFreeSize((ADDRESS)A,(v+1)*sizeof(int)) |
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50 | #define freeN(A,k) omFreeSize((ADDRESS)A,k*sizeof(number)) |
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51 | |
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52 | |
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53 | // some forward declarations: |
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54 | |
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55 | |
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56 | // polynomial multiplication functions for p_Procs : |
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57 | poly gnc_pp_Mult_mm(const poly p, const poly m, const ring r, poly &last); |
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58 | poly gnc_p_Mult_mm(poly p, const poly m, const ring r); |
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59 | poly gnc_mm_Mult_p(const poly m, poly p, const ring r); |
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60 | poly gnc_mm_Mult_pp(const poly m, const poly p, const ring r); |
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61 | |
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62 | |
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63 | // set pProcs for r and global variable p_Procs as for general non-commutative algebras. |
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64 | void gnc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs); |
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65 | |
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66 | /* syzygies : */ |
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67 | poly gnc_CreateSpolyOld(const poly p1, const poly p2/*, poly spNoether*/, const ring r); |
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68 | poly gnc_ReduceSpolyOld(const poly p1, poly p2/*, poly spNoether*/, const ring r); |
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69 | |
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70 | poly gnc_CreateSpolyNew(const poly p1, const poly p2/*, poly spNoether*/, const ring r); |
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71 | poly gnc_ReduceSpolyNew(const poly p1, poly p2/*, poly spNoether*/, const ring r); |
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72 | |
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73 | |
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74 | |
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75 | void gnc_kBucketPolyRedNew(kBucket_pt b, poly p, number *c); |
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76 | void gnc_kBucketPolyRed_ZNew(kBucket_pt b, poly p, number *c); |
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77 | |
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78 | void gnc_kBucketPolyRedOld(kBucket_pt b, poly p, number *c); |
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79 | void gnc_kBucketPolyRed_ZOld(kBucket_pt b, poly p, number *c); |
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80 | |
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81 | |
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82 | // poly gnc_ReduceSpolyNew(poly p1, poly p2, poly spNoether, const ring r); |
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83 | // void gnc_ReduceSpolyTail(poly p1, poly q, poly q2, poly spNoether, const ring r); |
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84 | |
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85 | // void nc_kBucketPolyRed(kBucket_pt b, poly p); |
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86 | |
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87 | ideal gnc_gr_mora(const ideal, const ideal, const intvec *, const intvec *, kStrategy); // Not yet! |
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88 | ideal gnc_gr_bba (const ideal F, const ideal Q, const intvec *, const intvec *, kStrategy strat); |
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89 | |
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90 | |
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91 | #if 0 |
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92 | // deprecated functions: |
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93 | // 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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94 | // poly gnc_p_Minus_mm_Mult_qq(poly p, const poly m, poly q, const ring r); |
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95 | // 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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96 | // 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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97 | #endif |
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98 | |
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99 | |
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100 | |
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101 | /*2 |
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102 | * returns the LCM of the head terms of a and b |
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103 | * without coefficient!!! |
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104 | */ |
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105 | poly p_Lcm(const poly a, const poly b, const long lCompM, const ring r) |
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106 | { |
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107 | poly m = // p_ISet(1, r); |
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108 | p_Init(r); |
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109 | |
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110 | const int pVariables = r->N; |
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111 | |
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112 | for (int i = pVariables; i; i--) |
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113 | { |
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114 | const int lExpA = p_GetExp (a, i, r); |
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115 | const int lExpB = p_GetExp (b, i, r); |
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116 | |
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117 | p_SetExp (m, i, si_max(lExpA, lExpB), r); |
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118 | } |
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119 | |
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120 | p_SetComp (m, lCompM, r); |
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121 | |
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122 | p_Setm(m,r); |
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123 | |
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124 | #ifdef PDEBUG |
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125 | // p_Test(m,r); |
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126 | #endif |
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127 | |
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128 | n_New(&(p_GetCoeff(m, r)), r); |
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129 | |
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130 | return(m); |
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131 | }; |
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132 | |
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133 | poly p_Lcm(const poly a, const poly b, const ring r) |
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134 | { |
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135 | #ifdef PDEBUG |
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136 | p_Test(a, r); |
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137 | p_Test(b, r); |
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138 | #endif |
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139 | |
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140 | const long lCompP1 = p_GetComp(a, r); |
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141 | const long lCompP2 = p_GetComp(b, r); |
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142 | |
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143 | const poly m = p_Lcm(a, b, si_max(lCompP1, lCompP2), r); |
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144 | |
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145 | #ifdef PDEBUG |
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146 | // p_Test(m,r); |
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147 | #endif |
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148 | return(m); |
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149 | }; |
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150 | |
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151 | |
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152 | |
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153 | /////////////////////////////////////////////////////////////////////////////// |
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154 | poly nc_p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, |
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155 | const int, const poly, const ring r) |
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156 | { |
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157 | poly mc = p_Neg( p_Copy(m, r), r ); |
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158 | poly mmc = nc_mm_Mult_pp( mc, q, r ); |
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159 | p_Delete(&mc, r); |
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160 | |
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161 | p = p_Add_q(p, mmc, r); |
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162 | |
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163 | lp = pLength(p); // ring independent! |
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164 | |
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165 | return(p); |
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166 | } |
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167 | |
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168 | // returns p + m*q destroys p, const: q, m |
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169 | poly nc_p_Plus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, |
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170 | const int, const ring r) |
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171 | { |
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172 | p = p_Add_q(p, nc_mm_Mult_pp( m, q, r ), r); |
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173 | |
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174 | lp = pLength(p); |
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175 | |
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176 | return(p); |
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177 | } |
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178 | |
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179 | #if 0 |
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180 | 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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181 | { |
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182 | poly t; |
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183 | int i; |
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184 | |
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185 | return gnc_p_Minus_mm_Mult_qq(p, m, q, d1, i, t, r); |
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186 | } |
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187 | #endif |
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188 | |
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189 | |
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190 | //----------- auxiliary routines-------------------------- |
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191 | poly _gnc_p_Mult_q(poly p, poly q, const int copy, const ring r) |
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192 | /* destroy p,q unless copy=1 */ |
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193 | { |
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194 | poly res=NULL; |
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195 | poly ghost=NULL; |
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196 | poly qq,pp; |
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197 | if (copy) |
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198 | { |
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199 | qq=p_Copy(q,r); |
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200 | pp=p_Copy(p,r); |
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201 | } |
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202 | else |
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203 | { |
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204 | qq=q; |
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205 | pp=p; |
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206 | } |
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207 | while (qq!=NULL) |
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208 | { |
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209 | res=p_Add_q(res, pp_Mult_mm(pp, qq, r), r); // p_Head(qq, r)? |
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210 | qq=p_LmDeleteAndNext(qq,r); |
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211 | } |
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212 | p_Delete(&pp,r); |
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213 | return(res); |
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214 | } |
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215 | |
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216 | // return pPolyP * pPolyQ; destroy or reuse pPolyP and pPolyQ |
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217 | poly _nc_p_Mult_q(poly pPolyP, poly pPolyQ, const ring rRing) |
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218 | { |
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219 | assume( rIsPluralRing(rRing) ); |
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220 | |
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221 | poly pResult = NULL; |
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222 | |
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223 | // always length(q) times "p * q[j]" |
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224 | for( ; pPolyQ!=NULL; pPolyQ = p_LmDeleteAndNext( pPolyQ, rRing ) ) |
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225 | pResult = p_Add_q( pResult, pp_Mult_mm( pPolyP, pPolyQ, rRing), rRing ); |
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226 | // rRing->p_Procs->pp_Mult_mm() <--> sca_nc_pp_Mult_mm |
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227 | |
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228 | p_Delete( &pPolyP, rRing ); |
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229 | |
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230 | #ifdef PDEBUG |
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231 | p_Test(pResult,rRing); |
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232 | #endif |
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233 | |
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234 | return(pResult); |
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235 | } |
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236 | |
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237 | |
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238 | // return pPolyP * pPolyQ; preserve pPolyP and pPolyQ |
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239 | poly _nc_pp_Mult_qq(const poly pPolyP, const poly pPolyQ, const ring rRing) |
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240 | { |
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241 | assume( rIsPluralRing(rRing) ); |
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242 | |
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243 | poly pResult = NULL; |
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244 | |
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245 | // always length(q) times "p * q[j]" |
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246 | for( poly q = pPolyQ; q !=NULL; q = pNext(q) ) |
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247 | pResult = p_Add_q( pResult, pp_Mult_mm(pPolyP, q, rRing), rRing ); |
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248 | |
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249 | #ifdef PDEBUG |
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250 | p_Test(pResult,rRing); |
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251 | #endif |
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252 | |
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253 | return(pResult); |
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254 | } |
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255 | |
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256 | |
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257 | |
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258 | poly gnc_mm_Mult_nn (int *F, int *G, const ring r); |
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259 | poly gnc_mm_Mult_uu (int *F,int jG,int bG, const ring r); |
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260 | |
