1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: polys.cc,v 1.8 1997-10-20 10:52:01 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 | |
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23 | /* ----------- global variables, set by pChangeRing --------------------- */ |
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24 | /* initializes the internal data from the exp vector */ |
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25 | pSetmProc pSetm; |
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26 | /* computes length and maximal degree of a POLYnomial */ |
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27 | pLDegProc pLDeg; |
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28 | /* computes the degree of the initial term, used for std */ |
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29 | pFDegProc pFDeg; |
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30 | /* the monomial ordering of the head monomials a and b */ |
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31 | pCompProc pComp0; |
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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 | /* the number of variables */ |
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35 | int pVariables; |
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36 | /* 1 for polynomial ring, -1 otherwise */ |
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37 | int pOrdSgn; |
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38 | /* TRUE for momomial output as x2y, FALSE for x^2*y */ |
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39 | int pShortOut = (int)TRUE; |
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40 | // it is of type int, not BOOLEAN because it is also in ip |
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41 | /* TRUE if the monomial ordering is not compatible with pFDeg */ |
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42 | BOOLEAN pLexOrder; |
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43 | /* TRUE if the monomial ordering has polynomial and power series blocks */ |
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44 | BOOLEAN pMixedOrder; |
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45 | |
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46 | #ifdef TEST_MAC_ORDER |
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47 | int pComponentOrder; |
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48 | #else |
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49 | static int pComponentOrder; |
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50 | #endif |
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51 | |
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52 | #ifdef DRING |
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53 | int p2; |
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54 | BOOLEAN pDRING=FALSE; |
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55 | #endif |
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56 | |
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57 | #ifdef SRING |
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58 | int pAltVars; |
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59 | BOOLEAN pSRING=FALSE; |
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60 | #endif |
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61 | |
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62 | #ifdef SDRING |
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63 | BOOLEAN pSDRING=FALSE; |
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64 | #include "polys.inc" |
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65 | #endif |
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66 | /* ----------- global variables, set by procedures from hecke/kstd1 ----- */ |
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67 | /* the highest monomial below pHEdge */ |
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68 | poly ppNoether = NULL; |
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69 | |
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70 | /* -------------- static variables --------------------------------------- */ |
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71 | /*is the basic comparing procedure during a computation of syzygies*/ |
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72 | static pCompProc pCompOld; |
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73 | /*for grouping module indecees during computations*/ |
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74 | static int maxBound = 0; |
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75 | /*contains the headterms for the Schreyer orderings*/ |
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76 | static int* SchreyerOrd; |
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77 | static int maxSchreyer=0; |
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78 | static int indexShift=0; |
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79 | static pLDegProc pLDegOld; |
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80 | |
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81 | typedef int (*bcompProc)(poly p1, poly p2, int i1, int i2, short * w); |
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82 | static bcompProc bcomph[20]; |
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83 | static short** polys_wv; |
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84 | static short * firstwv; |
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85 | static int * block0; |
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86 | static int * block1; |
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87 | static int firstBlockEnds; |
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88 | static int * order; |
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89 | |
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90 | /*0 implementation*/ |
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91 | /*-------- the several possibilities for pSetm:-----------------------*/ |
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92 | /*2 |
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93 | * define the order of p with respect to lex. ordering, N=1 |
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94 | */ |
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95 | static void setlex1(poly p) |
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96 | { |
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97 | p->Order = (int)p->exp[1]; |
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98 | } |
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99 | |
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100 | /*2 |
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101 | * define the order of p with respect to lex. ordering, N>1 |
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102 | */ |
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103 | static void setlex2(poly p) |
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104 | { |
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105 | p->Order = (((int)p->exp[1])<<(sizeof(short)*8))+(int)p->exp[2]; |
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106 | } |
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107 | |
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108 | /*2 |
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109 | * define the order of p with respect to a degree ordering |
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110 | */ |
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111 | static void setdeg1(poly p) |
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112 | { |
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113 | int i, j = p->exp[1]; |
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114 | |
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115 | for (i = firstBlockEnds; i>1; i--) j += p->exp[i]; |
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116 | p->Order = j; |
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117 | } |
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118 | |
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119 | /*2 |
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120 | * define the order of p with respect to a degree ordering |
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121 | * with weigthts |
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122 | */ |
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123 | static void setdeg1w(poly p) |
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124 | { |
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125 | int i, j = 0; |
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126 | |
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127 | for (i = firstBlockEnds; i>0; i--) |
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128 | { |
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129 | j += ((int)p->exp[i])*firstwv[i-1]; |
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130 | } |
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131 | p->Order = j; |
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132 | } |
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133 | |
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134 | /*-------- the several possibilities for pComp0:-----------------------*/ |
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135 | /*2 |
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136 | * compare the head monomial of p1 and p2 with degrevlex |
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137 | * handle also module case, pVariables >2 |
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138 | */ |
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139 | //static int comp1lpc(poly p1, poly p2) |
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140 | //{ |
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141 | // int i; |
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142 | // |
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143 | // for (i=1; i<=pVariables; i++) |
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144 | // { |
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145 | // if (p1->exp[i] > p2->exp[i]) return 1; |
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146 | // if (p1->exp[i] < p2->exp[i]) return -1; |
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147 | // } |
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148 | // /*4 handle module case:*/ |
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149 | // if (p1->exp[0]==p2->exp[0]) return 0; |
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150 | // else if (p1->exp[0] > p2->exp[0]) return -pComponentOrder; |
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151 | // return pComponentOrder; |
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152 | //} |
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153 | static int comp1lpc(poly p1, poly p2) |
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154 | { |
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155 | int dd=p1->Order - p2->Order; |
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156 | if (dd > 0) return 1; |
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157 | if (dd < 0) return -1; |
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158 | |
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159 | short *m1=p1->exp+3; |
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160 | short *m2=p2->exp+3; |
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161 | int i=pVariables-2; |
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162 | short d; |
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163 | |
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164 | loop |
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165 | { |
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166 | d= *m1 - *m2; |
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167 | if ( d > 0 /* *m1 > *m2*/) return 1; |
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168 | if ( d < 0 /* *m1 < *m2*/) return -1; |
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169 | i--; |
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170 | if (i==0) |
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171 | { |
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172 | /*4 handle module case:*/ |
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173 | if (p1->exp[0]==p2->exp[0]) return 0; |
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174 | else if (p1->exp[0] > p2->exp[0]) return -pComponentOrder; |
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175 | return pComponentOrder; |
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176 | } |
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177 | m1++;m2++; |
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178 | } |
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179 | } |
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180 | |
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181 | /*2 |
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182 | * compare the head monomial of p1 and p2 with degrevlex |
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183 | * handle also module case, pVariables <=2 |
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184 | */ |
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185 | static int comp2lpc(poly p1, poly p2) |
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186 | { |
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187 | int d=p1->Order - p2->Order; |
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188 | if (d > 0) |
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189 | return 1; |
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190 | if (d < 0) |
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191 | return -1; |
