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: sca.cc |
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6 | * Purpose: supercommutative kernel procedures |
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7 | * Author: motsak (Oleksandr Motsak) |
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8 | * Created: 2006/12/18 |
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9 | *******************************************************************/ |
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10 | |
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11 | // set it here if needed. |
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12 | #define OUTPUT 0 |
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13 | #define MYTEST 0 |
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14 | |
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15 | #if MYTEST |
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16 | #define OM_CHECK 4 |
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17 | #define OM_TRACK 5 |
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18 | #endif |
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19 | |
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20 | // #define PDEBUG 2 |
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21 | |
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22 | |
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23 | |
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24 | #include <misc/auxiliary.h> |
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25 | |
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26 | #ifdef HAVE_PLURAL |
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27 | |
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28 | // for |
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29 | #define PLURAL_INTERNAL_DECLARATIONS |
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30 | |
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31 | #include <polys/nc/sca.h> |
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32 | #include <polys/nc/nc.h> |
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33 | #include <polys/nc/gb_hack.h> |
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34 | // #include <polys/gring.h> |
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35 | |
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36 | |
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37 | #include <coeffs/numbers.h> |
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38 | #include <polys/coeffrings.h> |
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39 | |
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40 | |
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41 | // #include <polys/febase.h> |
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42 | #include <misc/options.h> |
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43 | |
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44 | #include <polys/monomials/p_polys.h> |
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45 | |
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46 | // #include <polys/kutil.h> |
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47 | #include <polys/simpleideals.h> |
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48 | #include <misc/intvec.h> |
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49 | |
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50 | #include <polys/monomials/ring.h> |
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51 | #include <polys/kbuckets.h> |
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52 | // #include <polys/kstd1.h> |
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53 | #include <polys/sbuckets.h> |
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54 | |
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55 | #include <polys/prCopy.h> |
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56 | |
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57 | #include <polys/operations/p_Mult_q.h> |
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58 | #include <polys/templates/p_MemAdd.h> |
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59 | |
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60 | // #include <polys/kutil.h> |
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61 | // #include <polys/kstd1.h> |
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62 | |
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63 | #include <polys/weight.h> |
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64 | |
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65 | |
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66 | // poly functions defined in p_Procs : |
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67 | |
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68 | // return pPoly * pMonom; preserve pPoly and pMonom. |
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69 | poly sca_pp_Mult_mm(const poly pPoly, const poly pMonom, const ring rRing, poly &); |
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70 | |
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71 | // return pMonom * pPoly; preserve pPoly and pMonom. |
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72 | static poly sca_mm_Mult_pp(const poly pMonom, const poly pPoly, const ring rRing); |
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73 | |
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74 | // return pPoly * pMonom; preserve pMonom, destroy or reuse pPoly. |
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75 | poly sca_p_Mult_mm(poly pPoly, const poly pMonom, const ring rRing); |
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76 | |
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77 | // return pMonom * pPoly; preserve pMonom, destroy or reuse pPoly. |
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78 | static poly sca_mm_Mult_p(const poly pMonom, poly pPoly, const ring rRing); |
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79 | |
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80 | |
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81 | // compute the spolynomial of p1 and p2 |
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82 | poly sca_SPoly(const poly p1, const poly p2, const ring r); |
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83 | poly sca_ReduceSpoly(const poly p1, poly p2, const ring r); |
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84 | |
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85 | |
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86 | //////////////////////////////////////////////////////////////////////////////////////////////////// |
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87 | // Super Commutative Algebra extension by Oleksandr |
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88 | //////////////////////////////////////////////////////////////////////////////////////////////////// |
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89 | |
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90 | // returns the sign of: lm(pMonomM) * lm(pMonomMM), |
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91 | // preserves input, may return +/-1, 0 |
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92 | static inline int sca_Sign_mm_Mult_mm( const poly pMonomM, const poly pMonomMM, const ring rRing ) |
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93 | { |
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94 | #ifdef PDEBUG |
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95 | p_Test(pMonomM, rRing); |
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96 | p_Test(pMonomMM, rRing); |
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97 | #endif |
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98 | |
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99 | const short iFirstAltVar = scaFirstAltVar(rRing); |
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100 | const short iLastAltVar = scaLastAltVar(rRing); |
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101 | |
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102 | register unsigned int tpower = 0; |
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103 | register unsigned int cpower = 0; |
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104 | |
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105 | for( register short j = iLastAltVar; j >= iFirstAltVar; j-- ) |
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106 | { |
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107 | const unsigned int iExpM = p_GetExp(pMonomM, j, rRing); |
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108 | const unsigned int iExpMM = p_GetExp(pMonomMM, j, rRing); |
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109 | |
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110 | #ifdef PDEBUG |
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111 | assume( iExpM <= 1); |
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112 | assume( iExpMM <= 1); |
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113 | #endif |
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114 | |
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115 | if( iExpMM != 0 ) // TODO: think about eliminating there if-s... |
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116 | { |
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117 | if( iExpM != 0 ) |
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118 | { |
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119 | return 0; // lm(pMonomM) * lm(pMonomMM) == 0 |
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120 | } |
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121 | tpower ^= cpower; // compute degree of (-1). |
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122 | } |
