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 1.38 2007-01-25 19:42:26 motsak Exp $ |
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10 | *******************************************************************/ |
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11 | #include "mod2.h" |
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12 | #ifdef HAVE_PLURAL |
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13 | #define PLURAL_INTERNAL_DECLARATIONS |
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14 | |
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15 | #include "febase.h" |
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16 | #include "ring.h" |
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17 | #include "polys.h" |
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18 | #include "numbers.h" |
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19 | #include "ideals.h" |
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20 | #include "matpol.h" |
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21 | #include "kbuckets.h" |
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22 | #include "kstd1.h" |
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23 | #include "sbuckets.h" |
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24 | #include "prCopy.h" |
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25 | #include "p_Mult_q.h" |
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26 | |
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27 | #include "gring.h" |
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28 | |
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29 | // dirty tricks: |
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30 | #include "p_MemAdd.h" |
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31 | |
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32 | /* global nc_macros : */ |
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33 | |
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34 | #define freeT(A,v) omFreeSize((ADDRESS)A,(v+1)*sizeof(int)) |
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35 | #define freeN(A,k) omFreeSize((ADDRESS)A,k*sizeof(number)) |
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36 | |
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37 | |
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38 | |
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39 | poly nc_p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, |
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40 | const int, const poly, const ring r) |
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41 | { |
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42 | poly mc = p_Neg( p_Copy(m, r), r ); |
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43 | poly mmc = nc_mm_Mult_pp( mc, q, r ); |
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44 | p_Delete(&mc, r); |
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45 | |
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46 | p = p_Add_q(p, mmc, r); |
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47 | |
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48 | lp = pLength(p); // ring independent! |
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49 | |
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50 | return(p); |
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51 | } |
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52 | |
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53 | // returns p + m*q destroys p, const: q, m |
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54 | poly nc_p_Plus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, |
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55 | const int, const ring r) |
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56 | { |
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57 | p = p_Add_q(p, nc_mm_Mult_pp( m, q, r ), r); |
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58 | |
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59 | lp = pLength(p); |
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60 | |
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61 | return(p); |
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62 | } |
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63 | |
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64 | #if 0 |
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65 | 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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66 | { |
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67 | poly t; |
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68 | int i; |
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69 | |
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70 | return gnc_p_Minus_mm_Mult_qq(p, m, q, d1, i, t, r); |
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71 | } |
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72 | #endif |
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73 | |
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74 | |
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75 | //----------- auxiliary routines-------------------------- |
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76 | poly _gnc_p_Mult_q(poly p, poly q, const int copy, const ring r) |
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77 | /* destroy p,q unless copy=1 */ |
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78 | { |
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79 | poly res=NULL; |
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80 | poly ghost=NULL; |
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81 | poly qq,pp; |
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82 | if (copy) |
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83 | { |
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84 | qq=p_Copy(q,r); |
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85 | pp=p_Copy(p,r); |
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86 | } |
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87 | else |
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88 | { |
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89 | qq=q; |
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90 | pp=p; |
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91 | } |
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92 | while (qq!=NULL) |
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93 | { |
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94 | res=p_Add_q(res, pp_Mult_mm(pp, qq, r), r); // p_Head(qq, r)? |
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95 | qq=p_LmDeleteAndNext(qq,r); |
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96 | } |
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97 | p_Delete(&pp,r); |
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98 | return(res); |
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99 | } |
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100 | |
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101 | // return pPolyP * pPolyQ; destroy or reuse pPolyP and pPolyQ |
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102 | poly _nc_p_Mult_q(poly pPolyP, poly pPolyQ, const ring rRing) |
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103 | { |
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104 | assume( rIsPluralRing(rRing) ); |
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105 | |
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106 | poly pResult = NULL; |
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107 | |
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108 | // always length(q) times "p * q[j]" |
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109 | for( ; pPolyQ!=NULL; pPolyQ = p_LmDeleteAndNext( pPolyQ, rRing ) ) |
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110 | pResult = p_Add_q( pResult, pp_Mult_mm( pPolyP, pPolyQ, rRing), rRing ); |
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111 | // rRing->p_Procs->pp_Mult_mm() <--> sca_nc_pp_Mult_mm |
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112 | |
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113 | p_Delete( &pPolyP, rRing ); |
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114 | |
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115 | #ifdef PDEBUG |
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116 | p_Test(pResult,rRing); |
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117 | #endif |
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118 | |
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119 | return(pResult); |
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120 | } |
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121 | |
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122 | |
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123 | // return pPolyP * pPolyQ; preserve pPolyP and pPolyQ |
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124 | poly _nc_pp_Mult_qq(const poly pPolyP, const poly pPolyQ, const ring rRing) |
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125 | { |
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126 | assume( rIsPluralRing(rRing) ); |
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127 | |
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128 | poly pResult = NULL; |
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129 | |
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130 | // always length(q) times "p * q[j]" |
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131 | for( poly q = pPolyQ; q !=NULL; q = pNext(q) ) |
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132 | pResult = p_Add_q( pResult, pp_Mult_mm(pPolyP, q, rRing), rRing ); |
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133 | |
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134 | #ifdef PDEBUG |
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135 | p_Test(pResult,rRing); |
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136 | #endif |
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137 | |
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138 | return(pResult); |
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139 | } |
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140 | |
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141 | |
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142 | |
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143 | poly gnc_mm_Mult_nn (int *F, int *G, const ring r); |
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144 | poly gnc_mm_Mult_uu (int *F,int jG,int bG, const ring r); |
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145 | |
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146 | /* #define nc_uu_Mult_ww nc_uu_Mult_ww_vert */ |
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147 | poly gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r); |
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148 | /* poly nc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r); */ |
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149 | /* poly nc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r); */ |
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150 | /* poly nc_uu_Mult_ww_hvdiag (int i, int a, int j, int b, const ring r); */ |
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151 | /* not written yet */ |
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152 | |
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153 | |
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154 | poly gnc_p_Mult_mm_Common(poly p, const poly m, int side, const ring r) |
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155 | /* p is poly, m is mono with coeff, destroys p */ |
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156 | /* if side==1, computes p_Mult_mm; otherwise, mm_Mult_p */ |
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157 | { |
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158 | if ((p==NULL) || (m==NULL)) return NULL; |
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159 | /* if (pNext(p)==NULL) return(nc_mm_Mult_nn(p,pCopy(m),r)); */ |
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160 | /* excluded - the cycle will do it anyway - OK. */ |
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161 | if (p_IsConstant(m,r)) return(p_Mult_nn(p,p_GetCoeff(m,r),r)); |
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162 | |
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163 | #ifdef PDEBUG |
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164 | p_Test(p,r); |
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165 | p_Test(m,r); |
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166 | #endif |
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167 | poly v=NULL; |
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168 | int rN=r->N; |
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169 | int *P=(int *)omAlloc0((rN+1)*sizeof(int)); |
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170 | int *M=(int *)omAlloc0((rN+1)*sizeof(int)); |
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171 | /* coefficients: */ |
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172 | number cP,cM,cOut; |
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173 | p_GetExpV(m, M, r); |
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174 | cM=p_GetCoeff(m,r); |
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175 | /* components:*/ |
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176 | const int expM=p_GetComp(m,r); |
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177 | int expP=0; |
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178 | int expOut=0; |
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179 | /* bucket constraints: */ |
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180 | int UseBuckets=1; |
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181 | if (pLength(p)< MIN_LENGTH_BUCKET || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
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182 | sBucket_pt bu_out; |
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183 | poly out=NULL; |
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184 | if (UseBuckets) bu_out=sBucketCreate(r); |
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185 | |
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186 | while (p!=NULL) |
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187 | { |
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188 | #ifdef PDEBUG |
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189 | p_Test(p,r); |
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190 | #endif |
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191 | expP=p_GetComp(p,r); |
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192 | if (expP==0) |
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193 | { |
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194 | expOut=expM; |
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195 | } |
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196 | else |
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197 | { |
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198 | if (expM==0) |