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192 | if (p1->exp[0]==p2->exp[0]) |
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193 | return 0; |
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194 | else if (p1->exp[0] > p2->exp[0]) |
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195 | return -pComponentOrder; |
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196 | return pComponentOrder; |
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197 | } |
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198 | |
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199 | static int comp1dpc(poly p1, poly p2) |
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200 | { |
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201 | /*4 compare monomials by order then revlex*/ |
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202 | int d=p1->Order - p2->Order; |
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203 | if (d == 0 /*p1->Order == p2->Order*/) |
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204 | { |
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205 | int i = pVariables; |
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206 | if ((p1->exp[i] == p2->exp[i])) |
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207 | { |
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208 | do |
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209 | { |
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210 | i--; |
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211 | if (i <= 1) |
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212 | { |
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213 | /*4 handle module case:*/ |
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214 | if (p1->exp[0]==p2->exp[0]) |
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215 | return 0; |
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216 | else if (p1->exp[0] > p2->exp[0]) |
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217 | return -pComponentOrder; |
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218 | else |
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219 | return pComponentOrder; |
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220 | } |
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221 | } while ((p1->exp[i] == p2->exp[i])); |
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222 | } |
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223 | if (p1->exp[i] < p2->exp[i]) |
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224 | return 1; |
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225 | return -1; |
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226 | } |
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227 | else if (d > 0 /*p1->Order > p2->Order*/) |
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228 | return 1; |
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229 | return -1; |
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230 | } |
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231 | //static int comp1dpc(poly p1, poly p2) |
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232 | //{ |
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233 | // /*4 compare monomials by order then revlex*/ |
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234 | // int d=p1->Order - p2->Order; |
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235 | // if (d==0 /*p1->Order == p2->Order*/) |
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236 | // { |
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237 | // int i=pVariables; |
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238 | // short *m1=p1->exp+/*pVariables*/ i; |
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239 | // short *m2=p2->exp+/*pVariables*/ i; |
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240 | // d=(*m1)-(*m2); |
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241 | // while ( d==0 /* *m1 == *m2*/) |
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242 | // { |
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243 | // i--; |
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244 | // if (i<0) |
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245 | // { |
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246 | // /*4 handle module case:*/ |
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247 | // if (p1->exp[0]==p2->exp[0]) return 0; |
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248 | // else if ( p1->exp[0] > p2->exp[0] ) return -pComponentOrder; |
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249 | // return pComponentOrder; |
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250 | // } |
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251 | // m1--;m2--; |
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252 | // d=(*m1)-(*m2); |
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253 | // } |
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254 | // if (d<0 /* *m1 < *m2*/ ) return 1; |
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255 | // return -1; |
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256 | // } |
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257 | // else if ( d > 0 /*p1->Order > p2->Order*/) return 1; |
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258 | // return -1; |
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259 | //} |
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260 | |
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261 | static int comp1Dpc(poly p1, poly p2) |
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262 | { |
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263 | int i; |
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264 | |
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265 | /*4 compare monomials by order then revlex*/ |
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266 | int d=p1->Order - p2->Order; |
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267 | if ( d > 0 /*p1->Order > p2->Order*/) |
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268 | return 1; |
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269 | else if (d < 0 /*p1->Order < p2->Order*/) |
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270 | return -1; |
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271 | for (i = 1; i<=pVariables; i++) |
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272 | { |
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273 | if (p1->exp[i] > p2->exp[i]) |
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274 | return 1; |
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275 | else if (p1->exp[i] < p2->exp[i]) |
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276 | return -1; |
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277 | } |
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278 | /*4 handle module case:*/ |
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279 | if (p1->exp[0]==p2->exp[0]) |
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280 | return 0; |
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281 | else if (p1->exp[0] > p2->exp[0]) |
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282 | return -pComponentOrder; |
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283 | return pComponentOrder; |
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284 | } |
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285 | |
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286 | //static int comp1lsc(poly p1, poly p2) |
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287 | //{ |
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288 | // int i; |
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289 | // |
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290 | // for (i=1; i<=pVariables; i++) |
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291 | // { |
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292 | // if (p1->exp[i] > p2->exp[i]) return -1; |
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293 | // if (p1->exp[i] < p2->exp[i]) return 1; |
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294 | // } |
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295 | // /*4 handle module case:*/ |
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296 | // if (p1->exp[0]==p2->exp[0]) return 0; |
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297 | // else if (p1->exp[0] > p2->exp[0]) return -pComponentOrder; |
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298 | // return pComponentOrder; |
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299 | //} |
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300 | static int comp1lsc(poly p1, poly p2) |
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301 | { |
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302 | int i; |
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303 | short *m1=p1->exp+1; |
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304 | short *m2=p2->exp+1; |
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305 | |
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306 | for (i=pVariables; i>0; i--,m1++,m2++) |
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307 | { |
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308 | if (*m1 > *m2) return -1; |
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309 | else if (*m1 < *m2) return 1; |
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310 | } |
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311 | /*4 handle module case:*/ |
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312 | if (p1->exp[0]==p2->exp[0]) |
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313 | return 0; |
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314 | else if (p1->exp[0] > p2->exp[0]) |
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315 | return -pComponentOrder; |
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316 | return pComponentOrder; |
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317 | } |
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318 | |
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319 | //static int comp1dsc(poly p1, poly p2) |
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320 | //{ |
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321 | // int i; |
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322 | // |
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323 | // /*4 compare monomials by order then revlex*/ |
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324 | // if (p1->Order == p2->Order) |
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325 | // { |
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326 | // i = pVariables; |
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327 | // if ((p1->exp[i] == p2->exp[i])) |
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328 | // { |
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329 | // do |
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330 | // { |
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331 | // i--; |
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332 | // if (i <= 1) |
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333 | // { |
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334 | // /*4 handle module case:*/ |
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335 | // if (p1->exp[0]==p2->exp[0]) return 0; |
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336 | // else if (p1->exp[0] > p2->exp[0]) return -pComponentOrder; |
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337 | // return pComponentOrder; |
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338 | // } |
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339 | // } while ((p1->exp[i] == p2->exp[i])); |
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340 | // } |
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341 | // if (p1->exp[i] < p2->exp[i]) return 1; |
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342 | // return -1; |
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343 | // } |
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344 | // else if (p1->Order > p2->Order) return -1; |
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345 | // return 1; |
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346 | //} |
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347 | static int comp1dsc(poly p1, poly p2) |
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348 | { |
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349 | /*4 compare monomials by order then revlex*/ |
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350 | int d=p1->Order - p2->Order; |
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351 | if (d==0 /*p1->Order == p2->Order*/) |
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352 | { |
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353 | int i=pVariables; |
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354 | short *m1=p1->exp+/*pVariables*/ i; |
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355 | short *m2=p2->exp+/*pVariables*/ i; |
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356 | while ((*m1 == *m2)) |
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357 | { |
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358 | i--; |
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359 | if (i==0) |
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360 | { |
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361 | /*4 handle module case:*/ |
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362 | //if (/*p1->exp[0]==p2->exp[0]*/ *m1==*m2) return 0; |
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363 | //else if ( *m1 > *m2) return -pComponentOrder; |
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364 | if (p1->exp[0]==p2->exp[0]) |