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123 | cpower ^= iExpM; |
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124 | } |
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125 | |
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126 | #ifdef PDEBUG |
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127 | assume(tpower <= 1); |
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128 | #endif |
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129 | |
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130 | // 1 => -1 // degree is odd => negate coeff. |
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131 | // 0 => 1 |
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132 | |
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133 | return(1 - (tpower << 1) ); |
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134 | } |
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135 | |
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136 | |
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137 | |
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138 | |
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139 | // returns and changes pMonomM: lt(pMonomM) = lt(pMonomM) * lt(pMonomMM), |
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140 | // preserves pMonomMM. may return NULL! |
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141 | // if result != NULL => next(result) = next(pMonomM), lt(result) = lt(pMonomM) * lt(pMonomMM) |
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142 | // if result == NULL => pMonomM MUST BE deleted manually! |
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143 | static inline poly sca_m_Mult_mm( poly pMonomM, const poly pMonomMM, const ring rRing ) |
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144 | { |
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145 | #ifdef PDEBUG |
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146 | p_Test(pMonomM, rRing); |
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147 | p_Test(pMonomMM, rRing); |
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148 | #endif |
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149 | |
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150 | const unsigned int iFirstAltVar = scaFirstAltVar(rRing); |
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151 | const unsigned int iLastAltVar = scaLastAltVar(rRing); |
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152 | |
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153 | register unsigned int tpower = 0; |
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154 | register unsigned int cpower = 0; |
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155 | |
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156 | for( register unsigned int j = iLastAltVar; j >= iFirstAltVar; j-- ) |
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157 | { |
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158 | const unsigned int iExpM = p_GetExp(pMonomM, j, rRing); |
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159 | const unsigned int iExpMM = p_GetExp(pMonomMM, j, rRing); |
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160 | |
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161 | #ifdef PDEBUG |
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162 | assume( iExpM <= 1); |
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163 | assume( iExpMM <= 1); |
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164 | #endif |
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165 | |
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166 | if( iExpMM != 0 ) |
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167 | { |
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168 | if( iExpM != 0 ) // result is zero! |
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169 | { |
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170 | return NULL; // we do nothing with pMonomM in this case! |
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171 | } |
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172 | |
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173 | tpower ^= cpower; // compute degree of (-1). |
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174 | } |
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175 | |
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176 | cpower ^= iExpM; |
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177 | } |
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178 | |
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179 | #ifdef PDEBUG |
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180 | assume(tpower <= 1); |
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181 | #endif |
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182 | |
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183 | p_ExpVectorAdd(pMonomM, pMonomMM, rRing); // "exponents" are additive!!! |
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184 | |
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185 | number nCoeffM = p_GetCoeff(pMonomM, rRing); // no new copy! should be deleted! |
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186 | |
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187 | if( (tpower) != 0 ) // degree is odd => negate coeff. |
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188 | nCoeffM = n_InpNeg(nCoeffM, rRing); // negate nCoeff (will destroy the original number) |
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189 | |
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190 | const number nCoeffMM = p_GetCoeff(pMonomMM, rRing); // no new copy! |
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191 | |
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192 | number nCoeff = n_Mult(nCoeffM, nCoeffMM, rRing); // new number! |
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193 | |
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194 | p_SetCoeff(pMonomM, nCoeff, rRing); // delete lc(pMonomM) and set lc(pMonomM) = nCoeff |
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195 | |
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196 | #ifdef PDEBUG |
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197 | p_LmTest(pMonomM, rRing); |
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198 | #endif |
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199 | |
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200 | return(pMonomM); |
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201 | } |
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202 | |
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203 | // returns and changes pMonomM: lt(pMonomM) = lt(pMonomMM) * lt(pMonomM), |
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204 | // preserves pMonomMM. may return NULL! |
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205 | // if result != NULL => next(result) = next(pMonomM), lt(result) = lt(pMonomMM) * lt(pMonomM) |
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206 | // if result == NULL => pMonomM MUST BE deleted manually! |
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207 | static inline poly sca_mm_Mult_m( const poly pMonomMM, poly pMonomM, const ring rRing ) |
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208 | { |
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209 | #ifdef PDEBUG |
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210 | p_Test(pMonomM, rRing); |
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211 | p_Test(pMonomMM, rRing); |
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212 | #endif |
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213 | |
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214 | const unsigned int iFirstAltVar = scaFirstAltVar(rRing); |
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215 | const unsigned int iLastAltVar = scaLastAltVar(rRing); |
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216 | |
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217 | register unsigned int tpower = 0; |
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218 | register unsigned int cpower = 0; |
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219 | |
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220 | for( register unsigned int j = iLastAltVar; j >= iFirstAltVar; j-- ) |
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221 | { |
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222 | const unsigned int iExpMM = p_GetExp(pMonomMM, j, rRing); |
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223 | const unsigned int iExpM = p_GetExp(pMonomM, j, rRing); |
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224 | |
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225 | #ifdef PDEBUG |
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226 | assume( iExpM <= 1); |
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227 | assume( iExpMM <= 1); |
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228 | #endif |
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229 | |
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230 | if( iExpM != 0 ) |
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231 | { |
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232 | if( iExpMM != 0 ) // result is zero! |
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233 | { |
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234 | return NULL; // we do nothing with pMonomM in this case! |
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235 | } |
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236 | |
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237 | tpower ^= cpower; // compute degree of (-1). |
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238 | } |
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239 | |