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261 | /* #define nc_uu_Mult_ww nc_uu_Mult_ww_vert */ |
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262 | poly gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r); |
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263 | /* poly nc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r); */ |
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264 | /* poly nc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r); */ |
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265 | /* poly nc_uu_Mult_ww_hvdiag (int i, int a, int j, int b, const ring r); */ |
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266 | /* not written yet */ |
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267 | |
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268 | |
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269 | poly gnc_p_Mult_mm_Common(poly p, const poly m, int side, const ring r) |
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270 | /* p is poly, m is mono with coeff, destroys p */ |
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271 | /* if side==1, computes p_Mult_mm; otherwise, mm_Mult_p */ |
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272 | { |
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273 | if ((p==NULL) || (m==NULL)) return NULL; |
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274 | /* if (pNext(p)==NULL) return(nc_mm_Mult_nn(p,pCopy(m),r)); */ |
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275 | /* excluded - the cycle will do it anyway - OK. */ |
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276 | if (p_IsConstant(m,r)) return(p_Mult_nn(p,p_GetCoeff(m,r),r)); |
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277 | |
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278 | #ifdef PDEBUG |
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279 | p_Test(p,r); |
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280 | p_Test(m,r); |
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281 | #endif |
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282 | poly v=NULL; |
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283 | int rN=r->N; |
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284 | int *P=(int *)omAlloc0((rN+1)*sizeof(int)); |
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285 | int *M=(int *)omAlloc0((rN+1)*sizeof(int)); |
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286 | /* coefficients: */ |
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287 | number cP,cM,cOut; |
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288 | p_GetExpV(m, M, r); |
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289 | cM=p_GetCoeff(m,r); |
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290 | /* components:*/ |
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291 | const int expM=p_GetComp(m,r); |
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292 | int expP=0; |
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293 | int expOut=0; |
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294 | /* bucket constraints: */ |
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295 | int UseBuckets=1; |
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296 | if (pLength(p)< MIN_LENGTH_BUCKET || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
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297 | sBucket_pt bu_out; |
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298 | poly out=NULL; |
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299 | if (UseBuckets) bu_out=sBucketCreate(r); |
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300 | |
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301 | while (p!=NULL) |
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302 | { |
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303 | #ifdef PDEBUG |
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304 | p_Test(p,r); |
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305 | #endif |
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306 | expP=p_GetComp(p,r); |
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307 | if (expP==0) |
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308 | { |
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309 | expOut=expM; |
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310 | } |
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311 | else |
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312 | { |
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313 | if (expM==0) |
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314 | { |
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315 | expOut=expP; |
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316 | #ifdef PDEBUG |
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317 | if (side) |
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318 | { |
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319 | Print("gnc_p_Mult_mm: Multiplication in the left module from the right"); |
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320 | } |
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321 | #endif |
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322 | } |
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323 | else |
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324 | { |
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325 | /* REPORT_ERROR */ |
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326 | #ifdef PDEBUG |
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327 | const char* s; |
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328 | if (side==1) s="gnc_p_Mult_mm"; |
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329 | else s="gnc_mm_Mult_p"; |
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330 | Print("%s: exponent mismatch %d and %d\n",s,expP,expM); |
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331 | #endif |
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332 | expOut=0; |
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333 | } |
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334 | } |
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335 | p_GetExpV(p,P,r); |
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336 | cP=p_GetCoeff(p,r); |
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337 | cOut=n_Mult(cP,cM,r); |
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338 | if (side==1) |
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339 | { |
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340 | v = gnc_mm_Mult_nn(P, M, r); |
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341 | } |
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342 | else |
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343 | { |
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344 | v = gnc_mm_Mult_nn(M, P, r); |
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345 | } |
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346 | v = p_Mult_nn(v,cOut,r); |
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347 | p_SetCompP(v,expOut,r); |
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348 | if (UseBuckets) sBucket_Add_p(bu_out,v,pLength(v)); |
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349 | else out = p_Add_q(out,v,r); |
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350 | p_DeleteLm(&p,r); |
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351 | } |
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352 | freeT(P,rN); |
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353 | freeT(M,rN); |
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354 | if (UseBuckets) |
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355 | { |
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356 | out = NULL; |
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357 | int len = pLength(out); |
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358 | sBucketDestroyAdd(bu_out, &out, &len); |
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359 | } |
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360 | #ifdef PDEBUG |
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361 | p_Test(out,r); |
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362 | #endif |
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363 | return(out); |
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364 | } |
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365 | |
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366 | /* poly functions defined in p_Procs : */ |
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367 | poly gnc_pp_Mult_mm(const poly p, const poly m, const ring r, poly &last) |
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368 | { |
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369 | return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 1, r) ); |
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370 | } |
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371 | |
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372 | poly gnc_p_Mult_mm(poly p, const poly m, const ring r) |
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373 | { |
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374 | return( gnc_p_Mult_mm_Common(p, m, 1, r) ); |
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375 | } |
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376 | |
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377 | poly gnc_mm_Mult_p(const poly m, poly p, const ring r) |
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378 | { |
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379 | return( gnc_p_Mult_mm_Common(p, m, 0, r) ); |
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380 | } |
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381 | |
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382 | poly gnc_mm_Mult_pp(const poly m, const poly p, const ring r) |
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383 | { |
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384 | return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 0, r) ); |
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385 | } |
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386 | |
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387 | |
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388 | |
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389 | poly gnc_mm_Mult_nn(int *F0, int *G0, const ring r) |
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390 | /* destroys nothing, no coeffs and exps */ |
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391 | { |
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392 | poly out=NULL; |
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393 | int i,j; |
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394 | int iF,jG,iG; |
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395 | int rN=r->N; |
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396 | int ExpSize=(((rN+1)*sizeof(int)+sizeof(long)-1)/sizeof(long))*sizeof(long); |
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397 | |
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398 | int *F=(int *)omAlloc0((rN+1)*sizeof(int)); |
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399 | int *G=(int *)omAlloc0((rN+1)*sizeof(int)); |
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400 | |
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401 | memcpy(F, F0,(rN+1)*sizeof(int)); |
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402 | // pExpVectorCopy(F,F0); |
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403 | memcpy(G, G0,(rN+1)*sizeof(int)); |
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404 | // pExpVectorCopy(G,G0); |
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405 | F[0]=0; /* important for p_MemAdd */ |
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406 | G[0]=0; |
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407 | |
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408 | iF=rN; |
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409 | while ((F[iF]==0)&&(iF>=1)) iF--; /* last exp_num of F */ |
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410 | if (iF==0) /* F0 is zero vector */ |
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411 | { |
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412 | out=pOne(); |
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413 | p_SetExpV(out,G0,r); |
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414 | p_Setm(out,r); |
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415 | freeT(F,rN); |
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416 | freeT(G,rN); |
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417 | return(out); |
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418 | } |
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419 | jG=1; |
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420 | while ((G[jG]==0)&&(jG<rN)) jG++; /* first exp_num of G */ |
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421 | iG=rN; |
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422 | while ((G[iG]==0)&&(iG>1)) iG--; /* last exp_num of G */ |
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423 | |
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424 | out=pOne(); |
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425 | |
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426 | if (iF<=jG) |
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427 | /* i.e. no mixed exp_num , MERGE case */ |
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428 | { |
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429 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
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430 | p_SetExpV(out,F,r); |
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431 | p_Setm(out,r); |
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432 | // omFreeSize((ADDRESS)F,ExpSize); |
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433 | freeT(F,rN); |
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434 | freeT(G,rN); |
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435 | return(out); |
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436 | } |
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437 | |
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438 | number cff=n_Init(1,r); |
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439 | number tmp_num=NULL; |
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440 | int cpower=0; |
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441 | |
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442 | if (ncRingType(r)==nc_skew) |
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443 | { |
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444 | if (r->GetNC()->IsSkewConstant==1) |
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445 | { |
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446 | int tpower=0; |
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447 | for(j=jG; j<=iG; j++) |
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448 | { |
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449 | if (G[j]!=0) |
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450 | { |
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451 | cpower = 0; |
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452 | for(i=j+1; i<=iF; i++) |
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453 | { |
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454 | cpower = cpower + F[i]; |
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455 | } |
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456 | cpower = cpower*G[j]; |
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457 | tpower = tpower + cpower; |
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458 | } |
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459 | } |
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460 | cff = n_Copy(p_GetCoeff(MATELEM(r->GetNC()->COM,1,2),r),r); |
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461 | nPower(cff,tpower,&tmp_num); |
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462 | n_Delete(&cff,r); |
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463 | cff = tmp_num; |
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464 | } |
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465 | else /* skew commutative with nonequal coeffs */ |
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466 | { |
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467 | number totcff=n_Init(1,r); |
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468 | for(j=jG; j<=iG; j++) |
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469 | { |
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470 | if (G[j]!=0) |
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471 | { |
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472 | cpower = 0; |
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473 | for(i=j+1; i<=iF; i++) |
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474 | { |
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475 | if (F[i]!=0) |
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476 | { |
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477 | cpower = F[i]*G[j]; |