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199 | { |
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200 | expOut=expP; |
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201 | #ifdef PDEBUG |
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202 | if (side) |
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203 | { |
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204 | Print("Multiplication in the left module from the right"); |
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205 | } |
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206 | #endif |
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207 | } |
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208 | else |
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209 | { |
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210 | /* REPORT_ERROR */ |
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211 | #ifdef PDEBUG |
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212 | const char* s; |
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213 | if (side==1) s="gnc_p_Mult_mm"; |
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214 | else s="gnc_mm_Mult_p"; |
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215 | Print("%s: exponent mismatch %d and %d\n",s,expP,expM); |
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216 | #endif |
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217 | expOut=0; |
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218 | } |
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219 | } |
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220 | p_GetExpV(p,P,r); |
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221 | cP=p_GetCoeff(p,r); |
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222 | cOut=n_Mult(cP,cM,r); |
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223 | if (side==1) |
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224 | { |
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225 | v = gnc_mm_Mult_nn(P, M, r); |
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226 | } |
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227 | else |
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228 | { |
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229 | v = gnc_mm_Mult_nn(M, P, r); |
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230 | } |
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231 | v = p_Mult_nn(v,cOut,r); |
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232 | p_SetCompP(v,expOut,r); |
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233 | if (UseBuckets) sBucket_Add_p(bu_out,v,pLength(v)); |
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234 | else out = p_Add_q(out,v,r); |
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235 | p_DeleteLm(&p,r); |
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236 | } |
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237 | freeT(P,rN); |
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238 | freeT(M,rN); |
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239 | if (UseBuckets) |
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240 | { |
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241 | out = NULL; |
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242 | int len = pLength(out); |
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243 | sBucketDestroyAdd(bu_out, &out, &len); |
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244 | } |
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245 | #ifdef PDEBUG |
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246 | p_Test(out,r); |
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247 | #endif |
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248 | return(out); |
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249 | } |
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250 | |
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251 | /* poly functions defined in p_Procs : */ |
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252 | poly gnc_pp_Mult_mm(const poly p, const poly m, const ring r, poly &last) |
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253 | { |
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254 | return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 1, r) ); |
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255 | } |
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256 | |
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257 | poly gnc_p_Mult_mm(poly p, const poly m, const ring r) |
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258 | { |
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259 | return( gnc_p_Mult_mm_Common(p, m, 1, r) ); |
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260 | } |
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261 | |
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262 | poly gnc_mm_Mult_p(const poly m, poly p, const ring r) |
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263 | { |
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264 | return( gnc_p_Mult_mm_Common(p, m, 0, r) ); |
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265 | } |
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266 | |
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267 | poly gnc_mm_Mult_pp(const poly m, const poly p, const ring r) |
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268 | { |
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269 | return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 0, r) ); |
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270 | } |
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271 | |
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272 | |
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273 | |
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274 | poly gnc_mm_Mult_nn(int *F0, int *G0, const ring r) |
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275 | /* destroys nothing, no coeffs and exps */ |
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276 | { |
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277 | poly out=NULL; |
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278 | int i,j; |
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279 | int iF,jG,iG; |
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280 | int rN=r->N; |
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281 | int ExpSize=(((rN+1)*sizeof(int)+sizeof(long)-1)/sizeof(long))*sizeof(long); |
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282 | |
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283 | int *F=(int *)omAlloc0((rN+1)*sizeof(int)); |
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284 | int *G=(int *)omAlloc0((rN+1)*sizeof(int)); |
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285 | |
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286 | memcpy(F, F0,(rN+1)*sizeof(int)); |
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287 | // pExpVectorCopy(F,F0); |
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288 | memcpy(G, G0,(rN+1)*sizeof(int)); |
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289 | // pExpVectorCopy(G,G0); |
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290 | F[0]=0; /* important for p_MemAdd */ |
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291 | G[0]=0; |
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292 | |
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293 | iF=rN; |
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294 | while ((F[iF]==0)&&(iF>=1)) iF--; /* last exp_num of F */ |
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295 | if (iF==0) /* F0 is zero vector */ |
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296 | { |
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297 | out=pOne(); |
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298 | p_SetExpV(out,G0,r); |
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299 | p_Setm(out,r); |
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300 | freeT(F,rN); |
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301 | freeT(G,rN); |
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302 | return(out); |
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303 | } |
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304 | jG=1; |
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305 | while ((G[jG]==0)&&(jG<rN)) jG++; /* first exp_num of G */ |
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306 | iG=rN; |
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307 | while ((G[iG]==0)&&(iG>1)) iG--; /* last exp_num of G */ |
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308 | |
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309 | out=pOne(); |
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310 | |
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311 | if (iF<=jG) |
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312 | /* i.e. no mixed exp_num , MERGE case */ |
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313 | { |
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314 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
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315 | p_SetExpV(out,F,r); |
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316 | p_Setm(out,r); |
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317 | // omFreeSize((ADDRESS)F,ExpSize); |
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318 | freeT(F,rN); |
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319 | freeT(G,rN); |
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320 | return(out); |
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321 | } |
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322 | |
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323 | number cff=n_Init(1,r); |
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324 | number tmp_num=NULL; |
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325 | int cpower=0; |
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326 | |
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327 | if (r->nc->type==nc_skew) |
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328 | { |
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329 | if (r->nc->IsSkewConstant==1) |
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330 | { |
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331 | int tpower=0; |
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332 | for(j=jG; j<=iG; j++) |
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333 | { |
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334 | if (G[j]!=0) |
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335 | { |
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336 | cpower = 0; |
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337 | for(i=j+1; i<=iF; i++) |
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338 | { |
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339 | cpower = cpower + F[i]; |
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340 | } |
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341 | cpower = cpower*G[j]; |
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342 | tpower = tpower + cpower; |
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343 | } |
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344 | } |
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345 | cff = n_Copy(p_GetCoeff(MATELEM(r->nc->COM,1,2),r),r); |
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346 | nPower(cff,tpower,&tmp_num); |
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347 | n_Delete(&cff,r); |
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348 | cff = tmp_num; |
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349 | } |
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350 | else /* skew commutative with nonequal coeffs */ |
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351 | { |
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352 | number totcff=n_Init(1,r); |
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353 | for(j=jG; j<=iG; j++) |
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354 | { |
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355 | if (G[j]!=0) |
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356 | { |
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357 | cpower = 0; |
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358 | for(i=j+1; i<=iF; i++) |
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359 | { |
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360 | if (F[i]!=0) |
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361 | { |
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362 | cpower = F[i]*G[j]; |
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363 | cff = n_Copy(p_GetCoeff(MATELEM(r->nc->COM,j,i),r),r); |
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364 | nPower(cff,cpower,&tmp_num); |
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365 | cff = nMult(totcff,tmp_num); |
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366 | nDelete(&totcff); |
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367 | nDelete(&tmp_num); |
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368 | totcff = n_Copy(cff,r); |
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369 | n_Delete(&cff,r); |
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370 | } |
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371 | } /* end 2nd for */ |
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372 | } |
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373 | } |
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374 | cff=totcff; |
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375 | } |
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376 | p_MemAdd_LengthGeneral(F, G, ExpSize/sizeof(long)); |
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377 | p_SetExpV(out,F,r); |
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378 | p_Setm(out,r); |
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379 | p_SetCoeff(out,cff,r); |
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380 | // p_MemAdd_NegWeightAdjust(p, r); ??? do we need this? |
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381 | freeT(F,rN); |
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382 | freeT(G,rN); |
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383 | return(out); |
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384 | } /* end nc_skew */ |
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385 | |
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386 | /* now we have to destroy out! */ |
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387 | p_Delete(&out,r); |
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388 | out = NULL; |
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389 | |
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390 | if (iG==jG) |
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391 | /* g is univariate monomial */ |
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392 | { |
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393 | /* if (ri->nc->type==nc_skew) -- postpone to TU */ |
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394 | out = gnc_mm_Mult_uu(F,jG,G[jG],r); |