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240 | cpower ^= iExpMM; |
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241 | } |
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242 | |
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243 | #ifdef PDEBUG |
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244 | assume(tpower <= 1); |
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245 | #endif |
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246 | |
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247 | p_ExpVectorAdd(pMonomM, pMonomMM, rRing); // "exponents" are additive!!! |
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248 | |
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249 | number nCoeffM = p_GetCoeff(pMonomM, rRing); // no new copy! should be deleted! |
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250 | |
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251 | if( (tpower) != 0 ) // degree is odd => negate coeff. |
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252 | nCoeffM = n_InpNeg(nCoeffM, rRing); // negate nCoeff (will destroy the original number), creates new number! |
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253 | |
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254 | const number nCoeffMM = p_GetCoeff(pMonomMM, rRing); // no new copy! |
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255 | |
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256 | number nCoeff = n_Mult(nCoeffM, nCoeffMM, rRing); // new number! |
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257 | |
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258 | p_SetCoeff(pMonomM, nCoeff, rRing); // delete lc(pMonomM) and set lc(pMonomM) = nCoeff |
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259 | |
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260 | #ifdef PDEBUG |
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261 | p_LmTest(pMonomM, rRing); |
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262 | #endif |
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263 | |
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264 | return(pMonomM); |
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265 | } |
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266 | |
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267 | |
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268 | |
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269 | // returns: result = lt(pMonom1) * lt(pMonom2), |
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270 | // preserves pMonom1, pMonom2. may return NULL! |
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271 | // if result != NULL => next(result) = NULL, lt(result) = lt(pMonom1) * lt(pMonom2) |
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272 | static inline poly sca_mm_Mult_mm( poly pMonom1, const poly pMonom2, const ring rRing ) |
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273 | { |
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274 | #ifdef PDEBUG |
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275 | p_Test(pMonom1, rRing); |
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276 | p_Test(pMonom2, rRing); |
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277 | #endif |
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278 | |
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279 | const unsigned int iFirstAltVar = scaFirstAltVar(rRing); |
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280 | const unsigned int iLastAltVar = scaLastAltVar(rRing); |
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281 | |
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282 | register unsigned int tpower = 0; |
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283 | register unsigned int cpower = 0; |
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284 | |
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285 | for( register unsigned int j = iLastAltVar; j >= iFirstAltVar; j-- ) |
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286 | { |
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287 | const unsigned int iExp1 = p_GetExp(pMonom1, j, rRing); |
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288 | const unsigned int iExp2 = p_GetExp(pMonom2, j, rRing); |
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289 | |
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290 | #ifdef PDEBUG |
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291 | assume( iExp1 <= 1); |
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292 | assume( iExp2 <= 1); |
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293 | #endif |
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294 | |
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295 | if( iExp2 != 0 ) |
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296 | { |
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297 | if( iExp1 != 0 ) // result is zero! |
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298 | { |
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299 | return NULL; |
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300 | } |
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301 | tpower ^= cpower; // compute degree of (-1). |
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302 | } |
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303 | cpower ^= iExp1; |
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304 | } |
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305 | |
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306 | #ifdef PDEBUG |
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307 | assume(cpower <= 1); |
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308 | #endif |
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309 | |
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310 | poly pResult; |
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311 | p_AllocBin(pResult,rRing->PolyBin,rRing); |
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312 | |
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313 | p_ExpVectorSum(pResult, pMonom1, pMonom2, rRing); // "exponents" are additive!!! |
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314 | |
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315 | pNext(pResult) = NULL; |
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316 | |
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317 | const number nCoeff1 = p_GetCoeff(pMonom1, rRing); // no new copy! |
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318 | const number nCoeff2 = p_GetCoeff(pMonom2, rRing); // no new copy! |
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319 | |
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320 | number nCoeff = n_Mult(nCoeff1, nCoeff2, rRing); // new number! |
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321 | |
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322 | if( (tpower) != 0 ) // degree is odd => negate coeff. |
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323 | nCoeff = n_InpNeg(nCoeff, rRing); // negate nCoeff (will destroy the original number) |
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324 | |
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325 | p_SetCoeff0(pResult, nCoeff, rRing); // set lc(pResult) = nCoeff, no destruction! |
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326 | |
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327 | #ifdef PDEBUG |
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328 | p_LmTest(pResult, rRing); |
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329 | #endif |
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330 | |
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331 | return(pResult); |
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332 | } |
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333 | |
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334 | // returns: result = x_i * lt(pMonom), |
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335 | // preserves pMonom. may return NULL! |
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336 | // if result != NULL => next(result) = NULL, lt(result) = x_i * lt(pMonom) |
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337 | static inline poly sca_xi_Mult_mm(short i, const poly pMonom, const ring rRing) |
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338 | { |
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339 | #ifdef PDEBUG |
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340 | p_Test(pMonom, rRing); |
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341 | #endif |
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342 | |
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343 | assume( i <= scaLastAltVar(rRing)); |
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344 | assume( scaFirstAltVar(rRing) <= i ); |
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345 | |
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346 | if( p_GetExp(pMonom, i, rRing) != 0 ) // => result is zero! |
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347 | return NULL; |
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348 | |
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349 | const short iFirstAltVar = scaFirstAltVar(rRing); |
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350 | |
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351 | register unsigned int cpower = 0; |
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352 | |
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353 | for( register short j = iFirstAltVar; j < i ; j++ ) |
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354 | cpower ^= p_GetExp(pMonom, j, rRing); |
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355 | |
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356 | #ifdef PDEBUG |
