1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: polys1.cc,v 1.35 2009-02-26 14:23:07 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 | * independent of representation |
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9 | */ |
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10 | |
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11 | /* includes */ |
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12 | #include <string.h> |
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13 | #include "mod2.h" |
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14 | #include "structs.h" |
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15 | #include "numbers.h" |
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16 | #include "ffields.h" |
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17 | #include "omalloc.h" |
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18 | #include "febase.h" |
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19 | #include "weight.h" |
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20 | #include "intvec.h" |
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21 | #include "longalg.h" |
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22 | #include "ring.h" |
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23 | #include "ideals.h" |
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24 | #include "polys.h" |
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25 | //#include "ipid.h" |
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26 | #ifdef HAVE_FACTORY |
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27 | #include "clapsing.h" |
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28 | #endif |
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29 | |
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30 | #ifdef HAVE_RATGRING |
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31 | #include "ratgring.h" |
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32 | #endif |
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33 | |
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34 | /*-------- several access procedures to monomials -------------------- */ |
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35 | /* |
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36 | * the module weights for std |
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37 | */ |
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38 | static pFDegProc pOldFDeg; |
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39 | static pLDegProc pOldLDeg; |
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40 | static intvec * pModW; |
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41 | static BOOLEAN pOldLexOrder; |
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42 | |
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43 | static long pModDeg(poly p, ring r = currRing) |
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44 | { |
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45 | long d=pOldFDeg(p, r); |
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46 | int c=p_GetComp(p, r); |
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47 | if ((c>0) && (pModW->range(c-1))) d+= (*pModW)[c-1]; |
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48 | return d; |
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49 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
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50 | } |
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51 | |
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52 | void pSetModDeg(intvec *w) |
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53 | { |
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54 | if (w!=NULL) |
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55 | { |
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56 | pModW = w; |
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57 | pOldFDeg = pFDeg; |
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58 | pOldLDeg = pLDeg; |
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59 | pOldLexOrder = pLexOrder; |
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60 | pSetDegProcs(pModDeg); |
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61 | pLexOrder = TRUE; |
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62 | } |
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63 | else |
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64 | { |
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65 | pModW = NULL; |
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66 | pRestoreDegProcs(pOldFDeg, pOldLDeg); |
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67 | pLexOrder = pOldLexOrder; |
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68 | } |
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69 | } |
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70 | |
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71 | |
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72 | /*2 |
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73 | * subtract p2 from p1, p1 and p2 are destroyed |
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74 | * do not put attention on speed: the procedure is only used in the interpreter |
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75 | */ |
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76 | poly pSub(poly p1, poly p2) |
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77 | { |
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78 | return pAdd(p1, pNeg(p2)); |
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79 | } |
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80 | |
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81 | /*3 |
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82 | * create binomial coef. |
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83 | */ |
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84 | static number* pnBin(int exp) |
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85 | { |
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86 | int e, i, h; |
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87 | number x, y, *bin=NULL; |
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88 | |
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89 | x = nInit(exp); |
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90 | if (nIsZero(x)) |
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91 | { |
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92 | nDelete(&x); |
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93 | return bin; |
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94 | } |
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95 | h = (exp >> 1) + 1; |
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96 | bin = (number *)omAlloc0(h*sizeof(number)); |
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97 | bin[1] = x; |
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98 | if (exp < 4) |
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99 | return bin; |
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100 | i = exp - 1; |
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101 | for (e=2; e<h; e++) |
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102 | { |
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103 | x = nInit(i); |
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104 | i--; |
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105 | y = nMult(x,bin[e-1]); |
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106 | nDelete(&x); |
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107 | x = nInit(e); |
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108 | bin[e] = nIntDiv(y,x); |