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365 | return 0; |
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366 | else if ( p1->exp[0] > p2->exp[0]) |
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367 | return -pComponentOrder; |
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368 | else |
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369 | return pComponentOrder; |
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370 | } |
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371 | m1--; |
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372 | m2--; |
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373 | } |
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374 | if (*m1 < *m2) |
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375 | return 1; |
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376 | return -1; |
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377 | } |
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378 | else if ( d > 0 /*p1->Order > p2->Order*/) |
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379 | return -1; |
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380 | return 1; |
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381 | } |
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382 | |
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383 | static int comp1Dsc(poly p1, poly p2) |
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384 | { |
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385 | int i; |
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386 | |
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387 | /*4 compare monomials by order then revlex*/ |
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388 | int d=p1->Order - p2->Order; |
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389 | if (d > 0 /*p1->Order > p2->Order*/) |
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390 | return -1; |
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391 | else if (d < 0 /*p1->Order < p2->Order*/) |
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392 | return 1; |
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393 | for (i = 1; i<=pVariables; i++) |
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394 | { |
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395 | if (p1->exp[i] > p2->exp[i]) |
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396 | return 1; |
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397 | else if (p1->exp[i] < p2->exp[i]) |
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398 | return -1; |
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399 | } |
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400 | /*4 handle module case:*/ |
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401 | if (p1->exp[0]==p2->exp[0]) |
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402 | return 0; |
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403 | else if (p1->exp[0] > p2->exp[0]) |
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404 | return -pComponentOrder; |
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405 | return pComponentOrder; |
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406 | } |
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407 | |
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408 | //static int comp1clp(poly p1, poly p2) |
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409 | //{ |
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410 | // int i; |
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411 | // |
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412 | // if (p1->exp[0] == p2->exp[0]) |
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413 | // { |
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414 | // for (i=1; i<=pVariables; i++) |
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415 | // { |
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416 | // if (p1->exp[i] > p2->exp[i]) return 1; |
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417 | // if (p1->exp[i] < p2->exp[i]) return -1; |
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418 | // } |
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419 | // return 0; |
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420 | // } |
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421 | // /*4 handle module case:*/ |
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422 | // else if (p1->exp[0] > p2->exp[0]) return -pComponentOrder; |
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423 | // return pComponentOrder; |
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424 | //} |
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425 | static int comp1clp(poly p1, poly p2) |
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426 | { |
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427 | int i; |
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428 | short *m1=p1->exp; |
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429 | short *m2=p2->exp; |
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430 | |
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431 | if (*m1 == *m2) |
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432 | { |
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433 | m1++; |
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434 | m2++; |
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435 | for (i=pVariables; i>0; i--,m1++,m2++) |
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436 | { |
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437 | if (*m1 > *m2) |
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438 | return 1; |
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439 | if (*m1 < *m2) |
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440 | return -1; |
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441 | } |
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442 | return 0; |
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443 | } |
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444 | /*4 handle module case:*/ |
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445 | else if (*m1 > *m2) |
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446 | return -pComponentOrder; |
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447 | return pComponentOrder; |
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448 | } |
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449 | |
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450 | static int comp2clp(poly p1, poly p2) |
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451 | { |
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452 | if (p1->exp[0]==p2->exp[0]) |
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453 | { |
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454 | int dd=p1->Order - p2->Order; |
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455 | if (dd > 0) |
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456 | return 1; |
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457 | if (dd < 0) |
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458 | return -1; |
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459 | return 0; |
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460 | } |
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461 | else if (p1->exp[0] > p2->exp[0]) |
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462 | return -pComponentOrder; |
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463 | return pComponentOrder; |
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464 | } |
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465 | |
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466 | static int comp1cdp(poly p1, poly p2) |
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467 | { |
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468 | int i; |
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469 | |
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470 | /*4 compare monomials by order then revlex*/ |
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471 | if (p1->exp[0] == p2->exp[0]) |
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472 | { |
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473 | int d= p1->Order - p2->Order; |
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474 | if (d == 0 /*p1->Order == p2->Order*/) |
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475 | { |
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476 | i = pVariables; |
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477 | if ((p1->exp[i] == p2->exp[i])) |
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478 | { |
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479 | do |
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480 | { |
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481 | i--; |
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482 | if (i <= 1) |
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483 | return 0; |
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484 | } while ((p1->exp[i] == p2->exp[i])); |
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485 | } |
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486 | if (p1->exp[i] < p2->exp[i]) |
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487 | return 1; |
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488 | return -1; |
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489 | } |
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490 | else if (d > 0 /*p1->Order > p2->Order*/) |
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491 | return 1; |
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492 | return -1; |
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493 | } |
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494 | /*4 handle module case:*/ |
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495 | else if (p1->exp[0] > p2->exp[0]) return -pComponentOrder; |
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496 | return pComponentOrder; |
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497 | } |
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498 | |
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499 | static int comp1cDp(poly p1, poly p2) |
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500 | { |
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501 | int i; |
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502 | |
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503 | /*4 compare monomials by order then revlex*/ |
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504 | if (p1->exp[0] == p2->exp[0]) |
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505 | { |
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506 | int d= p1->Order - p2->Order; |
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507 | if ( d > 0 /*p1->Order > p2->Order*/) |
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508 | return 1; |
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509 | else if (d < 0 /*p1->Order < p2->Order*/) |
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510 | return -1; |
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511 | for (i = 1; i<=pVariables; i++) |
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512 | { |
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513 | if (p1->exp[i] > p2->exp[i]) |
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514 | return 1; |
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515 | else if (p1->exp[i] < p2->exp[i]) |
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516 | return -1; |
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517 | } |
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518 | return 0; |
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519 | } |
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520 | /*4 handle module case:*/ |
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521 | else if (p1->exp[0] > p2->exp[0]) |
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522 | return -pComponentOrder; |
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523 | return pComponentOrder; |
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524 | } |
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525 | |
---|
526 | //static int comp1cls(poly p1, poly p2) |
---|
527 | //{ |
---|
528 | // int i; |
---|
529 | // |
---|
530 | // if (p1->exp[0] == p2->exp[0]) |
---|
531 | // { |
---|
532 | // for (i=1; i<=pVariables; i++) |
---|
533 | // { |
---|
534 | // if (p1->exp[i] > p2->exp[i]) return -1; |
---|
535 | // if (p1->exp[i] < p2->exp[i]) return 1; |
---|
536 | // } |
---|
537 | // return 0; |
---|
538 | // } |
---|
539 | // /*4 handle module case:*/ |
---|
540 | // else if (p1->exp[0] > p2->exp[0]) return -pComponentOrder; |
---|
541 | // return pComponentOrder; |
---|
542 | //} |
---|
543 | static int comp1cls(poly p1, poly p2) |
---|
544 | { |
---|
545 | int i; |
---|
546 | short *m1=p1->exp; |
---|
547 | short *m2=p2->exp; |
---|
548 | |
---|
549 | if (*m1 == *m2) |
---|
550 | { |
---|
551 | m1++; |
---|
552 | m2++; |
---|
553 | for (i=pVariables; i>0; i--,m1++,m2++) |
---|
554 | { |
---|
555 | if (*m1 > *m2) |
---|
556 | return -1; |
---|
557 | else if (*m1 < *m2) |
---|
558 | return 1; |
---|
559 | } |
---|
560 | return 0; |
---|
561 | } |
---|
562 | /*4 handle module case:*/ |
---|
563 | else if (*m1 > *m2) |
---|
564 | return -pComponentOrder; |
---|
565 | return pComponentOrder; |
---|
566 | } |
---|
567 | |
---|
568 | static int comp1cds(poly p1, poly p2) |
---|
569 | { |
---|
570 | int i; |
---|
571 | short *m1=p1->exp; |
---|
572 | short *m2=p2->exp; |
---|
573 | |
---|
574 | /*4 compare monomials by order then revlex*/ |
---|
575 | if (*m1 == *m2) |
---|
576 | { |
---|
577 | int d= p1->Order - p2->Order; |
---|
578 | if ( d == 0 /*p1->Order == p2->Order*/) |
---|
579 | { |