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357 | assume(cpower <= 1); |
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358 | #endif |
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359 | |
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360 | poly pResult = p_LmInit(pMonom, rRing); |
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361 | |
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362 | p_SetExp(pResult, i, 1, rRing); // pResult*=X_i && |
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363 | p_Setm(pResult, rRing); // addjust degree after previous step! |
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364 | |
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365 | number nCoeff = n_Copy(p_GetCoeff(pMonom, rRing), rRing); // new number! |
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366 | |
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367 | if( cpower != 0 ) // degree is odd => negate coeff. |
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368 | nCoeff = n_InpNeg(nCoeff, rRing); // negate nCoeff (will destroy the original number) |
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369 | |
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370 | p_SetCoeff0(pResult, nCoeff, rRing); // set lc(pResult) = nCoeff, no destruction! |
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371 | |
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372 | #ifdef PDEBUG |
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373 | p_LmTest(pResult, rRing); |
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374 | #endif |
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375 | |
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376 | return(pResult); |
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377 | } |
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378 | |
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379 | //-----------------------------------------------------------------------------------// |
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380 | |
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381 | // return poly = pPoly * pMonom; preserve pMonom, destroy or reuse pPoly. |
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382 | poly sca_p_Mult_mm(poly pPoly, const poly pMonom, const ring rRing) |
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383 | { |
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384 | assume( rIsSCA(rRing) ); |
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385 | |
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386 | #ifdef PDEBUG |
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387 | // Print("sca_p_Mult_mm\n"); // ! |
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388 | |
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389 | p_Test(pPoly, rRing); |
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390 | p_Test(pMonom, rRing); |
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391 | #endif |
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392 | |
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393 | if( pPoly == NULL ) |
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394 | return NULL; |
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395 | |
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396 | assume(pMonom !=NULL); |
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397 | //if( pMonom == NULL ) |
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398 | //{ |
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399 | // // pPoly != NULL => |
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400 | // p_Delete( &pPoly, rRing ); |
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401 | // return NULL; |
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402 | //} |
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403 | |
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404 | const int iComponentMonomM = p_GetComp(pMonom, rRing); |
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405 | |
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406 | poly p = pPoly; poly* ppPrev = &pPoly; |
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407 | |
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408 | loop |
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409 | { |
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410 | #ifdef PDEBUG |
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411 | p_Test(p, rRing); |
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412 | #endif |
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413 | const int iComponent = p_GetComp(p, rRing); |
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414 | |
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415 | if( iComponent!=0 ) |
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416 | { |
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417 | if( iComponentMonomM!=0 ) // TODO: make global if on iComponentMonomM =?= 0 |
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418 | { |
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419 | // REPORT_ERROR |
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420 | Werror("sca_p_Mult_mm: exponent mismatch %d and %d\n", iComponent, iComponentMonomM); |
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421 | // what should we do further?!? |
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422 | |
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423 | p_Delete( &pPoly, rRing); // delete the result AND rest |
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424 | return NULL; |
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425 | } |
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426 | #ifdef PDEBUG |
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427 | if(iComponentMonomM==0 ) |
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428 | { |
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429 | dReportError("sca_p_Mult_mm: Multiplication in the left module from the right"); |
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430 | } |
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431 | #endif |
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432 | } |
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433 | |
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434 | // terms will be in the same order because of quasi-ordering! |
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435 | poly v = sca_m_Mult_mm(p, pMonom, rRing); |
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436 | |
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437 | if( v != NULL ) |
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438 | { |
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439 | ppPrev = &pNext(p); // fixed! |
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440 | |
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441 | // *p is changed if v != NULL ( p == v ) |
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442 | pIter(p); |
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443 | |
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444 | if( p == NULL ) |
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445 | break; |
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446 | } |
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447 | else |
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448 | { // Upps! Zero!!! we must kill this term! |
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449 | |
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450 | // |
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451 | p = p_LmDeleteAndNext(p, rRing); |
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452 | |
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453 | *ppPrev = p; |
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454 | |
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455 | if( p == NULL ) |
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456 | break; |
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457 | } |
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458 | } |
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459 | |
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460 | #ifdef PDEBUG |
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461 | p_Test(pPoly,rRing); |
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462 | #endif |
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463 | |
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464 | return(pPoly); |
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465 | } |
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466 | |
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467 | // return new poly = pPoly * pMonom; preserve pPoly and pMonom. |
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468 | poly sca_pp_Mult_mm(const poly pPoly, const poly pMonom, const ring rRing) |
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469 | { |
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470 | assume( rIsSCA(rRing) ); |
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471 | |
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472 | #ifdef PDEBUG |
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473 | // Print("sca_pp_Mult_mm\n"); // ! |
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474 | |
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475 | p_Test(pPoly, rRing); |
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476 | p_Test(pMonom, rRing); |
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477 | #endif |
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478 | |
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479 | if (/*(*/ pPoly == NULL /*)*/) /*|| ( pMonom == NULL )*/ |
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480 | return NULL; |