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109 | nDelete(&x); |
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110 | nDelete(&y); |
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111 | } |
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112 | return bin; |
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113 | } |
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114 | |
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115 | static void pnFreeBin(number *bin, int exp) |
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116 | { |
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117 | int e, h = (exp >> 1) + 1; |
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118 | |
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119 | if (bin[1] != NULL) |
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120 | { |
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121 | for (e=1; e<h; e++) |
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122 | nDelete(&(bin[e])); |
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123 | } |
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124 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
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125 | } |
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126 | |
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127 | /*3 |
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128 | * compute for a monomial m |
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129 | * the power m^exp, exp > 1 |
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130 | * destroys p |
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131 | */ |
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132 | static poly pMonPower(poly p, int exp) |
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133 | { |
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134 | int i; |
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135 | |
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136 | if(!nIsOne(pGetCoeff(p))) |
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137 | { |
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138 | number x, y; |
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139 | y = pGetCoeff(p); |
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140 | nPower(y,exp,&x); |
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141 | nDelete(&y); |
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142 | pSetCoeff0(p,x); |
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143 | } |
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144 | for (i=pVariables; i!=0; i--) |
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145 | { |
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146 | pMultExp(p,i, exp); |
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147 | } |
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148 | pSetm(p); |
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149 | return p; |
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150 | } |
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151 | |
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152 | /*3 |
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153 | * compute for monomials p*q |
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154 | * destroys p, keeps q |
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155 | */ |
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156 | static void pMonMult(poly p, poly q) |
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157 | { |
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158 | number x, y; |
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159 | int i; |
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160 | |
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161 | y = pGetCoeff(p); |
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162 | x = nMult(y,pGetCoeff(q)); |
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163 | nDelete(&y); |
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164 | pSetCoeff0(p,x); |
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165 | //for (i=pVariables; i!=0; i--) |
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166 | //{ |
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167 | // pAddExp(p,i, pGetExp(q,i)); |
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168 | //} |
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169 | //p->Order += q->Order; |
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170 | pExpVectorAdd(p,q); |
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171 | } |
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172 | |
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173 | /*3 |
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174 | * compute for monomials p*q |
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175 | * keeps p, q |
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176 | */ |
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177 | static poly pMonMultC(poly p, poly q) |
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178 | { |
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179 | number x; |
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180 | int i; |
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181 | poly r = pInit(); |
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182 | |
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183 | x = nMult(pGetCoeff(p),pGetCoeff(q)); |
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184 | pSetCoeff0(r,x); |
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185 | pExpVectorSum(r,p, q); |
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186 | return r; |
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187 | } |
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188 | |
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189 | /* |
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190 | * compute for a poly p = head+tail, tail is monomial |
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191 | * (head + tail)^exp, exp > 1 |
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192 | * with binomial coef. |
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193 | */ |
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194 | static poly pTwoMonPower(poly p, int exp) |
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195 | { |
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196 | int eh, e; |
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197 | long al; |
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198 | poly *a; |
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199 | poly tail, b, res, h; |
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200 | number x; |
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201 | number *bin = pnBin(exp); |
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202 | |
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203 | tail = pNext(p); |
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204 | if (bin == NULL) |
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205 | { |
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206 | pMonPower(p,exp); |
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207 | pMonPower(tail,exp); |
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208 | #ifdef PDEBUG |
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209 | pTest(p); |
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210 | #endif |
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211 | return p; |
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212 | } |
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213 | eh = exp >> 1; |
