1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: polys.cc,v 1.28 1998-05-28 16:50:50 Singular Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT - all basic methods to manipulate polynomials |
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8 | */ |
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9 | |
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10 | /* includes */ |
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11 | #include <stdio.h> |
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12 | #include <string.h> |
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13 | #include <ctype.h> |
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14 | #include "mod2.h" |
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15 | #include "tok.h" |
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16 | #include "mmemory.h" |
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17 | #include "febase.h" |
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18 | #include "numbers.h" |
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19 | #include "polys.h" |
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20 | #include "ring.h" |
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21 | #include "binom.h" |
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22 | #include "ipid.h" |
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23 | #include "polys-comp.h" |
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24 | |
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25 | /* ----------- global variables, set by pChangeRing --------------------- */ |
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26 | /* initializes the internal data from the exp vector */ |
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27 | pSetmProc pSetm; |
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28 | /* computes length and maximal degree of a POLYnomial */ |
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29 | pLDegProc pLDeg; |
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30 | /* computes the degree of the initial term, used for std */ |
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31 | pFDegProc pFDeg; |
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32 | /* the monomial ordering of the head monomials a and b */ |
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33 | /* returns -1 if a comes before b, 0 if a=b, 1 otherwise */ |
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34 | pCompProc pComp0; |
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35 | |
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36 | int pVariables; // number of variables |
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37 | int pVariablesW; // number of words of pVariables exponents |
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38 | int pVariables1W; // number of words of (pVariables+1) exponents |
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39 | int pMonomSize; // size of monom (in bytes) |
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40 | int pMonomSizeW; // size of monom (in words) |
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41 | int pLexSgn; // 1, for lex monom comps; -1 otherwise (exception: ls) |
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42 | int pVarOffset; // controls the way exponents are stored in a vector |
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43 | int pVarLowIndex; // lowest exponent index |
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44 | int pVarHighIndex; // highest exponent index |
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45 | int pVarCompIndex; // Location of component in exponent vector |
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46 | |
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47 | /* 1 for polynomial ring, -1 otherwise */ |
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48 | int pOrdSgn; |
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49 | /* TRUE for momomial output as x2y, FALSE for x^2*y */ |
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50 | int pShortOut = (int)TRUE; |
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51 | // it is of type int, not BOOLEAN because it is also in ip |
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52 | /* TRUE if the monomial ordering is not compatible with pFDeg */ |
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53 | BOOLEAN pLexOrder; |
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54 | /* TRUE if the monomial ordering has polynomial and power series blocks */ |
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55 | BOOLEAN pMixedOrder; |
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56 | /* 1 for c ordering, -1 otherwise (i.e. for C ordering) */ |
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57 | int pComponentOrder; |
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58 | |
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59 | #ifdef DRING |
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60 | int p2; |
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61 | BOOLEAN pDRING=FALSE; |
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62 | #endif |
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63 | |
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64 | #ifdef SRING |
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65 | int pAltVars; |
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66 | BOOLEAN pSRING=FALSE; |
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67 | #endif |
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68 | |
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69 | #ifdef SDRING |
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70 | BOOLEAN pSDRING=FALSE; |
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71 | #include "polys.inc" |
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72 | #endif |
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73 | |
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74 | /* ----------- global variables, set by procedures from hecke/kstd1 ----- */ |
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75 | /* the highest monomial below pHEdge */ |
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76 | poly ppNoether = NULL; |
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77 | |
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78 | /* -------------- static variables --------------------------------------- */ |
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79 | /*is the basic comparing procedure during a computation of syzygies*/ |
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80 | static pCompProc pCompOld; |
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81 | /*for grouping module indicies during computations*/ |
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82 | int pMaxBound = 0; |
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83 | |
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84 | /*contains the headterms for the Schreyer orderings*/ |
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85 | static int* SchreyerOrd; |
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86 | static int maxSchreyer=0; |
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87 | static int indexShift=0; |
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88 | static pLDegProc pLDegOld; |
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89 | |
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90 | typedef int (*bcompProc)(poly p1, poly p2, int i1, int i2, short * w); |
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91 | static bcompProc bcomph[20]; |
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92 | static short** polys_wv; |
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93 | static short * firstwv; |
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94 | static int * block0; |
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95 | static int * block1; |
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96 | static int firstBlockEnds; |
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97 | static int * order; |
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98 | |
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99 | /*0 implementation*/ |
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100 | /*-------- the several possibilities for pSetm:-----------------------*/ |
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101 | |
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102 | /* Remark: These could be made more efficient by avoiding using pGetExp */ |
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103 | |
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104 | /*2 |
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105 | * define the order of p with respect to lex. ordering, N=1 |
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106 | */ |
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107 | static void setlex1(poly p) |
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108 | { |
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109 | p->Order = (Order_t)pGetExp(p,1); |
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110 | } |
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111 | |
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112 | /*2 |
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113 | * define the order of p with respect to lex. ordering, N>1 |
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114 | */ |
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115 | static void setlex2(poly p) |
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116 | { |
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117 | p->Order = (((Order_t)pGetExp(p,1))<<(sizeof(Exponent_t)*8)) |
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118 | + (Order_t)pGetExp(p,2); |
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119 | } |
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120 | |
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121 | /*2 |
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122 | * define the order of p with respect to a degree ordering |
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123 | */ |
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124 | static void setdeg1(poly p) |
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125 | { |
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126 | p->Order = pExpQuerSum1(p, firstBlockEnds); |
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127 | } |
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128 | |
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129 | /*2 |
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130 | * define the order of p with respect to a degree ordering |
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131 | * with weigthts |
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132 | */ |
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133 | static void setdeg1w(poly p) |
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134 | { |
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135 | Order_t i, j = 0; |
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136 | |
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137 | for (i = firstBlockEnds; i>0; i--) |
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138 | { |
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139 | j += ((Order_t) pGetExp(p,i))*firstwv[i-1]; |
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140 | } |
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141 | p->Order = j; |
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142 | } |
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143 | |
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144 | |
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145 | /*-------- IMPLEMENTATION OF MONOMIAL COMPARISONS ---------------------*/ |
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146 | |
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147 | |
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148 | #define NonZeroR(l, actionG, actionS) \ |