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481 | |
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482 | const int iComponentMonomM = p_GetComp(pMonom, rRing); |
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483 | |
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484 | poly pResult = NULL; |
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485 | poly* ppPrev = &pResult; |
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486 | |
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487 | for( poly p = pPoly; p!= NULL; pIter(p) ) |
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488 | { |
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489 | #ifdef PDEBUG |
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490 | p_Test(p, rRing); |
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491 | #endif |
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492 | const int iComponent = p_GetComp(p, rRing); |
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493 | |
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494 | if( iComponent!=0 ) |
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495 | { |
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496 | if( iComponentMonomM!=0 ) // TODO: make global if on iComponentMonomM =?= 0 |
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497 | { |
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498 | // REPORT_ERROR |
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499 | Werror("sca_pp_Mult_mm: exponent mismatch %d and %d\n", iComponent, iComponentMonomM); |
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500 | // what should we do further?!? |
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501 | |
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502 | p_Delete( &pResult, rRing); // delete the result |
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503 | return NULL; |
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504 | } |
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505 | |
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506 | #ifdef PDEBUG |
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507 | if(iComponentMonomM==0 ) |
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508 | { |
---|
509 | dReportError("sca_pp_Mult_mm: Multiplication in the left module from the right"); |
---|
510 | } |
---|
511 | #endif |
---|
512 | } |
---|
513 | |
---|
514 | // terms will be in the same order because of quasi-ordering! |
---|
515 | poly v = sca_mm_Mult_mm(p, pMonom, rRing); |
---|
516 | |
---|
517 | if( v != NULL ) |
---|
518 | { |
---|
519 | *ppPrev = v; |
---|
520 | ppPrev = &pNext(v); |
---|
521 | } |
---|
522 | } |
---|
523 | |
---|
524 | #ifdef PDEBUG |
---|
525 | p_Test(pResult,rRing); |
---|
526 | #endif |
---|
527 | |
---|
528 | return(pResult); |
---|
529 | } |
---|
530 | |
---|
531 | //-----------------------------------------------------------------------------------// |
---|
532 | |
---|
533 | // return x_i * pPoly; preserve pPoly. |
---|
534 | static inline poly sca_xi_Mult_pp(short i, const poly pPoly, const ring rRing) |
---|
535 | { |
---|
536 | assume( rIsSCA(rRing) ); |
---|
537 | |
---|
538 | #ifdef PDEBUG |
---|
539 | p_Test(pPoly, rRing); |
---|
540 | #endif |
---|
541 | |
---|
542 | assume(i <= scaLastAltVar(rRing)); |
---|
543 | assume(scaFirstAltVar(rRing) <= i); |
---|
544 | |
---|
545 | if( pPoly == NULL ) |
---|
546 | return NULL; |
---|
547 | |
---|
548 | poly pResult = NULL; |
---|
549 | poly* ppPrev = &pResult; |
---|
550 | |
---|
551 | for( poly p = pPoly; p!= NULL; pIter(p) ) |
---|
552 | { |
---|
553 | |
---|
554 | // terms will be in the same order because of quasi-ordering! |
---|
555 | poly v = sca_xi_Mult_mm(i, p, rRing); |
---|
556 | |
---|
557 | #ifdef PDEBUG |
---|
558 | p_Test(v, rRing); |
---|
559 | #endif |
---|
560 | |
---|
561 | if( v != NULL ) |
---|
562 | { |
---|
563 | *ppPrev = v; |
---|
564 | ppPrev = &pNext(*ppPrev); |
---|
565 | } |
---|
566 | } |
---|
567 | |
---|
568 | |
---|
569 | #ifdef PDEBUG |
---|
570 | p_Test(pResult, rRing); |
---|
571 | #endif |
---|
572 | |
---|
573 | return(pResult); |
---|
574 | } |
---|
575 | |
---|
576 | |
---|
577 | // return new poly = pMonom * pPoly; preserve pPoly and pMonom. |
---|
578 | static poly sca_mm_Mult_pp(const poly pMonom, const poly pPoly, const ring rRing) |
---|
579 | { |
---|
580 | assume( rIsSCA(rRing) ); |
---|
581 | |
---|
582 | #ifdef PDEBUG |
---|
583 | // Print("sca_mm_Mult_pp\n"); // ! |
---|
584 | |
---|
585 | p_Test(pPoly, rRing); |
---|
586 | p_Test(pMonom, rRing); |
---|
587 | #endif |
---|
588 | |
---|
589 | if ((pPoly==NULL) || (pMonom==NULL)) return NULL; |
---|
590 | |
---|
591 | assume( (pPoly != NULL) && (pMonom !=NULL)); |
---|
592 | |
---|
593 | const int iComponentMonomM = p_GetComp(pMonom, rRing); |
---|
594 | |
---|
595 | poly pResult = NULL; |
---|
596 | poly* ppPrev = &pResult; |
---|
597 | |
---|
598 | for( poly p = pPoly; p!= NULL; pIter(p) ) |
---|
599 | { |
---|
600 | #ifdef PDEBUG |
---|
601 | p_Test(p, rRing); |
---|
602 | #endif |
---|
603 | const int iComponent = p_GetComp(p, rRing); |
---|
604 | |
---|
605 | if( iComponentMonomM!=0 ) |
---|
606 | { |
---|
607 | if( iComponent!=0 ) // TODO: make global if on iComponentMonomM =?= 0 |
---|
608 | { |
---|
609 | // REPORT_ERROR |
---|
610 | Werror("sca_mm_Mult_pp: exponent mismatch %d and %d\n", iComponent, iComponentMonomM); |
---|
611 | // what should we do further?!? |
---|
612 | |
---|
613 | p_Delete( &pResult, rRing); // delete the result |
---|
614 | return NULL; |
---|
615 | } |
---|
616 | #ifdef PDEBUG |
---|
617 | if(iComponent==0 ) |
---|
618 | { |
---|
619 | dReportError("sca_mm_Mult_pp: Multiplication in the left module from the right!"); |
---|
620 | // PrintS("mm = "); p_Write(pMonom, rRing); |
---|
621 | // PrintS("pp = "); p_Write(pPoly, rRing); |
---|
622 | // assume(iComponent!=0); |
---|
623 | } |
---|
624 | #endif |
---|
625 | } |
---|
626 | |
---|
627 | // terms will be in the same order because of quasi-ordering! |
---|
628 | poly v = sca_mm_Mult_mm(pMonom, p, rRing); |
---|
629 | |
---|
630 | if( v != NULL ) |
---|
631 | { |
---|
632 | *ppPrev = v; |
---|
633 | ppPrev = &pNext(*ppPrev); // nice line ;-) |
---|
634 | } |
---|
635 | } |
---|
636 | |
---|
637 | #ifdef PDEBUG |
---|
638 | p_Test(pResult,rRing); |
---|
639 | #endif |
---|
640 | |
---|
641 | return(pResult); |
---|
642 | } |
---|
643 | |
---|
644 | |
---|
645 | // return poly = pMonom * pPoly; preserve pMonom, destroy or reuse pPoly. |
---|
646 | static poly sca_mm_Mult_p(const poly pMonom, poly pPoly, const ring rRing) // !!!!! the MOST used procedure !!!!! |
---|
647 | { |
---|
648 | assume( rIsSCA(rRing) ); |
---|
649 | |
---|
650 | #ifdef PDEBUG |
---|
651 | p_Test(pPoly, rRing); |
---|
652 | p_Test(pMonom, rRing); |
---|
653 | #endif |
---|
654 | |
---|
655 | if( pPoly == NULL ) |
---|
656 | return NULL; |
---|
657 | |
---|
658 | assume(pMonom!=NULL); |
---|
659 | //if( pMonom == NULL ) |
---|
660 | //{ |
---|
661 | // // pPoly != NULL => |
---|
662 | // p_Delete( &pPoly, rRing ); |
---|
663 | // return NULL; |
---|
664 | //} |
---|
665 | |
---|
666 | const int iComponentMonomM = p_GetComp(pMonom, rRing); |
---|
667 | |
---|
668 | poly p = pPoly; poly* ppPrev = &pPoly; |
---|
669 | |
---|
670 | loop |
---|
671 | { |
---|
672 | #ifdef PDEBUG |
---|
673 | if( !p_Test(p, rRing) ) |
---|
674 | { |
---|
675 | PrintS("p is wrong!"); |
---|
676 | p_Write(p,rRing); |
---|
677 | } |
---|
678 | #endif |
---|
679 | |
---|
680 | const int iComponent = p_GetComp(p, rRing); |
---|
681 | |
---|
682 | if( iComponentMonomM!=0 ) |
---|
683 | { |
---|
684 | if( iComponent!=0 ) |
---|
685 | { |
---|
686 | // REPORT_ERROR |
---|
687 | Werror("sca_mm_Mult_p: exponent mismatch %d and %d\n", iComponent, iComponentMonomM); |
---|
688 | // what should we do further?!? |
---|
689 | |
---|
690 | p_Delete( &pPoly, rRing); // delete the result |
---|
691 | return NULL; |
---|
692 | } |
---|
693 | #ifdef PDEBUG |
---|
694 | if(iComponent==0) |
---|
695 | { |
---|
696 | dReportError("sca_mm_Mult_p: Multiplication in the left module from the right!"); |
---|
697 | // PrintS("mm = "); p_Write(pMonom, rRing); |
---|
698 | // PrintS("p = "); p_Write(pPoly, rRing); |
---|
699 | // assume(iComponent!=0); |
---|
700 | } |
---|
701 | #endif |
---|
702 | } |
---|
703 | |
---|
704 | // terms will be in the same order because of quasi-ordering! |
---|
705 | poly v = sca_mm_Mult_m(pMonom, p, rRing); |
---|
706 | |
---|
707 | if( v != NULL ) |
---|
708 | { |
---|
709 | ppPrev = &pNext(p); |
---|
710 | |
---|
711 | // *p is changed if v != NULL ( p == v ) |
---|
712 | pIter(p); |
---|
713 | |
---|
714 | if( p == NULL ) |
---|
715 | break; |
---|
716 | } |
---|
717 | else |
---|
718 | { // Upps! Zero!!! we must kill this term! |
---|
719 | p = p_LmDeleteAndNext(p, rRing); |
---|
720 | |
---|
721 | *ppPrev = p; |
---|
722 | |
---|
723 | if( p == NULL ) |
---|
724 | break; |
---|
725 | } |
---|
726 | } |
---|
727 | |
---|
728 | #ifdef PDEBUG |
---|
729 | if( !p_Test(pPoly, rRing) ) |
---|
730 | { |
---|
731 | PrintS("pPoly is wrong!"); |
---|
732 | p_Write(pPoly, rRing); |
---|
733 | } |
---|
734 | #endif |
---|
735 | |
---|
736 | return(pPoly); |
---|
737 | } |
---|
738 | |
---|
739 | //-----------------------------------------------------------------------------------// |
---|
740 | |
---|
741 | #ifdef PDEBUG |
---|
742 | #endif |
---|
743 | |
---|
744 | |
---|
745 | |
---|
746 | |
---|
747 | //-----------------------------------------------------------------------------------// |
---|
748 | |
---|
749 | // GB computation routines: |
---|
750 | |
---|
751 | /*4 |
---|
752 | * creates the S-polynomial of p1 and p2 |
---|
753 | * does not destroy p1 and p2 |
---|
754 | */ |
---|
755 | poly sca_SPoly( const poly p1, const poly p2, const ring r ) |
---|
756 | { |
---|
757 | assume( rIsSCA(r) ); |
---|