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214 | al = (exp + 1) * sizeof(poly); |
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215 | a = (poly *)omAlloc(al); |
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216 | a[1] = p; |
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217 | for (e=1; e<exp; e++) |
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218 | { |
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219 | a[e+1] = pMonMultC(a[e],p); |
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220 | } |
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221 | res = a[exp]; |
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222 | b = pHead(tail); |
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223 | for (e=exp-1; e>eh; e--) |
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224 | { |
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225 | h = a[e]; |
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226 | x = nMult(bin[exp-e],pGetCoeff(h)); |
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227 | pSetCoeff(h,x); |
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228 | pMonMult(h,b); |
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229 | res = pNext(res) = h; |
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230 | pMonMult(b,tail); |
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231 | } |
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232 | for (e=eh; e!=0; e--) |
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233 | { |
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234 | h = a[e]; |
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235 | x = nMult(bin[e],pGetCoeff(h)); |
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236 | pSetCoeff(h,x); |
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237 | pMonMult(h,b); |
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238 | res = pNext(res) = h; |
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239 | pMonMult(b,tail); |
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240 | } |
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241 | pDeleteLm(&tail); |
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242 | pNext(res) = b; |
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243 | pNext(b) = NULL; |
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244 | res = a[exp]; |
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245 | omFreeSize((ADDRESS)a, al); |
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246 | pnFreeBin(bin, exp); |
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247 | // tail=res; |
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248 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
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249 | // { |
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250 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
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251 | // { |
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252 | // pDeleteLm(&pNext(tail)); |
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253 | // } |
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254 | // else |
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255 | // pIter(tail); |
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256 | // } |
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257 | #ifdef PDEBUG |
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258 | pTest(res); |
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259 | #endif |
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260 | return res; |
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261 | } |
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262 | |
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263 | static poly pPow(poly p, int i) |
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264 | { |
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265 | poly rc = pCopy(p); |
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266 | i -= 2; |
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267 | do |
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268 | { |
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269 | rc = pMult(rc,pCopy(p)); |
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270 | pNormalize(rc); |
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271 | i--; |
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272 | } |
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273 | while (i != 0); |
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274 | return pMult(rc,p); |
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275 | } |
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276 | |
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277 | /*2 |
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278 | * returns the i-th power of p |
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279 | * p will be destroyed |
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280 | */ |
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281 | poly pPower(poly p, int i) |
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282 | { |
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283 | poly rc=NULL; |
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284 | |
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285 | if (i==0) |
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286 | { |
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287 | pDelete(&p); |
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288 | return pOne(); |
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289 | } |
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290 | |
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291 | if(p!=NULL) |
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292 | { |
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293 | if ( (i > 0) && ((unsigned long ) i > (currRing->bitmask))) |
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294 | { |
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295 | Werror("exponent %d is too large, max. is %d",i,currRing->bitmask); |
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296 | return NULL; |
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297 | } |
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298 | switch (i) |
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299 | { |
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300 | // cannot happen, see above |
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301 | // case 0: |
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302 | // { |
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303 | // rc=pOne(); |
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304 | // pDelete(&p); |
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305 | // break; |
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306 | // } |
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307 | case 1: |
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308 | rc=p; |
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309 | break; |
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310 | case 2: |
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311 | rc=pMult(pCopy(p),p); |
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312 | break; |
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313 | default: |
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314 | if (i < 0) |
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315 | { |
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316 | pDelete(&p); |
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317 | return NULL; |
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318 | } |