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149 | do \ |
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150 | { \ |
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151 | long _l = l; \ |
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152 | if (_l) \ |
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153 | { \ |
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154 | if (_l > 0) actionG; \ |
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155 | actionS; \ |
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156 | } \ |
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157 | } \ |
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158 | while(0) |
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159 | |
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160 | #define Mreturn(d, multiplier) \ |
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161 | { \ |
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162 | if (d > 0) return multiplier; \ |
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163 | return -multiplier; \ |
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164 | } |
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165 | |
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166 | static int pComp_otEXP_nwONE(poly p1, poly p2); |
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167 | static int pComp_otCOMPEXP_nwONE(poly p1, poly p2); |
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168 | static int pComp_otEXPCOMP_nwONE(poly p1, poly p2); |
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169 | static int pComp_otEXP_nwTWO(poly p1, poly p2); |
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170 | static int pComp_otCOMPEXP_nwTWO(poly p1, poly p2); |
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171 | static int pComp_otEXPCOMP_nwTWO(poly p1, poly p2); |
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172 | static int pComp_otEXP_nwEVEN(poly p1, poly p2); |
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173 | static int pComp_otCOMPEXP_nwEVEN(poly p1, poly p2); |
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174 | static int pComp_otEXPCOMP_nwEVEN(poly p1, poly p2); |
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175 | static int pComp_otEXP_nwODD(poly p1, poly p2); |
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176 | static int pComp_otCOMPEXP_nwODD(poly p1, poly p2); |
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177 | static int pComp_otEXPCOMP_nwODD(poly p1, poly p2); |
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178 | |
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179 | |
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180 | // comp_nwONE is used if pVariables1W == 1 and component is compatible |
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181 | // with ordering |
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182 | static int pComp_otEXP_nwONE(poly p1, poly p2) |
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183 | { |
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184 | register long d = pGetOrder(p1) - pGetOrder(p2); |
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185 | |
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186 | if (d) Mreturn(d, pOrdSgn); |
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187 | _pMonComp_otEXP_nwONE(p1, p2, d, goto NotEqual, return 0); |
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188 | |
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189 | NotEqual: |
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190 | Mreturn(d, pLexSgn); |
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191 | } |
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192 | |
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193 | // comp_otEXPCOMP_nwONE : pVariables1W == 1, priority is |
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194 | // given to exponents, component is incompatible with ordering |
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195 | static int pComp_otEXPCOMP_nwONE(poly p1, poly p2) |
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196 | { |
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197 | register long d = pGetOrder(p1) - pGetOrder(p2); |
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198 | |
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199 | if (d) Mreturn(d, pOrdSgn); |
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200 | _pMonComp_otEXPCOMP_nwONE(p1, p2, d, goto NotEqual , return 0); |
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201 | |
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202 | NotEqual: |
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203 | Mreturn(d, pLexSgn) |
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204 | } |
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205 | |
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206 | // comp_otEXPCOMP_nwONE : pVariables1W == 1, priority is given to component, |
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207 | // component is incompatible with ordering |
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208 | static int pComp_otCOMPEXP_nwONE(poly p1, poly p2) |
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209 | { |
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210 | register long d = pGetComp(p2) - pGetComp(p1); |
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211 | if (d) Mreturn(d, pComponentOrder); |
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212 | d = pGetOrder(p1) - pGetOrder(p2); |
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213 | if (d) Mreturn(d, pOrdSgn); |
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214 | _pMonComp_otEXP_nwONE(p1, p2, d, goto NotEqual , return 0); |
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215 | |
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216 | NotEqual: |
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217 | Mreturn(d, pLexSgn); |
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218 | } |
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219 | |
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220 | // comp_nwTWO : pVariables1W == 2 and component is compatible with ordering |
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221 | static int pComp_otEXP_nwTWO(poly p1, poly p2) |
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222 | { |
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223 | register long d = pGetOrder(p1) - pGetOrder(p2); |
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224 | |
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225 | if (d) Mreturn(d, pOrdSgn); |
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226 | _pMonComp_otEXP_nwTWO(p1, p2, d, goto NotEqual , return 0); |
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227 | |
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228 | NotEqual: |
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229 | Mreturn(d, pLexSgn); |
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230 | } |
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231 | |
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232 | // comp_otEXPCOMP_nwTWO : pVariables1W == 2, priority is given to exponents, |
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233 | // component is incompatible with ordering |
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234 | static int pComp_otEXPCOMP_nwTWO(poly p1, poly p2) |
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235 | { |
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236 | register long d = pGetOrder(p1) - pGetOrder(p2); |
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237 | |
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238 | if (d) Mreturn(d, pOrdSgn); |
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239 | _pMonComp_otEXPCOMP_nwTWO(p1, p2, d, goto NotEqual, return 0); |
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240 | |
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241 | NotEqual: |
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242 | Mreturn(d, pLexSgn); |
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243 | } |
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244 | |
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245 | // comp_otEXPCOMP_nwTWO : pVariables1W == 2, priority is given to component, |
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246 | // component is incompatible with ordering |
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247 | static int pComp_otCOMPEXP_nwTWO(poly p1, poly p2) |
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248 | { |
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249 | register long d = pGetComp(p2) - pGetComp(p1); |
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250 | if (d) Mreturn(d, pComponentOrder); |
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251 | d = pGetOrder(p1) - pGetOrder(p2); |
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252 | if (d) Mreturn(d, pOrdSgn); |
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253 | _pMonComp_otEXP_nwTWO(p1, p2, d, goto NotEqual , return 0); |
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254 | |
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255 | NotEqual: |
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256 | Mreturn(d, pLexSgn); |
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257 | } |
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258 | |
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259 | // comp_nwEVEN : pVariables1W == 2*i and component is compatible |
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260 | // with ordering |
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261 | static int pComp_otEXP_nwEVEN(poly p1, poly p2) |
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262 | { |
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263 | register long d = pGetOrder(p1) - pGetOrder(p2); |
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264 | |
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265 | if (d) Mreturn(d, pOrdSgn); |
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266 | _pMonComp_otEXP_nwEVEN(p1, p2, pVariables1W, d, goto NotEqual , return 0); |
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267 | |
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268 | NotEqual: |
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269 | Mreturn(d, pLexSgn); |
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270 | } |
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271 | |
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272 | // comp_otEXPCOMP_nwEVEN : pVariables1W == 2*i, priority is given to exponents, |
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273 | // component is incompatible with ordering |
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274 | static int pComp_otEXPCOMP_nwEVEN(poly p1, poly p2) |
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275 | { |
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276 | register long d = pGetOrder(p1) - pGetOrder(p2); |
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277 | |
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278 | if (d) Mreturn(d, pOrdSgn); |
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279 | _pMonComp_otEXPCOMP_nwEVEN(p1, p2, pVariables1W, d, goto NotEqual , return 0); |
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280 | |
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281 | NotEqual: |
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282 | Mreturn(d, pLexSgn); |
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283 | } |
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284 | |
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285 | // comp_otEXPCOMP_nwEVEN : pVariables1W == 2*i, priority is given to component, |
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286 | // component is incompatible with ordering |
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287 | static int pComp_otCOMPEXP_nwEVEN(poly p1, poly p2) |
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288 | { |