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395 | freeT(F,rN); |
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396 | freeT(G,rN); |
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397 | return(out); |
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398 | } |
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399 | |
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400 | number n1=n_Init(1,r); |
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401 | int *Prv=(int *)omAlloc0((rN+1)*sizeof(int)); |
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402 | int *Nxt=(int *)omAlloc0((rN+1)*sizeof(int)); |
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403 | |
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404 | int *log=(int *)omAlloc0((rN+1)*sizeof(int)); |
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405 | int cnt=0; int cnf=0; |
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406 | |
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407 | /* splitting F wrt jG */ |
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408 | for (i=1;i<=jG;i++) |
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409 | { |
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410 | Prv[i]=F[i]; Nxt[i]=0; /* mult at the very end */ |
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411 | if (F[i]!=0) cnf++; |
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412 | } |
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413 | |
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414 | if (cnf==0) freeT(Prv,rN); |
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415 | |
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416 | for (i=jG+1;i<=rN;i++) |
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417 | { |
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418 | Nxt[i]=F[i]; |
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419 | /* if (cnf!=0) Prv[i]=0; */ |
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420 | if (F[i]!=0) |
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421 | { |
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422 | cnt++; |
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423 | } /* effective part for F */ |
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424 | } |
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425 | freeT(F,rN); |
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426 | cnt=0; |
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427 | |
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428 | for (i=1;i<=rN;i++) |
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429 | { |
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430 | if (G[i]!=0) |
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431 | { |
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432 | cnt++; |
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433 | log[cnt]=i; |
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434 | } /* lG for G */ |
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435 | } |
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436 | |
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437 | /* ---------------------- A C T I O N ------------------------ */ |
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438 | poly D=NULL; |
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439 | poly Rout=NULL; |
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440 | number *c=(number *)omAlloc0((rN+1)*sizeof(number)); |
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441 | c[0]=n_Init(1,r); |
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442 | |
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443 | int *Op=Nxt; |
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444 | int *On=G; |
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445 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
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446 | |
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447 | for (i=jG;i<=rN;i++) U[i]=Nxt[i]+G[i]; /* make leadterm */ |
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448 | Nxt=NULL; |
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449 | G=NULL; |
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450 | cnt=1; |
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451 | int t=0; |
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452 | poly w=NULL; |
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453 | poly Pn=pOne(); |
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454 | p_SetExpV(Pn,On,r); |
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455 | p_Setm(Pn,r); |
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456 | |
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457 | while (On[iG]!=0) |
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458 | { |
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459 | t=log[cnt]; |
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460 | |
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461 | w=gnc_mm_Mult_uu(Op,t,On[t],r); |
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462 | c[cnt]=n_Mult(c[cnt-1],p_GetCoeff(w,r),r); |
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463 | D = pNext(w); /* getting coef and rest D */ |
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464 | p_DeleteLm(&w,r); |
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465 | w=NULL; |
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466 | |
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467 | Op[t] += On[t]; /* update exp_vectors */ |
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468 | On[t] = 0; |
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469 | |
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470 | if (t!=iG) /* not the last step */ |
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471 | { |
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472 | p_SetExpV(Pn,On,r); |
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473 | p_Setm(Pn,r); |
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474 | #ifdef PDEBUG |
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475 | p_Test(Pn,r); |
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476 | #endif |
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477 | |
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478 | // if (pNext(D)==0) |
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479 | // is D a monomial? could be postponed higher |
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480 | // { |
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481 | // Rout=nc_mm_Mult_nn(D,Pn,r); |
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482 | // } |
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483 | // else |
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484 | // { |
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485 | Rout=gnc_p_Mult_mm(D,Pn,r); |
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486 | // } |
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487 | } |
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488 | else |
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489 | { |
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490 | Rout=D; |
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491 | D=NULL; |
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492 | } |
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493 | |
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494 | if (Rout!=NULL) |
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495 | { |
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496 | Rout=p_Mult_nn(Rout,c[cnt-1],r); /* Rest is ready */ |
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497 | out=p_Add_q(out,Rout,r); |
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498 | Rout=NULL; |
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499 | } |
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500 | cnt++; |
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501 | } |
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502 | freeT(On,rN); |
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503 | freeT(Op,rN); |
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504 | p_Delete(&Pn,r); |
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505 | omFreeSize((ADDRESS)log,(rN+1)*sizeof(int)); |
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506 | |
---|
507 | /* leadterm and Prv-part */ |
---|
508 | |
---|
509 | Rout=pOne(); |
---|
510 | /* U is lead.monomial */ |
---|
511 | U[0]=0; |
---|
512 | p_SetExpV(Rout,U,r); |
---|
513 | p_Setm(Rout,r); /* use again this name Rout */ |
---|
514 | #ifdef PDEBUG |
---|
515 | p_Test(Rout,r); |
---|
516 | #endif |
---|
517 | p_SetCoeff(Rout,c[cnt-1],r); |
---|
518 | out=p_Add_q(out,Rout,r); |
---|
519 | freeT(U,rN); |
---|
520 | freeN(c,rN+1); |
---|
521 | if (cnf!=0) /* Prv is non-zero vector */ |
---|
522 | { |
---|
523 | Rout=pOne(); |
---|
524 | Prv[0]=0; |
---|
525 | p_SetExpV(Rout,Prv,r); |
---|
526 | p_Setm(Rout,r); |
---|
527 | #ifdef PDEBUG |
---|
528 | p_Test(Rout,r); |
---|
529 | #endif |
---|
530 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
531 | freeT(Prv,rN); |
---|
532 | p_Delete(&Rout,r); |
---|
533 | } |
---|
534 | return (out); |
---|
535 | } |
---|
536 | |
---|
537 | |
---|
538 | poly gnc_mm_Mult_uu(int *F,int jG,int bG, const ring r) |
---|
539 | /* f=mono(F),g=(x_iG)^bG */ |
---|
540 | { |
---|
541 | poly out=NULL; |
---|
542 | int i; |
---|
543 | number num=NULL; |
---|
544 | |
---|
545 | int rN=r->N; |
---|
546 | int iF=r->N; |
---|
547 | while ((F[iF]==0)&&(iF>0)) iF-- ; /* last exponent_num of F */ |
---|
548 | |
---|
549 | if (iF==0) /* F==zero vector in other words */ |
---|
550 | { |
---|
551 | out=pOne(); |
---|
552 | p_SetExp(out,jG,bG,r); |
---|
553 | p_Setm(out,r); |
---|
554 | return(out); |
---|
555 | } |
---|
556 | |
---|
557 | int jF=1; |
---|
558 | while ((F[jF]==0)&&(jF<=rN)) jF++; /* first exp of F */ |
---|
559 | |
---|
560 | if (iF<=jG) /* i.e. no mixed exp_num */ |
---|
561 | { |
---|
562 | out=pOne(); |
---|
563 | F[jG]=F[jG]+bG; |
---|
564 | p_SetExpV(out,F,r); |
---|
565 | p_Setm(out,r); |
---|
566 | return(out); |
---|
567 | } |
---|
568 | |
---|
569 | if (iF==jF) /* uni times uni */ |
---|
570 | { |
---|
571 | out=gnc_uu_Mult_ww(iF,F[iF],jG,bG,r); |
---|
572 | return(out); |
---|
573 | } |
---|
574 | |
---|
575 | /* Now: F is mono with >=2 exponents, jG<iF */ |
---|
576 | /* check the quasi-commutative case */ |
---|
577 | // matrix LCOM=r->nc->COM; |
---|
578 | // number rescoef=n_Init(1,r); |
---|
579 | // number tmpcoef=n_Init(1,r); |
---|
580 | // int tmpint; |
---|
581 | // i=iF; |
---|
582 | // while (i>=jG+1) |
---|
583 | // /* all the non-zero exponents */ |
---|
584 | // { |
---|
585 | // if (MATELEM(LCOM,jG,i)!=NULL) |
---|
586 | // { |
---|
587 | // tmpcoef=pGetCoeff(MATELEM(LCOM,jG,i)); |
---|
588 | // tmpint=(int)F[i]; |
---|
589 | // nPower(tmpcoef,F[i],&tmpcoef); |
---|
590 | // rescoef=nMult(rescoef,tmpcoef); |
---|
591 | // i--; |
---|
592 | // } |
---|
593 | // else |
---|
594 | // { |
---|
595 | // if (F[i]!=0) break; |
---|
596 | // } |
---|
597 | // } |
---|
598 | // if (iF==i) |
---|
599 | // /* no action took place*/ |
---|
600 | // { |
---|
601 | |
---|
602 | // } |
---|
603 | // else /* power the result up to bG */ |
---|
604 | // { |
---|
605 | // nPower(rescoef,bG,&rescoef); |
---|
606 | // /* + cleanup, post-processing */ |
---|
607 | // } |
---|
608 | |
---|
609 | int *Prv=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
610 | int *Nxt=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
611 | int *lF=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
612 | int cnt=0; int cnf=0; |
---|
613 | /* splitting F wrt jG */ |
---|
614 | for (i=1;i<=jG;i++) /* mult at the very end */ |
---|
615 | { |
---|
616 | Prv[i]=F[i]; Nxt[i]=0; |
---|
617 | if (F[i]!=0) cnf++; |
---|
618 | } |
---|
619 | if (cnf==0) freeT(Prv,rN); |
---|
620 | for (i=jG+1;i<=rN;i++) |
---|
621 | { |
---|
622 | Nxt[i]=F[i]; |
---|
623 | if (cnf!=0) { Prv[i]=0;} |
---|
624 | if (F[i]!=0) |
---|
625 | { |
---|
626 | cnt++; |
---|
627 | lF[cnt]=i; |
---|
628 | } /* eff_part,lF_for_F */ |
---|
629 | } |
---|
630 | |
---|
631 | if (cnt==1) /* Nxt consists of 1 nonzero el-t only */ |
---|
632 | { |
---|
633 | int q=lF[1]; |
---|
634 | poly Rout=pOne(); |
---|
635 | out=gnc_uu_Mult_ww(q,Nxt[q],jG,bG,r); |
---|
636 | freeT(Nxt,rN); |
---|
637 | |
---|
638 | if (cnf!=0) |
---|
639 | { |
---|
640 | Prv[0]=0; |
---|
641 | p_SetExpV(Rout,Prv,r); |
---|
642 | p_Setm(Rout,r); |
---|
643 | #ifdef PDEBUG |
---|
644 | p_Test(Rout,r); |
---|
645 | #endif |
---|
646 | freeT(Prv,rN); |
---|
647 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
648 | } |
---|
649 | |
---|
650 | omFreeSize((ADDRESS)lF,(rN+1)*sizeof(int)); |
---|
651 | p_Delete(&Rout,r); |
---|
652 | return (out); |
---|
653 | } |
---|
654 | /* -------------------- MAIN ACTION --------------------- */ |
---|
655 | |
---|
656 | poly D=NULL; |
---|
657 | poly Rout=NULL; |
---|
658 | number *c=(number *)omAlloc0((cnt+2)*sizeof(number)); |
---|
659 | c[cnt+1]=n_Init(1,r); |
---|
660 | i=cnt+2; /* later in freeN */ |
---|
661 | int *Op=Nxt; |
---|
662 | int *On=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
663 | int *U=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
664 | |
---|
665 | |
---|
666 | // pExpVectorCopy(U,Nxt); |
---|
667 | memcpy(U, Nxt,(rN+1)*sizeof(int)); |
---|
668 | U[jG] = U[jG] + bG; |
---|
669 | |
---|
670 | /* Op=Nxt and initial On=(0); */ |
---|
671 | Nxt=NULL; |
---|
672 | |
---|
673 | poly Pp; |
---|
674 | poly Pn; |
---|
675 | int t=0; |
---|
676 | int first=lF[1]; |
---|
677 | int nlast=lF[cnt]; |
---|
678 | int kk=0; |
---|
679 | /* cnt--; */ |
---|
680 | /* now lF[cnt] should be <=iF-1 */ |
---|
681 | |
---|
682 | while (Op[first]!=0) |
---|
683 | { |
---|
684 | t=lF[cnt]; /* cnt as it was computed */ |
---|
685 | |
---|
686 | poly w=gnc_uu_Mult_ww(t,Op[t],jG,bG,r); |
---|
687 | c[cnt]=n_Copy(p_GetCoeff(w,r),r); |
---|
688 | D = pNext(w); /* getting coef and rest D */ |
---|
689 | p_DeleteLm(&w,r); |
---|
690 | w=NULL; |
---|
691 | |
---|
692 | Op[t]= 0; |
---|
693 | Pp=pOne(); |
---|
694 | p_SetExpV(Pp,Op,r); |
---|
695 | p_Setm(Pp,r); |
---|
696 | |
---|
697 | if (t<nlast) |
---|
698 | { |
---|
699 | kk=lF[cnt+1]; |
---|
700 | On[kk]=F[kk]; |
---|
701 | |
---|
702 | Pn=pOne(); |
---|
703 | p_SetExpV(Pn,On,r); |
---|
704 | p_Setm(Pn,r); |
---|
705 | |
---|
706 | if (t!=first) /* typical expr */ |
---|
707 | { |
---|
708 | w=gnc_p_Mult_mm(D,Pn,r); |
---|
709 | Rout=gnc_mm_Mult_p(Pp,w,r); |
---|
710 | w=NULL; |
---|
711 | } |
---|
712 | else /* last step */ |
---|
713 | { |
---|
714 | On[t]=0; |
---|
715 | p_SetExpV(Pn,On,r); |
---|
716 | p_Setm(Pn,r); |
---|
717 | Rout=gnc_p_Mult_mm(D,Pn,r); |
---|
718 | } |
---|
719 | #ifdef PDEBUG |
---|
720 | p_Test(Pp,r); |
---|
721 | #endif |
---|
722 | p_Delete(&Pn,r); |
---|
723 | } |
---|
724 | else /* first step */ |
---|
725 | { |
---|
726 | Rout=gnc_mm_Mult_p(Pp,D,r); |
---|
727 | } |
---|
728 | #ifdef PDEBUG |
---|
729 | p_Test(Pp,r); |
---|
730 | #endif |
---|
731 | p_Delete(&Pp,r); |
---|
732 | num=n_Mult(c[cnt+1],c[cnt],r); |
---|
733 | n_Delete(&c[cnt],r); |
---|
734 | c[cnt]=num; |
---|
735 | Rout=p_Mult_nn(Rout,c[cnt+1],r); /* Rest is ready */ |