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478 | cff = n_Copy(p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r),r); |
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479 | nPower(cff,cpower,&tmp_num); |
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480 | cff = nMult(totcff,tmp_num); |
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481 | nDelete(&totcff); |
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482 | nDelete(&tmp_num); |
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483 | totcff = n_Copy(cff,r); |
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484 | n_Delete(&cff,r); |
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485 | } |
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486 | } /* end 2nd for */ |
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487 | } |
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488 | } |
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489 | cff=totcff; |
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490 | } |
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491 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
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492 | p_SetExpV(out,F,r); |
---|
493 | p_Setm(out,r); |
---|
494 | p_SetCoeff(out,cff,r); |
---|
495 | // p_MemAdd_NegWeightAdjust(p, r); ??? do we need this? |
---|
496 | freeT(F,rN); |
---|
497 | freeT(G,rN); |
---|
498 | return(out); |
---|
499 | } /* end nc_skew */ |
---|
500 | |
---|
501 | /* now we have to destroy out! */ |
---|
502 | p_Delete(&out,r); |
---|
503 | out = NULL; |
---|
504 | |
---|
505 | if (iG==jG) |
---|
506 | /* g is univariate monomial */ |
---|
507 | { |
---|
508 | /* if (ri->GetNC()->type==nc_skew) -- postpone to TU */ |
---|
509 | out = gnc_mm_Mult_uu(F,jG,G[jG],r); |
---|
510 | freeT(F,rN); |
---|
511 | freeT(G,rN); |
---|
512 | return(out); |
---|
513 | } |
---|
514 | |
---|
515 | number n1=n_Init(1,r); |
---|
516 | int *Prv=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
517 | int *Nxt=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
518 | |
---|
519 | int *log=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
520 | int cnt=0; int cnf=0; |
---|
521 | |
---|
522 | /* splitting F wrt jG */ |
---|
523 | for (i=1;i<=jG;i++) |
---|
524 | { |
---|
525 | Prv[i]=F[i]; Nxt[i]=0; /* mult at the very end */ |
---|
526 | if (F[i]!=0) cnf++; |
---|
527 | } |
---|
528 | |
---|
529 | if (cnf==0) freeT(Prv,rN); |
---|
530 | |
---|
531 | for (i=jG+1;i<=rN;i++) |
---|
532 | { |
---|
533 | Nxt[i]=F[i]; |
---|
534 | /* if (cnf!=0) Prv[i]=0; */ |
---|
535 | if (F[i]!=0) |
---|
536 | { |
---|
537 | cnt++; |
---|
538 | } /* effective part for F */ |
---|
539 | } |
---|
540 | freeT(F,rN); |
---|
541 | cnt=0; |
---|
542 | |
---|
543 | for (i=1;i<=rN;i++) |
---|
544 | { |
---|
545 | if (G[i]!=0) |
---|
546 | { |
---|
547 | cnt++; |
---|
548 | log[cnt]=i; |
---|
549 | } /* lG for G */ |
---|
550 | } |
---|
551 | |
---|
552 | /* ---------------------- A C T I O N ------------------------ */ |
---|
553 | poly D=NULL; |
---|
554 | poly Rout=NULL; |
---|
555 | number *c=(number *)omAlloc0((rN+1)*sizeof(number)); |
---|
556 | c[0]=n_Init(1,r); |
---|
557 | |
---|
558 | int *Op=Nxt; |
---|
559 | int *On=G; |
---|
560 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
561 | |
---|
562 | for (i=jG;i<=rN;i++) U[i]=Nxt[i]+G[i]; /* make leadterm */ |
---|
563 | Nxt=NULL; |
---|
564 | G=NULL; |
---|
565 | cnt=1; |
---|
566 | int t=0; |
---|
567 | poly w=NULL; |
---|
568 | poly Pn=pOne(); |
---|
569 | p_SetExpV(Pn,On,r); |
---|
570 | p_Setm(Pn,r); |
---|
571 | |
---|
572 | while (On[iG]!=0) |
---|
573 | { |
---|
574 | t=log[cnt]; |
---|
575 | |
---|
576 | w=gnc_mm_Mult_uu(Op,t,On[t],r); |
---|
577 | c[cnt]=n_Mult(c[cnt-1],p_GetCoeff(w,r),r); |
---|
578 | D = pNext(w); /* getting coef and rest D */ |
---|
579 | p_DeleteLm(&w,r); |
---|
580 | w=NULL; |
---|
581 | |
---|
582 | Op[t] += On[t]; /* update exp_vectors */ |
---|
583 | On[t] = 0; |
---|
584 | |
---|
585 | if (t!=iG) /* not the last step */ |
---|
586 | { |
---|
587 | p_SetExpV(Pn,On,r); |
---|
588 | p_Setm(Pn,r); |
---|
589 | #ifdef PDEBUG |
---|
590 | p_Test(Pn,r); |
---|
591 | #endif |
---|
592 | |
---|
593 | // if (pNext(D)==0) |
---|
594 | // is D a monomial? could be postponed higher |
---|
595 | // { |
---|
596 | // Rout=nc_mm_Mult_nn(D,Pn,r); |
---|
597 | // } |
---|
598 | // else |
---|
599 | // { |
---|
600 | Rout=gnc_p_Mult_mm(D,Pn,r); |
---|
601 | // } |
---|
602 | } |
---|
603 | else |
---|
604 | { |
---|
605 | Rout=D; |
---|
606 | D=NULL; |
---|
607 | } |
---|
608 | |
---|
609 | if (Rout!=NULL) |
---|
610 | { |
---|
611 | Rout=p_Mult_nn(Rout,c[cnt-1],r); /* Rest is ready */ |
---|
612 | out=p_Add_q(out,Rout,r); |
---|
613 | Rout=NULL; |
---|
614 | } |
---|
615 | cnt++; |
---|
616 | } |
---|
617 | freeT(On,rN); |
---|
618 | freeT(Op,rN); |
---|
619 | p_Delete(&Pn,r); |
---|
620 | omFreeSize((ADDRESS)log,(rN+1)*sizeof(int)); |
---|
621 | |
---|
622 | /* leadterm and Prv-part */ |
---|
623 | |
---|
624 | Rout=pOne(); |
---|
625 | /* U is lead.monomial */ |
---|
626 | U[0]=0; |
---|
627 | p_SetExpV(Rout,U,r); |
---|
628 | p_Setm(Rout,r); /* use again this name Rout */ |
---|
629 | #ifdef PDEBUG |
---|
630 | p_Test(Rout,r); |
---|
631 | #endif |
---|
632 | p_SetCoeff(Rout,c[cnt-1],r); |
---|
633 | out=p_Add_q(out,Rout,r); |
---|
634 | freeT(U,rN); |
---|
635 | freeN(c,rN+1); |
---|
636 | if (cnf!=0) /* Prv is non-zero vector */ |
---|
637 | { |
---|
638 | Rout=pOne(); |
---|
639 | Prv[0]=0; |
---|
640 | p_SetExpV(Rout,Prv,r); |
---|
641 | p_Setm(Rout,r); |
---|
642 | #ifdef PDEBUG |
---|
643 | p_Test(Rout,r); |
---|
644 | #endif |
---|
645 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
646 | freeT(Prv,rN); |
---|
647 | p_Delete(&Rout,r); |
---|
648 | } |
---|
649 | return (out); |
---|
650 | } |
---|
651 | |
---|
652 | |
---|
653 | poly gnc_mm_Mult_uu(int *F,int jG,int bG, const ring r) |
---|
654 | /* f=mono(F),g=(x_iG)^bG */ |
---|
655 | { |
---|
656 | poly out=NULL; |
---|
657 | int i; |
---|
658 | number num=NULL; |
---|
659 | |
---|
660 | int rN=r->N; |
---|
661 | int iF=r->N; |
---|
662 | while ((F[iF]==0)&&(iF>0)) iF-- ; /* last exponent_num of F */ |
---|
663 | |
---|
664 | if (iF==0) /* F==zero vector in other words */ |
---|
665 | { |
---|
666 | out=pOne(); |
---|
667 | p_SetExp(out,jG,bG,r); |
---|
668 | p_Setm(out,r); |
---|
669 | return(out); |
---|
670 | } |
---|
671 | |
---|
672 | int jF=1; |
---|
673 | while ((F[jF]==0)&&(jF<=rN)) jF++; /* first exp of F */ |
---|
674 | |
---|
675 | if (iF<=jG) /* i.e. no mixed exp_num */ |
---|
676 | { |
---|
677 | out=pOne(); |
---|
678 | F[jG]=F[jG]+bG; |
---|
679 | p_SetExpV(out,F,r); |
---|
680 | p_Setm(out,r); |
---|
681 | return(out); |
---|
682 | } |
---|
683 | |
---|
684 | if (iF==jF) /* uni times uni */ |
---|
685 | { |
---|
686 | out=gnc_uu_Mult_ww(iF,F[iF],jG,bG,r); |
---|
687 | return(out); |
---|
688 | } |
---|
689 | |
---|
690 | /* Now: F is mono with >=2 exponents, jG<iF */ |
---|
691 | /* check the quasi-commutative case */ |
---|
692 | // matrix LCOM=r->GetNC()->COM; |
---|
693 | // number rescoef=n_Init(1,r); |
---|
694 | // number tmpcoef=n_Init(1,r); |
---|
695 | // int tmpint; |
---|
696 | // i=iF; |
---|
697 | // while (i>=jG+1) |
---|
698 | // /* all the non-zero exponents */ |
---|
699 | // { |
---|
700 | // if (MATELEM(LCOM,jG,i)!=NULL) |
---|
701 | // { |
---|
702 | // tmpcoef=pGetCoeff(MATELEM(LCOM,jG,i)); |
---|
703 | // tmpint=(int)F[i]; |
---|
704 | // nPower(tmpcoef,F[i],&tmpcoef); |
---|
705 | // rescoef=nMult(rescoef,tmpcoef); |
---|
706 | // i--; |
---|
707 | // } |
---|
708 | // else |
---|
709 | // { |
---|
710 | // if (F[i]!=0) break; |
---|
711 | // } |
---|
712 | // } |
---|
713 | // if (iF==i) |
---|
714 | // /* no action took place*/ |
---|
715 | // { |
---|
716 | |
---|
717 | // } |
---|
718 | // else /* power the result up to bG */ |
---|
719 | // { |
---|
720 | // nPower(rescoef,bG,&rescoef); |
---|
721 | // /* + cleanup, post-processing */ |
---|
722 | // } |
---|
723 | |
---|
724 | int *Prv=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
725 | int *Nxt=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
726 | int *lF=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
727 | int cnt=0; int cnf=0; |
---|
728 | /* splitting F wrt jG */ |
---|
729 | for (i=1;i<=jG;i++) /* mult at the very end */ |
---|
730 | { |
---|
731 | Prv[i]=F[i]; Nxt[i]=0; |
---|
732 | if (F[i]!=0) cnf++; |
---|
733 | } |
---|
734 | if (cnf==0) freeT(Prv,rN); |
---|
735 | for (i=jG+1;i<=rN;i++) |
---|
736 | { |
---|
737 | Nxt[i]=F[i]; |
---|
738 | if (cnf!=0) { Prv[i]=0;} |
---|
739 | if (F[i]!=0) |
---|
740 | { |
---|
741 | cnt++; |
---|
742 | lF[cnt]=i; |
---|
743 | } /* eff_part,lF_for_F */ |
---|
744 | } |
---|
745 | |
---|
746 | if (cnt==1) /* Nxt consists of 1 nonzero el-t only */ |
---|
747 | { |
---|
748 | int q=lF[1]; |
---|
749 | poly Rout=pOne(); |
---|
750 | out=gnc_uu_Mult_ww(q,Nxt[q],jG,bG,r); |
---|
751 | freeT(Nxt,rN); |
---|
752 | |
---|
753 | if (cnf!=0) |
---|
754 | { |
---|
755 | Prv[0]=0; |
---|
756 | p_SetExpV(Rout,Prv,r); |
---|
757 | p_Setm(Rout,r); |
---|
758 | #ifdef PDEBUG |
---|
759 | p_Test(Rout,r); |
---|
760 | #endif |
---|
761 | freeT(Prv,rN); |
---|
762 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
763 | } |
---|
764 | |
---|
765 | omFreeSize((ADDRESS)lF,(rN+1)*sizeof(int)); |
---|
766 | p_Delete(&Rout,r); |
---|
767 | return (out); |
---|
768 | } |
---|
769 | /* -------------------- MAIN ACTION --------------------- */ |
---|
770 | |
---|
771 | poly D=NULL; |
---|
772 | poly Rout=NULL; |
---|
773 | number *c=(number *)omAlloc0((cnt+2)*sizeof(number)); |
---|
774 | c[cnt+1]=n_Init(1,r); |
---|
775 | i=cnt+2; /* later in freeN */ |
---|
776 | int *Op=Nxt; |
---|
777 | int *On=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
778 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
779 | |
---|
780 | |
---|
781 | // pExpVectorCopy(U,Nxt); |
---|
782 | memcpy(U, Nxt,(rN+1)*sizeof(int)); |
---|
783 | U[jG] = U[jG] + bG; |
---|
784 | |
---|
785 | /* Op=Nxt and initial On=(0); */ |
---|
786 | Nxt=NULL; |
---|
787 | |
---|
788 | poly Pp; |
---|
789 | poly Pn; |
---|
790 | int t=0; |
---|
791 | int first=lF[1]; |
---|
792 | int nlast=lF[cnt]; |
---|
793 | int kk=0; |
---|
794 | /* cnt--; */ |
---|
795 | /* now lF[cnt] should be <=iF-1 */ |
---|
796 | |
---|
797 | while (Op[first]!=0) |
---|
798 | { |
---|
799 | t=lF[cnt]; /* cnt as it was computed */ |
---|
800 | |
---|
801 | poly w=gnc_uu_Mult_ww(t,Op[t],jG,bG,r); |
---|
802 | c[cnt]=n_Copy(p_GetCoeff(w,r),r); |
---|
803 | D = pNext(w); /* getting coef and rest D */ |
---|
804 | p_DeleteLm(&w,r); |
---|
805 | w=NULL; |
---|
806 | |
---|
807 | Op[t]= 0; |
---|
808 | Pp=pOne(); |
---|
809 | p_SetExpV(Pp,Op,r); |
---|
810 | p_Setm(Pp,r); |
---|
811 | |
---|
812 | if (t<nlast) |
---|
813 | { |
---|
814 | kk=lF[cnt+1]; |
---|
815 | On[kk]=F[kk]; |
---|
816 | |
---|
817 | Pn=pOne(); |
---|
818 | p_SetExpV(Pn,On,r); |
---|
819 | p_Setm(Pn,r); |
---|
820 | |
---|
821 | if (t!=first) /* typical expr */ |
---|
822 | { |
---|
823 | w=gnc_p_Mult_mm(D,Pn,r); |
---|
824 | Rout=gnc_mm_Mult_p(Pp,w,r); |
---|
825 | w=NULL; |
---|
826 | } |
---|
827 | else /* last step */ |
---|
828 | { |
---|
829 | On[t]=0; |
---|
830 | p_SetExpV(Pn,On,r); |
---|
831 | p_Setm(Pn,r); |
---|
832 | Rout=gnc_p_Mult_mm(D,Pn,r); |
---|
833 | } |
---|
834 | #ifdef PDEBUG |
---|
835 | p_Test(Pp,r); |
---|
836 | #endif |
---|
837 | p_Delete(&Pn,r); |
---|
838 | } |
---|
839 | else /* first step */ |
---|
840 | { |
---|
841 | Rout=gnc_mm_Mult_p(Pp,D,r); |
---|
842 | } |
---|
843 | #ifdef PDEBUG |
---|
844 | p_Test(Pp,r); |
---|
845 | #endif |
---|
846 | p_Delete(&Pp,r); |
---|
847 | num=n_Mult(c[cnt+1],c[cnt],r); |
---|
848 | n_Delete(&c[cnt],r); |
---|
849 | c[cnt]=num; |
---|
850 | Rout=p_Mult_nn(Rout,c[cnt+1],r); /* Rest is ready */ |
---|
851 | out=p_Add_q(out,Rout,r); |
---|
852 | Pp=NULL; |
---|
853 | cnt--; |
---|
854 | } |
---|
855 | /* only to feel safe:*/ |
---|
856 | Pn=Pp=NULL; |
---|
857 | freeT(On,rN); |
---|
858 | freeT(Op,rN); |
---|
859 | |
---|
860 | /* leadterm and Prv-part with coef 1 */ |
---|
861 | /* U[0]=exp; */ |
---|
862 | /* U[jG]=U[jG]+bG; */ |
---|
863 | /* make leadterm */ |
---|
864 | /* ??????????? we have done it already :-0 */ |
---|
865 | Rout=pOne(); |
---|
866 | p_SetExpV(Rout,U,r); |
---|
867 | p_Setm(Rout,r); /* use again this name */ |
---|
868 | p_SetCoeff(Rout,c[cnt+1],r); /* last computed coef */ |
---|
869 | out=p_Add_q(out,Rout,r); |
---|
870 | Rout=NULL; |
---|
871 | freeT(U,rN); |
---|
872 | freeN(c,i); |
---|
873 | omFreeSize((ADDRESS)lF,(rN+1)*sizeof(int)); |
---|
874 | |
---|
875 | if (cnf!=0) |
---|
876 | { |
---|
877 | Rout=pOne(); |
---|
878 | p_SetExpV(Rout,Prv,r); |
---|
879 | p_Setm(Rout,r); |
---|
880 | freeT(Prv,rN); |
---|
881 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
882 | p_Delete(&Rout,r); |
---|
883 | } |
---|
884 | return (out); |
---|
885 | } |
---|
886 | |
---|
887 | poly gnc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r) |
---|
888 | { |
---|
889 | int k,m; |
---|
890 | int rN=r->N; |
---|
891 | matrix cMT=r->GetNC()->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
892 | |
---|
893 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r); |
---|
894 | /* var(j); */ |
---|
895 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); |
---|
896 | /*var(i); for convenience */ |
---|
897 | #ifdef PDEBUG |
---|
898 | p_Test(x,r); |
---|
899 | p_Test(y,r); |
---|
900 | #endif |
---|
901 | poly t=NULL; |
---|
902 | /* ------------ Main Cycles ----------------------------*/ |
---|
903 | |
---|
904 | for (k=2;k<=a;k++) |
---|
905 | { |
---|
906 | t = nc_p_CopyGet(MATELEM(cMT,k,1),r); |
---|
907 | |
---|
908 | if (t==NULL) /* not computed yet */ |
---|
909 | { |
---|
910 | t = nc_p_CopyGet(MATELEM(cMT,k-1,1),r); |
---|
911 | // t=p_Copy(MATELEM(cMT,k-1,1),r); |
---|
912 | t = gnc_mm_Mult_p(y,t,r); |
---|
913 | MATELEM(cMT,k,1) = nc_p_CopyPut(t,r); |
---|
914 | // omCheckAddr(cMT->m); |
---|
915 | p_Delete(&t,r); |
---|
916 | } |
---|
917 | t=NULL; |
---|
918 | } |
---|
919 | |
---|
920 | for (m=2;m<=b;m++) |
---|
921 | { |
---|
922 | t = nc_p_CopyGet(MATELEM(cMT,a,m),r); |
---|
923 | // t=MATELEM(cMT,a,m); |
---|
924 | if (t==NULL) //not computed yet |
---|
925 | { |
---|
926 | t = nc_p_CopyGet(MATELEM(cMT,a,m-1),r); |
---|
927 | // t=p_Copy(MATELEM(cMT,a,m-1),r); |
---|
928 | t = gnc_p_Mult_mm(t,x,r); |
---|
929 | MATELEM(cMT,a,m) = nc_p_CopyPut(t,r); |
---|
930 | // MATELEM(cMT,a,m) = t; |
---|
931 | // omCheckAddr(cMT->m); |
---|
932 | p_Delete(&t,r); |
---|
933 | } |
---|
934 | t=NULL; |
---|
935 | } |
---|
936 | p_Delete(&x,r); |
---|
937 | p_Delete(&y,r); |
---|
938 | // t=MATELEM(cMT,a,b); |
---|
939 | t= nc_p_CopyGet(MATELEM(cMT,a,b),r); |
---|
940 | // return(p_Copy(t,r)); |
---|
941 | /* since the last computed element was cMT[a,b] */ |
---|
942 | return(t); |
---|
943 | } |
---|
944 | |
---|
945 | poly gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r) |
---|
946 | /* (x_i)^a times (x_j)^b */ |
---|
947 | /* x_i = y, x_j = x ! */ |
---|
948 | { |
---|
949 | /* Check zero exceptions, (q-)commutativity and is there something to do? */ |
---|
950 | assume(a!=0); |
---|
951 | assume(b!=0); |
---|
952 | poly out=pOne(); |
---|
953 | if (i<=j) |
---|
954 | { |
---|
955 | p_SetExp(out,i,a,r); |
---|
956 | p_AddExp(out,j,b,r); |
---|
957 | p_Setm(out,r); |
---|
958 | return(out); |
---|
959 | }/* zero exeptions and usual case */ |
---|
960 | /* if ((a==0)||(b==0)||(i<=j)) return(out); */ |
---|
961 | |
---|
962 | if (MATELEM(r->GetNC()->COM,j,i)!=NULL) |
---|
963 | /* commutative or quasicommutative case */ |
---|
964 | { |
---|
965 | p_SetExp(out,i,a,r); |
---|
966 | p_AddExp(out,j,b,r); |
---|
967 | p_Setm(out,r); |
---|
968 | if (r->cf->nIsOne(p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r))) /* commutative case */ |
---|
969 | { |
---|
970 | return(out); |
---|
971 | } |
---|
972 | else |
---|
973 | { |
---|
974 | number tmp_number=p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r); /* quasicommutative case */ |
---|
975 | nPower(tmp_number,a*b,&tmp_number); |
---|
976 | p_SetCoeff(out,tmp_number,r); |
---|
977 | return(out); |
---|
978 | } |
---|
979 | }/* end_of commutative or quasicommutative case */ |
---|
980 | p_Delete(&out,r); |
---|
981 | |
---|
982 | /* we are here if i>j and variables do not commute or quasicommute */ |
---|
983 | /* in fact, now a>=1 and b>=1; and j<i */ |
---|
984 | /* now check whether the polynomial is already computed */ |
---|
985 | int rN=r->N; |
---|
986 | int vik = UPMATELEM(j,i,rN); |
---|
987 | int cMTsize=r->GetNC()->MTsize[vik]; |
---|
988 | int newcMTsize=0; |
---|
989 | newcMTsize=si_max(a,b); |
---|
990 | |
---|
991 | if (newcMTsize<=cMTsize) |
---|
992 | { |
---|
993 | out = nc_p_CopyGet(MATELEM(r->GetNC()->MT[vik],a,b),r); |
---|
994 | if (out !=NULL) return (out); |
---|
995 | } |
---|
996 | int k,m; |
---|
997 | if (newcMTsize > cMTsize) |
---|
998 | { |
---|
999 | int inM=(((newcMTsize+6)/7)*7); |
---|
1000 | assume (inM>=newcMTsize); |
---|
1001 | newcMTsize = inM; |
---|
1002 | // matrix tmp = (matrix)omAlloc0(inM*inM*sizeof(poly)); |
---|
1003 | matrix tmp = mpNew(newcMTsize,newcMTsize); |
---|
1004 | |
---|
1005 | for (k=1;k<=cMTsize;k++) |
---|
1006 | { |
---|
1007 | for (m=1;m<=cMTsize;m++) |
---|
1008 | { |
---|
1009 | out = MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m); |
---|
1010 | if ( out != NULL ) |
---|
1011 | { |
---|