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289 | register long d = pGetComp(p2) - pGetComp(p1); |
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290 | if (d) Mreturn(d, pComponentOrder); |
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291 | d = pGetOrder(p1) - pGetOrder(p2); |
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292 | if (d) Mreturn(d, pOrdSgn); |
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293 | _pMonComp_otEXP_nwEVEN(p1, p2, pVariablesW, d, goto NotEqual, return 0); |
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294 | |
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295 | NotEqual: |
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296 | Mreturn(d, pLexSgn); |
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297 | } |
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298 | |
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299 | // comp_nwODD : pVariables1W == 2*i and component is compatible |
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300 | // with ordering |
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301 | static int pComp_otEXP_nwODD(poly p1, poly p2) |
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302 | { |
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303 | register long d = pGetOrder(p1) - pGetOrder(p2); |
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304 | |
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305 | if (d) Mreturn(d, pOrdSgn); |
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306 | _pMonComp_otEXP_nwODD(p1, p2, pVariables1W, d, goto NotEqual, return 0); |
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307 | |
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308 | NotEqual: |
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309 | Mreturn(d, pLexSgn); |
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310 | } |
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311 | |
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312 | // comp_otEXPCOMP_nwODD : pVariables1W == 2*i, priority is given to exponents, |
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313 | // component is incompatible with ordering |
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314 | static int pComp_otEXPCOMP_nwODD(poly p1, poly p2) |
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315 | { |
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316 | register long d = pGetOrder(p1) - pGetOrder(p2); |
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317 | if (d) |
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318 | { |
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319 | if (d > 0) return pOrdSgn; |
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320 | return -pOrdSgn; |
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321 | } |
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322 | |
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323 | _pMonComp_otEXPCOMP_nwODD(p1, p2, pVariables1W, d, goto NotEqual , return 0); |
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324 | |
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325 | NotEqual: |
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326 | Mreturn(d, pLexSgn); |
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327 | } |
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328 | |
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329 | // comp_otCOMPEXP_nwODD : pVariables1W == 2*i, priority is given to component, |
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330 | // component is incompatible with ordering |
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331 | static int pComp_otCOMPEXP_nwODD(poly p1, poly p2) |
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332 | { |
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333 | register long d = pGetComp(p2) - pGetComp(p1); |
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334 | if (d) Mreturn(d, pComponentOrder); |
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335 | d = pGetOrder(p1) - pGetOrder(p2); |
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336 | if (d) Mreturn(d, pOrdSgn); |
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337 | _pMonComp_otEXP_nwODD(p1, p2, pVariablesW, d, goto NotEqual, return 0); |
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338 | |
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339 | NotEqual: |
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340 | Mreturn(d, pLexSgn); |
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341 | } |
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342 | /*2 |
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343 | * compare the head monomial of p1 and p2 with weight vector |
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344 | */ |
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345 | static int comp1a ( poly p1, poly p2, int f, int l, short * w ) |
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346 | { |
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347 | int d= pGetOrder(p1) - pGetOrder(p2); |
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348 | if ( d > 0 /*p1->Order > p2->Order*/ ) |
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349 | return 1; |
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350 | else if ( d < 0 /*p1->Order < p2->Order*/ ) |
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351 | return -1; |
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352 | return 0; |
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353 | } |
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354 | |
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355 | /*---------------------------------------------------*/ |
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356 | |
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357 | /* These functions could be made faster if you use pointers to the |
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358 | * exponent vectors and pointer arithmetic instead of using the |
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359 | * macro pGetExp !!! |
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360 | */ |
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361 | |
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362 | /*2 |
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363 | * compare the head monomial of p1 and p2 with lexicographic ordering |
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364 | */ |
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365 | static int comp_lp ( poly p1, poly p2, int f, int l, short * w ) |
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366 | { |
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367 | int i = f; |
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368 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
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369 | i++; |
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370 | if ( i > l ) |
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371 | return 0; |
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372 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
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373 | return 1; |
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374 | return -1; |
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375 | } |
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376 | |
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377 | /*2 |
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378 | * compare the head monomial of p1 and p2 with degree reverse lexicographic |
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379 | * ordering |
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380 | */ |
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381 | static int comp_dp ( poly p1, poly p2, int f, int l, short * w ) |
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382 | { |
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383 | int i, s1 = 0, s2 = 0; |
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384 | |
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385 | for ( i = f; i <= l; i++ ) |
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386 | { |
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387 | s1 += pGetExp(p1,i); |
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388 | s2 += pGetExp(p2,i); |
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389 | } |
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390 | if ( s1 == s2 ) |
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391 | { |
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392 | i = l; |
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393 | while ( (i >= f ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
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394 | i--; |
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395 | if ( i < f ) |
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396 | return 0; |
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397 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
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398 | return -1; |
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399 | return 1; |
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400 | } |
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401 | if ( s1 > s2 ) |
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402 | return 1; |
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403 | return -1; |
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404 | } |
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405 | |
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406 | /*2 |
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407 | * compare the head monomial of p1 and p2 with degree lexicographic ordering |
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408 | */ |
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409 | static int comp_Dp ( poly p1, poly p2, int f, int l, short * w ) |
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410 | { |
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411 | int i, s1 = 0, s2 = 0; |
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412 | |
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413 | for ( i = f; i <= l; i++ ) |
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414 | { |
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415 | s1 += pGetExp(p1,i); |
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416 | s2 += pGetExp(p2,i); |
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417 | } |
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418 | if ( s1 == s2 ) |
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419 | { |
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420 | i = f; |
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421 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
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422 | i++; |
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423 | if ( i > l ) |
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424 | return 0; |
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425 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
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426 | return 1; |
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427 | return -1; |
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428 | } |
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429 | if ( s1 > s2 ) |
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430 | return 1; |
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431 | return -1; |
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432 | } |
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433 | |
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434 | /*2 |
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435 | * compare the head monomial of p1 and p2 with weighted degree reverse |
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436 | * lexicographic ordering |
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437 | */ |