---|
580 | i = pVariables; |
---|
581 | m1=p1->exp+pVariables; |
---|
582 | m2=p2->exp+pVariables; |
---|
583 | if ((*m1 == *m2)) |
---|
584 | { |
---|
585 | do |
---|
586 | { |
---|
587 | i--; |
---|
588 | if (i <= 1) |
---|
589 | return 0; |
---|
590 | m1--; |
---|
591 | m2--; |
---|
592 | } while ((*m1 == *m2)); |
---|
593 | } |
---|
594 | if (*m1 < *m2) |
---|
595 | return 1; |
---|
596 | return -1; |
---|
597 | } |
---|
598 | else if ( d > 0 /*p1->Order > p2->Order*/) |
---|
599 | return -1; |
---|
600 | return 1; |
---|
601 | } |
---|
602 | /*4 handle module case:*/ |
---|
603 | else if (*m1 > *m2) |
---|
604 | return -pComponentOrder; |
---|
605 | return pComponentOrder; |
---|
606 | } |
---|
607 | //static int comp1cds(poly p1, poly p2) |
---|
608 | //{ |
---|
609 | // int i; |
---|
610 | // |
---|
611 | // /*4 compare monomials by order then revlex*/ |
---|
612 | // if (p1->exp[0] == p2->exp[0]) |
---|
613 | // { |
---|
614 | // if (p1->Order == p2->Order) |
---|
615 | // { |
---|
616 | // i = pVariables; |
---|
617 | // if ((p1->exp[i] == p2->exp[i])) |
---|
618 | // { |
---|
619 | // do |
---|
620 | // { |
---|
621 | // i--; |
---|
622 | // if (i <= 1) return 0; |
---|
623 | // } while ((p1->exp[i] == p2->exp[i])); |
---|
624 | // } |
---|
625 | // if (p1->exp[i] < p2->exp[i]) return 1; |
---|
626 | // return -1; |
---|
627 | // } |
---|
628 | // else if (p1->Order > p2->Order) return -1; |
---|
629 | // return 1; |
---|
630 | // } |
---|
631 | // /*4 handle module case:*/ |
---|
632 | // else if (p1->exp[0] > p2->exp[0]) return -pComponentOrder; |
---|
633 | // return pComponentOrder; |
---|
634 | //} |
---|
635 | |
---|
636 | static int comp1cDs(poly p1, poly p2) |
---|
637 | { |
---|
638 | int i; |
---|
639 | |
---|
640 | /*4 compare monomials by order then revlex*/ |
---|
641 | if (p1->exp[0] == p2->exp[0]) |
---|
642 | { |
---|
643 | int d= p1->Order - p2->Order; |
---|
644 | if (d > 0 /*p1->Order > p2->Order*/) |
---|
645 | return -1; |
---|
646 | else if (d < 0 /*p1->Order < p2->Order*/) |
---|
647 | return 1; |
---|
648 | for (i = 1; i<=pVariables; i++) |
---|
649 | { |
---|
650 | if (p1->exp[i] > p2->exp[i]) |
---|
651 | return 1; |
---|
652 | else if (p1->exp[i] < p2->exp[i]) |
---|
653 | return -1; |
---|
654 | } |
---|
655 | return 0; |
---|
656 | } |
---|
657 | /*4 handle module case:*/ |
---|
658 | else if (p1->exp[0] > p2->exp[0]) |
---|
659 | return -pComponentOrder; |
---|
660 | return pComponentOrder; |
---|
661 | } |
---|
662 | |
---|
663 | /*2 |
---|
664 | * compare the head monomial of p1 and p2 with weight vector |
---|
665 | */ |
---|
666 | static int comp1a ( poly p1, poly p2, int f, int l, short * w ) |
---|
667 | { |
---|
668 | int d= p1->Order - p2->Order; |
---|
669 | if ( d > 0 /*p1->Order > p2->Order*/ ) |
---|
670 | return 1; |
---|
671 | else if ( d < 0 /*p1->Order < p2->Order*/ ) |
---|
672 | return -1; |
---|
673 | return 0; |
---|
674 | } |
---|
675 | |
---|
676 | |
---|
677 | /*---------------------------------------------------*/ |
---|
678 | |
---|
679 | /* These functions could be made faster if you use pointers to the |
---|
680 | * exponent vectors and pointer arithmetic instead of using the |
---|
681 | * macro pGetExp !!! |
---|
682 | */ |
---|
683 | |
---|
684 | /*2 |
---|
685 | * compare the head monomial of p1 and p2 with lexicographic ordering |
---|
686 | */ |
---|
687 | //static int comp_lp ( poly p1, poly p2, int f, int l, short * w ) |
---|
688 | //{ |
---|
689 | // int i = f; |
---|
690 | // short *m1=p1->exp+f; |
---|
691 | // short *m2=p2->exp+f; |
---|
692 | // while ( ( i <= l ) && ( *m1 == *m2 ) ) { i++;m1++;m2++; } |
---|
693 | // if ( i > l ) return 0; |
---|
694 | // if ( *m1 > *m2 ) return 1; |
---|
695 | // return -1; |
---|
696 | //} |
---|
697 | static int comp_lp ( poly p1, poly p2, int f, int l, short * w ) |
---|
698 | { |
---|
699 | int i = f; |
---|
700 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
701 | i++; |
---|
702 | if ( i > l ) |
---|
703 | return 0; |
---|
704 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
---|
705 | return 1; |
---|
706 | return -1; |
---|
707 | } |
---|
708 | |
---|
709 | /*2 |
---|
710 | * compare the head monomial of p1 and p2 with degree reverse lexicographic |
---|
711 | * ordering |
---|
712 | */ |
---|
713 | //static int comp_dp ( poly p1, poly p2, int f, int l, short * w ) |
---|
714 | //{ |
---|
715 | // int i, s1 = 0, s2 = 0; |
---|
716 | // short *m1=p1->exp+f; |
---|
717 | // short *m2=p2->exp+f; |
---|
718 | // |
---|
719 | // for ( i = f; i <= l; i++,m1++,m2++ ) |
---|
720 | // { |
---|
721 | // s1 += (*m1); |
---|
722 | // s2 += (*m2); |
---|
723 | // } |
---|
724 | // if ( s1 == s2 ) |
---|
725 | // { |
---|
726 | // i = l; |
---|
727 | // while ( (i >= f ) && ( *m1 == *m2 ) ) { i--;m1--;m2--; } |
---|
728 | // if ( i < f ) return 0; |
---|
729 | // if ( *m1 > *m2 ) return -1; |
---|
730 | // return 1; |
---|
731 | // } |
---|
732 | // if ( s1 > s2 ) return 1; |
---|
733 | // return -1; |
---|
734 | //} |
---|
735 | static int comp_dp ( poly p1, poly p2, int f, int l, short * w ) |
---|
736 | { |
---|
737 | int i, s1 = 0, s2 = 0; |
---|
738 | |
---|
739 | for ( i = f; i <= l; i++ ) |
---|
740 | { |
---|
741 | s1 += pGetExp(p1,i); |
---|
742 | s2 += pGetExp(p2,i); |
---|
743 | } |
---|
744 | if ( s1 == s2 ) |
---|
745 | { |
---|
746 | i = l; |
---|
747 | while ( (i >= f ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
748 | i--; |
---|
749 | if ( i < f ) |
---|
750 | return 0; |
---|
751 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
---|
752 | return -1; |
---|
753 | return 1; |
---|
754 | } |
---|
755 | if ( s1 > s2 ) |
---|
756 | return 1; |
---|
757 | return -1; |
---|
758 | } |
---|
759 | |
---|
760 | /*2 |
---|
761 | * compare the head monomial of p1 and p2 with degree lexicographic ordering |
---|
762 | */ |
---|
763 | //static int comp_Dp ( poly p1, poly p2, int f, int l, short * w ) |
---|
764 | //{ |
---|
765 | // int i, s1 = 0, s2 = 0; |
---|
766 | // short *m1=p1->exp+f; |
---|
767 | // short *m2=p2->exp+f; |
---|
768 | // |
---|
769 | // for ( i = f; i <= l; i++,m1++,m2++ ) |
---|
770 | // { |
---|
771 | // s1 += (*m1); |
---|
772 | // s2 += (*m2); |
---|
773 | // } |
---|
774 | // if ( s1 == s2 ) |
---|
775 | // { |
---|
776 | // i = f; |
---|
777 | // while ( (i <= l ) && ( *m1 == *m2 ) ) { i++;m1++;m2++; } |
---|
778 | // if ( i > l ) return 0; |
---|
779 | // if ( *m1 > *m2 ) return 1; |
---|
780 | // return -1; |
---|
781 | // } |
---|
782 | // if ( s1 > s2 ) return 1; |
---|
783 | // return -1; |
---|
784 | //} |
---|
785 | static int comp_Dp ( poly p1, poly p2, int f, int l, short * w ) |
---|
786 | { |
---|
787 | int i, s1 = 0, s2 = 0; |
---|
788 | |
---|
789 | for ( i = f; i <= l; i++ ) |
---|
790 | { |
---|
791 | s1 += pGetExp(p1,i); |
---|
792 | s2 += pGetExp(p2,i); |
---|
793 | } |
---|
794 | if ( s1 == s2 ) |
---|
795 | { |
---|
796 | i = f; |
---|
797 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
798 | i++; |
---|
799 | if ( i > l ) |
---|
800 | return 0; |
---|
801 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
---|
802 | return 1; |
---|
803 | return -1; |
---|
804 | } |
---|
805 | if ( s1 > s2 ) |
---|
806 | return 1; |
---|
807 | return -1; |
---|
808 | } |
---|
809 | |
---|
810 | /*2 |
---|
811 | * compare the head monomial of p1 and p2 with weighted degree reverse |
---|
812 | * lexicographic ordering |
---|
813 | */ |
---|
814 | static int comp_wp ( poly p1, poly p2, int f, int l, short * w ) |
---|
815 | { |
---|
816 | int i, s1 = 0, s2 = 0; |
---|
817 | |
---|
818 | for ( i = f; i <= l; i++, w++ ) |
---|
819 | { |
---|
820 | s1 += (int)pGetExp(p1,i)*(*w); |
---|
821 | s2 += (int)pGetExp(p2,i)*(*w); |
---|
822 | } |
---|
823 | if ( s1 == s2 ) |
---|
824 | { |
---|
825 | i = l; |
---|
826 | while ( ( i >= f ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
827 | i--; |
---|
828 | if ( i < f ) |
---|
829 | return 0; |
---|
830 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
---|
831 | return -1; |
---|
832 | return 1; |
---|
833 | } |
---|
834 | if ( s1 > s2 ) |
---|
835 | return 1; |
---|
836 | return -1; |
---|
837 | } |
---|
838 | |
---|
839 | /*2 |
---|
840 | * compare the head monomial of p1 and p2 with weighted degree lexicographic |
---|
841 | * ordering |
---|
842 | */ |
---|
843 | static int comp_Wp ( poly p1, poly p2, int f, int l, short * w ) |
---|
844 | { |
---|
845 | int i, s1 = 0, s2 = 0; |
---|
846 | |
---|
847 | for ( i = f; i <= l; i++, w++ ) |
---|
848 | { |
---|
849 | s1 += (int)pGetExp(p1,i)*(*w); |
---|
850 | s2 += (int)pGetExp(p2,i)*(*w); |
---|
851 | } |
---|
852 | if ( s1 == s2 ) |
---|
853 | { |
---|
854 | i = f; |
---|
855 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
856 | i++; |
---|
857 | if ( i > l ) |
---|
858 | return 0; |
---|
859 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
---|
860 | return 1; |
---|
861 | return -1; |
---|
862 | } |
---|
863 | if ( s1 > s2 ) |
---|
864 | return 1; |
---|
865 | return -1; |
---|
866 | } |
---|
867 | |
---|
868 | /*2 |
---|
869 | * compare the head monomial of p1 and p2 with lexicographic ordering |
---|
870 | * (power series case) |
---|
871 | */ |
---|
872 | static int comp_ls ( poly p1, poly p2, int f, int l, short * w ) |
---|
873 | { |
---|
874 | int i; |
---|
875 | |
---|
876 | i = f; |
---|
877 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
878 | i++; |
---|
879 | if ( i > l ) |
---|
880 | return 0; |
---|
881 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
882 | return 1; |
---|
883 | return -1; |
---|
884 | } |
---|
885 | |
---|
886 | /*2 |
---|
887 | * compare the head monomial of p1 and p2 with degree reverse lexicographic |
---|
888 | * ordering (power series case) |
---|
889 | */ |
---|
890 | static int comp_ds ( poly p1, poly p2, int f, int l, short * w ) |
---|
891 | { |
---|
892 | int i, s1 = 0, s2 = 0; |
---|
893 | |
---|
894 | for ( i = f; i <= l; i++ ) |
---|
895 | { |
---|
896 | s1 += pGetExp(p1,i); |
---|
897 | s2 += pGetExp(p2,i); |
---|
898 | } |
---|
899 | if ( s1 == s2 ) |
---|
900 | { |
---|
901 | i = l; |
---|
902 | while ( ( i >= f ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
903 | i--; |
---|
904 | if ( i < f ) |
---|
905 | return 0; |
---|
906 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
907 | return 1; |
---|
908 | return -1; |
---|
909 | } |
---|
910 | if ( s1 < s2 ) |
---|
911 | return 1; |
---|
912 | return -1; |
---|
913 | } |
---|
914 | |
---|
915 | /*2 |
---|
916 | * compare the head monomial of p1 and p2 with degree lexicographic ordering |
---|
917 | * (power series case) |
---|
918 | */ |
---|
919 | static int comp_Ds ( poly p1, poly p2, int f, int l, short * w ) |
---|
920 | { |
---|
921 | int i, s1 = 0, s2 = 0; |
---|
922 | |
---|
923 | for ( i = f; i <= l; i++ ) |
---|
924 | { |
---|
925 | s1 += pGetExp(p1,i); |
---|
926 | s2 += pGetExp(p2,i); |
---|
927 | } |
---|
928 | if ( s1 == s2 ) |
---|
929 | { |
---|
930 | i = f; |
---|
931 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
932 | i++; |
---|
933 | if ( i > l ) |
---|
934 | return 0; |
---|
935 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
936 | return -1; |
---|
937 | return 1; |
---|
938 | } |
---|
939 | if ( s1 < s2 ) |
---|
940 | return 1; |
---|
941 | return -1; |
---|
942 | } |
---|
943 | |
---|
944 | /*2 |
---|
945 | * compare the head monomial of p1 and p2 with weighted degree reverse |
---|
946 | * lexicographic ordering (power series case) |
---|
947 | */ |
---|
948 | static int comp_ws ( poly p1, poly p2, int f, int l, short * w ) |
---|
949 | { |
---|
950 | int i, s1 = 0, s2 = 0; |
---|
951 | |
---|
952 | for ( i = f; i <= l; i++, w++ ) |
---|
953 | { |
---|
954 | s1 += (int)pGetExp(p1,i)*(*w); |
---|
955 | s2 += (int)pGetExp(p2,i)*(*w); |
---|
956 | } |
---|
957 | if ( s1 == s2 ) |
---|
958 | { |
---|
959 | i = l; |
---|
960 | while ( ( i >= f ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
961 | i--; |
---|
962 | if ( i < f ) |
---|
963 | return 0; |
---|
964 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
965 | return 1; |
---|
966 | return -1; |
---|
967 | } |
---|
968 | if ( s1 < s2 ) |
---|
969 | return 1; |
---|
970 | return -1; |
---|
971 | } |
---|
972 | |
---|
973 | /*2 |
---|
974 | * compare the head monomial of p1 and p2 with weighted degree lexicographic |
---|
975 | * ordering (power series case) |
---|
976 | */ |
---|
977 | static int comp_Ws ( poly p1, poly p2, int f, int l, short * w ) |
---|
978 | { |
---|
979 | int i, s1 = 0, s2 = 0; |
---|
980 | |
---|
981 | for ( i = f; i <= l; i++, w++ ) |
---|
982 | { |
---|
983 | s1 += (int)pGetExp(p1,i)*(*w); |
---|
984 | s2 += (int)pGetExp(p2,i)*(*w); |
---|
985 | } |
---|
986 | if ( s1 == s2 ) |
---|
987 | { |
---|
988 | i = f; |
---|
989 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
990 | i++; |
---|
991 | if ( i > l ) |
---|
992 | return 0; |
---|
993 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
994 | return -1; |
---|
995 | return 1; |
---|
996 | } |
---|
997 | if ( s1 < s2 ) |
---|
998 | return 1; |
---|
999 | return -1; |
---|
1000 | } |
---|
1001 | |
---|
1002 | /*2 |
---|
1003 | * compare the head monomial of p1 and p2 with matrix order |
---|
1004 | * w contains a series of l-f+1 lines |
---|
1005 | */ |
---|
1006 | static int comp_M ( poly p1, poly p2, int f, int l, short * w ) |
---|
1007 | { |
---|
1008 | int i, j, s1, s2; |
---|
1009 | |
---|
1010 | for ( i = f; i <= l; i++ ) |
---|
1011 | { |
---|
1012 | s1 = s2 = 0; |
---|
1013 | for ( j = f; j <= l; j++, w++ ) |
---|
1014 | { |
---|
1015 | s1 += (int)pGetExp(p1,j)*(int)(*w); |
---|
1016 | s2 += (int)pGetExp(p2,j)*(int)(*w); |
---|
1017 | } |
---|
1018 | if ( s1 < s2 ) |
---|
1019 | return -1; |
---|
1020 | if ( s1 > s2 ) |
---|
1021 | return 1; |
---|
1022 | /* now w points to the last element of the current row, the next w++ */ |
---|
1023 | /* moves on to the first element of the next row ! */ |
---|
1024 | } |
---|
1025 | return 0; |
---|
1026 | } |
---|
1027 | |
---|
1028 | /*2 |
---|
1029 | * compare the head monomial of p1 and p2 with weight vector |