1012 | MATELEM(tmp,k,m) = out;/*MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m)*/ |
---|
1013 | // omCheckAddr(tmp->m); |
---|
1014 | MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m)=NULL; |
---|
1015 | // omCheckAddr(r->GetNC()->MT[UPMATELEM(j,i,rN)]->m); |
---|
1016 | } |
---|
1017 | } |
---|
1018 | } |
---|
1019 | id_Delete((ideal *)&(r->GetNC()->MT[UPMATELEM(j,i,rN)]),r); |
---|
1020 | r->GetNC()->MT[UPMATELEM(j,i,rN)] = tmp; |
---|
1021 | tmp=NULL; |
---|
1022 | r->GetNC()->MTsize[UPMATELEM(j,i,rN)] = newcMTsize; |
---|
1023 | } |
---|
1024 | /* The update of multiplication matrix is finished */ |
---|
1025 | pDelete(&out); |
---|
1026 | out = gnc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
1027 | // out = nc_uu_Mult_ww_horvert(i, a, j, b, r); |
---|
1028 | return(out); |
---|
1029 | } |
---|
1030 | |
---|
1031 | poly gnc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r) |
---|
1032 | |
---|
1033 | { |
---|
1034 | int k,m; |
---|
1035 | int rN=r->N; |
---|
1036 | matrix cMT=r->GetNC()->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
1037 | |
---|
1038 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r);/* var(j); */ |
---|
1039 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); /*var(i); for convenience */ |
---|
1040 | #ifdef PDEBUG |
---|
1041 | p_Test(x,r); |
---|
1042 | p_Test(y,r); |
---|
1043 | #endif |
---|
1044 | |
---|
1045 | poly t=NULL; |
---|
1046 | |
---|
1047 | int toXY; |
---|
1048 | int toYX; |
---|
1049 | |
---|
1050 | if (a==1) /* y*x^b, b>=2 */ |
---|
1051 | { |
---|
1052 | toXY=b-1; |
---|
1053 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=2)) toXY--; |
---|
1054 | for (m=toXY+1;m<=b;m++) |
---|
1055 | { |
---|
1056 | t=MATELEM(cMT,1,m); |
---|
1057 | if (t==NULL) /* remove after debug */ |
---|
1058 | { |
---|
1059 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
1060 | t = gnc_p_Mult_mm(t,x,r); |
---|
1061 | MATELEM(cMT,1,m) = t; |
---|
1062 | /* omCheckAddr(cMT->m); */ |
---|
1063 | } |
---|
1064 | else |
---|
1065 | { |
---|
1066 | /* Error, should never get there */ |
---|
1067 | WarnS("Error: a=1; MATELEM!=0"); |
---|
1068 | } |
---|
1069 | t=NULL; |
---|
1070 | } |
---|
1071 | return(p_Copy(MATELEM(cMT,1,b),r)); |
---|
1072 | } |
---|
1073 | |
---|
1074 | if (b==1) /* y^a*x, a>=2 */ |
---|
1075 | { |
---|
1076 | toYX=a-1; |
---|
1077 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=2)) toYX--; |
---|
1078 | for (m=toYX+1;m<=a;m++) |
---|
1079 | { |
---|
1080 | t=MATELEM(cMT,m,1); |
---|
1081 | if (t==NULL) /* remove after debug */ |
---|
1082 | { |
---|
1083 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
1084 | t = gnc_mm_Mult_p(y,t,r); |
---|
1085 | MATELEM(cMT,m,1) = t; |
---|
1086 | /* omCheckAddr(cMT->m); */ |
---|
1087 | } |
---|
1088 | else |
---|
1089 | { |
---|
1090 | /* Error, should never get there */ |
---|
1091 | WarnS("Error: b=1, MATELEM!=0"); |
---|
1092 | } |
---|
1093 | t=NULL; |
---|
1094 | } |
---|
1095 | return(p_Copy(MATELEM(cMT,a,1),r)); |
---|
1096 | } |
---|
1097 | |
---|
1098 | /* ------------ Main Cycles ----------------------------*/ |
---|
1099 | /* a>1, b>1 */ |
---|
1100 | |
---|
1101 | int dXY=0; int dYX=0; |
---|
1102 | /* dXY = distance for computing x-mult, then y-mult */ |
---|
1103 | /* dYX = distance for computing y-mult, then x-mult */ |
---|
1104 | int toX=a-1; int toY=b-1; /* toX = to axe X, toY = to axe Y */ |
---|
1105 | toXY=b-1; toYX=a-1; |
---|
1106 | /* if toX==0, toXY = dist. to computed y * x^toXY */ |
---|
1107 | /* if toY==0, toYX = dist. to computed y^toYX * x */ |
---|
1108 | while ( (MATELEM(cMT,toX,b)==NULL) && (toX>=1)) toX--; |
---|
1109 | if (toX==0) /* the whole column is not computed yet */ |
---|
1110 | { |
---|
1111 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=1)) toXY--; |
---|
1112 | /* toXY >=1 */ |
---|
1113 | dXY=b-1-toXY; |
---|
1114 | } |
---|
1115 | dXY=dXY+a-toX; /* the distance to nearest computed y^toX x^b */ |
---|
1116 | |
---|
1117 | while ( (MATELEM(cMT,a,toY)==NULL) && (toY>=1)) toY--; |
---|
1118 | if (toY==0) /* the whole row is not computed yet */ |
---|
1119 | { |
---|
1120 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=1)) toYX--; |
---|
1121 | /* toYX >=1 */ |
---|
1122 | dYX=a-1-toYX; |
---|
1123 | } |
---|
1124 | dYX=dYX+b-toY; /* the distance to nearest computed y^a x^toY */ |
---|
1125 | |
---|
1126 | if (dYX>=dXY) |
---|
1127 | { |
---|
1128 | /* first x, then y */ |
---|
1129 | if (toX==0) /* start with the row*/ |
---|
1130 | { |
---|
1131 | for (m=toXY+1;m<=b;m++) |
---|
1132 | { |
---|
1133 | t=MATELEM(cMT,1,m); |
---|
1134 | if (t==NULL) /* remove after debug */ |
---|
1135 | { |
---|
1136 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
1137 | t = gnc_p_Mult_mm(t,x,r); |
---|
1138 | MATELEM(cMT,1,m) = t; |
---|
1139 | /* omCheckAddr(cMT->m); */ |
---|
1140 | } |
---|
1141 | else |
---|
1142 | { |
---|
1143 | /* Error, should never get there */ |
---|
1144 | WarnS("dYX>=dXY,toXY; MATELEM==0"); |
---|
1145 | } |
---|
1146 | t=NULL; |
---|
1147 | } |
---|
1148 | toX=1; /* y*x^b is computed */ |
---|
1149 | } |
---|
1150 | /* Now toX>=1 */ |
---|
1151 | for (k=toX+1;k<=a;k++) |
---|
1152 | { |
---|
1153 | t=MATELEM(cMT,k,b); |
---|
1154 | if (t==NULL) /* remove after debug */ |
---|
1155 | { |
---|
1156 | t = p_Copy(MATELEM(cMT,k-1,b),r); |
---|
1157 | t = gnc_mm_Mult_p(y,t,r); |
---|
1158 | MATELEM(cMT,k,b) = t; |
---|
1159 | /* omCheckAddr(cMT->m); */ |
---|
1160 | } |
---|
1161 | else |
---|
1162 | { |
---|
1163 | /* Error, should never get there */ |
---|
1164 | WarnS("dYX>=dXY,toX; MATELEM==0"); |
---|
1165 | } |
---|
1166 | t=NULL; |
---|
1167 | } |
---|
1168 | } /* endif (dYX>=dXY) */ |
---|
1169 | |
---|
1170 | |
---|
1171 | if (dYX<dXY) |
---|
1172 | { |
---|
1173 | /* first y, then x */ |
---|
1174 | if (toY==0) /* start with the column*/ |
---|
1175 | { |
---|
1176 | for (m=toYX+1;m<=a;m++) |
---|
1177 | { |
---|
1178 | t=MATELEM(cMT,m,1); |
---|
1179 | if (t==NULL) /* remove after debug */ |
---|
1180 | { |
---|
1181 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
1182 | t = gnc_mm_Mult_p(y,t,r); |
---|
1183 | MATELEM(cMT,m,1) = t; |
---|
1184 | /* omCheckAddr(cMT->m); */ |
---|
1185 | } |
---|
1186 | else |
---|
1187 | { |
---|
1188 | /* Error, should never get there */ |
---|
1189 | WarnS("dYX<dXY,toYX; MATELEM==0"); |
---|
1190 | } |
---|
1191 | t=NULL; |
---|
1192 | } |
---|
1193 | toY=1; /* y^a*x is computed */ |
---|
1194 | } |
---|
1195 | /* Now toY>=1 */ |
---|
1196 | for (k=toY+1;k<=b;k++) |
---|
1197 | { |
---|
1198 | t=MATELEM(cMT,a,k); |
---|
1199 | if (t==NULL) /* remove after debug */ |
---|
1200 | { |
---|
1201 | t = p_Copy(MATELEM(cMT,a,k-1),r); |
---|
1202 | t = gnc_p_Mult_mm(t,x,r); |
---|
1203 | MATELEM(cMT,a,k) = t; |
---|
1204 | /* omCheckAddr(cMT->m); */ |
---|
1205 | } |
---|
1206 | else |
---|
1207 | { |
---|
1208 | /* Error, should never get there */ |
---|
1209 | WarnS("dYX<dXY,toY; MATELEM==0"); |
---|
1210 | } |
---|
1211 | t=NULL; |
---|
1212 | } |
---|
1213 | } /* endif (dYX<dXY) */ |
---|
1214 | |
---|
1215 | p_Delete(&x,r); |
---|
1216 | p_Delete(&y,r); |
---|
1217 | t=p_Copy(MATELEM(cMT,a,b),r); |
---|
1218 | return(t); /* since the last computed element was cMT[a,b] */ |
---|
1219 | } |
---|
1220 | |
---|
1221 | |
---|
1222 | /* ----------------------------- Syzygies ---------------------- */ |
---|
1223 | |
---|
1224 | /*2 |
---|
1225 | * reduction of p2 with p1 |
---|
1226 | * do not destroy p1, but p2 |
---|
1227 | * p1 divides p2 -> for use in NF algorithm |
---|
1228 | */ |
---|
1229 | poly gnc_ReduceSpolyOld(const poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1230 | { |
---|
1231 | assume(p_LmDivisibleBy(p1, p2, r)); |
---|
1232 | |
---|
1233 | if (p_GetComp(p1,r)!=p_GetComp(p2,r) |
---|
1234 | && (p_GetComp(p1,r)!=0) |
---|
1235 | && (p_GetComp(p2,r)!=0)) |
---|
1236 | { |
---|
1237 | #ifdef PDEBUG |
---|
1238 | Print("nc_ReduceSpolyOld: different components"); |
---|
1239 | #endif |
---|
1240 | return(NULL); |
---|
1241 | } |
---|
1242 | poly m = pOne(); |
---|
1243 | p_ExpVectorDiff(m,p2,p1,r); |
---|
1244 | //p_Setm(m,r); |
---|
1245 | #ifdef PDEBUG |
---|
1246 | p_Test(m,r); |
---|
1247 | #endif |
---|
1248 | /* pSetComp(m,r)=0? */ |
---|
1249 | poly N = nc_mm_Mult_p(m, p_Head(p1,r), r); |
---|
1250 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
1251 | number cF = n_Copy( p_GetCoeff(p2, r),r); |
---|
1252 | /* GCD stuff */ |
---|
1253 | number cG = nGcd(C, cF, r); |
---|
1254 | if ( !nEqual(cG, n_Init(1,r) ) ) |
---|
1255 | { |
---|
1256 | cF = nDiv(cF, cG); |
---|
1257 | C = nDiv(C, cG); |
---|
1258 | } |
---|
1259 | p2 = p_Mult_nn(p2, C, r); |
---|
1260 | poly out = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
1261 | N = p_Add_q(N, out, r); |
---|
1262 | p_Test(p2,r); |
---|
1263 | p_Test(N,r); |
---|
1264 | number MinusOne = n_Init(-1,r); |
---|
1265 | if (!n_Equal(cF,MinusOne,r)) |
---|
1266 | { |
---|
1267 | cF = n_Neg(cF,r); |
---|
1268 | N = p_Mult_nn(N, cF, r); |
---|
1269 | p_Test(N,r); |
---|
1270 | } |
---|
1271 | out = p_Add_q(p2,N,r); |
---|
1272 | p_Test(out,r); |
---|
1273 | if ( out!=NULL ) pContent(out); |
---|
1274 | p_Delete(&m,r); |
---|
1275 | n_Delete(&cF,r); |
---|
1276 | n_Delete(&C,r); |
---|
1277 | n_Delete(&MinusOne,r); |
---|
1278 | return(out); |
---|
1279 | |
---|
1280 | } |
---|
1281 | |
---|
1282 | poly gnc_ReduceSpolyNew(const poly p1, poly p2, const ring r) |
---|
1283 | { |
---|
1284 | assume(p_LmDivisibleBy(p1, p2, r)); |
---|
1285 | |
---|
1286 | const long lCompP1 = p_GetComp(p1,r); |
---|
1287 | const long lCompP2 = p_GetComp(p2,r); |
---|
1288 | |
---|
1289 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
1290 | { |
---|
1291 | #ifdef PDEBUG |
---|
1292 | Werror("gnc_ReduceSpolyNew: different non-zero components!"); |
---|
1293 | #endif |
---|
1294 | return(NULL); |
---|
1295 | } |
---|
1296 | |
---|
1297 | poly m = pOne(); |
---|
1298 | p_ExpVectorDiff(m, p2, p1, r); |
---|
1299 | //p_Setm(m,r); |
---|
1300 | #ifdef PDEBUG |
---|
1301 | p_Test(m,r); |
---|
1302 | #endif |
---|
1303 | |
---|
1304 | /* pSetComp(m,r)=0? */ |
---|
1305 | poly N = nc_mm_Mult_p(m, p_Head(p1,r), r); |
---|
1306 | |
---|
1307 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
1308 | number cF = n_Copy( p_GetCoeff(p2, r), r); |
---|
1309 | |
---|
1310 | /* GCD stuff */ |
---|
1311 | number cG = nGcd(C, cF, r); |
---|
1312 | |
---|
1313 | if (!n_IsOne(cG, r)) |
---|
1314 | { |
---|
1315 | cF = n_Div(cF, cG, r); |
---|
1316 | C = n_Div(C, cG, r); |
---|
1317 | } |
---|
1318 | |
---|
1319 | p2 = p_Mult_nn(p2, C, r); // p2 !!! |
---|
1320 | p_Test(p2,r); |
---|
1321 | n_Delete(&C,r); |
---|
1322 | |
---|
1323 | poly out = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
1324 | p_Delete(&m,r); |
---|
1325 | |
---|
1326 | N = p_Add_q(N, out, r); |
---|
1327 | p_Test(N,r); |
---|
1328 | |
---|
1329 | if (!n_IsMOne(cF,r)) // ??? |
---|
1330 | { |
---|
1331 | cF = n_Neg(cF,r); |
---|
1332 | N = p_Mult_nn(N, cF, r); |
---|
1333 | p_Test(N,r); |
---|
1334 | } |
---|
1335 | |
---|
1336 | out = p_Add_q(p2,N,r); // delete N, p2 |
---|
1337 | p_Test(out,r); |
---|
1338 | if ( out!=NULL ) pContent(out); |
---|
1339 | n_Delete(&cF,r); |
---|
1340 | return(out); |
---|
1341 | } |
---|
1342 | |
---|
1343 | |
---|
1344 | /*4 |
---|
1345 | * creates the S-polynomial of p1 and p2 |
---|
1346 | * do not destroy p1 and p2 |
---|
1347 | */ |
---|
1348 | poly gnc_CreateSpolyOld(poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1349 | { |
---|
1350 | if ((p_GetComp(p1,r)!=p_GetComp(p2,r)) |
---|
1351 | && (p_GetComp(p1,r)!=0) |
---|
1352 | && (p_GetComp(p2,r)!=0)) |
---|
1353 | { |
---|
1354 | #ifdef PDEBUG |
---|
1355 | Print("gnc_CreateSpolyOld : different components!"); |
---|
1356 | #endif |
---|
1357 | return(NULL); |
---|
1358 | } |
---|
1359 | if ((ncRingType(r)==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
1360 | { |
---|
1361 | return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
1362 | } |
---|
1363 | poly pL=pOne(); |
---|
1364 | poly m1=pOne(); |
---|
1365 | poly m2=pOne(); |
---|
1366 | pLcm(p1,p2,pL); |
---|
1367 | p_Setm(pL,r); |
---|
1368 | #ifdef PDEBUG |
---|
1369 | p_Test(pL,r); |
---|
1370 | #endif |
---|
1371 | p_ExpVectorDiff(m1,pL,p1,r); |
---|
1372 | //p_SetComp(m1,0,r); |
---|
1373 | //p_Setm(m1,r); |
---|
1374 | #ifdef PDEBUG |
---|
1375 | p_Test(m1,r); |
---|
1376 | #endif |
---|
1377 | p_ExpVectorDiff(m2,pL,p2,r); |
---|
1378 | //p_SetComp(m2,0,r); |
---|
1379 | //p_Setm(m2,r); |
---|
1380 | #ifdef PDEBUG |
---|
1381 | p_Test(m2,r); |
---|
1382 | #endif |
---|
1383 | p_Delete(&pL,r); |
---|
1384 | /* zero exponents ! */ |
---|
1385 | poly M1 = nc_mm_Mult_p(m1,p_Head(p1,r),r); |
---|
1386 | number C1 = n_Copy(p_GetCoeff(M1,r),r); |
---|
1387 | poly M2 = nc_mm_Mult_p(m2,p_Head(p2,r),r); |
---|
1388 | number C2 = n_Copy(p_GetCoeff(M2,r),r); |
---|
1389 | /* GCD stuff */ |
---|
1390 | number C = nGcd(C1,C2,r); |
---|
1391 | if (!nEqual(C,n_Init(1,r))) |
---|
1392 | { |
---|
1393 | C1=nDiv(C1,C); |
---|
1394 | C2=nDiv(C2,C); |
---|
1395 | } |
---|
1396 | M1=p_Mult_nn(M1,C2,r); |
---|
1397 | p_SetCoeff(m1,C2,r); |
---|
1398 | number MinusOne=n_Init(-1,r); |
---|
1399 | if (n_Equal(C1,MinusOne,r)) |
---|
1400 | { |
---|
1401 | M2=p_Add_q(M1,M2,r); |
---|
1402 | } |
---|
1403 | else |
---|
1404 | { |
---|
1405 | C1=n_Neg(C1,r); |
---|
1406 | M2=p_Mult_nn(M2,C1,r); |
---|
1407 | M2=p_Add_q(M1,M2,r); |
---|
1408 | p_SetCoeff(m2,C1,r); |
---|
1409 | } |
---|
1410 | /* M1 is killed, M2=res = C2 M1 - C1 M2 */ |
---|
1411 | poly tmp=p_Copy(p1,r); |
---|
1412 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
1413 | M1=nc_mm_Mult_p(m1,tmp,r); |
---|
1414 | tmp=p_Copy(p2,r); |
---|
1415 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
1416 | M2=p_Add_q(M2,M1,r); |
---|
1417 | M1=nc_mm_Mult_p(m2,tmp,r); |
---|
1418 | M2=p_Add_q(M2,M1,r); |
---|
1419 | p_Delete(&m1,r); |
---|
1420 | p_Delete(&m2,r); |
---|
1421 | // n_Delete(&C1,r); |
---|
1422 | // n_Delete(&C2,r); |
---|
1423 | n_Delete(&MinusOne,r); |
---|
1424 | #ifdef PDEBUG |
---|
1425 | p_Test(M2,r); |
---|
1426 | #endif |
---|
1427 | if (M2!=NULL) pCleardenom(M2); |
---|
1428 | if (M2!=NULL) pContent(M2); |
---|
1429 | return(M2); |
---|
1430 | } |
---|
1431 | |
---|
1432 | poly gnc_CreateSpolyNew(poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1433 | { |
---|
1434 | assume(r == currRing); |
---|
1435 | |
---|
1436 | #ifdef PDEBUG |
---|
1437 | pTest(p1); |
---|
1438 | pTest(p2); |
---|
1439 | #if MYTEST |
---|
1440 | Print("p1: "); pWrite(p1); |
---|
1441 | Print("p2: "); pWrite(p2); |
---|
1442 | #endif |
---|
1443 | #endif |
---|
1444 | |
---|
1445 | const long lCompP1 = p_GetComp(p1,r); |
---|
1446 | const long lCompP2 = p_GetComp(p2,r); |
---|
1447 | |
---|
1448 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
1449 | { |
---|
1450 | #ifdef PDEBUG |
---|
1451 | Werror("gnc_CreateSpolyNew: different non-zero components!"); |
---|
1452 | #endif |
---|
1453 | return(NULL); |
---|
1454 | } |
---|
1455 | |
---|
1456 | #ifdef PDEBUG |
---|
1457 | if (lCompP1!=lCompP2) |
---|
1458 | { |
---|
1459 | WarnS("gnc_CreateSpolyNew: vector & poly in SPoly!"); |
---|
1460 | } |
---|
1461 | #endif |
---|
1462 | |
---|
1463 | |
---|
1464 | // if ((r->GetNC()->type==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
1465 | // { |
---|
1466 | // return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
1467 | // } |
---|
1468 | |
---|
1469 | // poly pL=p_ISet(1, r); |
---|
1470 | |
---|
1471 | poly m1=p_ISet(1, r); |
---|
1472 | poly m2=p_ISet(1, r); |
---|
1473 | |
---|
1474 | poly pL = p_Lcm(p1,p2,r); // pL = lcm( lm(p1), lm(p2) ) |
---|
1475 | |
---|
1476 | |
---|
1477 | #ifdef PDEBUG |
---|
1478 | // p_Test(pL,r); |
---|
1479 | #endif |
---|
1480 | |
---|
1481 | p_ExpVectorDiff(m1, pL, p1, r); // m1 = pL / lm(p1) |
---|
1482 | //p_SetComp(m1,0,r); |
---|
1483 | //p_Setm(m1,r); |
---|
1484 | |
---|
1485 | #ifdef PDEBUG |
---|
1486 | p_Test(m1,r); |
---|
1487 | #endif |
---|
1488 | // assume(p_GetComp(m1,r) == 0); |
---|
1489 | |
---|
1490 | p_ExpVectorDiff(m2, pL, p2, r); // m2 = pL / lm(p2) |
---|
1491 | |
---|
1492 | //p_SetComp(m2,0,r); |
---|
1493 | //p_Setm(m2,r); |
---|
1494 | #ifdef PDEBUG |
---|
1495 | p_Test(m2,r); |
---|
1496 | #endif |
---|
1497 | |
---|
1498 | #ifdef PDEBUG |
---|
1499 | #if MYTEST |
---|
1500 | Print("m1: "); pWrite(m1); |
---|
1501 | Print("m2: "); pWrite(m2); |
---|
1502 | #endif |
---|
1503 | #endif |
---|
1504 | |
---|
1505 | |
---|
1506 | // assume(p_GetComp(m2,r) == 0); |
---|
1507 | |
---|
1508 | #ifdef PDEBUG |
---|
1509 | #if 0 |
---|
1510 | if( (p_GetComp(m2,r) != 0) || (p_GetComp(m1,r) != 0) ) |
---|
1511 | { |
---|
1512 | WarnS("gnc_CreateSpolyNew: wrong monomials!"); |
---|
1513 | |
---|
1514 | |
---|
1515 | #ifdef RDEBUG |
---|
1516 | PrintS("m1 = "); p_Write(m1, r); |
---|
1517 | pDebugPrintR(m1, r); |
---|
1518 | |
---|
1519 | PrintS("m2 = "); p_Write(m2, r); |
---|
1520 | pDebugPrintR(m2, r); |
---|
1521 | |
---|
1522 | PrintS("p1 = "); p_Write(p1, r); |
---|
1523 | pDebugPrintR(p1, r); |
---|
1524 | |
---|
1525 | PrintS("p2 = "); p_Write(p2, r); |
---|
1526 | pDebugPrintR(p2, r); |
---|
1527 | |
---|
1528 | PrintS("pL = "); p_Write(pL, r); |
---|
1529 | pDebugPrintR(pL, r); |
---|
1530 | #endif |
---|
1531 | |
---|
1532 | } |
---|
1533 | |
---|
1534 | #endif |
---|
1535 | #endif |
---|
1536 | |
---|
1537 | p_Delete(&pL,r); |
---|
1538 | |
---|
1539 | /* zero exponents !? */ |
---|
1540 | poly M1 = nc_mm_Mult_p(m1,p_Head(p1,r),r); // M1 = m1 * lt(p1) |