---|
736 | out=p_Add_q(out,Rout,r); |
---|
737 | Pp=NULL; |
---|
738 | cnt--; |
---|
739 | } |
---|
740 | /* only to feel safe:*/ |
---|
741 | Pn=Pp=NULL; |
---|
742 | freeT(On,rN); |
---|
743 | freeT(Op,rN); |
---|
744 | |
---|
745 | /* leadterm and Prv-part with coef 1 */ |
---|
746 | /* U[0]=exp; */ |
---|
747 | /* U[jG]=U[jG]+bG; */ |
---|
748 | /* make leadterm */ |
---|
749 | /* ??????????? we have done it already :-0 */ |
---|
750 | Rout=pOne(); |
---|
751 | p_SetExpV(Rout,U,r); |
---|
752 | p_Setm(Rout,r); /* use again this name */ |
---|
753 | p_SetCoeff(Rout,c[cnt+1],r); /* last computed coef */ |
---|
754 | out=p_Add_q(out,Rout,r); |
---|
755 | Rout=NULL; |
---|
756 | freeT(U,rN); |
---|
757 | freeN(c,i); |
---|
758 | omFreeSize((ADDRESS)lF,(rN+1)*sizeof(int)); |
---|
759 | |
---|
760 | if (cnf!=0) |
---|
761 | { |
---|
762 | Rout=pOne(); |
---|
763 | p_SetExpV(Rout,Prv,r); |
---|
764 | p_Setm(Rout,r); |
---|
765 | freeT(Prv,rN); |
---|
766 | out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */ |
---|
767 | p_Delete(&Rout,r); |
---|
768 | } |
---|
769 | return (out); |
---|
770 | } |
---|
771 | |
---|
772 | poly gnc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r) |
---|
773 | { |
---|
774 | int k,m; |
---|
775 | int rN=r->N; |
---|
776 | matrix cMT=r->nc->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
777 | |
---|
778 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r); |
---|
779 | /* var(j); */ |
---|
780 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); |
---|
781 | /*var(i); for convenience */ |
---|
782 | #ifdef PDEBUG |
---|
783 | p_Test(x,r); |
---|
784 | p_Test(y,r); |
---|
785 | #endif |
---|
786 | poly t=NULL; |
---|
787 | /* ------------ Main Cycles ----------------------------*/ |
---|
788 | |
---|
789 | for (k=2;k<=a;k++) |
---|
790 | { |
---|
791 | t = nc_p_CopyGet(MATELEM(cMT,k,1),r); |
---|
792 | |
---|
793 | if (t==NULL) /* not computed yet */ |
---|
794 | { |
---|
795 | t = nc_p_CopyGet(MATELEM(cMT,k-1,1),r); |
---|
796 | // t=p_Copy(MATELEM(cMT,k-1,1),r); |
---|
797 | t = gnc_mm_Mult_p(y,t,r); |
---|
798 | MATELEM(cMT,k,1) = nc_p_CopyPut(t,r); |
---|
799 | // omCheckAddr(cMT->m); |
---|
800 | p_Delete(&t,r); |
---|
801 | } |
---|
802 | t=NULL; |
---|
803 | } |
---|
804 | |
---|
805 | for (m=2;m<=b;m++) |
---|
806 | { |
---|
807 | t = nc_p_CopyGet(MATELEM(cMT,a,m),r); |
---|
808 | // t=MATELEM(cMT,a,m); |
---|
809 | if (t==NULL) //not computed yet |
---|
810 | { |
---|
811 | t = nc_p_CopyGet(MATELEM(cMT,a,m-1),r); |
---|
812 | // t=p_Copy(MATELEM(cMT,a,m-1),r); |
---|
813 | t = gnc_p_Mult_mm(t,x,r); |
---|
814 | MATELEM(cMT,a,m) = nc_p_CopyPut(t,r); |
---|
815 | // MATELEM(cMT,a,m) = t; |
---|
816 | // omCheckAddr(cMT->m); |
---|
817 | p_Delete(&t,r); |
---|
818 | } |
---|
819 | t=NULL; |
---|
820 | } |
---|
821 | p_Delete(&x,r); |
---|
822 | p_Delete(&y,r); |
---|
823 | // t=MATELEM(cMT,a,b); |
---|
824 | t= nc_p_CopyGet(MATELEM(cMT,a,b),r); |
---|
825 | // return(p_Copy(t,r)); |
---|
826 | /* since the last computed element was cMT[a,b] */ |
---|
827 | return(t); |
---|
828 | } |
---|
829 | |
---|
830 | poly gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r) |
---|
831 | /* (x_i)^a times (x_j)^b */ |
---|
832 | /* x_i = y, x_j = x ! */ |
---|
833 | { |
---|
834 | /* Check zero exceptions, (q-)commutativity and is there something to do? */ |
---|
835 | assume(a!=0); |
---|
836 | assume(b!=0); |
---|
837 | poly out=pOne(); |
---|
838 | if (i<=j) |
---|
839 | { |
---|
840 | p_SetExp(out,i,a,r); |
---|
841 | p_AddExp(out,j,b,r); |
---|
842 | p_Setm(out,r); |
---|
843 | return(out); |
---|
844 | }/* zero exeptions and usual case */ |
---|
845 | /* if ((a==0)||(b==0)||(i<=j)) return(out); */ |
---|
846 | |
---|
847 | if (MATELEM(r->nc->COM,j,i)!=NULL) |
---|
848 | /* commutative or quasicommutative case */ |
---|
849 | { |
---|
850 | p_SetExp(out,i,a,r); |
---|
851 | p_AddExp(out,j,b,r); |
---|
852 | p_Setm(out,r); |
---|
853 | if (r->cf->nIsOne(p_GetCoeff(MATELEM(r->nc->COM,j,i),r))) /* commutative case */ |
---|
854 | { |
---|
855 | return(out); |
---|
856 | } |
---|
857 | else |
---|
858 | { |
---|
859 | number tmp_number=p_GetCoeff(MATELEM(r->nc->COM,j,i),r); /* quasicommutative case */ |
---|
860 | nPower(tmp_number,a*b,&tmp_number); |
---|
861 | p_SetCoeff(out,tmp_number,r); |
---|
862 | return(out); |
---|
863 | } |
---|
864 | }/* end_of commutative or quasicommutative case */ |
---|
865 | p_Delete(&out,r); |
---|
866 | |
---|
867 | /* we are here if i>j and variables do not commute or quasicommute */ |
---|
868 | /* in fact, now a>=1 and b>=1; and j<i */ |
---|
869 | /* now check whether the polynomial is already computed */ |
---|
870 | int rN=r->N; |
---|
871 | int vik = UPMATELEM(j,i,rN); |
---|
872 | int cMTsize=r->nc->MTsize[vik]; |
---|
873 | int newcMTsize=0; |
---|
874 | newcMTsize=si_max(a,b); |
---|
875 | |
---|
876 | if (newcMTsize<=cMTsize) |
---|
877 | { |
---|
878 | out = nc_p_CopyGet(MATELEM(r->nc->MT[vik],a,b),r); |
---|
879 | if (out !=NULL) return (out); |
---|
880 | } |
---|
881 | int k,m; |
---|
882 | if (newcMTsize > cMTsize) |
---|
883 | { |
---|
884 | int inM=(((newcMTsize+6)/7)*7); |
---|
885 | assume (inM>=newcMTsize); |
---|
886 | newcMTsize = inM; |
---|
887 | // matrix tmp = (matrix)omAlloc0(inM*inM*sizeof(poly)); |
---|
888 | matrix tmp = mpNew(newcMTsize,newcMTsize); |
---|
889 | |
---|
890 | for (k=1;k<=cMTsize;k++) |
---|
891 | { |
---|
892 | for (m=1;m<=cMTsize;m++) |
---|
893 | { |
---|
894 | out = MATELEM(r->nc->MT[UPMATELEM(j,i,rN)],k,m); |
---|
895 | if ( out != NULL ) |
---|
896 | { |
---|
897 | MATELEM(tmp,k,m) = out;/*MATELEM(r->nc->MT[UPMATELEM(j,i,rN)],k,m)*/ |
---|
898 | // omCheckAddr(tmp->m); |
---|
899 | MATELEM(r->nc->MT[UPMATELEM(j,i,rN)],k,m)=NULL; |
---|
900 | // omCheckAddr(r->nc->MT[UPMATELEM(j,i,rN)]->m); |
---|
901 | } |
---|
902 | } |
---|
903 | } |
---|
904 | id_Delete((ideal *)&(r->nc->MT[UPMATELEM(j,i,rN)]),r); |
---|
905 | r->nc->MT[UPMATELEM(j,i,rN)] = tmp; |
---|
906 | tmp=NULL; |
---|
907 | r->nc->MTsize[UPMATELEM(j,i,rN)] = newcMTsize; |
---|
908 | } |
---|
909 | /* The update of multiplication matrix is finished */ |
---|
910 | pDelete(&out); |
---|
911 | out = gnc_uu_Mult_ww_vert(i, a, j, b, r); |
---|
912 | // out = nc_uu_Mult_ww_horvert(i, a, j, b, r); |
---|
913 | return(out); |
---|
914 | } |
---|
915 | |
---|
916 | poly gnc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r) |
---|
917 | |
---|
918 | { |
---|
919 | int k,m; |
---|
920 | int rN=r->N; |
---|
921 | matrix cMT=r->nc->MT[UPMATELEM(j,i,rN)]; /* cMT=current MT */ |
---|
922 | |
---|
923 | poly x=pOne();p_SetExp(x,j,1,r);p_Setm(x,r);/* var(j); */ |
---|
924 | poly y=pOne();p_SetExp(y,i,1,r);p_Setm(y,r); /*var(i); for convenience */ |
---|
925 | #ifdef PDEBUG |
---|
926 | p_Test(x,r); |
---|
927 | p_Test(y,r); |
---|
928 | #endif |
---|
929 | |
---|
930 | poly t=NULL; |
---|
931 | |
---|
932 | int toXY; |
---|
933 | int toYX; |
---|
934 | |
---|
935 | if (a==1) /* y*x^b, b>=2 */ |
---|
936 | { |
---|
937 | toXY=b-1; |
---|
938 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=2)) toXY--; |
---|
939 | for (m=toXY+1;m<=b;m++) |
---|
940 | { |
---|
941 | t=MATELEM(cMT,1,m); |
---|
942 | if (t==NULL) /* remove after debug */ |
---|
943 | { |
---|
944 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
945 | t = gnc_p_Mult_mm(t,x,r); |
---|
946 | MATELEM(cMT,1,m) = t; |
---|
947 | /* omCheckAddr(cMT->m); */ |
---|
948 | } |
---|
949 | else |
---|
950 | { |
---|
951 | /* Error, should never get there */ |
---|
952 | WarnS("Error: a=1; MATELEM!=0"); |
---|
953 | } |
---|
954 | t=NULL; |
---|
955 | } |
---|
956 | return(p_Copy(MATELEM(cMT,1,b),r)); |
---|
957 | } |
---|
958 | |
---|
959 | if (b==1) /* y^a*x, a>=2 */ |
---|
960 | { |
---|
961 | toYX=a-1; |
---|
962 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=2)) toYX--; |
---|
963 | for (m=toYX+1;m<=a;m++) |
---|
964 | { |
---|
965 | t=MATELEM(cMT,m,1); |
---|
966 | if (t==NULL) /* remove after debug */ |
---|
967 | { |
---|
968 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
969 | t = gnc_mm_Mult_p(y,t,r); |
---|
970 | MATELEM(cMT,m,1) = t; |
---|
971 | /* omCheckAddr(cMT->m); */ |
---|
972 | } |
---|
973 | else |
---|
974 | { |
---|
975 | /* Error, should never get there */ |
---|
976 | WarnS("Error: b=1, MATELEM!=0"); |
---|
977 | } |
---|
978 | t=NULL; |
---|
979 | } |
---|
980 | return(p_Copy(MATELEM(cMT,a,1),r)); |
---|
981 | } |
---|
982 | |
---|
983 | /* ------------ Main Cycles ----------------------------*/ |
---|
984 | /* a>1, b>1 */ |
---|
985 | |
---|
986 | int dXY=0; int dYX=0; |
---|
987 | /* dXY = distance for computing x-mult, then y-mult */ |
---|
988 | /* dYX = distance for computing y-mult, then x-mult */ |
---|
989 | int toX=a-1; int toY=b-1; /* toX = to axe X, toY = to axe Y */ |
---|
990 | toXY=b-1; toYX=a-1; |
---|
991 | /* if toX==0, toXY = dist. to computed y * x^toXY */ |
---|
992 | /* if toY==0, toYX = dist. to computed y^toYX * x */ |
---|
993 | while ( (MATELEM(cMT,toX,b)==NULL) && (toX>=1)) toX--; |
---|
994 | if (toX==0) /* the whole column is not computed yet */ |
---|
995 | { |
---|
996 | while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=1)) toXY--; |
---|
997 | /* toXY >=1 */ |
---|
998 | dXY=b-1-toXY; |
---|
999 | } |
---|
1000 | dXY=dXY+a-toX; /* the distance to nearest computed y^toX x^b */ |
---|
1001 | |
---|
1002 | while ( (MATELEM(cMT,a,toY)==NULL) && (toY>=1)) toY--; |
---|
1003 | if (toY==0) /* the whole row is not computed yet */ |
---|
1004 | { |
---|
1005 | while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=1)) toYX--; |
---|
1006 | /* toYX >=1 */ |
---|
1007 | dYX=a-1-toYX; |
---|
1008 | } |
---|
1009 | dYX=dYX+b-toY; /* the distance to nearest computed y^a x^toY */ |
---|
1010 | |
---|
1011 | if (dYX>=dXY) |
---|
1012 | { |
---|
1013 | /* first x, then y */ |
---|
1014 | if (toX==0) /* start with the row*/ |
---|
1015 | { |
---|
1016 | for (m=toXY+1;m<=b;m++) |
---|
1017 | { |
---|
1018 | t=MATELEM(cMT,1,m); |
---|
1019 | if (t==NULL) /* remove after debug */ |
---|
1020 | { |
---|
1021 | t = p_Copy(MATELEM(cMT,1,m-1),r); |
---|
1022 | t = gnc_p_Mult_mm(t,x,r); |
---|
1023 | MATELEM(cMT,1,m) = t; |
---|
1024 | /* omCheckAddr(cMT->m); */ |
---|
1025 | } |
---|
1026 | else |
---|
1027 | { |
---|
1028 | /* Error, should never get there */ |
---|
1029 | WarnS("dYX>=dXY,toXY; MATELEM==0"); |
---|
1030 | } |
---|
1031 | t=NULL; |
---|
1032 | } |
---|
1033 | toX=1; /* y*x^b is computed */ |
---|
1034 | } |
---|
1035 | /* Now toX>=1 */ |
---|
1036 | for (k=toX+1;k<=a;k++) |
---|
1037 | { |
---|
1038 | t=MATELEM(cMT,k,b); |
---|
1039 | if (t==NULL) /* remove after debug */ |
---|
1040 | { |
---|
1041 | t = p_Copy(MATELEM(cMT,k-1,b),r); |
---|
1042 | t = gnc_mm_Mult_p(y,t,r); |
---|
1043 | MATELEM(cMT,k,b) = t; |
---|
1044 | /* omCheckAddr(cMT->m); */ |
---|
1045 | } |
---|
1046 | else |
---|
1047 | { |
---|
1048 | /* Error, should never get there */ |
---|
1049 | WarnS("dYX>=dXY,toX; MATELEM==0"); |
---|
1050 | } |
---|
1051 | t=NULL; |
---|
1052 | } |
---|
1053 | } /* endif (dYX>=dXY) */ |
---|
1054 | |
---|
1055 | |
---|
1056 | if (dYX<dXY) |
---|
1057 | { |
---|
1058 | /* first y, then x */ |
---|
1059 | if (toY==0) /* start with the column*/ |
---|
1060 | { |
---|
1061 | for (m=toYX+1;m<=a;m++) |
---|
1062 | { |
---|
1063 | t=MATELEM(cMT,m,1); |
---|
1064 | if (t==NULL) /* remove after debug */ |
---|
1065 | { |
---|
1066 | t = p_Copy(MATELEM(cMT,m-1,1),r); |
---|
1067 | t = gnc_mm_Mult_p(y,t,r); |
---|
1068 | MATELEM(cMT,m,1) = t; |
---|
1069 | /* omCheckAddr(cMT->m); */ |
---|
1070 | } |
---|
1071 | else |
---|
1072 | { |
---|
1073 | /* Error, should never get there */ |
---|
1074 | WarnS("dYX<dXY,toYX; MATELEM==0"); |
---|
1075 | } |
---|
1076 | t=NULL; |
---|
1077 | } |
---|
1078 | toY=1; /* y^a*x is computed */ |
---|
1079 | } |
---|
1080 | /* Now toY>=1 */ |
---|
1081 | for (k=toY+1;k<=b;k++) |
---|
1082 | { |
---|
1083 | t=MATELEM(cMT,a,k); |
---|
1084 | if (t==NULL) /* remove after debug */ |
---|
1085 | { |
---|
1086 | t = p_Copy(MATELEM(cMT,a,k-1),r); |
---|
1087 | t = gnc_p_Mult_mm(t,x,r); |
---|
1088 | MATELEM(cMT,a,k) = t; |
---|
1089 | /* omCheckAddr(cMT->m); */ |
---|
1090 | } |
---|
1091 | else |
---|
1092 | { |
---|
1093 | /* Error, should never get there */ |
---|
1094 | WarnS("dYX<dXY,toY; MATELEM==0"); |
---|
1095 | } |
---|
1096 | t=NULL; |
---|
1097 | } |
---|
1098 | } /* endif (dYX<dXY) */ |
---|
1099 | |
---|
1100 | p_Delete(&x,r); |
---|
1101 | p_Delete(&y,r); |
---|
1102 | t=p_Copy(MATELEM(cMT,a,b),r); |
---|
1103 | return(t); /* since the last computed element was cMT[a,b] */ |
---|
1104 | } |
---|
1105 | |
---|
1106 | |
---|
1107 | /* ----------------------------- Syzygies ---------------------- */ |
---|
1108 | |
---|
1109 | /*2 |
---|
1110 | * reduction of p2 with p1 |
---|
1111 | * do not destroy p1, but p2 |
---|
1112 | * p1 divides p2 -> for use in NF algorithm |
---|
1113 | */ |
---|
1114 | poly gnc_ReduceSpolyOld(const poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1115 | { |
---|
1116 | if (p_GetComp(p1,r)!=p_GetComp(p2,r) |
---|
1117 | && (p_GetComp(p1,r)!=0) |
---|
1118 | && (p_GetComp(p2,r)!=0)) |
---|
1119 | { |
---|
1120 | #ifdef PDEBUG |
---|
1121 | Print("nc_ReduceSpolyOld: different components"); |
---|
1122 | #endif |
---|
1123 | return(NULL); |
---|
1124 | } |
---|
1125 | poly m = pOne(); |
---|
1126 | p_ExpVectorDiff(m,p2,p1,r); |
---|
1127 | //p_Setm(m,r); |
---|
1128 | #ifdef PDEBUG |
---|
1129 | p_Test(m,r); |
---|
1130 | #endif |
---|
1131 | /* pSetComp(m,r)=0? */ |
---|
1132 | poly N = mm_Mult_p(m, p_Head(p1,r), r); |
---|
1133 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
1134 | number cF = n_Copy( p_GetCoeff(p2, r),r); |
---|
1135 | /* GCD stuff */ |
---|
1136 | number cG = nGcd(C, cF, r); |
---|
1137 | if ( !nEqual(cG, n_Init(1,r) ) ) |
---|
1138 | { |
---|
1139 | cF = nDiv(cF, cG); |
---|
1140 | C = nDiv(C, cG); |
---|
1141 | } |
---|
1142 | p2 = p_Mult_nn(p2, C, r); |
---|
1143 | poly out = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
1144 | N = p_Add_q(N, out, r); |
---|
1145 | p_Test(p2,r); |
---|
1146 | p_Test(N,r); |
---|
1147 | number MinusOne = n_Init(-1,r); |
---|
1148 | if (!n_Equal(cF,MinusOne,r)) |
---|
1149 | { |
---|
1150 | cF = n_Neg(cF,r); |
---|
1151 | N = p_Mult_nn(N, cF, r); |
---|
1152 | p_Test(N,r); |
---|
1153 | } |
---|
1154 | out = p_Add_q(p2,N,r); |
---|
1155 | p_Test(out,r); |
---|
1156 | if ( out!=NULL ) pContent(out); |
---|
1157 | p_Delete(&m,r); |
---|
1158 | n_Delete(&cF,r); |
---|
1159 | n_Delete(&C,r); |
---|
1160 | n_Delete(&MinusOne,r); |
---|
1161 | return(out); |
---|
1162 | |
---|
1163 | } |
---|
1164 | |
---|
1165 | poly gnc_ReduceSpolyNew(const poly p1, poly p2, const ring r) |
---|
1166 | { |
---|
1167 | const long lCompP1 = p_GetComp(p1,r); |
---|
1168 | const long lCompP2 = p_GetComp(p2,r); |
---|
1169 | |
---|
1170 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
1171 | { |
---|
1172 | #ifdef PDEBUG |
---|
1173 | Werror("gnc_ReduceSpolyNew: different non-zero components!"); |
---|
1174 | #endif |
---|
1175 | return(NULL); |
---|
1176 | } |
---|
1177 | |
---|
1178 | poly m = pOne(); |
---|
1179 | p_ExpVectorDiff(m, p2, p1, r); |
---|
1180 | //p_Setm(m,r); |
---|
1181 | #ifdef PDEBUG |
---|
1182 | p_Test(m,r); |
---|
1183 | #endif |
---|
1184 | |
---|
1185 | /* pSetComp(m,r)=0? */ |
---|
1186 | poly N = mm_Mult_p(m, p_Head(p1,r), r); |
---|
1187 | |
---|
