1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: polys.cc,v 1.53 2000-01-31 14:57:32 Singular Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT - all basic methods to manipulate polynomials |
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8 | */ |
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9 | |
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10 | /* includes */ |
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11 | #include <stdio.h> |
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12 | #include <string.h> |
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13 | #include <ctype.h> |
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14 | #include "mod2.h" |
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15 | #include "tok.h" |
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16 | #include "mmemory.h" |
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17 | #include "febase.h" |
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18 | #include "numbers.h" |
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19 | #include "polys.h" |
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20 | #include "ring.h" |
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21 | #include "binom.h" |
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22 | #include "polys-comp.h" |
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23 | |
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24 | /* ----------- global variables, set by pSetGlobals --------------------- */ |
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25 | /* initializes the internal data from the exp vector */ |
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26 | pSetmProc pSetm; |
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27 | /* computes length and maximal degree of a POLYnomial */ |
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28 | pLDegProc pLDeg; |
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29 | /* computes the degree of the initial term, used for std */ |
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30 | pFDegProc pFDeg; |
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31 | /* the monomial ordering of the head monomials a and b */ |
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32 | /* returns -1 if a comes before b, 0 if a=b, 1 otherwise */ |
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33 | |
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34 | int pVariables; // number of variables |
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35 | //int pVariablesW; // number of words of pVariables exponents |
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36 | //int pVariables1W; // number of words of (pVariables+1) exponents |
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37 | int pMonomSize; // size of monom (in bytes) |
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38 | int pMonomSizeW; // size of monom (in words) |
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39 | int *pVarOffset; // controls the way exponents are stored in a vector |
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40 | //int pVarLowIndex; // lowest exponent index |
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41 | //int pVarHighIndex; // highest exponent index |
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42 | //int pVarCompIndex; // Location of component in exponent vector |
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43 | |
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44 | /* 1 for polynomial ring, -1 otherwise */ |
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45 | int pOrdSgn; |
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46 | /* TRUE for momomial output as x2y, FALSE for x^2*y */ |
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47 | int pShortOut = (int)TRUE; |
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48 | // it is of type int, not BOOLEAN because it is also in ip |
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49 | /* TRUE if the monomial ordering is not compatible with pFDeg */ |
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50 | BOOLEAN pLexOrder; |
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51 | /* TRUE if the monomial ordering has polynomial and power series blocks */ |
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52 | BOOLEAN pMixedOrder; |
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53 | /* 1 for c ordering, -1 otherwise (i.e. for C ordering) */ |
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54 | int pComponentOrder; |
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55 | |
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56 | /* ----------- global variables, set by procedures from hecke/kstd1 ----- */ |
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57 | /* the highest monomial below pHEdge */ |
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58 | poly ppNoether = NULL; |
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59 | |
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60 | /* -------------- static variables --------------------------------------- */ |
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61 | /*is the basic comparing procedure during a computation of syzygies*/ |
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62 | //static pCompProc pCompOld; |
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63 | |
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64 | /*contains the headterms for the Schreyer orderings*/ |
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65 | static int* SchreyerOrd; |
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66 | static int maxSchreyer=0; |
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67 | static int indexShift=0; |
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68 | static pLDegProc pLDegOld; |
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69 | |
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70 | static int** polys_wv; |
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71 | static short * firstwv; |
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72 | static int * block0; |
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73 | static int * block1; |
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74 | static int firstBlockEnds; |
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75 | static int * order; |
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76 | |
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77 | /*0 implementation*/ |
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78 | /*-------- the several possibilities for pSetm:-----------------------*/ |
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79 | |
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80 | void rSetm(poly p) |
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81 | { |
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82 | int pos=0; |
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83 | if (currRing->typ!=NULL) |
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84 | { |
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85 | loop |
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86 | { |
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87 | sro_ord* o=&(currRing->typ[pos]); |
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88 | switch(o->ord_typ) |
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89 | { |
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90 | case ro_dp: |
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91 | { |
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92 | int a,e; |
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93 | a=o->data.dp.start; |
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94 | e=o->data.dp.end; |
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95 | long ord=0; |
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96 | for(int i=a;i<=e;i++) ord+=pGetExp(p,i); |
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97 | p->exp.l[o->data.dp.place]=ord; |
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98 | break; |
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99 | } |
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100 | case ro_wp: |
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101 | { |
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102 | int a,e; |
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103 | a=o->data.wp.start; |
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104 | e=o->data.wp.end; |
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105 | int *w=o->data.wp.weights; |
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106 | long ord=0; |
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107 | for(int i=a;i<=e;i++) ord+=pGetExp(p,i)*w[i-a]; |
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108 | p->exp.l[o->data.wp.place]=ord; |
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109 | break; |
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110 | } |
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111 | case ro_cp: |
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112 | { |
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113 | int a,e; |
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114 | a=o->data.cp.start; |
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115 | e=o->data.cp.end; |
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116 | int pl=o->data.cp.place; |
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117 | for(int i=a;i<=e;i++) { p->exp.e[pl]=pGetExp(p,i); pl++; } |
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118 | break; |
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119 | } |
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120 | case ro_syzcomp: |
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121 | { |
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122 | int c=pGetComp(p); |
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123 | long sc = c; |