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319 | else |
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320 | { |
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321 | #ifdef HAVE_PLURAL |
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322 | if (rIsPluralRing(currRing)) /* in the NC case nothing helps :-( */ |
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323 | { |
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324 | int j=i; |
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325 | rc = pCopy(p); |
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326 | while (j>1) |
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327 | { |
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328 | rc = pMult(pCopy(p),rc); |
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329 | j--; |
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330 | } |
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331 | pDelete(&p); |
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332 | return rc; |
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333 | } |
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334 | #endif |
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335 | rc = pNext(p); |
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336 | if (rc == NULL) |
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337 | return pMonPower(p,i); |
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338 | /* else: binom ?*/ |
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339 | int char_p=rChar(currRing); |
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340 | if ((pNext(rc) != NULL) |
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341 | #ifdef HAVE_RINGS |
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342 | || rField_is_Ring(currRing) |
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343 | #endif |
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344 | ) |
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345 | return pPow(p,i); |
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346 | if ((char_p==0) || (i<=char_p)) |
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347 | return pTwoMonPower(p,i); |
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348 | poly p_p=pTwoMonPower(pCopy(p),char_p); |
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349 | return pMult(pPower(p,i-char_p),p_p); |
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350 | } |
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351 | /*end default:*/ |
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352 | } |
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353 | } |
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354 | return rc; |
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355 | } |
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356 | |
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357 | /*2 |
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358 | * returns the partial differentiate of a by the k-th variable |
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359 | * does not destroy the input |
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360 | */ |
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361 | poly pDiff(poly a, int k) |
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362 | { |
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363 | poly res, f, last; |
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364 | number t; |
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365 | |
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366 | last = res = NULL; |
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367 | while (a!=NULL) |
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368 | { |
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369 | if (pGetExp(a,k)!=0) |
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370 | { |
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371 | f = pLmInit(a); |
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372 | t = nInit(pGetExp(a,k)); |
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373 | pSetCoeff0(f,nMult(t,pGetCoeff(a))); |
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374 | nDelete(&t); |
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375 | if (nIsZero(pGetCoeff(f))) |
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376 | pDeleteLm(&f); |
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377 | else |
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378 | { |
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379 | pDecrExp(f,k); |
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380 | pSetm(f); |
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381 | if (res==NULL) |
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382 | { |
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383 | res=last=f; |
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384 | } |
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385 | else |
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386 | { |
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387 | pNext(last)=f; |
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388 | last=f; |
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389 | } |
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390 | } |
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391 | } |
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392 | pIter(a); |
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393 | } |
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394 | return res; |
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395 | } |
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396 | |
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397 | static poly pDiffOpM(poly a, poly b,BOOLEAN multiply) |
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398 | { |
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399 | int i,j,s; |
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400 | number n,h,hh; |
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401 | poly p=pOne(); |
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402 | n=nMult(pGetCoeff(a),pGetCoeff(b)); |
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403 | for(i=pVariables;i>0;i--) |
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404 | { |
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405 | s=pGetExp(b,i); |
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406 | if (s<pGetExp(a,i)) |
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407 | { |
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408 | nDelete(&n); |
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409 | pDeleteLm(&p); |
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410 | return NULL; |
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411 | } |
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412 | if (multiply) |
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413 | { |
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414 | for(j=pGetExp(a,i); j>0;j--) |
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415 | { |
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416 | h = nInit(s); |
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417 | hh=nMult(n,h); |
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418 | nDelete(&h); |
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419 | nDelete(&n); |
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420 | n=hh; |
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421 | s--; |
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422 | } |
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423 | pSetExp(p,i,s); |
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424 | } |