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438 | static int comp_wp ( poly p1, poly p2, int f, int l, short * w ) |
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439 | { |
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440 | int i, s1 = 0, s2 = 0; |
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441 | |
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442 | for ( i = f; i <= l; i++, w++ ) |
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443 | { |
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444 | s1 += (int)pGetExp(p1,i)*(*w); |
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445 | s2 += (int)pGetExp(p2,i)*(*w); |
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446 | } |
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447 | if ( s1 == s2 ) |
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448 | { |
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449 | i = l; |
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450 | while ( ( i >= f ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
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451 | i--; |
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452 | if ( i < f ) |
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453 | return 0; |
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454 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
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455 | return -1; |
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456 | return 1; |
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457 | } |
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458 | if ( s1 > s2 ) |
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459 | return 1; |
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460 | return -1; |
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461 | } |
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462 | |
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463 | /*2 |
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464 | * compare the head monomial of p1 and p2 with weighted degree lexicographic |
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465 | * ordering |
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466 | */ |
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467 | static int comp_Wp ( poly p1, poly p2, int f, int l, short * w ) |
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468 | { |
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469 | int i, s1 = 0, s2 = 0; |
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470 | |
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471 | for ( i = f; i <= l; i++, w++ ) |
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472 | { |
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473 | s1 += (int)pGetExp(p1,i)*(*w); |
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474 | s2 += (int)pGetExp(p2,i)*(*w); |
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475 | } |
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476 | if ( s1 == s2 ) |
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477 | { |
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478 | i = f; |
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479 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
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480 | i++; |
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481 | if ( i > l ) |
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482 | return 0; |
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483 | if ( pGetExp(p1,i) > pGetExp(p2,i) ) |
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484 | return 1; |
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485 | return -1; |
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486 | } |
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487 | if ( s1 > s2 ) |
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488 | return 1; |
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489 | return -1; |
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490 | } |
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491 | |
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492 | /*2 |
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493 | * compare the head monomial of p1 and p2 with lexicographic ordering |
---|
494 | * (power series case) |
---|
495 | */ |
---|
496 | static int comp_ls ( poly p1, poly p2, int f, int l, short * w ) |
---|
497 | { |
---|
498 | int i; |
---|
499 | |
---|
500 | i = f; |
---|
501 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
502 | i++; |
---|
503 | if ( i > l ) |
---|
504 | return 0; |
---|
505 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
506 | return 1; |
---|
507 | return -1; |
---|
508 | } |
---|
509 | |
---|
510 | /*2 |
---|
511 | * compare the head monomial of p1 and p2 with degree reverse lexicographic |
---|
512 | * ordering (power series case) |
---|
513 | */ |
---|
514 | static int comp_ds ( poly p1, poly p2, int f, int l, short * w ) |
---|
515 | { |
---|
516 | int i, s1 = 0, s2 = 0; |
---|
517 | |
---|
518 | for ( i = f; i <= l; i++ ) |
---|
519 | { |
---|
520 | s1 += pGetExp(p1,i); |
---|
521 | s2 += pGetExp(p2,i); |
---|
522 | } |
---|
523 | if ( s1 == s2 ) |
---|
524 | { |
---|
525 | i = l; |
---|
526 | while ( ( i >= f ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
527 | i--; |
---|
528 | if ( i < f ) |
---|
529 | return 0; |
---|
530 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
531 | return 1; |
---|
532 | return -1; |
---|
533 | } |
---|
534 | if ( s1 < s2 ) |
---|
535 | return 1; |
---|
536 | return -1; |
---|
537 | } |
---|
538 | |
---|
539 | /*2 |
---|
540 | * compare the head monomial of p1 and p2 with degree lexicographic ordering |
---|
541 | * (power series case) |
---|
542 | */ |
---|
543 | static int comp_Ds ( poly p1, poly p2, int f, int l, short * w ) |
---|
544 | { |
---|
545 | int i, s1 = 0, s2 = 0; |
---|
546 | |
---|
547 | for ( i = f; i <= l; i++ ) |
---|
548 | { |
---|
549 | s1 += pGetExp(p1,i); |
---|
550 | s2 += pGetExp(p2,i); |
---|
551 | } |
---|
552 | if ( s1 == s2 ) |
---|
553 | { |
---|
554 | i = f; |
---|
555 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
556 | i++; |
---|
557 | if ( i > l ) |
---|
558 | return 0; |
---|
559 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
560 | return -1; |
---|
561 | return 1; |
---|
562 | } |
---|
563 | if ( s1 < s2 ) |
---|
564 | return 1; |
---|
565 | return -1; |
---|
566 | } |
---|
567 | |
---|
568 | /*2 |
---|
569 | * compare the head monomial of p1 and p2 with weighted degree reverse |
---|
570 | * lexicographic ordering (power series case) |
---|
571 | */ |
---|
572 | static int comp_ws ( poly p1, poly p2, int f, int l, short * w ) |
---|
573 | { |
---|
574 | int i, s1 = 0, s2 = 0; |
---|
575 | |
---|
576 | for ( i = f; i <= l; i++, w++ ) |
---|
577 | { |
---|
578 | s1 += (int)pGetExp(p1,i)*(*w); |
---|
579 | s2 += (int)pGetExp(p2,i)*(*w); |
---|
580 | } |
---|
581 | if ( s1 == s2 ) |
---|
582 | { |
---|
583 | i = l; |
---|
584 | while ( ( i >= f ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
585 | i--; |
---|
586 | if ( i < f ) |
---|
587 | return 0; |
---|
588 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
589 | return 1; |
---|
590 | return -1; |
---|
591 | } |
---|
592 | if ( s1 < s2 ) |
---|
593 | return 1; |
---|
594 | return -1; |
---|
595 | } |
---|
596 | |
---|
597 | /*2 |
---|
598 | * compare the head monomial of p1 and p2 with weighted degree lexicographic |
---|
599 | * ordering (power series case) |
---|
600 | */ |
---|
601 | static int comp_Ws ( poly p1, poly p2, int f, int l, short * w ) |
---|
602 | { |
---|
603 | int i, s1 = 0, s2 = 0; |
---|
604 | |
---|
605 | for ( i = f; i <= l; i++, w++ ) |
---|
606 | { |
---|
607 | s1 += (int)pGetExp(p1,i)*(*w); |
---|
608 | s2 += (int)pGetExp(p2,i)*(*w); |
---|
609 | } |
---|
610 | if ( s1 == s2 ) |
---|
611 | { |
---|
612 | i = f; |
---|
613 | while ( ( i <= l ) && ( pGetExp(p1,i) == pGetExp(p2,i) ) ) |
---|
614 | i++; |
---|
615 | if ( i > l ) |
---|
616 | return 0; |
---|
617 | if ( pGetExp(p1,i) < pGetExp(p2,i) ) |
---|
618 | return -1; |
---|
619 | return 1; |
---|
620 | } |
---|
621 | if ( s1 < s2 ) |
---|
622 | return 1; |
---|
623 | return -1; |
---|
624 | } |
---|
625 | |
---|
626 | /*2 |
---|
627 | * compare the head monomial of p1 and p2 with matrix order |
---|
628 | * w contains a series of l-f+1 lines |
---|
629 | */ |
---|
630 | static int comp_M ( poly p1, poly p2, int f, int l, short * w ) |
---|
631 | { |
---|
632 | int i, j, s1, s2; |
---|
633 | |
---|
634 | for ( i = f; i <= l; i++ ) |
---|
635 | { |
---|
636 | s1 = s2 = 0; |
---|
637 | for ( j = f; j <= l; j++, w++ ) |
---|
638 | { |
---|
639 | s1 += (int)pGetExp(p1,j)*(int)(*w); |
---|
640 | s2 += (int)pGetExp(p2,j)*(int)(*w); |
---|
641 | } |
---|
642 | if ( s1 < s2 ) |
---|
643 | return -1; |
---|
644 | if ( s1 > s2 ) |
---|
645 | return 1; |
---|
646 | /* now w points to the last element of the current row, the next w++ */ |
---|
647 | /* moves on to the first element of the next row ! */ |
---|
648 | } |
---|
649 | return 0; |
---|
650 | } |
---|
651 | |
---|
652 | /*2 |
---|
653 | * compare the head monomial of p1 and p2 with weight vector |
---|
654 | */ |
---|
655 | static int comp_a ( poly p1, poly p2, int f, int l, short * w ) |
---|
656 | { |
---|
657 | int i, s1 = 0, s2 = 0; |
---|
658 | |
---|
659 | for ( i = f; i <= l; i++, w++ ) |
---|
660 | { |
---|
661 | s1 += (int)pGetExp(p1,i)*(*w); |
---|
662 | s2 += (int)pGetExp(p2,i)*(*w); |
---|
663 | } |
---|
664 | if ( s1 > s2 ) |
---|
665 | return 1; |
---|
666 | if ( s1 < s2 ) |
---|
667 | return -1; |
---|
668 | return 0; |
---|
669 | } |
---|
670 | |
---|
671 | /*2 |
---|
672 | * compare the head monomial of p1 and p2 with module component |
---|
673 | */ |
---|
674 | static int comp_c ( poly p1, poly p2, int f, int l, short * w ) |
---|
675 | { |
---|
676 | if ( pGetComp(p1) > pGetComp(p2) ) |
---|
677 | return -pComponentOrder; |
---|
678 | if ( pGetComp(p1) < pGetComp(p2) ) |
---|
679 | return pComponentOrder; |
---|
680 | return 0; |
---|
681 | } |
---|
682 | |
---|
683 | /*---------------------------------------------------------------*/ |
---|
684 | |
---|
685 | /*2 |
---|
686 | * compare p1 and p2 by a block ordering |
---|
687 | * uses (*bcomph[])() to do the real work |
---|
688 | */ |
---|
689 | static int BlockComp(poly p1, poly p2) |
---|
690 | { |
---|
691 | int res, i, e, a; |
---|
692 | |
---|
693 | /*4 compare in all blocks,* |
---|
694 | * each block has var numbers a(=block0[i]) to e (=block1[i])* |
---|
695 | * the block number starts with 0*/ |
---|
696 | e = 0; |
---|
697 | i = 0; |
---|
698 | loop |
---|
699 | { |
---|
700 | a = block0[i]; |
---|
701 | e = block1[i]; |
---|
702 | res = (*bcomph[i])(p1, p2, a, e , polys_wv[i]); |
---|
703 | if (res) |
---|
704 | return res; |
---|
705 | i++; |
---|
706 | if (order[i]==0) |
---|
707 | break; |
---|
708 | } |
---|
709 | return 0; |
---|
710 | } |
---|
711 | |
---|
712 | int pComp(poly p1, poly p2) |
---|
713 | { |
---|
714 | if (p2==NULL) |
---|
715 | return 1; |
---|
716 | if (p1==NULL) |
---|
717 | return -1; |
---|
718 | return pComp0(p1,p2); |
---|
719 | } |
---|
720 | |
---|
721 | /*----------pComp handling for syzygies---------------------*/ |
---|
722 | static void newHeadsB(polyset actHeads,int length) |
---|
723 | { |
---|
724 | int i; |
---|
725 | int* newOrder=(int*)Alloc(length*sizeof(int)); |
---|
726 | |
---|
727 | for (i=0;i<length;i++) |
---|
728 | { |
---|
729 | if (actHeads[i]!=NULL) |
---|
730 | { |
---|
731 | newOrder[i] = SchreyerOrd[pGetComp(actHeads[i])-1]; |
---|
732 | } |
---|
733 | else |
---|
734 | { |
---|
735 | newOrder[i]=0; |
---|
736 | } |
---|
737 | } |
---|
738 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
739 | SchreyerOrd = newOrder; |
---|
740 | maxSchreyer = length; |
---|
741 | /* |
---|
742 | *for (i=0;i<maxSchreyer;i++); Print("%d ",SchreyerOrd[i]); |
---|
743 | *PrintLn(); |
---|
744 | */ |
---|
745 | } |
---|
746 | |
---|
747 | int mcompSchrB(poly p1,poly p2) |
---|
748 | { |
---|
749 | int CompP1=pGetComp(p1),CompP2=pGetComp(p2),result, |
---|
750 | cP1=SchreyerOrd[CompP1-1],cP2=SchreyerOrd[CompP2-1]; |