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124 | if (o->data.syzcomp.ShiftedComponents != NULL) |
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125 | { |
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126 | assume(o->data.syzcomp.Components != NULL); |
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127 | assume(c == 0 || o->data.syzcomp.Components[c] != 0); |
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128 | sc = |
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129 | o->data.syzcomp.ShiftedComponents[o->data.syzcomp.Components[c]]; |
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130 | assume(c == 0 || sc != 0); |
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131 | } |
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132 | p->exp.l[o->data.syzcomp.place]=sc; |
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133 | break; |
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134 | } |
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135 | case ro_syz: |
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136 | { |
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137 | int c=pGetComp(p); |
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138 | if (c > o->data.syz.limit) |
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139 | p->exp.l[o->data.syz.place] = o->data.syz.curr_index; |
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140 | else if (c > 0) |
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141 | p->exp.l[o->data.syz.place]= o->data.syz.syz_index[c]; |
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142 | else |
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143 | { |
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144 | assume(c == 0); |
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145 | p->exp.l[o->data.syz.place]= 0; |
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146 | } |
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147 | break; |
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148 | } |
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149 | default: |
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150 | Print("wrong ord in rSetm:%d\n",o->ord_typ); |
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151 | return; |
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152 | } |
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153 | pos++; |
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154 | if(pos==currRing->OrdSize) return; |
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155 | } |
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156 | } |
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157 | } |
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158 | |
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159 | void rSetmS(poly p, int* Components, long* ShiftedComponents) |
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160 | { |
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161 | int pos=0; |
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162 | assume(Components != NULL && ShiftedComponents != NULL); |
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163 | if (currRing->typ!=NULL) |
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164 | { |
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165 | loop |
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166 | { |
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167 | sro_ord* o=&(currRing->typ[pos]); |
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168 | switch(o->ord_typ) |
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169 | { |
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170 | case ro_dp: |
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171 | { |
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172 | int a,e; |
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173 | a=o->data.dp.start; |
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174 | e=o->data.dp.end; |
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175 | long ord=0; |
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176 | for(int i=a;i<=e;i++) ord+=pGetExp(p,i); |
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177 | p->exp.l[o->data.dp.place]=ord; |
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178 | break; |
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179 | } |
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180 | case ro_wp: |
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181 | { |
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182 | int a,e; |
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183 | a=o->data.wp.start; |
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184 | e=o->data.wp.end; |
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185 | int *w=o->data.wp.weights; |
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186 | long ord=0; |
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187 | for(int i=a;i<=e;i++) ord+=pGetExp(p,i)*w[i-a]; |
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188 | p->exp.l[o->data.wp.place]=ord; |
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189 | break; |
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190 | } |
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191 | case ro_cp: |
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192 | { |
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193 | int a,e; |
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194 | a=o->data.cp.start; |
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195 | e=o->data.cp.end; |
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196 | int pl=o->data.cp.place; |
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197 | for(int i=a;i<=e;i++) { p->exp.e[pl]=pGetExp(p,i); pl++; } |
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198 | break; |
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199 | } |
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200 | case ro_syzcomp: |
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201 | { |
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202 | #if 1 |
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203 | int c=pGetComp(p); |
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204 | long sc = ShiftedComponents[Components[c]]; |
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205 | assume(c == 0 || Components[c] != 0); |
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206 | assume(c == 0 || sc != 0); |
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207 | p->exp.l[o->data.syzcomp.place]=sc; |
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208 | #endif |
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209 | break; |
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210 | } |
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211 | default: |
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212 | Print("wrong ord in rSetm:%d\n",o->ord_typ); |
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213 | return; |
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214 | } |
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215 | pos++; |
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216 | if(pos==currRing->OrdSize) return; |
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217 | } |
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218 | } |
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219 | } |
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220 | |
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221 | /*-------- IMPLEMENTATION OF MONOMIAL COMPARISONS ---------------------*/ |
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222 | |
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223 | |
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224 | #define NonZeroR(l, actionG, actionS) \ |
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225 | do \ |
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226 | { \ |
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227 | long _l = l; \ |
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228 | if (_l) \ |
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229 | { \ |
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230 | if (_l > 0) actionG; \ |
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231 | actionS; \ |
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232 | } \ |
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233 | } \ |
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234 | while(0) |
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235 | |
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236 | #define Mreturn(d, multiplier) \ |
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237 | { \ |
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238 | if (d > 0) return multiplier; \ |
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239 | return -multiplier; \ |
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240 | } |
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241 | |
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242 | |
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243 | /*---------------------------------------------------*/ |
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244 | |
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245 | int pComp(poly p1, poly p2) |
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246 | { |
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247 | if (p2==NULL) |
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248 | return 1; |
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249 | if (p1==NULL) |
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250 | return -1; |
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251 | return pComp0(p1,p2); |
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252 | } |
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253 | |
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254 | |