---|
1541 | poly M2 = nc_mm_Mult_p(m2,p_Head(p2,r),r); // M2 = m2 * lt(p2) |
---|
1542 | |
---|
1543 | #ifdef PDEBUG |
---|
1544 | p_Test(M1,r); |
---|
1545 | p_Test(M2,r); |
---|
1546 | |
---|
1547 | #if MYTEST |
---|
1548 | Print("M1: "); pWrite(M1); |
---|
1549 | Print("M2: "); pWrite(M2); |
---|
1550 | #endif |
---|
1551 | #endif |
---|
1552 | |
---|
1553 | if(M1 == NULL || M2 == NULL) |
---|
1554 | { |
---|
1555 | #ifdef PDEBUG |
---|
1556 | Print("\np1 = "); |
---|
1557 | p_Write(p1, r); |
---|
1558 | |
---|
1559 | Print("m1 = "); |
---|
1560 | p_Write(m1, r); |
---|
1561 | |
---|
1562 | Print("p2 = "); |
---|
1563 | p_Write(p2, r); |
---|
1564 | |
---|
1565 | Print("m2 = "); |
---|
1566 | p_Write(m2, r); |
---|
1567 | |
---|
1568 | Werror("ERROR in nc_CreateSpoly: result of multiplication is Zero!\n"); |
---|
1569 | #endif |
---|
1570 | return(NULL); |
---|
1571 | } |
---|
1572 | |
---|
1573 | number C1 = n_Copy(p_GetCoeff(M1,r),r); // C1 = lc(M1) |
---|
1574 | number C2 = n_Copy(p_GetCoeff(M2,r),r); // C2 = lc(M2) |
---|
1575 | |
---|
1576 | /* GCD stuff */ |
---|
1577 | number C = nGcd(C1, C2, r); // C = gcd(C1, C2) |
---|
1578 | |
---|
1579 | if (!n_IsOne(C, r)) // if C != 1 |
---|
1580 | { |
---|
1581 | C1=n_Div(C1, C, r); // C1 = C1 / C |
---|
1582 | C2=n_Div(C2, C, r); // C2 = C2 / C |
---|
1583 | } |
---|
1584 | |
---|
1585 | n_Delete(&C,r); // destroy the number C |
---|
1586 | |
---|
1587 | C1=n_Neg(C1,r); |
---|
1588 | |
---|
1589 | // number MinusOne=n_Init(-1,r); |
---|
1590 | // if (n_Equal(C1,MinusOne,r)) // lc(M1) / gcd( lc(M1), lc(M2)) == -1 ???? |
---|
1591 | // { |
---|
1592 | // M2=p_Add_q(M1,M2,r); // ????? |
---|
1593 | // } |
---|
1594 | // else |
---|
1595 | // { |
---|
1596 | M1=p_Mult_nn(M1,C2,r); // M1 = (C2*lc(p1)) * (lcm(lm(p1),lm(p2)) / lm(p1)) * lm(p1) |
---|
1597 | |
---|
1598 | #ifdef PDEBUG |
---|
1599 | p_Test(M1,r); |
---|
1600 | #endif |
---|
1601 | |
---|
1602 | M2=p_Mult_nn(M2,C1,r); // M2 =(-C1*lc(p2)) * (lcm(lm(p1),lm(p2)) / lm(p2)) * lm(p2) |
---|
1603 | |
---|
1604 | |
---|
1605 | |
---|
1606 | #ifdef PDEBUG |
---|
1607 | p_Test(M2,r); |
---|
1608 | |
---|
1609 | #if MYTEST |
---|
1610 | Print("M1: "); pWrite(M1); |
---|
1611 | Print("M2: "); pWrite(M2); |
---|
1612 | #endif |
---|
1613 | #endif |
---|
1614 | |
---|
1615 | #endif |
---|
1616 | |
---|
1617 | M2=p_Add_q(M1,M2,r); // M1 is killed, M2 = spoly(lt(p1), lt(p2)) = C2*M1 - C1*M2 |
---|
1618 | |
---|
1619 | #ifdef PDEBUG |
---|
1620 | p_Test(M2,r); |
---|
1621 | |
---|
1622 | #if MYTEST |
---|
1623 | Print("M2: "); pWrite(M2); |
---|
1624 | #endif |
---|
1625 | |
---|
1626 | #endif |
---|
1627 | |
---|
1628 | // M2 == 0 for supercommutative algebras! |
---|
1629 | // } |
---|
1630 | // n_Delete(&MinusOne,r); |
---|
1631 | |
---|
1632 | p_SetCoeff(m1,C2,r); // lc(m1) = C2!!! |
---|
1633 | p_SetCoeff(m2,C1,r); // lc(m2) = C1!!! |
---|
1634 | |
---|
1635 | #ifdef PDEBUG |
---|
1636 | p_Test(m1,r); |
---|
1637 | p_Test(m2,r); |
---|
1638 | #endif |
---|
1639 | |
---|
1640 | // poly tmp = p_Copy(p1,r); // tmp = p1 |
---|
1641 | // tmp=p_LmDeleteAndNext(tmp,r); // tmp = tail(p1) |
---|
1642 | //#ifdef PDEBUG |
---|
1643 | // p_Test(tmp,r); |
---|
1644 | //#endif |
---|
1645 | |
---|
1646 | M1 = nc_mm_Mult_pp(m1, pNext(p1), r); // M1 = m1 * tail(p1), delete tmp // ??? |
---|
1647 | |
---|
1648 | #ifdef PDEBUG |
---|
1649 | p_Test(M1,r); |
---|
1650 | |
---|
1651 | #if MYTEST |
---|
1652 | Print("M1: "); pWrite(M1); |
---|
1653 | #endif |
---|
1654 | |
---|
1655 | #endif |
---|
1656 | |
---|
1657 | M2=p_Add_q(M2,M1,r); // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1), delete M1 |
---|
1658 | #ifdef PDEBUG |
---|
1659 | p_Test(M2,r); |
---|
1660 | |
---|
1661 | #if MYTEST |
---|
1662 | Print("M2: "); pWrite(M2); |
---|
1663 | #endif |
---|
1664 | |
---|
1665 | #endif |
---|
1666 | |
---|
1667 | // tmp=p_Copy(p2,r); // tmp = p2 |
---|
1668 | // tmp=p_LmDeleteAndNext(tmp,r); // tmp = tail(p2) |
---|
1669 | |
---|
1670 | //#ifdef PDEBUG |
---|
1671 | // p_Test(tmp,r); |
---|
1672 | //#endif |
---|
1673 | |
---|
1674 | M1 = nc_mm_Mult_pp(m2, pNext(p2), r); // M1 = m2 * tail(p2), detele tmp |
---|
1675 | |
---|
1676 | #ifdef PDEBUG |
---|
1677 | p_Test(M1,r); |
---|
1678 | |
---|
1679 | #if MYTEST |
---|
1680 | Print("M1: "); pWrite(M1); |
---|
1681 | #endif |
---|
1682 | |
---|
1683 | #endif |
---|
1684 | |
---|
1685 | M2 = p_Add_q(M2,M1,r); // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1) + m2*tail(p2) |
---|
1686 | |
---|
1687 | #ifdef PDEBUG |
---|
1688 | p_Test(M2,r); |
---|
1689 | |
---|
1690 | #if MYTEST |
---|
1691 | Print("M2: "); pWrite(M2); |
---|
1692 | #endif |
---|
1693 | |
---|
1694 | #endif |
---|
1695 | // delete M1 |
---|
1696 | |
---|
1697 | p_Delete(&m1,r); // => n_Delete(&C1,r); |
---|
1698 | p_Delete(&m2,r); // => n_Delete(&C2,r); |
---|
1699 | |
---|
1700 | #ifdef PDEBUG |
---|
1701 | p_Test(M2,r); |
---|
1702 | #endif |
---|
1703 | |
---|
1704 | if (M2!=NULL) pCleardenom(M2); //? |
---|
1705 | // if (M2!=NULL) pContent(M2); |
---|
1706 | |
---|
1707 | return(M2); |
---|
1708 | } |
---|
1709 | |
---|
1710 | |
---|
1711 | |
---|
1712 | |
---|
1713 | #if 0 |
---|
1714 | /*5 |
---|
1715 | * reduction of tail(q) with p1 |
---|
1716 | * lead(p1) divides lead(pNext(q2)) and pNext(q2) is reduced |
---|
1717 | * do not destroy p1, but tail(q) |
---|
1718 | */ |
---|
1719 | void gnc_ReduceSpolyTail(poly p1, poly q, poly q2, poly spNoether, const ring r) |
---|
1720 | { |
---|
1721 | poly a1=p_Head(p1,r); |
---|
1722 | poly Q=pNext(q2); |
---|
1723 | number cQ=p_GetCoeff(Q,r); |
---|
1724 | poly m=pOne(); |
---|
1725 | p_ExpVectorDiff(m,Q,p1,r); |
---|
1726 | // p_SetComp(m,0,r); |
---|
1727 | //p_Setm(m,r); |
---|
1728 | #ifdef PDEBUG |
---|
1729 | p_Test(m,r); |
---|
1730 | #endif |
---|
1731 | /* pSetComp(m,r)=0? */ |
---|
1732 | poly M = nc_mm_Mult_pp(m, p1,r); |
---|
1733 | number C=p_GetCoeff(M,r); |
---|
1734 | M=p_Add_q(M,nc_mm_Mult_p(m,p_LmDeleteAndNext(p_Copy(p1,r),r),r),r); // _pp? |
---|
1735 | q=p_Mult_nn(q,C,r); |
---|
1736 | number MinusOne=n_Init(-1,r); |
---|
1737 | if (!n_Equal(cQ,MinusOne,r)) |
---|
1738 | { |
---|
1739 | cQ=nNeg(cQ); |
---|
1740 | M=p_Mult_nn(M,cQ,r); |
---|
1741 | } |
---|
1742 | Q=p_Add_q(Q,M,r); |
---|
1743 | pNext(q2)=Q; |
---|
1744 | |
---|
1745 | p_Delete(&m,r); |
---|
1746 | n_Delete(&C,r); |
---|
1747 | n_Delete(&cQ,r); |
---|
1748 | n_Delete(&MinusOne,r); |
---|
1749 | /* return(q); */ |
---|
1750 | } |
---|
1751 | #endif |
---|
1752 | |
---|
1753 | |
---|
1754 | /*6 |
---|
1755 | * creates the commutative lcm(lm(p1),lm(p2)) |
---|
1756 | * do not destroy p1 and p2 |
---|
1757 | */ |
---|
1758 | poly nc_CreateShortSpoly(poly p1, poly p2, const ring r) |
---|
1759 | { |
---|
1760 | #ifdef PDEBUG |
---|
1761 | p_Test(p1, r); |
---|
1762 | p_Test(p2, r); |
---|
1763 | #endif |
---|
1764 | |
---|
1765 | const long lCompP1 = p_GetComp(p1,r); |
---|
1766 | const long lCompP2 = p_GetComp(p2,r); |
---|
1767 | |
---|
1768 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
1769 | { |
---|
1770 | #ifdef PDEBUG |
---|
1771 | Werror("nc_CreateShortSpoly: wrong module components!"); // !!!! |
---|
1772 | #endif |
---|
1773 | return(NULL); |
---|
1774 | } |
---|
1775 | |
---|
1776 | poly m = p_Lcm(p1, p2, si_max(lCompP1, lCompP2), r); |
---|
1777 | |
---|
1778 | // n_Delete(&p_GetCoeff(m, r), r); |
---|
1779 | // pSetCoeff0(m, NULL); |
---|
1780 | |
---|
1781 | #ifdef PDEBUG |
---|
1782 | // p_Test(m,r); |
---|
1783 | #endif |
---|
1784 | |
---|
1785 | return(m); |
---|
1786 | } |
---|
1787 | |
---|
1788 | void gnc_kBucketPolyRedOld(kBucket_pt b, poly p, number *c) |
---|
1789 | { |
---|
1790 | // b will not be multiplied by any constant in this impl. |
---|
1791 | // ==> *c=1 |
---|
1792 | *c=nInit(1); |
---|
1793 | poly m=pOne(); |
---|
1794 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
1795 | //pSetm(m); |
---|
1796 | #ifdef PDEBUG |
---|
1797 | pTest(m); |
---|
1798 | #endif |
---|
1799 | poly pp= nc_mm_Mult_pp(m,p,currRing); |
---|
1800 | assume(pp!=NULL); |
---|
1801 | pDelete(&m); |
---|
1802 | number n=nCopy(pGetCoeff(pp)); |
---|
1803 | number MinusOne=nInit(-1); |
---|
1804 | number nn; |
---|
1805 | if (!nEqual(n,MinusOne)) |
---|
1806 | { |
---|
1807 | nn=nNeg(nInvers(n)); |
---|
1808 | } |
---|
1809 | else nn=nInit(1); |
---|
1810 | nDelete(&n); |
---|
1811 | n=nMult(nn,pGetCoeff(kBucketGetLm(b))); |
---|
1812 | nDelete(&nn); |
---|
1813 | pp=p_Mult_nn(pp,n,currRing); |
---|
1814 | nDelete(&n); |
---|
1815 | nDelete(&MinusOne); |
---|
1816 | int l=pLength(pp); |
---|
1817 | kBucket_Add_q(b,pp,&l); |
---|
1818 | } |
---|
1819 | |
---|
1820 | void gnc_kBucketPolyRedNew(kBucket_pt b, poly p, number *c) |
---|
1821 | { |
---|
1822 | #ifdef PDEBUG |
---|
1823 | // Print(">*"); |
---|
1824 | #endif |
---|
1825 | |
---|
1826 | #ifdef KDEBUG |
---|
1827 | if( !kbTest(b) )Werror("nc_kBucketPolyRed: broken bucket!"); |
---|
1828 | #endif |
---|
1829 | |
---|
1830 | #ifdef PDEBUG |
---|
1831 | pTest(p); |
---|
1832 | #if MYTEST |
---|
1833 | Print("p: "); pWrite(p); |
---|
1834 | #endif |
---|
1835 | #endif |
---|
1836 | |
---|
1837 | // b will not be multiplied by any constant in this impl. |
---|
1838 | // ==> *c=1 |
---|
1839 | *c=nInit(1); |
---|
1840 | poly m = pOne(); |
---|
1841 | const poly pLmB = kBucketGetLm(b); // no new copy! |
---|
1842 | |
---|
1843 | assume( pLmB != NULL ); |
---|
1844 | |
---|
1845 | #ifdef PDEBUG |
---|
1846 | pTest(pLmB); |
---|
1847 | |
---|
1848 | #if MYTEST |
---|
1849 | Print("pLmB: "); pWrite(pLmB); |
---|
1850 | #endif |
---|
1851 | #endif |
---|
1852 | |
---|
1853 | pExpVectorDiff(m, pLmB, p); |
---|
1854 | //pSetm(m); |
---|
1855 | |
---|
1856 | #ifdef PDEBUG |
---|
1857 | pTest(m); |
---|
1858 | #if MYTEST |
---|
1859 | Print("m: "); pWrite(m); |
---|
1860 | #endif |
---|
1861 | #endif |
---|
1862 | |
---|
1863 | poly pp = nc_mm_Mult_pp(m, p, currRing); |
---|
1864 | pDelete(&m); |
---|
1865 | |
---|
1866 | assume( pp != NULL ); |
---|
1867 | const number n = pGetCoeff(pp); // bug! |
---|
1868 | number nn; |
---|
1869 | |
---|
1870 | if (!n_IsMOne(n,currRing) ) // does this improve performance??!? also see below... // TODO: check later on. |
---|
1871 | { |
---|
1872 | nn=nNeg(nInvers(nCopy(n))); |
---|
1873 | } |
---|
1874 | else nn=nInit(1); // if n == -1 => nn = 1 and -1/n otherwise |
---|
1875 | |
---|
1876 | number t = nMult(nn,pGetCoeff(pLmB)); |
---|
1877 | nDelete(&nn); |
---|
1878 | |
---|
1879 | pp = p_Mult_nn(pp,t,currRing); |
---|
1880 | nDelete(&t); |
---|
1881 | |
---|
1882 | int l = pLength(pp); |
---|
1883 | |
---|
1884 | #ifdef PDEBUG |
---|
1885 | pTest(pp); |
---|
1886 | // Print("PP: "); pWrite(pp); |
---|
1887 | #endif |
---|
1888 | |
---|
1889 | kBucket_Add_q(b,pp,&l); |
---|
1890 | |
---|
1891 | |
---|
1892 | #ifdef PDEBUG |
---|
1893 | // Print("*>"); |
---|
1894 | #endif |
---|
1895 | } |
---|
1896 | |
---|
1897 | |
---|
1898 | void gnc_kBucketPolyRed_ZOld(kBucket_pt b, poly p, number *c) |
---|
1899 | { |
---|
1900 | // b is multiplied by a constant in this impl. |
---|
1901 | poly m=pOne(); |
---|
1902 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
1903 | //pSetm(m); |
---|
1904 | #ifdef PDEBUG |
---|
1905 | pTest(m); |
---|
1906 | #endif |
---|
1907 | if(p_IsConstant(m,currRing)){ |
---|
1908 | pDelete(&m); |
---|
1909 | *c = kBucketPolyRed(b,p,pLength(p),NULL); |
---|
1910 | return; |
---|
1911 | } |
---|
1912 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
1913 | number c2,cc; |
---|
1914 | pCleardenom_n(pp,c2); |
---|
1915 | pDelete(&m); |
---|
1916 | *c = kBucketPolyRed(b,pp,pLength(pp),NULL); |
---|
1917 | //cc=*c; |
---|
1918 | //*c=nMult(*c,c2); |
---|
1919 | nDelete(&c2); |
---|
1920 | //nDelete(&cc); |
---|
1921 | pDelete(&pp); |
---|
1922 | |
---|
1923 | } |
---|
1924 | |
---|
1925 | void gnc_kBucketPolyRed_ZNew(kBucket_pt b, poly p, number *c) |
---|
1926 | { |
---|
1927 | // b is multiplied by a constant in this impl. |
---|
1928 | poly m=pOne(); |
---|
1929 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
1930 | //pSetm(m); |
---|
1931 | #ifdef PDEBUG |
---|
1932 | pTest(m); |
---|
1933 | #endif |
---|
1934 | |
---|
1935 | if(p_IsConstant(m,currRing)) |
---|
1936 | { |
---|
1937 | pDelete(&m); |
---|
1938 | *c = kBucketPolyRed(b,p,pLength(p),NULL); |
---|
1939 | return; |
---|
1940 | } |
---|
1941 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
1942 | number c2,cc; |
---|
1943 | pCleardenom_n(pp,c2); |
---|
1944 | pDelete(&m); |
---|
1945 | *c = kBucketPolyRed(b,pp,pLength(pp),NULL); |
---|
1946 | //cc=*c; |
---|
1947 | //*c=nMult(*c,c2); |
---|
1948 | nDelete(&c2); |
---|
1949 | //nDelete(&cc); |
---|
1950 | pDelete(&pp); |
---|
1951 | |
---|
1952 | } |
---|
1953 | |
---|
1954 | |
---|
1955 | inline void nc_PolyPolyRedOld(poly &b, poly p, number *c) |
---|
1956 | // reduces b with p, do not delete both |
---|
1957 | { |
---|
1958 | // b will not by multiplied by any constant in this impl. |
---|
1959 | // ==> *c=1 |
---|
1960 | *c=nInit(1); |
---|
1961 | poly m=pOne(); |
---|
1962 | pExpVectorDiff(m,pHead(b),p); |
---|
1963 | //pSetm(m); |
---|
1964 | #ifdef PDEBUG |
---|
1965 | pTest(m); |
---|
1966 | #endif |
---|
1967 | poly pp=nc_mm_Mult_pp(m,p,currRing); |
---|
1968 | assume(pp!=NULL); |
---|
1969 | |
---|
1970 | pDelete(&m); |
---|
1971 | number n=nCopy(pGetCoeff(pp)); |
---|
1972 | number MinusOne=nInit(-1); |
---|
1973 | number nn; |
---|
1974 | if (!nEqual(n,MinusOne)) |
---|
1975 | { |
---|
1976 | nn=nNeg(nInvers(n)); |
---|
1977 | } |
---|
1978 | else nn=nInit(1); |
---|
1979 | nDelete(&n); |
---|
1980 | n=nMult(nn,pGetCoeff(b)); |
---|
1981 | nDelete(&nn); |
---|
1982 | pp=p_Mult_nn(pp,n,currRing); |
---|
1983 | nDelete(&n); |
---|
1984 | nDelete(&MinusOne); |
---|
1985 | b=p_Add_q(b,pp,currRing); |
---|
1986 | } |
---|
1987 | |
---|
1988 | |
---|
1989 | inline void nc_PolyPolyRedNew(poly &b, poly p, number *c) |
---|
1990 | // reduces b with p, do not delete both |
---|
1991 | { |
---|
1992 | #ifdef PDEBUG |
---|
1993 | pTest(b); |
---|
1994 | pTest(p); |
---|
1995 | #endif |
---|
1996 | |
---|
1997 | #if MYTEST |
---|
1998 | PrintS("nc_PolyPolyRedNew("); |
---|
1999 | pWrite0(b); |
---|
2000 | PrintS(", "); |
---|
2001 | pWrite0(p); |
---|
2002 | PrintS(", *c): "); |
---|
2003 | #endif |
---|
2004 | |
---|
2005 | // b will not by multiplied by any constant in this impl. |
---|
2006 | // ==> *c=1 |
---|
2007 | *c=nInit(1); |
---|
2008 | |
---|
2009 | poly pp = NULL; |
---|
2010 | |
---|
2011 | // there is a problem when p is a square(=>0!) |
---|
2012 | |
---|
2013 | while((b != NULL) && (pp == NULL)) |
---|
2014 | { |
---|
2015 | |
---|
2016 | // poly pLmB = pHead(b); |
---|
2017 | poly m = pOne(); |
---|
2018 | pExpVectorDiff(m, b, p); |
---|
2019 | // pDelete(&pLmB); |
---|
2020 | //pSetm(m); |
---|
2021 | |
---|
2022 | #ifdef PDEBUG |
---|
2023 | pTest(m); |
---|
2024 | pTest(b); |
---|
2025 | #endif |
---|
2026 | |
---|
2027 | pp = nc_mm_Mult_pp(m, p, currRing); |
---|
2028 | |
---|
2029 | #if MYTEST |
---|
2030 | PrintS("\n{b': "); |
---|
2031 | pWrite0(b); |
---|
2032 | PrintS(", m: "); |
---|
2033 | pWrite0(m); |
---|
2034 | PrintS(", pp: "); |
---|
2035 | pWrite0(pp); |
---|
2036 | PrintS(" }\n"); |
---|
2037 | #endif |
---|
2038 | |
---|
2039 | pDelete(&m); // one m for all tries! |
---|
2040 | |
---|
2041 | // assume( pp != NULL ); |
---|
2042 | |
---|
2043 | if( pp == NULL ) |
---|
2044 | { |
---|
2045 | b = p_LmDeleteAndNext(b, currRing); |
---|
2046 | |
---|
2047 | if( !p_DivisibleBy(p, b, currRing) ) |
---|
2048 | return; |
---|
2049 | |
---|
2050 | } |
---|
2051 | } |
---|
2052 | |
---|
2053 | #if MYTEST |
---|
2054 | PrintS("{b': "); |
---|
2055 | pWrite0(b); |
---|
2056 | PrintS(", pp: "); |
---|
2057 | pWrite0(pp); |
---|
2058 | PrintS(" }\n"); |
---|
2059 | #endif |
---|
2060 | |
---|
2061 | |
---|
2062 | if(b == NULL) return; |
---|
2063 | |
---|
2064 | |
---|
2065 | assume(pp != NULL); |
---|
2066 | |
---|
2067 | const number n = pGetCoeff(pp); // no new copy |
---|
2068 | |
---|
2069 | number nn; |
---|
2070 | |
---|
2071 | if (!n_IsMOne(n, currRing)) // TODO: as above. |
---|
2072 | { |
---|
2073 | nn=nNeg(nInvers(nCopy(n))); |
---|
2074 | } |
---|
2075 | else nn=nInit(1); |
---|
2076 | |
---|
2077 | number t = nMult(nn, pGetCoeff(b)); |
---|
2078 | nDelete(&nn); |
---|
2079 | |
---|
2080 | pp=p_Mult_nn(pp, t, currRing); |
---|
2081 | nDelete(&t); |
---|
2082 | |
---|
2083 | b=p_Add_q(b,pp,currRing); |
---|
2084 | |
---|
2085 | } |
---|
2086 | |
---|
2087 | void nc_PolyPolyRed(poly &b, poly p, number *c) |
---|
2088 | { |
---|
2089 | #if 0 |
---|
2090 | nc_PolyPolyRedOld(b, p, c); |
---|
2091 | #else |
---|
2092 | nc_PolyPolyRedNew(b, p, c); |
---|
2093 | #endif |
---|
2094 | } |
---|
2095 | |
---|
2096 | |
---|
2097 | poly nc_mm_Bracket_nn(poly m1, poly m2); |
---|
2098 | |
---|
2099 | poly nc_p_Bracket_qq(poly p, poly q) |
---|
2100 | /* returns [p,q], destroys p */ |
---|
2101 | { |
---|
2102 | |
---|
2103 | if (!rIsPluralRing(currRing)) return(NULL); |
---|
2104 | if (pComparePolys(p,q)) return(NULL); |
---|
2105 | /* Components !? */ |
---|
2106 | poly Q=NULL; |
---|
2107 | number coef=NULL; |
---|
2108 | poly res=NULL; |
---|
2109 | poly pres=NULL; |
---|
2110 | int UseBuckets=1; |
---|
2111 | if ((pLength(p)< MIN_LENGTH_BUCKET/2) && (pLength(q)< MIN_LENGTH_BUCKET/2) || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
---|
2112 | sBucket_pt bu_out; |
---|
2113 | if (UseBuckets) bu_out=sBucketCreate(currRing); |
---|
2114 | while (p!=NULL) |