---|
751 | |
---|
752 | if (CompP1==CompP2) return pCompOld(p1,p2); |
---|
753 | pSetComp(p1,cP1); |
---|
754 | pSetComp(p2,cP2); |
---|
755 | result = pCompOld(p1,p2); |
---|
756 | pSetComp(p1,CompP1); |
---|
757 | pSetComp(p2,CompP2); |
---|
758 | if (!result) |
---|
759 | { |
---|
760 | if (CompP1>CompP2) |
---|
761 | return -1; |
---|
762 | else if (CompP1<CompP2) |
---|
763 | return 1; |
---|
764 | } |
---|
765 | return result; |
---|
766 | } |
---|
767 | |
---|
768 | |
---|
769 | static void newHeadsM(polyset actHeads,int length) |
---|
770 | { |
---|
771 | int i; |
---|
772 | int* newOrder= |
---|
773 | (int*)Alloc0((length+maxSchreyer-indexShift)*sizeof(int)); |
---|
774 | |
---|
775 | //for (i=0;i<length+maxSchreyer-indexShift;i++) |
---|
776 | // newOrder[i]=0; |
---|
777 | for (i=indexShift;i<maxSchreyer;i++) |
---|
778 | { |
---|
779 | newOrder[i-indexShift] = SchreyerOrd[i]; |
---|
780 | SchreyerOrd[i] = 0; |
---|
781 | } |
---|
782 | for (i=maxSchreyer-indexShift;i<length+maxSchreyer-indexShift;i++) |
---|
783 | newOrder[i] = newOrder[pGetComp(actHeads[i-maxSchreyer+indexShift])-1]; |
---|
784 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
785 | SchreyerOrd = newOrder; |
---|
786 | indexShift = maxSchreyer-indexShift; |
---|
787 | maxSchreyer = length+indexShift; |
---|
788 | } |
---|
789 | |
---|
790 | /*2 |
---|
791 | * compute the length of a polynomial (in l) |
---|
792 | * and the degree of the monomial with maximal degree: |
---|
793 | * this is NOT the last one and the module component |
---|
794 | * has to be <= indexShift |
---|
795 | */ |
---|
796 | static int ldegSchrM(poly p,int *l) |
---|
797 | { |
---|
798 | int t,max; |
---|
799 | |
---|
800 | (*l)=1; |
---|
801 | max=pFDeg(p); |
---|
802 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=indexShift)) |
---|
803 | { |
---|
804 | pIter(p); |
---|
805 | t=pFDeg(p); |
---|
806 | if (t>max) max=t; |
---|
807 | (*l)++; |
---|
808 | } |
---|
809 | return max; |
---|
810 | } |
---|
811 | |
---|
812 | int mcompSchrM(poly p1,poly p2) |
---|
813 | { |
---|
814 | if ( pGetComp(p1)<=indexShift) |
---|
815 | { |
---|
816 | if ( pGetComp(p2)>indexShift) return 1; |
---|
817 | } |
---|
818 | else if ( pGetComp(p2)<=indexShift) return -1; |
---|
819 | return mcompSchrB(p1,p2); |
---|
820 | } |
---|
821 | |
---|
822 | void pSetSchreyerOrdM(polyset nextOrder, int length,int comps) |
---|
823 | { |
---|
824 | int i; |
---|
825 | |
---|
826 | if (length!=0) |
---|
827 | { |
---|
828 | if (maxSchreyer!=0) |
---|
829 | newHeadsM(nextOrder, length); |
---|
830 | else |
---|
831 | { |
---|
832 | indexShift = comps; |
---|
833 | if (indexShift==0) indexShift = 1; |
---|
834 | SchreyerOrd = (int*)Alloc((indexShift+length)*sizeof(int)); |
---|
835 | maxSchreyer = length+indexShift; |
---|
836 | for (i=0;i<indexShift;i++) |
---|
837 | SchreyerOrd[i] = i; |
---|
838 | for (i=indexShift;i<maxSchreyer;i++) |
---|
839 | SchreyerOrd[i] = pGetComp(nextOrder[i-indexShift]); |
---|
840 | pCompOld = pComp0; |
---|
841 | pComp0 = mcompSchrM; |
---|
842 | pLDegOld = pLDeg; |
---|
843 | pLDeg = ldegSchrM; |
---|
844 | } |
---|
845 | } |
---|
846 | else |
---|
847 | { |
---|
848 | if (maxSchreyer!=0) |
---|
849 | { |
---|
850 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
851 | maxSchreyer = 0; |
---|
852 | indexShift = 0; |
---|
853 | pComp0 = pCompOld; |
---|
854 | pLDeg = pLDegOld; |
---|
855 | } |
---|
856 | } |
---|
857 | } |
---|
858 | |
---|
859 | /*2 |
---|
860 | *the pComp0 for normal syzygies |
---|
861 | *compares monomials in the usual ring order (pCompOld) |
---|
862 | *but groups module indecees according indexBounds befor |
---|
863 | */ |
---|
864 | static int mcompSyz(poly p1,poly p2) |
---|
865 | { |
---|
866 | if (pGetComp(p1)<=pMaxBound) |
---|
867 | { |
---|
868 | if (pGetComp(p2)>pMaxBound) return 1; |
---|
869 | } |
---|
870 | else if (pGetComp(p2)<=pMaxBound) |
---|
871 | { |
---|
872 | return -1; |
---|
873 | } |
---|
874 | return pCompOld(p1,p2); |
---|
875 | } |
---|
876 | |
---|
877 | void pSetSyzComp(int k) |
---|
878 | { |
---|
879 | if (k!=0) |
---|
880 | { |
---|
881 | if (pMaxBound==0) |
---|
882 | { |
---|
883 | pCompOld = pComp0; |
---|
884 | pComp0 = mcompSyz; |
---|
885 | } |
---|
886 | pMaxBound = k; |
---|
887 | } |
---|
888 | else |
---|
889 | { |
---|
890 | if (pMaxBound!=0) |
---|
891 | { |
---|
892 | pComp0 = pCompOld; |
---|
893 | pMaxBound = 0; |
---|
894 | } |
---|
895 | } |
---|
896 | } |
---|
897 | |
---|
898 | /*2 |
---|
899 | * the type of the module ordering: C: -1, c: 1 |
---|
900 | */ |
---|
901 | int pModuleOrder() |
---|
902 | { |
---|
903 | return pComponentOrder; |
---|
904 | } |
---|
905 | |
---|
906 | /* -------------------------------------------------------------------*/ |
---|
907 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
908 | /*2 |
---|
909 | * compute the degree of the leading monomial of p |
---|
910 | * the ordering is compatible with degree, use a->order |
---|
911 | */ |
---|
912 | int pDeg(poly a) |
---|
913 | { |
---|
914 | return ((a!=NULL) ? (a->Order) : (-1)); |
---|
915 | } |
---|
916 | |
---|
917 | /*2 |
---|
918 | * compute the degree of the leading monomial of p |
---|
919 | * with respect to weigths 1 |
---|
920 | * (all are 1 so save multiplications or they are of different signs) |
---|
921 | * the ordering is not compatible with degree so do not use p->Order |
---|
922 | */ |
---|
923 | int pTotaldegree(poly p) |
---|
924 | { |
---|
925 | return pExpQuerSum(p); |
---|
926 | } |
---|
927 | |
---|
928 | /*2 |
---|
929 | * compute the degree of the leading monomial of p |
---|
930 | * with respect to weigths from the ordering |
---|
931 | * the ordering is not compatible with degree so do not use p->Order |
---|
932 | */ |
---|
933 | int pWTotaldegree(poly p) |
---|
934 | { |
---|
935 | int i, k; |
---|
936 | int j =0; |
---|
937 | |
---|
938 | // iterate through each block: |
---|
939 | for (i=0;order[i]!=0;i++) |
---|
940 | { |
---|
941 | switch(order[i]) |
---|
942 | { |
---|
943 | case ringorder_wp: |
---|
944 | case ringorder_ws: |
---|
945 | case ringorder_Wp: |
---|
946 | case ringorder_Ws: |
---|
947 | for (k=block0[i];k<=block1[i];k++) |
---|
948 | { // in jedem block: |
---|
949 | j+= pGetExp(p,k)*polys_wv[i][k-block0[i]]; |
---|
950 | } |
---|
951 | break; |
---|
952 | case ringorder_M: |
---|
953 | case ringorder_lp: |
---|
954 | case ringorder_dp: |
---|
955 | case ringorder_ds: |
---|
956 | case ringorder_Dp: |
---|
957 | case ringorder_Ds: |
---|
958 | for (k=block0[i];k<=block1[i];k++) |
---|
959 | { |
---|
960 | j+= pGetExp(p,k); |
---|
961 | } |
---|
962 | break; |
---|
963 | case ringorder_c: |
---|
964 | case ringorder_C: |
---|
965 | break; |
---|
966 | case ringorder_a: |
---|
967 | for (k=block0[i];k<=block1[i];k++) |
---|
968 | { // only one line |
---|
969 | j+= pGetExp(p,k)*polys_wv[i][k-block0[i]]; |
---|
970 | } |
---|
971 | return j; |
---|
972 | } |
---|
973 | } |
---|
974 | return j; |
---|
975 | } |
---|
976 | /* ---------------------------------------------------------------------*/ |
---|
977 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
978 | /* compute in l also the pLength of p */ |
---|
979 | |
---|
980 | /*2 |
---|
981 | * compute the length of a polynomial (in l) |
---|
982 | * and the degree of the monomial with maximal degree: the last one |
---|
983 | */ |
---|
984 | static int ldeg0(poly p,int *l) |
---|
985 | { |
---|
986 | Exponent_t k= pGetComp(p); |
---|
987 | int ll=1; |
---|
988 | |
---|
989 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))==k)) |
---|
990 | { |
---|
991 | pIter(p); |
---|
992 | ll++; |
---|
993 | } |
---|
994 | *l=ll; |
---|
995 | return (p->Order); |
---|
996 | } |
---|
997 | |
---|
998 | /*2 |
---|
999 | * compute the length of a polynomial (in l) |
---|
1000 | * and the degree of the monomial with maximal degree: the last one |
---|
1001 | * but search in all components before syzcomp |
---|
1002 | */ |
---|
1003 | static int ldeg0c(poly p,int *l) |
---|
1004 | { |
---|
1005 | int o=pFDeg(p); |
---|
1006 | int ll=1; |
---|
1007 | |
---|
1008 | if (pMaxBound/*syzComp*/==0) |
---|
1009 | { |
---|
1010 | while ((p=pNext(p))!=NULL) |
---|
1011 | { |
---|
1012 | o=pFDeg(p); |
---|
1013 | ll++; |
---|
1014 | } |
---|
1015 | } |
---|
1016 | else |
---|
1017 | { |
---|
1018 | while ((p=pNext(p))!=NULL) |
---|
1019 | { |
---|
1020 | if (pGetComp(p)<=pMaxBound/*syzComp*/) |
---|
1021 | { |
---|
1022 | o=pFDeg(p); |
---|
1023 | ll++; |
---|
1024 | } |
---|
1025 | else break; |
---|
1026 | } |
---|
1027 | } |
---|
1028 | *l=ll; |
---|
1029 | return o; |
---|
1030 | } |
---|
1031 | |
---|
1032 | /*2 |
---|
1033 | * compute the length of a polynomial (in l) |
---|
1034 | * and the degree of the monomial with maximal degree: the first one |
---|
1035 | * this works for the polynomial case with degree orderings |
---|
1036 | * (both c,dp and dp,c) |
---|
1037 | */ |
---|
1038 | static int ldegb(poly p,int *l) |
---|
1039 | { |
---|
1040 | Exponent_t k= pGetComp(p); |
---|
1041 | int o = p->Order; |
---|
1042 | int ll=1; |
---|
1043 | |
---|
1044 | while (((p=pNext(p))!=NULL) && (pGetComp(p)==k)) |
---|
1045 | { |
---|
1046 | ll++; |
---|
1047 | } |
---|
1048 | *l=ll; |
---|
1049 | return o; |
---|
1050 | } |
---|
1051 | |
---|
1052 | /*2 |
---|
1053 | * compute the length of a polynomial (in l) |
---|
1054 | * and the degree of the monomial with maximal degree: |
---|
1055 | * this is NOT the last one, we have to look for it |
---|
1056 | */ |
---|
1057 | static int ldeg1(poly p,int *l) |
---|
1058 | { |
---|
1059 | Exponent_t k= pGetComp(p); |
---|
1060 | int ll=1; |
---|
1061 | int t,max; |
---|
1062 | |
---|
1063 | max=pFDeg(p); |
---|
1064 | while (((p=pNext(p))!=NULL) && (pGetComp(p)==k)) |
---|
1065 | { |
---|
1066 | t=pFDeg(p); |
---|
1067 | if (t>max) max=t; |
---|
1068 | ll++; |
---|
1069 | } |
---|
1070 | *l=ll; |
---|
1071 | return max; |
---|
1072 | } |
---|
1073 | |
---|
1074 | /*2 |
---|
1075 | * compute the length of a polynomial (in l) |
---|
1076 | * and the degree of the monomial with maximal degree: |
---|
1077 | * this is NOT the last one, we have to look for it |
---|
1078 | * in all components |
---|
1079 | */ |
---|
1080 | static int ldeg1c(poly p,int *l) |
---|
1081 | { |
---|
1082 | int ll=1; |
---|
1083 | int t,max; |
---|
1084 | |
---|
1085 | max=pFDeg(p); |
---|
1086 | while ((p=pNext(p))!=NULL) |
---|
1087 | { |
---|
1088 | if ((pMaxBound/*syzComp*/==0) || (pGetComp(p)<=pMaxBound/*syzComp*/)) |
---|
1089 | { |
---|
1090 | if ((t=pFDeg(p))>max) max=t; |
---|
1091 | ll++; |
---|
1092 | } |
---|
1093 | else break; |
---|
1094 | } |
---|
1095 | *l=ll; |
---|
1096 | return max; |
---|
1097 | } |
---|
1098 | |
---|
1099 | /* -------------------------------------------------------- */ |
---|
1100 | /* set the variables for a choosen ordering */ |
---|
1101 | |
---|
1102 | |
---|
1103 | /* |
---|
1104 | * sets the comparision routine for monomials: for simple monomial orderings |
---|
1105 | * Priority is given to exponent vector |
---|
1106 | */ |
---|
1107 | static void SimpleChoose(int o_r, int comp_order, pCompProc *p) |
---|
1108 | { |
---|
1109 | switch(o_r) |
---|
1110 | { |
---|
1111 | case ringorder_dp: |
---|
1112 | case ringorder_wp: |
---|
1113 | case ringorder_ds: |
---|
1114 | case ringorder_ws: |
---|
1115 | case ringorder_ls: |
---|
1116 | case ringorder_unspec: |
---|
1117 | pSetVarIndicies_RevLex(pVariables); |
---|
1118 | pLexSgn = -1; |
---|
1119 | if (comp_order == ringorder_C || o_r == ringorder_unspec) |
---|
1120 | { |
---|
1121 | if (pVariables1W == 1) *p = pComp_otEXPCOMP_nwONE; |
---|
1122 | else if (pVariables1W == 2) *p = pComp_otEXPCOMP_nwTWO; |
---|
1123 | else if (pVariables1W & 1) *p = pComp_otEXPCOMP_nwODD; |
---|
1124 | else *p = pComp_otEXPCOMP_nwEVEN; |
---|
1125 | } |
---|
1126 | else |
---|
1127 | { |
---|
1128 | // component is compatible with exponent vector |
---|
1129 | if (pVariables1W == 1) *p = pComp_otEXP_nwONE; |
---|
1130 | else if (pVariables1W == 2) *p = pComp_otEXP_nwTWO; |
---|
1131 | else if (pVariables1W & 1) *p = pComp_otEXP_nwODD; |
---|
1132 | else *p = pComp_otEXP_nwEVEN; |
---|
1133 | } |
---|
1134 | break; |
---|
1135 | |
---|
1136 | #ifdef PDEBUG |
---|
1137 | case ringorder_lp: |
---|