1188 | number C = n_Copy( p_GetCoeff(N, r), r); |
---|
1189 | number cF = n_Copy( p_GetCoeff(p2, r), r); |
---|
1190 | |
---|
1191 | /* GCD stuff */ |
---|
1192 | number cG = nGcd(C, cF, r); |
---|
1193 | |
---|
1194 | if (!n_IsOne(cG, r)) |
---|
1195 | { |
---|
1196 | cF = n_Div(cF, cG, r); |
---|
1197 | C = n_Div(C, cG, r); |
---|
1198 | } |
---|
1199 | |
---|
1200 | p2 = p_Mult_nn(p2, C, r); // p2 !!! |
---|
1201 | p_Test(p2,r); |
---|
1202 | n_Delete(&C,r); |
---|
1203 | |
---|
1204 | poly out = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
1205 | p_Delete(&m,r); |
---|
1206 | |
---|
1207 | N = p_Add_q(N, out, r); |
---|
1208 | p_Test(N,r); |
---|
1209 | |
---|
1210 | if (!n_IsMOne(cF,r)) // ??? |
---|
1211 | { |
---|
1212 | cF = n_Neg(cF,r); |
---|
1213 | N = p_Mult_nn(N, cF, r); |
---|
1214 | p_Test(N,r); |
---|
1215 | } |
---|
1216 | |
---|
1217 | out = p_Add_q(p2,N,r); // delete N, p2 |
---|
1218 | p_Test(out,r); |
---|
1219 | if ( out!=NULL ) pContent(out); |
---|
1220 | n_Delete(&cF,r); |
---|
1221 | return(out); |
---|
1222 | } |
---|
1223 | |
---|
1224 | |
---|
1225 | /*4 |
---|
1226 | * creates the S-polynomial of p1 and p2 |
---|
1227 | * do not destroy p1 and p2 |
---|
1228 | */ |
---|
1229 | poly gnc_CreateSpolyOld(poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1230 | { |
---|
1231 | if ((p_GetComp(p1,r)!=p_GetComp(p2,r)) |
---|
1232 | && (p_GetComp(p1,r)!=0) |
---|
1233 | && (p_GetComp(p2,r)!=0)) |
---|
1234 | { |
---|
1235 | #ifdef PDEBUG |
---|
1236 | Print("gnc_CreateSpolyOld : different components!"); |
---|
1237 | #endif |
---|
1238 | return(NULL); |
---|
1239 | } |
---|
1240 | if ((r->nc->type==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
1241 | { |
---|
1242 | return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
1243 | } |
---|
1244 | poly pL=pOne(); |
---|
1245 | poly m1=pOne(); |
---|
1246 | poly m2=pOne(); |
---|
1247 | pLcm(p1,p2,pL); |
---|
1248 | p_Setm(pL,r); |
---|
1249 | #ifdef PDEBUG |
---|
1250 | p_Test(pL,r); |
---|
1251 | #endif |
---|
1252 | p_ExpVectorDiff(m1,pL,p1,r); |
---|
1253 | //p_SetComp(m1,0,r); |
---|
1254 | //p_Setm(m1,r); |
---|
1255 | #ifdef PDEBUG |
---|
1256 | p_Test(m1,r); |
---|
1257 | #endif |
---|
1258 | p_ExpVectorDiff(m2,pL,p2,r); |
---|
1259 | //p_SetComp(m2,0,r); |
---|
1260 | //p_Setm(m2,r); |
---|
1261 | #ifdef PDEBUG |
---|
1262 | p_Test(m2,r); |
---|
1263 | #endif |
---|
1264 | p_Delete(&pL,r); |
---|
1265 | /* zero exponents ! */ |
---|
1266 | poly M1 = mm_Mult_p(m1,p_Head(p1,r),r); |
---|
1267 | number C1 = n_Copy(p_GetCoeff(M1,r),r); |
---|
1268 | poly M2 = mm_Mult_p(m2,p_Head(p2,r),r); |
---|
1269 | number C2 = n_Copy(p_GetCoeff(M2,r),r); |
---|
1270 | /* GCD stuff */ |
---|
1271 | number C = nGcd(C1,C2,r); |
---|
1272 | if (!nEqual(C,n_Init(1,r))) |
---|
1273 | { |
---|
1274 | C1=nDiv(C1,C); |
---|
1275 | C2=nDiv(C2,C); |
---|
1276 | } |
---|
1277 | M1=p_Mult_nn(M1,C2,r); |
---|
1278 | p_SetCoeff(m1,C2,r); |
---|
1279 | number MinusOne=n_Init(-1,r); |
---|
1280 | if (n_Equal(C1,MinusOne,r)) |
---|
1281 | { |
---|
1282 | M2=p_Add_q(M1,M2,r); |
---|
1283 | } |
---|
1284 | else |
---|
1285 | { |
---|
1286 | C1=n_Neg(C1,r); |
---|
1287 | M2=p_Mult_nn(M2,C1,r); |
---|
1288 | M2=p_Add_q(M1,M2,r); |
---|
1289 | p_SetCoeff(m2,C1,r); |
---|
1290 | } |
---|
1291 | /* M1 is killed, M2=res = C2 M1 - C1 M2 */ |
---|
1292 | poly tmp=p_Copy(p1,r); |
---|
1293 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
1294 | M1=mm_Mult_p(m1,tmp,r); |
---|
1295 | tmp=p_Copy(p2,r); |
---|
1296 | tmp=p_LmDeleteAndNext(tmp,r); |
---|
1297 | M2=p_Add_q(M2,M1,r); |
---|
1298 | M1=mm_Mult_p(m2,tmp,r); |
---|
1299 | M2=p_Add_q(M2,M1,r); |
---|
1300 | p_Delete(&m1,r); |
---|
1301 | p_Delete(&m2,r); |
---|
1302 | // n_Delete(&C1,r); |
---|
1303 | // n_Delete(&C2,r); |
---|
1304 | n_Delete(&MinusOne,r); |
---|
1305 | #ifdef PDEBUG |
---|
1306 | p_Test(M2,r); |
---|
1307 | #endif |
---|
1308 | if (M2!=NULL) pCleardenom(M2); |
---|
1309 | if (M2!=NULL) pContent(M2); |
---|
1310 | return(M2); |
---|
1311 | } |
---|
1312 | |
---|
1313 | poly gnc_CreateSpolyNew(poly p1, poly p2/*,poly spNoether*/, const ring r) |
---|
1314 | { |
---|
1315 | const long lCompP1 = p_GetComp(p1,r); |
---|
1316 | const long lCompP2 = p_GetComp(p2,r); |
---|
1317 | |
---|
1318 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
1319 | { |
---|
1320 | #ifdef PDEBUG |
---|
1321 | Werror("gnc_CreateSpolyNew: different non-zero components!"); |
---|
1322 | #endif |
---|
1323 | return(NULL); |
---|
1324 | } |
---|
1325 | |
---|
1326 | // if ((r->nc->type==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */ |
---|
1327 | // { |
---|
1328 | // return(nc_p_Bracket_qq(pCopy(p2),p1)); |
---|
1329 | // } |
---|
1330 | |
---|
1331 | poly pL=pOne(); |
---|
1332 | |
---|
1333 | poly m1=pOne(); |
---|
1334 | poly m2=pOne(); |
---|
1335 | |
---|
1336 | pLcm(p1,p2,pL); // pL = lcm( lm(p1), lm(p2) ) |
---|
1337 | |
---|
1338 | p_Setm(pL,r); |
---|
1339 | |
---|
1340 | #ifdef PDEBUG |
---|
1341 | p_Test(pL,r); |
---|
1342 | #endif |
---|
1343 | |
---|
1344 | p_ExpVectorDiff(m1,pL,p1,r); // m1 = pL / lm(p1) |
---|
1345 | //p_SetComp(m1,0,r); |
---|
1346 | //p_Setm(m1,r); |
---|
1347 | #ifdef PDEBUG |
---|
1348 | p_Test(m1,r); |
---|
1349 | #endif |
---|
1350 | |
---|
1351 | p_ExpVectorDiff(m2,pL,p2,r); // m2 = pL / lm(p2) |
---|
1352 | |
---|
1353 | //p_SetComp(m2,0,r); |
---|
1354 | //p_Setm(m2,r); |
---|
1355 | #ifdef PDEBUG |
---|
1356 | p_Test(m2,r); |
---|
1357 | #endif |
---|
1358 | |
---|
1359 | p_Delete(&pL,r); |
---|
1360 | |
---|
1361 | /* zero exponents !? */ |
---|
1362 | poly M1 = mm_Mult_p(m1,p_Head(p1,r),r); // M1 = m1 * lt(p1) |
---|
1363 | poly M2 = mm_Mult_p(m2,p_Head(p2,r),r); // M2 = m2 * lt(p2) |
---|
1364 | |
---|
1365 | if(M1 == NULL || M2 == NULL) |
---|
1366 | { |
---|
1367 | #ifdef PDEBUG |
---|
1368 | Print("\np1 = "); |
---|
1369 | p_Write(p1, r); |
---|
1370 | |
---|
1371 | Print("m1 = "); |
---|
1372 | p_Write(m1, r); |
---|
1373 | |
---|
1374 | Print("p2 = "); |
---|
1375 | p_Write(p2, r); |
---|
1376 | |
---|
1377 | Print("m2 = "); |
---|
1378 | p_Write(m2, r); |
---|
1379 | |
---|
1380 | Werror("ERROR in nc_CreateSpoly: result of multiplication is Zero!\n"); |
---|
1381 | #endif |
---|
1382 | return(NULL); |
---|
1383 | } |
---|
1384 | |
---|
1385 | number C1 = n_Copy(p_GetCoeff(M1,r),r); // C1 = lc(M1) |
---|
1386 | number C2 = n_Copy(p_GetCoeff(M2,r),r); // C2 = lc(M2) |
---|
1387 | |
---|
1388 | /* GCD stuff */ |
---|
1389 | number C = nGcd(C1, C2, r); // C = gcd(C1, C2) |
---|
1390 | |
---|
1391 | if (!n_IsOne(C, r)) // if C != 1 |
---|
1392 | { |
---|
1393 | C1=n_Div(C1, C, r); // C1 = C1 / C |
---|
1394 | C2=n_Div(C2, C, r); // C2 = C2 / C |
---|
1395 | } |
---|
1396 | |
---|
1397 | n_Delete(&C,r); // destroy the number C |
---|
1398 | |
---|
1399 | C1=n_Neg(C1,r); |
---|
1400 | |
---|
1401 | // number MinusOne=n_Init(-1,r); |
---|
1402 | // if (n_Equal(C1,MinusOne,r)) // lc(M1) / gcd( lc(M1), lc(M2)) == -1 ???? |
---|
1403 | // { |
---|
1404 | // M2=p_Add_q(M1,M2,r); // ????? |
---|
1405 | // } |
---|
1406 | // else |
---|
1407 | // { |
---|
1408 | M1=p_Mult_nn(M1,C2,r); // M1 = (C2*lc(p1)) * (lcm(lm(p1),lm(p2)) / lm(p1)) * lm(p1) |
---|
1409 | M2=p_Mult_nn(M2,C1,r); // M2 =(-C1*lc(p2)) * (lcm(lm(p1),lm(p2)) / lm(p2)) * lm(p2) |
---|
1410 | M2=p_Add_q(M1,M2,r); // M1 is killed, M2 = spoly(lt(p1), lt(p2)) = C2*M1 - C1*M2 |
---|
1411 | // M2 == 0 for supercommutative algebras! |
---|
1412 | // } |
---|
1413 | // n_Delete(&MinusOne,r); |
---|
1414 | |
---|
1415 | p_SetCoeff(m1,C2,r); // lc(m1) = C2!!! |
---|
1416 | p_SetCoeff(m2,C1,r); // lc(m2) = C1!!! |
---|
1417 | |
---|
1418 | |
---|
1419 | poly tmp=p_Copy(p1,r); // tmp = p1 |
---|
1420 | tmp=p_LmDeleteAndNext(tmp,r); // tmp = tail(p1) |
---|
1421 | M1 = mm_Mult_p(m1,tmp,r); // M1 = m1 * tail(p1), delete tmp |
---|
1422 | tmp=p_Copy(p2,r); // tmp = p2 |
---|
1423 | tmp=p_LmDeleteAndNext(tmp,r); // tmp = tail(p2) |
---|
1424 | M2=p_Add_q(M2,M1,r); // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1), delete M1 |
---|
1425 | M1 = mm_Mult_p(m2,tmp,r); // M1 = m2 * tail(p2), detele tmp |
---|
1426 | M2=p_Add_q(M2,M1,r); // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1) + m2*tail(p2) |
---|
1427 | // delete M1 |
---|
1428 | |
---|
1429 | p_Delete(&m1,r); // => n_Delete(&C1,r); |
---|
1430 | p_Delete(&m2,r); // => n_Delete(&C2,r); |
---|
1431 | |
---|
1432 | #ifdef PDEBUG |
---|
1433 | p_Test(M2,r); |
---|
1434 | #endif |
---|
1435 | |
---|
1436 | if (M2!=NULL) pCleardenom(M2); |
---|
1437 | // if (M2!=NULL) pContent(M2); |
---|
1438 | |
---|
1439 | return(M2); |
---|
1440 | } |
---|
1441 | |
---|
1442 | |
---|
1443 | |
---|
1444 | |
---|
1445 | #if 0 |
---|
1446 | /*5 |
---|
1447 | * reduction of tail(q) with p1 |
---|
1448 | * lead(p1) divides lead(pNext(q2)) and pNext(q2) is reduced |
---|
1449 | * do not destroy p1, but tail(q) |
---|
1450 | */ |
---|
1451 | void gnc_ReduceSpolyTail(poly p1, poly q, poly q2, poly spNoether, const ring r) |
---|
1452 | { |
---|
1453 | poly a1=p_Head(p1,r); |
---|
1454 | poly Q=pNext(q2); |
---|
1455 | number cQ=p_GetCoeff(Q,r); |
---|
1456 | poly m=pOne(); |
---|
1457 | p_ExpVectorDiff(m,Q,p1,r); |
---|
1458 | // p_SetComp(m,0,r); |
---|
1459 | //p_Setm(m,r); |
---|
1460 | #ifdef PDEBUG |
---|
1461 | p_Test(m,r); |
---|
1462 | #endif |
---|
1463 | /* pSetComp(m,r)=0? */ |
---|
1464 | poly M = nc_mm_Mult_pp(m, p1,r); |
---|
1465 | number C=p_GetCoeff(M,r); |
---|
1466 | M=p_Add_q(M,mm_Mult_p(m,p_LmDeleteAndNext(p_Copy(p1,r),r),r),r); // _pp? |
---|
1467 | q=p_Mult_nn(q,C,r); |
---|
1468 | number MinusOne=n_Init(-1,r); |
---|
1469 | if (!n_Equal(cQ,MinusOne,r)) |
---|
1470 | { |
---|
1471 | cQ=nNeg(cQ); |
---|
1472 | M=p_Mult_nn(M,cQ,r); |
---|
1473 | } |
---|
1474 | Q=p_Add_q(Q,M,r); |
---|
1475 | pNext(q2)=Q; |
---|
1476 | |
---|
1477 | p_Delete(&m,r); |
---|
1478 | n_Delete(&C,r); |
---|
1479 | n_Delete(&cQ,r); |
---|
1480 | n_Delete(&MinusOne,r); |
---|
1481 | /* return(q); */ |
---|
1482 | } |
---|
1483 | #endif |
---|
1484 | |
---|
1485 | |
---|
1486 | /*6 |
---|
1487 | * creates the commutative lcm(lm(p1),lm(p2)) |
---|
1488 | * do not destroy p1 and p2 |
---|
1489 | */ |
---|
1490 | poly nc_CreateShortSpoly(poly p1, poly p2, const ring r) |
---|
1491 | { |
---|
1492 | if (p_GetComp(p1,r)!=p_GetComp(p2,r)) |
---|
1493 | { |
---|
1494 | #ifdef PDEBUG |
---|
1495 | Werror("nc_CreateShortSpoly: exponent mismatch!"); |
---|
1496 | #endif |
---|
1497 | return(NULL); |
---|
1498 | } |
---|
1499 | poly m=pOne(); |
---|
1500 | pLcm(p1,p2,m); |
---|
1501 | p_Setm(m,r); |
---|
1502 | #ifdef PDEBUG |
---|
1503 | p_Test(m,r); |
---|
1504 | #endif |
---|
1505 | return(m); |
---|
1506 | } |
---|
1507 | |
---|
1508 | void gnc_kBucketPolyRedOld(kBucket_pt b, poly p, number *c) |
---|
1509 | { |
---|
1510 | // b will not be multiplied by any constant in this impl. |
---|
1511 | // ==> *c=1 |
---|
1512 | *c=nInit(1); |
---|
1513 | poly m=pOne(); |
---|
1514 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
1515 | //pSetm(m); |
---|
1516 | #ifdef PDEBUG |
---|
1517 | pTest(m); |
---|
1518 | #endif |
---|
1519 | poly pp= nc_mm_Mult_pp(m,p,currRing); |
---|
1520 | pDelete(&m); |
---|
1521 | number n=nCopy(pGetCoeff(pp)); |
---|
1522 | number MinusOne=nInit(-1); |
---|
1523 | number nn; |
---|
1524 | if (!nEqual(n,MinusOne)) |
---|
1525 | { |
---|
1526 | nn=nNeg(nInvers(n)); |
---|
1527 | } |
---|
1528 | else nn=nInit(1); |
---|
1529 | nDelete(&n); |
---|
1530 | n=nMult(nn,pGetCoeff(kBucketGetLm(b))); |
---|
1531 | nDelete(&nn); |
---|
1532 | pp=p_Mult_nn(pp,n,currRing); |
---|
1533 | nDelete(&n); |
---|
1534 | nDelete(&MinusOne); |
---|
1535 | int l=pLength(pp); |
---|
1536 | kBucket_Add_q(b,pp,&l); |
---|
1537 | } |
---|
1538 | |
---|
1539 | void gnc_kBucketPolyRedNew(kBucket_pt b, poly p, number *c) |
---|
1540 | { |
---|
1541 | #ifdef PDEBUG |
---|
1542 | // Print(">*"); |
---|
1543 | #endif |
---|
1544 | |
---|
1545 | #ifdef KDEBUG |
---|
1546 | if( !kbTest(b) )Werror("nc_kBucketPolyRed: broken bucket!"); |
---|
1547 | #endif |
---|
1548 | |
---|
1549 | #ifdef PDEBUG |
---|
1550 | pTest(p); |
---|
1551 | // Print("p: "); pWrite(p); |
---|
1552 | #endif |
---|
1553 | |
---|
1554 | // b will not be multiplied by any constant in this impl. |
---|
1555 | // ==> *c=1 |
---|
1556 | *c=nInit(1); |
---|
1557 | poly m = pOne(); |
---|
1558 | const poly pLmB = kBucketGetLm(b); // no new copy! |
---|
1559 | |
---|
1560 | |
---|
1561 | #ifdef PDEBUG |
---|
1562 | pTest(pLmB); |
---|
1563 | // Print("pLmB: "); pWrite(pLmB); |
---|
1564 | #endif |
---|
1565 | |
---|
1566 | pExpVectorDiff(m, pLmB, p); |
---|
1567 | //pSetm(m); |
---|
1568 | |
---|
1569 | #ifdef PDEBUG |
---|
1570 | pTest(m); |
---|
1571 | #endif |
---|
1572 | |
---|
1573 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
1574 | pDelete(&m); |
---|
1575 | |
---|
1576 | const number n = pGetCoeff(pp); |
---|
1577 | number nn; |
---|
1578 | |
---|
1579 | if (!n_IsMOne(n,currRing) ) // does this improve performance??!? also see below... // TODO: check later on. |
---|
1580 | { |
---|
1581 | nn=nNeg(nInvers(nCopy(n))); |
---|
1582 | } |
---|
1583 | else nn=nInit(1); // if n == -1 => nn = 1 and -1/n otherwise |
---|
1584 | |
---|
1585 | number t = nMult(nn,pGetCoeff(pLmB)); |
---|
1586 | nDelete(&nn); |
---|
1587 | |
---|
1588 | pp = p_Mult_nn(pp,t,currRing); |
---|
1589 | nDelete(&t); |
---|
1590 | |
---|
1591 | int l = pLength(pp); |
---|
1592 | |
---|
1593 | #ifdef PDEBUG |
---|
1594 | pTest(pp); |
---|
1595 | // Print("PP: "); pWrite(pp); |
---|
1596 | #endif |
---|
1597 | |
---|
1598 | kBucket_Add_q(b,pp,&l); |
---|
1599 | |
---|
1600 | |
---|
1601 | #ifdef PDEBUG |
---|
1602 | // Print("*>"); |
---|
1603 | #endif |
---|
1604 | } |
---|
1605 | |
---|
1606 | |
---|
1607 | void gnc_kBucketPolyRed_ZOld(kBucket_pt b, poly p, number *c) |
---|
1608 | { |
---|
1609 | // b is multiplied by a constant in this impl. |
---|
1610 | poly m=pOne(); |
---|
1611 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
1612 | //pSetm(m); |
---|
1613 | #ifdef PDEBUG |
---|
1614 | pTest(m); |
---|
1615 | #endif |
---|
1616 | if(p_IsConstant(m,currRing)){ |
---|
1617 | pDelete(&m); |
---|
1618 | *c = kBucketPolyRed(b,p,pLength(p),NULL); |
---|
1619 | return; |
---|
1620 | } |
---|
1621 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
1622 | number c2,cc; |
---|
1623 | pCleardenom_n(pp,c2); |
---|
1624 | pDelete(&m); |
---|
1625 | *c = kBucketPolyRed(b,pp,pLength(pp),NULL); |
---|
1626 | //cc=*c; |
---|
1627 | //*c=nMult(*c,c2); |
---|
1628 | nDelete(&c2); |
---|
1629 | //nDelete(&cc); |
---|
1630 | pDelete(&pp); |
---|
1631 | |
---|
1632 | } |
---|
1633 | |
---|
1634 | void gnc_kBucketPolyRed_ZNew(kBucket_pt b, poly p, number *c) |
---|
1635 | { |
---|
1636 | // b is multiplied by a constant in this impl. |
---|
1637 | poly m=pOne(); |
---|
1638 | pExpVectorDiff(m,kBucketGetLm(b),p); |
---|
1639 | //pSetm(m); |
---|
1640 | #ifdef PDEBUG |
---|
1641 | pTest(m); |
---|
1642 | #endif |
---|
1643 | |
---|
1644 | if(p_IsConstant(m,currRing)) |
---|
1645 | { |
---|
1646 | pDelete(&m); |
---|
1647 | *c = kBucketPolyRed(b,p,pLength(p),NULL); |
---|
1648 | return; |
---|
1649 | } |
---|
1650 | poly pp = nc_mm_Mult_pp(m,p,currRing); |
---|
1651 | number c2,cc; |
---|
1652 | pCleardenom_n(pp,c2); |
---|
1653 | pDelete(&m); |
---|
1654 | *c = kBucketPolyRed(b,pp,pLength(pp),NULL); |
---|
1655 | //cc=*c; |
---|
1656 | //*c=nMult(*c,c2); |
---|
1657 | nDelete(&c2); |