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255 | /*----------pComp handling for syzygies---------------------*/ |
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256 | static void newHeadsB(polyset actHeads,int length) |
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257 | { |
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258 | int i; |
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259 | int* newOrder=(int*)Alloc(length*sizeof(int)); |
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260 | |
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261 | for (i=0;i<length;i++) |
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262 | { |
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263 | if (actHeads[i]!=NULL) |
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264 | { |
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265 | newOrder[i] = SchreyerOrd[pGetComp(actHeads[i])-1]; |
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266 | } |
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267 | else |
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268 | { |
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269 | newOrder[i]=0; |
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270 | } |
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271 | } |
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272 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
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273 | SchreyerOrd = newOrder; |
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274 | maxSchreyer = length; |
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275 | /* |
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276 | *for (i=0;i<maxSchreyer;i++); Print("%d ",SchreyerOrd[i]); |
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277 | *PrintLn(); |
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278 | */ |
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279 | } |
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280 | |
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281 | int mcompSchrB(poly p1,poly p2) |
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282 | { |
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283 | int CompP1=pGetComp(p1),CompP2=pGetComp(p2),result, |
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284 | cP1=SchreyerOrd[CompP1-1],cP2=SchreyerOrd[CompP2-1]; |
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285 | |
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286 | //if (CompP1==CompP2) return pCompOld(p1,p2); |
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287 | if (CompP1==CompP2) return pComp0(p1,p2); |
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288 | pSetComp(p1,cP1); |
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289 | pSetComp(p2,cP2); |
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290 | //result = pCompOld(p1,p2); |
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291 | result = pComp0(p1,p2); |
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292 | pSetComp(p1,CompP1); |
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293 | pSetComp(p2,CompP2); |
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294 | if (!result) |
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295 | { |
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296 | if (CompP1>CompP2) |
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297 | return -1; |
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298 | else if (CompP1<CompP2) |
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299 | return 1; |
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300 | } |
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301 | return result; |
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302 | } |
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303 | |
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304 | |
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305 | static void newHeadsM(polyset actHeads,int length) |
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306 | { |
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307 | int i; |
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308 | int* newOrder= |
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309 | (int*)Alloc0((length+maxSchreyer-indexShift)*sizeof(int)); |
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310 | |
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311 | //for (i=0;i<length+maxSchreyer-indexShift;i++) |
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312 | // newOrder[i]=0; |
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313 | for (i=indexShift;i<maxSchreyer;i++) |
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314 | { |
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315 | newOrder[i-indexShift] = SchreyerOrd[i]; |
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316 | SchreyerOrd[i] = 0; |
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317 | } |
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318 | for (i=maxSchreyer-indexShift;i<length+maxSchreyer-indexShift;i++) |
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319 | newOrder[i] = newOrder[pGetComp(actHeads[i-maxSchreyer+indexShift])-1]; |
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320 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
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321 | SchreyerOrd = newOrder; |
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322 | indexShift = maxSchreyer-indexShift; |
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323 | maxSchreyer = length+indexShift; |
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324 | } |
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325 | |
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326 | /*2 |
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327 | * compute the length of a polynomial (in l) |
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328 | * and the degree of the monomial with maximal degree: |
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329 | * this is NOT the last one and the module component |
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330 | * has to be <= indexShift |
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331 | */ |
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332 | static int ldegSchrM(poly p,int *l) |
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333 | { |
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334 | int t,max; |
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335 | |
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336 | (*l)=1; |
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337 | max=pFDeg(p); |
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338 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=indexShift)) |
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339 | { |
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340 | pIter(p); |
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341 | t=pFDeg(p); |
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342 | if (t>max) max=t; |
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343 | (*l)++; |
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344 | } |
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345 | return max; |
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346 | } |
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347 | |
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348 | int mcompSchrM(poly p1,poly p2) |
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349 | { |
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350 | if ( pGetComp(p1)<=indexShift) |
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351 | { |
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352 | if ( pGetComp(p2)>indexShift) return 1; |
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353 | } |
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354 | else if ( pGetComp(p2)<=indexShift) return -1; |
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355 | return mcompSchrB(p1,p2); |
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356 | } |
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357 | |
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358 | void pSetSchreyerOrdM(polyset nextOrder, int length,int comps) |
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359 | { |
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360 | int i; |
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361 | |
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362 | if (length!=0) |
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363 | { |
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364 | if (maxSchreyer!=0) |
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365 | newHeadsM(nextOrder, length); |
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366 | else |
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367 | { |
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368 | indexShift = comps; |
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369 | if (indexShift==0) indexShift = 1; |
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370 | SchreyerOrd = (int*)Alloc((indexShift+length)*sizeof(int)); |
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371 | maxSchreyer = length+indexShift; |
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372 | for (i=0;i<indexShift;i++) |
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373 | SchreyerOrd[i] = i; |
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374 | for (i=indexShift;i<maxSchreyer;i++) |
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375 | SchreyerOrd[i] = pGetComp(nextOrder[i-indexShift]); |
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376 | //pCompOld = pComp0; |
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377 | //pComp0 = mcompSchrM; |
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378 | pLDegOld = pLDeg; |