1138 | case ringorder_Dp: |
---|
1139 | case ringorder_Wp: |
---|
1140 | case ringorder_Ds: |
---|
1141 | case ringorder_Ws: |
---|
1142 | #else |
---|
1143 | default: |
---|
1144 | #endif |
---|
1145 | pSetVarIndicies_Lex(pVariables); |
---|
1146 | pLexSgn = 1; |
---|
1147 | if (comp_order == ringorder_c) |
---|
1148 | { |
---|
1149 | if (pVariables1W == 1) *p = pComp_otEXPCOMP_nwONE; |
---|
1150 | else if (pVariables1W == 2) *p = pComp_otEXPCOMP_nwTWO; |
---|
1151 | else if (pVariables1W & 1) *p = pComp_otEXPCOMP_nwODD; |
---|
1152 | else *p = pComp_otEXPCOMP_nwEVEN; |
---|
1153 | } |
---|
1154 | else |
---|
1155 | { |
---|
1156 | // component is compatible with exponent vector |
---|
1157 | if (pVariables1W == 1) *p = pComp_otEXP_nwONE; |
---|
1158 | else if (pVariables1W == 2) *p = pComp_otEXP_nwTWO; |
---|
1159 | else if (pVariables1W & 1) *p = pComp_otEXP_nwODD; |
---|
1160 | else *p = pComp_otEXP_nwEVEN; |
---|
1161 | } |
---|
1162 | #ifdef PDEBUG |
---|
1163 | break; |
---|
1164 | default: |
---|
1165 | Werror("wrong internal ordering:%d at %s, l:%d\n",o_r,__FILE__,__LINE__); |
---|
1166 | #endif |
---|
1167 | } |
---|
1168 | |
---|
1169 | if (o_r == ringorder_lp || o_r == ringorder_ls) |
---|
1170 | { |
---|
1171 | pLexOrder=TRUE; |
---|
1172 | pFDeg = pTotaldegree; |
---|
1173 | pLDeg = ldeg1c; |
---|
1174 | if (o_r == ringorder_ls) |
---|
1175 | pSetVarIndicies_Lex(pVariables); |
---|
1176 | } |
---|
1177 | } |
---|
1178 | |
---|
1179 | /* |
---|
1180 | * sets the comparision routine for monomials: for simple monomial orderings |
---|
1181 | * Priority is given to component |
---|
1182 | */ |
---|
1183 | static void SimpleChooseC(int o_r, pCompProc *p) |
---|
1184 | { |
---|
1185 | switch(o_r) |
---|
1186 | { |
---|
1187 | case ringorder_dp: |
---|
1188 | case ringorder_wp: |
---|
1189 | case ringorder_ds: |
---|
1190 | case ringorder_ls: |
---|
1191 | case ringorder_ws: |
---|
1192 | pSetVarIndicies_RevLex(pVariables); |
---|
1193 | pLexSgn = -1; |
---|
1194 | if (pVariablesW == 1) |
---|
1195 | *p = pComp_otCOMPEXP_nwONE; |
---|
1196 | else if (pVariablesW == 2) |
---|
1197 | *p = pComp_otCOMPEXP_nwTWO; |
---|
1198 | else if (pVariablesW & 1) |
---|
1199 | *p = pComp_otCOMPEXP_nwODD; |
---|
1200 | else |
---|
1201 | *p = pComp_otCOMPEXP_nwEVEN; |
---|
1202 | break; |
---|
1203 | |
---|
1204 | #ifdef PDEBUG |
---|
1205 | case ringorder_lp: |
---|
1206 | case ringorder_Dp: |
---|
1207 | case ringorder_Wp: |
---|
1208 | case ringorder_Ds: |
---|
1209 | case ringorder_Ws: |
---|
1210 | #else |
---|
1211 | default: |
---|
1212 | #endif |
---|
1213 | pSetVarIndicies_Lex(pVariables); |
---|
1214 | pLexSgn = 1; |
---|
1215 | if (pVariablesW == 1) |
---|
1216 | *p = pComp_otCOMPEXP_nwONE; |
---|
1217 | else if (pVariablesW == 2) |
---|
1218 | *p = pComp_otCOMPEXP_nwTWO; |
---|
1219 | else if (pVariablesW & 1) |
---|
1220 | *p = pComp_otCOMPEXP_nwODD; |
---|
1221 | else |
---|
1222 | *p = pComp_otCOMPEXP_nwEVEN; |
---|
1223 | #ifdef PDEBUG |
---|
1224 | break; |
---|
1225 | default: |
---|
1226 | Werror("wrong internal ordering:%d at %s, l:%d\n",o_r,__FILE__,__LINE__); |
---|
1227 | #endif |
---|
1228 | } |
---|
1229 | if (o_r == ringorder_lp || o_r == ringorder_ls) |
---|
1230 | { |
---|
1231 | pLexOrder=TRUE; |
---|
1232 | pFDeg = pTotaldegree; |
---|
1233 | pLDeg = ldeg1c; |
---|
1234 | if (o_r == ringorder_ls) |
---|
1235 | pSetVarIndicies_Lex(pVariables); |
---|
1236 | } |
---|
1237 | } |
---|
1238 | |
---|
1239 | /*2 |
---|
1240 | * sets pSetm |
---|
1241 | * (according o_r = order of first block) |
---|
1242 | */ |
---|
1243 | static void SetpSetm(int o_r, int ip) |
---|
1244 | { |
---|
1245 | switch(o_r) |
---|
1246 | { |
---|
1247 | case ringorder_lp: |
---|
1248 | case ringorder_ls: |
---|
1249 | if (pVariables>1) |
---|
1250 | pSetm= setlex2; |
---|
1251 | else |
---|
1252 | pSetm= setlex1; |
---|
1253 | break; |
---|
1254 | case ringorder_dp: |
---|
1255 | case ringorder_Dp: |
---|
1256 | case ringorder_ds: |
---|
1257 | case ringorder_Ds: |
---|
1258 | case ringorder_unspec: |
---|
1259 | pSetm= setdeg1; |
---|
1260 | break; |
---|
1261 | case ringorder_a: |
---|
1262 | case ringorder_wp: |
---|
1263 | case ringorder_Wp: |
---|
1264 | case ringorder_ws: |
---|
1265 | case ringorder_Ws: |
---|
1266 | case ringorder_M: |
---|
1267 | pSetm= setdeg1w; |
---|
1268 | firstwv=polys_wv[ip]; |
---|
1269 | break; |
---|
1270 | case ringorder_c: |
---|
1271 | case ringorder_C: |
---|
1272 | return; |
---|
1273 | /*do not set firstBlockEnds for this orderings*/ |
---|
1274 | #ifdef TEST |
---|
1275 | default: |
---|
1276 | Werror("wrong internal ordering:%d at %s, l:%d\n",o_r,__FILE__,__LINE__); |
---|
1277 | #endif |
---|
1278 | } |
---|
1279 | firstBlockEnds=block1[ip]; |
---|
1280 | } |
---|
1281 | |
---|
1282 | |
---|
1283 | /*2 |
---|
1284 | * sets the comparision routine for monomials: for all but the first |
---|
1285 | * block of variables (ip is the block number, o_r the number of the ordering) |
---|
1286 | */ |
---|
1287 | static void HighSet(int ip, int o_r) |
---|
1288 | { |
---|
1289 | switch(o_r) |
---|
1290 | { |
---|
1291 | case ringorder_lp: |
---|
1292 | bcomph[ip]=comp_lp; |
---|
1293 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1294 | break; |
---|
1295 | case ringorder_dp: |
---|
1296 | bcomph[ip]=comp_dp; |
---|
1297 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1298 | break; |
---|
1299 | case ringorder_Dp: |
---|
1300 | bcomph[ip]=comp_Dp; |
---|
1301 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1302 | break; |
---|
1303 | case ringorder_wp: |
---|
1304 | bcomph[ip]=comp_wp; |
---|
1305 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1306 | break; |
---|
1307 | case ringorder_Wp: |
---|
1308 | bcomph[ip]=comp_Wp; |
---|
1309 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1310 | break; |
---|
1311 | case ringorder_ls: |
---|
1312 | bcomph[ip]=comp_ls; |
---|
1313 | break; |
---|
1314 | case ringorder_ds: |
---|
1315 | bcomph[ip]=comp_ds; |
---|
1316 | break; |
---|
1317 | case ringorder_Ds: |
---|
1318 | bcomph[ip]=comp_Ds; |
---|
1319 | break; |
---|
1320 | case ringorder_ws: |
---|
1321 | bcomph[ip]=comp_ws; |
---|
1322 | break; |
---|
1323 | case ringorder_Ws: |
---|
1324 | bcomph[ip]=comp_Ws; |
---|
1325 | break; |
---|
1326 | case ringorder_c: |
---|
1327 | pComponentOrder=1; |
---|
1328 | bcomph[ip]=comp_c; |
---|
1329 | break; |
---|
1330 | case ringorder_C: |
---|
1331 | pComponentOrder=-1; |
---|
1332 | bcomph[ip]=comp_c; |
---|
1333 | break; |
---|
1334 | case ringorder_M: |
---|
1335 | bcomph[ip]=comp_M; |
---|
1336 | pMixedOrder=TRUE; |
---|
1337 | break; |
---|
1338 | case ringorder_a: |
---|
1339 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
1340 | if (ip==0) |
---|
1341 | bcomph[0]=comp1a; |
---|
1342 | else |
---|
1343 | bcomph[ip]=comp_a; |
---|
1344 | break; |
---|
1345 | #ifdef TEST |
---|
1346 | default: |
---|
1347 | Werror("wrong internal ordering:%d at %s, l:%d\n",o_r,__FILE__,__LINE__); |
---|
1348 | #endif |
---|
1349 | } |
---|
1350 | } |
---|
1351 | |
---|
1352 | /* -------------------------------------------------------- */ |
---|
1353 | /*2 |
---|
1354 | * change all variables to fit the description of the new ring |
---|
1355 | */ |
---|
1356 | |
---|
1357 | void pChangeRing(int n, int Sgn, int * orders, int * b0, int * b1, |
---|
1358 | short ** wv) |
---|
1359 | { |
---|
1360 | sip_sring tmpR; |
---|
1361 | memset(&tmpR, 0, sizeof(sip_sring)); |
---|
1362 | tmpR.N = n; |
---|
1363 | tmpR.OrdSgn = Sgn; |
---|
1364 | tmpR.order = orders; |
---|
1365 | tmpR.block0 = b0; |
---|
1366 | tmpR.block1 = b1; |
---|
1367 | tmpR.wvhdl = wv; |
---|
1368 | pSetGlobals(&tmpR); |
---|
1369 | } |
---|
1370 | |
---|
1371 | void pSetGlobals(ring r, BOOLEAN complete) |
---|
1372 | { |
---|
1373 | int i; |
---|
1374 | pComponentOrder=1; |
---|
1375 | if (ppNoether!=NULL) pDelete(&ppNoether); |
---|
1376 | #ifdef SRING |
---|
1377 | pSRING=FALSE; |
---|
1378 | pAltVars=r->N+1; |
---|
1379 | #endif |
---|
1380 | pVariables = r->N; |
---|
1381 | |
---|
1382 | // set the various size parameters and initialize memory |
---|
1383 | if ((((pVariables+1)*sizeof(Exponent_t)) % sizeof(void*)) == 0) |
---|
1384 | pVariables1W = (pVariables+1)*sizeof(Exponent_t) / sizeof(void*); |
---|
1385 | else |
---|
1386 | pVariables1W = ((pVariables+1)*sizeof(Exponent_t) / sizeof(void*)) + 1; |
---|
1387 | |
---|
1388 | if ((((pVariables)*sizeof(Exponent_t)) % sizeof(void*)) == 0) |
---|
1389 | pVariablesW = (pVariables)*sizeof(Exponent_t) / sizeof(void*); |
---|
1390 | else |
---|
1391 | pVariablesW = ((pVariables)*sizeof(Exponent_t) / sizeof(void*)) + 1; |
---|
1392 | |
---|
1393 | pMonomSize = POLYSIZE + (pVariables + 1) * sizeof(Exponent_t); |
---|
1394 | if ((pMonomSize % sizeof(void*)) == 0) |
---|
1395 | { |
---|
1396 | pMonomSizeW = pMonomSize/sizeof(void*); |
---|
1397 | } |
---|
1398 | else |
---|
1399 | { |
---|
1400 | pMonomSizeW = pMonomSize/sizeof(void*) + 1; |
---|
1401 | pMonomSize = pMonomSizeW*sizeof(void*); |
---|
1402 | } |
---|
1403 | |
---|
1404 | // Set default Var Indicies |
---|
1405 | pSetVarIndicies(pVariables); |
---|
1406 | |
---|
1407 | // Initialize memory management |
---|
1408 | mmSpecializeBlock(pMonomSize); |
---|
1409 | |
---|
1410 | pOrdSgn = r->OrdSgn; |
---|
1411 | pVectorOut=(r->order[0]==ringorder_c); |
---|
1412 | order=r->order; |
---|
1413 | block0=r->block0; |
---|
1414 | block1=r->block1; |
---|
1415 | firstwv=NULL; |
---|
1416 | polys_wv=r->wvhdl; |
---|
1417 | /*------- only one real block ----------------------*/ |
---|
1418 | pLexOrder=FALSE; |
---|
1419 | pMixedOrder=FALSE; |
---|
1420 | pFDeg=pDeg; |
---|
1421 | if (pOrdSgn == 1) pLDeg = ldegb; |
---|
1422 | else pLDeg = ldeg0; |
---|
1423 | /*======== ordering type is (_,c) =========================*/ |
---|
1424 | if ((order[0]==ringorder_unspec) |
---|
1425 | ||( |
---|
1426 | ((order[1]==ringorder_c)||(order[1]==ringorder_C)) |
---|
1427 | && (order[0]!=ringorder_M) |
---|
1428 | && (order[2]==0)) |
---|
1429 | ) |
---|
1430 | { |
---|
1431 | if ((order[0]!=ringorder_unspec) |
---|
1432 | && (order[1]==ringorder_C)) |
---|
1433 | pComponentOrder=-1; |
---|
1434 | if (pOrdSgn == -1) pLDeg = ldeg0c; |
---|
1435 | SimpleChoose(order[0],order[1], &pComp0); |
---|
1436 | SetpSetm(order[0],0); |
---|
1437 | } |
---|
1438 | /*======== ordering type is (c,_) =========================*/ |
---|
1439 | else if (((order[0]==ringorder_c)||(order[0]==ringorder_C)) |
---|
1440 | && (order[1]!=ringorder_M) |
---|
1441 | && (order[2]==0)) |
---|
1442 | { |
---|
1443 | /* pLDeg = ldeg0; is standard*/ |
---|
1444 | if (order[0]==ringorder_C) |
---|
1445 | pComponentOrder=-1; |
---|
1446 | SimpleChooseC(order[1], &pComp0); |
---|
1447 | SetpSetm(order[1],1); |
---|
1448 | } |
---|
1449 | /*------- more than one block ----------------------*/ |
---|
1450 | else |
---|
1451 | { |
---|
1452 | //pLexOrder=TRUE; |
---|
1453 | pVectorOut=order[0]==ringorder_c; |
---|
1454 | if ((pVectorOut)||(order[0]==ringorder_C)) |
---|
1455 | { |
---|
1456 | if(block1[1]!=pVariables) pLexOrder=TRUE; |
---|
1457 | } |
---|
1458 | else |
---|
1459 | { |
---|
1460 | if(block1[0]!=pVariables) pLexOrder=TRUE; |
---|
1461 | } |
---|
1462 | /*the number of orderings:*/ |
---|
1463 | i = 0; |
---|
1464 | while (order[++i] != 0); |
---|
1465 | do |
---|
1466 | { |
---|
1467 | i--; |
---|
1468 | HighSet(i, order[i]);/*sets also pMixedOrder to TRUE, if...*/ |
---|
1469 | SetpSetm(order[i],i); |
---|
1470 | } |
---|
1471 | while (i != 0); |
---|
1472 | |
---|
1473 | pComp0 = BlockComp; |
---|
1474 | if ((order[0]!=ringorder_c)&&(order[0]!=ringorder_C)) |
---|
1475 | { |
---|
1476 | pLDeg = ldeg1c; |
---|
1477 | } |
---|
1478 | else |
---|
1479 | { |
---|
1480 | pLDeg = ldeg1; |
---|
1481 | } |
---|
1482 | pFDeg = pWTotaldegree; // may be improved: pTotaldegree for lp/dp/ls/.. blocks |
---|
1483 | } |
---|
1484 | if (complete) |
---|
1485 | { |
---|
1486 | if ((pLexOrder) || (pOrdSgn==-1)) |
---|
1487 | { |
---|
1488 | test &= ~Sy_bit(OPT_REDTAIL); /* noredTail */ |
---|
1489 | } |
---|
1490 | } |
---|
1491 | } |
---|
1492 | |
---|
1493 | /* -------------------------------------------------------- */ |
---|
1494 | |
---|
1495 | static BOOLEAN pMultT_nok; |
---|
1496 | /*2 |
---|