---|
1658 | //nDelete(&cc); |
---|
1659 | pDelete(&pp); |
---|
1660 | |
---|
1661 | } |
---|
1662 | |
---|
1663 | |
---|
1664 | inline void nc_PolyPolyRedOld(poly &b, poly p, number *c) |
---|
1665 | // reduces b with p, do not delete both |
---|
1666 | { |
---|
1667 | // b will not by multiplied by any constant in this impl. |
---|
1668 | // ==> *c=1 |
---|
1669 | *c=nInit(1); |
---|
1670 | poly m=pOne(); |
---|
1671 | pExpVectorDiff(m,pHead(b),p); |
---|
1672 | //pSetm(m); |
---|
1673 | #ifdef PDEBUG |
---|
1674 | pTest(m); |
---|
1675 | #endif |
---|
1676 | poly pp=nc_mm_Mult_pp(m,p,currRing); |
---|
1677 | pDelete(&m); |
---|
1678 | number n=nCopy(pGetCoeff(pp)); |
---|
1679 | number MinusOne=nInit(-1); |
---|
1680 | number nn; |
---|
1681 | if (!nEqual(n,MinusOne)) |
---|
1682 | { |
---|
1683 | nn=nNeg(nInvers(n)); |
---|
1684 | } |
---|
1685 | else nn=nInit(1); |
---|
1686 | nDelete(&n); |
---|
1687 | n=nMult(nn,pGetCoeff(b)); |
---|
1688 | nDelete(&nn); |
---|
1689 | pp=p_Mult_nn(pp,n,currRing); |
---|
1690 | nDelete(&n); |
---|
1691 | nDelete(&MinusOne); |
---|
1692 | b=p_Add_q(b,pp,currRing); |
---|
1693 | } |
---|
1694 | |
---|
1695 | |
---|
1696 | |
---|
1697 | inline void nc_PolyPolyRedNew(poly &b, poly p, number *c) |
---|
1698 | // reduces b with p, do not delete both |
---|
1699 | { |
---|
1700 | // b will not by multiplied by any constant in this impl. |
---|
1701 | // ==> *c=1 |
---|
1702 | *c=nInit(1); |
---|
1703 | poly m=pOne(); |
---|
1704 | |
---|
1705 | poly pLmB = pHead(b); |
---|
1706 | pExpVectorDiff(m, pLmB, p); |
---|
1707 | pDelete(&pLmB); |
---|
1708 | //pSetm(m); |
---|
1709 | #ifdef PDEBUG |
---|
1710 | pTest(m); |
---|
1711 | #endif |
---|
1712 | poly pp=nc_mm_Mult_pp(m, p, currRing); |
---|
1713 | pDelete(&m); |
---|
1714 | |
---|
1715 | const number n = pGetCoeff(pp); // no new copy |
---|
1716 | |
---|
1717 | number nn; |
---|
1718 | |
---|
1719 | if (!n_IsMOne(n, currRing)) // TODO: as above. |
---|
1720 | { |
---|
1721 | nn=nNeg(nInvers(nCopy(n))); |
---|
1722 | } |
---|
1723 | else nn=nInit(1); |
---|
1724 | |
---|
1725 | number t = nMult(nn, pGetCoeff(b)); |
---|
1726 | nDelete(&nn); |
---|
1727 | |
---|
1728 | pp=p_Mult_nn(pp, t, currRing); |
---|
1729 | nDelete(&t); |
---|
1730 | |
---|
1731 | b=p_Add_q(b,pp,currRing); |
---|
1732 | |
---|
1733 | } |
---|
1734 | |
---|
1735 | void nc_PolyPolyRed(poly &b, poly p, number *c) |
---|
1736 | { |
---|
1737 | nc_PolyPolyRedOld(b, p, c); |
---|
1738 | } |
---|
1739 | |
---|
1740 | |
---|
1741 | poly nc_mm_Bracket_nn(poly m1, poly m2); |
---|
1742 | |
---|
1743 | poly nc_p_Bracket_qq(poly p, poly q) |
---|
1744 | /* returns [p,q], destroys p */ |
---|
1745 | { |
---|
1746 | if (!rIsPluralRing(currRing)) return(NULL); |
---|
1747 | if (pComparePolys(p,q)) return(NULL); |
---|
1748 | /* Components !? */ |
---|
1749 | poly Q=NULL; |
---|
1750 | number coef=NULL; |
---|
1751 | poly res=NULL; |
---|
1752 | poly pres=NULL; |
---|
1753 | int UseBuckets=1; |
---|
1754 | if ((pLength(p)< MIN_LENGTH_BUCKET/2) && (pLength(q)< MIN_LENGTH_BUCKET/2) || TEST_OPT_NOT_BUCKETS) UseBuckets=0; |
---|
1755 | sBucket_pt bu_out; |
---|
1756 | if (UseBuckets) bu_out=sBucketCreate(currRing); |
---|
1757 | while (p!=NULL) |
---|
1758 | { |
---|
1759 | Q=q; |
---|
1760 | while(Q!=NULL) |
---|
1761 | { |
---|
1762 | pres=nc_mm_Bracket_nn(p,Q); /* since no coeffs are taken into account there */ |
---|
1763 | if (pres!=NULL) |
---|
1764 | { |
---|
1765 | coef = nMult(pGetCoeff(p),pGetCoeff(Q)); |
---|
1766 | pres = p_Mult_nn(pres,coef,currRing); |
---|
1767 | if (UseBuckets) sBucket_Add_p(bu_out,pres,pLength(pres)); |
---|
1768 | else res=p_Add_q(res,pres,currRing); |
---|
1769 | nDelete(&coef); |
---|
1770 | } |
---|
1771 | pIter(Q); |
---|
1772 | } |
---|
1773 | p=pLmDeleteAndNext(p); |
---|
1774 | } |
---|
1775 | if (UseBuckets) |
---|
1776 | { |
---|
1777 | res = NULL; |
---|
1778 | int len = pLength(res); |
---|
1779 | sBucketDestroyAdd(bu_out, &res, &len); |
---|
1780 | } |
---|
1781 | return(res); |
---|
1782 | } |
---|
1783 | |
---|
1784 | poly nc_mm_Bracket_nn(poly m1, poly m2) |
---|
1785 | /*returns [m1,m2] for two monoms, destroys nothing */ |
---|
1786 | /* without coeffs */ |
---|
1787 | { |
---|
1788 | if (pLmIsConstant(m1) || pLmIsConstant(m1)) return(NULL); |
---|
1789 | if (pLmCmp(m1,m2)==0) return(NULL); |
---|
1790 | int rN=currRing->N; |
---|
1791 | int *M1=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
1792 | int *M2=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
1793 | int *PREFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
1794 | int *SUFFIX=(int *)omAlloc0((rN+1)*sizeof(int)); |
---|
1795 | pGetExpV(m1,M1); |
---|
1796 | pGetExpV(m2,M2); |
---|
1797 | poly res=NULL; |
---|
1798 | poly ares=NULL; |
---|
1799 | poly bres=NULL; |
---|
1800 | poly prefix=NULL; |
---|
1801 | poly suffix=NULL; |
---|
1802 | int nMin,nMax; |
---|
1803 | number nTmp=NULL; |
---|
1804 | int i,j,k; |
---|
1805 | for (i=1;i<=rN;i++) |
---|
1806 | { |
---|
1807 | if (M2[i]!=0) |
---|
1808 | { |
---|
1809 | ares=NULL; |
---|
1810 | for (j=1;j<=rN;j++) |
---|
1811 | { |
---|
1812 | if (M1[j]!=0) |
---|
1813 | { |
---|
1814 | bres=NULL; |
---|
1815 | /* compute [ x_j^M1[j],x_i^M2[i] ] */ |
---|
1816 | if (i<j) {nMax=j; nMin=i;} else {nMax=i; nMin=j;} |
---|
1817 | if ( (i==j) || ((MATELEM(currRing->nc->COM,nMin,nMax)!=NULL) && nIsOne(pGetCoeff(MATELEM(currRing->nc->C,nMin,nMax))) )) /* not (the same exp. or commuting exps)*/ |
---|
1818 | { bres=NULL; } |
---|
1819 | else |
---|
1820 | { |
---|
1821 | if (i<j) { bres=gnc_uu_Mult_ww(j,M1[j],i,M2[i],currRing); } |
---|
1822 | else bres=gnc_uu_Mult_ww(i,M2[i],j,M1[j],currRing); |
---|
1823 | if (nIsOne(pGetCoeff(bres))) |
---|
1824 | { |
---|
1825 | bres=pLmDeleteAndNext(bres); |
---|
1826 | } |
---|
1827 | else |
---|
1828 | { |
---|
1829 | nTmp=nSub(pGetCoeff(bres),nInit(1)); |
---|
1830 | pSetCoeff(bres,nTmp); /* only lc ! */ |
---|
1831 | } |
---|
1832 | #ifdef PDEBUG |
---|
1833 | pTest(bres); |
---|
1834 | #endif |
---|
1835 | if (i>j) bres=p_Neg(bres, currRing); |
---|
1836 | } |
---|
1837 | if (bres!=NULL) |
---|
1838 | { |
---|
1839 | /* now mult (prefix, bres, suffix) */ |
---|
1840 | memcpy(SUFFIX, M1,(rN+1)*sizeof(int)); |
---|
1841 | memcpy(PREFIX, M1,(rN+1)*sizeof(int)); |
---|
1842 | for (k=1;k<=j;k++) SUFFIX[k]=0; |
---|
1843 | for (k=j;k<=rN;k++) PREFIX[k]=0; |
---|
1844 | SUFFIX[0]=0; |
---|
1845 | PREFIX[0]=0; |
---|
1846 | prefix=pOne(); |
---|
1847 | suffix=pOne(); |
---|
1848 | pSetExpV(prefix,PREFIX); |
---|
1849 | pSetm(prefix); |
---|
1850 | pSetExpV(suffix,SUFFIX); |
---|
1851 | pSetm(suffix); |
---|
1852 | if (!pLmIsConstant(prefix)) bres = gnc_mm_Mult_p(prefix, bres,currRing); |
---|
1853 | if (!pLmIsConstant(suffix)) bres = gnc_p_Mult_mm(bres, suffix,currRing); |
---|
1854 | ares=p_Add_q(ares, bres,currRing); |
---|
1855 | /* What to give free? */ |
---|
1856 | /* Do we have to free PREFIX/SUFFIX? it seems so */ |
---|
1857 | pDelete(&prefix); |
---|
1858 | pDelete(&suffix); |
---|
1859 | } |
---|
1860 | } |
---|
1861 | } |
---|
1862 | if (ares!=NULL) |
---|
1863 | { |
---|
1864 | /* now mult (prefix, bres, suffix) */ |
---|
1865 | memcpy(SUFFIX, M2,(rN+1)*sizeof(int)); |
---|
1866 | memcpy(PREFIX, M2,(rN+1)*sizeof(int)); |
---|
1867 | for (k=1;k<=i;k++) SUFFIX[k]=0; |
---|
1868 | for (k=i;k<=rN;k++) PREFIX[k]=0; |
---|
1869 | SUFFIX[0]=0; |
---|
1870 | PREFIX[0]=0; |
---|
1871 | prefix=pOne(); |
---|
1872 | suffix=pOne(); |
---|
1873 | pSetExpV(prefix,PREFIX); |
---|
1874 | pSetm(prefix); |
---|
1875 | pSetExpV(suffix,SUFFIX); |
---|
1876 | pSetm(suffix); |
---|
1877 | bres=ares; |
---|
1878 | if (!pLmIsConstant(prefix)) bres = gnc_mm_Mult_p(prefix, bres,currRing); |
---|
1879 | if (!pLmIsConstant(suffix)) bres = gnc_p_Mult_mm(bres, suffix,currRing); |
---|
1880 | res=p_Add_q(res, bres,currRing); |
---|
1881 | pDelete(&prefix); |
---|
1882 | pDelete(&suffix); |
---|
1883 | } |
---|
1884 | } |
---|
1885 | } |
---|
1886 | freeT(M1, rN); |
---|
1887 | freeT(M2, rN); |
---|
1888 | freeT(PREFIX, rN); |
---|
1889 | freeT(SUFFIX, rN); |
---|
1890 | pTest(res); |
---|
1891 | return(res); |
---|
1892 | } |
---|
1893 | |
---|
1894 | ideal twostd(ideal I) |
---|
1895 | { |
---|
1896 | int i; |
---|
1897 | int j; |
---|
1898 | int s; |
---|
1899 | int flag; |
---|
1900 | poly p=NULL; |
---|
1901 | poly q=NULL; |
---|
1902 | ideal J=kStd(I, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
1903 | idSkipZeroes(J); |
---|
1904 | ideal K=NULL; |
---|
1905 | poly varj=NULL; |
---|
1906 | ideal Q=NULL; |
---|
1907 | ideal id_tmp=NULL; |
---|
1908 | int rN=currRing->N; |
---|
1909 | int iSize=0; |
---|
1910 | loop |
---|
1911 | { |
---|
1912 | flag=0; |
---|
1913 | K=NULL; |
---|
1914 | s=idElem(J); |
---|
1915 | for (i=0;i<=s-1;i++) |
---|
1916 | { |
---|
1917 | p=J->m[i]; |
---|
1918 | for (j=1;j<=rN;j++) |
---|
1919 | { |
---|
1920 | varj = pOne(); |
---|
1921 | pSetExp(varj,j,1); |
---|
1922 | pSetm(varj); |
---|
1923 | q = pp_Mult_mm(p,varj,currRing); |
---|
1924 | pDelete(&varj); |
---|
1925 | q = nc_ReduceSPoly(p,q,currRing); |
---|
1926 | q = kNF(J,currQuotient,q,0,0); |
---|
1927 | if (q!=NULL) |
---|
1928 | { |
---|
1929 | if (pIsConstant(q)) |
---|
1930 | { |
---|
1931 | Q=idInit(1,1); |
---|
1932 | Q->m[0]=pOne(); |
---|
1933 | idDelete(&J); |
---|
1934 | pDelete(&q); |
---|
1935 | if (K!=NULL) idDelete(&K); |
---|
1936 | return(Q); |
---|
1937 | } |
---|
1938 | flag=1; |
---|
1939 | Q=idInit(1,1); |
---|
1940 | Q->m[0]=q; |
---|
1941 | id_tmp=idSimpleAdd(K,Q); |
---|
1942 | idDelete(&K); |
---|
1943 | K=id_tmp; |
---|
1944 | idDelete(&Q); |
---|
1945 | } |
---|
1946 | } |
---|
1947 | } |
---|
1948 | if (flag==0) |
---|
1949 | /* i.e. all elements are two-sided */ |
---|
1950 | { |
---|
1951 | idDelete(&K); |
---|
1952 | return(J); |
---|
1953 | } |
---|
1954 | /* now we update GrBasis J with K */ |
---|
1955 | // iSize=IDELEMS(J); |
---|
1956 | iSize=idElem(J); |
---|
1957 | id_tmp=idSimpleAdd(J,K); |
---|
1958 | idDelete(&K); |
---|
1959 | idDelete(&J); |
---|
1960 | BITSET save_test=test; |
---|
1961 | test|=Sy_bit(OPT_SB_1); |
---|
1962 | J=kStd(id_tmp, currQuotient, testHomog,NULL,NULL,0,iSize); |
---|
1963 | test=save_test; |
---|
1964 | idSkipZeroes(J); |
---|
1965 | } |
---|
1966 | } |
---|
1967 | |
---|
1968 | matrix nc_PrintMat(int a, int b, ring r, int metric) |
---|
1969 | /* returns matrix with the info on noncomm multiplication */ |
---|
1970 | { |
---|
1971 | |
---|
1972 | if ( (a==b) || !rIsPluralRing(r) ) return(NULL); |
---|
1973 | int i; |
---|
1974 | int j; |
---|
1975 | if (a>b) {j=b; i=a;} |
---|
1976 | else {j=a; i=b;} |
---|
1977 | /* i<j */ |
---|
1978 | int rN=r->N; |
---|
1979 | int size=r->nc->MTsize[UPMATELEM(i,j,rN)]; |
---|
1980 | matrix M = r->nc->MT[UPMATELEM(i,j,rN)]; |
---|
1981 | /* return(M); */ |
---|
1982 | int sizeofres; |
---|
1983 | if (metric==0) |
---|
1984 | { |
---|
1985 | sizeofres=sizeof(int); |
---|
1986 | } |
---|
1987 | if (metric==1) |
---|
1988 | { |
---|
1989 | sizeofres=sizeof(number); |
---|
1990 | } |
---|
1991 | matrix res=mpNew(size,size); |
---|
1992 | int s; |
---|
1993 | int t; |
---|
1994 | int length; |
---|
1995 | long totdeg; |
---|
1996 | poly p; |
---|
1997 | for(s=1;s<=size;s++) |
---|
1998 | { |
---|
1999 | for(t=1;t<=size;t++) |
---|
2000 | { |
---|
2001 | p=MATELEM(M,s,t); |
---|
2002 | if (p==NULL) |
---|
2003 | { |
---|
2004 | MATELEM(res,s,t)=0; |
---|
2005 | } |
---|
2006 | else |
---|
2007 | { |
---|
2008 | length = pLength(p); |
---|
2009 | if (metric==0) /* length */ |
---|
2010 | { |
---|
2011 | MATELEM(res,s,t)= p_ISet(length,r); |
---|
2012 | } |
---|
2013 | else if (metric==1) /* sum of deg divided by the length */ |
---|
2014 | { |
---|
2015 | totdeg=0; |
---|
2016 | while (p!=NULL) |
---|
2017 | { |
---|
2018 | totdeg=totdeg+pDeg(p,r); |
---|
2019 | pIter(p); |
---|
2020 | } |
---|
2021 | number ntd = nInit(totdeg); |
---|
2022 | number nln = nInit(length); |
---|
2023 | number nres=nDiv(ntd,nln); |
---|
2024 | nDelete(&ntd); |
---|
2025 | nDelete(&nln); |
---|
2026 | MATELEM(res,s,t)=p_NSet(nres,r); |
---|
2027 | } |
---|
2028 | } |
---|
2029 | } |
---|
2030 | } |
---|
2031 | return(res); |
---|
2032 | } |
---|
2033 | |
---|
2034 | void ncKill(ring r) |
---|
2035 | /* kills the nc extension of ring r */ |
---|
2036 | { |
---|
2037 | int i,j; |
---|
2038 | int rN=r->N; |
---|
2039 | if ( rN > 1 ) |
---|
2040 | { |
---|
2041 | for(i=1;i<rN;i++) |
---|
2042 | { |
---|
2043 | for(j=i+1;j<=rN;j++) |
---|
2044 | { |
---|
2045 | id_Delete((ideal *)&(r->nc->MT[UPMATELEM(i,j,rN)]),r->nc->basering); |
---|
2046 | } |
---|
2047 | } |
---|
2048 | omFreeSize((ADDRESS)r->nc->MT,rN*(rN-1)/2*sizeof(matrix)); |
---|
2049 | omFreeSize((ADDRESS)r->nc->MTsize,rN*(rN-1)/2*sizeof(int)); |
---|
2050 | id_Delete((ideal *)&(r->nc->COM),r->nc->basering); |
---|
2051 | } |
---|
2052 | id_Delete((ideal *)&(r->nc->C),r->nc->basering); |
---|
2053 | id_Delete((ideal *)&(r->nc->D),r->nc->basering); |
---|
2054 | r->nc->basering->ref--; |
---|
2055 | if (r->nc->basering<=0) |
---|
2056 | { |
---|
2057 | rKill(r->nc->basering); |
---|
2058 | } |
---|
2059 | omFreeSize((ADDRESS)r->nc,sizeof(nc_struct)); |
---|
2060 | r->nc=NULL; |
---|
2061 | } |
---|
2062 | |
---|
2063 | void ncCleanUp(ring r) |
---|
2064 | { |
---|
2065 | /* small CleanUp of r->nc */ |
---|
2066 | omFreeSize((ADDRESS)r->nc,sizeof(nc_struct)); |
---|
2067 | r->nc = NULL; |
---|
2068 | } |
---|
2069 | |
---|
2070 | poly nc_p_CopyGet(poly a, const ring r) |
---|
2071 | /* for use in getting the mult. matrix elements*/ |
---|
2072 | /* ring r must be a currRing! */ |
---|
2073 | /* for consistency, copies a poly from the comm. r->nc->basering */ |
---|
2074 | /* to its image in NC ring */ |
---|
2075 | { |
---|
2076 | if (r != currRing) |
---|
2077 | { |
---|
2078 | #ifdef PDEBUF |
---|
2079 | Werror("nc_p_CopyGet call not in currRing"); |
---|
2080 | #endif |
---|
2081 | return(NULL); |
---|
2082 | } |
---|
2083 | if (!rIsPluralRing(r)) return(p_Copy(a,r)); |
---|
2084 | if (r==r->nc->basering) return(p_Copy(a,r)); |
---|
2085 | else |
---|
2086 | { |
---|
2087 | return(prCopyR_NoSort(a,r->nc->basering,r)); |
---|
2088 | } |
---|
2089 | } |
---|
2090 | |
---|
2091 | poly nc_p_CopyPut(poly a, const ring r) |
---|
2092 | /* for use in defining the mult. matrix elements*/ |
---|
2093 | /* ring r must be a currRing! */ |
---|
2094 | /* for consistency, puts a polynomial from the NC ring */ |
---|
2095 | /* to its presentation in the comm. r->nc->basering */ |
---|
2096 | { |
---|
2097 | if (r != currRing) |
---|
2098 | { |
---|
2099 | #ifdef PDEBUF |
---|
2100 | Werror("nc_p_CopyGet call not in currRing"); |
---|
2101 | #endif |
---|
2102 | return(NULL); |
---|
2103 | } |
---|
2104 | if (!rIsPluralRing(r)) return(p_Copy(a,r)); |
---|
2105 | if (r==r->nc->basering) return(p_Copy(a,r)); |
---|
2106 | else |
---|
2107 | { |
---|
2108 | return(prCopyR_NoSort(a,r,r->nc->basering)); |
---|
2109 | } |
---|
2110 | } |
---|
2111 | |
---|
2112 | BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r) |
---|
2113 | /* returns TRUE if there were errors */ |
---|
2114 | /* checks whether product of vars from PolyVar defines */ |
---|
2115 | /* an admissible subalgebra of r */ |
---|
2116 | /* r is indeed currRing and assumed to be noncomm. */ |
---|
2117 | { |
---|
2118 | ring save = currRing; |
---|
2119 | int WeChangeRing = 0; |
---|
2120 | if (currRing != r) |
---|
2121 | { |