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379 | pLDeg = ldegSchrM; |
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380 | } |
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381 | } |
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382 | else |
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383 | { |
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384 | if (maxSchreyer!=0) |
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385 | { |
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386 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
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387 | maxSchreyer = 0; |
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388 | indexShift = 0; |
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389 | //pComp0 = pCompOld; |
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390 | pLDeg = pLDegOld; |
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391 | } |
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392 | } |
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393 | } |
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394 | |
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395 | /*2 |
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396 | * the type of the module ordering: C: -1, c: 1 |
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397 | */ |
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398 | int pModuleOrder() |
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399 | { |
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400 | return pComponentOrder; |
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401 | } |
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402 | |
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403 | /* -------------------------------------------------------------------*/ |
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404 | /* several possibilities for pFDeg: the degree of the head term */ |
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405 | /*2 |
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406 | * compute the degree of the leading monomial of p |
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407 | * the ordering is compatible with degree, use a->order |
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408 | */ |
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409 | int pDeg(poly a) |
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410 | { |
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411 | return pGetOrder(a); |
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412 | } |
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413 | |
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414 | /*2 |
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415 | * compute the degree of the leading monomial of p |
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416 | * with respect to weigths 1 |
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417 | * (all are 1 so save multiplications or they are of different signs) |
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418 | * the ordering is not compatible with degree so do not use p->Order |
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419 | */ |
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420 | int pTotaldegree(poly p) |
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421 | { |
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422 | return pExpQuerSum(p); |
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423 | } |
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424 | |
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425 | /*2 |
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426 | * compute the degree of the leading monomial of p |
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427 | * with respect to weigths from the ordering |
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428 | * the ordering is not compatible with degree so do not use p->Order |
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429 | */ |
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430 | int pWTotaldegree(poly p) |
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431 | { |
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432 | assume(p != NULL); |
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433 | int i, k; |
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434 | int j =0; |
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435 | |
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436 | // iterate through each block: |
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437 | for (i=0;order[i]!=0;i++) |
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438 | { |
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439 | switch(order[i]) |
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440 | { |
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441 | case ringorder_wp: |
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442 | case ringorder_ws: |
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443 | case ringorder_Wp: |
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444 | case ringorder_Ws: |
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445 | for (k=block0[i];k<=block1[i];k++) |
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446 | { // in jedem block: |
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447 | j+= pGetExp(p,k)*polys_wv[i][k-block0[i]]; |
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448 | } |
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449 | break; |
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450 | case ringorder_M: |
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451 | case ringorder_lp: |
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452 | case ringorder_dp: |
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453 | case ringorder_ds: |
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454 | case ringorder_Dp: |
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455 | case ringorder_Ds: |
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456 | for (k=block0[i];k<=block1[i];k++) |
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457 | { |
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458 | j+= pGetExp(p,k); |
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459 | } |
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460 | break; |
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461 | case ringorder_c: |
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462 | case ringorder_C: |
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463 | case ringorder_S: |
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464 | case ringorder_s: |
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465 | break; |
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466 | case ringorder_a: |
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467 | for (k=block0[i];k<=block1[i];k++) |
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468 | { // only one line |
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469 | j+= pGetExp(p,k)*polys_wv[i][k-block0[i]]; |
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470 | } |
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471 | return j; |
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472 | } |
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473 | } |
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474 | return j; |
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475 | } |
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476 | int pWDegree(poly p) |
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477 | { |
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478 | int i, k; |
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479 | int j =0; |
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480 | |
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481 | for(i=1;i<=pVariables;i++) |
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482 | j+=pGetExp(p,i)*pWeight(i); |
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483 | return j; |
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484 | } |
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485 | |
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486 | /* ---------------------------------------------------------------------*/ |
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487 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
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488 | /* compute in l also the pLength of p */ |
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489 | |
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490 | /*2 |
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491 | * compute the length of a polynomial (in l) |
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492 | * and the degree of the monomial with maximal degree: the last one |
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493 | */ |
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494 | static int ldeg0(poly p,int *l) |
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495 | { |
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496 | Exponent_t k= pGetComp(p); |
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497 | int ll=1; |
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498 | |
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499 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))==k)) |
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500 | { |
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501 | pIter(p); |
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502 | ll++; |
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503 | } |
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504 | *l=ll; |
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505 | return pGetOrder(p); |
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506 | } |