758 | |
---|
759 | const long lCompP1 = p_GetComp(p1,r); |
---|
760 | const long lCompP2 = p_GetComp(p2,r); |
---|
761 | |
---|
762 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
763 | { |
---|
764 | #ifdef PDEBUG |
---|
765 | dReportError("sca_SPoly: different non-zero components!\n"); |
---|
766 | #endif |
---|
767 | return(NULL); |
---|
768 | } |
---|
769 | |
---|
770 | poly pL = p_Lcm(p1, p2, si_max(lCompP1, lCompP2), r); // pL = lcm( lm(p1), lm(p2) ) |
---|
771 | |
---|
772 | poly m1 = p_One( r); |
---|
773 | p_ExpVectorDiff(m1, pL, p1, r); // m1 = pL / lm(p1) |
---|
774 | |
---|
775 | //p_SetComp(m1,0,r); |
---|
776 | //p_Setm(m1,r); |
---|
777 | #ifdef PDEBUG |
---|
778 | p_Test(m1,r); |
---|
779 | #endif |
---|
780 | |
---|
781 | |
---|
782 | poly m2 = p_One( r); |
---|
783 | p_ExpVectorDiff (m2, pL, p2, r); // m2 = pL / lm(p2) |
---|
784 | |
---|
785 | //p_SetComp(m2,0,r); |
---|
786 | //p_Setm(m2,r); |
---|
787 | #ifdef PDEBUG |
---|
788 | p_Test(m2,r); |
---|
789 | #endif |
---|
790 | |
---|
791 | p_Delete(&pL,r); |
---|
792 | |
---|
793 | number C1 = n_Copy(p_GetCoeff(p1,r),r); // C1 = lc(p1) |
---|
794 | number C2 = n_Copy(p_GetCoeff(p2,r),r); // C2 = lc(p2) |
---|
795 | |
---|
796 | number C = n_Gcd(C1,C2,r); // C = gcd(C1, C2) |
---|
797 | |
---|
798 | if (!n_IsOne(C, r)) // if C != 1 |
---|
799 | { |
---|
800 | C1=n_Div(C1, C, r); // C1 = C1 / C |
---|
801 | C2=n_Div(C2, C, r); // C2 = C2 / C |
---|
802 | } |
---|
803 | |
---|
804 | n_Delete(&C,r); // destroy the number C |
---|
805 | |
---|
806 | const int iSignSum = sca_Sign_mm_Mult_mm (m1, p1, r) + sca_Sign_mm_Mult_mm (m2, p2, r); |
---|
807 | // zero if different signs |
---|
808 | |
---|
809 | assume( (iSignSum*iSignSum == 0) || (iSignSum*iSignSum == 4) ); |
---|
810 | |
---|
811 | if( iSignSum != 0 ) // the same sign! |
---|
812 | C2=n_InpNeg (C2, r); |
---|
813 | |
---|
814 | p_SetCoeff(m1, C2, r); // lc(m1) = C2!!! |
---|
815 | p_SetCoeff(m2, C1, r); // lc(m2) = C1!!! |
---|
816 | |
---|
817 | poly tmp1 = nc_mm_Mult_pp (m1, pNext(p1), r); // tmp1 = m1 * tail(p1), |
---|
818 | p_Delete(&m1,r); // => n_Delete(&C1,r); |
---|
819 | |
---|
820 | poly tmp2 = nc_mm_Mult_pp (m2, pNext(p2), r); // tmp1 = m2 * tail(p2), |
---|
821 | p_Delete(&m2,r); // => n_Delete(&C1,r); |
---|
822 | |
---|
823 | poly spoly = p_Add_q (tmp1, tmp2, r); // spoly = spoly(lt(p1), lt(p2)) + m1 * tail(p1), delete tmp1,2 |
---|
824 | |
---|
825 | if (spoly!=NULL) p_Cleardenom (spoly, r); |
---|
826 | // if (spoly!=NULL) p_Content (spoly); // r? |
---|
827 | |
---|
828 | #ifdef PDEBUG |
---|
829 | p_Test (spoly, r); |
---|
830 | #endif |
---|
831 | |
---|
832 | return(spoly); |
---|
833 | } |
---|
834 | |
---|
835 | |
---|
836 | |
---|
837 | |
---|
838 | /*2 |
---|
839 | * reduction of p2 with p1 |
---|
840 | * do not destroy p1, but p2 |
---|
841 | * p1 divides p2 -> for use in NF algorithm |
---|
842 | */ |
---|
843 | poly sca_ReduceSpoly(const poly p1, poly p2, const ring r) |
---|
844 | { |
---|
845 | assume( rIsSCA(r) ); |
---|
846 | |
---|
847 | assume( p1 != NULL ); |
---|
848 | |
---|
849 | const long lCompP1 = p_GetComp (p1, r); |
---|
850 | const long lCompP2 = p_GetComp (p2, r); |
---|
851 | |
---|
852 | if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0)) |
---|
853 | { |
---|
854 | #ifdef PDEBUG |
---|
855 | dReportError("sca_ReduceSpoly: different non-zero components!"); |
---|
856 | #endif |
---|
857 | return(NULL); |
---|
858 | } |
---|
859 | |
---|
860 | poly m = p_ISet (1, r); |
---|
861 | p_ExpVectorDiff (m, p2, p1, r); // m = lm(p2) / lm(p1) |
---|
862 | //p_Setm(m,r); |
---|
863 | #ifdef PDEBUG |
---|
864 | p_Test (m,r); |
---|
865 | #endif |
---|
866 | |
---|
867 | number C1 = n_Copy( p_GetCoeff(p1, r), r); |
---|
868 | number C2 = n_Copy( p_GetCoeff(p2, r), r); |
---|
869 | |
---|
870 | /* GCD stuff */ |
---|
871 | number C = n_Gcd(C1, C2, r); |
---|
872 | |
---|
873 | if (!n_IsOne(C, r)) |
---|
874 | { |
---|
875 | C1 = n_Div(C1, C, r); |
---|
876 | C2 = n_Div(C2, C, r); |
---|
877 | } |
---|
878 | n_Delete(&C,r); |
---|
879 | |
---|
880 | const int iSign = sca_Sign_mm_Mult_mm( m, p1, r ); |
---|
881 | |
---|
882 | if(iSign == 1) |
---|
883 | C2 = n_InpNeg(C2,r); |
---|
884 | |
---|
885 | p_SetCoeff(m, C2, r); |
---|
886 | |
---|
887 | #ifdef PDEBUG |
---|
888 | p_Test(m,r); |
---|
889 | #endif |
---|
890 | |
---|
891 | p2 = p_LmDeleteAndNext( p2, r ); |
---|
892 | |
---|
893 | p2 = p_Mult_nn(p2, C1, r); // p2 !!! |
---|
894 | n_Delete(&C1,r); |
---|
895 | |
---|
896 | poly T = nc_mm_Mult_pp(m, pNext(p1), r); |
---|
897 | p_Delete(&m, r); |
---|
898 | |
---|
899 | p2 = p_Add_q(p2, T, r); |
---|
900 | |
---|
901 | if ( p2!=NULL ) p_Content(p2,r); |
---|
902 | |
---|
903 | #ifdef PDEBUG |
---|
904 | p_Test(p2,r); |
---|
905 | #endif |
---|
906 | |
---|
907 | return(p2); |
---|
908 | } |
---|
909 | |
---|
910 | // should be used only inside nc_SetupQuotient! |
---|
911 | // Check whether this our case: |
---|
912 | // 1. rG is a commutative polynomial ring \otimes anticommutative algebra |
---|
913 | // 2. factor ideal rGR->qideal contains squares of all alternating variables. |
---|
914 | // |
---|
915 | // if yes, make rGR a super-commutative algebra! |
---|
916 | // NOTE: Factors of SuperCommutative Algebras are supported this way! |
---|
917 | // |
---|
918 | // rG == NULL means that there is no separate base G-algebra in this case take rGR == rG |
---|
919 | |
---|
920 | // special case: bCopy == true (default value: false) |
---|
921 | // meaning: rGR copies structure from rG |
---|
922 | // (maybe with some minor changes, which don't change the type!) |
---|
923 | bool sca_SetupQuotient(ring rGR, ring rG, bool bCopy) |
---|
924 | { |
---|
925 | |
---|
926 | ////////////////////////////////////////////////////////////////////////// |
---|
927 | // checks... |
---|
928 | ////////////////////////////////////////////////////////////////////////// |
---|
929 | if( rG == NULL ) |
---|
930 | rG = rGR; |
---|
931 | |
---|
932 | assume(rGR != NULL); |
---|
933 | assume(rG != NULL); |
---|
934 | assume(rIsPluralRing(rG)); |
---|
935 | |
---|
936 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
937 | PrintS("sca_SetupQuotient(rGR, rG, bCopy)"); |
---|
938 | |
---|
939 | { |
---|
940 | PrintS("\nrG: \n"); rWrite(rG); |
---|
941 | PrintS("\nrGR: \n"); rWrite(rGR); |
---|
942 | PrintLn(); |
---|
943 | } |
---|
944 | #endif |
---|
945 | |
---|
946 | |
---|
947 | if(bCopy) |
---|
948 | { |
---|
949 | if(rIsSCA(rG) && (rG != rGR)) |
---|
950 | return sca_Force(rGR, scaFirstAltVar(rG), scaLastAltVar(rG)); |
---|
951 | else |
---|
952 | return false; |
---|
953 | } |
---|
954 | |
---|
955 | assume(!bCopy); |
---|
956 | |
---|
957 | const int N = rG->N; |
---|
958 | |
---|
959 | if(N < 2) |
---|
960 | return false; |
---|
961 | |
---|
962 | |
---|
963 | // if( (ncRingType(rG) != nc_skew) || (ncRingType(rG) != nc_comm) ) |
---|
964 | // return false; |
---|
965 | |
---|
966 | #if OUTPUT |
---|
967 | PrintS("sca_SetupQuotient: qring?\n"); |
---|
968 | #endif |
---|
969 | |
---|
970 | if(rGR->qideal == NULL) // there should be a factor! |
---|
971 | return false; |
---|
972 | |
---|
973 | #if OUTPUT |
---|
974 | PrintS("sca_SetupQuotient: qideal!!!\n"); |
---|
975 | #endif |
---|
976 | |
---|
977 | // if((rG->qideal != NULL) && (rG != rGR) ) // we cannot change from factor to factor at the time, sorry! |
---|
978 | // return false; |
---|
979 | |
---|
980 | |
---|
981 | int iAltVarEnd = -1; |
---|
982 | int iAltVarStart = N+1; |
---|
983 | |
---|
984 | const nc_struct* NC = rG->GetNC(); |
---|
985 | const ring rBase = rG; //NC->basering; |
---|
986 | const matrix C = NC->C; // live in rBase! |
---|
987 | const matrix D = NC->D; // live in rBase! |
---|
988 | |
---|
989 | #if OUTPUT |
---|
990 | PrintS("sca_SetupQuotient: AltVars?!\n"); |
---|
991 | #endif |
---|
992 | |
---|
993 | for(int i = 1; i < N; i++) |
---|
994 | { |
---|
995 | for(int j = i + 1; j <= N; j++) |
---|
996 | { |
---|
997 | if( MATELEM(D,i,j) != NULL) // !!!??? |
---|
998 | { |
---|
999 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1000 | Print("Nonzero D[%d, %d]\n", i, j); |
---|
1001 | #endif |
---|
1002 | return false; |
---|
1003 | } |
---|
1004 | |
---|
1005 | |
---|
1006 | assume(MATELEM(C,i,j) != NULL); // after CallPlural! |
---|
1007 | number c = p_GetCoeff(MATELEM(C,i,j), rBase); |
---|
1008 | |
---|
1009 | if( n_IsMOne(c, rBase) ) // !!!??? |
---|
1010 | { |
---|
1011 | if( i < iAltVarStart) |
---|
1012 | iAltVarStart = i; |
---|
1013 | |
---|
1014 | if( j > iAltVarEnd) |
---|
1015 | iAltVarEnd = j; |
---|
1016 | } else |
---|
1017 | { |
---|
1018 | if( !n_IsOne(c, rBase) ) |
---|
1019 | { |
---|
1020 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1021 | Print("Wrong Coeff at: [%d, %d]\n", i, j); |
---|
1022 | #endif |
---|
1023 | return false; |
---|
1024 | } |
---|
1025 | } |
---|
1026 | } |
---|
1027 | } |
---|
1028 | |
---|
1029 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1030 | Print("AltVars?1: [%d, %d]\n", iAltVarStart, iAltVarEnd); |
---|
1031 | #endif |
---|
1032 | |
---|
1033 | |
---|
1034 | if( (iAltVarEnd == -1) || (iAltVarStart == (N+1)) ) |
---|
1035 | return false; // either no alternating varables, or a single one => we are in commutative case! |
---|
1036 | |
---|
1037 | |
---|
1038 | for(int i = 1; i < N; i++) |
---|
1039 | { |
---|
1040 | for(int j = i + 1; j <= N; j++) |
---|
1041 | { |
---|
1042 | assume(MATELEM(C,i,j) != NULL); // after CallPlural! |
---|
1043 | number c = p_GetCoeff(MATELEM(C,i,j), rBase); |
---|
1044 | |
---|
1045 | if( (iAltVarStart <= i) && (j <= iAltVarEnd) ) // S <= i < j <= E |
---|
1046 | { // anticommutative part |
---|
1047 | if( !n_IsMOne(c, rBase) ) |
---|
1048 | { |
---|
1049 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1050 | Print("Wrong Coeff at: [%d, %d]\n", i, j); |
---|
1051 | #endif |
---|
1052 | return false; |
---|
1053 | } |
---|
1054 | } else |
---|