---|
2122 | rChangeCurrRing(r); |
---|
2123 | WeChangeRing = 1; |
---|
2124 | } |
---|
2125 | int rN=r->N; |
---|
2126 | int *ExpVar=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
2127 | int *ExpTmp=(int*)omAlloc0((rN+1)*sizeof(int)); |
---|
2128 | p_GetExpV(PolyVar, ExpVar, r); |
---|
2129 | int i; int j; int k; |
---|
2130 | poly test=NULL; |
---|
2131 | int OK=1; |
---|
2132 | for (i=1; i<rN; i++) |
---|
2133 | { |
---|
2134 | if (ExpVar[i]==0) /* i.e. not in PolyVar */ |
---|
2135 | { |
---|
2136 | for (j=i+1; j<=rN; j++) |
---|
2137 | { |
---|
2138 | if (ExpVar[j]==0) |
---|
2139 | { |
---|
2140 | test = nc_p_CopyGet(MATELEM(r->nc->D,i,j),r); |
---|
2141 | while (test!=NULL) |
---|
2142 | { |
---|
2143 | p_GetExpV(test, ExpTmp, r); |
---|
2144 | OK=1; |
---|
2145 | for (k=1;k<=rN;k++) |
---|
2146 | { |
---|
2147 | if (ExpTmp[k]!=0) |
---|
2148 | { |
---|
2149 | if (ExpVar[k]!=0) OK=0; |
---|
2150 | } |
---|
2151 | } |
---|
2152 | if (!OK) return(TRUE); |
---|
2153 | pIter(test); |
---|
2154 | } |
---|
2155 | } |
---|
2156 | } |
---|
2157 | } |
---|
2158 | } |
---|
2159 | p_Delete(&test,r); |
---|
2160 | freeT(ExpVar,rN); |
---|
2161 | freeT(ExpTmp,rN); |
---|
2162 | if ( WeChangeRing ) |
---|
2163 | rChangeCurrRing(save); |
---|
2164 | return(FALSE); |
---|
2165 | } |
---|
2166 | |
---|
2167 | BOOLEAN nc_CheckOrdCondition(matrix D, ring r) |
---|
2168 | /* returns TRUE if there were errors */ |
---|
2169 | /* checks whether the current ordering */ |
---|
2170 | /* is admissible for r and D == r->nc->D */ |
---|
2171 | /* to be executed in a currRing */ |
---|
2172 | { |
---|
2173 | /* analyze D: an upper triangular matrix of polys */ |
---|
2174 | /* check the ordering condition for D */ |
---|
2175 | ring save = currRing; |
---|
2176 | int WeChangeRing = 0; |
---|
2177 | if (r != currRing) |
---|
2178 | { |
---|
2179 | rChangeCurrRing(r); |
---|
2180 | WeChangeRing = 1; |
---|
2181 | } |
---|
2182 | poly p,q; |
---|
2183 | int i,j; |
---|
2184 | int report = 0; |
---|
2185 | for(i=1; i<r->N; i++) |
---|
2186 | { |
---|
2187 | for(j=i+1; j<=r->N; j++) |
---|
2188 | { |
---|
2189 | p = nc_p_CopyGet(MATELEM(D,i,j),r); |
---|
2190 | if ( p != NULL) |
---|
2191 | { |
---|
2192 | q = p_ISet(1,r); // replaces pOne(); |
---|
2193 | p_SetExp(q,i,1,r); |
---|
2194 | p_SetExp(q,j,1,r); |
---|
2195 | p_Setm(q,r); |
---|
2196 | if (p_LmCmp(q,p,r) != 1) /* i.e. lm(p)==xy < lm(q)==D_ij */ |
---|
2197 | { |
---|
2198 | Print("Bad ordering at %d,%d\n",i,j); |
---|
2199 | #ifdef PDEBUG |
---|
2200 | p_Write(p,r); |
---|
2201 | p_Write(q,r); |
---|
2202 | #endif |
---|
2203 | report = 1; |
---|
2204 | } |
---|
2205 | p_Delete(&q,r); |
---|
2206 | p_Delete(&p,r); |
---|
2207 | p = NULL; |
---|
2208 | } |
---|
2209 | } |
---|
2210 | } |
---|
2211 | if ( WeChangeRing ) |
---|
2212 | rChangeCurrRing(save); |
---|
2213 | return(report); |
---|
2214 | } |
---|
2215 | |
---|
2216 | |
---|
2217 | |
---|
2218 | BOOLEAN nc_CallPlural(matrix CCC, matrix DDD, poly CCN, poly DDN, ring r) |
---|
2219 | /* returns TRUE if there were errors */ |
---|
2220 | /* analyze inputs, check them for consistency */ |
---|
2221 | /* detects nc_type, DO NOT initialize multiplication but call for it at the end*/ |
---|
2222 | /* checks the ordering condition and evtl. NDC */ |
---|
2223 | { |
---|
2224 | matrix CC = NULL; |
---|
2225 | matrix DD = NULL; |
---|
2226 | poly CN = NULL; |
---|
2227 | poly DN = NULL; |
---|
2228 | matrix C; |
---|
2229 | matrix D; |
---|
2230 | number nN,pN,qN; |
---|
2231 | int tmpIsSkewConstant; |
---|
2232 | int i,j; |
---|
2233 | if (r->nc != NULL) |
---|
2234 | { |
---|
2235 | WarnS("redefining algebra structure"); |
---|
2236 | if (r->nc->ref>1) /* in use by somebody else */ |
---|
2237 | { |
---|
2238 | r->nc->ref--; |
---|
2239 | } |
---|
2240 | else /* kill the previous nc data */ |
---|
2241 | { |
---|
2242 | ncKill(r); |
---|
2243 | } |
---|
2244 | } |
---|
2245 | ring save = currRing; |
---|
2246 | int WeChangeRing = 0; |
---|
2247 | if (currRing!=r) |
---|
2248 | { |
---|
2249 | rChangeCurrRing(r); |
---|
2250 | WeChangeRing = 1; |
---|
2251 | } |
---|
2252 | r->nc = (nc_struct *)omAlloc0(sizeof(nc_struct)); |
---|
2253 | r->nc->ref = 1; |
---|
2254 | r->nc->basering = r; |
---|
2255 | r->ref++; |
---|
2256 | r->nc->type = nc_undef; |
---|
2257 | |
---|
2258 | /* initialition of the matrix C */ |
---|
2259 | /* check the correctness of arguments */ |
---|
2260 | |
---|
2261 | if ((CCC != NULL) && ( (MATCOLS(CCC)==1) || MATROWS(CCC)==1 ) ) |
---|
2262 | { |
---|
2263 | CN = MATELEM(CCC,1,1); |
---|
2264 | } |
---|
2265 | else |
---|
2266 | { |
---|
2267 | if ((CCC != NULL) && ( (MATCOLS(CCC)!=r->N) || (MATROWS(CCC)!=r->N) )) |
---|
2268 | { |
---|
2269 | Werror("Square %d x %d matrix expected",r->N,r->N); |
---|
2270 | ncCleanUp(r); |
---|
2271 | if (WeChangeRing) |
---|
2272 | rChangeCurrRing(save); |
---|
2273 | return TRUE; |
---|
2274 | } |
---|
2275 | } |
---|
2276 | if (( CCC != NULL) && (CC == NULL)) CC = mpCopy(CCC); |
---|
2277 | if (( CCN != NULL) && (CN == NULL)) CN = CCN; |
---|
2278 | |
---|
2279 | /* initialition of the matrix D */ |
---|
2280 | /* check the correctness of arguments */ |
---|
2281 | |
---|
2282 | if ((DDD != NULL) && ( (MATCOLS(DDD)==1) || MATROWS(DDD)==1 ) ) |
---|
2283 | { |
---|
2284 | DN = MATELEM(DDD,1,1); |
---|
2285 | } |
---|
2286 | else |
---|
2287 | { |
---|
2288 | if ((DDD != NULL) && ( (MATCOLS(DDD)!=r->N) || (MATROWS(DDD)!=r->N) )) |
---|
2289 | { |
---|
2290 | Werror("Square %d x %d matrix expected",r->N,r->N); |
---|
2291 | ncCleanUp(r); |
---|
2292 | if (WeChangeRing) |
---|
2293 | rChangeCurrRing(save); |
---|
2294 | return TRUE; |
---|
2295 | } |
---|
2296 | } |
---|
2297 | if (( DDD != NULL) && (DD == NULL)) DD = mpCopy(DDD); |
---|
2298 | if (( DDN != NULL) && (DN == NULL)) DN = DDN; |
---|
2299 | |
---|
2300 | /* further checks */ |
---|
2301 | |
---|
2302 | if (CN != NULL) /* create matrix C = CN * Id */ |
---|
2303 | { |
---|
2304 | nN = p_GetCoeff(CN,r); |
---|
2305 | if (n_IsZero(nN,r)) |
---|
2306 | { |
---|
2307 | Werror("Incorrect input : zero coefficients are not allowed"); |
---|
2308 | ncCleanUp(r); |
---|
2309 | if (WeChangeRing) |
---|
2310 | rChangeCurrRing(save); |
---|
2311 | return TRUE; |
---|
2312 | } |
---|
2313 | if (nIsOne(nN)) |
---|
2314 | { |
---|
2315 | r->nc->type = nc_lie; |
---|
2316 | } |
---|
2317 | else |
---|
2318 | { |
---|
2319 | r->nc->type = nc_general; |
---|
2320 | } |
---|
2321 | r->nc->IsSkewConstant = 1; |
---|
2322 | C = mpNew(r->N,r->N); |
---|
2323 | for(i=1; i<r->N; i++) |
---|
2324 | { |
---|
2325 | for(j=i+1; j<=r->N; j++) |
---|
2326 | { |
---|
2327 | MATELEM(C,i,j) = nc_p_CopyPut(CN,r); |
---|
2328 | } |
---|
2329 | } |
---|
2330 | } |
---|
2331 | if ( (CN == NULL) && (CC != NULL) ) /* copy matrix C */ |
---|
2332 | { |
---|
2333 | C = mpCopy(CC); |
---|
2334 | /* analyze C */ |
---|
2335 | if ( MATELEM(C,1,2) == NULL ) |
---|
2336 | pN = NULL; /* check the consistency later */ |
---|
2337 | else |
---|
2338 | pN = p_GetCoeff(MATELEM(C,1,2),r); |
---|
2339 | tmpIsSkewConstant = 1; |
---|
2340 | for(i=1; i<r->N; i++) |
---|
2341 | { |
---|
2342 | for(j=i+1; j<=r->N; j++) |
---|
2343 | { |
---|
2344 | if (MATELEM(C,i,j) == NULL) |
---|
2345 | qN = NULL; |
---|
2346 | else |
---|
2347 | qN = p_GetCoeff(MATELEM(C,i,j),r); |
---|
2348 | if ( qN == NULL ) /* check the consistency: Cij!=0 */ |
---|
2349 | // find also illegal pN |
---|
2350 | { |
---|
2351 | Werror("Incorrect input : matrix of coefficients contains zeros in the upper triangle"); |
---|
2352 | ncCleanUp(r); |
---|
2353 | if (WeChangeRing) |
---|
2354 | rChangeCurrRing(save); |
---|
2355 | return TRUE; |
---|
2356 | } |
---|
2357 | if (!nEqual(pN,qN)) tmpIsSkewConstant = 0; |
---|
2358 | } |
---|
2359 | } |
---|
2360 | r->nc->IsSkewConstant=tmpIsSkewConstant; |
---|
2361 | if ( (tmpIsSkewConstant) && (nIsOne(pN)) ) |
---|
2362 | { |
---|
2363 | r->nc->type = nc_lie; |
---|
2364 | } |
---|
2365 | else |
---|
2366 | { |
---|
2367 | r->nc->type = nc_general; |
---|
2368 | } |
---|
2369 | } |
---|
2370 | |
---|
2371 | /* initialition of the matrix D */ |
---|
2372 | if ( DD == NULL ) |
---|
2373 | /* we treat DN only (it could also be NULL) */ |
---|
2374 | { |
---|
2375 | D = mpNew(r->N,r->N); |
---|
2376 | if (DN == NULL) |
---|
2377 | { |
---|
2378 | if ( (r->nc->type == nc_lie) || (r->nc->type == nc_undef) ) |
---|
2379 | { |
---|
2380 | r->nc->type = nc_comm; /* it was nc_skew earlier */ |
---|
2381 | } |
---|
2382 | else /* nc_general, nc_skew */ |
---|
2383 | { |
---|
2384 | r->nc->type = nc_skew; |
---|
2385 | } |
---|
2386 | } |
---|
2387 | else /* DN != NULL */ |
---|
2388 | { |
---|
2389 | for(i=1; i<r->N; i++) |
---|
2390 | { |
---|
2391 | for(j=i+1; j<=r->N; j++) |
---|
2392 | { |
---|
2393 | MATELEM(D,i,j) = nc_p_CopyPut(DN,r); |
---|
2394 | } |
---|
2395 | } |
---|
2396 | } |
---|
2397 | } |
---|
2398 | else /* DD != NULL */ |
---|
2399 | { |
---|
2400 | D = mpCopy(DD); |
---|
2401 | } |
---|
2402 | /* analyze D */ |
---|
2403 | /* check the ordering condition for D (both matrix and poly cases) */ |
---|
2404 | |
---|
2405 | if ( nc_CheckOrdCondition(D, r) ) |
---|
2406 | { |
---|
2407 | ncCleanUp(r); |
---|
2408 | if (WeChangeRing) |
---|
2409 | rChangeCurrRing(save); |
---|
2410 | Werror("Matrix of polynomials violates the ordering condition"); |
---|
2411 | return TRUE; |
---|
2412 | } |
---|
2413 | r->nc->C = C; |
---|
2414 | r->nc->D = D; |
---|
2415 | if (WeChangeRing) |
---|
2416 | rChangeCurrRing(save); |
---|
2417 | return nc_InitMultiplication(r); |
---|
2418 | } |
---|
2419 | |
---|
2420 | BOOLEAN nc_InitMultiplication(ring r) |
---|
2421 | { |
---|
2422 | /* returns TRUE if there were errors */ |
---|
2423 | /* initialize the multiplication: */ |
---|
2424 | /* r->nc->MTsize, r->nc->MT, r->nc->COM, */ |
---|
2425 | /* and r->nc->IsSkewConstant for the skew case */ |
---|
2426 | if (rVar(r)==1) |
---|
2427 | { |
---|
2428 | r->nc->type=nc_comm; |
---|
2429 | r->nc->IsSkewConstant=1; |
---|
2430 | return FALSE; |
---|
2431 | } |
---|
2432 | ring save = currRing; |
---|
2433 | int WeChangeRing = 0; |
---|
2434 | if (currRing!=r) |
---|
2435 | { |
---|
2436 | rChangeCurrRing(r); |
---|
2437 | WeChangeRing = 1; |
---|
2438 | } |
---|
2439 | assume( currRing == r->nc->basering ); // otherwise we cannot work with all these matrices! |
---|
2440 | |
---|
2441 | int i,j; |
---|
2442 | r->nc->MT = (matrix *)omAlloc0((r->N*(r->N-1))/2*sizeof(matrix)); |
---|
2443 | r->nc->MTsize = (int *)omAlloc0((r->N*(r->N-1))/2*sizeof(int)); |
---|
2444 | idTest(((ideal)r->nc->C)); |
---|
2445 | matrix COM = mpCopy(r->nc->C); |
---|
2446 | poly p,q; |
---|
2447 | short DefMTsize=7; |
---|
2448 | int IsNonComm=0; |
---|
2449 | int tmpIsSkewConstant; |
---|
2450 | |
---|
2451 | for(i=1; i<r->N; i++) |
---|
2452 | { |
---|
2453 | for(j=i+1; j<=r->N; j++) |
---|
2454 | { |
---|
2455 | if ( MATELEM(r->nc->D,i,j) == NULL ) /* quasicommutative case */ |
---|
2456 | { |
---|
2457 | /* 1x1 mult.matrix */ |
---|
2458 | r->nc->MTsize[UPMATELEM(i,j,r->N)] = 1; |
---|
2459 | r->nc->MT[UPMATELEM(i,j,r->N)] = mpNew(1,1); |
---|
2460 | } |
---|
2461 | else /* pure noncommutative case */ |
---|
2462 | { |
---|
2463 | /* TODO check the special multiplication properties */ |
---|
2464 | IsNonComm = 1; |
---|
2465 | p_Delete(&(MATELEM(COM,i,j)),r); |
---|
2466 | //MATELEM(COM,i,j) = NULL; // done by p_Delete |
---|
2467 | r->nc->MTsize[UPMATELEM(i,j,r->N)] = DefMTsize; /* default sizes */ |
---|
2468 | r->nc->MT[UPMATELEM(i,j,r->N)] = mpNew(DefMTsize, DefMTsize); |
---|
2469 | } |
---|
2470 | /* set MT[i,j,1,1] to c_i_j*x_i*x_j + D_i_j */ |
---|
2471 | p = p_ISet(1,r); /* instead of p = pOne(); */ |
---|
2472 | if (MATELEM(r->nc->C,i,j)!=NULL) |
---|
2473 | p_SetCoeff(p,n_Copy(pGetCoeff(MATELEM(r->nc->C,i,j)),r),r); |
---|
2474 | p_SetExp(p,i,1,r); |
---|
2475 | p_SetExp(p,j,1,r); |
---|
2476 | p_Setm(p,r); |
---|
2477 | p_Test(MATELEM(r->nc->D,i,j),r->nc->basering); |
---|
2478 | q = nc_p_CopyGet(MATELEM(r->nc->D,i,j),r); |
---|
2479 | p = p_Add_q(p,q,r); |
---|
2480 | MATELEM(r->nc->MT[UPMATELEM(i,j,r->N)],1,1) = nc_p_CopyPut(p,r); |
---|
2481 | p_Delete(&p,r); |
---|
2482 | // p = NULL;// done by p_Delete |
---|
2483 | } |
---|
2484 | } |
---|
2485 | if (r->nc->type==nc_undef) |
---|
2486 | { |
---|
2487 | if (IsNonComm==1) |
---|
2488 | { |
---|
2489 | // assume(pN!=NULL); |
---|
2490 | // if ((tmpIsSkewConstant==1) && (nIsOne(pGetCoeff(pN)))) r->nc->type=nc_lie; |
---|
2491 | // else r->nc->type=nc_general; |
---|
2492 | } |
---|
2493 | if (IsNonComm==0) |
---|
2494 | { |
---|
2495 | r->nc->type=nc_skew; /* TODO: check whether it is commutative */ |
---|
2496 | r->nc->IsSkewConstant=tmpIsSkewConstant; |
---|
2497 | } |
---|
2498 | } |
---|
2499 | r->nc->COM=COM; |
---|
2500 | |
---|
2501 | SetProcsGNC(r, r->p_Procs); |
---|
2502 | |
---|
2503 | |
---|
2504 | if (WeChangeRing) |
---|
2505 | { |
---|
2506 | rChangeCurrRing(save); |
---|
2507 | } |
---|
2508 | return FALSE; |
---|
2509 | } |
---|
2510 | |
---|
2511 | void SetProcsGNC(ring& rGR, p_Procs_s* p_Procs) |
---|
2512 | { |
---|
2513 | |
---|
2514 | // "commutative" |
---|
2515 | rGR->p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
2516 | rGR->p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
2517 | rGR->p_Procs->p_Minus_mm_Mult_qq = NULL; // gnc_p_Minus_mm_Mult_qq_ign; // should not be used!!! |
---|
2518 | |
---|
2519 | p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
2520 | p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
2521 | p_Procs->p_Minus_mm_Mult_qq = NULL; // gnc_p_Minus_mm_Mult_qq_ign; // should not be used!!! |
---|
2522 | |
---|
2523 | |
---|
2524 | // non-commutaitve |
---|
2525 | rGR->nc->p_Procs.mm_Mult_p = gnc_mm_Mult_p; |
---|
2526 | rGR->nc->p_Procs.mm_Mult_pp = gnc_mm_Mult_pp; |
---|
2527 | |
---|
2528 | rGR->nc->p_Procs.GB = gnc_gr_bba; // bba even for local case! |
---|
2529 | |
---|
2530 | // rGR->nc->p_Procs.GlobalGB = gnc_gr_bba; |
---|
2531 | // rGR->nc->p_Procs.LocalGB = gnc_gr_mora; |
---|
2532 | |
---|
2533 | |
---|
2534 | #if 0 |
---|
2535 | // Previous Plural's implementation... |
---|
2536 | rGR->nc->p_Procs.SPoly = gnc_CreateSpolyOld; |
---|
2537 | rGR->nc->p_Procs.ReduceSPoly = gnc_ReduceSpolyOld; |
---|
2538 | |
---|
2539 | rGR->nc->p_Procs.BucketPolyRed = gnc_kBucketPolyRedOld; |
---|
2540 | rGR->nc->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZOld; |
---|
2541 | #else |
---|
2542 | rGR->nc->p_Procs.SPoly = gnc_CreateSpolyNew; |
---|
2543 | rGR->nc->p_Procs.ReduceSPoly = gnc_ReduceSpolyNew; |
---|
2544 | |
---|
2545 | rGR->nc->p_Procs.BucketPolyRed = gnc_kBucketPolyRedNew; |
---|
2546 | rGR->nc->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZNew; |
---|
2547 | #endif |
---|
2548 | |
---|
2549 | |
---|
2550 | |
---|
2551 | |
---|
2552 | #if 0 |
---|
2553 | p_Procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
2554 | _p_procs->p_Mult_mm = gnc_p_Mult_mm; |
---|
2555 | |
---|
2556 | p_Procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
2557 | _p_procs->pp_Mult_mm = gnc_pp_Mult_mm; |
---|
2558 | |
---|
2559 | p_Procs->p_Minus_mm_Mult_qq = NULL; // gnc_p_Minus_mm_Mult_qq_ign; |
---|
2560 | _p_procs->p_Minus_mm_Mult_qq= NULL; // gnc_p_Minus_mm_Mult_qq_ign; |
---|
2561 | |
---|
2562 | r->nc->mmMultP() = gnc_mm_Mult_p; |
---|
2563 | r->nc->mmMultPP() = gnc_mm_Mult_pp; |
---|
2564 | |
---|
2565 | r->nc->GB() = gnc_gr_bba; |
---|
2566 | |
---|