---|
1030 | */ |
---|
1031 | static int comp_a ( poly p1, poly p2, int f, int l, short * w ) |
---|
1032 | { |
---|
1033 | int i, s1 = 0, s2 = 0; |
---|
1034 | |
---|
1035 | for ( i = f; i <= l; i++, w++ ) |
---|
1036 | { |
---|
1037 | s1 += (int)pGetExp(p1,i)*(*w); |
---|
1038 | s2 += (int)pGetExp(p2,i)*(*w); |
---|
1039 | } |
---|
1040 | if ( s1 > s2 ) |
---|
1041 | return 1; |
---|
1042 | if ( s1 < s2 ) |
---|
1043 | return -1; |
---|
1044 | return 0; |
---|
1045 | } |
---|
1046 | |
---|
1047 | /*2 |
---|
1048 | * compare the head monomial of p1 and p2 with module component |
---|
1049 | */ |
---|
1050 | static int comp_c ( poly p1, poly p2, int f, int l, short * w ) |
---|
1051 | { |
---|
1052 | if ( pGetComp(p1) > pGetComp(p2) ) |
---|
1053 | return -pComponentOrder; |
---|
1054 | if ( pGetComp(p1) < pGetComp(p2) ) |
---|
1055 | return pComponentOrder; |
---|
1056 | return 0; |
---|
1057 | } |
---|
1058 | |
---|
1059 | /*---------------------------------------------------------------*/ |
---|
1060 | |
---|
1061 | /*2 |
---|
1062 | * compare p1 and p2 by a block ordering |
---|
1063 | * uses (*bcomph[])() to do the real work |
---|
1064 | */ |
---|
1065 | static int BlockComp(poly p1, poly p2) |
---|
1066 | { |
---|
1067 | int res, i, e, a; |
---|
1068 | |
---|
1069 | /*4 compare in all blocks,* |
---|
1070 | * each block has var numbers a(=block0[i]) to e (=block1[i])* |
---|
1071 | * the block number starts with 0*/ |
---|
1072 | e = 0; |
---|
1073 | i = 0; |
---|
1074 | loop |
---|
1075 | { |
---|
1076 | a = block0[i]; |
---|
1077 | e = block1[i]; |
---|
1078 | res = (*bcomph[i])(p1, p2, a, e , polys_wv[i]); |
---|
1079 | if (res) |
---|
1080 | return res; |
---|
1081 | i++; |
---|
1082 | if (order[i]==0) |
---|
1083 | break; |
---|
1084 | } |
---|
1085 | return 0; |
---|
1086 | } |
---|
1087 | |
---|
1088 | int pComp(poly p1, poly p2) |
---|
1089 | { |
---|
1090 | if (p2==NULL) |
---|
1091 | return 1; |
---|
1092 | if (p1==NULL) |
---|
1093 | return -1; |
---|
1094 | return pComp0(p1,p2); |
---|
1095 | } |
---|
1096 | |
---|
1097 | /*----------pComp handling for syzygies---------------------*/ |
---|
1098 | static void newHeadsB(polyset actHeads,int length) |
---|
1099 | { |
---|
1100 | int i; |
---|
1101 | int* newOrder=(int*)Alloc(length*sizeof(int)); |
---|
1102 | |
---|
1103 | for (i=0;i<length;i++) |
---|
1104 | { |
---|
1105 | if (actHeads[i]) |
---|
1106 | { |
---|
1107 | newOrder[i] = SchreyerOrd[pGetComp(actHeads[i])-1]; |
---|
1108 | } |
---|
1109 | else |
---|
1110 | { |
---|
1111 | newOrder[i]=0; |
---|
1112 | } |
---|
1113 | } |
---|
1114 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
1115 | SchreyerOrd = newOrder; |
---|
1116 | maxSchreyer = length; |
---|
1117 | /* |
---|
1118 | *for (i=0;i<maxSchreyer;i++); Print("%d ",SchreyerOrd[i]); |
---|
1119 | *PrintLn(); |
---|
1120 | */ |
---|
1121 | } |
---|
1122 | |
---|
1123 | int mcompSchrB(poly p1,poly p2) |
---|
1124 | { |
---|
1125 | int CompP1=pGetComp(p1),CompP2=pGetComp(p2),result, |
---|
1126 | cP1=SchreyerOrd[CompP1-1],cP2=SchreyerOrd[CompP2-1]; |
---|
1127 | |
---|
1128 | if (CompP1==CompP2) return pCompOld(p1,p2); |
---|
1129 | pSetComp(p1,cP1); |
---|
1130 | pSetComp(p2,cP2); |
---|
1131 | result = pCompOld(p1,p2); |
---|
1132 | pSetComp(p1,CompP1); |
---|
1133 | pSetComp(p2,CompP2); |
---|
1134 | if (!result) |
---|
1135 | { |
---|
1136 | if (CompP1>CompP2) |
---|
1137 | return -1; |
---|
1138 | else if (CompP1<CompP2) |
---|
1139 | return 1; |
---|
1140 | } |
---|
1141 | return result; |
---|
1142 | } |
---|
1143 | |
---|
1144 | void pSetSchreyerOrdB(polyset nextOrder, int length) |
---|
1145 | { |
---|
1146 | int i; |
---|
1147 | |
---|
1148 | if (length) |
---|
1149 | { |
---|
1150 | if (maxSchreyer) |
---|
1151 | newHeadsB(nextOrder, length); |
---|
1152 | else |
---|
1153 | { |
---|
1154 | SchreyerOrd = (int*)Alloc(length*sizeof(int)); |
---|
1155 | for (i=0;i<length;i++) SchreyerOrd[i] = pGetComp(nextOrder[i]); |
---|
1156 | maxSchreyer = length; |
---|
1157 | pCompOld = pComp0; |
---|
1158 | pComp0 = mcompSchrB; |
---|
1159 | } |
---|
1160 | } |
---|
1161 | else |
---|
1162 | { |
---|
1163 | if (maxSchreyer!=0) |
---|
1164 | { |
---|
1165 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
1166 | maxSchreyer = 0; |
---|
1167 | pComp0 = pCompOld; |
---|
1168 | } |
---|
1169 | } |
---|
1170 | } |
---|
1171 | |
---|
1172 | static void newHeadsM(polyset actHeads,int length) |
---|
1173 | { |
---|
1174 | int i; |
---|
1175 | int* newOrder= |
---|
1176 | (int*)Alloc((length+maxSchreyer-indexShift)*sizeof(int)); |
---|
1177 | |
---|
1178 | for (i=0;i<length+maxSchreyer-indexShift;i++) |
---|
1179 | newOrder[i]=0; |
---|
1180 | for (i=indexShift;i<maxSchreyer;i++) |
---|
1181 | { |
---|
1182 | newOrder[i-indexShift] = SchreyerOrd[i]; |
---|
1183 | SchreyerOrd[i] = 0; |
---|
1184 | } |
---|
1185 | for (i=maxSchreyer-indexShift;i<length+maxSchreyer-indexShift;i++) |
---|
1186 | newOrder[i] = newOrder[pGetComp(actHeads[i-maxSchreyer+indexShift])-1]; |
---|
1187 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
1188 | SchreyerOrd = newOrder; |
---|
1189 | indexShift = maxSchreyer-indexShift; |
---|
1190 | maxSchreyer = length+indexShift; |
---|
1191 | } |
---|
1192 | |
---|
1193 | /*2 |
---|
1194 | * compute the length of a polynomial (in l) |
---|
1195 | * and the degree of the monomial with maximal degree: |
---|
1196 | * this is NOT the last one and the module component |
---|
1197 | * has to be <= indexShift |
---|
1198 | */ |
---|
1199 | static int ldegSchrM(poly p,int *l) |
---|
1200 | { |
---|
1201 | int t,max; |
---|
1202 | |
---|
1203 | (*l)=1; |
---|
1204 | max=pFDeg(p); |
---|
1205 | while ((pNext(p)!=NULL) && (pNext(p)->exp[0]<=indexShift)) |
---|
1206 | { |
---|
1207 | pIter(p); |
---|
1208 | t=pFDeg(p); |
---|
1209 | if (t>max) max=t; |
---|
1210 | (*l)++; |
---|
1211 | } |
---|
1212 | return max; |
---|
1213 | } |
---|
1214 | |
---|
1215 | int mcompSchrM(poly p1,poly p2) |
---|
1216 | { |
---|
1217 | if (p1->exp[0]<=indexShift) |
---|
1218 | { |
---|
1219 | if (p2->exp[0]>indexShift) return 1; |
---|
1220 | } |
---|
1221 | else if (p2->exp[0]<=indexShift) return -1; |
---|
1222 | return mcompSchrB(p1,p2); |
---|
1223 | } |
---|
1224 | |
---|
1225 | void pSetSchreyerOrdM(polyset nextOrder, int length,int comps) |
---|
1226 | { |
---|
1227 | int i; |
---|
1228 | |
---|
1229 | if (length!=0) |
---|
1230 | { |
---|
1231 | if (maxSchreyer!=0) |
---|
1232 | newHeadsM(nextOrder, length); |
---|
1233 | else |
---|
1234 | { |
---|
1235 | indexShift = comps; |
---|
1236 | if (!indexShift) indexShift = 1; |
---|
1237 | SchreyerOrd = (int*)Alloc((indexShift+length)*sizeof(int)); |
---|
1238 | maxSchreyer = length+indexShift; |
---|
1239 | for (i=0;i<indexShift;i++) |
---|
1240 | SchreyerOrd[i] = i; |
---|
1241 | for (i=indexShift;i<maxSchreyer;i++) |
---|
1242 | SchreyerOrd[i] = pGetComp(nextOrder[i-indexShift]); |
---|
1243 | pCompOld = pComp0; |
---|
1244 | pComp0 = mcompSchrM; |
---|
1245 | pLDegOld = pLDeg; |
---|
1246 | pLDeg = ldegSchrM; |
---|
1247 | } |
---|
1248 | } |
---|
1249 | else |
---|
1250 | { |
---|
1251 | if (maxSchreyer!=0) |
---|
1252 | { |
---|
1253 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
1254 | maxSchreyer = 0; |
---|
1255 | indexShift = 0; |
---|
1256 | pComp0 = pCompOld; |
---|
1257 | pLDeg = pLDegOld; |
---|
1258 | } |
---|
1259 | } |
---|
1260 | } |
---|
1261 | |
---|
1262 | /*2 |
---|
1263 | *the pComp0 for normal syzygies |
---|
1264 | *compares monomials in the usual ring order (pCompOld) |
---|
1265 | *but groups module indecees according indexBounds befor |
---|
1266 | */ |
---|
1267 | static int mcompSyz(poly p1,poly p2) |
---|
1268 | { |
---|
1269 | if (pGetComp(p1)<=maxBound) |
---|
1270 | { |
---|
1271 | if (pGetComp(p2)>maxBound) return 1; |
---|
1272 | } |
---|
1273 | else if (pGetComp(p2)<=maxBound) |
---|
1274 | { |
---|
1275 | if (pGetComp(p1)>maxBound) return -1; |
---|
1276 | } |
---|
1277 | return pCompOld(p1,p2); |
---|
1278 | } |
---|
1279 | |
---|
1280 | void pSetSyzComp(int k) |
---|
1281 | { |
---|
1282 | if (k!=0) |
---|
1283 | { |
---|
1284 | if (maxBound==0) |
---|
1285 | { |
---|
1286 | pCompOld = pComp0; |
---|
1287 | pComp0 = mcompSyz; |
---|
1288 | } |
---|
1289 | maxBound = k; |
---|
1290 | } |
---|
1291 | else |
---|
1292 | { |
---|
1293 | if (maxBound!=0) |
---|
1294 | { |
---|
1295 | pComp0 = pCompOld; |
---|
1296 | maxBound = 0; |
---|
1297 | } |
---|
1298 | } |
---|
1299 | } |
---|
1300 | |
---|
1301 | /*2 |
---|
1302 | * the type of the module ordering: C: -1, c: 1 |
---|
1303 | */ |
---|
1304 | int pModuleOrder() |
---|
1305 | { |
---|
1306 | return pComponentOrder; |
---|
1307 | } |
---|
1308 | |
---|
1309 | /* -------------------------------------------------------------------*/ |
---|
1310 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
1311 | /*2 |
---|
1312 | * compute the degree of the leading monomial of p |
---|
1313 | * the ordering is compatible with degree, use a->order |
---|
1314 | */ |
---|
1315 | int pDeg(poly a) |
---|
1316 | { |
---|
1317 | return ((a!=NULL) ? (a->Order) : (-1)); |
---|
1318 | } |
---|
1319 | |
---|
1320 | /*2 |
---|
1321 | * compute the degree of the leading monomial of p |
---|
1322 | * with respect to weigths 1 |
---|
1323 | * (all are 1 so save multiplications or they are of different signs) |
---|
1324 | * the ordering is not compatible with degree so do not use p->Order |
---|
1325 | */ |
---|
1326 | int pTotaldegree(poly p) |
---|
1327 | { |
---|
1328 | int i; |
---|
1329 | int j =(int)p->exp[1]; |
---|
1330 | |
---|
1331 | for (i=pVariables; i>1; i--) |
---|
1332 | j += (int)p->exp[i]; |
---|
1333 | return j; |
---|
1334 | } |
---|
1335 | |
---|
1336 | /*2 |
---|
1337 | * compute the degree of the leading monomial of p |
---|
1338 | * with respect to weigths from the ordering |
---|
1339 | * the ordering is not compatible with degree so do not use p->Order |
---|
1340 | */ |
---|
1341 | int pWTotaldegree(poly p) |
---|
1342 | { |
---|
1343 | int i, k; |
---|
1344 | int j =0; |
---|
1345 | |
---|
1346 | // iterate through each block: |
---|
1347 | for (i=0;order[i]!=0;i++) |
---|
1348 | { |
---|
1349 | switch(order[i]) |
---|
1350 | { |
---|
1351 | case ringorder_wp: |
---|
1352 | case ringorder_ws: |
---|
1353 | case ringorder_Wp: |
---|
1354 | case ringorder_Ws: |
---|
1355 | for (k=block0[i];k<=block1[i];k++) |
---|
1356 | { // in jedem block: |
---|
1357 | j+=p->exp[k]*polys_wv[i][k-block0[i]]; |
---|
1358 | } |
---|
1359 | break; |
---|
1360 | case ringorder_M: |
---|
1361 | case ringorder_lp: |
---|
1362 | case ringorder_dp: |
---|
1363 | case ringorder_ds: |
---|
1364 | case ringorder_Dp: |
---|
1365 | case ringorder_Ds: |
---|
1366 | for (k=block0[i];k<=block1[i];k++) |
---|
1367 | { |
---|
1368 | j+=p->exp[k]; |
---|
1369 | } |
---|
1370 | break; |
---|
1371 | case ringorder_c: |
---|
1372 | case ringorder_C: |
---|
1373 | break; |
---|
1374 | case ringorder_a: |
---|
1375 | for (k=block0[i];k<=block1[i];k++) |
---|
1376 | { // only one line |
---|
1377 | j+=p->exp[k]*polys_wv[i][k-block0[i]]; |
---|
1378 | } |
---|
1379 | return j; |
---|
1380 | } |
---|
1381 | } |
---|
1382 | return j; |
---|
1383 | } |
---|
1384 | /* ---------------------------------------------------------------------*/ |
---|
1385 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
1386 | /* compute in l also the pLength of p */ |
---|
1387 | |
---|
1388 | /*2 |
---|
1389 | * compute the length of a polynomial (in l) |
---|
1390 | * and the degree of the monomial with maximal degree: the last one |
---|
1391 | */ |
---|
1392 | static int ldeg0(poly p,int *l) |
---|
1393 | { |
---|
1394 | short k=p->exp[0]; |
---|
1395 | int ll=1; |
---|
1396 | |
---|
1397 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))==k)) |
---|
1398 | { |
---|
1399 | pIter(p); |
---|
1400 | ll++; |
---|
1401 | } |
---|
1402 | *l=ll; |
---|
1403 | return (p->Order); |
---|
1404 | } |
---|
1405 | |
---|
1406 | /*2 |
---|
1407 | * compute the length of a polynomial (in l) |
---|
1408 | * and the degree of the monomial with maximal degree: the last one |
---|
1409 | * but search in all components before syzcomp |
---|
1410 | */ |
---|
1411 | static int ldeg0c(poly p,int *l) |
---|
1412 | { |
---|
1413 | int o=pFDeg(p); |
---|
1414 | int ll=1; |
---|
1415 | |
---|
1416 | if (maxBound/*syzComp*/==0) |
---|
1417 | { |
---|
1418 | while ((p=pNext(p))!=NULL) |
---|
1419 | { |
---|
1420 | o=pFDeg(p); |
---|
1421 | ll++; |
---|
1422 | } |
---|
1423 | } |
---|
1424 | else |
---|
1425 | { |
---|
1426 | while ((p=pNext(p))!=NULL) |
---|
1427 | { |
---|
1428 | if (pGetComp(p)<=maxBound/*syzComp*/) |
---|
1429 | { |
---|
1430 | o=pFDeg(p); |
---|
1431 | ll++; |
---|
1432 | } |
---|
1433 | else break; |
---|
1434 | } |
---|
1435 | } |
---|
1436 | *l=ll; |
---|
1437 | return o; |
---|
1438 | } |
---|
1439 | |
---|
1440 | /*2 |
---|
1441 | * compute the length of a polynomial (in l) |
---|
1442 | * and the degree of the monomial with maximal degree: the first one |
---|
1443 | * this works for the polynomial case with degree orderings |
---|
1444 | * (both c,dp and dp,c) |
---|
1445 | */ |
---|
1446 | static int ldegb(poly p,int *l) |
---|
1447 | { |
---|
1448 | short k=p->exp[0]; |
---|
1449 | int o = p->Order; |
---|
1450 | int ll=1; |
---|
1451 | |
---|
1452 | while (((p=pNext(p))!=NULL) && (pGetComp(p)==k)) |
---|
1453 | { |
---|
1454 | ll++; |
---|
1455 | } |
---|
1456 | *l=ll; |
---|
1457 | return o; |
---|
1458 | } |
---|
1459 | |
---|
1460 | /*2 |
---|
1461 | * compute the length of a polynomial (in l) |
---|
1462 | * and the degree of the monomial with maximal degree: |
---|
1463 | * this is NOT the last one, we have to look for it |
---|
1464 | */ |
---|
1465 | static int ldeg1(poly p,int *l) |
---|
1466 | { |
---|
1467 | short k=p->exp[0]; |
---|
1468 | int ll=1; |
---|
1469 | int t,max; |
---|
1470 | |
---|
1471 | max=pFDeg(p); |
---|
1472 | while (((p=pNext(p))!=NULL) && (pGetComp(p)==k)) |
---|
1473 | { |
---|
1474 | t=pFDeg(p); |
---|
1475 | if (t>max) max=t; |