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425 | else |
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426 | { |
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427 | pSetExp(p,i,s-pGetExp(a,i)); |
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428 | } |
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429 | } |
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430 | pSetm(p); |
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431 | /*if (multiply)*/ pSetCoeff(p,n); |
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432 | return p; |
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433 | } |
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434 | |
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435 | poly pDiffOp(poly a, poly b,BOOLEAN multiply) |
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436 | { |
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437 | poly result=NULL; |
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438 | poly h; |
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439 | for(;a!=NULL;pIter(a)) |
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440 | { |
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441 | for(h=b;h!=NULL;pIter(h)) |
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442 | { |
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443 | result=pAdd(result,pDiffOpM(a,h,multiply)); |
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444 | } |
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445 | } |
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446 | return result; |
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447 | } |
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448 | |
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449 | |
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450 | void pSplit(poly p, poly *h) |
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451 | { |
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452 | *h=pNext(p); |
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453 | pNext(p)=NULL; |
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454 | } |
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455 | |
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456 | |
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457 | |
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458 | int pMaxCompProc(poly p) |
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459 | { |
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460 | return pMaxComp(p); |
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461 | } |
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462 | |
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463 | /*2 |
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464 | * handle memory request for sets of polynomials (ideals) |
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465 | * l is the length of *p, increment is the difference (may be negative) |
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466 | */ |
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467 | void pEnlargeSet(polyset *p, int l, int increment) |
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468 | { |
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469 | int i; |
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470 | polyset h; |
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471 | |
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472 | h=(polyset)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
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473 | if (increment>0) |
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474 | { |
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475 | //for (i=l; i<l+increment; i++) |
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476 | // h[i]=NULL; |
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477 | memset(&(h[l]),0,increment*sizeof(poly)); |
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478 | } |
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479 | *p=h; |
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480 | } |
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481 | |
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482 | number pInitContent(poly ph); |
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483 | number pInitContent_a(poly ph); |
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484 | |
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485 | void pContent(poly ph) |
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486 | { |
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487 | #ifdef HAVE_RINGS |
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488 | if (rField_is_Ring(currRing)) |
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489 | { |
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490 | if ((ph!=NULL) && rField_has_Units(currRing)) |
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491 | { |
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492 | number k = nGetUnit(pGetCoeff(ph)); |
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493 | if (!nIsOne(k)) |
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494 | { |
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495 | number tmpGMP = k; |
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496 | k = nInvers(k); |
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497 | nDelete(&tmpGMP); |
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498 | poly h = pNext(ph); |
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499 | pSetCoeff(ph, nMult(pGetCoeff(ph), k)); |
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500 | while (h != NULL) |
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501 | { |
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502 | pSetCoeff(h, nMult(pGetCoeff(h), k)); |
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503 | pIter(h); |
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504 | } |
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505 | } |
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506 | nDelete(&k); |
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507 | } |
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508 | return; |
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509 | } |
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510 | #endif |
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511 | number h,d; |
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512 | poly p; |
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513 | |
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514 | if(TEST_OPT_CONTENTSB) return; |
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515 | if(pNext(ph)==NULL) |
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516 | { |
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517 | pSetCoeff(ph,nInit(1)); |
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518 | } |
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519 | else |
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520 | { |
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521 | nNormalize(pGetCoeff(ph)); |
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522 | if(!nGreaterZero(pGetCoeff(ph))) ph = pNeg(ph); |
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523 | if (rField_is_Q()) |
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524 | { |
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525 | h=pInitContent(ph); |
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526 | p=ph; |
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527 | } |
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528 | else if ((rField_is_Extension()) |