---|
2115 | { |
---|
2116 | Q=q; |
---|
2117 | while(Q!=NULL) |
---|
2118 | { |
---|
2119 | pres=nc_mm_Bracket_nn(p,Q); /* since no coeffs are taken into account there */ |
---|
2120 | if (pres!=NULL) |
---|
2121 | { |
---|
2122 | coef = nMult(pGetCoeff(p),pGetCoeff(Q)); |
---|
2123 | pres = p_Mult_nn(pres,coef,currRing); |
---|
2124 | if (UseBuckets) sBucket_Add_p(bu_out,pres,pLength(pres)); |
---|
2125 | else res=p_Add_q(res,pres,currRing); |
---|
2126 | nDelete(&coef); |
---|
2127 | } |
---|
2128 | pIter(Q); |
---|
2129 | } |
---|
2130 | p=pLmDeleteAndNext(p); |
---|
2131 | } |
---|
2132 | if (UseBuckets) |
---|
2133 | { |
---|
2134 | res = NULL; |
---|
2135 | int len = pLength(res); |
---|
2136 | sBucketDestroyAdd(bu_out, &res, &len); |
---|
2137 | } |
---|
2138 | return(res); |
---|
2139 | } |
---|
2140 | |
---|
2141 | poly nc_mm_Bracket_nn(poly m1, poly m2) |
---|
2142 | /*returns [m1,m2] for two monoms, destroys nothing */ |
---|
2143 | /* without coeffs */ |
---|
2144 | { |
---|
2145 | if (pLmIsConstant(m1) || pLmIsConstant(m1)) return(NULL); |
---|
2146 | if (pLmCmp(m1,m2)==0) return(NULL); |
---|
2147 | int rN=currRing->N; |
---|
2148 | int *M1=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2149 | int *M2=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2150 | int *PREFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2151 | int *SUFFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2152 | pGetExpV(m1,M1); |
---|
2153 | pGetExpV(m2,M2); |
---|
2154 | poly res=NULL; |
---|
2155 | poly ares=NULL; |
---|
2156 | poly bres=NULL; |
---|
2157 | poly prefix=NULL; |
---|
2158 | poly suffix=NULL; |
---|
2159 | int nMin,nMax; |
---|
2160 | number nTmp=NULL; |
---|
2161 | int i,j,k; |
---|
2162 | for (i=1;i<=rN;i++) |
---|
2163 | { |
---|
2164 | if (M2[i]!=0) |
---|
2165 | { |
---|
2166 | ares=NULL; |
---|
2167 | for (j=1;j<=rN;j++) |
---|
2168 | { |
---|
2169 | if (M1[j]!=0) |
---|
2170 | { |
---|
2171 | bres=NULL; |
---|
2172 | /* compute [ x_j^M1[j],x_i^M2[i] ] */ |
---|
2173 | if (i<j) {nMax=j; nMin=i;} else {nMax=i; nMin=j;} |
---|
2174 | 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)*/ |
---|
2175 | { bres=NULL; } |
---|
2176 | else |
---|
2177 | { |
---|
2178 | if (i<j) { bres=gnc_uu_Mult_ww(j,M1[j],i,M2[i],currRing); } |
---|
2179 | else bres=gnc_uu_Mult_ww(i,M2[i],j,M1[j],currRing); |
---|
2180 | if (nIsOne(pGetCoeff(bres))) |
---|
2181 | { |
---|
2182 | bres=pLmDeleteAndNext(bres); |
---|
2183 | } |
---|
2184 | else |
---|
2185 | { |
---|
2186 | nTmp=nSub(pGetCoeff(bres),nInit(1)); |
---|
2187 | pSetCoeff(bres,nTmp); /* only lc ! */ |
---|
2188 | } |
---|
2189 | #ifdef PDEBUG |
---|
2190 | pTest(bres); |
---|
2191 | #endif |
---|
2192 | if (i>j) bres=p_Neg(bres, currRing); |
---|
2193 | } |
---|
2194 | if (bres!=NULL) |
---|
2195 | { |
---|
2196 | /* now mult (prefix, bres, suffix) */ |
---|
2197 | memcpy(SUFFIX, M1,(rN+1)*sizeof(int)); |
---|
2198 | memcpy(PREFIX, M1,(rN+1)*sizeof(int)); |
---|
2199 | for (k=1;k<=j;k++) SUFFIX[k]=0; |
---|
2200 | for (k=j;k<=rN;k++) PREFIX[k]=0; |
---|
2201 | SUFFIX[0]=0; |
---|
2202 | PREFIX[0]=0; |
---|
2203 | prefix=pOne(); |
---|
2204 | suffix=pOne(); |
---|
2205 | pSetExpV(prefix,PREFIX); |
---|
2206 | pSetm(prefix); |
---|
2207 | pSetExpV(suffix,SUFFIX); |
---|
2208 | pSetm(suffix); |
---|
2209 | if (!pLmIsConstant(prefix)) bres = gnc_mm_Mult_p(prefix, bres,currRing); |
---|
2210 | if (!pLmIsConstant(suffix)) bres = gnc_p_Mult_mm(bres, suffix,currRing); |
---|
2211 | ares=p_Add_q(ares, bres,currRing); |
---|
2212 | /* What to give free? */ |
---|
2213 | /* Do we have to free PREFIX/SUFFIX? it seems so */ |
---|
2214 | pDelete(&prefix); |
---|
2215 | pDelete(&suffix); |
---|
2216 | } |
---|
2217 | } |
---|
2218 | } |
---|
2219 | if (ares!=NULL) |
---|
2220 | { |
---|
2221 | /* now mult (prefix, bres, suffix) */ |
---|
2222 | memcpy(SUFFIX, M2,(rN+1)*sizeof(int)); |
---|
2223 | memcpy(PREFIX, M2,(rN+1)*sizeof(int)); |
---|
2224 | for (k=1;k<=i;k++) SUFFIX[k]=0; |
---|
2225 | for (k=i;k<=rN;k++) PREFIX[k]=0; |
---|
2226 | SUFFIX[0]=0; |
---|
2227 | PREFIX[0]=0; |
---|
2228 | prefix=pOne(); |
---|
2229 | suffix=pOne(); |
---|
2230 | pSetExpV(prefix,PREFIX); |
---|
2231 | pSetm(prefix); |
---|
2232 | pSetExpV(suffix,SUFFIX); |
---|
2233 | pSetm(suffix); |
---|
2234 | bres=ares; |
---|
2235 | if (!pLmIsConstant(prefix)) bres = gnc_mm_Mult_p(prefix, bres,currRing); |
---|
2236 | if (!pLmIsConstant(suffix)) bres = gnc_p_Mult_mm(bres, suffix,currRing); |
---|
2237 | res=p_Add_q(res, bres,currRing); |
---|
2238 | pDelete(&prefix); |
---|
2239 | pDelete(&suffix); |
---|
2240 | } |
---|
2241 | } |
---|
2242 | } |
---|
2243 | freeT(M1, rN); |
---|
2244 | freeT(M2, rN); |
---|
2245 | freeT(PREFIX, rN); |
---|
2246 | freeT(SUFFIX, rN); |
---|
2247 | pTest(res); |
---|
2248 | return(res); |
---|
2249 | } |
---|
2250 | |
---|
2251 | ideal twostd(ideal I) // works in currRing only! |
---|
2252 | { |
---|
2253 | ideal J = kStd(I, currQuotient, testHomog, NULL, NULL, 0, 0, NULL); // in currRing!!! |
---|
2254 | idSkipZeroes(J); // ring independent! |
---|
2255 | |
---|
2256 | const int rN = currRing->N; |
---|
2257 | |
---|
2258 | loop |
---|
2259 | { |
---|
2260 | ideal K = NULL; |
---|
2261 | const int s = idElem(J); // ring independent |
---|
2262 | |
---|
2263 | for(int i = 0; i < s; i++) |
---|
2264 | { |
---|
2265 | const poly p = J->m[i]; |
---|
2266 | |
---|
2267 | #ifdef PDEBUG |
---|
2268 | p_Test(p, currRing); |
---|
2269 | #if 0 |
---|
2270 | Print("p: "); // ! |
---|
2271 | p_Write(p, currRing); |
---|
2272 | #endif |
---|
2273 | #endif |
---|
2274 | |
---|
2275 | for (int j = 1; j <= rN; j++) // for all j = 1..N |
---|
2276 | { |
---|
2277 | poly varj = p_ISet(1, currRing); |
---|
2278 | p_SetExp(varj, j, 1, currRing); |
---|
2279 | p_Setm(varj, currRing); |
---|
2280 | |
---|
2281 | poly q = pp_Mult_mm(p, varj, currRing); // q = J[i] * var(j), |
---|
2282 | |
---|
2283 | #ifdef PDEBUG |
---|
2284 | p_Test(varj, currRing); |
---|
2285 | p_Test(p, currRing); |
---|
2286 | p_Test(q, currRing); |
---|
2287 | #if 0 |
---|
2288 | Print("Reducing p: "); // ! |
---|
2289 | p_Write(p, currRing); |
---|
2290 | Print("With q: "); // ! |
---|
2291 | p_Write(q, currRing); |
---|
2292 | #endif |
---|
2293 | #endif |
---|
2294 | |
---|
2295 | p_Delete(&varj, currRing); |
---|
2296 | |
---|
2297 | if (q != NULL) |
---|
2298 | { |
---|
2299 | #ifdef PDEBUG |
---|
2300 | #if 0 |
---|
2301 | Print("Reducing q[j = %d]: ", j); // ! |
---|
2302 | p_Write(q, currRing); |
---|
2303 | |
---|
2304 | Print("With p:"); |
---|
2305 | p_Write(p, currRing); |
---|
2306 | |
---|
2307 | #endif |
---|
2308 | #endif |
---|
2309 | |
---|
2310 | // bug: lm(p) may not divide lm(p * var(i)) in a SCA! |
---|
2311 | if( p_LmDivisibleBy(p, q, currRing) ) |
---|
2312 | q = nc_ReduceSpoly(p, q, currRing); |
---|
2313 | |
---|
2314 | |
---|
2315 | #ifdef PDEBUG |
---|
2316 | p_Test(q, currRing); |
---|
2317 | #if 0 |
---|
2318 | Print("reductum q/p: "); |
---|
2319 | p_Write(q, currRing); |
---|
2320 | |
---|
2321 | // Print("With J!\n"); |
---|
2322 | #endif |
---|
2323 | #endif |
---|
2324 | |
---|
2325 | // if( q != NULL) |
---|
2326 | q = kNF(J, currQuotient, q, 0, KSTD_NF_NONORM); // in currRing!!! |
---|
2327 | |
---|
2328 | #ifdef PDEBUG |
---|
2329 | p_Test(q, currRing); |
---|
2330 | #if 0 |
---|
2331 | Print("NF(J/currQuotient)=> q: "); // ! |
---|
2332 | p_Write(q, currRing); |
---|
2333 | #endif |
---|
2334 | #endif |
---|
2335 | if (q!=NULL) |
---|
2336 | { |
---|
2337 | if (p_IsConstant(q, currRing)) // => return (1)! |
---|
2338 | { |
---|
2339 | p_Delete(&q, currRing); |
---|
2340 | id_Delete(&J, currRing); |
---|
2341 | |
---|
2342 | if (K != NULL) |
---|
2343 | id_Delete(&K, currRing); |
---|
2344 | |
---|
2345 | ideal Q = idInit(1,1); // ring independent! |
---|
2346 | Q->m[0] = p_ISet(1,currRing); |
---|
2347 | |
---|
2348 | return(Q); |
---|
2349 | } |
---|
2350 | |
---|
2351 | // flag = false; |
---|
2352 | |
---|
2353 | // K += q: |
---|
2354 | |
---|
2355 | ideal Q = idInit(1,1); // ring independent |
---|
2356 | Q->m[0]=q; |
---|
2357 | |
---|
2358 | if( K == NULL ) |
---|
2359 | K = Q; |
---|
2360 | else |
---|
2361 | { |
---|
2362 | ideal id_tmp = idSimpleAdd(K, Q); // in currRing |
---|
2363 | id_Delete(&K, currRing); |
---|
2364 | id_Delete(&Q, currRing); |
---|
2365 | K = id_tmp; // K += Q |
---|
2366 | } |
---|
2367 | } |
---|
2368 | |
---|
2369 | |
---|
2370 | } // if q != NULL |
---|
2371 | } // for all variables |
---|
2372 | |
---|
2373 | } |
---|
2374 | |
---|
2375 | if (K == NULL) // nothing new: i.e. all elements are two-sided |
---|
2376 | return(J); |
---|
2377 | /* now we update GrBasis J with K */ |
---|
2378 | // iSize=IDELEMS(J); |
---|
2379 | #ifdef PDEBUG |
---|
2380 | idTest(J); // in currRing! |
---|
2381 | #if 0 |
---|
2382 | Print("J:"); |
---|
2383 | idPrint(J); |
---|
2384 | PrintLn(); |
---|
2385 | #endif // debug |
---|
2386 | #endif |
---|
2387 | |
---|
2388 | |
---|
2389 | |
---|
2390 | #ifdef PDEBUG |
---|
2391 | idTest(K); // in currRing! |
---|
2392 | #if 0 |
---|
2393 | Print("+K:"); |
---|
2394 | idPrint(K); |
---|
2395 | PrintLn(); |
---|
2396 | #endif // debug |
---|
2397 | #endif |
---|
2398 | |
---|
2399 | |
---|
2400 | int iSize = idElem(J); // ring independent |
---|
2401 | |
---|
2402 | // J += K: |
---|
2403 | ideal id_tmp = idSimpleAdd(J,K); // in currRing |
---|
2404 | id_Delete(&K, currRing); id_Delete(&J, currRing); |
---|
2405 | |
---|
2406 | #if 1 |
---|
2407 | BITSET save_test=test; |
---|
2408 | test|=Sy_bit(OPT_SB_1); // ring independent |
---|
2409 | J = kStd(id_tmp, currQuotient, testHomog, NULL, NULL, 0, iSize); // J = J + K, J - std // in currRing! |
---|
2410 | test = save_test; |
---|
2411 | #else |
---|
2412 | J=kStd(id_tmp, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
2413 | #endif |
---|
2414 | |
---|
2415 | id_Delete(&id_tmp, currRing); |
---|
2416 | idSkipZeroes(J); // ring independent |
---|
2417 | |
---|
2418 | #ifdef PDEBUG |
---|
2419 | idTest(J); // in currRing! |
---|
2420 | #if 0 |
---|
2421 | Print("J:"); |
---|
2422 | idPrint(J); |
---|
2423 | PrintLn(); |
---|
2424 | #endif // debug |
---|
2425 | #endif |
---|
2426 | } // loop |
---|
2427 | } |
---|
2428 | |
---|
2429 | |
---|
2430 | matrix nc_PrintMat(int a, int b, ring r, int metric) |
---|
2431 | /* returns matrix with the info on noncomm multiplication */ |
---|
2432 | { |
---|
2433 | |
---|
2434 | if ( (a==b) || !rIsPluralRing(r) ) return(NULL); |
---|
2435 | int i; |
---|
2436 | int j; |
---|
2437 | if (a>b) {j=b; i=a;} |
---|
2438 | else {j=a; i=b;} |
---|
2439 | /* i<j */ |
---|
2440 | int rN=r->N; |
---|
2441 | int size=r->GetNC()->MTsize[UPMATELEM(i,j,rN)]; |
---|
2442 | matrix M = r->GetNC()->MT[UPMATELEM(i,j,rN)]; |
---|
2443 | /* return(M); */ |
---|
2444 | int sizeofres; |
---|
2445 | if (metric==0) |
---|
2446 | { |
---|
2447 | sizeofres=sizeof(int); |
---|
2448 | } |
---|
2449 | if (metric==1) |
---|
2450 | { |
---|
2451 | sizeofres=sizeof(number); |
---|
2452 | } |
---|
2453 | matrix res=mpNew(size,size); |
---|
2454 | int s; |
---|
2455 | int t; |
---|
2456 | int length; |
---|
2457 | long totdeg; |
---|
2458 | poly p; |
---|
2459 | for(s=1;s<=size;s++) |
---|
2460 | { |
---|
2461 | for(t=1;t<=size;t++) |
---|
2462 | { |
---|
2463 | p=MATELEM(M,s,t); |
---|
2464 | if (p==NULL) |
---|
2465 | { |
---|
2466 | MATELEM(res,s,t)=0; |
---|
2467 | } |
---|
2468 | else |
---|
2469 | { |
---|
2470 | length = pLength(p); |
---|
2471 | if (metric==0) /* length */ |
---|
2472 | { |
---|
2473 | MATELEM(res,s,t)= p_ISet(length,r); |
---|
2474 | } |
---|
2475 | else if (metric==1) /* sum of deg divided by the length */ |
---|
2476 | { |
---|
2477 | totdeg=0; |
---|
2478 | while (p!=NULL) |
---|
2479 | { |
---|
2480 | totdeg=totdeg+pDeg(p,r); |
---|
2481 | pIter(p); |
---|
2482 | } |
---|
2483 | number ntd = nInit(totdeg); |
---|
2484 | number nln = nInit(length); |
---|
2485 | number nres=nDiv(ntd,nln); |
---|
2486 | nDelete(&ntd); |
---|
2487 | nDelete(&nln); |
---|
2488 | MATELEM(res,s,t)=p_NSet(nres,r); |
---|
2489 | } |
---|
2490 | } |
---|
2491 | } |
---|
2492 | } |
---|
2493 | return(res); |
---|
2494 | } |
---|
2495 | |
---|
2496 | void ncKill(ring r) |
---|
2497 | // kills the nc extension of ring r |
---|
2498 | { |
---|
2499 | if (r->GetNC()->ref >= 1) /* in use by somebody else */ |
---|
2500 | { |
---|
2501 | r->GetNC()->ref--; |
---|
2502 | r->GetNC() = NULL; // don't cleanup, just dereference |
---|
2503 | return; |
---|
2504 | } |
---|
2505 | /* otherwise kill the previous nc data */ |
---|
2506 | |
---|
2507 | assume( r->GetNC()->ref == 0 ); |
---|
2508 | |
---|
2509 | int i,j; |
---|
2510 | int rN=r->N; |
---|
2511 | if ( rN > 1 ) |
---|
2512 | { |
---|
2513 | for(i=1;i<rN;i++) |
---|
2514 | { |
---|
2515 | for(j=i+1;j<=rN;j++) |
---|
2516 | { |
---|
2517 | id_Delete((ideal *)&(r->GetNC()->MT[UPMATELEM(i,j,rN)]),r->GetNC()->basering); |
---|
2518 | } |
---|
2519 | } |
---|
2520 | omFreeSize((ADDRESS)r->GetNC()->MT,rN*(rN-1)/2*sizeof(matrix)); |
---|
2521 | omFreeSize((ADDRESS)r->GetNC()->MTsize,rN*(rN-1)/2*sizeof(int)); |
---|
2522 | id_Delete((ideal *)&(r->GetNC()->COM),r->GetNC()->basering); |
---|
2523 | } |
---|
2524 | id_Delete((ideal *)&(r->GetNC()->C),r->GetNC()->basering); |
---|
2525 | id_Delete((ideal *)&(r->GetNC()->D),r->GetNC()->basering); |
---|
2526 | |
---|
2527 | if( rIsSCA(r) && (r->GetNC()->SCAQuotient() != NULL) ) |
---|
2528 | { |
---|
2529 | id_Delete(&r->GetNC()->SCAQuotient(), r->GetNC()->basering); |
---|
2530 | } |
---|
2531 | |
---|
2532 | r->GetNC()->basering->ref--; |
---|
2533 | |
---|
2534 | if ((r->GetNC()->basering->ref<=0)&&(r->GetNC()->basering->GetNC()==NULL)) |
---|
2535 | { |
---|
2536 | rKill(r->GetNC()->basering); |
---|
2537 | } |
---|
2538 | |
---|
2539 | ncCleanUp(r); |
---|
2540 | } |
---|
2541 | |
---|
2542 | inline void ncCleanUp(nc_struct* p) |
---|
2543 | { |
---|
2544 | assume(p != NULL); |
---|
2545 | omFreeSize((ADDRESS)p,sizeof(nc_struct)); |
---|
2546 | } |
---|
2547 | |
---|
2548 | inline void ncCleanUp(ring r) |
---|
2549 | { |
---|
2550 | /* small CleanUp of r->GetNC() */ |
---|
2551 | assume(r != NULL); |
---|
2552 | ncCleanUp(r->GetNC()); |
---|
2553 | r->GetNC() = NULL; |
---|
2554 | } |
---|
2555 | |
---|
2556 | // inline |
---|
2557 | void nc_rCopy0(ring res, const ring r) |
---|
2558 | { |
---|
2559 | assume(rIsPluralRing(r)); |
---|
2560 | assume( res != r ); |
---|
2561 | |
---|
2562 | res->GetNC() = r->GetNC(); |
---|
2563 | res->GetNC()->ref++; |
---|
2564 | nc_p_ProcsSet(res, res->p_Procs); |
---|
2565 | } |
---|
2566 | |
---|
2567 | |
---|
2568 | |
---|
2569 | poly nc_p_CopyGet(poly a, const ring r) |
---|
2570 | /* for use in getting the mult. matrix elements*/ |
---|
2571 | /* ring r must be a currRing! */ |
---|
2572 | /* for consistency, copies a poly from the comm. r->GetNC()->basering */ |
---|
2573 | /* to its image in NC ring */ |
---|
2574 | { |
---|
2575 | if (r != currRing) |
---|
2576 | { |
---|
2577 | #ifdef PDEBUF |
---|
2578 | Werror("nc_p_CopyGet call not in currRing"); |
---|
2579 | #endif |
---|
2580 | return(NULL); |
---|
2581 | } |
---|
2582 | if (!rIsPluralRing(r)) return(p_Copy(a,r)); |
---|
2583 | if (r==r->GetNC()->basering) return(p_Copy(a,r)); |
---|
2584 | else |
---|
2585 | { |
---|
2586 | return(prCopyR_NoSort(a,r->GetNC()->basering,r)); |
---|
2587 | } |
---|
2588 | } |
---|
2589 | |
---|
2590 | poly nc_p_CopyPut(poly a, const ring r) |
---|
2591 | /* for use in defining the mult. matrix elements*/ |
---|
2592 | /* ring r must be a currRing! */ |
---|
2593 | /* for consistency, puts a polynomial from the NC ring */ |
---|
2594 | /* to its presentation in the comm. r->GetNC()->basering */ |
---|
2595 | { |
---|
2596 | if (r != currRing) |
---|
2597 | { |
---|
2598 | #ifdef PDEBUF |
---|
2599 | Werror("nc_p_CopyGet call not in currRing"); |
---|
2600 | #endif |
---|
2601 | return(NULL); |
---|
2602 | } |
---|
2603 | |
---|
2604 | if (!rIsPluralRing(r)) return(p_Copy(a,r)); |
---|
2605 | if (r==r->GetNC()->basering) return(p_Copy(a,r)); |
---|
2606 | else |
---|
2607 | { |
---|
2608 | return(prCopyR_NoSort(a,r,r->GetNC()->basering)); |
---|
2609 | } |
---|
2610 | } |
---|
2611 | |
---|
2612 | BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r) |
---|
2613 | /* returns TRUE if there were errors */ |
---|
2614 | /* checks whether product of vars from PolyVar defines */ |
---|
2615 | /* an admissible subalgebra of r */ |
---|
2616 | /* r is indeed currRing and assumed to be noncomm. */ |
---|
2617 | { |
---|
2618 | ring save = currRing; |
---|
2619 | int WeChangeRing = 0; |
---|
2620 | if (currRing != r) |
---|
2621 | { |
---|
2622 | rChangeCurrRing(r); |
---|
2623 | WeChangeRing = 1; |
---|
2624 | } |
---|
2625 | int rN=r->N; |
---|
2626 | int *ExpVar=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
2627 | int *ExpTmp=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
2628 | p_GetExpV(PolyVar, ExpVar, r); |
---|
2629 | int i; int j; int k; |
---|
2630 | poly test=NULL; |
---|
2631 | int OK=1; |
---|
2632 | for (i=1; i<rN; i++) |
---|
2633 | { |
---|
2634 | if (ExpVar[i]==0) /* i.e. not in PolyVar */ |
---|
2635 | { |
---|
2636 | for (j=i+1; j<=rN; j++) |
---|
2637 | { |
---|
2638 | if (ExpVar[j]==0) |
---|
2639 | { |
---|
2640 | test = nc_p_CopyGet(MATELEM(r->GetNC()->D,i,j),r); |
---|
2641 | while (test!=NULL) |
---|
2642 | { |
---|
2643 | p_GetExpV(test, ExpTmp, r); |
---|
2644 | OK=1; |
---|
2645 | for (k=1;k<=rN;k++) |
---|
2646 | { |
---|
2647 | if (ExpTmp[k]!=0) |