---|
1476 | ll++; |
---|
1477 | } |
---|
1478 | *l=ll; |
---|
1479 | return max; |
---|
1480 | } |
---|
1481 | |
---|
1482 | /*2 |
---|
1483 | * compute the length of a polynomial (in l) |
---|
1484 | * and the degree of the monomial with maximal degree: |
---|
1485 | * this is NOT the last one, we have to look for it |
---|
1486 | * in all components |
---|
1487 | */ |
---|
1488 | static int ldeg1c(poly p,int *l) |
---|
1489 | { |
---|
1490 | int ll=1; |
---|
1491 | int t,max; |
---|
1492 | |
---|
1493 | max=pFDeg(p); |
---|
1494 | while ((p=pNext(p))!=NULL) |
---|
1495 | { |
---|
1496 | if ((maxBound/*syzComp*/==0) || (pGetComp(p)<=maxBound/*syzComp*/)) |
---|
1497 | { |
---|
1498 | if ((t=pFDeg(p))>max) max=t; |
---|
1499 | ll++; |
---|
1500 | } |
---|
1501 | else break; |
---|
1502 | } |
---|
1503 | *l=ll; |
---|
1504 | return max; |
---|
1505 | } |
---|
1506 | |
---|
1507 | /* -------------------------------------------------------- */ |
---|
1508 | /* set the variables for a choosen ordering */ |
---|
1509 | |
---|
1510 | /*2 |
---|
1511 | * sets the comparision routine for monomials: for the first block |
---|
1512 | * of variables (or is the number of the ordering) |
---|
1513 | */ |
---|
1514 | static void SimpleChoose(int or, pCompProc *p) |
---|
1515 | { |
---|
1516 | switch(or) |
---|
1517 | { |
---|
1518 | case ringorder_lp: |
---|
1519 | if (pVariables<3) *p= comp2lpc; |
---|
1520 | else *p= comp1lpc; |
---|
1521 | pLexOrder=TRUE; |
---|
1522 | pFDeg = pTotaldegree; |
---|
1523 | pLDeg = ldeg1c; |
---|
1524 | break; |
---|
1525 | case ringorder_unspec: |
---|
1526 | case ringorder_dp: |
---|
1527 | *p= comp1dpc; |
---|
1528 | break; |
---|
1529 | case ringorder_Dp: |
---|
1530 | *p= comp1Dpc; |
---|
1531 | break; |
---|
1532 | case ringorder_wp: |
---|
1533 | *p= comp1dpc; |
---|
1534 | break; |
---|
1535 | case ringorder_Wp: |
---|
1536 | *p= comp1Dpc; |
---|
1537 | break; |
---|
1538 | case ringorder_ls: |
---|
1539 | *p= comp1lsc; |
---|
1540 | pLexOrder=TRUE; |
---|
1541 | pFDeg = pTotaldegree; |
---|
1542 | pLDeg = ldeg1c; |
---|
1543 | break; |
---|
1544 | case ringorder_ds: |
---|
1545 | *p= comp1dsc; |
---|
1546 | break; |
---|
1547 | case ringorder_Ds: |
---|
1548 | *p= comp1Dsc; |
---|
1549 | break; |
---|
1550 | case ringorder_ws: |
---|
1551 | *p= comp1dsc; |
---|
1552 | break; |
---|
1553 | case ringorder_Ws: |
---|
1554 | *p= comp1Dsc; |
---|
1555 | break; |
---|
1556 | #ifdef TEST |
---|
1557 | default: |
---|
1558 | Werror("wrong internal ordering:%d at %s, l:%d\n",or,__FILE__,__LINE__); |
---|
1559 | #endif |
---|
1560 | } |
---|
1561 | } |
---|
1562 | |
---|
1563 | /*2 |
---|
1564 | * sets pSetm |
---|
1565 | * (according or = order of first block) |
---|
1566 | */ |
---|
1567 | static void SetpSetm(int or, int ip) |
---|
1568 | { |
---|
1569 | switch(or) |
---|
1570 | { |
---|
1571 | case ringorder_lp: |
---|
1572 | case ringorder_ls: |
---|
1573 | if (pVariables>1) |
---|
1574 | pSetm= setlex2; |
---|
1575 | else |
---|
1576 | pSetm= setlex1; |
---|
1577 | break; |
---|
1578 | case ringorder_dp: |
---|
1579 | case ringorder_Dp: |
---|
1580 | case ringorder_ds: |
---|
1581 | case ringorder_Ds: |
---|
1582 | case ringorder_unspec: |
---|
1583 | pSetm= setdeg1; |
---|
1584 | break; |
---|
1585 | case ringorder_a: |
---|
1586 | case ringorder_wp: |
---|
1587 | case ringorder_Wp: |
---|
1588 | case ringorder_ws: |
---|
1589 | case ringorder_Ws: |
---|
1590 | case ringorder_M: |
---|
1591 | pSetm= setdeg1w; |
---|
1592 | firstwv=polys_wv[ip]; |
---|
1593 | break; |
---|
1594 | case ringorder_c: |
---|
1595 | case ringorder_C: |
---|
1596 | return; |
---|
1597 | /*do not set firstBlockEnds for this orderings*/ |
---|
1598 | #ifdef TEST |
---|
1599 | default: |
---|
1600 | Werror("wrong internal ordering:%d at %s, l:%d\n",or,__FILE__,__LINE__); |
---|
1601 | #endif |
---|
1602 | } |
---|
1603 | firstBlockEnds=block1[ip]; |
---|
1604 | } |
---|
1605 | |
---|
1606 | /*2 |
---|
1607 | * sets the comparision routine for monomials: for the first block |
---|
1608 | * of variables (or is the number of the ordering) |
---|
1609 | */ |
---|
1610 | static void SimpleChooseC(int or, pCompProc *p) |
---|
1611 | { |
---|
1612 | switch(or) |
---|
1613 | { |
---|
1614 | case ringorder_lp: |
---|
1615 | if (pVariables <3) *p= comp2clp; |
---|
1616 | else *p= comp1clp; |
---|
1617 | pLexOrder=TRUE; |
---|
1618 | pFDeg = pTotaldegree; |
---|
1619 | pLDeg = ldeg1; |
---|
1620 | break; |
---|
1621 | case ringorder_dp: |
---|
1622 | *p= comp1cdp; |
---|
1623 | break; |
---|
1624 | case ringorder_Dp: |
---|
1625 | *p= comp1cDp; |
---|
1626 | break; |
---|
1627 | case ringorder_wp: |
---|
1628 | *p= comp1cdp; |
---|
1629 | break; |
---|
1630 | case ringorder_Wp: |
---|
1631 | *p= comp1cDp; |
---|
1632 | break; |
---|
1633 | case ringorder_ls: |
---|
1634 | *p= comp1cls; |
---|
1635 | pLexOrder=TRUE; |
---|
1636 | pFDeg = pTotaldegree; |
---|
1637 | pLDeg = ldeg1; |
---|
1638 | break; |
---|
1639 | case ringorder_ds: |
---|
1640 | *p= comp1cds; |
---|
1641 | break; |
---|
1642 | case ringorder_Ds: |
---|
1643 | *p= comp1cDs; |
---|
1644 | break; |
---|
1645 | case ringorder_ws: |
---|
1646 | *p= comp1cds; |
---|
1647 | break; |
---|
1648 | case ringorder_Ws: |
---|
1649 | *p= comp1cDs; |
---|
1650 | break; |
---|
1651 | #ifdef TEST |
---|
1652 | default: |
---|
1653 | Werror("wrong internal ordering:%d at %s, l:%d\n",or,__FILE__,__LINE__); |
---|
1654 | #endif |
---|
1655 | } |
---|
1656 | } |
---|
1657 | |
---|
1658 | /*2 |
---|
1659 | * sets the comparision routine for monomials: for all but the first |
---|
1660 | * block of variables (ip is the block number, or the number of the ordering) |
---|
1661 | */ |
---|
1662 | static void HighSet(int ip, int or) |
---|
1663 | { |
---|
1664 | switch(or) |
---|
1665 | { |
---|
1666 | case ringorder_lp: |
---|
1667 | bcomph[ip]=comp_lp; |
---|
1668 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1669 | break; |
---|
1670 | case ringorder_dp: |
---|
1671 | bcomph[ip]=comp_dp; |
---|
1672 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1673 | break; |
---|
1674 | case ringorder_Dp: |
---|
1675 | bcomph[ip]=comp_Dp; |
---|
1676 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1677 | break; |
---|
1678 | case ringorder_wp: |
---|
1679 | bcomph[ip]=comp_wp; |
---|
1680 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1681 | break; |
---|
1682 | case ringorder_Wp: |
---|
1683 | bcomph[ip]=comp_Wp; |
---|
1684 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1685 | break; |
---|
1686 | case ringorder_ls: |
---|
1687 | bcomph[ip]=comp_ls; |
---|
1688 | break; |
---|
1689 | case ringorder_ds: |
---|
1690 | bcomph[ip]=comp_ds; |
---|
1691 | break; |
---|
1692 | case ringorder_Ds: |
---|
1693 | bcomph[ip]=comp_Ds; |
---|
1694 | break; |
---|
1695 | case ringorder_ws: |
---|
1696 | bcomph[ip]=comp_ws; |
---|
1697 | break; |
---|
1698 | case ringorder_Ws: |
---|
1699 | bcomph[ip]=comp_Ws; |
---|
1700 | break; |
---|
1701 | case ringorder_c: |
---|
1702 | pComponentOrder=1; |
---|
1703 | bcomph[ip]=comp_c; |
---|
1704 | break; |
---|
1705 | case ringorder_C: |
---|
1706 | pComponentOrder=-1; |
---|
1707 | bcomph[ip]=comp_c; |
---|
1708 | break; |
---|
1709 | case ringorder_M: |
---|
1710 | bcomph[ip]=comp_M; |
---|
1711 | pMixedOrder=TRUE; |
---|
1712 | break; |
---|
1713 | case ringorder_a: |
---|
1714 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1715 | if (ip==0) |
---|
1716 | bcomph[0]=comp1a; |
---|
1717 | else |
---|
1718 | bcomph[ip]=comp_a; |
---|
1719 | break; |
---|
1720 | #ifdef TEST |
---|
1721 | default: |
---|
1722 | Werror("wrong internal ordering:%d at %s, l:%d\n",or,__FILE__,__LINE__); |
---|
1723 | #endif |
---|
1724 | } |
---|
1725 | } |
---|
1726 | |
---|
1727 | /* -------------------------------------------------------- */ |
---|
1728 | /*2 |
---|
1729 | * change all variables to fit the description of the new ring |
---|
1730 | */ |
---|
1731 | void pChangeRing(int n, int Sgn, int * orders, int * b0, int * b1, |
---|
1732 | short ** wv) |
---|
1733 | { |
---|
1734 | |
---|
1735 | int i; |
---|
1736 | pComponentOrder=1; |
---|
1737 | if (ppNoether!=NULL) pDelete(&ppNoether); |
---|
1738 | #ifdef SRING |
---|
1739 | pSRING=FALSE; |
---|
1740 | pAltVars=n+1; |
---|
1741 | #endif |
---|
1742 | |
---|
1743 | pVariables = n; |
---|
1744 | pOrdSgn = Sgn; |
---|
1745 | pVectorOut=(orders[0]==ringorder_c); |
---|
1746 | order=orders; |
---|
1747 | block0=b0; |
---|
1748 | block1=b1; |
---|
1749 | firstwv=NULL; |
---|
1750 | polys_wv=wv; |
---|
1751 | /*------- only one real block ----------------------*/ |
---|
1752 | pLexOrder=FALSE; |
---|
1753 | pMixedOrder=FALSE; |
---|
1754 | pFDeg=pDeg; |
---|
1755 | if (pOrdSgn == 1) pLDeg = ldegb; |
---|
1756 | else pLDeg = ldeg0; |
---|
1757 | /*======== ordering type is (_,c) =========================*/ |
---|
1758 | if ((orders[0]==ringorder_unspec) |
---|
1759 | ||( |
---|
1760 | ((orders[1]==ringorder_c)||(orders[1]==ringorder_C)) |
---|
1761 | && (orders[0]!=ringorder_M) |
---|
1762 | && (orders[2]==0)) |
---|
1763 | ) |
---|
1764 | { |
---|
1765 | if (pOrdSgn == -1) pLDeg = ldeg0c; |
---|
1766 | SimpleChoose(orders[0],&pComp0); |
---|
1767 | SetpSetm(orders[0],0); |
---|
1768 | if ((orders[0]!=ringorder_unspec) |
---|
1769 | && (orders[1]==ringorder_C)) |
---|
1770 | pComponentOrder=-1; |
---|
1771 | #ifdef TEST_MAC_ORDER |
---|
1772 | if (orders[0]==ringorder_dp) |
---|
1773 | bBinomSet(); |
---|
1774 | #endif |
---|
1775 | } |
---|
1776 | /*======== ordering type is (c,_) =========================*/ |
---|
1777 | else if (((orders[0]==ringorder_c)||(orders[0]==ringorder_C)) |
---|
1778 | && (orders[1]!=ringorder_M) |
---|
1779 | && (orders[2]==0)) |
---|
1780 | { |
---|
1781 | /* pLDeg = ldeg0; is standard*/ |
---|
1782 | SimpleChooseC(orders[1],&pComp0); |
---|
1783 | SetpSetm(orders[1],1); |
---|
1784 | if (orders[0]==ringorder_C) |
---|
1785 | pComponentOrder=-1; |
---|
1786 | } |
---|
1787 | /*------- more than one block ----------------------*/ |
---|
1788 | else |
---|
1789 | { |
---|
1790 | //pLexOrder=TRUE; |
---|
1791 | pVectorOut=orders[0]==ringorder_c; |
---|
1792 | if ((pVectorOut)||(orders[0]==ringorder_C)) |
---|
1793 | { |
---|
1794 | if(block1[1]!=pVariables) pLexOrder=TRUE; |
---|
1795 | } |
---|
1796 | else |
---|
1797 | { |
---|
1798 | if(block1[0]!=pVariables) pLexOrder=TRUE; |
---|
1799 | } |
---|
1800 | /*the number of orderings:*/ |
---|
1801 | i = 0; |
---|
1802 | while (orders[++i] != 0); |
---|
1803 | do |
---|
1804 | { |
---|
1805 | i--; |
---|
1806 | HighSet(i, orders[i]);/*sets also pMixedOrder to TRUE, if...*/ |
---|
1807 | SetpSetm(orders[i],i); |
---|
1808 | } |
---|
1809 | while (i != 0); |
---|
1810 | |
---|
1811 | pComp0 = BlockComp; |
---|
1812 | if ((orders[0]!=ringorder_c)&&(orders[0]!=ringorder_C)) |
---|
1813 | { |
---|
1814 | pLDeg = ldeg1c; |
---|
1815 | } |
---|
1816 | else |
---|
1817 | { |
---|
1818 | pLDeg = ldeg1; |
---|
1819 | } |
---|
1820 | pFDeg = pWTotaldegree; // may be improved: pTotaldegree for lp/dp/ls/.. blocks |
---|
1821 | } |
---|
1822 | pMonomSize = POLYSIZE + (pVariables + 1) * sizeof(short); |
---|
1823 | mmSpecializeBlock(pMonomSize); |
---|
1824 | if ((pLexOrder) || (pOrdSgn==-1)) |
---|
1825 | { |
---|
1826 | test &= ~Sy_bit(OPT_REDTAIL); /* noredTail */ |
---|
1827 | } |
---|
1828 | } |
---|
1829 | |
---|
1830 | /* -------------------------------------------------------- */ |
---|
1831 | |
---|
1832 | static BOOLEAN pMultT_nok; |
---|
1833 | /*2 |
---|
1834 | * update the polynomial a by multipying it by |
---|
1835 | * the (number) coefficient |
---|
1836 | * and the exponent vector (of) exp (a well initialized polynomial) |
---|
1837 | */ |
---|
1838 | poly pMultT(poly a, poly exp ) |
---|
1839 | { |
---|
1840 | int i; |
---|
1841 | number t,x,y=pGetCoeff(exp); |
---|
1842 | poly aa=a; |
---|
1843 | poly prev=NULL; |
---|
1844 | #ifdef SDRING |
---|
1845 | poly pDRINGres=NULL; |
---|
1846 | #endif |
---|
1847 | |
---|
1848 | pMultT_nok = pGetComp(exp); |
---|
1849 | #ifdef PDEBUG |
---|
1850 | pTest(a); |
---|
1851 | pTest(exp); |
---|
1852 | #endif |
---|
1853 | while (a !=NULL) |
---|
1854 | { |
---|
1855 | x=pGetCoeff(a); |
---|
1856 | t=nMult(x/*pGetCoeff(a)*/,y/*pGetCoeff(exp)*/); |
---|
1857 | nDelete(&x/*pGetCoeff(a)*/); |
---|
1858 | pSetCoeff0(a,t); |
---|
1859 | if (nIsZero(t)) |
---|
1860 | { |
---|
1861 | if (prev==NULL) { pDelete1(&a); aa=a; } |
---|
1862 | else { pDelete1(&prev->next); a=prev->next;} |
---|
1863 | } |
---|
1864 | else |
---|
1865 | { |
---|
1866 | #ifdef DRING |
---|
1867 | if (pDRING) |
---|
1868 | { |
---|
1869 | if (pdDFlag(a)==1) |
---|
1870 | { |
---|
1871 | if (pdDFlag(exp)==1) |
---|
1872 | { |
---|
1873 | pDRINGres=pAdd(pDRINGres,pMultDD(a,exp)); |
---|
1874 | } |
---|
1875 | else |
---|
1876 | { |
---|
1877 | pDRINGres=pAdd(pDRINGres,pMultDT(a,exp)); |
---|
1878 | } |
---|
1879 | } |
---|
1880 | else |
---|
1881 | { |
---|
1882 | if (pdDFlag(exp)==1) |
---|
1883 | { |
---|
1884 | pDRINGres=pAdd(pDRINGres,pMultDD(a,exp)); |
---|
1885 | } |
---|
1886 | else |
---|
1887 | { |
---|
1888 | pDRINGres=pAdd(pDRINGres,pMultTT(a,exp)); |
---|
1889 | } |
---|
1890 | } |
---|
1891 | } |
---|
1892 | else |
---|
1893 | #endif |
---|
1894 | #ifdef SRING |
---|
1895 | if (pSRING) |
---|
1896 | { |
---|
1897 | pDRINGres=pAdd(pDRINGres,psMultM(a,exp)); |
---|
1898 | } |
---|
1899 | else |
---|
1900 | #endif |
---|
1901 | { |
---|
1902 | for (i=pVariables; i != 0; i--) |
---|
1903 | { |
---|
1904 | a->exp[i] += exp->exp[i]; |
---|
1905 | } |
---|
1906 | #ifndef TEST_MAC_ORDER |
---|
1907 | a->Order += exp->Order; |
---|
1908 | #else |
---|
1909 | pSetm(a); |
---|
1910 | #endif |
---|
1911 | if (pMultT_nok) |
---|
1912 | { |
---|
1913 | if (pGetComp(a) == 0) |
---|
1914 | { |
---|
1915 | a->exp[0] = pGetComp(exp); |
---|
1916 | } |
---|
1917 | else |
---|
1918 | { |
---|
1919 | return NULL /*FALSE*/; |
---|
1920 | } |
---|
1921 | } |
---|
1922 | } |
---|
1923 | prev=a; |
---|
1924 | pIter(a); |
---|
1925 | } |
---|
1926 | } |
---|