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507 | |
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508 | /*2 |
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509 | * compute the length of a polynomial (in l) |
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510 | * and the degree of the monomial with maximal degree: the last one |
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511 | * but search in all components before syzcomp |
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512 | */ |
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513 | static int ldeg0c(poly p,int *l) |
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514 | { |
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515 | int o=pFDeg(p); |
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516 | int ll=1; |
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517 | |
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518 | if (! rIsSyzIndexRing(currRing)) |
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519 | { |
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520 | while ((p=pNext(p))!=NULL) |
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521 | { |
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522 | o=pFDeg(p); |
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523 | ll++; |
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524 | } |
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525 | } |
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526 | else |
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527 | { |
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528 | int curr_limit = rGetCurrSyzLimit(); |
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529 | while ((p=pNext(p))!=NULL) |
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530 | { |
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531 | if (pGetComp(p)<=curr_limit/*syzComp*/) |
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532 | { |
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533 | o=pFDeg(p); |
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534 | ll++; |
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535 | } |
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536 | else break; |
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537 | } |
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538 | } |
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539 | *l=ll; |
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540 | return o; |
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541 | } |
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542 | |
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543 | /*2 |
---|
544 | * compute the length of a polynomial (in l) |
---|
545 | * and the degree of the monomial with maximal degree: the first one |
---|
546 | * this works for the polynomial case with degree orderings |
---|
547 | * (both c,dp and dp,c) |
---|
548 | */ |
---|
549 | static int ldegb(poly p,int *l) |
---|
550 | { |
---|
551 | Exponent_t k= pGetComp(p); |
---|
552 | int o = pFDeg(p); |
---|
553 | int ll=1; |
---|
554 | |
---|
555 | while (((p=pNext(p))!=NULL) && (pGetComp(p)==k)) |
---|
556 | { |
---|
557 | ll++; |
---|
558 | } |
---|
559 | *l=ll; |
---|
560 | return o; |
---|
561 | } |
---|
562 | |
---|
563 | /*2 |
---|
564 | * compute the length of a polynomial (in l) |
---|
565 | * and the degree of the monomial with maximal degree: |
---|
566 | * this is NOT the last one, we have to look for it |
---|
567 | */ |
---|
568 | static int ldeg1(poly p,int *l) |
---|
569 | { |
---|
570 | Exponent_t k= pGetComp(p); |
---|
571 | int ll=1; |
---|
572 | int t,max; |
---|
573 | |
---|
574 | max=pFDeg(p); |
---|
575 | while (((p=pNext(p))!=NULL) && (pGetComp(p)==k)) |
---|
576 | { |
---|
577 | t=pFDeg(p); |
---|
578 | if (t>max) max=t; |
---|
579 | ll++; |
---|
580 | } |
---|
581 | *l=ll; |
---|
582 | return max; |
---|
583 | } |
---|
584 | |
---|
585 | /*2 |
---|
586 | * compute the length of a polynomial (in l) |
---|
587 | * and the degree of the monomial with maximal degree: |
---|
588 | * this is NOT the last one, we have to look for it |
---|
589 | * in all components |
---|
590 | */ |
---|
591 | static int ldeg1c(poly p,int *l) |
---|
592 | { |
---|
593 | int ll=1; |
---|
594 | int t,max; |
---|
595 | |
---|
596 | max=pFDeg(p); |
---|
597 | while ((p=pNext(p))!=NULL) |
---|
598 | { |
---|
599 | if (! rIsSyzIndexRing(currRing) || |
---|
600 | (pGetComp(p)<=rGetCurrSyzLimit())) |
---|
601 | { |
---|
602 | if ((t=pFDeg(p))>max) max=t; |
---|
603 | ll++; |
---|
604 | } |
---|
605 | else break; |
---|
606 | } |
---|
607 | *l=ll; |
---|
608 | return max; |
---|
609 | } |
---|
610 | |
---|
611 | /* -------------------------------------------------------- */ |
---|
612 | /* set the variables for a choosen ordering */ |
---|
613 | |
---|
614 | |
---|
615 | /*2 |
---|
616 | * sets the comparision routine for monomials: for all but the first |
---|
617 | * block of variables (ip is the block number, o_r the number of the ordering) |
---|
618 | */ |
---|
619 | static void HighSet(int ip, int o_r) |
---|
620 | { |
---|
621 | switch(o_r) |
---|
622 | { |
---|
623 | case ringorder_lp: |
---|
624 | case ringorder_dp: |
---|
625 | case ringorder_Dp: |
---|
626 | case ringorder_wp: |
---|
627 | case ringorder_Wp: |
---|
628 | case ringorder_a: |
---|
629 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
630 | break; |
---|
631 | case ringorder_ls: |
---|
632 | case ringorder_ds: |
---|
633 | case ringorder_Ds: |
---|
634 | case ringorder_ws: |
---|
635 | case ringorder_Ws: |
---|
636 | case ringorder_s: |
---|
637 | break; |
---|
638 | case ringorder_c: |
---|
639 | pComponentOrder=1; |
---|
640 | break; |
---|
641 | case ringorder_C: |
---|
642 | case ringorder_S: |
---|
643 | pComponentOrder=-1; |
---|
644 | break; |
---|
645 | case ringorder_M: |
---|
646 | pMixedOrder=TRUE; |
---|
647 | break; |
---|
648 | #ifdef TEST |
---|
649 | default: |
---|
650 | Werror("wrong internal ordering:%d at %s, l:%d\n",o_r,__FILE__,__LINE__); |
---|
651 | #endif |
---|
652 | } |
---|
653 | } |
---|
654 | |
---|
655 | /* -------------------------------------------------------- */ |
---|
656 | /*2 |
---|
657 | * change all variables to fit the description of the new ring |
---|
658 | */ |
---|
659 | |
---|
660 | //void pChangeRing(ring newRing) |
---|
661 | //{ |
---|
662 | // rComplete(newRing); |
---|
663 | // pSetGlobals(newRing); |
---|
664 | //} |
---|
665 | |
---|
666 | void pSetGlobals(ring r, BOOLEAN complete) |
---|
667 | { |
---|
668 | int i; |
---|
669 | pComponentOrder=1; |
---|
670 | if (ppNoether!=NULL) pDelete(&ppNoether); |
---|
671 | pVariables = r->N; |
---|
672 | |
---|
673 | // set the various size parameters and initialize memory |
---|
674 | pMonomSize = POLYSIZE + r->ExpLSize * sizeof(long); |
---|
675 | pMonomSizeW = pMonomSize/sizeof(void*); |
---|
676 | |
---|
677 | // Initialize memory management |
---|
678 | mm_specHeap = r->mm_specHeap; |
---|
679 | |
---|
680 | pVarOffset = r->VarOffset; |
---|
681 | |
---|
682 | pOrdSgn = r->OrdSgn; |
---|
683 | pVectorOut=(r->order[0]==ringorder_c); |
---|
684 | order=r->order; |
---|
685 | block0=r->block0; |
---|
686 | block1=r->block1; |
---|
687 | firstwv=NULL; |
---|
688 | polys_wv=r->wvhdl; |
---|
689 | if (order[0]==ringorder_S ||order[0]==ringorder_s) |
---|
690 | { |
---|
691 | order++; |
---|
692 | block0++; |
---|
693 | block1++; |
---|
694 | polys_wv++; |
---|
695 | } |
---|
696 | pFDeg=pTotaldegree; |
---|
697 | /*------- only one real block ----------------------*/ |
---|
698 | pLexOrder=FALSE; |
---|
699 | pMixedOrder=FALSE; |
---|
700 | if (pOrdSgn == 1) pLDeg = ldegb; |
---|
701 | else pLDeg = ldeg0; |
---|
702 | /*======== ordering type is (_,c) =========================*/ |
---|
703 | if ((order[0]==ringorder_unspec) |
---|
704 | ||( |
---|
705 | ((order[1]==ringorder_c)||(order[1]==ringorder_C) |
---|
706 | ||(order[1]==ringorder_S) |
---|
707 | ||(order[1]==ringorder_s)) |
---|
708 | && (order[0]!=ringorder_M) |
---|
709 | && (order[2]==0)) |
---|
710 | ) |
---|
711 | { |
---|
712 | if ((order[0]!=ringorder_unspec) |
---|
713 | && ((order[1]==ringorder_C)||(order[1]==ringorder_S)|| |
---|
714 | (order[1]==ringorder_s))) |
---|
715 | pComponentOrder=-1; |
---|
716 | if (pOrdSgn == -1) pLDeg = ldeg0c; |
---|
717 | if ((order[0] == ringorder_lp) || (order[0] == ringorder_ls)) |
---|
718 | { |
---|
719 | pLexOrder=TRUE; |
---|
720 | pLDeg = ldeg1c; |
---|
721 | } |
---|
722 | if (order[0] == ringorder_wp || order[0] == ringorder_Wp || |
---|
723 | order[0] == ringorder_ws || order[0] == ringorder_Ws) |
---|
724 | pFDeg = pWTotaldegree; |
---|
725 | firstBlockEnds=block1[0]; |
---|
726 | } |
---|
727 | /*======== ordering type is (c,_) =========================*/ |
---|
728 | else if (((order[0]==ringorder_c) |
---|
729 | ||(order[0]==ringorder_C) |
---|
730 | ||(order[0]==ringorder_S) |
---|
731 | ||(order[0]==ringorder_s)) |
---|
732 | && (order[1]!=ringorder_M) |
---|
733 | && (order[2]==0)) |
---|
734 | { |
---|
735 | /* pLDeg = ldeg0; is standard*/ |
---|
736 | if ((order[0]==ringorder_C)||(order[0]==ringorder_S)|| |
---|
737 | order[0]==ringorder_s) |
---|
738 | pComponentOrder=-1; |
---|
739 | if ((order[1] == ringorder_lp) || (order[1] == ringorder_ls)) |
---|
740 | { |
---|
741 | pLexOrder=TRUE; |
---|
742 | pLDeg = ldeg1c; |
---|
743 | } |
---|
744 | firstBlockEnds=block1[1]; |
---|
745 | if (order[1] == ringorder_wp || order[1] == ringorder_Wp || |
---|
746 | order[1] == ringorder_ws || order[1] == ringorder_Ws) |
---|
747 | pFDeg = pWTotaldegree; |
---|
748 | } |
---|
749 | /*------- more than one block ----------------------*/ |
---|
750 | else |
---|
751 | { |
---|
752 | //pGetVarIndicies(pVariables, pVarOffset, pVarCompIndex, pVarLowIndex, |
---|
753 | // pVarHighIndex); |
---|
754 | //pLexOrder=TRUE; |
---|
755 | pVectorOut=order[0]==ringorder_c; |
---|
756 | if ((pVectorOut)||(order[0]==ringorder_C)||(order[0]==ringorder_S)||(order[0]==ringorder_s)) |
---|
757 | { |