---|
2648 | { |
---|
2649 | if (ExpVar[k]!=0) OK=0; |
---|
2650 | } |
---|
2651 | } |
---|
2652 | if (!OK) return(TRUE); |
---|
2653 | pIter(test); |
---|
2654 | } |
---|
2655 | } |
---|
2656 | } |
---|
2657 | } |
---|
2658 | } |
---|
2659 | p_Delete(&test,r); |
---|
2660 | freeT(ExpVar,rN); |
---|
2661 | freeT(ExpTmp,rN); |
---|
2662 | if ( WeChangeRing ) |
---|
2663 | rChangeCurrRing(save); |
---|
2664 | return(FALSE); |
---|
2665 | } |
---|
2666 | |
---|
2667 | |
---|
2668 | BOOLEAN gnc_CheckOrdCondition(matrix D, ring r) |
---|
2669 | /* returns TRUE if there were errors */ |
---|
2670 | /* checks whether the current ordering */ |
---|
2671 | /* is admissible for r and D == r->GetNC()->D */ |
---|
2672 | /* to be executed in a currRing */ |
---|
2673 | { |
---|
2674 | /* analyze D: an upper triangular matrix of polys */ |
---|
2675 | /* check the ordering condition for D */ |
---|
2676 | ring save = currRing; |
---|
2677 | int WeChangeRing = 0; |
---|
2678 | if (r != currRing) |
---|
2679 | { |
---|
2680 | rChangeCurrRing(r); |
---|
2681 | WeChangeRing = 1; |
---|
2682 | } |
---|
2683 | poly p,q; |
---|
2684 | int i,j; |
---|
2685 | int report = 0; |
---|
2686 | for(i=1; i<r->N; i++) |
---|
2687 | { |
---|
2688 | for(j=i+1; j<=r->N; j++) |
---|
2689 | { |
---|
2690 | p = nc_p_CopyGet(MATELEM(D,i,j),r); |
---|
2691 | if ( p != NULL) |
---|
2692 | { |
---|
2693 | q = p_ISet(1,r); // replaces pOne(); |
---|
2694 | p_SetExp(q,i,1,r); |
---|
2695 | p_SetExp(q,j,1,r); |
---|
2696 | p_Setm(q,r); |
---|
2697 | if (p_LmCmp(q,p,r) != 1) /* i.e. lm(p)==xy < lm(q)==D_ij */ |
---|
2698 | { |
---|
2699 | Werror("Bad ordering at %d,%d\n",i,j); |
---|
2700 | #ifdef PDEBUG |
---|
2701 | p_Write(p,r); |
---|
2702 | p_Write(q,r); |
---|
2703 | #endif |
---|
2704 | report = 1; |
---|
2705 | } |
---|
2706 | p_Delete(&q,r); |
---|
2707 | p_Delete(&p,r); |
---|
2708 | p = NULL; |
---|
2709 | } |
---|
2710 | } |
---|
2711 | } |
---|
2712 | if ( WeChangeRing ) |
---|
2713 | rChangeCurrRing(save); |
---|
2714 | return(report); |
---|
2715 | } |
---|
2716 | |
---|
2717 | |
---|
2718 | |
---|
2719 | BOOLEAN nc_CallPlural( |
---|
2720 | matrix CCC, matrix DDD, |
---|
2721 | poly CCN, poly DDN, |
---|
2722 | ring r, |
---|
2723 | bool bSetupQuotient, bool bCopyInput, bool bBeQuiet, |
---|
2724 | ring curr) |
---|
2725 | /* returns TRUE if there were errors */ |
---|
2726 | /* analyze inputs, check them for consistency */ |
---|
2727 | /* detects nc_type, DO NOT initialize multiplication but call for it at the end*/ |
---|
2728 | /* checks the ordering condition and evtl. NDC */ |
---|
2729 | // NOTE: all the data belong to the curr, |
---|
2730 | // we change r which may be the same ring, and must have the same representation! |
---|
2731 | { |
---|
2732 | // assume( curr != r ); |
---|
2733 | assume( rSamePolyRep(r, curr) ); |
---|
2734 | |
---|
2735 | |
---|
2736 | if( r->N == 1 ) // clearly commutative!!! |
---|
2737 | { |
---|
2738 | assume( |
---|
2739 | ( (CCC != NULL) && (MATCOLS(CCC) == 1) && (MATROWS(CCC) == 1) && (MATELEM(CCC,1,1) == NULL) ) || |
---|
2740 | ( (CCN == NULL) ) |
---|
2741 | ); |
---|
2742 | |
---|
2743 | assume( |
---|
2744 | ( (DDD != NULL) && (MATCOLS(DDD) == 1) && (MATROWS(DDD) == 1) && (MATELEM(DDD,1,1) == NULL) ) || |
---|
2745 | ( (DDN == NULL) ) |
---|
2746 | ); |
---|
2747 | |
---|
2748 | |
---|
2749 | } |
---|
2750 | |
---|
2751 | |
---|
2752 | // there must be: |
---|
2753 | assume( (CCC != NULL) != (CCN != NULL) ); // exactly one data about coeffs (C). |
---|
2754 | assume( !((DDD != NULL) && (DDN != NULL)) ); // at most one data about tails (D). |
---|
2755 | |
---|
2756 | ring save = currRing; |
---|
2757 | |
---|
2758 | if( save != curr ) |
---|
2759 | rChangeCurrRing(curr); |
---|
2760 | |
---|
2761 | #if OUTPUT |
---|
2762 | if( CCC != NULL ) |
---|
2763 | { |
---|
2764 | PrintS("nc_CallPlural(), Input data, CCC: \n"); |
---|
2765 | iiWriteMatrix(CCC, "C", 2, 4); |
---|
2766 | } |
---|
2767 | if( DDD != NULL ) |
---|
2768 | { |
---|
2769 | PrintS("nc_CallPlural(), Input data, DDD: \n"); |
---|
2770 | iiWriteMatrix(DDD, "D", 2, 4); |
---|
2771 | } |
---|
2772 | #endif |
---|
2773 | |
---|
2774 | |
---|
2775 | #ifndef NDEBUG |
---|
2776 | idTest((ideal)CCC); |
---|
2777 | idTest((ideal)DDD); |
---|
2778 | pTest(CCN); |
---|
2779 | pTest(DDN); |
---|
2780 | #endif |
---|
2781 | |
---|
2782 | if( (!bBeQuiet) && (r->GetNC() != NULL) ) |
---|
2783 | WarnS("going to redefine the algebra structure"); |
---|
2784 | |
---|
2785 | if( currRing != r ) |
---|
2786 | rChangeCurrRing(r); |
---|
2787 | |
---|
2788 | #ifndef NDEBUG |
---|
2789 | idTest((ideal)CCC); |
---|
2790 | idTest((ideal)DDD); |
---|
2791 | pTest(CCN); |
---|
2792 | pTest(DDN); |
---|
2793 | #endif |
---|
2794 | |
---|
2795 | matrix CC = NULL; |
---|
2796 | poly CN = NULL; |
---|
2797 | matrix C; bool bCnew = false; |
---|
2798 | |
---|
2799 | matrix DD = NULL; |
---|
2800 | poly DN = NULL; |
---|
2801 | matrix D; bool bDnew = false; |
---|
2802 | |
---|
2803 | number nN, pN, qN; |
---|
2804 | |
---|
2805 | bool IsSkewConstant = false, tmpIsSkewConstant; |
---|
2806 | int i, j; |
---|
2807 | |
---|
2808 | nc_type nctype = nc_undef; |
---|
2809 | |
---|
2810 | ////////////////////////////////////////////////////////////////// |
---|
2811 | // check the correctness of arguments, without any real chagnes!!! |
---|
2812 | |
---|
2813 | |
---|
2814 | |
---|
2815 | // check C |
---|
2816 | if ((CCC != NULL) && ( (MATCOLS(CCC)==1) || MATROWS(CCC)==1 ) ) |
---|
2817 | { |
---|
2818 | CN = MATELEM(CCC,1,1); |
---|
2819 | } |
---|
2820 | else |
---|
2821 | { |
---|
2822 | if ((CCC != NULL) && ( (MATCOLS(CCC)!=r->N) || (MATROWS(CCC)!=r->N) )) |
---|
2823 | { |
---|
2824 | Werror("Square %d x %d matrix expected", r->N, r->N); |
---|
2825 | |
---|
2826 | if( currRing != save ) |
---|
2827 | rChangeCurrRing(save); |
---|
2828 | return TRUE; |
---|
2829 | } |
---|
2830 | } |
---|
2831 | if (( CCC != NULL) && (CC == NULL)) CC = CCC; // mpCopy(CCC); // bug!? |
---|
2832 | if (( CCN != NULL) && (CN == NULL)) CN = CCN; |
---|
2833 | |
---|
2834 | // check D |
---|
2835 | if ((DDD != NULL) && ( (MATCOLS(DDD)==1) || MATROWS(DDD)==1 ) ) |
---|
2836 | { |
---|
2837 | DN = MATELEM(DDD,1,1); |
---|
2838 | } |
---|
2839 | else |
---|
2840 | { |
---|
2841 | if ((DDD != NULL) && ( (MATCOLS(DDD)!=r->N) || (MATROWS(DDD)!=r->N) )) |
---|
2842 | { |
---|
2843 | Werror("Square %d x %d matrix expected",r->N,r->N); |
---|
2844 | |
---|
2845 | if( currRing != save ) |
---|
2846 | rChangeCurrRing(save); |
---|
2847 | return TRUE; |
---|
2848 | } |
---|
2849 | } |
---|
2850 | |
---|
2851 | if (( DDD != NULL) && (DD == NULL)) DD = DDD; // mpCopy(DDD); // ??? |
---|
2852 | if (( DDN != NULL) && (DN == NULL)) DN = DDN; |
---|
2853 | |
---|
2854 | // further checks and some analysis: |
---|
2855 | // all data in 'curr'! |
---|
2856 | if (CN != NULL) /* create matrix C = CN * Id */ |
---|
2857 | { |
---|
2858 | nN = p_GetCoeff(CN, curr); |
---|
2859 | if (n_IsZero(nN, curr)) |
---|
2860 | { |
---|
2861 | Werror("Incorrect input : zero coefficients are not allowed"); |
---|
2862 | |
---|
2863 | if( currRing != save ) |
---|
2864 | rChangeCurrRing(save); |
---|
2865 | return TRUE; |
---|
2866 | } |
---|
2867 | |
---|
2868 | if (n_IsOne(nN, curr)) |
---|
2869 | nctype = nc_lie; |
---|
2870 | else |
---|
2871 | nctype = nc_general; |
---|
2872 | |
---|
2873 | IsSkewConstant = true; |
---|
2874 | |
---|
2875 | C = mpNew(r->N,r->N); // ring independent! |
---|
2876 | bCnew = true; |
---|
2877 | |
---|
2878 | for(i=1; i<r->N; i++) |
---|
2879 | for(j=i+1; j<=r->N; j++) |
---|
2880 | MATELEM(C,i,j) = prCopyR_NoSort(CN, curr, r); // nc_p_CopyPut(CN, r); // copy CN from curr into r |
---|
2881 | } else |
---|
2882 | if ( (CN == NULL) && (CC != NULL) ) /* copy matrix C */ |
---|
2883 | { |
---|
2884 | /* analyze C */ |
---|
2885 | |
---|
2886 | pN = NULL; /* check the consistency later */ |
---|
2887 | |
---|
2888 | if( r->N > 1 ) |
---|
2889 | if ( MATELEM(CC,1,2) != NULL ) |
---|
2890 | pN = p_GetCoeff(MATELEM(CC,1,2), curr); |
---|
2891 | |
---|
2892 | tmpIsSkewConstant = true; |
---|
2893 | |
---|
2894 | for(i=1; i<r->N; i++) |
---|
2895 | for(j=i+1; j<=r->N; j++) |
---|
2896 | { |
---|
2897 | if (MATELEM(CC,i,j) == NULL) |
---|
2898 | qN = NULL; |
---|
2899 | else |
---|
2900 | qN = p_GetCoeff(MATELEM(CC,i,j),curr); |
---|
2901 | |
---|
2902 | if ( qN == NULL ) /* check the consistency: Cij!=0 */ |
---|
2903 | // find also illegal pN |
---|
2904 | { |
---|
2905 | Werror("Incorrect input : matrix of coefficients contains zeros in the upper triangle"); |
---|
2906 | |
---|
2907 | if( currRing != save ) |
---|
2908 | rChangeCurrRing(save); |
---|
2909 | return TRUE; |
---|
2910 | } |
---|
2911 | |
---|
2912 | if (!n_Equal(pN, qN, curr)) tmpIsSkewConstant = false; |
---|
2913 | } |
---|
2914 | |
---|
2915 | if( bCopyInput ) |
---|
2916 | { |
---|
2917 | C = mpCopy(CC, curr, r); // Copy C into r!!!??? |
---|
2918 | bCnew = true; |
---|
2919 | } |
---|
2920 | else |
---|
2921 | C = CC; |
---|
2922 | |
---|
2923 | IsSkewConstant = tmpIsSkewConstant; |
---|
2924 | |
---|
2925 | if ( tmpIsSkewConstant && n_IsOne(pN, curr) ) |
---|
2926 | nctype = nc_lie; |
---|
2927 | else |
---|
2928 | nctype = nc_general; |
---|
2929 | } |
---|
2930 | |
---|
2931 | /* initialition of the matrix D */ |
---|
2932 | if ( DD == NULL ) /* we treat DN only (it could also be NULL) */ |
---|
2933 | { |
---|
2934 | D = mpNew(r->N,r->N); bDnew = true; |
---|
2935 | |
---|
2936 | if (DN == NULL) |
---|
2937 | { |
---|
2938 | if ( (nctype == nc_lie) || (nctype == nc_undef) ) |
---|
2939 | nctype = nc_comm; /* it was nc_skew earlier */ |
---|
2940 | else /* nc_general, nc_skew */ |
---|
2941 | nctype = nc_skew; |
---|
2942 | } |
---|
2943 | else /* DN != NULL */ |
---|
2944 | for(i=1; i<r->N; i++) |
---|
2945 | for(j=i+1; j<=r->N; j++) |
---|
2946 | MATELEM(D,i,j) = prCopyR_NoSort(DN, curr, r); // project DN into r->GetNC()->basering! |
---|
2947 | } |
---|
2948 | else /* DD != NULL */ |
---|
2949 | { |
---|
2950 | bool b = true; // DD == null ? |
---|
2951 | |
---|
2952 | for(int i = 1; (i < r->N) && b; i++) |
---|
2953 | for(int j = i+1; (j <= r->N) && b; j++) |
---|
2954 | if (MATELEM(DD, i, j) != NULL) |
---|
2955 | { |
---|
2956 | b = false; |
---|
2957 | break; |
---|
2958 | } |
---|
2959 | |
---|
2960 | if (b) // D == NULL!!! |
---|
2961 | { |
---|
2962 | if ( (nctype == nc_lie) || (nctype == nc_undef) ) |
---|
2963 | nctype = nc_comm; /* it was nc_skew earlier */ |
---|
2964 | else /* nc_general, nc_skew */ |
---|
2965 | nctype = nc_skew; |
---|
2966 | } |
---|
2967 | |
---|
2968 | if( bCopyInput ) |
---|
2969 | { |
---|
2970 | D = mpCopy(DD, curr, r); // Copy DD into r!!! |
---|
2971 | bDnew = true; |
---|
2972 | } |
---|
2973 | else |
---|
2974 | D = DD; |
---|
2975 | |
---|
2976 | } |
---|
2977 | |
---|
2978 | assume( C != NULL ); |
---|
2979 | assume( D != NULL ); |
---|
2980 | |
---|
2981 | #if OUTPUT |
---|
2982 | PrintS("nc_CallPlural(), Computed data, C: \n"); |
---|
2983 | iiWriteMatrix(C, "C", 2, 4); |
---|
2984 | |
---|
2985 | PrintS("nc_CallPlural(), Computed data, D: \n"); |
---|
2986 | iiWriteMatrix(D, "D", 2, 4); |
---|
2987 | |
---|
2988 | Print("\nTemporary: type = %d, IsSkewConstant = %d\n", nctype, IsSkewConstant); |
---|
2989 | #endif |
---|
2990 | |
---|
2991 | |
---|
2992 | |
---|
2993 | |
---|
2994 | // check the ordering condition for D (both matrix and poly cases): |
---|
2995 | if ( gnc_CheckOrdCondition(D, r) ) |
---|
2996 | { |
---|
2997 | if( bCnew ) mpDelete( &C, r ); |
---|
2998 | if( bDnew ) mpDelete( &D, r ); |
---|
2999 | |
---|
3000 | Werror("Matrix of polynomials violates the ordering condition"); |
---|
3001 | |
---|
3002 | if( currRing != save ) |
---|
3003 | rChangeCurrRing(save); |
---|
3004 | return TRUE; |
---|
3005 | } |
---|
3006 | |
---|
3007 | // okay now we are ready for this!!! |
---|
3008 | |
---|
3009 | // create new non-commutative structure |
---|
3010 | nc_struct *nc_new = (nc_struct *)omAlloc0(sizeof(nc_struct)); |
---|
3011 | |
---|
3012 | ncRingType(nc_new) = nctype; |
---|
3013 | |
---|
3014 | nc_new->C = C; // if C and D were given by matrices at the beginning they are in r |
---|
3015 | nc_new->D = D; // otherwise they should be in r->GetNC()->basering(polynomial * Id_{N}) |
---|
3016 | |
---|
3017 | nc_new->IsSkewConstant = (IsSkewConstant?1:0); |
---|
3018 | |
---|
3019 | nc_new->ref = 1; |
---|
3020 | nc_new->basering = r; // !? |
---|
3021 | |
---|
3022 | // Setup new NC structure!!! |
---|
3023 | if (r->GetNC() != NULL) |
---|
3024 | ncKill(r); |
---|
3025 | |
---|
3026 | r->ref++; // ? |
---|
3027 | r->GetNC() = nc_new; |
---|
3028 | |
---|
3029 | if( currRing != save ) |
---|
3030 | rChangeCurrRing(save); |
---|
3031 | |
---|
3032 | return gnc_InitMultiplication(r, bSetupQuotient); |
---|
3033 | } |
---|
3034 | |
---|
3035 | ////////////////////////////////////////////////////////////////////////////// |
---|
3036 | BOOLEAN gnc_InitMultiplication(ring r, bool bSetupQuotient) |
---|
3037 | { |
---|
3038 | /* returns TRUE if there were errors */ |
---|
3039 | /* initialize the multiplication: */ |
---|
3040 | /* r->GetNC()->MTsize, r->GetNC()->MT, r->GetNC()->COM, */ |
---|
3041 | /* and r->GetNC()->IsSkewConstant for the skew case */ |
---|
3042 | if (rVar(r)==1) |
---|
3043 | { |
---|
3044 | ncRingType(r, nc_comm); |
---|
3045 | r->GetNC()->IsSkewConstant=1; |
---|
3046 | return FALSE; |
---|
3047 | } |
---|
3048 | |
---|
3049 | ring save = currRing; |
---|
3050 | |
---|
3051 | int WeChangeRing = 0; |
---|
3052 | if (currRing!=r) |
---|
3053 | { |
---|
3054 | rChangeCurrRing(r); |
---|
3055 | WeChangeRing = 1; |
---|
3056 | } |
---|
3057 | assume( (currRing == r->GetNC()->basering) |
---|
3058 | || ((currRing->GetNC()!=NULL) && (currRing->GetNC()->basering==r->GetNC()->basering)) ); // otherwise we cannot work with all these matrices! |
---|
3059 | |
---|
3060 | int i,j; |
---|
3061 | r->GetNC()->MT = (matrix *)omAlloc0((r->N*(r->N-1))/2*sizeof(matrix)); |
---|
3062 | r->GetNC()->MTsize = (int *)omAlloc0((r->N*(r->N-1))/2*sizeof(int)); |
---|
3063 | idTest(((ideal)r->GetNC()->C)); |
---|
3064 | matrix COM = mpCopy(r->GetNC()->C); |
---|
3065 | poly p,q; |
---|
3066 | short DefMTsize=7; |
---|
3067 | int IsNonComm=0; |
---|
3068 | int tmpIsSkewConstant; |
---|
3069 | |
---|
3070 | for(i=1; i<r->N; i++) |
---|
3071 | { |
---|
3072 | for(j=i+1; j<=r->N; j++) |
---|
3073 | { |
---|
3074 | if ( MATELEM(r->GetNC()->D,i,j) == NULL ) /* quasicommutative case */ |
---|
3075 | { |
---|
3076 | /* 1x1 mult.matrix */ |
---|
3077 | r->GetNC()->MTsize[UPMATELEM(i,j,r->N)] = 1; |
---|
3078 | r->GetNC()->MT[UPMATELEM(i,j,r->N)] = mpNew(1,1); |
---|
3079 | } |
---|
3080 | else /* pure noncommutative case */ |
---|
3081 | { |
---|
3082 | /* TODO check the special multiplication properties */ |
---|
3083 | IsNonComm = 1; |
---|
3084 | p_Delete(&(MATELEM(COM,i,j)),r); |
---|
3085 | //MATELEM(COM,i,j) = NULL; // done by p_Delete |
---|
3086 | r->GetNC()->MTsize[UPMATELEM(i,j,r->N)] = DefMTsize; /* default sizes */ |
---|
3087 | r->GetNC()->MT[UPMATELEM(i,j,r->N)] = mpNew(DefMTsize, DefMTsize); |
---|
3088 | } |
---|
3089 | /* set MT[i,j,1,1] to c_i_j*x_i*x_j + D_i_j */ |
---|
3090 | p = p_ISet(1,r); /* instead of p = pOne(); */ |
---|
3091 | if (MATELEM(r->GetNC()->C,i,j)!=NULL) |
---|
3092 | p_SetCoeff(p,n_Copy(pGetCoeff(MATELEM(r->GetNC()->C,i,j)),r),r); |
---|
3093 | p_SetExp(p,i,1,r); |
---|
3094 | p_SetExp(p,j,1,r); |
---|
3095 | p_Setm(p,r); |
---|
3096 | p_Test(MATELEM(r->GetNC()->D,i,j),r->GetNC()->basering); |
---|
3097 | q = nc_p_CopyGet(MATELEM(r->GetNC()->D,i,j),r); |
---|
3098 | p = p_Add_q(p,q,r); |
---|
3099 | MATELEM(r->GetNC()->MT[UPMATELEM(i,j,r->N)],1,1) = nc_p_CopyPut(p,r); |
---|
3100 | p_Delete(&p,r); |
---|
3101 | // p = NULL;// done by p_Delete |
---|
3102 | } |
---|
3103 | } |
---|
3104 | if (ncRingType(r)==nc_undef) |
---|
3105 | { |
---|
3106 | if (IsNonComm==1) |
---|
3107 | { |
---|
3108 | // assume(pN!=NULL); |
---|
3109 | // if ((tmpIsSkewConstant==1) && (nIsOne(pGetCoeff(pN)))) r->GetNC()->type=nc_lie; |
---|
3110 | // else r->GetNC()->type=nc_general; |
---|
3111 | } |
---|
3112 | if (IsNonComm==0) |
---|
3113 | { |
---|
3114 | ncRingType(r, nc_skew); /* TODO: check whether it is commutative */ |
---|
3115 | r->GetNC()->IsSkewConstant=tmpIsSkewConstant; |
---|
3116 | } |
---|
3117 | } |
---|
3118 | r->GetNC()->COM=COM; |
---|
3119 | |
---|
3120 | nc_p_ProcsSet(r, r->p_Procs); |
---|
3121 | |
---|
3122 | if(bSetupQuotient) // Test me!!! |
---|
3123 | { |
---|
3124 | nc_SetupQuotient(r); |
---|
3125 | } |
---|
3126 | |
---|
3127 | if (save != currRing) |
---|
3128 | rChangeCurrRing(save); |
---|
3129 | |
---|
3130 | return FALSE; |
---|
3131 | } |
---|
3132 | |
---|
3133 | void gnc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs) |
---|
3134 | { |
---|
3135 | // "commutative" |
---|
3136 | p_Procs->p_Mult_mm = rGR->p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
3137 | p_Procs->pp_Mult_mm = rGR->p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
3138 | p_Procs->p_Minus_mm_Mult_qq = rGR->p_Procs->p_Minus_mm_Mult_qq = NULL; |
---|
3139 | // gnc_p_Minus_mm_Mult_qq_ign; // should not be used!!!??? |
---|
3140 | |
---|
3141 | |
---|
3142 | |
---|
3143 | // non-commutaitve multiplication by monomial from the left |
---|
3144 | rGR->GetNC()->p_Procs.mm_Mult_p = gnc_mm_Mult_p; |
---|
3145 | rGR->GetNC()->p_Procs.mm_Mult_pp = gnc_mm_Mult_pp; |
---|
3146 | |
---|