1927 | pMultT_nok=0; |
---|
1928 | #ifdef DRING |
---|
1929 | if (pDRING) |
---|
1930 | { |
---|
1931 | pDelete(&aa); |
---|
1932 | return pDRINGres; |
---|
1933 | } |
---|
1934 | #endif |
---|
1935 | #ifdef SRING |
---|
1936 | if (pSRING) |
---|
1937 | { |
---|
1938 | pDelete(&aa); |
---|
1939 | return pDRINGres; |
---|
1940 | } |
---|
1941 | #endif |
---|
1942 | return aa; /*TRUE*/ |
---|
1943 | } |
---|
1944 | |
---|
1945 | /*2 |
---|
1946 | * multiply p1 with p2, p1 and p2 are destroyed |
---|
1947 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
1948 | */ |
---|
1949 | poly pMult(poly p1, poly p2) |
---|
1950 | { |
---|
1951 | poly res, r, rn, a; |
---|
1952 | BOOLEAN cont; |
---|
1953 | |
---|
1954 | if ((p1!=NULL) && (p2!=NULL)) |
---|
1955 | { |
---|
1956 | #ifdef PDEBUG |
---|
1957 | pTest(p1); |
---|
1958 | pTest(p2); |
---|
1959 | #endif |
---|
1960 | cont = TRUE; |
---|
1961 | a = p1; |
---|
1962 | if (pNext(p2)!=NULL) |
---|
1963 | a = pCopy(a); |
---|
1964 | else |
---|
1965 | cont = FALSE; |
---|
1966 | res = pMultT(a, p2); |
---|
1967 | if (pMultT_nok) |
---|
1968 | { |
---|
1969 | if (cont) pDelete(&p1); |
---|
1970 | pDelete(&res); |
---|
1971 | pDelete(&p2); |
---|
1972 | return NULL; |
---|
1973 | } |
---|
1974 | pDelete1(&p2); |
---|
1975 | r = res; |
---|
1976 | if (r!=NULL) rn = pNext(r); |
---|
1977 | else rn=NULL; |
---|
1978 | while (cont) |
---|
1979 | { |
---|
1980 | if (pNext(p2)==NULL) |
---|
1981 | { |
---|
1982 | a = p1; |
---|
1983 | cont = FALSE; |
---|
1984 | } |
---|
1985 | else |
---|
1986 | { |
---|
1987 | a = pCopy(p1); |
---|
1988 | } |
---|
1989 | a=pMultT(a, p2); //sets pMultT_nok |
---|
1990 | if (pMultT_nok) |
---|
1991 | { |
---|
1992 | if (cont) pDelete(&p1); |
---|
1993 | pDelete(&a); |
---|
1994 | pDelete(&res); |
---|
1995 | pDelete(&p2); |
---|
1996 | return NULL; |
---|
1997 | } |
---|
1998 | while ((rn!=NULL) && (pComp0(rn,a)>0)) |
---|
1999 | { |
---|
2000 | r = rn; |
---|
2001 | pIter(rn); |
---|
2002 | } |
---|
2003 | if (r!=NULL) pNext(r) = rn = pAdd(a, rn); |
---|
2004 | else res=r=a; |
---|
2005 | pDelete1(&p2); |
---|
2006 | } |
---|
2007 | return res; |
---|
2008 | } |
---|
2009 | pDelete(&p1); |
---|
2010 | pDelete(&p2); |
---|
2011 | return NULL; |
---|
2012 | } |
---|
2013 | |
---|
2014 | /*2 |
---|
2015 | * update a by multiplying it with c (c will not be destroyed) |
---|
2016 | */ |
---|
2017 | void pMultN(poly a, number c) |
---|
2018 | { |
---|
2019 | number t; |
---|
2020 | |
---|
2021 | while (a!=NULL) |
---|
2022 | { |
---|
2023 | t=nMult(pGetCoeff(a), c); |
---|
2024 | //nNormalize(t); |
---|
2025 | pSetCoeff(a,t); |
---|
2026 | pIter(a); |
---|
2027 | } |
---|
2028 | } |
---|
2029 | |
---|
2030 | /*2 |
---|
2031 | * return a copy of the poly a times the number c (a,c will not be destroyed) |
---|
2032 | */ |
---|
2033 | poly pMultCopyN(poly a, number c) |
---|
2034 | { |
---|
2035 | poly result=NULL,hp; |
---|
2036 | |
---|
2037 | if (a != NULL) |
---|
2038 | { |
---|
2039 | result=pNew(); |
---|
2040 | memcpy4(result,a,pMonomSize); |
---|
2041 | pNext(result)=NULL; |
---|
2042 | pGetCoeff(result)=nMult(pGetCoeff(a),c); |
---|
2043 | pIter(a); |
---|
2044 | hp=result; |
---|
2045 | while (a) |
---|
2046 | { |
---|
2047 | hp=pNext(hp)=pNew(); |
---|
2048 | memcpy4(hp,a,pMonomSize); |
---|
2049 | pSetCoeff0(hp,nMult(pGetCoeff(a), c)); |
---|
2050 | pIter(a); |
---|
2051 | } |
---|
2052 | pNext(hp)=NULL; |
---|
2053 | } |
---|
2054 | return result; |
---|
2055 | } |
---|
2056 | |
---|
2057 | /* -------------------------------------------------------- */ |
---|
2058 | /*2 |
---|
2059 | * are the head monomials (without coeff) equal ? |
---|
2060 | */ |
---|
2061 | BOOLEAN pEqual(poly a, poly b) |
---|
2062 | { |
---|
2063 | int i; |
---|
2064 | short *e1=a->exp; |
---|
2065 | short *e2=b->exp; |
---|
2066 | |
---|
2067 | if (a->Order != b->Order) return FALSE; |
---|
2068 | for (i=pVariables; i>=0; i--,e1++,e2++) |
---|
2069 | if (*e1 != *e2) return FALSE; |
---|
2070 | return TRUE; |
---|
2071 | } |
---|
2072 | |
---|
2073 | /*2 |
---|
2074 | * returns TRUE if the head term of b is a multiple of the head term of a |
---|
2075 | */ |
---|
2076 | #ifdef macintosh |
---|
2077 | BOOLEAN pDivisibleBy(poly a, poly b) |
---|
2078 | { |
---|
2079 | if ((a!=NULL)&&((a->exp[0]==0) || (a->exp[0] == b->exp[0]))) |
---|
2080 | { |
---|
2081 | int i=pVariables; |
---|
2082 | short *e1=&(a->exp[1]); |
---|
2083 | short *e2=&(b->exp[1]); |
---|
2084 | if ((*e1) > (*e2)) return FALSE; |
---|
2085 | do |
---|
2086 | { |
---|
2087 | i--; |
---|
2088 | if (i == 0) return TRUE; |
---|
2089 | e1++; |
---|
2090 | e2++; |
---|
2091 | } while ((*e1) <= (*e2)); |
---|
2092 | } |
---|
2093 | return FALSE; |
---|
2094 | } |
---|
2095 | #endif |
---|
2096 | |
---|
2097 | /*2 |
---|
2098 | * assumes that the head term of b is a multiple of the head term of a |
---|
2099 | * and return the multiplicant *m |
---|
2100 | */ |
---|
2101 | poly pDivide(poly a, poly b) |
---|
2102 | { |
---|
2103 | int i; |
---|
2104 | poly result=pInit(); |
---|
2105 | |
---|
2106 | for(i=(int)pVariables; i>=0; i--) |
---|
2107 | result->exp[i] = a->exp[i]-b->exp[i]; |
---|
2108 | pSetm(result); |
---|
2109 | return result; |
---|
2110 | } |
---|
2111 | |
---|
2112 | /*2 |
---|
2113 | * divides a by the monomial b, ignores monomials wihich are not divisible |
---|
2114 | * assumes that b is not NULL |
---|
2115 | */ |
---|
2116 | poly pDivideM(poly a, poly b) |
---|
2117 | { |
---|
2118 | if (a==NULL) return NULL; |
---|
2119 | poly result=a; |
---|
2120 | poly prev=NULL; |
---|
2121 | int i; |
---|
2122 | number inv=nInvers(pGetCoeff(b)); |
---|
2123 | |
---|
2124 | while (a!=NULL) |
---|
2125 | { |
---|
2126 | if (pDivisibleBy(b,a)) |
---|
2127 | { |
---|
2128 | for(i=(int)pVariables; i>=0; i--) |
---|
2129 | a->exp[i]-=b->exp[i]; |
---|
2130 | pSetm(a); |
---|
2131 | prev=a; |
---|
2132 | pIter(a); |
---|
2133 | } |
---|
2134 | else |
---|
2135 | { |
---|
2136 | if (prev==NULL) |
---|
2137 | { |
---|
2138 | pDelete1(&result); |
---|
2139 | a=result; |
---|
2140 | } |
---|
2141 | else |
---|
2142 | { |
---|
2143 | pDelete1(&pNext(prev)); |
---|
2144 | a=pNext(prev); |
---|
2145 | } |
---|
2146 | } |
---|
2147 | } |
---|
2148 | pMultN(result,inv); |
---|
2149 | nDelete(&inv); |
---|
2150 | pDelete(&b); |
---|
2151 | return result; |
---|
2152 | } |
---|
2153 | |
---|
2154 | /*2 |
---|
2155 | * returns the LCM of the head terms of a and b in *m |
---|
2156 | */ |
---|
2157 | void pLcm(poly a, poly b, poly m) |
---|
2158 | { |
---|
2159 | int i; |
---|
2160 | for (i=pVariables; i>=0; i--) |
---|
2161 | { |
---|
2162 | m->exp[i] = max(a->exp[i],b->exp[i]); |
---|
2163 | } |
---|
2164 | } |
---|
2165 | |
---|
2166 | /*2 |
---|
2167 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
2168 | */ |
---|
2169 | poly pmInit(char *st, BOOLEAN &ok) |
---|
2170 | { |
---|
2171 | int i,j; |
---|
2172 | ok=FALSE; |
---|
2173 | BOOLEAN b=FALSE; |
---|
2174 | poly rc = pInit(); |
---|
2175 | char *s = nRead(st,&(rc->coef)); |
---|
2176 | if (s==st) |
---|
2177 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
2178 | { |
---|
2179 | j = rIsRingVar(s); |
---|
2180 | if (j >= 0) |
---|
2181 | { |
---|
2182 | rc->exp[1+j] += (short)1; |
---|
2183 | goto done; |
---|
2184 | } |
---|
2185 | } |
---|
2186 | else |
---|
2187 | b=TRUE; |
---|
2188 | while (*s!='\0') |
---|
2189 | { |
---|
2190 | char ss[2]; |
---|
2191 | ss[0] = *s++; |
---|
2192 | ss[1] = '\0'; |
---|
2193 | j = rIsRingVar(ss); |
---|
2194 | if (j >= 0) |
---|
2195 | { |
---|
2196 | s = eati(s,&i); |
---|
2197 | rc->exp[1+j] += (short)i; |
---|
2198 | } |
---|
2199 | else |
---|
2200 | { |
---|
2201 | if ((s!=st)&&isdigit(st[0])) |
---|
2202 | { |
---|
2203 | errorreported=TRUE; |
---|
2204 | } |
---|
2205 | pDelete(&rc); |
---|
2206 | return NULL; |
---|
2207 | } |
---|
2208 | } |
---|
2209 | done: |
---|
2210 | ok=!errorreported; |
---|
2211 | if (nIsZero(pGetCoeff(rc))) pDelete1(&rc); |
---|
2212 | else |
---|
2213 | { |
---|
2214 | #ifdef DRING |
---|
2215 | if (pDRING) |
---|
2216 | { |
---|
2217 | for(i=1;i<=pdN;i++) |
---|
2218 | { |
---|
2219 | if(rc->exp[pdDX(i)]>0) |
---|
2220 | { |
---|
2221 | pdDFlag(rc)=1; |
---|
2222 | break; |
---|
2223 | } |
---|
2224 | } |
---|
2225 | } |
---|
2226 | #endif |
---|
2227 | pSetm(rc); |
---|
2228 | } |
---|
2229 | return rc; |
---|
2230 | } |
---|
2231 | |
---|
2232 | /*2 |
---|
2233 | *make p homgeneous by multiplying the monomials by powers of x_varnum |
---|
2234 | */ |
---|
2235 | poly pHomogen (poly p, int varnum) |
---|
2236 | { |
---|
2237 | poly q=NULL; |
---|
2238 | poly res; |
---|
2239 | int o,ii; |
---|
2240 | |
---|
2241 | if (p!=NULL) |
---|
2242 | { |
---|
2243 | if ((varnum < 1) || (varnum > pVariables)) |
---|
2244 | { |
---|
2245 | return NULL; |
---|
2246 | } |
---|
2247 | o=pWTotaldegree(p); |
---|
2248 | q=pNext(p); |
---|
2249 | while (q != NULL) |
---|
2250 | { |
---|
2251 | ii=pWTotaldegree(q); |
---|
2252 | if (ii>o) o=ii; |
---|
2253 | pIter(q); |
---|
2254 | } |
---|
2255 | q = pCopy(p); |
---|
2256 | res = q; |
---|
2257 | while (q != NULL) |
---|
2258 | { |
---|
2259 | ii = o-pWTotaldegree(q); |
---|
2260 | if (ii!=0) |
---|
2261 | { |
---|
2262 | q->exp[varnum] += (short)ii; |
---|
2263 | pSetm(q); |
---|
2264 | } |
---|
2265 | pIter(q); |
---|
2266 | } |
---|
2267 | q = pOrdPoly(res); |
---|
2268 | } |
---|
2269 | return q; |
---|
2270 | } |
---|
2271 | |
---|
2272 | /*2 |
---|
2273 | *re-orders a polynomial |
---|
2274 | */ |
---|
2275 | poly pOrdPolySchreyer(poly p) |
---|
2276 | { |
---|
2277 | poly qq,result=p; |
---|
2278 | |
---|
2279 | if (p == NULL) return NULL; |
---|
2280 | while ((pNext(p) != NULL) && (pComp(p,pNext(p))==1)) pIter(p); |
---|
2281 | if (pNext(p)==NULL) return result; |
---|
2282 | qq = pNext(p); |
---|
2283 | pNext(p) = NULL; |
---|
2284 | qq = pOrdPolySchreyer(qq); |
---|
2285 | return pAdd(result,qq); |
---|
2286 | } |
---|
2287 | |
---|
2288 | /*2 |
---|
2289 | *replaces the maximal powers of the leading monomial of p2 in p1 by |
---|
2290 | *the same powers of n, utility for dehomogenization |
---|
2291 | */ |
---|
2292 | poly pDehomogen (poly p1,poly p2,number n) |
---|
2293 | { |
---|
2294 | polyset P; |
---|
2295 | int SizeOfSet=5; |
---|
2296 | int i; |
---|
2297 | poly p; |
---|
2298 | number nn; |
---|
2299 | |
---|
2300 | P = (polyset)Alloc(5*sizeof(poly)); |
---|
2301 | for (i=0; i<5; i++) |
---|
2302 | { |
---|
2303 | P[i] = NULL; |
---|
2304 | } |
---|
2305 | pCancelPolyByMonom(p1,p2,&P,&SizeOfSet); |
---|
2306 | p = P[0]; |
---|
2307 | //P[0] = NULL ;// for safety, may be remoeved later |
---|
2308 | for (i=1; i<SizeOfSet; i++) |
---|
2309 | { |
---|
2310 | if (P[i] != NULL) |
---|
2311 | { |
---|
2312 | nPower(n,i,&nn); |
---|
2313 | pMultN(P[i],nn); |
---|
2314 | p = pAdd(p,P[i]); |
---|
2315 | //P[i] =NULL; // for safety, may be removed later |
---|
2316 | nDelete(&nn); |
---|
2317 | } |
---|
2318 | } |
---|
2319 | Free((ADDRESS)P,SizeOfSet*sizeof(poly)); |
---|
2320 | return p; |
---|
2321 | } |
---|
2322 | |
---|
2323 | /*4 |
---|
2324 | *Returns the exponent of the maximal power of the leading monomial of |
---|
2325 | *p2 in that of p1 |
---|
2326 | */ |
---|
2327 | static int pGetMaxPower (poly p1,poly p2) |
---|
2328 | { |
---|
2329 | int i,k,res = 32000; /*a very large integer*/ |
---|
2330 | |
---|
2331 | if (p1 == NULL) return 0; |
---|
2332 | for (i=1; i<=pVariables; i++) |
---|
2333 | { |
---|
2334 | if (p2->exp[i] != 0) |
---|
2335 | { |
---|
2336 | k = p1->exp[i] / p2->exp[i]; |
---|
2337 | if (k < res) res = k; |
---|
2338 | } |
---|
2339 | } |
---|
2340 | return res; |
---|
2341 | } |
---|
2342 | |
---|
2343 | /*2 |
---|
2344 | *Returns as i-th entry of P the coefficient of the (i-1) power of |
---|
2345 | *the leading monomial of p2 in p1 |
---|
2346 | */ |
---|
2347 | void pCancelPolyByMonom (poly p1,poly p2,polyset * P,int * SizeOfSet) |
---|
2348 | { |
---|
2349 | int maxPow; |
---|
2350 | poly p,qp,Coeff; |
---|
2351 | |
---|
2352 | if (*P == NULL) |
---|
2353 | { |
---|
2354 | *P = (polyset) Alloc(5*sizeof(poly)); |
---|
2355 | *SizeOfSet = 5; |
---|
2356 | } |
---|
2357 | p = pCopy(p1); |
---|
2358 | while (p != NULL) |
---|
2359 | { |
---|
2360 | qp = p->next; |
---|
2361 | p->next = NULL; |
---|
2362 | maxPow = pGetMaxPower(p,p2); |
---|
2363 | Coeff = pDivByMonom(p,p2); |
---|
2364 | if (maxPow > *SizeOfSet) |
---|
2365 | { |
---|
2366 | pEnlargeSet(P,*SizeOfSet,maxPow+1-*SizeOfSet); |
---|
2367 | *SizeOfSet = maxPow+1; |
---|
2368 | } |
---|
2369 | (*P)[maxPow] = pAdd((*P)[maxPow],Coeff); |
---|
2370 | pDelete(&p); |
---|
2371 | p = qp; |
---|
2372 | } |
---|
2373 | } |
---|
2374 | |
---|
2375 | /*2 |
---|
2376 | *returns the leading monomial of p1 divided by the maximal power of that |
---|
2377 | *of p2 |
---|
2378 | */ |
---|
2379 | poly pDivByMonom (poly p1,poly p2) |
---|
2380 | { |
---|
2381 | int k, i; |
---|
2382 | |
---|
2383 | if (p1 == NULL) return NULL; |
---|
2384 | k = pGetMaxPower(p1,p2); |
---|
2385 | if (k == 0) |
---|
2386 | return pHead(p1); |
---|
2387 | else |
---|
2388 | { |
---|
2389 | number n; |
---|
2390 | poly p = pNew(); |
---|
2391 | |
---|
2392 | p->next = NULL; |
---|
2393 | for (i=1; i<=pVariables; i++) |
---|
2394 | { |
---|
2395 | p->exp[i] = p1->exp[i]-k*p2->exp[i]; |
---|
2396 | } |
---|
2397 | nPower(p2->coef,k,&n); |
---|
2398 | pSetCoeff0(p,nDiv(p1->coef,n)); |
---|
2399 | nDelete(&n); |
---|
2400 | pSetm(p); |
---|
2401 | return p; |
---|
2402 | } |
---|
2403 | } |
---|
2404 | /*----------utilities for syzygies--------------*/ |
---|
2405 | poly pTakeOutComp(poly * p, int k) |
---|
2406 | { |
---|
2407 | poly q = *p,qq=NULL,result = NULL; |
---|
2408 | |
---|
2409 | if (q==NULL) return NULL; |
---|
2410 | if (pGetComp(q)==k) |
---|
2411 | { |
---|
2412 | result = q; |
---|
2413 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
2414 | { |
---|
2415 | pSetComp(q,0); |
---|
2416 | qq = q; |
---|
2417 | pIter(q); |
---|
2418 | } |
---|
2419 | *p = q; |
---|
2420 | pNext(qq) = NULL; |