2567 | r->nc->SPoly() = gnc_CreateSpoly; |
---|
2568 | r->nc->ReduceSPoly() = gnc_ReduceSpoly; |
---|
2569 | |
---|
2570 | #endif |
---|
2571 | } |
---|
2572 | |
---|
2573 | |
---|
2574 | /* substitute the n-th variable by e in p |
---|
2575 | * destroy p |
---|
2576 | * e is not a constant |
---|
2577 | */ |
---|
2578 | poly nc_pSubst(poly p, int n, poly e) |
---|
2579 | { |
---|
2580 | int rN=currRing->N; |
---|
2581 | int *PRE = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2582 | int *SUF = (int *)omAlloc0((rN+1)*sizeof(int)); |
---|
2583 | int i,j,pow; |
---|
2584 | number C; |
---|
2585 | poly suf,pre; |
---|
2586 | poly res = NULL; |
---|
2587 | poly out = NULL; |
---|
2588 | while ( p!= NULL ) |
---|
2589 | { |
---|
2590 | C = pGetCoeff(p); |
---|
2591 | pGetExpV(p, PRE); /* faster splitting? */ |
---|
2592 | pow = PRE[n]; PRE[n]=0; |
---|
2593 | res = NULL; |
---|
2594 | if (pow!=0) |
---|
2595 | { |
---|
2596 | for (i=n+1; i<=rN; i++) |
---|
2597 | { |
---|
2598 | SUF[i] = PRE[i]; |
---|
2599 | PRE[i] = 0; |
---|
2600 | } |
---|
2601 | res = pPower(pCopy(e),pow); |
---|
2602 | /* multiply with prefix */ |
---|
2603 | pre = pOne(); |
---|
2604 | pSetExpV(pre,PRE); |
---|
2605 | pSetm(pre); |
---|
2606 | res = mm_Mult_p(pre,res,currRing); |
---|
2607 | /* multiply with suffix */ |
---|
2608 | suf = pOne(); |
---|
2609 | pSetExpV(suf,SUF); |
---|
2610 | pSetm(suf); |
---|
2611 | res = p_Mult_mm(res,suf,currRing); |
---|
2612 | res = p_Mult_nn(res,C,currRing); |
---|
2613 | pSetComp(res,PRE[0]); |
---|
2614 | } |
---|
2615 | else /* pow==0 */ |
---|
2616 | { |
---|
2617 | res = pHead(p); |
---|
2618 | } |
---|
2619 | p = pLmDeleteAndNext(p); |
---|
2620 | out = pAdd(out,res); |
---|
2621 | } |
---|
2622 | freeT(PRE,rN); |
---|
2623 | freeT(SUF,rN); |
---|
2624 | return(out); |
---|
2625 | } |
---|
2626 | |
---|
2627 | static ideal idPrepareStd(ideal T, ideal s, int k) |
---|
2628 | { |
---|
2629 | /* T is a left SB, without zeros, s is a list with zeros */ |
---|
2630 | #ifdef PDEBUG |
---|
2631 | if (IDELEMS(s)!=IDELEMS(T)) |
---|
2632 | { |
---|
2633 | Print("ideals of diff. size!!!"); |
---|
2634 | } |
---|
2635 | #endif |
---|
2636 | ideal t = idCopy(T); |
---|
2637 | int j,rs=idRankFreeModule(s),rt=idRankFreeModule(t); |
---|
2638 | poly p,q; |
---|
2639 | |
---|
2640 | ideal res = idInit(2*idElem(t),1+idElem(t)); |
---|
2641 | if (rs == 0) |
---|
2642 | { |
---|
2643 | for (j=0; j<IDELEMS(t); j++) |
---|
2644 | { |
---|
2645 | if (s->m[j]!=NULL) pSetCompP(s->m[j],1); |
---|
2646 | if (t->m[j]!=NULL) pSetCompP(t->m[j],1); |
---|
2647 | } |
---|
2648 | k = si_max(k,1); |
---|
2649 | } |
---|
2650 | for (j=0; j<IDELEMS(t); j++) |
---|
2651 | { |
---|
2652 | if (s->m[j]!=NULL) |
---|
2653 | { |
---|
2654 | p = s->m[j]; |
---|
2655 | q = pOne(); |
---|
2656 | pSetComp(q,k+1+j); |
---|
2657 | pSetmComp(q); |
---|
2658 | #if 0 |
---|
2659 | while (pNext(p)) pIter(p); |
---|
2660 | pNext(p) = q; |
---|
2661 | #else |
---|
2662 | p = pAdd(p,q); |
---|
2663 | s->m[j] = p; |
---|
2664 | #ifdef PDEBUG |
---|
2665 | pTest(p); |
---|
2666 | #endif |
---|
2667 | #endif |
---|
2668 | } |
---|
2669 | } |
---|
2670 | res = idSimpleAdd(t,s); |
---|
2671 | idDelete(&t); |
---|
2672 | res->rank = 1+idElem(T); |
---|
2673 | return(res); |
---|
2674 | } |
---|
2675 | |
---|
2676 | ideal Approx_Step(ideal L) |
---|
2677 | { |
---|
2678 | int N=currRing->N; |
---|
2679 | int i,j; // k=syzcomp |
---|
2680 | int flag, flagcnt=0, syzcnt=0; |
---|
2681 | int syzcomp = 0; |
---|
2682 | int k=1; /* for ideals not modules */ |
---|
2683 | ideal I = kStd(L, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
2684 | idSkipZeroes(I); |
---|
2685 | ideal s_I; |
---|
2686 | int idI = idElem(I); |
---|
2687 | ideal trickyQuotient,s_trickyQuotient; |
---|
2688 | if (currQuotient !=NULL) |
---|
2689 | { |
---|
2690 | trickyQuotient = idSimpleAdd(currQuotient,I); |
---|
2691 | } |
---|
2692 | else |
---|
2693 | trickyQuotient = I; |
---|
2694 | idSkipZeroes(trickyQuotient); |
---|
2695 | poly *var = (poly *)omAlloc0((N+1)*sizeof(poly)); |
---|
2696 | // poly *W = (poly *)omAlloc0((2*N+1)*sizeof(poly)); |
---|
2697 | resolvente S = (resolvente)omAlloc0((N+1)*sizeof(ideal)); |
---|
2698 | ideal SI, res; |
---|
2699 | matrix MI; |
---|
2700 | poly x=pOne(); |
---|
2701 | var[0]=x; |
---|
2702 | ideal h2, h3, s_h2, s_h3; |
---|
2703 | poly p,q,qq; |
---|
2704 | /* init vars */ |
---|
2705 | for (i=1; i<=N; i++ ) |
---|
2706 | { |
---|
2707 | x = pOne(); |
---|
2708 | pSetExp(x,i,1); |
---|
2709 | pSetm(x); |
---|
2710 | var[i]=pCopy(x); |
---|
2711 | } |
---|
2712 | /* init NF's */ |
---|
2713 | for (i=1; i<=N; i++ ) |
---|
2714 | { |
---|
2715 | h2 = idInit(idI,1); |
---|
2716 | flag = 0; |
---|
2717 | for (j=0; j< idI; j++ ) |
---|
2718 | { |
---|
2719 | q = pp_Mult_mm(I->m[j],var[i],currRing); |
---|
2720 | q = kNF(I,currQuotient,q,0,0); |
---|
2721 | if (q!=0) |
---|
2722 | { |
---|
2723 | h2->m[j]=pCopy(q); |
---|
2724 | // pShift(&(h2->m[flag]),1); |
---|
2725 | flag++; |
---|
2726 | pDelete(&q); |
---|
2727 | } |
---|
2728 | else |
---|
2729 | h2->m[j]=0; |
---|
2730 | } |
---|
2731 | /* W[1..idElems(I)] */ |
---|
2732 | if (flag >0) |
---|
2733 | { |
---|
2734 | /* compute syzygies with values in I*/ |
---|
2735 | // idSkipZeroes(h2); |
---|
2736 | // h2 = idSimpleAdd(h2,I); |
---|
2737 | // h2->rank=flag+idI+1; |
---|
2738 | idTest(h2); |
---|
2739 | idShow(h2); |
---|
2740 | ring orig_ring=currRing; |
---|
2741 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2742 | syzcomp = 1; |
---|
2743 | rSetSyzComp(syzcomp); |
---|
2744 | if (orig_ring != syz_ring) |
---|
2745 | { |
---|
2746 | s_h2=idrCopyR_NoSort(h2,orig_ring); |
---|
2747 | // s_trickyQuotient=idrCopyR_NoSort(trickyQuotient,orig_ring); |
---|
2748 | // rDebugPrint(syz_ring); |
---|
2749 | s_I=idrCopyR_NoSort(I,orig_ring); |
---|
2750 | } |
---|
2751 | else |
---|
2752 | { |
---|
2753 | s_h2 = h2; |
---|
2754 | s_I = I; |
---|
2755 | // s_trickyQuotient=trickyQuotient; |
---|
2756 | } |
---|
2757 | idTest(s_h2); |
---|
2758 | // idTest(s_trickyQuotient); |
---|
2759 | Print(".proceeding with the variable %d\n",i); |
---|
2760 | s_h3 = idPrepareStd(s_I, s_h2, 1); |
---|
2761 | BITSET save_test=test; |
---|
2762 | test|=Sy_bit(OPT_SB_1); |
---|
2763 | idTest(s_h3); |
---|
2764 | idDelete(&s_h2); |
---|
2765 | s_h2=idCopy(s_h3); |
---|
2766 | idDelete(&s_h3); |
---|
2767 | Print("...computing Syz"); |
---|
2768 | s_h3 = kStd(s_h2, currQuotient,(tHomog)FALSE,NULL,NULL,syzcomp,idI); |
---|
2769 | test=save_test; |
---|
2770 | idShow(s_h3); |
---|
2771 | if (orig_ring != syz_ring) |
---|
2772 | { |
---|
2773 | idDelete(&s_h2); |
---|
2774 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
2775 | { |
---|
2776 | if (s_h3->m[j] != NULL) |
---|
2777 | { |
---|
2778 | if (p_MinComp(s_h3->m[j],syz_ring) > syzcomp) /* i.e. it is a syzygy */ |
---|
2779 | pShift(&s_h3->m[j], -syzcomp); |
---|
2780 | else |
---|
2781 | pDelete(&s_h3->m[j]); |
---|
2782 | } |
---|
2783 | } |
---|
2784 | idSkipZeroes(s_h3); |
---|
2785 | s_h3->rank -= syzcomp; |
---|
2786 | rChangeCurrRing(orig_ring); |
---|
2787 | // s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
2788 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
2789 | rKill(syz_ring); |
---|
2790 | } |
---|
2791 | idTest(s_h3); |
---|
2792 | S[syzcnt]=kStd(s_h3,currQuotient,(tHomog)FALSE,NULL,NULL); |
---|
2793 | syzcnt++; |
---|
2794 | idDelete(&s_h3); |
---|
2795 | } /* end if flag >0 */ |
---|
2796 | else |
---|
2797 | { |
---|
2798 | flagcnt++; |
---|
2799 | } |
---|
2800 | } |
---|
2801 | if (flagcnt == N) |
---|
2802 | { |
---|
2803 | Print("the input is a two--sided ideal"); |
---|
2804 | return(I); |
---|
2805 | } |
---|
2806 | if (syzcnt >0) |
---|
2807 | { |
---|
2808 | Print("..computing Intersect of %d modules\n",syzcnt); |
---|
2809 | if (syzcnt == 1) |
---|
2810 | SI = S[0]; |
---|
2811 | else |
---|
2812 | SI = idMultSect(S, syzcnt); |
---|
2813 | idShow(SI); |
---|
2814 | MI = idModule2Matrix(SI); |
---|
2815 | res= idInit(MATCOLS(MI),1); |
---|
2816 | for (i=1; i<= MATCOLS(MI); i++) |
---|
2817 | { |
---|
2818 | p = NULL; |
---|
2819 | for (j=0; j< idElem(I); j++) |
---|
2820 | { |
---|
2821 | q = pCopy(MATELEM(MI,j+1,i)); |
---|
2822 | if (q!=NULL) |
---|
2823 | { |
---|
2824 | q = pMult(q,pCopy(I->m[j])); |
---|
2825 | p = pAdd(p,q); |
---|
2826 | } |
---|
2827 | } |
---|
2828 | res->m[i-1]=p; |
---|
2829 | } |
---|
2830 | Print("final std"); |
---|
2831 | res = kStd(res, currQuotient,testHomog,NULL,NULL,0,0,NULL); |
---|
2832 | idSkipZeroes(res); |
---|
2833 | return(res); |
---|
2834 | } |
---|
2835 | else |
---|
2836 | { |
---|
2837 | Print("No syzygies"); |
---|
2838 | return(I); |
---|
2839 | } |
---|
2840 | } |
---|
2841 | |
---|
2842 | |
---|
2843 | ring nc_rCreateNCcomm(ring r) |
---|
2844 | /* creates a commutative nc extension; "converts" comm.ring to a Plural ring */ |
---|
2845 | { |
---|
2846 | if (rIsPluralRing(r)) return r; |
---|
2847 | ring save = currRing; |
---|
2848 | int WeChangeRing = 0; |
---|
2849 | if (currRing!=r) |
---|
2850 | { |
---|
2851 | rChangeCurrRing(r); |
---|
2852 | WeChangeRing = 1; |
---|
2853 | } |
---|
2854 | r->nc = (nc_struct *)omAlloc0(sizeof(nc_struct)); |
---|
2855 | r->nc->ref = 1; |
---|
2856 | r->nc->basering = r; |
---|
2857 | r->nc->type = nc_comm; |
---|
2858 | r->nc->IsSkewConstant = 1; |
---|
2859 | matrix C = mpNew(r->N,r->N); |
---|
2860 | matrix D = mpNew(r->N,r->N); |
---|
2861 | int i,j; |
---|
2862 | for(i=1; i<r->N; i++) |
---|
2863 | { |
---|
2864 | for(j=i+1; j<=r->N; j++) |
---|
2865 | { |
---|
2866 | MATELEM(C,i,j) = pOne(); |
---|
2867 | } |
---|
2868 | } |
---|
2869 | r->nc->C = C; |
---|
2870 | r->nc->D = D; |
---|
2871 | if (nc_InitMultiplication(r)) |
---|
2872 | { |
---|
2873 | WarnS("Error initializing multiplication!"); |
---|
2874 | } |
---|
2875 | if (WeChangeRing) |
---|
2876 | { |
---|
2877 | rChangeCurrRing(save); |
---|
2878 | } |
---|
2879 | return r; |
---|
2880 | } |
---|
2881 | |
---|
2882 | poly p_CopyEmbed(poly p, ring srcRing, int shift, int par_shift) |
---|
2883 | /* NOT USED ANYMORE: replaced by maFindPerm in ring.cc */ |
---|
2884 | /* for use with embeddings: currRing is a sum of smaller rings */ |
---|
2885 | /* and srcRing is one of such smaller rings */ |
---|
2886 | /* shift defines the position of a subring in srcRing */ |
---|
2887 | /* par_shift defines the position of a subfield in basefield of CurrRing */ |
---|
2888 | { |
---|
2889 | if (currRing == srcRing) |
---|
2890 | { |
---|
2891 | return(p_Copy(p,currRing)); |
---|
2892 | } |
---|
2893 | nMapFunc nMap=nSetMap(srcRing); |
---|
2894 | poly q; |
---|
2895 | // if ( nMap == nCopy) |
---|
2896 | // { |
---|
2897 | // q = prCopyR(p,srcRing); |
---|
2898 | // } |
---|
2899 | // else |
---|
2900 | { |
---|
2901 | int *perm = (int *)omAlloc0((srcRing->N+1)*sizeof(int)); |
---|
2902 | int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
2903 | // int *par_perm = (int *)omAlloc0((srcRing->P+1)*sizeof(int)); |
---|
2904 | int i; |
---|
2905 | // if (srcRing->P > 0) |
---|
2906 | // { |
---|
2907 | // for (i=0; i<srcRing->P; i++) |
---|
2908 | // par_perm[i]=-i; |
---|
2909 | // } |
---|
2910 | if ((shift<0) || (shift > currRing->N)) |
---|
2911 | { |
---|
2912 | Werror("bad shifts in p_CopyEmbed"); |
---|
2913 | return(0); |
---|
2914 | } |
---|
2915 | for (i=1; i<= srcRing->N; i++) |
---|
2916 | { |
---|
2917 | perm[i] = shift+i; |
---|
2918 | } |
---|
2919 | q = pPermPoly(p,perm,srcRing,nMap,par_perm,srcRing->P); |
---|
2920 | } |
---|
2921 | return(q); |
---|
2922 | } |
---|
2923 | |
---|
2924 | poly pOppose(ring Rop, poly p) |
---|
2925 | /* opposes a vector p from Rop to currRing */ |
---|
2926 | { |
---|
2927 | /* the simplest case:*/ |
---|
2928 | if ( Rop == currRing ) return(pCopy(p)); |
---|
2929 | /* check Rop == rOpposite(currRing) */ |
---|
2930 | if ( !rIsLikeOpposite(currRing, Rop) ) |
---|
2931 | { |
---|
2932 | WarnS("an opposite ring should be used"); |
---|
2933 | return NULL; |
---|
2934 | } |
---|
2935 | /* nMapFunc nMap = nSetMap(Rop);*/ |
---|
2936 | /* since we know that basefields coinside! */ |
---|
2937 | int *perm=(int *)omAlloc0((Rop->N+1)*sizeof(int)); |
---|
2938 | if (!p_IsConstantPoly(p, Rop)) |
---|
2939 | { |
---|
2940 | /* we know perm exactly */ |
---|
2941 | int i; |
---|
2942 | for(i=1; i<=Rop->N; i++) |
---|
2943 | { |
---|
2944 | perm[i] = Rop->N+1-i; |
---|
2945 | } |
---|
2946 | } |
---|
2947 | poly res = pPermPoly(p, perm, Rop, nCopy); |
---|
2948 | omFreeSize((ADDRESS)perm,(Rop->N+1)*sizeof(int)); |
---|
2949 | return res; |
---|
2950 | } |
---|
2951 | |
---|
2952 | ideal idOppose(ring Rop, ideal I) |
---|
2953 | /* opposes a module I from Rop to currRing */ |
---|
2954 | { |
---|
2955 | /* the simplest case:*/ |
---|
2956 | if ( Rop == currRing ) return idCopy(I); |
---|
2957 | /* check Rop == rOpposite(currRing) */ |
---|
2958 | if (!rIsLikeOpposite(currRing, Rop)) |
---|
2959 | { |
---|
2960 | WarnS("an opposite ring should be used"); |
---|
2961 | return NULL; |
---|
2962 | } |
---|
2963 | int i; |
---|
2964 | ideal idOp = idInit(I->ncols, I->rank); |
---|
2965 | for (i=0; i< (I->ncols)*(I->nrows); i++) |
---|
2966 | { |
---|
2967 | idOp->m[i] = pOppose(Rop,I->m[i]); |
---|
2968 | } |
---|
2969 | idTest(idOp); |
---|
2970 | return idOp; |
---|
2971 | } |
---|
2972 | |
---|
2973 | BOOLEAN rIsLikeOpposite(ring rBase, ring rCandidate) |
---|
2974 | /* checks whether rings rBase and rCandidate */ |
---|
2975 | /* could be opposite to each other */ |
---|
2976 | /* returns TRUE if it is so */ |
---|
2977 | { |
---|
2978 | /* the same basefield */ |
---|
2979 | int diagnose = TRUE; |
---|
2980 | ring save = currRing; |
---|
2981 | rChangeCurrRing(rBase); |
---|
2982 | nMapFunc nMap = nSetMap(rCandidate); |
---|
2983 | if (nMap != nCopy) diagnose = FALSE; |
---|
2984 | rChangeCurrRing(save); |
---|
2985 | /* same number of variables */ |
---|
2986 | if (rBase->N != rCandidate->N) diagnose = FALSE; |
---|
2987 | /* nc and comm ring */ |
---|
2988 | if ( rIsPluralRing(rBase) != rIsPluralRing(rCandidate) ) diagnose = FALSE; |
---|
2989 | /* both are qrings */ |
---|
2990 | /* NO CHECK, since it is used in building opposite qring */ |
---|
2991 | /* if ( ((rBase->qideal != NULL) && (rCandidate->qideal == NULL)) */ |
---|
2992 | /* || ((rBase->qideal == NULL) && (rCandidate->qideal != NULL)) ) */ |
---|
2993 | /* diagnose = FALSE; */ |
---|
2994 | /* TODO: varnames are e->E etc */ |
---|
2995 | return diagnose; |
---|
2996 | } |
---|
2997 | |
---|
2998 | #endif |
---|
2999 | |
---|
3000 | |
---|
3001 | // int Commutative_Context(ring r, leftv expression) |
---|
3002 | // /* returns 1 if expression consists */ |
---|
3003 | // /* of commutative elements */ |
---|
3004 | // { |
---|
3005 | // /* crucial: poly -> ideal, module, matrix */ |
---|
3006 | // } |
---|
3007 | |
---|
3008 | // int Comm_Context_Poly(ring r, poly p) |
---|
3009 | // { |
---|
3010 | // poly COMM=r->nc->COMM; |
---|
3011 | // poly pp=pOne(); |
---|
3012 | // memset(pp->exp,0,r->ExpL_Size*sizeof(long)); |
---|
3013 | // while (p!=NULL) |
---|
3014 | // { |
---|
3015 | // for (i=0;i<=r->ExpL_Size;i++) |
---|
3016 | // { |
---|
3017 | // if ((p->exp[i]) && (pp->exp[i])) return(FALSE); |
---|
3018 | // /* nonzero exponent of non-comm variable */ |
---|
3019 | // } |
---|
3020 | // pIter(p); |
---|
3021 | // } |
---|
3022 | // return(TRUE); |
---|
3023 | // } |
---|