1497 | * update the polynomial a by multipying it by |
---|
1498 | * the (number) coefficient |
---|
1499 | * and the exponent vector (of) exp (a well initialized polynomial) |
---|
1500 | */ |
---|
1501 | poly pMultT(poly a, poly exp ) |
---|
1502 | { |
---|
1503 | int i; |
---|
1504 | number t,x,y=pGetCoeff(exp); |
---|
1505 | poly aa=a; |
---|
1506 | poly prev=NULL; |
---|
1507 | #ifdef SDRING |
---|
1508 | poly pDRINGres=NULL; |
---|
1509 | #endif |
---|
1510 | |
---|
1511 | pMultT_nok = pGetComp(exp); |
---|
1512 | #ifdef PDEBUG |
---|
1513 | pTest(a); |
---|
1514 | pTest(exp); |
---|
1515 | #endif |
---|
1516 | while (a !=NULL) |
---|
1517 | { |
---|
1518 | x=pGetCoeff(a); |
---|
1519 | t=nMult(x/*pGetCoeff(a)*/,y/*pGetCoeff(exp)*/); |
---|
1520 | nDelete(&x/*pGetCoeff(a)*/); |
---|
1521 | pSetCoeff0(a,t); |
---|
1522 | if (nIsZero(t)) |
---|
1523 | { |
---|
1524 | if (prev==NULL) { pDelete1(&a); aa=a; } |
---|
1525 | else { pDelete1(&prev->next); a=prev->next;} |
---|
1526 | } |
---|
1527 | else |
---|
1528 | { |
---|
1529 | #ifdef DRING |
---|
1530 | if (pDRING) |
---|
1531 | { |
---|
1532 | if (pdDFlag(a)==1) |
---|
1533 | { |
---|
1534 | if (pdDFlag(exp)==1) |
---|
1535 | { |
---|
1536 | pDRINGres=pAdd(pDRINGres,pMultDD(a,exp)); |
---|
1537 | } |
---|
1538 | else |
---|
1539 | { |
---|
1540 | pDRINGres=pAdd(pDRINGres,pMultDT(a,exp)); |
---|
1541 | } |
---|
1542 | } |
---|
1543 | else |
---|
1544 | { |
---|
1545 | if (pdDFlag(exp)==1) |
---|
1546 | { |
---|
1547 | pDRINGres=pAdd(pDRINGres,pMultDD(a,exp)); |
---|
1548 | } |
---|
1549 | else |
---|
1550 | { |
---|
1551 | pDRINGres=pAdd(pDRINGres,pMultTT(a,exp)); |
---|
1552 | } |
---|
1553 | } |
---|
1554 | } |
---|
1555 | else |
---|
1556 | #endif |
---|
1557 | #ifdef SRING |
---|
1558 | if (pSRING) |
---|
1559 | { |
---|
1560 | pDRINGres=pAdd(pDRINGres,psMultM(a,exp)); |
---|
1561 | } |
---|
1562 | else |
---|
1563 | #endif |
---|
1564 | { |
---|
1565 | for (i=pVariables; i != 0; i--) |
---|
1566 | { |
---|
1567 | pAddExp(a,i, pGetExp(exp,i)); |
---|
1568 | } |
---|
1569 | #ifdef TEST_MAC_ORDER |
---|
1570 | if (bNoAdd) |
---|
1571 | pSetm(a); |
---|
1572 | else |
---|
1573 | #endif |
---|
1574 | a->Order += exp->Order; |
---|
1575 | if (pMultT_nok) |
---|
1576 | { |
---|
1577 | if (pGetComp(a) == 0) |
---|
1578 | { |
---|
1579 | pSetComp(a, pGetComp(exp)); |
---|
1580 | } |
---|
1581 | else |
---|
1582 | { |
---|
1583 | return NULL /*FALSE*/; |
---|
1584 | } |
---|
1585 | } |
---|
1586 | } |
---|
1587 | prev=a; |
---|
1588 | pIter(a); |
---|
1589 | } |
---|
1590 | } |
---|
1591 | pMultT_nok=0; |
---|
1592 | #ifdef DRING |
---|
1593 | if (pDRING) |
---|
1594 | { |
---|
1595 | pDelete(&aa); |
---|
1596 | return pDRINGres; |
---|
1597 | } |
---|
1598 | #endif |
---|
1599 | #ifdef SRING |
---|
1600 | if (pSRING) |
---|
1601 | { |
---|
1602 | pDelete(&aa); |
---|
1603 | return pDRINGres; |
---|
1604 | } |
---|
1605 | #endif |
---|
1606 | return aa; /*TRUE*/ |
---|
1607 | } |
---|
1608 | |
---|
1609 | /*2 |
---|
1610 | * multiply p1 with p2, p1 and p2 are destroyed |
---|
1611 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
1612 | */ |
---|
1613 | poly pMult(poly p1, poly p2) |
---|
1614 | { |
---|
1615 | poly res, r, rn, a; |
---|
1616 | BOOLEAN cont; |
---|
1617 | |
---|
1618 | if ((p1!=NULL) && (p2!=NULL)) |
---|
1619 | { |
---|
1620 | #ifdef PDEBUG |
---|
1621 | pTest(p1); |
---|
1622 | pTest(p2); |
---|
1623 | #endif |
---|
1624 | cont = TRUE; |
---|
1625 | a = p1; |
---|
1626 | if (pNext(p2)!=NULL) |
---|
1627 | a = pCopy(a); |
---|
1628 | else |
---|
1629 | cont = FALSE; |
---|
1630 | res = pMultT(a, p2); |
---|
1631 | if (pMultT_nok) |
---|
1632 | { |
---|
1633 | if (cont) pDelete(&p1); |
---|
1634 | pDelete(&res); |
---|
1635 | pDelete(&p2); |
---|
1636 | return NULL; |
---|
1637 | } |
---|
1638 | pDelete1(&p2); |
---|
1639 | r = res; |
---|
1640 | if (r!=NULL) rn = pNext(r); |
---|
1641 | else rn=NULL; |
---|
1642 | while (cont) |
---|
1643 | { |
---|
1644 | if (pNext(p2)==NULL) |
---|
1645 | { |
---|
1646 | a = p1; |
---|
1647 | cont = FALSE; |
---|
1648 | } |
---|
1649 | else |
---|
1650 | { |
---|
1651 | a = pCopy(p1); |
---|
1652 | } |
---|
1653 | a=pMultT(a, p2); //sets pMultT_nok |
---|
1654 | if (pMultT_nok) |
---|
1655 | { |
---|
1656 | if (cont) pDelete(&p1); |
---|
1657 | pDelete(&a); |
---|
1658 | pDelete(&res); |
---|
1659 | pDelete(&p2); |
---|
1660 | return NULL; |
---|
1661 | } |
---|
1662 | while ((rn!=NULL) && (pComp0(rn,a)>0)) |
---|
1663 | { |
---|
1664 | r = rn; |
---|
1665 | pIter(rn); |
---|
1666 | } |
---|
1667 | if (r!=NULL) pNext(r) = rn = pAdd(a, rn); |
---|
1668 | else res=r=a; |
---|
1669 | pDelete1(&p2); |
---|
1670 | } |
---|
1671 | return res; |
---|
1672 | } |
---|
1673 | pDelete(&p1); |
---|
1674 | pDelete(&p2); |
---|
1675 | return NULL; |
---|
1676 | } |
---|
1677 | |
---|
1678 | /*2 |
---|
1679 | * update a by multiplying it with c (c will not be destroyed) |
---|
1680 | */ |
---|
1681 | void pMultN(poly a, number c) |
---|
1682 | { |
---|
1683 | number t; |
---|
1684 | |
---|
1685 | while (a!=NULL) |
---|
1686 | { |
---|
1687 | t=nMult(pGetCoeff(a), c); |
---|
1688 | //nNormalize(t); |
---|
1689 | pSetCoeff(a,t); |
---|
1690 | pIter(a); |
---|
1691 | } |
---|
1692 | } |
---|
1693 | |
---|
1694 | /*2 |
---|
1695 | * return a copy of the poly a times the number c (a,c will not be destroyed) |
---|
1696 | */ |
---|
1697 | poly pMultCopyN(poly a, number c) |
---|
1698 | { |
---|
1699 | poly result=NULL,hp; |
---|
1700 | |
---|
1701 | if (a != NULL) |
---|
1702 | { |
---|
1703 | result=pNew(); |
---|
1704 | pCopy2(result,a); |
---|
1705 | pNext(result)=NULL; |
---|
1706 | pGetCoeff(result)=nMult(pGetCoeff(a),c); |
---|
1707 | pIter(a); |
---|
1708 | hp=result; |
---|
1709 | while (a) |
---|
1710 | { |
---|
1711 | hp=pNext(hp)=pNew(); |
---|
1712 | pCopy2(hp,a); |
---|
1713 | pSetCoeff0(hp,nMult(pGetCoeff(a), c)); |
---|
1714 | pIter(a); |
---|
1715 | } |
---|
1716 | pNext(hp)=NULL; |
---|
1717 | } |
---|
1718 | return result; |
---|
1719 | } |
---|
1720 | |
---|
1721 | /*2 |
---|
1722 | * assumes that the head term of b is a multiple of the head term of a |
---|
1723 | * and return the multiplicant *m |
---|
1724 | */ |
---|
1725 | poly pDivide(poly a, poly b) |
---|
1726 | { |
---|
1727 | int i; |
---|
1728 | poly result=pInit(); |
---|
1729 | |
---|
1730 | for(i=(int)pVariables; i; i--) |
---|
1731 | pSetExp(result,i, pGetExp(a,i)- pGetExp(b,i)); |
---|
1732 | pSetComp(result, pGetComp(a) - pGetComp(b)); |
---|
1733 | pSetm(result); |
---|
1734 | return result; |
---|
1735 | } |
---|
1736 | |
---|
1737 | /*2 |
---|
1738 | * divides a by the monomial b, ignores monomials wihich are not divisible |
---|
1739 | * assumes that b is not NULL |
---|
1740 | */ |
---|
1741 | poly pDivideM(poly a, poly b) |
---|
1742 | { |
---|
1743 | if (a==NULL) return NULL; |
---|
1744 | poly result=a; |
---|
1745 | poly prev=NULL; |
---|
1746 | int i; |
---|
1747 | number inv=nInvers(pGetCoeff(b)); |
---|
1748 | |
---|
1749 | while (a!=NULL) |
---|
1750 | { |
---|
1751 | if (pDivisibleBy(b,a)) |
---|
1752 | { |
---|
1753 | for(i=(int)pVariables; i; i--) |
---|
1754 | pSubExp(a,i, pGetExp(b,i)); |
---|
1755 | pSubComp(a, pGetComp(b)); |
---|
1756 | pSetm(a); |
---|
1757 | prev=a; |
---|
1758 | pIter(a); |
---|
1759 | } |
---|
1760 | else |
---|
1761 | { |
---|
1762 | if (prev==NULL) |
---|
1763 | { |
---|
1764 | pDelete1(&result); |
---|
1765 | a=result; |
---|
1766 | } |
---|
1767 | else |
---|
1768 | { |
---|
1769 | pDelete1(&pNext(prev)); |
---|
1770 | a=pNext(prev); |
---|
1771 | } |
---|
1772 | } |
---|
1773 | } |
---|
1774 | pMultN(result,inv); |
---|
1775 | nDelete(&inv); |
---|
1776 | pDelete(&b); |
---|
1777 | return result; |
---|
1778 | } |
---|
1779 | |
---|
1780 | /*2 |
---|
1781 | * returns the LCM of the head terms of a and b in *m |
---|
1782 | */ |
---|
1783 | void pLcm(poly a, poly b, poly m) |
---|
1784 | { |
---|
1785 | int i; |
---|
1786 | for (i=pVariables; i; i--) |
---|
1787 | { |
---|
1788 | pSetExp(m,i, max( pGetExp(a,i), pGetExp(b,i))); |
---|
1789 | } |
---|
1790 | pSetComp(m, max(pGetComp(a), pGetComp(b))); |
---|
1791 | } |
---|
1792 | |
---|
1793 | /*2 |
---|
1794 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
1795 | */ |
---|
1796 | poly pmInit(char *st, BOOLEAN &ok) |
---|
1797 | { |
---|
1798 | int i,j; |
---|
1799 | ok=FALSE; |
---|
1800 | BOOLEAN b=FALSE; |
---|
1801 | poly rc = pInit(); |
---|
1802 | char *s = nRead(st,&(rc->coef)); |
---|
1803 | if (s==st) |
---|
1804 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
1805 | { |
---|
1806 | j = rIsRingVar(s); |
---|
1807 | if (j >= 0) |
---|
1808 | { |
---|
1809 | pIncrExp(rc,1+j); |
---|
1810 | goto done; |
---|
1811 | } |
---|
1812 | } |
---|
1813 | else |
---|
1814 | b=TRUE; |
---|
1815 | while (*s!='\0') |
---|
1816 | { |
---|
1817 | char ss[2]; |
---|
1818 | ss[0] = *s++; |
---|
1819 | ss[1] = '\0'; |
---|
1820 | j = rIsRingVar(ss); |
---|
1821 | if (j >= 0) |
---|
1822 | { |
---|
1823 | s = eati(s,&i); |
---|
1824 | pAddExp(rc,1+j, (Exponent_t)i); |
---|
1825 | } |
---|
1826 | else |
---|
1827 | { |
---|
1828 | if ((s!=st)&&isdigit(st[0])) |
---|
1829 | { |
---|
1830 | errorreported=TRUE; |
---|
1831 | } |
---|
1832 | pDelete(&rc); |
---|
1833 | return NULL; |
---|
1834 | } |
---|
1835 | } |
---|
1836 | done: |
---|
1837 | ok=!errorreported; |
---|
1838 | if (nIsZero(pGetCoeff(rc))) pDelete1(&rc); |
---|
1839 | else |
---|
1840 | { |
---|
1841 | #ifdef DRING |
---|
1842 | if (pDRING) |
---|
1843 | { |
---|
1844 | for(i=1;i<=pdN;i++) |
---|
1845 | { |
---|
1846 | if(pGetExp(rc,pdDX(i))>0) |
---|
1847 | { |
---|
1848 | pdSetDFlag(rc,1); |
---|
1849 | break; |
---|
1850 | } |
---|
1851 | } |
---|
1852 | } |
---|
1853 | #endif |
---|
1854 | pSetm(rc); |
---|
1855 | } |
---|
1856 | return rc; |
---|
1857 | } |
---|
1858 | |
---|
1859 | /*2 |
---|
1860 | *make p homgeneous by multiplying the monomials by powers of x_varnum |
---|
1861 | */ |
---|
1862 | poly pHomogen (poly p, int varnum) |
---|
1863 | { |
---|
1864 | poly q=NULL; |
---|
1865 | poly res; |
---|
1866 | int o,ii; |
---|
1867 | |
---|
1868 | if (p!=NULL) |
---|
1869 | { |
---|
1870 | if ((varnum < 1) || (varnum > pVariables)) |
---|
1871 | { |
---|
1872 | return NULL; |
---|
1873 | } |
---|
1874 | o=pWTotaldegree(p); |
---|
1875 | q=pNext(p); |
---|
1876 | while (q != NULL) |
---|
1877 | { |
---|
1878 | ii=pWTotaldegree(q); |
---|
1879 | if (ii>o) o=ii; |
---|
1880 | pIter(q); |
---|
1881 | } |
---|
1882 | q = pCopy(p); |
---|
1883 | res = q; |
---|
1884 | while (q != NULL) |
---|
1885 | { |
---|
1886 | ii = o-pWTotaldegree(q); |
---|
1887 | if (ii!=0) |
---|
1888 | { |
---|
1889 | pAddExp(q,varnum, (Exponent_t)ii); |
---|
1890 | pSetm(q); |
---|
1891 | } |
---|
1892 | pIter(q); |
---|
1893 | } |
---|
1894 | q = pOrdPolyInsertSetm(res); |
---|
1895 | } |
---|
1896 | return q; |
---|
1897 | } |
---|
1898 | |
---|
1899 | |
---|
1900 | /*2 |
---|
1901 | *replaces the maximal powers of the leading monomial of p2 in p1 by |
---|
1902 | *the same powers of n, utility for dehomogenization |
---|
1903 | */ |
---|
1904 | poly pDehomogen (poly p1,poly p2,number n) |
---|
1905 | { |
---|
1906 | polyset P; |
---|
1907 | int SizeOfSet=5; |
---|
1908 | int i; |
---|
1909 | poly p; |
---|
1910 | number nn; |
---|
1911 | |
---|
1912 | P = (polyset)Alloc0(5*sizeof(poly)); |
---|
1913 | //for (i=0; i<5; i++) |
---|
1914 | //{ |
---|
1915 | // P[i] = NULL; |
---|
1916 | //} |
---|
1917 | pCancelPolyByMonom(p1,p2,&P,&SizeOfSet); |
---|
1918 | p = P[0]; |
---|
1919 | //P[0] = NULL ;// for safety, may be remoeved later |
---|
1920 | for (i=1; i<SizeOfSet; i++) |
---|
1921 | { |
---|
1922 | if (P[i] != NULL) |
---|
1923 | { |
---|
1924 | nPower(n,i,&nn); |
---|
1925 | pMultN(P[i],nn); |
---|
1926 | p = pAdd(p,P[i]); |
---|
1927 | //P[i] =NULL; // for safety, may be removed later |
---|
1928 | nDelete(&nn); |
---|
1929 | } |
---|
1930 | } |
---|
1931 | Free((ADDRESS)P,SizeOfSet*sizeof(poly)); |
---|
1932 | return p; |
---|
1933 | } |
---|
1934 | |
---|
1935 | /*4 |
---|
1936 | *Returns the exponent of the maximal power of the leading monomial of |
---|
1937 | *p2 in that of p1 |
---|
1938 | */ |
---|
1939 | static int pGetMaxPower (poly p1,poly p2) |
---|
1940 | { |
---|