---|
2421 | } |
---|
2422 | if (q==NULL) return result; |
---|
2423 | if (pGetComp(q) > k) pGetComp(q)--; |
---|
2424 | poly pNext_q; |
---|
2425 | while ((pNext_q=pNext(q))!=NULL) |
---|
2426 | { |
---|
2427 | if (pGetComp(pNext_q)==k) |
---|
2428 | { |
---|
2429 | if (result==NULL) |
---|
2430 | { |
---|
2431 | result = pNext_q; |
---|
2432 | qq = result; |
---|
2433 | } |
---|
2434 | else |
---|
2435 | { |
---|
2436 | pNext(qq) = pNext_q; |
---|
2437 | pIter(qq); |
---|
2438 | } |
---|
2439 | pNext(q) = pNext(pNext_q); |
---|
2440 | pNext(qq) =NULL; |
---|
2441 | pSetComp(qq,0); |
---|
2442 | } |
---|
2443 | else |
---|
2444 | { |
---|
2445 | /*pIter(q);*/ q=pNext_q; |
---|
2446 | if (pGetComp(q) > k) pGetComp(q)--; |
---|
2447 | } |
---|
2448 | } |
---|
2449 | return result; |
---|
2450 | } |
---|
2451 | |
---|
2452 | poly pTakeOutComp1(poly * p, int k) |
---|
2453 | { |
---|
2454 | poly q = *p; |
---|
2455 | |
---|
2456 | if (q==NULL) return NULL; |
---|
2457 | |
---|
2458 | poly qq=NULL,result = NULL; |
---|
2459 | |
---|
2460 | if (pGetComp(q)==k) |
---|
2461 | { |
---|
2462 | result = q; /* *p */ |
---|
2463 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
2464 | { |
---|
2465 | pSetComp(q,0); |
---|
2466 | qq = q; |
---|
2467 | pIter(q); |
---|
2468 | } |
---|
2469 | *p = q; |
---|
2470 | pNext(qq) = NULL; |
---|
2471 | } |
---|
2472 | if (q==NULL) return result; |
---|
2473 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2474 | while (pNext(q)!=NULL) |
---|
2475 | { |
---|
2476 | if (pGetComp(pNext(q))==k) |
---|
2477 | { |
---|
2478 | if (result==NULL) |
---|
2479 | { |
---|
2480 | result = pNext(q); |
---|
2481 | qq = result; |
---|
2482 | } |
---|
2483 | else |
---|
2484 | { |
---|
2485 | pNext(qq) = pNext(q); |
---|
2486 | pIter(qq); |
---|
2487 | } |
---|
2488 | pNext(q) = pNext(pNext(q)); |
---|
2489 | pNext(qq) =NULL; |
---|
2490 | pSetComp(qq,0); |
---|
2491 | } |
---|
2492 | else |
---|
2493 | { |
---|
2494 | pIter(q); |
---|
2495 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2496 | } |
---|
2497 | } |
---|
2498 | return result; |
---|
2499 | } |
---|
2500 | |
---|
2501 | void pDeleteComp(poly * p,int k) |
---|
2502 | { |
---|
2503 | poly q; |
---|
2504 | |
---|
2505 | while ((*p!=NULL) && (pGetComp(*p)==k)) pDelete1(p); |
---|
2506 | if (*p==NULL) return; |
---|
2507 | q = *p; |
---|
2508 | if (pGetComp(q)>k) pGetComp(q)--; |
---|
2509 | while (pNext(q)!=NULL) |
---|
2510 | { |
---|
2511 | if (pGetComp(pNext(q))==k) |
---|
2512 | pDelete1(&(pNext(q))); |
---|
2513 | else |
---|
2514 | { |
---|
2515 | pIter(q); |
---|
2516 | if (pGetComp(q)>k) pGetComp(q)--; |
---|
2517 | } |
---|
2518 | } |
---|
2519 | } |
---|
2520 | /*----------end of utilities for syzygies--------------*/ |
---|
2521 | |
---|
2522 | /*2 |
---|
2523 | * pair has no common factor ? or is no polynomial |
---|
2524 | */ |
---|
2525 | BOOLEAN pHasNotCF(poly p1, poly p2) |
---|
2526 | { |
---|
2527 | #ifdef SRING |
---|
2528 | if (pSRING) |
---|
2529 | return FALSE; |
---|
2530 | #endif |
---|
2531 | short * m1 = p1->exp; |
---|
2532 | short * m2 = p2->exp; |
---|
2533 | |
---|
2534 | if (((*m1) > 0)||((*m2) > 0)) |
---|
2535 | return FALSE; |
---|
2536 | int i = 1; |
---|
2537 | loop |
---|
2538 | { |
---|
2539 | m1++;m2++; |
---|
2540 | if (((*m1) > 0) && ((*m2) > 0)) |
---|
2541 | return FALSE; |
---|
2542 | if (i == pVariables) |
---|
2543 | return TRUE; |
---|
2544 | i++; |
---|
2545 | } |
---|
2546 | } |
---|
2547 | |
---|
2548 | /* |
---|
2549 | *void pSFactors(poly f, poly g, poly a, poly b) |
---|
2550 | *{ |
---|
2551 | * int i,d; |
---|
2552 | * |
---|
2553 | * for (i=pVariables;i>0;i--) |
---|
2554 | * { |
---|
2555 | * d = f->exp[i]-g->exp[i]; |
---|
2556 | * if (d >= 0) |
---|
2557 | * { |
---|
2558 | * a->exp[i] = 0; |
---|
2559 | * b->exp[i] = d; |
---|
2560 | * } |
---|
2561 | * else |
---|
2562 | * { |
---|
2563 | * a->exp[i] = -d; |
---|
2564 | * b->exp[i] = 0; |
---|
2565 | * } |
---|
2566 | * } |
---|
2567 | * a->exp[0] = 0; |
---|
2568 | * b->exp[0] = 0; |
---|
2569 | * pSetm(a); |
---|
2570 | * pSetm(b); |
---|
2571 | *} |
---|
2572 | */ |
---|
2573 | |
---|
2574 | /* |
---|
2575 | *void pSDiv(poly f, poly g, poly b) |
---|
2576 | *{ |
---|
2577 | * int i,d; |
---|
2578 | * |
---|
2579 | * for (i=pVariables;i>0;i--) |
---|
2580 | * { |
---|
2581 | * d = f->exp[i]-g->exp[i]; |
---|
2582 | * b->exp[i] = d; |
---|
2583 | * } |
---|
2584 | * b->exp[0] = 0; |
---|
2585 | * pSetm(b); |
---|
2586 | *} |
---|
2587 | */ |
---|
2588 | |
---|
2589 | /*2 |
---|
2590 | * update the initial term of a polynomial a by multipying it by |
---|
2591 | * the (number) coefficient |
---|
2592 | * and the exponent vector (of) exp (a well initialized polynomial) |
---|
2593 | */ |
---|
2594 | /* |
---|
2595 | *void pSMultBy(poly f, poly m) |
---|
2596 | *{ |
---|
2597 | * number t; |
---|
2598 | * int i; |
---|
2599 | * // short notok; |
---|
2600 | * |
---|
2601 | * t=nMult(f->coef, m->coef); |
---|
2602 | * nDelete(&(f->coef)); |
---|
2603 | * f->coef = t; |
---|
2604 | * f->Order += m->Order; |
---|
2605 | * for (i=pVariables; i; i--) |
---|
2606 | * f->exp[i] += m->exp[i]; |
---|
2607 | * // if (notok) |
---|
2608 | * // { |
---|
2609 | * if (!(f->exp[0])) |
---|
2610 | * { |
---|
2611 | * f->exp[0] = m->exp[0]; |
---|
2612 | * } |
---|
2613 | * // else |
---|
2614 | * // { |
---|
2615 | * // HALT; |
---|
2616 | * // } |
---|
2617 | * // } |
---|
2618 | *} |
---|
2619 | */ |
---|
2620 | |
---|
2621 | /*2 |
---|
2622 | * creates a copy of the initial monomial of p |
---|
2623 | * sets the coeff of the copy to a defined value |
---|
2624 | */ |
---|
2625 | poly pCopy1(poly p) |
---|
2626 | { |
---|
2627 | poly w; |
---|
2628 | w = pNew(); |
---|
2629 | memcpy4(w,p,pMonomSize); |
---|
2630 | nNew(&(w->coef)); |
---|
2631 | pNext(w) = NULL; |
---|
2632 | return w; |
---|
2633 | } |
---|
2634 | |
---|
2635 | /*2 |
---|
2636 | *should return 1 if p divides q and p<q, |
---|
2637 | * -1 if q divides p and q<p |
---|
2638 | * 0 otherwise |
---|
2639 | */ |
---|
2640 | int pDivComp(poly p, poly q) |
---|
2641 | { |
---|
2642 | short * mp = p->exp; |
---|
2643 | short * mq = q->exp; |
---|
2644 | |
---|
2645 | if (*mp==*mq) |
---|
2646 | { |
---|
2647 | int i=pVariables; |
---|
2648 | BOOLEAN a=FALSE, b=FALSE; |
---|
2649 | for (; i>0; i--) |
---|
2650 | { |
---|
2651 | mp++;mq++; |
---|
2652 | if (*mp<*mq) |
---|
2653 | { |
---|
2654 | if (b) return 0; |
---|
2655 | a =TRUE; |
---|
2656 | } |
---|
2657 | else if (*mp>*mq) |
---|
2658 | { |
---|
2659 | if (a) return 0; |
---|
2660 | b = TRUE; |
---|
2661 | } |
---|
2662 | } |
---|
2663 | if (a) return 1; |
---|
2664 | else if (b) return -1; |
---|
2665 | } |
---|
2666 | return 0; |
---|
2667 | } |
---|
2668 | |
---|
2669 | /*2 |
---|
2670 | *divides p1 by its leading monomial |
---|
2671 | */ |
---|
2672 | void pNorm(poly p1) |
---|
2673 | { |
---|
2674 | poly h; |
---|
2675 | number k, c; |
---|
2676 | |
---|
2677 | if (p1!=NULL) |
---|
2678 | { |
---|
2679 | if (!nIsOne(pGetCoeff(p1))) |
---|
2680 | { |
---|
2681 | nNormalize(pGetCoeff(p1)); |
---|
2682 | k=pGetCoeff(p1); |
---|
2683 | c = nInit(1); |
---|
2684 | pSetCoeff0(p1,c); |
---|
2685 | h = pNext(p1); |
---|
2686 | while (h!=NULL) |
---|
2687 | { |
---|
2688 | c=nDiv(pGetCoeff(h),k); |
---|
2689 | if (!nIsOne(c)) nNormalize(c); |
---|
2690 | pSetCoeff(h,c); |
---|
2691 | pIter(h); |
---|
2692 | } |
---|
2693 | nDelete(&k); |
---|
2694 | } |
---|
2695 | else |
---|
2696 | { |
---|
2697 | h = pNext(p1); |
---|
2698 | while (h!=NULL) |
---|
2699 | { |
---|
2700 | nNormalize(pGetCoeff(h)); |
---|
2701 | pIter(h); |
---|
2702 | } |
---|
2703 | } |
---|
2704 | } |
---|
2705 | } |
---|
2706 | |
---|
2707 | /*2 |
---|
2708 | *normalize all coeffizients |
---|
2709 | */ |
---|
2710 | void pNormalize(poly p) |
---|
2711 | { |
---|
2712 | while (p!=NULL) |
---|
2713 | { |
---|
2714 | nTest(pGetCoeff(p)); |
---|
2715 | nNormalize(pGetCoeff(p)); |
---|
2716 | pIter(p); |
---|
2717 | } |
---|
2718 | } |
---|
2719 | |
---|
2720 | /*3 |
---|
2721 | * substitute the n-th variable by 1 in p |
---|
2722 | * destroy p |
---|
2723 | */ |
---|
2724 | static poly pSubst1 (poly p,int n) |
---|
2725 | { |
---|
2726 | poly qq,result = NULL; |
---|
2727 | |
---|
2728 | while (p != NULL) |
---|
2729 | { |
---|
2730 | qq = p; |
---|
2731 | pIter(p); |
---|
2732 | qq->next = NULL; |
---|
2733 | pSetExp(qq,n,0); |
---|
2734 | pSetm(qq); |
---|
2735 | result = pAdd(result,qq); |
---|
2736 | } |
---|
2737 | return result; |
---|
2738 | } |
---|
2739 | |
---|
2740 | /*2 |
---|
2741 | * substitute the n-th variable by e in p |
---|
2742 | * destroy p |
---|
2743 | */ |
---|
2744 | poly pSubst(poly p, int n, poly e) |
---|
2745 | { |
---|
2746 | if ((e!=NULL)&&(pIsConstant(e))&&(nIsOne(pGetCoeff(e)))) |
---|
2747 | return pSubst1(p,n); |
---|
2748 | |
---|
2749 | int exponent,i; |
---|
2750 | poly h, res, m; |
---|
2751 | short *me,*ee; |
---|
2752 | number nu,nu1; |
---|
2753 | |
---|
2754 | me=(short *)Alloc((pVariables+1)*sizeof(short)); |
---|
2755 | ee=(short *)Alloc((pVariables+1)*sizeof(short)); |
---|
2756 | if (e!=NULL) pGetExpV(e,ee); |
---|
2757 | res=NULL; |
---|
2758 | h=p; |
---|
2759 | while (h!=NULL) |
---|
2760 | { |
---|
2761 | if ((e!=NULL) || (pGetExp(h,n)==0)) |
---|
2762 | { |
---|
2763 | m=pHead(h); |
---|
2764 | pGetExpV(m,me); |
---|
2765 | exponent=me[n]; |
---|
2766 | me[n]=0; |
---|
2767 | for(i=1;i<=pVariables;i++) |
---|
2768 | me[i]+=exponent*ee[i]; |
---|
2769 | pSetExpV(m,me); |
---|
2770 | if (e!=NULL) |
---|
2771 | { |
---|
2772 | nPower(pGetCoeff(e),exponent,&nu); |
---|
2773 | nu1=nMult(pGetCoeff(m),nu); |
---|
2774 | nDelete(&nu); |
---|
2775 | pSetCoeff(m,nu1); |
---|
2776 | } |
---|
2777 | res=pAdd(res,m); |
---|
2778 | } |
---|
2779 | pDelete1(&h); |
---|
2780 | } |
---|
2781 | Free((ADDRESS)me,(pVariables+1)*sizeof(short)); |
---|
2782 | Free((ADDRESS)ee,(pVariables+1)*sizeof(short)); |
---|
2783 | return res; |
---|
2784 | } |
---|
2785 | |
---|
2786 | BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm) |
---|
2787 | { |
---|
2788 | int k, j; |
---|
2789 | |
---|
2790 | if (lcm==NULL) return FALSE; |
---|
2791 | |
---|
2792 | for (j=pVariables; j; j--) |
---|
2793 | if (p->exp[j] > lcm->exp[j]) return FALSE; |
---|
2794 | if (p->exp[0] != lcm->exp[0]) return FALSE; |
---|
2795 | for (j=pVariables; j; j--) |
---|
2796 | { |
---|
2797 | if (pGetExp(p1,j)!=pGetExp(lcm,j)) |
---|
2798 | { |
---|
2799 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
2800 | { |
---|
2801 | for (k=pVariables; k>j; k--) |
---|
2802 | { |
---|
2803 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
2804 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
2805 | return TRUE; |
---|
2806 | } |
---|
2807 | for (k=j-1; k; k--) |
---|
2808 | { |
---|
2809 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
2810 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
2811 | return TRUE; |
---|
2812 | } |
---|
2813 | return FALSE; |
---|
2814 | } |
---|
2815 | } |
---|
2816 | else if (pGetExp(p2,j)!=pGetExp(lcm,j)) |
---|
2817 | { |
---|
2818 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
2819 | { |
---|
2820 | for (k=pVariables; k>j; k--) |
---|
2821 | { |
---|
2822 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
2823 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
2824 | return TRUE; |
---|
2825 | } |
---|
2826 | for (k=j-1; k; k--) |
---|
2827 | { |
---|
2828 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
2829 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
2830 | return TRUE; |
---|
2831 | } |
---|
2832 | return FALSE; |
---|
2833 | } |
---|
2834 | } |
---|
2835 | } |
---|
2836 | return FALSE; |
---|
2837 | } |
---|
2838 | |
---|
2839 | int pWeight(int i) |
---|
2840 | { |
---|
2841 | if ((firstwv==NULL) || (i>firstBlockEnds)) |
---|
2842 | { |
---|
2843 | return 1; |
---|
2844 | } |
---|
2845 | return firstwv[i-1]; |
---|
2846 | } |
---|
2847 | |
---|
2848 | #ifdef PDEBUG |
---|
2849 | BOOLEAN pDBTest(poly p, char *f, int l) |
---|
2850 | { |
---|
2851 | poly old=NULL; |
---|
2852 | BOOLEAN ismod=FALSE; |
---|
2853 | while (p!=NULL) |
---|
2854 | { |
---|
2855 | #ifdef MDEBUG |
---|
2856 | if (!mmDBTestBlock(p,pMonomSize,f,l)) |
---|
2857 | return FALSE; |
---|
2858 | #endif |
---|
2859 | #ifdef LDEBUG |
---|
2860 | if (!nDBTest(p->coef,f,l)) |
---|
2861 | return FALSE; |
---|
2862 | #endif |
---|
2863 | if ((p->coef==NULL)&&(nGetChar()<2)) |
---|
2864 | { |
---|
2865 | Print("NULL coef in poly in %s:%d\n",f,l); |
---|
2866 | return FALSE; |
---|
2867 | } |
---|
2868 | if (nIsZero(p->coef)) |
---|
2869 | { |
---|
2870 | Print("zero coef in poly in %s:%d\n",f,l); |
---|
2871 | return FALSE; |
---|
2872 | } |
---|
2873 | int i=pVariables; |
---|
2874 | #ifndef DRING |
---|
2875 | for(;i>=0;i--) |
---|
2876 | { |
---|
2877 | if (pGetExp(p,i)<0) |
---|
2878 | { |
---|
2879 | Print("neg. Exponent in %s:%l\n",f,l); |
---|
2880 | return FALSE; |
---|
2881 | } |
---|
2882 | } |
---|
2883 | #endif |
---|
2884 | if (ismod==0) |
---|
2885 | { |
---|
2886 | if (pGetComp(p)>0) ismod=1; |
---|
2887 | else ismod=2; |
---|
2888 | } |
---|
2889 | else if (ismod==1) |
---|
2890 | { |
---|
2891 | if (pGetComp(p)==0) |
---|
2892 | { |
---|
2893 | Print("mix vec./poly in %s:%d\n",f,l); |
---|
2894 | return FALSE; |
---|
2895 | } |
---|
2896 | } |
---|
2897 | else if (ismod==2) |
---|
2898 | { |
---|
2899 | if (pGetComp(p)!=0) |
---|
2900 | { |
---|
2901 | Print("mix poly/vec. in %s:%d\n",f,l); |
---|
2902 | return FALSE; |
---|
2903 | } |
---|
2904 | } |
---|
2905 | i=p->Order; |
---|
2906 | pSetm(p); |
---|
2907 | if(i!=p->Order) |
---|
2908 | { |
---|
2909 | Print("wrong ord-field in %s:%d\n",f,l); |
---|
2910 | return FALSE; |
---|
2911 | } |
---|
2912 | old=p; |
---|
2913 | pIter(p); |
---|
2914 | if (pComp(old,p)!=1) |
---|
2915 | { |
---|
2916 | Print("wrong order in %s:%d\n",f,l); |
---|
2917 | return FALSE; |
---|
2918 | } |
---|
2919 | } |
---|
2920 | return TRUE; |
---|
2921 | } |
---|
2922 | #endif |
---|
2923 | |
---|