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529 | && ((rPar(currRing)>1)||(currRing->minpoly==NULL))) |
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530 | { |
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531 | h=pInitContent_a(ph); |
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532 | p=ph; |
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533 | } |
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534 | else |
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535 | { |
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536 | h=nCopy(pGetCoeff(ph)); |
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537 | p = pNext(ph); |
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538 | } |
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539 | while (p!=NULL) |
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540 | { |
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541 | nNormalize(pGetCoeff(p)); |
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542 | d=nGcd(h,pGetCoeff(p),currRing); |
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543 | nDelete(&h); |
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544 | h = d; |
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545 | if(nIsOne(h)) |
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546 | { |
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547 | break; |
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548 | } |
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549 | pIter(p); |
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550 | } |
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551 | p = ph; |
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552 | //number tmp; |
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553 | if(!nIsOne(h)) |
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554 | { |
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555 | while (p!=NULL) |
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556 | { |
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557 | //d = nDiv(pGetCoeff(p),h); |
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558 | //tmp = nIntDiv(pGetCoeff(p),h); |
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559 | //if (!nEqual(d,tmp)) |
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560 | //{ |
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561 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
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562 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
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563 | // nWrite(tmp);Print(StringAppendS("\n")); |
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564 | //} |
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565 | //nDelete(&tmp); |
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566 | d = nIntDiv(pGetCoeff(p),h); |
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567 | pSetCoeff(p,d); |
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568 | pIter(p); |
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569 | } |
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570 | } |
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571 | nDelete(&h); |
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572 | #ifdef HAVE_FACTORY |
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573 | if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
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574 | { |
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575 | singclap_divide_content(ph); |
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576 | if(!nGreaterZero(pGetCoeff(ph))) ph = pNeg(ph); |
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577 | } |
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578 | #endif |
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579 | if (rField_is_Q_a()) |
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580 | { |
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581 | number hzz = nlInit(1); |
---|
582 | h = nlInit(1); |
---|
583 | p=ph; |
---|
584 | while (p!=NULL) |
---|
585 | { // each monom: coeff in Q_a |
---|
586 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
587 | napoly c_n=c_n_n->z; |
---|
588 | while (c_n!=NULL) |
---|
589 | { // each monom: coeff in Q |
---|
590 | d=nlLcm(hzz,pGetCoeff(c_n),currRing->algring); |
---|
591 | n_Delete(&hzz,currRing->algring); |
---|
592 | hzz=d; |
---|
593 | pIter(c_n); |
---|
594 | } |
---|
595 | c_n=c_n_n->n; |
---|
596 | while (c_n!=NULL) |
---|
597 | { // each monom: coeff in Q |
---|
598 | d=nlLcm(h,pGetCoeff(c_n),currRing->algring); |
---|
599 | n_Delete(&h,currRing->algring); |
---|
600 | h=d; |
---|
601 | pIter(c_n); |
---|
602 | } |
---|
603 | pIter(p); |
---|
604 | } |
---|
605 | /* hzz contains the 1/lcm of all denominators in c_n_n->z*/ |
---|
606 | /* h contains the 1/lcm of all denominators in c_n_n->n*/ |
---|
607 | number htmp=nlInvers(h); |
---|
608 | number hzztmp=nlInvers(hzz); |
---|
609 | number hh=nlMult(hzz,h); |
---|
610 | nlDelete(&hzz,currRing->algring); |
---|
611 | nlDelete(&h,currRing->algring); |
---|
612 | number hg=nlGcd(hzztmp,htmp,currRing->algring); |
---|
613 | nlDelete(&hzztmp,currRing->algring); |
---|
614 | nlDelete(&htmp,currRing->algring); |
---|
615 | h=nlMult(hh,hg); |
---|
616 | nlDelete(&hg,currRing->algring); |
---|
617 | nlDelete(&hh,currRing->algring); |
---|
618 | nlNormalize(h); |
---|
619 | if(!nlIsOne(h)) |
---|
620 | { |
---|
621 | p=ph; |
---|
622 | while (p!=NULL) |
---|
623 | { // each monom: coeff in Q_a |
---|
624 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
625 | napoly c_n=c_n_n->z; |
---|
626 | while (c_n!=NULL) |
---|
627 | { // each monom: coeff in Q |
---|
628 | d=nlMult(h,pGetCoeff(c_n)); |
---|
629 | nlNormalize(d); |
---|
630 | nlDelete(&pGetCoeff(c_n),currRing->algring); |
---|
631 | pGetCoeff(c_n)=d; |
---|
632 | pIter(c_n); |
---|
633 | } |
---|
634 | c_n=c_n_n->n; |
---|
635 | while (c_n!=NULL) |
---|
636 | { // each monom: coeff in Q |
---|
637 | d=nlMult(h,pGetCoeff(c_n)); |
---|
638 | nlNormalize(d); |
---|
639 | nlDelete(&pGetCoeff(c_n),currRing->algring); |
---|
640 | pGetCoeff(c_n)=d; |
---|
641 | pIter(c_n); |
---|
642 | } |
---|
643 | pIter(p); |
---|
644 | } |
---|
645 | } |
---|
646 | nlDelete(&h,currRing->algring); |
---|
647 | } |
---|
648 | } |
---|
649 | } |
---|
650 | void pSimpleContent(poly ph,int smax) |
---|
651 | { |
---|
652 | if(TEST_OPT_CONTENTSB) return; |
---|
653 | if (ph==NULL) return; |
---|
654 | if (pNext(ph)==NULL) |
---|
655 | { |
---|
656 | pSetCoeff(ph,nInit(1)); |
---|
657 | return; |
---|
658 | } |
---|
659 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q())) |
---|
660 | { |
---|
661 | return; |
---|
662 | } |
---|
663 | number d=pInitContent(ph); |
---|
664 | if (nlSize(d)<=smax) |
---|
665 | { |
---|
666 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
667 | return; |
---|
668 | } |
---|
669 | poly p=ph; |
---|
670 | number h=d; |
---|
671 | if (smax==1) smax=2; |
---|
672 | while (p!=NULL) |
---|
673 | { |
---|
674 | #if 0 |
---|
675 | d=nlGcd(h,pGetCoeff(p),currRing); |
---|
676 | nlDelete(&h,currRing); |
---|
677 | h = d; |
---|
678 | #else |
---|
679 | nlInpGcd(h,pGetCoeff(p),currRing); |
---|
680 | #endif |
---|
681 | if(nlSize(h)<smax) |
---|
682 | { |
---|
683 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
684 | return; |
---|
685 | } |
---|
686 | pIter(p); |
---|
687 | } |
---|
688 | p = ph; |
---|
689 | if (!nlGreaterZero(pGetCoeff(p))) h=nlNeg(h); |
---|
690 | if(nlIsOne(h)) return; |
---|
691 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
692 | while (p!=NULL) |
---|
693 | { |
---|
694 | #if 1 |
---|
695 | d = nlIntDiv(pGetCoeff(p),h); |
---|
696 | pSetCoeff(p,d); |
---|