---|
758 | if(block1[1]!=pVariables) pLexOrder=TRUE; |
---|
759 | firstBlockEnds=block1[1]; |
---|
760 | } |
---|
761 | else |
---|
762 | { |
---|
763 | if(block1[0]!=pVariables) pLexOrder=TRUE; |
---|
764 | firstBlockEnds=block1[0]; |
---|
765 | } |
---|
766 | /*the number of orderings:*/ |
---|
767 | i = 0; |
---|
768 | while (order[++i] != 0); |
---|
769 | do |
---|
770 | { |
---|
771 | i--; |
---|
772 | HighSet(i, order[i]);/*sets also pMixedOrder to TRUE, if...*/ |
---|
773 | } |
---|
774 | while (i != 0); |
---|
775 | |
---|
776 | if ((order[0]!=ringorder_c) |
---|
777 | && (order[0]!=ringorder_C) |
---|
778 | && (order[0]!=ringorder_S) |
---|
779 | && (order[0]!=ringorder_s)) |
---|
780 | { |
---|
781 | pLDeg = ldeg1c; |
---|
782 | } |
---|
783 | else |
---|
784 | { |
---|
785 | pLDeg = ldeg1; |
---|
786 | } |
---|
787 | pFDeg = pWTotaldegree; // may be improved: pTotaldegree for lp/dp/ls/.. blocks |
---|
788 | } |
---|
789 | if (complete) |
---|
790 | { |
---|
791 | if ((pLexOrder) || (pOrdSgn==-1)) |
---|
792 | { |
---|
793 | test &= ~Sy_bit(OPT_REDTAIL); /* noredTail */ |
---|
794 | } |
---|
795 | pSetm=rSetm; |
---|
796 | } |
---|
797 | if (pFDeg!=pWTotaldegree) pFDeg=pTotaldegree; |
---|
798 | } |
---|
799 | |
---|
800 | /* -------------------------------------------------------- */ |
---|
801 | |
---|
802 | static Exponent_t pMultT_nok; |
---|
803 | /*2 |
---|
804 | * update the polynomial a by multipying it by |
---|
805 | * the (number) coefficient |
---|
806 | * and the exponent vector (of) exp (a well initialized polynomial) |
---|
807 | */ |
---|
808 | poly pMultT(poly a, poly exp ) |
---|
809 | { |
---|
810 | int i; |
---|
811 | number t,x,y=pGetCoeff(exp); |
---|
812 | poly aa=a; |
---|
813 | poly prev=NULL; |
---|
814 | |
---|
815 | pMultT_nok = pGetComp(exp); |
---|
816 | #ifdef PDEBUG |
---|
817 | pTest(a); |
---|
818 | pTest(exp); |
---|
819 | #endif |
---|
820 | while (a !=NULL) |
---|
821 | { |
---|
822 | x=pGetCoeff(a); |
---|
823 | t=nMult(x/*pGetCoeff(a)*/,y/*pGetCoeff(exp)*/); |
---|
824 | nDelete(&x/*pGetCoeff(a)*/); |
---|
825 | pSetCoeff0(a,t); |
---|
826 | if (nIsZero(t)) |
---|
827 | { |
---|
828 | if (prev==NULL) { pDelete1(&a); aa=a; } |
---|
829 | else { pDelete1(&prev->next); a=prev->next;} |
---|
830 | } |
---|
831 | else |
---|
832 | { |
---|
833 | { |
---|
834 | if (pMultT_nok) /* comp of exp != 0 */ |
---|
835 | { |
---|
836 | if (pGetComp(a) != 0) |
---|
837 | { |
---|
838 | return NULL /*FALSE*/; |
---|
839 | } |
---|
840 | } |
---|
841 | pMonAddOn(a,exp); |
---|
842 | } |
---|
843 | prev=a; |
---|
844 | pIter(a); |
---|
845 | } |
---|
846 | } |
---|
847 | pMultT_nok=0; |
---|
848 | pTest(aa); |
---|
849 | return aa; /*TRUE*/ |
---|
850 | } |
---|
851 | |
---|
852 | /*2 |
---|
853 | * multiply p1 with p2, p1 and p2 are destroyed |
---|
854 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
855 | */ |
---|
856 | poly pMult(poly p1, poly p2) |
---|
857 | { |
---|
858 | poly res, r, rn, a; |
---|
859 | BOOLEAN cont; |
---|
860 | |
---|
861 | if ((p1!=NULL) && (p2!=NULL)) |
---|
862 | { |
---|
863 | #ifdef PDEBUG |
---|
864 | pTest(p1); |
---|
865 | pTest(p2); |
---|
866 | #endif |
---|
867 | cont = TRUE; |
---|
868 | a = p1; |
---|
869 | if (pNext(p2)!=NULL) |
---|
870 | a = pCopy(a); |
---|
871 | else |
---|
872 | cont = FALSE; |
---|
873 | res = pMultT(a, p2); |
---|
874 | if (pMultT_nok) |
---|
875 | { |
---|
876 | if (cont) pDelete(&p1); |
---|
877 | pDelete(&res); |
---|
878 | pDelete(&p2); |
---|
879 | return NULL; |
---|
880 | } |
---|
881 | pTest(res); |
---|
882 | pDelete1(&p2); |
---|
883 | r = res; |
---|
884 | if (r!=NULL) rn = pNext(r); |
---|
885 | else rn=NULL; |
---|
886 | while (cont) |
---|
887 | { |
---|
888 | if (pNext(p2)==NULL) |
---|
889 | { |
---|
890 | a = p1; |
---|
891 | cont = FALSE; |
---|
892 | } |
---|
893 | else |
---|
894 | { |
---|
895 | a = pCopy(p1); |
---|
896 | } |
---|
897 | a=pMultT(a, p2); //sets pMultT_nok |
---|
898 | pTest(a); |
---|
899 | if (pMultT_nok) |
---|
900 | { |
---|
901 | if (cont) pDelete(&p1); |
---|
902 | pDelete(&a); |
---|
903 | pDelete(&res); |
---|
904 | pDelete(&p2); |
---|
905 | return NULL; |
---|
906 | } |
---|
907 | while ((rn!=NULL) && (pComp0(rn,a)>0)) |
---|
908 | { |
---|
909 | r = rn; |
---|
910 | pIter(rn); |
---|
911 | } |
---|
912 | if (r!=NULL) pNext(r) = rn = pAdd(a, rn); |
---|
913 | else res=r=a; |
---|
914 | pDelete1(&p2); |
---|
915 | } |
---|
916 | pTest(res); |
---|
917 | return res; |
---|
918 | } |
---|
919 | pDelete(&p1); |
---|
920 | pDelete(&p2); |
---|
921 | return NULL; |
---|
922 | } |
---|
923 | |
---|
924 | /*2 |
---|
925 | * update a by multiplying it with c (c will not be destroyed) |
---|
926 | */ |
---|
927 | void pMultN(poly a, number c) |
---|
928 | { |
---|
929 | number t; |
---|
930 | |
---|
931 | while (a!=NULL) |
---|
932 | { |
---|
933 | t=nMult(pGetCoeff(a), c); |
---|
934 | //nNormalize(t); |
---|
935 | pSetCoeff(a,t); |
---|
936 | pIter(a); |
---|
937 | } |
---|
938 | } |
---|
939 | |
---|
940 | /*2 |
---|
941 | * return a copy of the poly a times the number c (a,c will not be destroyed) |
---|
942 | */ |
---|
943 | poly pMultCopyN(poly a, number c) |
---|
944 | { |
---|
945 | poly result=NULL,hp; |
---|
946 | |
---|
947 | if (a != NULL) |
---|
948 | { |
---|
949 | result=pNew(); |
---|
950 | pCopy2(result,a); |
---|
951 | pNext(result)=NULL; |
---|
952 | pGetCoeff(result)=nMult(pGetCoeff(a),c); |
---|
953 | pIter(a); |
---|
954 | hp=result; |
---|
955 | while (a!=NULL) |
---|
956 | { |
---|
957 | hp=pNext(hp)=pNew(); |
---|
958 | pCopy2(hp,a); |
---|
959 | pSetCoeff0(hp,nMult(pGetCoeff(a), c)); |
---|
960 | pIter(a); |
---|
961 | } |
---|
962 | pNext(hp)=NULL; |
---|
963 | } |
---|
964 | return result; |
---|
965 | } |
---|
966 | |
---|
967 | /*2 |
---|
968 | * assumes that the head term of b is a multiple of the head term of a |
---|
969 | * and return the multiplicant *m |
---|
970 | */ |
---|
971 | poly pDivide(poly a, poly b) |
---|
972 | { |
---|
973 | int i; |
---|
974 | poly result=pInit(); |
---|
975 | |
---|
976 | for(i=(int)pVariables; i; i--) |
---|
977 | pSetExp(result,i, pGetExp(a,i)- pGetExp(b,i)); |
---|
978 | pSetComp(result, pGetComp(a) - pGetComp(b)); |
---|
979 | pSetm(result); |
---|
980 | return result; |
---|
981 | } |
---|
982 | |
---|
983 | /*2 |
---|
984 | * divides a by the monomial b, ignores monomials wihich are not divisible |
---|
985 | * assumes that b is not NULL |
---|
986 | */ |
---|
987 | poly pDivideM(poly a, poly b) |
---|
988 | { |
---|
989 | if (a==NULL) return NULL; |
---|
990 | poly result=a; |
---|
991 | poly prev=NULL; |
---|
992 | int i; |
---|
993 | number inv=nInvers(pGetCoeff(b)); |
---|
994 | |
---|
995 | while (a!=NULL) |
---|
996 | { |
---|
997 | if (pDivisibleBy(b,a)) |
---|
998 | { |
---|
999 | for(i=(int)pVariables; i; i--) |
---|
1000 | pSubExp(a,i, pGetExp(b,i)); |
---|
1001 | pSubComp(a, pGetComp(b)); |
---|
1002 | pSetm(a); |
---|
1003 | prev=a; |
---|
1004 | pIter(a); |
---|
1005 | } |
---|
1006 | else |
---|
1007 | { |
---|
1008 | if (prev==NULL) |
---|
1009 | { |
---|
1010 | pDelete1(&result); |
---|
1011 | a=result; |
---|
1012 | } |
---|
1013 | else |
---|
1014 | { |
---|
1015 | pDelete1(&pNext(prev)); |
---|
1016 | a=pNext(prev); |
---|
1017 | } |
---|
1018 | } |
---|
1019 | } |
---|
1020 | pMultN(result,inv); |
---|
1021 | nDelete(&inv); |
---|
1022 | pDelete(&b); |
---|
1023 | return result; |
---|
1024 | } |
---|
1025 | |
---|
1026 | /*2 |
---|
1027 | * returns the LCM of the head terms of a and b in *m |
---|
1028 | */ |
---|
1029 | void pLcm(poly a, poly b, poly m) |
---|
1030 | { |
---|
1031 | int i; |
---|
1032 | for (i=pVariables; i; i--) |
---|
1033 | { |
---|
1034 | pSetExp(m,i, max( pGetExp(a,i), pGetExp(b,i))); |
---|
1035 | } |
---|
1036 | pSetComp(m, max(pGetComp(a), pGetComp(b))); |
---|
1037 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
1038 | } |
---|
1039 | |
---|
1040 | /*2 |
---|
1041 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
1042 | */ |
---|
1043 | poly pmInit(char *st, BOOLEAN &ok) |
---|
1044 | { |
---|
1045 | int i,j; |
---|
1046 | ok=FALSE; |
---|
1047 | BOOLEAN b=FALSE; |
---|
1048 | poly rc = pInit(); |
---|
1049 | char *s = nRead(st,&(rc->coef)); |
---|
1050 | if (s==st) |
---|
1051 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
1052 | { |
---|
1053 | j = rIsRingVar(s); |
---|
1054 | if (j >= 0) |
---|
1055 | { |
---|
1056 | pIncrExp(rc,1+j); |
---|
1057 | goto done; |
---|
1058 | } |
---|
1059 | } |
---|
1060 | else |
---|
1061 | b=TRUE; |
---|
1062 | while (*s!='\0') |
---|
1063 | { |
---|
1064 | char ss[2]; |
---|
1065 | ss[0] = *s++; |
---|
1066 | ss[1] = '\0'; |
---|
1067 | j = rIsRingVar(ss); |
---|
1068 | if (j >= 0) |
---|
1069 | { |
---|
1070 | s = eati(s,&i); |
---|
1071 | pAddExp(rc,1+j, (Exponent_t)i); |
---|
1072 | } |
---|
1073 | else |
---|
1074 | { |
---|
1075 | if ((s!=st)&&isdigit(st[0])) |
---|
1076 | { |
---|
1077 | errorreported=TRUE; |
---|
1078 | } |
---|
1079 | pDelete(&rc); |
---|
1080 | return NULL; |
---|
1081 | } |
---|
1082 | } |
---|
1083 | done: |
---|
1084 | ok=!errorreported; |
---|
1085 | if (nIsZero(pGetCoeff(rc))) pDelete1(&rc); |
---|
1086 | else |
---|
1087 | { |
---|
1088 | pSetm(rc); |
---|
1089 | } |
---|
1090 | return rc; |
---|
1091 | } |
---|
1092 | |
---|
1093 | /*2 |
---|
1094 | *make p homgeneous by multiplying the monomials by powers of x_varnum |
---|
1095 | */ |
---|
1096 | poly pHomogen (poly p, int varnum) |
---|
1097 | { |
---|
1098 | poly q=NULL; |
---|
1099 | poly res; |
---|
1100 | int o,ii; |
---|
1101 | |
---|
1102 | if (p!=NULL) |
---|
1103 | { |
---|
1104 | if ((varnum < 1) || (varnum > pVariables)) |
---|
1105 | { |
---|
1106 | return NULL; |
---|
1107 | } |
---|
1108 | o=pWTotaldegree(p); |
---|
1109 | q=pNext(p); |
---|
1110 | while (q != NULL) |
---|
1111 | { |
---|
1112 | ii=pWTotaldegree(q); |
---|
1113 | if (ii>o) o=ii; |
---|
1114 | pIter(q); |
---|
1115 | } |
---|
1116 | q = pCopy(p); |
---|
1117 | res = q; |
---|
1118 | while (q != NULL) |
---|
1119 | { |
---|
1120 | ii = o-pWTotaldegree(q); |
---|
1121 | if (ii!=0) |