3147 | rGR->GetNC()->p_Procs.GB = gnc_gr_bba; // bba even for local case! |
---|
3148 | |
---|
3149 | // rGR->GetNC()->p_Procs.GlobalGB = gnc_gr_bba; |
---|
3150 | // rGR->GetNC()->p_Procs.LocalGB = gnc_gr_mora; |
---|
3151 | |
---|
3152 | |
---|
3153 | #if 0 |
---|
3154 | // Previous Plural's implementation... |
---|
3155 | rGR->GetNC()->p_Procs.SPoly = gnc_CreateSpolyOld; |
---|
3156 | rGR->GetNC()->p_Procs.ReduceSPoly = gnc_ReduceSpolyOld; |
---|
3157 | |
---|
3158 | rGR->GetNC()->p_Procs.BucketPolyRed = gnc_kBucketPolyRedOld; |
---|
3159 | rGR->GetNC()->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZOld; |
---|
3160 | #else |
---|
3161 | // A bit cleaned up and somewhat rewritten functions... |
---|
3162 | rGR->GetNC()->p_Procs.SPoly = gnc_CreateSpolyNew; |
---|
3163 | rGR->GetNC()->p_Procs.ReduceSPoly = gnc_ReduceSpolyNew; |
---|
3164 | |
---|
3165 | rGR->GetNC()->p_Procs.BucketPolyRed = gnc_kBucketPolyRedNew; |
---|
3166 | rGR->GetNC()->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZNew; |
---|
3167 | #endif |
---|
3168 | |
---|
3169 | |
---|
3170 | |
---|
3171 | |
---|
3172 | #if 0 |
---|
3173 | // Old Stuff |
---|
3174 | p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
3175 | _p_procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
3176 | |
---|
3177 | p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
3178 | _p_procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
3179 | |
---|
3180 | p_Procs->p_Minus_mm_Mult_qq = NULL; // gnc_p_Minus_mm_Mult_qq_ign; |
---|
3181 | _p_procs->p_Minus_mm_Mult_qq= NULL; // gnc_p_Minus_mm_Mult_qq_ign; |
---|
3182 | |
---|
3183 | r->GetNC()->mmMultP() = gnc_mm_Mult_p; |
---|
3184 | r->GetNC()->mmMultPP() = gnc_mm_Mult_pp; |
---|
3185 | |
---|
3186 | r->GetNC()->GB() = gnc_gr_bba; |
---|
3187 | |
---|
3188 | r->GetNC()->SPoly() = gnc_CreateSpoly; |
---|
3189 | r->GetNC()->ReduceSPoly() = gnc_ReduceSpoly; |
---|
3190 | |
---|
3191 | #endif |
---|
3192 | } |
---|
3193 | |
---|
3194 | |
---|
3195 | // set pProcs table for rGR and global variable p_Procs |
---|
3196 | void nc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs) |
---|
3197 | { |
---|
3198 | assume(rIsPluralRing(rGR)); |
---|
3199 | assume(p_Procs!=NULL); |
---|
3200 | |
---|
3201 | gnc_p_ProcsSet(rGR, p_Procs); |
---|
3202 | |
---|
3203 | if(rIsSCA(rGR) && bUseExtensions) |
---|
3204 | { |
---|
3205 | sca_p_ProcsSet(rGR, p_Procs); |
---|
3206 | } |
---|
3207 | } |
---|
3208 | |
---|
3209 | |
---|
3210 | |
---|
3211 | /* substitute the n-th variable by e in p |
---|
3212 | * destroy p |
---|
3213 | * e is not a constant |
---|
3214 | */ |
---|
3215 | poly nc_pSubst(poly p, int n, poly e) |
---|
3216 | { |
---|
3217 | int rN=currRing->N; |
---|
3218 | int *PRE = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
3219 | int *SUF = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
3220 | int i,j,pow; |
---|
3221 | number C; |
---|
3222 | poly suf,pre; |
---|
3223 | poly res = NULL; |
---|
3224 | poly out = NULL; |
---|
3225 | while ( p!= NULL ) |
---|
3226 | { |
---|
3227 | C = pGetCoeff(p); |
---|
3228 | pGetExpV(p, PRE); /* faster splitting? */ |
---|
3229 | pow = PRE[n]; PRE[n]=0; |
---|
3230 | res = NULL; |
---|
3231 | if (pow!=0) |
---|
3232 | { |
---|
3233 | for (i=n+1; i<=rN; i++) |
---|
3234 | { |
---|
3235 | SUF[i] = PRE[i]; |
---|
3236 | PRE[i] = 0; |
---|
3237 | } |
---|
3238 | res = pPower(pCopy(e),pow); |
---|
3239 | /* multiply with prefix */ |
---|
3240 | pre = pOne(); |
---|
3241 | pSetExpV(pre,PRE); |
---|
3242 | pSetm(pre); |
---|
3243 | res = nc_mm_Mult_p(pre,res,currRing); |
---|
3244 | /* multiply with suffix */ |
---|
3245 | suf = pOne(); |
---|
3246 | pSetExpV(suf,SUF); |
---|
3247 | pSetm(suf); |
---|
3248 | res = p_Mult_mm(res,suf,currRing); |
---|
3249 | res = p_Mult_nn(res,C,currRing); |
---|
3250 | pSetComp(res,PRE[0]); |
---|
3251 | } |
---|
3252 | else /* pow==0 */ |
---|
3253 | { |
---|
3254 | res = pHead(p); |
---|
3255 | } |
---|
3256 | p = pLmDeleteAndNext(p); |
---|
3257 | out = pAdd(out,res); |
---|
3258 | } |
---|
3259 | freeT(PRE,rN); |
---|
3260 | freeT(SUF,rN); |
---|
3261 | return(out); |
---|
3262 | } |
---|
3263 | |
---|
3264 | static ideal idPrepareStd(ideal T, ideal s, int k) |
---|
3265 | { |
---|
3266 | /* T is a left SB, without zeros, s is a list with zeros */ |
---|
3267 | #ifdef PDEBUG |
---|
3268 | if (IDELEMS(s)!=IDELEMS(T)) |
---|
3269 | { |
---|
3270 | Print("ideals of diff. size!!!"); |
---|
3271 | } |
---|
3272 | #endif |
---|
3273 | ideal t = idCopy(T); |
---|
3274 | int j,rs=idRankFreeModule(s),rt=idRankFreeModule(t); |
---|
3275 | poly p,q; |
---|
3276 | |
---|
3277 | ideal res = idInit(2*idElem(t),1+idElem(t)); |
---|
3278 | if (rs == 0) |
---|
3279 | { |
---|
3280 | for (j=0; j<IDELEMS(t); j++) |
---|
3281 | { |
---|
3282 | if (s->m[j]!=NULL) pSetCompP(s->m[j],1); |
---|
3283 | if (t->m[j]!=NULL) pSetCompP(t->m[j],1); |
---|
3284 | } |
---|
3285 | k = si_max(k,1); |
---|
3286 | } |
---|
3287 | for (j=0; j<IDELEMS(t); j++) |
---|
3288 | { |
---|
3289 | if (s->m[j]!=NULL) |
---|
3290 | { |
---|
3291 | p = s->m[j]; |
---|
3292 | q = pOne(); |
---|
3293 | pSetComp(q,k+1+j); |
---|
3294 | pSetmComp(q); |
---|
3295 | #if 0 |
---|
3296 | while (pNext(p)) pIter(p); |
---|
3297 | pNext(p) = q; |
---|
3298 | #else |
---|
3299 | p = pAdd(p,q); |
---|
3300 | s->m[j] = p; |
---|
3301 | #ifdef PDEBUG |
---|
3302 | pTest(p); |
---|
3303 | #endif |
---|
3304 | #endif |
---|
3305 | } |
---|
3306 | } |
---|
3307 | res = idSimpleAdd(t,s); |
---|
3308 | idDelete(&t); |
---|
3309 | res->rank = 1+idElem(T); |
---|
3310 | return(res); |
---|
3311 | } |
---|
3312 | |
---|
3313 | ideal Approx_Step(ideal L) |
---|
3314 | { |
---|
3315 | int N=currRing->N; |
---|
3316 | int i,j; // k=syzcomp |
---|
3317 | int flag, flagcnt=0, syzcnt=0; |
---|
3318 | int syzcomp = 0; |
---|
3319 | int k=1; /* for ideals not modules */ |
---|
3320 | ideal I = kStd(L, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
3321 | idSkipZeroes(I); |
---|
3322 | ideal s_I; |
---|
3323 | int idI = idElem(I); |
---|
3324 | ideal trickyQuotient,s_trickyQuotient; |
---|
3325 | if (currQuotient !=NULL) |
---|
3326 | { |
---|
3327 | trickyQuotient = idSimpleAdd(currQuotient,I); |
---|
3328 | } |
---|
3329 | else |
---|
3330 | trickyQuotient = I; |
---|
3331 | idSkipZeroes(trickyQuotient); |
---|
3332 | poly *var = (poly *)omAlloc0((N+1)*sizeof(poly)); |
---|
3333 | // poly *W = (poly *)omAlloc0((2*N+1)*sizeof(poly)); |
---|
3334 | resolvente S = (resolvente)omAlloc0((N+1)*sizeof(ideal)); |
---|
3335 | ideal SI, res; |
---|
3336 | matrix MI; |
---|
3337 | poly x=pOne(); |
---|
3338 | var[0]=x; |
---|
3339 | ideal h2, h3, s_h2, s_h3; |
---|
3340 | poly p,q,qq; |
---|
3341 | /* init vars */ |
---|
3342 | for (i=1; i<=N; i++ ) |
---|
3343 | { |
---|
3344 | x = pOne(); |
---|
3345 | pSetExp(x,i,1); |
---|
3346 | pSetm(x); |
---|
3347 | var[i]=pCopy(x); |
---|
3348 | } |
---|
3349 | /* init NF's */ |
---|
3350 | for (i=1; i<=N; i++ ) |
---|
3351 | { |
---|
3352 | h2 = idInit(idI,1); |
---|
3353 | flag = 0; |
---|
3354 | for (j=0; j< idI; j++ ) |
---|
3355 | { |
---|
3356 | q = pp_Mult_mm(I->m[j],var[i],currRing); |
---|
3357 | q = kNF(I,currQuotient,q,0,0); |
---|
3358 | if (q!=0) |
---|
3359 | { |
---|
3360 | h2->m[j]=pCopy(q); |
---|
3361 | // pShift(&(h2->m[flag]),1); |
---|
3362 | flag++; |
---|
3363 | pDelete(&q); |
---|
3364 | } |
---|
3365 | else |
---|
3366 | h2->m[j]=0; |
---|
3367 | } |
---|
3368 | /* W[1..idElems(I)] */ |
---|
3369 | if (flag >0) |
---|
3370 | { |
---|
3371 | /* compute syzygies with values in I*/ |
---|
3372 | // idSkipZeroes(h2); |
---|
3373 | // h2 = idSimpleAdd(h2,I); |
---|
3374 | // h2->rank=flag+idI+1; |
---|
3375 | idTest(h2); |
---|
3376 | idShow(h2); |
---|
3377 | ring orig_ring=currRing; |
---|
3378 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
3379 | syzcomp = 1; |
---|
3380 | rSetSyzComp(syzcomp); |
---|
3381 | if (orig_ring != syz_ring) |
---|
3382 | { |
---|
3383 | s_h2=idrCopyR_NoSort(h2,orig_ring); |
---|
3384 | // s_trickyQuotient=idrCopyR_NoSort(trickyQuotient,orig_ring); |
---|
3385 | // rDebugPrint(syz_ring); |
---|
3386 | s_I=idrCopyR_NoSort(I,orig_ring); |
---|
3387 | } |
---|
3388 | else |
---|
3389 | { |
---|
3390 | s_h2 = h2; |
---|
3391 | s_I = I; |
---|
3392 | // s_trickyQuotient=trickyQuotient; |
---|
3393 | } |
---|
3394 | idTest(s_h2); |
---|
3395 | // idTest(s_trickyQuotient); |
---|
3396 | Print(".proceeding with the variable %d\n",i); |
---|
3397 | s_h3 = idPrepareStd(s_I, s_h2, 1); |
---|
3398 | BITSET save_test=test; |
---|
3399 | test|=Sy_bit(OPT_SB_1); |
---|
3400 | idTest(s_h3); |
---|
3401 | idDelete(&s_h2); |
---|
3402 | s_h2=idCopy(s_h3); |
---|
3403 | idDelete(&s_h3); |
---|
3404 | Print("...computing Syz"); |
---|
3405 | s_h3 = kStd(s_h2, currQuotient,(tHomog)FALSE,NULL,NULL,syzcomp,idI); |
---|
3406 | test=save_test; |
---|
3407 | idShow(s_h3); |
---|
3408 | if (orig_ring != syz_ring) |
---|
3409 | { |
---|
3410 | idDelete(&s_h2); |
---|
3411 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
3412 | { |
---|
3413 | if (s_h3->m[j] != NULL) |
---|
3414 | { |
---|
3415 | if (p_MinComp(s_h3->m[j],syz_ring) > syzcomp) /* i.e. it is a syzygy */ |
---|
3416 | pShift(&s_h3->m[j], -syzcomp); |
---|
3417 | else |
---|
3418 | pDelete(&s_h3->m[j]); |
---|
3419 | } |
---|
3420 | } |
---|
3421 | idSkipZeroes(s_h3); |
---|
3422 | s_h3->rank -= syzcomp; |
---|
3423 | rChangeCurrRing(orig_ring); |
---|
3424 | // s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
3425 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
3426 | rKill(syz_ring); |
---|
3427 | } |
---|
3428 | idTest(s_h3); |
---|
3429 | S[syzcnt]=kStd(s_h3,currQuotient,(tHomog)FALSE,NULL,NULL); |
---|
3430 | syzcnt++; |
---|
3431 | idDelete(&s_h3); |
---|
3432 | } /* end if flag >0 */ |
---|
3433 | else |
---|
3434 | { |
---|
3435 | flagcnt++; |
---|
3436 | } |
---|
3437 | } |
---|
3438 | if (flagcnt == N) |
---|
3439 | { |
---|
3440 | Print("the input is a two--sided ideal"); |
---|
3441 | return(I); |
---|
3442 | } |
---|
3443 | if (syzcnt >0) |
---|
3444 | { |
---|
3445 | Print("..computing Intersect of %d modules\n",syzcnt); |
---|
3446 | if (syzcnt == 1) |
---|
3447 | SI = S[0]; |
---|
3448 | else |
---|
3449 | SI = idMultSect(S, syzcnt); |
---|
3450 | idShow(SI); |
---|
3451 | MI = idModule2Matrix(SI); |
---|
3452 | res= idInit(MATCOLS(MI),1); |
---|
3453 | for (i=1; i<= MATCOLS(MI); i++) |
---|
3454 | { |
---|
3455 | p = NULL; |
---|
3456 | for (j=0; j< idElem(I); j++) |
---|
3457 | { |
---|
3458 | q = pCopy(MATELEM(MI,j+1,i)); |
---|
3459 | if (q!=NULL) |
---|
3460 | { |
---|
3461 | q = pMult(q,pCopy(I->m[j])); |
---|
3462 | p = pAdd(p,q); |
---|
3463 | } |
---|
3464 | } |
---|
3465 | res->m[i-1]=p; |
---|
3466 | } |
---|
3467 | Print("final std"); |
---|
3468 | res = kStd(res, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
3469 | idSkipZeroes(res); |
---|
3470 | return(res); |
---|
3471 | } |
---|
3472 | else |
---|
3473 | { |
---|
3474 | Print("No syzygies"); |
---|
3475 | return(I); |
---|
3476 | } |
---|
3477 | } |
---|
3478 | |
---|
3479 | |
---|
3480 | // creates a commutative nc extension; "converts" comm.ring to a Plural ring |
---|
3481 | ring nc_rCreateNCcomm(ring r) |
---|
3482 | { |
---|
3483 | if (rIsPluralRing(r)) return r; |
---|
3484 | |
---|
3485 | matrix C = mpNew(r->N,r->N); // ring-independent!?! |
---|
3486 | matrix D = mpNew(r->N,r->N); |
---|
3487 | |
---|
3488 | for(int i=1; i<r->N; i++) |
---|
3489 | for(int j=i+1; j<=r->N; j++) |
---|
3490 | MATELEM(C,i,j) = p_ISet(1, r); |
---|
3491 | |
---|
3492 | if (nc_CallPlural(C, D, NULL, NULL, r)) // TODO: what about quotient ideal? |
---|
3493 | WarnS("Error initializing multiplication!"); // No reaction!??? |
---|
3494 | |
---|
3495 | return r; |
---|
3496 | } |
---|
3497 | |
---|
3498 | poly p_CopyEmbed(poly p, ring srcRing, int shift, int par_shift) |
---|
3499 | /* NOT USED ANYMORE: replaced by maFindPerm in ring.cc */ |
---|
3500 | /* for use with embeddings: currRing is a sum of smaller rings */ |
---|
3501 | /* and srcRing is one of such smaller rings */ |
---|
3502 | /* shift defines the position of a subring in srcRing */ |
---|
3503 | /* par_shift defines the position of a subfield in basefield of CurrRing */ |
---|
3504 | { |
---|
3505 | if (currRing == srcRing) |
---|
3506 | { |
---|
3507 | return(p_Copy(p,currRing)); |
---|
3508 | } |
---|
3509 | nMapFunc nMap=nSetMap(srcRing); |
---|
3510 | poly q; |
---|
3511 | // if ( nMap == nCopy) |
---|
3512 | // { |
---|
3513 | // q = prCopyR(p,srcRing); |
---|
3514 | // } |
---|
3515 | // else |
---|
3516 | { |
---|
3517 | int *perm = (int *)omAlloc0((srcRing->N+1)*sizeof(int)); |
---|
3518 | int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
3519 | // int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
3520 | int i; |
---|
3521 | // if (srcRing->P > 0) |
---|
3522 | // { |
---|
3523 | // for (i=0; i<srcRing->P; i++) |
---|
3524 | // par_perm[i]=-i; |
---|
3525 | // } |
---|
3526 | if ((shift<0) || (shift > currRing->N)) |
---|
3527 | { |
---|
3528 | Werror("bad shifts in p_CopyEmbed"); |
---|
3529 | return(0); |
---|
3530 | } |
---|
3531 | for (i=1; i<= srcRing->N; i++) |
---|
3532 | { |
---|
3533 | perm[i] = shift+i; |
---|
3534 | } |
---|
3535 | q = pPermPoly(p,perm,srcRing,nMap,par_perm,srcRing->P); |
---|
3536 | } |
---|
3537 | return(q); |
---|
3538 | } |
---|
3539 | |
---|
3540 | poly pOppose(ring Rop, poly p) |
---|
3541 | /* opposes a vector p from Rop to currRing */ |
---|
3542 | { |
---|
3543 | /* the simplest case:*/ |
---|
3544 | if ( Rop == currRing ) return(pCopy(p)); |
---|
3545 | /* check Rop == rOpposite(currRing) */ |
---|
3546 | if ( !rIsLikeOpposite(currRing, Rop) ) |
---|
3547 | { |
---|
3548 | WarnS("an opposite ring should be used"); |
---|
3549 | return NULL; |
---|
3550 | } |
---|
3551 | /* nMapFunc nMap = nSetMap(Rop);*/ |
---|
3552 | /* since we know that basefields coinside! */ |
---|
3553 | int *perm=(int *)omAlloc0((Rop->N+1)*sizeof(int)); |
---|
3554 | if (!p_IsConstantPoly(p, Rop)) |
---|
3555 | { |
---|
3556 | /* we know perm exactly */ |
---|
3557 | int i; |
---|
3558 | for(i=1; i<=Rop->N; i++) |
---|
3559 | { |
---|
3560 | perm[i] = Rop->N+1-i; |
---|
3561 | } |
---|
3562 | } |
---|
3563 | poly res = pPermPoly(p, perm, Rop, nCopy); |
---|
3564 | omFreeSize((ADDRESS)perm,(Rop->N+1)*sizeof(int)); |
---|
3565 | return res; |
---|
3566 | } |
---|
3567 | |
---|
3568 | ideal idOppose(ring Rop, ideal I) |
---|
3569 | /* opposes a module I from Rop to currRing */ |
---|
3570 | { |
---|
3571 | /* the simplest case:*/ |
---|
3572 | if ( Rop == currRing ) return idCopy(I); |
---|
3573 | /* check Rop == rOpposite(currRing) */ |
---|
3574 | if (!rIsLikeOpposite(currRing, Rop)) |
---|
3575 | { |
---|
3576 | WarnS("an opposite ring should be used"); |
---|
3577 | return NULL; |
---|
3578 | } |
---|
3579 | int i; |
---|
3580 | ideal idOp = idInit(I->ncols, I->rank); |
---|
3581 | for (i=0; i< (I->ncols)*(I->nrows); i++) |
---|
3582 | { |
---|
3583 | idOp->m[i] = pOppose(Rop,I->m[i]); |
---|
3584 | } |
---|
3585 | idTest(idOp); |
---|
3586 | return idOp; |
---|
3587 | } |
---|
3588 | |
---|
3589 | BOOLEAN rIsLikeOpposite(ring rBase, ring rCandidate) |
---|
3590 | /* checks whether rings rBase and rCandidate */ |
---|
3591 | /* could be opposite to each other */ |
---|
3592 | /* returns TRUE if it is so */ |
---|
3593 | { |
---|
3594 | /* the same basefield */ |
---|
3595 | int diagnose = TRUE; |
---|
3596 | ring save = currRing; |
---|
3597 | rChangeCurrRing(rBase); |
---|
3598 | nMapFunc nMap = nSetMap(rCandidate); |
---|
3599 | if (nMap != nCopy) diagnose = FALSE; |
---|
3600 | rChangeCurrRing(save); |
---|
3601 | /* same number of variables */ |
---|
3602 | if (rBase->N != rCandidate->N) diagnose = FALSE; |
---|
3603 | /* nc and comm ring */ |
---|
3604 | if ( rIsPluralRing(rBase) != rIsPluralRing(rCandidate) ) diagnose = FALSE; |
---|
3605 | /* both are qrings */ |
---|
3606 | /* NO CHECK, since it is used in building opposite qring */ |
---|
3607 | /* if ( ((rBase->qideal != NULL) && (rCandidate->qideal == NULL)) */ |
---|
3608 | /* || ((rBase->qideal == NULL) && (rCandidate->qideal != NULL)) ) */ |
---|
3609 | /* diagnose = FALSE; */ |
---|
3610 | /* TODO: varnames are e->E etc */ |
---|
3611 | return diagnose; |
---|
3612 | } |
---|
3613 | |
---|
3614 | |
---|
3615 | |
---|
3616 | bool nc_SetupQuotient(ring rGR, const ring rG) |
---|
3617 | { |
---|
3618 | // currently only super-commutative extension deals with factors. |
---|
3619 | if( bUseExtensions ) |
---|
3620 | return sca_SetupQuotient(rGR, rG); |
---|
3621 | |
---|
3622 | return false; |
---|
3623 | } |
---|
3624 | |
---|
3625 | |
---|
3626 | |
---|
3627 | // int Commutative_Context(ring r, leftv expression) |
---|
3628 | // /* returns 1 if expression consists */ |
---|
3629 | // /* of commutative elements */ |
---|
3630 | // { |
---|
3631 | // /* crucial: poly -> ideal, module, matrix */ |
---|
3632 | // } |
---|
3633 | |
---|
3634 | // int Comm_Context_Poly(ring r, poly p) |
---|
3635 | // { |
---|
3636 | // poly COMM=r->GetNC()->COMM; |
---|
3637 | // poly pp=pOne(); |
---|
3638 | // memset(pp->exp,0,r->ExpL_Size*sizeof(long)); |
---|
3639 | // while (p!=NULL) |
---|
3640 | // { |
---|
3641 | // for (i=0;i<=r->ExpL_Size;i++) |
---|
3642 | // { |
---|
3643 | // if ((p->exp[i]) && (pp->exp[i])) return(FALSE); |
---|
3644 | // /* nonzero exponent of non-comm variable */ |
---|
3645 | // } |
---|
3646 | // pIter(p); |
---|
3647 | // } |
---|
3648 | // return(TRUE); |
---|
3649 | // } |
---|