697 | #else |
---|
698 | nlInpIntDiv(pGetCoeff(p),h,currRing); |
---|
699 | #endif |
---|
700 | pIter(p); |
---|
701 | } |
---|
702 | nlDelete(&h,currRing); |
---|
703 | } |
---|
704 | |
---|
705 | number pInitContent(poly ph) |
---|
706 | // only for coefficients in Q |
---|
707 | #if 0 |
---|
708 | { |
---|
709 | assume(!TEST_OPT_CONTENTSB); |
---|
710 | assume(ph!=NULL); |
---|
711 | assume(pNext(ph)!=NULL); |
---|
712 | assume(rField_is_Q()); |
---|
713 | if (pNext(pNext(ph))==NULL) |
---|
714 | { |
---|
715 | return nlGetNom(pGetCoeff(pNext(ph)),currRing); |
---|
716 | } |
---|
717 | poly p=ph; |
---|
718 | number n1=nlGetNom(pGetCoeff(p),currRing); |
---|
719 | pIter(p); |
---|
720 | number n2=nlGetNom(pGetCoeff(p),currRing); |
---|
721 | pIter(p); |
---|
722 | number d; |
---|
723 | number t; |
---|
724 | loop |
---|
725 | { |
---|
726 | nlNormalize(pGetCoeff(p)); |
---|
727 | t=nlGetNom(pGetCoeff(p),currRing); |
---|
728 | if (nlGreaterZero(t)) |
---|
729 | d=nlAdd(n1,t); |
---|
730 | else |
---|
731 | d=nlSub(n1,t); |
---|
732 | nlDelete(&t,currRing); |
---|
733 | nlDelete(&n1,currRing); |
---|
734 | n1=d; |
---|
735 | pIter(p); |
---|
736 | if (p==NULL) break; |
---|
737 | nlNormalize(pGetCoeff(p)); |
---|
738 | t=nlGetNom(pGetCoeff(p),currRing); |
---|
739 | if (nlGreaterZero(t)) |
---|
740 | d=nlAdd(n2,t); |
---|
741 | else |
---|
742 | d=nlSub(n2,t); |
---|
743 | nlDelete(&t,currRing); |
---|
744 | nlDelete(&n2,currRing); |
---|
745 | n2=d; |
---|
746 | pIter(p); |
---|
747 | if (p==NULL) break; |
---|
748 | } |
---|
749 | d=nlGcd(n1,n2,currRing); |
---|
750 | nlDelete(&n1,currRing); |
---|
751 | nlDelete(&n2,currRing); |
---|
752 | return d; |
---|
753 | } |
---|
754 | #else |
---|
755 | { |
---|
756 | number d=pGetCoeff(ph); |
---|
757 | if(SR_HDL(d)&SR_INT) return d; |
---|
758 | int s=mpz_size1(&d->z); |
---|
759 | int s2=-1; |
---|
760 | number d2; |
---|
761 | loop |
---|
762 | { |
---|
763 | pIter(ph); |
---|
764 | if(ph==NULL) |
---|
765 | { |
---|
766 | if (s2==-1) return nlCopy(d); |
---|
767 | break; |
---|
768 | } |
---|
769 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
770 | { |
---|
771 | s2=s; |
---|
772 | d2=d; |
---|
773 | s=0; |
---|
774 | d=pGetCoeff(ph); |
---|
775 | if (s2==0) break; |
---|
776 | } |
---|
777 | else |
---|
778 | if (mpz_size1(&(pGetCoeff(ph)->z))<=s) |
---|
779 | { |
---|
780 | s2=s; |
---|
781 | d2=d; |
---|
782 | d=pGetCoeff(ph); |
---|
783 | s=mpz_size1(&d->z); |
---|
784 | } |
---|
785 | } |
---|
786 | return nlGcd(d,d2,currRing); |
---|
787 | } |
---|
788 | #endif |
---|
789 | |
---|
790 | number pInitContent_a(poly ph) |
---|
791 | // only for coefficients in K(a) anf K(a,...) |
---|
792 | { |
---|
793 | number d=pGetCoeff(ph); |
---|
794 | int s=naParDeg(d); |
---|
795 | if (s /* naParDeg(d)*/ <=1) return naCopy(d); |
---|
796 | int s2=-1; |
---|
797 | number d2; |
---|
798 | int ss; |
---|
799 | loop |
---|
800 | { |
---|
801 | pIter(ph); |
---|
802 | if(ph==NULL) |
---|
803 | { |
---|
804 | if (s2==-1) return naCopy(d); |
---|
805 | break; |
---|
806 | } |
---|
807 | if ((ss=naParDeg(pGetCoeff(ph)))<s) |
---|
808 | { |
---|
809 | s2=s; |
---|
810 | d2=d; |
---|
811 | s=ss; |
---|
812 | d=pGetCoeff(ph); |
---|
813 | if (s2<=1) break; |
---|
814 | } |
---|
815 | } |
---|
816 | return naGcd(d,d2,currRing); |
---|
817 | } |
---|
818 | |
---|
819 | |
---|
820 | //void pContent(poly ph) |
---|
821 | //{ |
---|
822 | // number h,d; |
---|
823 | // poly p; |
---|
824 | // |
---|
825 | // p = ph; |
---|
826 | // if(pNext(p)==NULL) |
---|
827 | // { |
---|
828 | // pSetCoeff(p,nInit(1)); |
---|
829 | // } |
---|
830 | // else |
---|
831 | // { |
---|
832 | //#ifdef PDEBUG |
---|
833 | // if (!pTest(p)) return; |
---|
834 | //#endif |
---|
835 | // nNormalize(pGetCoeff(p)); |
---|
836 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
837 | // { |
---|
838 | // ph = pNeg(ph); |
---|
839 | // nNormalize(pGetCoeff(p)); |
---|
840 | // } |
---|
841 | // h=pGetCoeff(p); |
---|
842 | // pIter(p); |
---|
843 | // while (p!=NULL) |
---|
844 | // { |
---|
845 | // nNormalize(pGetCoeff(p)); |
---|
846 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
847 | // pIter(p); |
---|
848 | // } |
---|
849 | // h=nCopy(h); |
---|
850 | // p=ph; |
---|
851 | // while (p!=NULL) |
---|
852 | // { |
---|
853 | // d=nGcd(h,pGetCoeff(p)); |
---|
854 | // nDelete(&h); |
---|
855 | // h = d; |
---|
856 | // if(nIsOne(h)) |
---|
857 | // { |
---|
858 | // break; |
---|
859 | // } |
---|
860 | // pIter(p); |
---|
861 | // } |
---|
862 | // p = ph; |
---|
863 | // //number tmp; |
---|
864 | // if(!nIsOne(h)) |
---|
865 | // { |
---|
866 | // while (p!=NULL) |
---|
867 | // { |
---|
868 | // d = nIntDiv(pGetCoeff(p),h); |
---|
869 | // pSetCoeff(p,d); |
---|
870 | // pIter(p); |
---|
871 | // } |
---|
872 | // } |
---|
873 | // nDelete(&h); |
---|
874 | //#ifdef HAVE_FACTORY |
---|
875 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
876 | // { |
---|
877 | // pTest(ph); |
---|
878 | // singclap_divide_content(ph); |
---|
879 | // pTest(ph); |
---|
880 | // } |
---|
881 | //#endif |
---|
882 | // } |
---|
883 | //} |
---|
884 | #if 0 |
---|
885 | void p_Content(poly ph, ring r) |
---|
886 | { |
---|
887 | number h,d; |
---|
888 | poly p; |
---|
889 | |
---|
890 | if(pNext(ph)==NULL) |
---|
891 | { |
---|
892 | pSetCoeff(ph,n_Init(1,r)); |
---|
893 | } |
---|
894 | else |
---|
895 | { |
---|
896 | n_Normalize(pGetCoeff(ph),r); |
---|
897 | if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
898 | h=n_Copy(pGetCoeff(ph),r); |
---|
899 | p = pNext(ph); |
---|
900 | while (p!=NULL) |
---|
901 | { |
---|
902 | n_Normalize(pGetCoeff(p),r); |
---|
903 | d=n_Gcd(h,pGetCoeff(p),r); |
---|
904 | n_Delete(&h,r); |
---|
905 | h = d; |
---|
906 | if(n_IsOne(h,r)) |
---|
907 | { |
---|
908 | break; |
---|
909 | } |
---|
910 | pIter(p); |
---|
911 | } |
---|
912 | p = ph; |
---|
913 | //number tmp; |
---|
914 | if(!n_IsOne(h,r)) |
---|
915 | { |
---|
916 | while (p!=NULL) |
---|
917 | { |
---|
918 | //d = nDiv(pGetCoeff(p),h); |
---|
919 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
920 | //if (!nEqual(d,tmp)) |
---|
921 | //{ |
---|
922 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
923 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
924 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
925 | //} |
---|
926 | //nDelete(&tmp); |
---|
927 | d = n_IntDiv(pGetCoeff(p),h,r); |
---|
928 | p_SetCoeff(p,d,r); |
---|
929 | pIter(p); |
---|
930 | } |
---|
931 | } |
---|
932 | n_Delete(&h,r); |
---|
933 | #ifdef HAVE_FACTORY |
---|
934 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
935 | //{ |
---|
936 | // singclap_divide_content(ph); |
---|
937 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
938 | //} |
---|
939 | #endif |
---|
940 | } |
---|
941 | } |
---|
942 | #endif |
---|
943 | |
---|
944 | poly pCleardenom(poly ph) |
---|
945 | { |
---|
946 | poly start=ph; |
---|
947 | number d, h; |
---|
948 | poly p; |
---|
949 | |
---|
950 | #ifdef HAVE_RINGS |
---|
951 | if (rField_is_Ring(currRing)) |
---|
952 | { |
---|
953 | pContent(ph); |
---|
954 | return start; |
---|
955 | } |
---|
956 | #endif |
---|
957 | if (rField_is_Zp() && TEST_OPT_INTSTRATEGY) return; |
---|
958 | p = ph; |
---|
959 | if(pNext(p)==NULL) |
---|
960 | { |
---|
961 | if (TEST_OPT_CONTENTSB) |
---|
962 | { |
---|
963 | number n=nGetDenom(pGetCoeff(p)); |
---|
964 | if (!nIsOne(n)) |
---|
965 | { |
---|
966 | number nn=nMult(pGetCoeff(p),n); |
---|
967 | nNormalize(nn); |
---|
968 | pSetCoeff(p,nn); |
---|
969 | } |
---|
970 | nDelete(&n); |
---|
971 | } |
---|
972 | else |
---|
973 | pSetCoeff(p,nInit(1)); |
---|
974 | } |
---|
975 | else |
---|
976 | { |
---|
977 | h = nInit(1); |
---|
978 | while (p!=NULL) |
---|
979 | { |
---|
980 | nNormalize(pGetCoeff(p)); |
---|