---|
1122 | { |
---|
1123 | pAddExp(q,varnum, (Exponent_t)ii); |
---|
1124 | pSetm(q); |
---|
1125 | } |
---|
1126 | pIter(q); |
---|
1127 | } |
---|
1128 | q = pOrdPolyInsertSetm(res); |
---|
1129 | } |
---|
1130 | return q; |
---|
1131 | } |
---|
1132 | |
---|
1133 | |
---|
1134 | /*2 |
---|
1135 | *replaces the maximal powers of the leading monomial of p2 in p1 by |
---|
1136 | *the same powers of n, utility for dehomogenization |
---|
1137 | */ |
---|
1138 | poly pDehomogen (poly p1,poly p2,number n) |
---|
1139 | { |
---|
1140 | polyset P; |
---|
1141 | int SizeOfSet=5; |
---|
1142 | int i; |
---|
1143 | poly p; |
---|
1144 | number nn; |
---|
1145 | |
---|
1146 | P = (polyset)Alloc0(5*sizeof(poly)); |
---|
1147 | //for (i=0; i<5; i++) |
---|
1148 | //{ |
---|
1149 | // P[i] = NULL; |
---|
1150 | //} |
---|
1151 | pCancelPolyByMonom(p1,p2,&P,&SizeOfSet); |
---|
1152 | p = P[0]; |
---|
1153 | //P[0] = NULL ;// for safety, may be remoeved later |
---|
1154 | for (i=1; i<SizeOfSet; i++) |
---|
1155 | { |
---|
1156 | if (P[i] != NULL) |
---|
1157 | { |
---|
1158 | nPower(n,i,&nn); |
---|
1159 | pMultN(P[i],nn); |
---|
1160 | p = pAdd(p,P[i]); |
---|
1161 | //P[i] =NULL; // for safety, may be removed later |
---|
1162 | nDelete(&nn); |
---|
1163 | } |
---|
1164 | } |
---|
1165 | Free((ADDRESS)P,SizeOfSet*sizeof(poly)); |
---|
1166 | return p; |
---|
1167 | } |
---|
1168 | |
---|
1169 | /*4 |
---|
1170 | *Returns the exponent of the maximal power of the leading monomial of |
---|
1171 | *p2 in that of p1 |
---|
1172 | */ |
---|
1173 | static int pGetMaxPower (poly p1,poly p2) |
---|
1174 | { |
---|
1175 | int i,k,res = 32000; /*a very large integer*/ |
---|
1176 | |
---|
1177 | if (p1 == NULL) return 0; |
---|
1178 | for (i=1; i<=pVariables; i++) |
---|
1179 | { |
---|
1180 | if ( pGetExp(p2,i) != 0) |
---|
1181 | { |
---|
1182 | k = pGetExp(p1,i) / pGetExp(p2,i); |
---|
1183 | if (k < res) res = k; |
---|
1184 | } |
---|
1185 | } |
---|
1186 | return res; |
---|
1187 | } |
---|
1188 | |
---|
1189 | /*2 |
---|
1190 | *Returns as i-th entry of P the coefficient of the (i-1) power of |
---|
1191 | *the leading monomial of p2 in p1 |
---|
1192 | */ |
---|
1193 | void pCancelPolyByMonom (poly p1,poly p2,polyset * P,int * SizeOfSet) |
---|
1194 | { |
---|
1195 | int maxPow; |
---|
1196 | poly p,qp,Coeff; |
---|
1197 | |
---|
1198 | if (*P == NULL) |
---|
1199 | { |
---|
1200 | *P = (polyset) Alloc(5*sizeof(poly)); |
---|
1201 | *SizeOfSet = 5; |
---|
1202 | } |
---|
1203 | p = pCopy(p1); |
---|
1204 | while (p != NULL) |
---|
1205 | { |
---|
1206 | qp = p->next; |
---|
1207 | p->next = NULL; |
---|
1208 | maxPow = pGetMaxPower(p,p2); |
---|
1209 | Coeff = pDivByMonom(p,p2); |
---|
1210 | if (maxPow > *SizeOfSet) |
---|
1211 | { |
---|
1212 | pEnlargeSet(P,*SizeOfSet,maxPow+1-*SizeOfSet); |
---|
1213 | *SizeOfSet = maxPow+1; |
---|
1214 | } |
---|
1215 | (*P)[maxPow] = pAdd((*P)[maxPow],Coeff); |
---|
1216 | pDelete(&p); |
---|
1217 | p = qp; |
---|
1218 | } |
---|
1219 | } |
---|
1220 | |
---|
1221 | /*2 |
---|
1222 | *returns the leading monomial of p1 divided by the maximal power of that |
---|
1223 | *of p2 |
---|
1224 | */ |
---|
1225 | poly pDivByMonom (poly p1,poly p2) |
---|
1226 | { |
---|
1227 | int k, i; |
---|
1228 | |
---|
1229 | if (p1 == NULL) return NULL; |
---|
1230 | k = pGetMaxPower(p1,p2); |
---|
1231 | if (k == 0) |
---|
1232 | return pHead(p1); |
---|
1233 | else |
---|
1234 | { |
---|
1235 | number n; |
---|
1236 | poly p = pInit(); |
---|
1237 | |
---|
1238 | p->next = NULL; |
---|
1239 | for (i=1; i<=pVariables; i++) |
---|
1240 | { |
---|
1241 | pSetExp(p,i, pGetExp(p1,i)-k* pGetExp(p2,i)); |
---|
1242 | } |
---|
1243 | nPower(p2->coef,k,&n); |
---|
1244 | pSetCoeff0(p,nDiv(p1->coef,n)); |
---|
1245 | nDelete(&n); |
---|
1246 | pSetm(p); |
---|
1247 | return p; |
---|
1248 | } |
---|
1249 | } |
---|
1250 | /*----------utilities for syzygies--------------*/ |
---|
1251 | poly pTakeOutComp(poly * p, int k) |
---|
1252 | { |
---|
1253 | poly q = *p,qq=NULL,result = NULL; |
---|
1254 | |
---|
1255 | if (q==NULL) return NULL; |
---|
1256 | if (pGetComp(q)==k) |
---|
1257 | { |
---|
1258 | result = q; |
---|
1259 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
1260 | { |
---|
1261 | pSetComp(q,0); |
---|
1262 | pSetmComp(q); |
---|
1263 | qq = q; |
---|
1264 | pIter(q); |
---|
1265 | } |
---|
1266 | *p = q; |
---|
1267 | pNext(qq) = NULL; |
---|
1268 | } |
---|
1269 | if (q==NULL) return result; |
---|
1270 | if (pGetComp(q) > k) |
---|
1271 | { |
---|
1272 | pDecrComp(q); |
---|
1273 | pSetmComp(q); |
---|
1274 | } |
---|
1275 | poly pNext_q; |
---|
1276 | while ((pNext_q=pNext(q))!=NULL) |
---|
1277 | { |
---|
1278 | if (pGetComp(pNext_q)==k) |
---|
1279 | { |
---|
1280 | if (result==NULL) |
---|
1281 | { |
---|
1282 | result = pNext_q; |
---|
1283 | qq = result; |
---|
1284 | } |
---|
1285 | else |
---|
1286 | { |
---|
1287 | pNext(qq) = pNext_q; |
---|
1288 | pIter(qq); |
---|
1289 | } |
---|
1290 | pNext(q) = pNext(pNext_q); |
---|
1291 | pNext(qq) =NULL; |
---|
1292 | pSetComp(qq,0); |
---|
1293 | pSetmComp(qq); |
---|
1294 | } |
---|
1295 | else |
---|
1296 | { |
---|
1297 | /*pIter(q);*/ q=pNext_q; |
---|
1298 | if (pGetComp(q) > k) |
---|
1299 | { |
---|
1300 | pDecrComp(q); |
---|
1301 | pSetmComp(q); |
---|
1302 | } |
---|
1303 | } |
---|
1304 | } |
---|
1305 | return result; |
---|
1306 | } |
---|
1307 | |
---|
1308 | // Splits *p into two polys: *q which consists of all monoms with |
---|
1309 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
1310 | void pTakeOutComp(poly *r_p, Exponent_t comp, poly *r_q, int *lq) |
---|
1311 | { |
---|
1312 | spolyrec pp, qq; |
---|
1313 | poly p, q, p_prev; |
---|
1314 | int l = 0; |
---|
1315 | |
---|
1316 | #ifdef HAVE_ASSUME |
---|
1317 | int lp = pLength(*r_p); |
---|
1318 | #endif |
---|
1319 | |
---|
1320 | pNext(&pp) = *r_p; |
---|
1321 | p = *r_p; |
---|
1322 | p_prev = &pp; |
---|
1323 | q = &qq; |
---|
1324 | |
---|
1325 | while(p != NULL) |
---|
1326 | { |
---|
1327 | while (pGetComp(p) == comp) |
---|
1328 | { |
---|
1329 | pNext(q) = p; |
---|
1330 | pIter(q); |
---|
1331 | pSetComp(p, 0); |
---|
1332 | pSetmComp(p); |
---|
1333 | pIter(p); |
---|
1334 | l++; |
---|
1335 | if (p == NULL) |
---|
1336 | { |
---|
1337 | pNext(p_prev) = NULL; |
---|
1338 | goto Finish; |
---|
1339 | } |
---|
1340 | } |
---|
1341 | pNext(p_prev) = p; |
---|
1342 | p_prev = p; |
---|
1343 | pIter(p); |
---|
1344 | } |
---|
1345 | |
---|
1346 | Finish: |
---|
1347 | pNext(q) = NULL; |
---|
1348 | *r_p = pNext(&pp); |
---|
1349 | *r_q = pNext(&qq); |
---|
1350 | *lq = l; |
---|
1351 | #ifdef HAVE_ASSUME |
---|
1352 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
1353 | #endif |
---|
1354 | pTest(*r_p); |
---|
1355 | pTest(*r_q); |
---|
1356 | } |
---|
1357 | |
---|
1358 | void pDecrOrdTakeOutComp(poly *r_p, Exponent_t comp, Order_t order, |
---|
1359 | poly *r_q, int *lq) |
---|
1360 | { |
---|
1361 | spolyrec pp, qq; |
---|
1362 | poly p, q, p_prev; |
---|
1363 | int l = 0; |
---|
1364 | |
---|
1365 | pNext(&pp) = *r_p; |
---|
1366 | p = *r_p; |
---|
1367 | p_prev = &pp; |
---|
1368 | q = &qq; |
---|
1369 | |
---|
1370 | #ifdef HAVE_ASSUME |
---|
1371 | if (p != NULL) |
---|
1372 | { |
---|
1373 | while (pNext(p) != NULL) |
---|
1374 | { |
---|
1375 | assume(pGetOrder(p) >= pGetOrder(pNext(p))); |
---|
1376 | pIter(p); |
---|
1377 | } |
---|
1378 | } |
---|
1379 | p = *r_p; |
---|
1380 | #endif |
---|
1381 | |
---|
1382 | while (p != NULL && pGetOrder(p) > order) pIter(p); |
---|
1383 | |
---|
1384 | while(p != NULL && pGetOrder(p) == order) |
---|
1385 | { |
---|
1386 | while (pGetComp(p) == comp) |
---|
1387 | { |
---|
1388 | pNext(q) = p; |
---|
1389 | pIter(q); |
---|
1390 | pIter(p); |
---|
1391 | pSetComp(p, 0); |
---|
1392 | pSetmComp(p); |
---|
1393 | l++; |
---|
1394 | if (p == NULL || pGetOrder(p) != order) |
---|
1395 | { |
---|
1396 | pNext(p_prev) = p; |
---|
1397 | goto Finish; |
---|
1398 | } |
---|
1399 | } |
---|
1400 | pNext(p_prev) = p; |
---|
1401 | p_prev = p; |
---|
1402 | pIter(p); |
---|
1403 | } |
---|
1404 | |
---|
1405 | Finish: |
---|
1406 | pNext(q) = NULL; |
---|
1407 | *r_p = pNext(&pp); |
---|
1408 | *r_q = pNext(&qq); |
---|
1409 | *lq = l; |
---|
1410 | } |
---|
1411 | |
---|
1412 | #if 1 |
---|
1413 | poly pTakeOutComp1(poly * p, int k) |
---|
1414 | { |
---|
1415 | poly q = *p; |
---|
1416 | |
---|
1417 | if (q==NULL) return NULL; |
---|
1418 | |
---|
1419 | poly qq=NULL,result = NULL; |
---|
1420 | |
---|
1421 | if (pGetComp(q)==k) |
---|
1422 | { |
---|
1423 | result = q; /* *p */ |
---|
1424 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
1425 | { |
---|
1426 | pSetComp(q,0); |
---|
1427 | pSetmComp(q); |
---|
1428 | qq = q; |
---|
1429 | pIter(q); |
---|
1430 | } |
---|
1431 | *p = q; |
---|
1432 | pNext(qq) = NULL; |
---|
1433 | } |
---|
1434 | if (q==NULL) return result; |
---|
1435 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
1436 | while (pNext(q)!=NULL) |
---|
1437 | { |
---|
1438 | if (pGetComp(pNext(q))==k) |
---|
1439 | { |
---|
1440 | if (result==NULL) |
---|
1441 | { |
---|
1442 | result = pNext(q); |
---|
1443 | qq = result; |
---|
1444 | } |
---|
1445 | else |
---|
1446 | { |
---|
1447 | pNext(qq) = pNext(q); |
---|
1448 | pIter(qq); |
---|
1449 | } |
---|
1450 | pNext(q) = pNext(pNext(q)); |
---|
1451 | pNext(qq) =NULL; |
---|
1452 | pSetComp(qq,0); |
---|
1453 | pSetmComp(qq); |
---|
1454 | } |
---|
1455 | else |
---|
1456 | { |
---|
1457 | pIter(q); |
---|
1458 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
1459 | } |
---|
1460 | } |
---|
1461 | return result; |
---|
1462 | } |
---|
1463 | #endif |
---|
1464 | |
---|
1465 | void pDeleteComp(poly * p,int k) |
---|
1466 | { |
---|
1467 | poly q; |
---|
1468 | |
---|
1469 | while ((*p!=NULL) && (pGetComp(*p)==k)) pDelete1(p); |
---|
1470 | if (*p==NULL) return; |
---|
1471 | q = *p; |
---|
1472 | if (pGetComp(q)>k) |
---|
1473 | { |
---|
1474 | pDecrComp(q); |
---|
1475 | pSetmComp(q); |
---|
1476 | } |
---|
1477 | while (pNext(q)!=NULL) |
---|
1478 | { |