1941 | int i,k,res = 32000; /*a very large integer*/ |
---|
1942 | |
---|
1943 | if (p1 == NULL) return 0; |
---|
1944 | for (i=1; i<=pVariables; i++) |
---|
1945 | { |
---|
1946 | if ( pGetExp(p2,i) != 0) |
---|
1947 | { |
---|
1948 | k = pGetExp(p1,i) / pGetExp(p2,i); |
---|
1949 | if (k < res) res = k; |
---|
1950 | } |
---|
1951 | } |
---|
1952 | return res; |
---|
1953 | } |
---|
1954 | |
---|
1955 | /*2 |
---|
1956 | *Returns as i-th entry of P the coefficient of the (i-1) power of |
---|
1957 | *the leading monomial of p2 in p1 |
---|
1958 | */ |
---|
1959 | void pCancelPolyByMonom (poly p1,poly p2,polyset * P,int * SizeOfSet) |
---|
1960 | { |
---|
1961 | int maxPow; |
---|
1962 | poly p,qp,Coeff; |
---|
1963 | |
---|
1964 | if (*P == NULL) |
---|
1965 | { |
---|
1966 | *P = (polyset) Alloc(5*sizeof(poly)); |
---|
1967 | *SizeOfSet = 5; |
---|
1968 | } |
---|
1969 | p = pCopy(p1); |
---|
1970 | while (p != NULL) |
---|
1971 | { |
---|
1972 | qp = p->next; |
---|
1973 | p->next = NULL; |
---|
1974 | maxPow = pGetMaxPower(p,p2); |
---|
1975 | Coeff = pDivByMonom(p,p2); |
---|
1976 | if (maxPow > *SizeOfSet) |
---|
1977 | { |
---|
1978 | pEnlargeSet(P,*SizeOfSet,maxPow+1-*SizeOfSet); |
---|
1979 | *SizeOfSet = maxPow+1; |
---|
1980 | } |
---|
1981 | (*P)[maxPow] = pAdd((*P)[maxPow],Coeff); |
---|
1982 | pDelete(&p); |
---|
1983 | p = qp; |
---|
1984 | } |
---|
1985 | } |
---|
1986 | |
---|
1987 | /*2 |
---|
1988 | *returns the leading monomial of p1 divided by the maximal power of that |
---|
1989 | *of p2 |
---|
1990 | */ |
---|
1991 | poly pDivByMonom (poly p1,poly p2) |
---|
1992 | { |
---|
1993 | int k, i; |
---|
1994 | |
---|
1995 | if (p1 == NULL) return NULL; |
---|
1996 | k = pGetMaxPower(p1,p2); |
---|
1997 | if (k == 0) |
---|
1998 | return pHead(p1); |
---|
1999 | else |
---|
2000 | { |
---|
2001 | number n; |
---|
2002 | poly p = pInit(); |
---|
2003 | |
---|
2004 | p->next = NULL; |
---|
2005 | for (i=1; i<=pVariables; i++) |
---|
2006 | { |
---|
2007 | pSetExp(p,i, pGetExp(p1,i)-k* pGetExp(p2,i)); |
---|
2008 | } |
---|
2009 | nPower(p2->coef,k,&n); |
---|
2010 | pSetCoeff0(p,nDiv(p1->coef,n)); |
---|
2011 | nDelete(&n); |
---|
2012 | pSetm(p); |
---|
2013 | return p; |
---|
2014 | } |
---|
2015 | } |
---|
2016 | /*----------utilities for syzygies--------------*/ |
---|
2017 | poly pTakeOutComp(poly * p, int k) |
---|
2018 | { |
---|
2019 | poly q = *p,qq=NULL,result = NULL; |
---|
2020 | |
---|
2021 | if (q==NULL) return NULL; |
---|
2022 | if (pGetComp(q)==k) |
---|
2023 | { |
---|
2024 | result = q; |
---|
2025 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
2026 | { |
---|
2027 | pSetComp(q,0); |
---|
2028 | qq = q; |
---|
2029 | pIter(q); |
---|
2030 | } |
---|
2031 | *p = q; |
---|
2032 | pNext(qq) = NULL; |
---|
2033 | } |
---|
2034 | if (q==NULL) return result; |
---|
2035 | if (pGetComp(q) > k) pDecrComp(q); |
---|
2036 | poly pNext_q; |
---|
2037 | while ((pNext_q=pNext(q))!=NULL) |
---|
2038 | { |
---|
2039 | if (pGetComp(pNext_q)==k) |
---|
2040 | { |
---|
2041 | if (result==NULL) |
---|
2042 | { |
---|
2043 | result = pNext_q; |
---|
2044 | qq = result; |
---|
2045 | } |
---|
2046 | else |
---|
2047 | { |
---|
2048 | pNext(qq) = pNext_q; |
---|
2049 | pIter(qq); |
---|
2050 | } |
---|
2051 | pNext(q) = pNext(pNext_q); |
---|
2052 | pNext(qq) =NULL; |
---|
2053 | pSetComp(qq,0); |
---|
2054 | } |
---|
2055 | else |
---|
2056 | { |
---|
2057 | /*pIter(q);*/ q=pNext_q; |
---|
2058 | if (pGetComp(q) > k) pDecrComp(q); |
---|
2059 | } |
---|
2060 | } |
---|
2061 | return result; |
---|
2062 | } |
---|
2063 | |
---|
2064 | poly pTakeOutComp1(poly * p, int k) |
---|
2065 | { |
---|
2066 | poly q = *p; |
---|
2067 | |
---|
2068 | if (q==NULL) return NULL; |
---|
2069 | |
---|
2070 | poly qq=NULL,result = NULL; |
---|
2071 | |
---|
2072 | if (pGetComp(q)==k) |
---|
2073 | { |
---|
2074 | result = q; /* *p */ |
---|
2075 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
2076 | { |
---|
2077 | pSetComp(q,0); |
---|
2078 | qq = q; |
---|
2079 | pIter(q); |
---|
2080 | } |
---|
2081 | *p = q; |
---|
2082 | pNext(qq) = NULL; |
---|
2083 | } |
---|
2084 | if (q==NULL) return result; |
---|
2085 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2086 | while (pNext(q)!=NULL) |
---|
2087 | { |
---|
2088 | if (pGetComp(pNext(q))==k) |
---|
2089 | { |
---|
2090 | if (result==NULL) |
---|
2091 | { |
---|
2092 | result = pNext(q); |
---|
2093 | qq = result; |
---|
2094 | } |
---|
2095 | else |
---|
2096 | { |
---|
2097 | pNext(qq) = pNext(q); |
---|
2098 | pIter(qq); |
---|
2099 | } |
---|
2100 | pNext(q) = pNext(pNext(q)); |
---|
2101 | pNext(qq) =NULL; |
---|
2102 | pSetComp(qq,0); |
---|
2103 | } |
---|
2104 | else |
---|
2105 | { |
---|
2106 | pIter(q); |
---|
2107 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2108 | } |
---|
2109 | } |
---|
2110 | return result; |
---|
2111 | } |
---|
2112 | |
---|
2113 | void pDeleteComp(poly * p,int k) |
---|
2114 | { |
---|
2115 | poly q; |
---|
2116 | |
---|
2117 | while ((*p!=NULL) && (pGetComp(*p)==k)) pDelete1(p); |
---|
2118 | if (*p==NULL) return; |
---|
2119 | q = *p; |
---|
2120 | if (pGetComp(q)>k) pDecrComp(q); |
---|
2121 | while (pNext(q)!=NULL) |
---|
2122 | { |
---|
2123 | if (pGetComp(pNext(q))==k) |
---|
2124 | pDelete1(&(pNext(q))); |
---|
2125 | else |
---|
2126 | { |
---|
2127 | pIter(q); |
---|
2128 | if (pGetComp(q)>k) pDecrComp(q); |
---|
2129 | } |
---|
2130 | } |
---|
2131 | } |
---|
2132 | /*----------end of utilities for syzygies--------------*/ |
---|
2133 | |
---|
2134 | /*2 |
---|
2135 | * pair has no common factor ? or is no polynomial |
---|
2136 | */ |
---|
2137 | BOOLEAN pHasNotCF(poly p1, poly p2) |
---|
2138 | { |
---|
2139 | #ifdef SRING |
---|
2140 | if (pSRING) |
---|
2141 | return FALSE; |
---|
2142 | #endif |
---|
2143 | |
---|
2144 | if (pGetComp(p1) > 0 || pGetComp(p2) > 0) |
---|
2145 | return FALSE; |
---|
2146 | int i = 1; |
---|
2147 | loop |
---|
2148 | { |
---|
2149 | if ((pGetExp(p1, i) > 0) && (pGetExp(p2, i) > 0)) return FALSE; |
---|
2150 | if (i == pVariables) return TRUE; |
---|
2151 | i++; |
---|
2152 | } |
---|
2153 | } |
---|
2154 | |
---|
2155 | |
---|
2156 | /*2 |
---|
2157 | *should return 1 if p divides q and p<q, |
---|
2158 | * -1 if q divides p and q<p |
---|
2159 | * 0 otherwise |
---|
2160 | */ |
---|
2161 | int pDivComp(poly p, poly q) |
---|
2162 | { |
---|
2163 | if (pGetComp(p) == pGetComp(q)) |
---|
2164 | { |
---|
2165 | int i=pVariables; |
---|
2166 | long d; |
---|
2167 | BOOLEAN a=FALSE, b=FALSE; |
---|
2168 | for (; i>0; i--) |
---|
2169 | { |
---|
2170 | d = pGetExpDiff(p, q, i); |
---|
2171 | if (d) |
---|
2172 | { |
---|
2173 | if (d < 0) |
---|
2174 | { |
---|
2175 | if (b) return 0; |
---|
2176 | a =TRUE; |
---|
2177 | } |
---|
2178 | else |
---|
2179 | { |
---|
2180 | if (a) return 0; |
---|
2181 | b = TRUE; |
---|
2182 | } |
---|
2183 | } |
---|
2184 | } |
---|
2185 | if (a) return 1; |
---|
2186 | else if (b) return -1; |
---|
2187 | } |
---|
2188 | return 0; |
---|
2189 | } |
---|
2190 | /*2 |
---|
2191 | *divides p1 by its leading monomial |
---|
2192 | */ |
---|
2193 | void pNorm(poly p1) |
---|
2194 | { |
---|
2195 | poly h; |
---|
2196 | number k, c; |
---|
2197 | |
---|
2198 | if (p1!=NULL) |
---|
2199 | { |
---|
2200 | if (!nIsOne(pGetCoeff(p1))) |
---|
2201 | { |
---|
2202 | nNormalize(pGetCoeff(p1)); |
---|
2203 | k=pGetCoeff(p1); |
---|
2204 | c = nInit(1); |
---|
2205 | pSetCoeff0(p1,c); |
---|
2206 | h = pNext(p1); |
---|
2207 | while (h!=NULL) |
---|
2208 | { |
---|
2209 | c=nDiv(pGetCoeff(h),k); |
---|
2210 | if (!nIsOne(c)) nNormalize(c); |
---|
2211 | pSetCoeff(h,c); |
---|
2212 | pIter(h); |
---|
2213 | } |
---|
2214 | nDelete(&k); |
---|
2215 | } |
---|
2216 | else |
---|
2217 | { |
---|
2218 | h = pNext(p1); |
---|
2219 | while (h!=NULL) |
---|
2220 | { |
---|
2221 | nNormalize(pGetCoeff(h)); |
---|
2222 | pIter(h); |
---|
2223 | } |
---|
2224 | } |
---|
2225 | } |
---|
2226 | } |
---|
2227 | |
---|
2228 | /*2 |
---|
2229 | *normalize all coeffizients |
---|
2230 | */ |
---|
2231 | void pNormalize(poly p) |
---|
2232 | { |
---|
2233 | while (p!=NULL) |
---|
2234 | { |
---|
2235 | nTest(pGetCoeff(p)); |
---|
2236 | nNormalize(pGetCoeff(p)); |
---|
2237 | pIter(p); |
---|
2238 | } |
---|
2239 | } |
---|
2240 | |
---|
2241 | /*3 |
---|
2242 | * substitute the n-th variable by 1 in p |
---|
2243 | * destroy p |
---|
2244 | */ |
---|
2245 | static poly pSubst1 (poly p,int n) |
---|
2246 | { |
---|
2247 | poly qq,result = NULL; |
---|
2248 | |
---|
2249 | while (p != NULL) |
---|
2250 | { |
---|
2251 | qq = p; |
---|
2252 | pIter(p); |
---|
2253 | qq->next = NULL; |
---|
2254 | pSetExp(qq,n,0); |
---|
2255 | pSetm(qq); |
---|
2256 | result = pAdd(result,qq); |
---|
2257 | } |
---|
2258 | return result; |
---|
2259 | } |
---|
2260 | |
---|
2261 | /*2 |
---|
2262 | * substitute the n-th variable by e in p |
---|
2263 | * destroy p |
---|
2264 | */ |
---|
2265 | poly pSubst(poly p, int n, poly e) |
---|
2266 | { |
---|
2267 | if ((e!=NULL)&&(pIsConstant(e))&&(nIsOne(pGetCoeff(e)))) |
---|
2268 | return pSubst1(p,n); |
---|
2269 | |
---|
2270 | int exponent,i; |
---|
2271 | poly h, res, m; |
---|
2272 | Exponent_t *me,*ee; |
---|
2273 | number nu,nu1; |
---|
2274 | |
---|
2275 | me=(Exponent_t *)Alloc((pVariables+1)*sizeof(Exponent_t)); |
---|
2276 | ee=(Exponent_t *)Alloc((pVariables+1)*sizeof(Exponent_t)); |
---|
2277 | if (e!=NULL) pGetExpV(e,ee); |
---|
2278 | res=NULL; |
---|
2279 | h=p; |
---|
2280 | while (h!=NULL) |
---|
2281 | { |
---|
2282 | if ((e!=NULL) || (pGetExp(h,n)==0)) |
---|
2283 | { |
---|
2284 | m=pHead(h); |
---|
2285 | pGetExpV(m,me); |
---|
2286 | exponent=me[n]; |
---|
2287 | me[n]=0; |
---|
2288 | for(i=pVariables;i>0;i--) |
---|
2289 | me[i]+=exponent*ee[i]; |
---|
2290 | pSetExpV(m,me); |
---|
2291 | if (e!=NULL) |
---|
2292 | { |
---|
2293 | nPower(pGetCoeff(e),exponent,&nu); |
---|
2294 | nu1=nMult(pGetCoeff(m),nu); |
---|
2295 | nDelete(&nu); |
---|
2296 | pSetCoeff(m,nu1); |
---|
2297 | } |
---|
2298 | res=pAdd(res,m); |
---|
2299 | } |
---|
2300 | pDelete1(&h); |
---|
2301 | } |
---|
2302 | Free((ADDRESS)me,(pVariables+1)*sizeof(Exponent_t)); |
---|
2303 | Free((ADDRESS)ee,(pVariables+1)*sizeof(Exponent_t)); |
---|
2304 | return res; |
---|
2305 | } |
---|
2306 | |
---|
2307 | BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm) |
---|
2308 | { |
---|
2309 | int k, j; |
---|
2310 | |
---|
2311 | if (lcm==NULL) return FALSE; |
---|
2312 | |
---|
2313 | for (j=pVariables; j; j--) |
---|
2314 | if ( pGetExp(p,j) > pGetExp(lcm,j)) return FALSE; |
---|
2315 | if ( pGetComp(p) != pGetComp(lcm)) return FALSE; |
---|
2316 | for (j=pVariables; j; j--) |
---|
2317 | { |
---|
2318 | if (pGetExp(p1,j)!=pGetExp(lcm,j)) |
---|
2319 | { |
---|
2320 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
2321 | { |
---|
2322 | for (k=pVariables; k>j; k--) |
---|
2323 | { |
---|
2324 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
2325 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
2326 | return TRUE; |
---|
2327 | } |
---|
2328 | for (k=j-1; k; k--) |
---|
2329 | { |
---|
2330 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
2331 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
2332 | return TRUE; |
---|
2333 | } |
---|
2334 | return FALSE; |
---|
2335 | } |
---|
2336 | } |
---|
2337 | else if (pGetExp(p2,j)!=pGetExp(lcm,j)) |
---|
2338 | { |
---|
2339 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
2340 | { |
---|
2341 | for (k=pVariables; k>j; k--) |
---|
2342 | { |
---|
2343 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
2344 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
2345 | return TRUE; |
---|
2346 | } |
---|
2347 | for (k=j-1; k!=0 ; k--) |
---|
2348 | { |
---|
2349 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
2350 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
2351 | return TRUE; |
---|
2352 | } |
---|
2353 | return FALSE; |
---|
2354 | } |
---|
2355 | } |
---|
2356 | } |
---|
2357 | return FALSE; |
---|
2358 | } |
---|
2359 | |
---|
2360 | int pWeight(int i) |
---|
2361 | { |
---|
2362 | if ((firstwv==NULL) || (i>firstBlockEnds)) |
---|
2363 | { |
---|
2364 | return 1; |
---|
2365 | } |
---|
2366 | return firstwv[i-1]; |
---|
2367 | } |
---|