1055 | { // should commute |
---|
1056 | if( !n_IsOne(c, rBase) ) |
---|
1057 | { |
---|
1058 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1059 | Print("Wrong Coeff at: [%d, %d]\n", i, j); |
---|
1060 | #endif |
---|
1061 | return false; |
---|
1062 | } |
---|
1063 | } |
---|
1064 | } |
---|
1065 | } |
---|
1066 | |
---|
1067 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1068 | Print("AltVars!?: [%d, %d]\n", iAltVarStart, iAltVarEnd); |
---|
1069 | #endif |
---|
1070 | |
---|
1071 | assume( 1 <= iAltVarStart ); |
---|
1072 | assume( iAltVarStart < iAltVarEnd ); |
---|
1073 | assume( iAltVarEnd <= N ); |
---|
1074 | |
---|
1075 | |
---|
1076 | // ring rSaveRing = assureCurrentRing(rG); |
---|
1077 | |
---|
1078 | |
---|
1079 | assume(rGR->qideal != NULL); |
---|
1080 | assume(rGR->N == rG->N); |
---|
1081 | // assume(rG->qideal == NULL); // ? |
---|
1082 | |
---|
1083 | const ideal idQuotient = rGR->qideal; |
---|
1084 | |
---|
1085 | |
---|
1086 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1087 | PrintS("Analyzing quotient ideal:\n"); |
---|
1088 | idPrint(idQuotient); // in rG!!! |
---|
1089 | #endif |
---|
1090 | |
---|
1091 | |
---|
1092 | // check for |
---|
1093 | // y_{iAltVarStart}^2, y_{iAltVarStart+1}^2, \ldots, y_{iAltVarEnd}^2 (iAltVarEnd > iAltVarStart) |
---|
1094 | // to be within quotient ideal. |
---|
1095 | |
---|
1096 | bool bSCA = true; |
---|
1097 | |
---|
1098 | int b = N+1; |
---|
1099 | int e = -1; |
---|
1100 | |
---|
1101 | if(rIsSCA(rG)) |
---|
1102 | { |
---|
1103 | b = si_min(b, scaFirstAltVar(rG)); |
---|
1104 | e = si_max(e, scaLastAltVar(rG)); |
---|
1105 | |
---|
1106 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1107 | Print("AltVars!?: [%d, %d]\n", b, e); |
---|
1108 | #endif |
---|
1109 | } |
---|
1110 | |
---|
1111 | for ( int i = iAltVarStart; (i <= iAltVarEnd) && bSCA; i++ ) |
---|
1112 | if( (i < b) || (i > e) ) // otherwise it's ok since rG is an SCA! |
---|
1113 | { |
---|
1114 | poly square = p_One( rG); |
---|
1115 | p_SetExp(square, i, 2, rG); // square = var(i)^2. |
---|
1116 | p_Setm(square, rG); |
---|
1117 | |
---|
1118 | // square = NF( var(i)^2 | Q ) |
---|
1119 | // NOTE: there is no better way to check this in general! |
---|
1120 | square = nc_NF(idQuotient, NULL, square, 0, 1, rG); // must ran in currRing == rG! |
---|
1121 | |
---|
1122 | if( square != NULL ) // var(i)^2 is not in Q? |
---|
1123 | { |
---|
1124 | p_Delete(&square, rG); |
---|
1125 | bSCA = false; |
---|
1126 | break; |
---|
1127 | } |
---|
1128 | } |
---|
1129 | |
---|
1130 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1131 | Print("ScaVars!: [%d, %d]\n", iAltVarStart, iAltVarEnd); |
---|
1132 | #endif |
---|
1133 | |
---|
1134 | |
---|
1135 | ////////////////////////////////////////////////////////////////////////// |
---|
1136 | // ok... here we go. let's setup it!!! |
---|
1137 | ////////////////////////////////////////////////////////////////////////// |
---|
1138 | ideal tempQ = id_KillSquares(idQuotient, iAltVarStart, iAltVarEnd, rG); // in rG!!! |
---|
1139 | |
---|
1140 | |
---|
1141 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1142 | PrintS("Quotient: \n"); |
---|
1143 | iiWriteMatrix((matrix)idQuotient,"__",1, rG, 0); |
---|
1144 | PrintS("tempSCAQuotient: \n"); |
---|
1145 | iiWriteMatrix((matrix)tempQ,"__",1, rG, 0); |
---|
1146 | #endif |
---|
1147 | |
---|
1148 | idSkipZeroes( tempQ ); |
---|
1149 | |
---|
1150 | ncRingType( rGR, nc_exterior ); |
---|
1151 | |
---|
1152 | scaFirstAltVar( rGR, iAltVarStart ); |
---|
1153 | scaLastAltVar( rGR, iAltVarEnd ); |
---|
1154 | |
---|
1155 | if( idIs0(tempQ) ) |
---|
1156 | rGR->GetNC()->SCAQuotient() = NULL; |
---|
1157 | else |
---|
1158 | rGR->GetNC()->SCAQuotient() = idrMoveR(tempQ, rG, rGR); // deletes tempQ! |
---|
1159 | |
---|
1160 | nc_p_ProcsSet(rGR, rGR->p_Procs); // !!!!!!!!!!!!!!!!! |
---|
1161 | |
---|
1162 | |
---|
1163 | #if ((defined(PDEBUG) && OUTPUT) || MYTEST) |
---|
1164 | PrintS("SCAQuotient: \n"); |
---|
1165 | if(tempQ != NULL) |
---|
1166 | iiWriteMatrix((matrix)tempQ,"__",1, rGR, 0); |
---|
1167 | else |
---|
1168 | PrintS("(NULL)\n"); |
---|
1169 | #endif |
---|
1170 | |
---|
1171 | return true; |
---|
1172 | } |
---|
1173 | |
---|
1174 | |
---|
1175 | bool sca_Force(ring rGR, int b, int e) |
---|
1176 | { |
---|
1177 | assume(rGR != NULL); |
---|
1178 | assume(rIsPluralRing(rGR)); |
---|
1179 | assume(!rIsSCA(rGR)); |
---|
1180 | |
---|
1181 | const int N = rGR->N; |
---|
1182 | |
---|
1183 | // ring rSaveRing = currRing; |
---|
1184 | // if(rSaveRing != rGR) |
---|
1185 | // rChangeCurrRing(rGR); |
---|
1186 | |
---|
1187 | const ideal idQuotient = rGR->qideal; |
---|
1188 | |
---|
1189 | ideal tempQ = idQuotient; |
---|
1190 | |
---|
1191 | if( b <= N && e >= 1 ) |
---|
1192 | tempQ = id_KillSquares(idQuotient, b, e, rGR); |
---|
1193 | |
---|
1194 | idSkipZeroes( tempQ ); |
---|
1195 | |
---|
1196 | ncRingType( rGR, nc_exterior ); |
---|
1197 | |
---|
1198 | if( idIs0(tempQ) ) |
---|
1199 | rGR->GetNC()->SCAQuotient() = NULL; |
---|
1200 | else |
---|
1201 | rGR->GetNC()->SCAQuotient() = tempQ; |
---|
1202 | |
---|
1203 | |
---|
1204 | scaFirstAltVar( rGR, b ); |
---|
1205 | scaLastAltVar( rGR, e ); |
---|
1206 | |
---|
1207 | |
---|
1208 | nc_p_ProcsSet(rGR, rGR->p_Procs); |
---|
1209 | |
---|
1210 | // if(rSaveRing != rGR) |
---|
1211 | // rChangeCurrRing(rSaveRing); |
---|
1212 | |
---|
1213 | return true; |
---|
1214 | } |
---|
1215 | |
---|
1216 | // return x_i * pPoly; preserve pPoly. |
---|
1217 | poly sca_pp_Mult_xi_pp(short i, const poly pPoly, const ring rRing) |
---|
1218 | { |
---|
1219 | assume(1 <= i); |
---|
1220 | assume(i <= rVar(rRing)); |
---|
1221 | |
---|
1222 | if(rIsSCA(rRing)) |
---|
1223 | return sca_xi_Mult_pp(i, pPoly, rRing); |
---|
1224 | |
---|
1225 | |
---|
1226 | |
---|
1227 | poly xi = p_One( rRing); |
---|
1228 | p_SetExp(xi, i, 1, rRing); |
---|
1229 | p_Setm(xi, rRing); |
---|
1230 | |
---|
1231 | poly pResult = pp_Mult_qq(xi, pPoly, rRing); |
---|
1232 | |
---|
1233 | p_Delete( &xi, rRing); |
---|
1234 | |
---|
1235 | return pResult; |
---|
1236 | |
---|
1237 | } |
---|
1238 | |
---|
1239 | void sca_p_ProcsSet(ring rGR, p_Procs_s* p_Procs) |
---|
1240 | { |
---|
1241 | |
---|
1242 | // "commutative" procedures: |
---|
1243 | rGR->p_Procs->p_Mult_mm = sca_p_Mult_mm; |
---|
1244 | rGR->p_Procs->pp_Mult_mm = sca_pp_Mult_mm; |
---|
1245 | |
---|
1246 | p_Procs->p_Mult_mm = sca_p_Mult_mm; |
---|
1247 | p_Procs->pp_Mult_mm = sca_pp_Mult_mm; |
---|
1248 | |
---|
1249 | // non-commutaitve |
---|
1250 | rGR->GetNC()->p_Procs.mm_Mult_p = sca_mm_Mult_p; |
---|
1251 | rGR->GetNC()->p_Procs.mm_Mult_pp = sca_mm_Mult_pp; |
---|
1252 | |
---|
1253 | // rGR->GetNC()->p_Procs.SPoly = sca_SPoly; |
---|
1254 | // rGR->GetNC()->p_Procs.ReduceSPoly = sca_ReduceSpoly; |
---|
1255 | |
---|
1256 | #if 0 |
---|
1257 | |
---|
1258 | // Multiplication procedures: |
---|
1259 | |
---|
1260 | p_Procs->p_Mult_mm = sca_p_Mult_mm; |
---|
1261 | _p_procs->p_Mult_mm = sca_p_Mult_mm; |
---|
1262 | |
---|
1263 | p_Procs->pp_Mult_mm = sca_pp_Mult_mm; |
---|
1264 | _p_procs->pp_Mult_mm = sca_pp_Mult_mm; |
---|
1265 | |
---|
1266 | r->GetNC()->mmMultP() = sca_mm_Mult_p; |
---|
1267 | r->GetNC()->mmMultPP() = sca_mm_Mult_pp; |
---|
1268 | |
---|
1269 | /* |
---|
1270 | // ??????????????????????????????????????? coefficients swell... |
---|
1271 | r->GetNC()->SPoly() = sca_SPoly; |
---|
1272 | r->GetNC()->ReduceSPoly() = sca_ReduceSpoly; |
---|
1273 | */ |
---|
1274 | // r->GetNC()->BucketPolyRed() = gnc_kBucketPolyRed; |
---|
1275 | // r->GetNC()->BucketPolyRed_Z()= gnc_kBucketPolyRed_Z; |
---|
1276 | #endif |
---|
1277 | |
---|
1278 | // local ordering => Mora, otherwise - Buchberger! |
---|
1279 | if (rHasLocalOrMixedOrdering(rGR)) |
---|
1280 | rGR->GetNC()->p_Procs.GB = cast_A_to_vptr(sca_mora); |
---|
1281 | else |
---|
1282 | rGR->GetNC()->p_Procs.GB = cast_A_to_vptr(sca_bba); // sca_gr_bba? |
---|
1283 | } |
---|
1284 | |
---|
1285 | |
---|
1286 | // bi-Degree (x, y) of monomial "m" |
---|
1287 | // x-es and y-s are weighted by wx and wy resp. |
---|
1288 | // [optional] components have weights by wCx and wCy. |
---|
1289 | static inline void m_GetBiDegree(const poly m, |
---|
1290 | const intvec *wx, const intvec *wy, |
---|
1291 | const intvec *wCx, const intvec *wCy, |
---|
1292 | int& dx, int& dy, const ring r) |
---|
1293 | { |
---|
1294 | const unsigned int N = r->N; |
---|
1295 | |
---|
1296 | p_Test(m, r); |
---|
1297 | |
---|
1298 | assume( wx != NULL ); |
---|
1299 | assume( wy != NULL ); |
---|
1300 | |
---|
1301 | assume( wx->cols() == 1 ); |
---|
1302 | assume( wy->cols() == 1 ); |
---|
1303 | |
---|
1304 | assume( (unsigned int)wx->rows() >= N ); |
---|
1305 | assume( (unsigned int)wy->rows() >= N ); |
---|
1306 | |
---|
1307 | int x = 0; |
---|
1308 | int y = 0; |
---|
1309 | |
---|
1310 | for(int i = N; i > 0; i--) |
---|
1311 | { |
---|
1312 | const int d = p_GetExp(m, i, r); |
---|
1313 | x += d * (*wx)[i-1]; |
---|
1314 | y += d * (*wy)[i-1]; |
---|
1315 | } |
---|
1316 | |
---|
1317 | if( (wCx != NULL) && (wCy != NULL) ) |
---|
1318 | { |
---|
1319 | const int c = p_GetComp(m, r); |
---|
1320 | |
---|
1321 | if( wCx->range(c) ) |
---|
1322 | x += (*wCx)[c]; |
---|
1323 | |
---|
1324 | if( wCy->range(c) ) |
---|
1325 | x += (*wCy)[c]; |
---|
1326 | } |
---|
1327 | |
---|
1328 | dx = x; |
---|
1329 | dy = y; |
---|
1330 | } |
---|
1331 | |
---|
1332 | // returns true if polynom p is bi-homogenous with respect to the given weights |
---|
1333 | // simultaneously sets bi-Degree |
---|
1334 | bool p_IsBiHomogeneous(const poly p, |
---|
1335 | const intvec *wx, const intvec *wy, |
---|
1336 | const intvec *wCx, const intvec *wCy, |
---|
1337 | int &dx, int &dy, |
---|
1338 | const ring r) |
---|
1339 | { |
---|
1340 | if( p == NULL ) |
---|
1341 | { |
---|
1342 | dx = 0; |
---|
1343 | dy = 0; |
---|
1344 | return true; |
---|