---|
1479 | if (pGetComp(pNext(q))==k) |
---|
1480 | pDelete1(&(pNext(q))); |
---|
1481 | else |
---|
1482 | { |
---|
1483 | pIter(q); |
---|
1484 | if (pGetComp(q)>k) |
---|
1485 | { |
---|
1486 | pDecrComp(q); |
---|
1487 | pSetmComp(q); |
---|
1488 | } |
---|
1489 | } |
---|
1490 | } |
---|
1491 | } |
---|
1492 | /*----------end of utilities for syzygies--------------*/ |
---|
1493 | |
---|
1494 | /*2 |
---|
1495 | * pair has no common factor ? or is no polynomial |
---|
1496 | */ |
---|
1497 | BOOLEAN pHasNotCF(poly p1, poly p2) |
---|
1498 | { |
---|
1499 | |
---|
1500 | if (pGetComp(p1) > 0 || pGetComp(p2) > 0) |
---|
1501 | return FALSE; |
---|
1502 | int i = 1; |
---|
1503 | loop |
---|
1504 | { |
---|
1505 | if ((pGetExp(p1, i) > 0) && (pGetExp(p2, i) > 0)) return FALSE; |
---|
1506 | if (i == pVariables) return TRUE; |
---|
1507 | i++; |
---|
1508 | } |
---|
1509 | } |
---|
1510 | |
---|
1511 | |
---|
1512 | /*2 |
---|
1513 | *should return 1 if p divides q and p<q, |
---|
1514 | * -1 if q divides p and q<p |
---|
1515 | * 0 otherwise |
---|
1516 | */ |
---|
1517 | int pDivComp(poly p, poly q) |
---|
1518 | { |
---|
1519 | if (pGetComp(p) == pGetComp(q)) |
---|
1520 | { |
---|
1521 | int i=pVariables; |
---|
1522 | long d; |
---|
1523 | BOOLEAN a=FALSE, b=FALSE; |
---|
1524 | for (; i>0; i--) |
---|
1525 | { |
---|
1526 | d = pGetExpDiff(p, q, i); |
---|
1527 | if (d) |
---|
1528 | { |
---|
1529 | if (d < 0) |
---|
1530 | { |
---|
1531 | if (b) return 0; |
---|
1532 | a =TRUE; |
---|
1533 | } |
---|
1534 | else |
---|
1535 | { |
---|
1536 | if (a) return 0; |
---|
1537 | b = TRUE; |
---|
1538 | } |
---|
1539 | } |
---|
1540 | } |
---|
1541 | if (a) return 1; |
---|
1542 | else if (b) return -1; |
---|
1543 | } |
---|
1544 | return 0; |
---|
1545 | } |
---|
1546 | /*2 |
---|
1547 | *divides p1 by its leading monomial |
---|
1548 | */ |
---|
1549 | void pNorm(poly p1) |
---|
1550 | { |
---|
1551 | poly h; |
---|
1552 | number k, c; |
---|
1553 | |
---|
1554 | if (p1!=NULL) |
---|
1555 | { |
---|
1556 | if (!nIsOne(pGetCoeff(p1))) |
---|
1557 | { |
---|
1558 | nNormalize(pGetCoeff(p1)); |
---|
1559 | k=pGetCoeff(p1); |
---|
1560 | c = nInit(1); |
---|
1561 | pSetCoeff0(p1,c); |
---|
1562 | h = pNext(p1); |
---|
1563 | while (h!=NULL) |
---|
1564 | { |
---|
1565 | c=nDiv(pGetCoeff(h),k); |
---|
1566 | if (!nIsOne(c)) nNormalize(c); |
---|
1567 | pSetCoeff(h,c); |
---|
1568 | pIter(h); |
---|
1569 | } |
---|
1570 | nDelete(&k); |
---|
1571 | } |
---|
1572 | else |
---|
1573 | { |
---|
1574 | h = pNext(p1); |
---|
1575 | while (h!=NULL) |
---|
1576 | { |
---|
1577 | nNormalize(pGetCoeff(h)); |
---|
1578 | pIter(h); |
---|
1579 | } |
---|
1580 | } |
---|
1581 | } |
---|
1582 | } |
---|
1583 | |
---|
1584 | /*2 |
---|
1585 | *normalize all coeffizients |
---|
1586 | */ |
---|
1587 | void pNormalize(poly p) |
---|
1588 | { |
---|
1589 | while (p!=NULL) |
---|
1590 | { |
---|
1591 | nTest(pGetCoeff(p)); |
---|
1592 | nNormalize(pGetCoeff(p)); |
---|
1593 | pIter(p); |
---|
1594 | } |
---|
1595 | } |
---|
1596 | |
---|
1597 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
1598 | // Poly with Exp(n) != 0 is reversed |
---|
1599 | static void pSplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero) |
---|
1600 | { |
---|
1601 | if (p == NULL) |
---|
1602 | { |
---|
1603 | *non_zero = NULL; |
---|
1604 | *zero = NULL; |
---|
1605 | return; |
---|
1606 | } |
---|
1607 | spolyrec sz; |
---|
1608 | poly z, n_z, next; |
---|
1609 | z = &sz; |
---|
1610 | n_z = NULL; |
---|
1611 | |
---|
1612 | while(p != NULL) |
---|
1613 | { |
---|
1614 | next = pNext(p); |
---|
1615 | if (pGetExp(p, n) == 0) |
---|
1616 | { |
---|
1617 | pNext(z) = p; |
---|
1618 | pIter(z); |
---|
1619 | } |
---|
1620 | else |
---|
1621 | { |
---|
1622 | pNext(p) = n_z; |
---|
1623 | n_z = p; |
---|
1624 | } |
---|
1625 | p = next; |
---|
1626 | } |
---|
1627 | pNext(z) = NULL; |
---|
1628 | *zero = pNext(&sz); |
---|
1629 | *non_zero = n_z; |
---|
1630 | return; |
---|
1631 | } |
---|
1632 | |
---|
1633 | /*3 |
---|
1634 | * substitute the n-th variable by 1 in p |
---|
1635 | * destroy p |
---|
1636 | */ |
---|
1637 | static poly pSubst1 (poly p,int n) |
---|
1638 | { |
---|
1639 | poly qq,result = NULL; |
---|
1640 | poly zero, non_zero; |
---|
1641 | |
---|
1642 | // reverse, so that add is likely to be linear |
---|
1643 | pSplitAndReversePoly(p, n, &non_zero, &zero); |
---|
1644 | |
---|
1645 | while (non_zero != NULL) |
---|
1646 | { |
---|
1647 | assume(pGetExp(non_zero, n) != 0); |
---|
1648 | qq = non_zero; |
---|
1649 | pIter(non_zero); |
---|
1650 | qq->next = NULL; |
---|
1651 | pSetExp(qq,n,0); |
---|
1652 | pSetm(qq); |
---|
1653 | result = pAdd(result,qq); |
---|
1654 | } |
---|
1655 | p = pAdd(result, zero); |
---|
1656 | pTest(p); |
---|
1657 | return p; |
---|
1658 | } |
---|
1659 | |
---|
1660 | /*3 |
---|
1661 | * substitute the n-th variable by number e in p |
---|
1662 | * destroy p |
---|
1663 | */ |
---|
1664 | static poly pSubst2 (poly p,int n, number e) |
---|
1665 | { |
---|
1666 | assume( ! nIsZero(e) ); |
---|
1667 | poly qq,result = NULL; |
---|
1668 | number nn, nm; |
---|
1669 | poly zero, non_zero; |
---|
1670 | |
---|
1671 | // reverse, so that add is likely to be linear |
---|
1672 | pSplitAndReversePoly(p, n, &non_zero, &zero); |
---|
1673 | |
---|
1674 | while (non_zero != NULL) |
---|
1675 | { |
---|
1676 | assume(pGetExp(non_zero, n) != 0); |
---|
1677 | qq = non_zero; |
---|
1678 | pIter(non_zero); |
---|
1679 | qq->next = NULL; |
---|
1680 | nPower(e, pGetExp(qq, n), &nn); |
---|
1681 | nm = nMult(nn, pGetCoeff(qq)); |
---|
1682 | pSetCoeff(qq, nm); |
---|
1683 | nDelete(&nn); |
---|
1684 | pSetExp(qq, n, 0); |
---|
1685 | pSetm(qq); |
---|
1686 | result = pAdd(result,qq); |
---|
1687 | } |
---|
1688 | p = pAdd(result, zero); |
---|
1689 | pTest(p); |
---|
1690 | return p; |
---|
1691 | } |
---|
1692 | |
---|
1693 | |
---|
1694 | /* delete monoms whose n-th exponent is different from zero */ |
---|
1695 | poly pSubst0(poly p, int n) |
---|
1696 | { |
---|
1697 | spolyrec res; |
---|
1698 | poly h = &res; |
---|
1699 | pNext(h) = p; |
---|
1700 | |
---|
1701 | while (pNext(h)!=NULL) |
---|
1702 | { |
---|
1703 | if (pGetExp(pNext(h),n)!=0) |
---|
1704 | { |
---|
1705 | pDelete1(&pNext(h)); |
---|
1706 | } |
---|
1707 | else |
---|
1708 | { |
---|
1709 | pIter(h); |
---|
1710 | } |
---|
1711 | } |
---|
1712 | pTest(pNext(&res)); |
---|
1713 | return pNext(&res); |
---|
1714 | } |
---|
1715 | |
---|
1716 | /*2 |
---|
1717 | * substitute the n-th variable by e in p |
---|
1718 | * destroy p |
---|
1719 | */ |
---|
1720 | poly pSubst(poly p, int n, poly e) |
---|
1721 | { |
---|
1722 | if (e == NULL) return pSubst0(p, n); |
---|
1723 | |
---|
1724 | if (pIsConstant(e)) |
---|
1725 | { |
---|
1726 | if (nIsOne(pGetCoeff(e))) return pSubst1(p,n); |
---|
1727 | else return pSubst2(p, n, pGetCoeff(e)); |
---|
1728 | } |
---|
1729 | |
---|
1730 | int exponent,i; |
---|
1731 | poly h, res, m; |
---|
1732 | Exponent_t *me,*ee; |
---|
1733 | number nu,nu1; |
---|
1734 | |
---|
1735 | me=(Exponent_t *)Alloc((pVariables+1)*sizeof(Exponent_t)); |
---|
1736 | ee=(Exponent_t *)Alloc((pVariables+1)*sizeof(Exponent_t)); |
---|
1737 | if (e!=NULL) pGetExpV(e,ee); |
---|
1738 | res=NULL; |
---|
1739 | h=p; |
---|
1740 | while (h!=NULL) |
---|
1741 | { |
---|
1742 | if ((e!=NULL) || (pGetExp(h,n)==0)) |
---|
1743 | { |
---|
1744 | m=pHead(h); |
---|
1745 | pGetExpV(m,me); |
---|
1746 | exponent=me[n]; |
---|
1747 | me[n]=0; |
---|
1748 | for(i=pVariables;i>0;i--) |
---|
1749 | me[i]+=exponent*ee[i]; |
---|
1750 | pSetExpV(m,me); |
---|
1751 | if (e!=NULL) |
---|
1752 | { |
---|
1753 | nPower(pGetCoeff(e),exponent,&nu); |
---|
1754 | nu1=nMult(pGetCoeff(m),nu); |
---|
1755 | nDelete(&nu); |
---|
1756 | pSetCoeff(m,nu1); |
---|
1757 | } |
---|
1758 | res=pAdd(res,m); |
---|
1759 | } |
---|
1760 | pDelete1(&h); |
---|
1761 | } |
---|
1762 | Free((ADDRESS)me,(pVariables+1)*sizeof(Exponent_t)); |
---|
1763 | Free((ADDRESS)ee,(pVariables+1)*sizeof(Exponent_t)); |
---|
1764 | return res; |
---|
1765 | } |
---|
1766 | |
---|
1767 | BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm) |
---|
1768 | { |
---|
1769 | int k, j; |
---|
1770 | |
---|
1771 | if (lcm==NULL) return FALSE; |
---|
1772 | |
---|
1773 | for (j=pVariables; j; j--) |
---|
1774 | if ( pGetExp(p,j) > pGetExp(lcm,j)) return FALSE; |
---|
1775 | if ( pGetComp(p) != pGetComp(lcm)) return FALSE; |
---|
1776 | for (j=pVariables; j; j--) |
---|
1777 | { |
---|
1778 | if (pGetExp(p1,j)!=pGetExp(lcm,j)) |
---|
1779 | { |
---|
1780 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
1781 | { |
---|
1782 | for (k=pVariables; k>j; k--) |
---|
1783 | { |
---|
1784 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1785 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
1786 | return TRUE; |
---|
1787 | } |
---|
1788 | for (k=j-1; k; k--) |
---|
1789 | { |
---|
1790 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1791 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
1792 | return TRUE; |
---|
1793 | } |
---|
1794 | return FALSE; |
---|
1795 | } |
---|
1796 | } |
---|
1797 | else if (pGetExp(p2,j)!=pGetExp(lcm,j)) |
---|
1798 | { |
---|
1799 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
1800 | { |
---|
1801 | for (k=pVariables; k>j; k--) |
---|
1802 | { |
---|
1803 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1804 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
1805 | return TRUE; |
---|
1806 | } |
---|
1807 | for (k=j-1; k!=0 ; k--) |
---|
1808 | { |
---|
1809 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1810 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
1811 | return TRUE; |
---|
1812 | } |
---|
1813 | return FALSE; |
---|
1814 | } |
---|
1815 | } |
---|
1816 | } |
---|
1817 | return FALSE; |
---|
1818 | } |
---|
1819 | |
---|
1820 | int pWeight(int i) |
---|
1821 | { |
---|
1822 | if ((firstwv==NULL) || (i>firstBlockEnds)) |
---|
1823 | { |
---|
1824 | return 1; |
---|
1825 | } |
---|
1826 | return firstwv[i-1]; |
---|
1827 | } |
---|
1828 | |
---|