1345 | } |
---|
1346 | |
---|
1347 | poly q = p; |
---|
1348 | |
---|
1349 | |
---|
1350 | int ddx, ddy; |
---|
1351 | |
---|
1352 | m_GetBiDegree( q, wx, wy, wCx, wCy, ddx, ddy, r); // get bi degree of lm(p) |
---|
1353 | |
---|
1354 | pIter(q); |
---|
1355 | |
---|
1356 | for(; q != NULL; pIter(q) ) |
---|
1357 | { |
---|
1358 | int x, y; |
---|
1359 | |
---|
1360 | m_GetBiDegree( q, wx, wy, wCx, wCy, x, y, r); // get bi degree of q |
---|
1361 | |
---|
1362 | if ( (x != ddx) || (y != ddy) ) return false; |
---|
1363 | } |
---|
1364 | |
---|
1365 | dx = ddx; |
---|
1366 | dy = ddy; |
---|
1367 | |
---|
1368 | return true; |
---|
1369 | } |
---|
1370 | |
---|
1371 | |
---|
1372 | // returns true if id is bi-homogenous without respect to the given weights |
---|
1373 | bool id_IsBiHomogeneous(const ideal id, |
---|
1374 | const intvec *wx, const intvec *wy, |
---|
1375 | const intvec *wCx, const intvec *wCy, |
---|
1376 | const ring r) |
---|
1377 | { |
---|
1378 | if (id == NULL) return true; // zero ideal |
---|
1379 | |
---|
1380 | const int iSize = IDELEMS(id); |
---|
1381 | |
---|
1382 | if (iSize == 0) return true; |
---|
1383 | |
---|
1384 | bool b = true; |
---|
1385 | int x, y; |
---|
1386 | |
---|
1387 | for(int i = iSize - 1; (i >= 0 ) && b; i--) |
---|
1388 | b = p_IsBiHomogeneous(id->m[i], wx, wy, wCx, wCy, x, y, r); |
---|
1389 | |
---|
1390 | return b; |
---|
1391 | } |
---|
1392 | |
---|
1393 | |
---|
1394 | // returns an intvector with [nvars(r)] integers [1/0] |
---|
1395 | // 1 - for commutative variables |
---|
1396 | // 0 - for anticommutative variables |
---|
1397 | intvec *ivGetSCAXVarWeights(const ring r) |
---|
1398 | { |
---|
1399 | const unsigned int N = r->N; |
---|
1400 | |
---|
1401 | const int CommutativeVariable = 0; // bug correction! |
---|
1402 | const int AntiCommutativeVariable = 0; |
---|
1403 | |
---|
1404 | intvec* w = new intvec(N, 1, CommutativeVariable); |
---|
1405 | |
---|
1406 | if(AntiCommutativeVariable != CommutativeVariable) |
---|
1407 | if( rIsSCA(r) ) |
---|
1408 | { |
---|
1409 | const unsigned int m_iFirstAltVar = scaFirstAltVar(r); |
---|
1410 | const unsigned int m_iLastAltVar = scaLastAltVar(r); |
---|
1411 | |
---|
1412 | for (unsigned int i = m_iFirstAltVar; i<= m_iLastAltVar; i++) |
---|
1413 | { |
---|
1414 | (*w)[i-1] = AntiCommutativeVariable; |
---|
1415 | } |
---|
1416 | } |
---|
1417 | |
---|
1418 | return w; |
---|
1419 | } |
---|
1420 | |
---|
1421 | |
---|
1422 | // returns an intvector with [nvars(r)] integers [1/0] |
---|
1423 | // 0 - for commutative variables |
---|
1424 | // 1 - for anticommutative variables |
---|
1425 | intvec *ivGetSCAYVarWeights(const ring r) |
---|
1426 | { |
---|
1427 | const unsigned int N = r->N; |
---|
1428 | |
---|
1429 | const int CommutativeVariable = 0; |
---|
1430 | const int AntiCommutativeVariable = 1; |
---|
1431 | |
---|
1432 | intvec* w = new intvec(N, 1, CommutativeVariable); |
---|
1433 | |
---|
1434 | if(AntiCommutativeVariable != CommutativeVariable) |
---|
1435 | if( rIsSCA(r) ) |
---|
1436 | { |
---|
1437 | const unsigned int m_iFirstAltVar = scaFirstAltVar(r); |
---|
1438 | const unsigned int m_iLastAltVar = scaLastAltVar(r); |
---|
1439 | |
---|
1440 | for (unsigned int i = m_iFirstAltVar; i<= m_iLastAltVar; i++) |
---|
1441 | { |
---|
1442 | (*w)[i-1] = AntiCommutativeVariable; |
---|
1443 | } |
---|
1444 | } |
---|
1445 | return w; |
---|
1446 | } |
---|
1447 | |
---|
1448 | |
---|
1449 | |
---|
1450 | |
---|
1451 | // reduce term lt(m) modulo <y_i^2> , i = iFirstAltVar .. iLastAltVar: |
---|
1452 | // either create a copy of m or return NULL |
---|
1453 | static inline poly m_KillSquares(const poly m, |
---|
1454 | const short iFirstAltVar, const short iLastAltVar, |
---|
1455 | const ring r) |
---|
1456 | { |
---|
1457 | #ifdef PDEBUG |
---|
1458 | p_Test(m, r); |
---|
1459 | assume( (iFirstAltVar >= 1) && (iLastAltVar <= rVar(r)) && (iFirstAltVar <= iLastAltVar) ); |
---|
1460 | |
---|
1461 | #if 0 |
---|
1462 | Print("m_KillSquares, m = "); // ! |
---|
1463 | p_Write(m, r); |
---|
1464 | #endif |
---|
1465 | #endif |
---|
1466 | |
---|
1467 | assume( m != NULL ); |
---|
1468 | |
---|
1469 | for(short k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
1470 | if( p_GetExp(m, k, r) > 1 ) |
---|
1471 | return NULL; |
---|
1472 | |
---|
1473 | return p_Head(m, r); |
---|
1474 | } |
---|
1475 | |
---|
1476 | |
---|
1477 | // reduce polynomial p modulo <y_i^2> , i = iFirstAltVar .. iLastAltVar |
---|
1478 | // returns a new poly! |
---|
1479 | poly p_KillSquares(const poly p, |
---|
1480 | const short iFirstAltVar, const short iLastAltVar, |
---|
1481 | const ring r) |
---|
1482 | { |
---|
1483 | #ifdef PDEBUG |
---|
1484 | p_Test(p, r); |
---|
1485 | |
---|
1486 | assume( (iFirstAltVar >= 1) && (iLastAltVar <= r->N) && (iFirstAltVar <= iLastAltVar) ); |
---|
1487 | |
---|
1488 | #if 0 |
---|
1489 | Print("p_KillSquares, p = "); // ! |
---|
1490 | p_Write(p, r); |
---|
1491 | #endif |
---|
1492 | #endif |
---|
1493 | |
---|
1494 | |
---|
1495 | if( p == NULL ) |
---|
1496 | return NULL; |
---|
1497 | |
---|
1498 | poly pResult = NULL; |
---|
1499 | poly* ppPrev = &pResult; |
---|
1500 | |
---|
1501 | for( poly q = p; q!= NULL; pIter(q) ) |
---|
1502 | { |
---|
1503 | #ifdef PDEBUG |
---|
1504 | p_Test(q, r); |
---|
1505 | #endif |
---|
1506 | |
---|
1507 | // terms will be in the same order because of quasi-ordering! |
---|
1508 | poly v = m_KillSquares(q, iFirstAltVar, iLastAltVar, r); |
---|
1509 | |
---|
1510 | if( v != NULL ) |
---|
1511 | { |
---|
1512 | *ppPrev = v; |
---|
1513 | ppPrev = &pNext(v); |
---|
1514 | } |
---|
1515 | |
---|
1516 | } |
---|
1517 | |
---|
1518 | #ifdef PDEBUG |
---|
1519 | p_Test(pResult, r); |
---|
1520 | #if 0 |
---|
1521 | Print("p_KillSquares => "); // ! |
---|
1522 | p_Write(pResult, r); |
---|
1523 | #endif |
---|
1524 | #endif |
---|
1525 | |
---|
1526 | return(pResult); |
---|
1527 | } |
---|
1528 | |
---|
1529 | |
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1530 | |
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1531 | |
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1532 | // reduces ideal id modulo <y_i^2> , i = iFirstAltVar .. iLastAltVar |
---|
1533 | // returns the reduced ideal or zero ideal. |
---|
1534 | ideal id_KillSquares(const ideal id, |
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1535 | const short iFirstAltVar, const short iLastAltVar, |
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1536 | const ring r, const bool bSkipZeroes) |
---|
1537 | { |
---|
1538 | if (id == NULL) return id; // zero ideal |
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1539 | |
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1540 | assume( (iFirstAltVar >= 1) && (iLastAltVar <= rVar(r)) && (iFirstAltVar <= iLastAltVar) ); |
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1541 | |
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1542 | const int iSize = IDELEMS(id); |
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1543 | |
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1544 | if (iSize == 0) return id; |
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1545 | |
---|
1546 | ideal temp = idInit(iSize, id->rank); |
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1547 | |
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1548 | #if 0 |
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1549 | PrintS("<id_KillSquares>\n"); |
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1550 | { |
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1551 | PrintS("ideal id: \n"); |
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1552 | for (unsigned int i = 0; i < IDELEMS(id); i++) |
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1553 | { |
---|
1554 | Print("; id[%d] = ", i+1); |
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1555 | p_Write(id->m[i], r); |
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1556 | } |
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1557 | PrintS(";\n"); |
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1558 | PrintLn(); |
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1559 | } |
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1560 | #endif |
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1561 | |
---|
1562 | |
---|
1563 | for (int j = 0; j < iSize; j++) |
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1564 | temp->m[j] = p_KillSquares(id->m[j], iFirstAltVar, iLastAltVar, r); |
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1565 | |
---|
1566 | if( bSkipZeroes ) |
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1567 | idSkipZeroes(temp); |
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1568 | |
---|
1569 | #if 0 |
---|
1570 | PrintS("<id_KillSquares>\n"); |
---|
1571 | { |
---|
1572 | PrintS("ideal temp: \n"); |
---|
1573 | for (int i = 0; i < IDELEMS(temp); i++) |
---|
1574 | { |
---|
1575 | Print("; temp[%d] = ", i+1); |
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1576 | p_Write(temp->m[i], r); |
---|
1577 | } |
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1578 | PrintS(";\n"); |
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1579 | PrintLn(); |
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1580 | } |
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1581 | PrintS("</id_KillSquares>\n"); |
---|
1582 | #endif |
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1583 | |
---|
1584 | // temp->rank = idRankFreeModule(temp, r); |
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1585 | |
---|
1586 | return temp; |
---|
1587 | } |
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1588 | |
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1589 | |
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1590 | |
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1591 | |
---|
1592 | #endif |
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