981 | d=nLcm(h,pGetCoeff(p),currRing); |
---|
982 | nDelete(&h); |
---|
983 | h=d; |
---|
984 | pIter(p); |
---|
985 | } |
---|
986 | /* contains the 1/lcm of all denominators */ |
---|
987 | if(!nIsOne(h)) |
---|
988 | { |
---|
989 | p = ph; |
---|
990 | while (p!=NULL) |
---|
991 | { |
---|
992 | /* should be: |
---|
993 | * number hh; |
---|
994 | * nGetDenom(p->coef,&hh); |
---|
995 | * nMult(&h,&hh,&d); |
---|
996 | * nNormalize(d); |
---|
997 | * nDelete(&hh); |
---|
998 | * nMult(d,p->coef,&hh); |
---|
999 | * nDelete(&d); |
---|
1000 | * nDelete(&(p->coef)); |
---|
1001 | * p->coef =hh; |
---|
1002 | */ |
---|
1003 | d=nMult(h,pGetCoeff(p)); |
---|
1004 | nNormalize(d); |
---|
1005 | pSetCoeff(p,d); |
---|
1006 | pIter(p); |
---|
1007 | } |
---|
1008 | nDelete(&h); |
---|
1009 | if (nGetChar()==1) |
---|
1010 | { |
---|
1011 | loop |
---|
1012 | { |
---|
1013 | h = nInit(1); |
---|
1014 | p=ph; |
---|
1015 | while (p!=NULL) |
---|
1016 | { |
---|
1017 | d=nLcm(h,pGetCoeff(p),currRing); |
---|
1018 | nDelete(&h); |
---|
1019 | h=d; |
---|
1020 | pIter(p); |
---|
1021 | } |
---|
1022 | /* contains the 1/lcm of all denominators */ |
---|
1023 | if(!nIsOne(h)) |
---|
1024 | { |
---|
1025 | p = ph; |
---|
1026 | while (p!=NULL) |
---|
1027 | { |
---|
1028 | /* should be: |
---|
1029 | * number hh; |
---|
1030 | * nGetDenom(p->coef,&hh); |
---|
1031 | * nMult(&h,&hh,&d); |
---|
1032 | * nNormalize(d); |
---|
1033 | * nDelete(&hh); |
---|
1034 | * nMult(d,p->coef,&hh); |
---|
1035 | * nDelete(&d); |
---|
1036 | * nDelete(&(p->coef)); |
---|
1037 | * p->coef =hh; |
---|
1038 | */ |
---|
1039 | d=nMult(h,pGetCoeff(p)); |
---|
1040 | nNormalize(d); |
---|
1041 | pSetCoeff(p,d); |
---|
1042 | pIter(p); |
---|
1043 | } |
---|
1044 | nDelete(&h); |
---|
1045 | } |
---|
1046 | else |
---|
1047 | { |
---|
1048 | nDelete(&h); |
---|
1049 | break; |
---|
1050 | } |
---|
1051 | } |
---|
1052 | } |
---|
1053 | } |
---|
1054 | if (h!=NULL) nDelete(&h); |
---|
1055 | |
---|
1056 | pContent(ph); |
---|
1057 | #ifdef HAVE_RATGRING |
---|
1058 | if (rIsRatGRing(currRing)) |
---|
1059 | { |
---|
1060 | pContentRat(ph); |
---|
1061 | start=ph; |
---|
1062 | } |
---|
1063 | #endif |
---|
1064 | } |
---|
1065 | return start; |
---|
1066 | } |
---|
1067 | |
---|
1068 | void pCleardenom_n(poly ph,number &c) |
---|
1069 | { |
---|
1070 | number d, h; |
---|
1071 | poly p; |
---|
1072 | |
---|
1073 | p = ph; |
---|
1074 | if(pNext(p)==NULL) |
---|
1075 | { |
---|
1076 | c=nInvers(pGetCoeff(p)); |
---|
1077 | pSetCoeff(p,nInit(1)); |
---|
1078 | } |
---|
1079 | else |
---|
1080 | { |
---|
1081 | h = nInit(1); |
---|
1082 | while (p!=NULL) |
---|
1083 | { |
---|
1084 | nNormalize(pGetCoeff(p)); |
---|
1085 | d=nLcm(h,pGetCoeff(p),currRing); |
---|
1086 | nDelete(&h); |
---|
1087 | h=d; |
---|
1088 | pIter(p); |
---|
1089 | } |
---|
1090 | c=h; |
---|
1091 | /* contains the 1/lcm of all denominators */ |
---|
1092 | if(!nIsOne(h)) |
---|
1093 | { |
---|
1094 | p = ph; |
---|
1095 | while (p!=NULL) |
---|
1096 | { |
---|
1097 | /* should be: |
---|
1098 | * number hh; |
---|
1099 | * nGetDenom(p->coef,&hh); |
---|
1100 | * nMult(&h,&hh,&d); |
---|
1101 | * nNormalize(d); |
---|
1102 | * nDelete(&hh); |
---|
1103 | * nMult(d,p->coef,&hh); |
---|
1104 | * nDelete(&d); |
---|
1105 | * nDelete(&(p->coef)); |
---|
1106 | * p->coef =hh; |
---|
1107 | */ |
---|
1108 | d=nMult(h,pGetCoeff(p)); |
---|
1109 | nNormalize(d); |
---|
1110 | pSetCoeff(p,d); |
---|
1111 | pIter(p); |
---|
1112 | } |
---|
1113 | if (nGetChar()==1) |
---|
1114 | { |
---|
1115 | loop |
---|
1116 | { |
---|
1117 | h = nInit(1); |
---|
1118 | p=ph; |
---|
1119 | while (p!=NULL) |
---|
1120 | { |
---|
1121 | d=nLcm(h,pGetCoeff(p),currRing); |
---|
1122 | nDelete(&h); |
---|
1123 | h=d; |
---|
1124 | pIter(p); |
---|
1125 | } |
---|
1126 | /* contains the 1/lcm of all denominators */ |
---|
1127 | if(!nIsOne(h)) |
---|
1128 | { |
---|
1129 | p = ph; |
---|
1130 | while (p!=NULL) |
---|
1131 | { |
---|
1132 | /* should be: |
---|
1133 | * number hh; |
---|
1134 | * nGetDenom(p->coef,&hh); |
---|
1135 | * nMult(&h,&hh,&d); |
---|
1136 | * nNormalize(d); |
---|
1137 | * nDelete(&hh); |
---|
1138 | * nMult(d,p->coef,&hh); |
---|
1139 | * nDelete(&d); |
---|
1140 | * nDelete(&(p->coef)); |
---|
1141 | * p->coef =hh; |
---|
1142 | */ |
---|
1143 | d=nMult(h,pGetCoeff(p)); |
---|
1144 | nNormalize(d); |
---|
1145 | pSetCoeff(p,d); |
---|
1146 | pIter(p); |
---|
1147 | } |
---|
1148 | number t=nMult(c,h); |
---|
1149 | nDelete(&c); |
---|
1150 | c=t; |
---|
1151 | } |
---|
1152 | else |
---|
1153 | { |
---|
1154 | break; |
---|
1155 | } |
---|
1156 | nDelete(&h); |
---|
1157 | } |
---|
1158 | } |
---|
1159 | } |
---|
1160 | } |
---|
1161 | } |
---|
1162 | |
---|
1163 | /*2 |
---|
1164 | *tests if p is homogeneous with respect to the actual weigths |
---|
1165 | */ |
---|
1166 | BOOLEAN pIsHomogeneous (poly p) |
---|
1167 | { |
---|
1168 | poly qp=p; |
---|
1169 | int o; |
---|
1170 | |
---|
1171 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
1172 | pFDegProc d=(pLexOrder ? pTotaldegree : pFDeg ); |
---|
1173 | o = d(p,currRing); |
---|
1174 | do |
---|
1175 | { |
---|
1176 | if (d(qp,currRing) != o) return FALSE; |
---|
1177 | pIter(qp); |
---|
1178 | } |
---|
1179 | while (qp != NULL); |
---|
1180 | return TRUE; |
---|
1181 | } |
---|
1182 | |
---|
1183 | // orders monoms of poly using merge sort (ususally faster than |
---|
1184 | // insertion sort). ASSUMES that pSetm was performed on monoms |
---|
1185 | poly pOrdPolyMerge(poly p) |
---|
1186 | { |
---|
1187 | poly qq,pp,result=NULL; |
---|
1188 | |
---|
1189 | if (p == NULL) return NULL; |
---|
1190 | |
---|
1191 | loop |
---|
1192 | { |
---|
1193 | qq = p; |
---|
1194 | loop |
---|
1195 | { |
---|
1196 | if (pNext(p) == NULL) |
---|
1197 | { |
---|
1198 | result=pAdd(result, qq); |
---|
1199 | pTest(result); |
---|
1200 | return result; |
---|
1201 | } |
---|
1202 | if (pLmCmp(p,pNext(p)) != 1) |
---|
1203 | { |
---|
1204 | pp = p; |
---|
1205 | pIter(p); |
---|
1206 | pNext(pp) = NULL; |
---|
1207 | result = pAdd(result, qq); |
---|
1208 | break; |
---|
1209 | } |
---|
1210 | pIter(p); |
---|
1211 | } |
---|
1212 | } |
---|
1213 | } |
---|
1214 | |
---|
1215 | // orders monoms of poly using insertion sort, performs pSetm on each monom |
---|
1216 | poly pOrdPolyInsertSetm(poly p) |
---|
1217 | { |
---|
1218 | poly qq,result = NULL; |
---|
1219 | |
---|
1220 | #if 0 |
---|
1221 | while (p != NULL) |
---|
1222 | { |
---|
1223 | qq = p; |
---|
1224 | pIter(p); |
---|
1225 | qq->next = NULL; |
---|
1226 | pSetm(qq); |
---|
1227 | result = pAdd(result,qq); |
---|
1228 | pTest(result); |
---|
1229 | } |
---|
1230 | #else |
---|
1231 | while (p != NULL) |
---|
1232 | { |
---|
1233 | qq = p; |
---|
1234 | pIter(p); |
---|
1235 | qq->next = result; |
---|
1236 | result = qq; |
---|
1237 | pSetm(qq); |
---|
1238 | } |
---|
1239 | p = result; |
---|
1240 | result = NULL; |
---|
1241 | while (p != NULL) |
---|
1242 | { |
---|
1243 | qq = p; |
---|
1244 | pIter(p); |
---|
1245 | qq->next = NULL; |
---|
1246 | result = pAdd(result, qq); |
---|
1247 | } |
---|
1248 | pTest(result); |
---|
1249 | #endif |
---|
1250 | return result; |
---|
1251 | } |
---|
1252 | |
---|
1253 | /*2 |
---|
1254 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
1255 | */ |
---|
1256 | poly pPermPoly (poly p, int * perm, const ring oldRing, nMapFunc nMap, |
---|
1257 | int *par_perm, int OldPar) |
---|
1258 | { |
---|
1259 | int OldpVariables = oldRing->N; |
---|
1260 | poly result = NULL; |
---|
1261 | poly result_last = NULL; |
---|
1262 | poly aq=NULL; /* the map coefficient */ |
---|
1263 | poly qq; /* the mapped monomial */ |
---|
1264 | |
---|
1265 | while (p != NULL) |
---|
1266 | { |
---|
1267 | if ((OldPar==0)||(rField_is_GF(oldRing))) |
---|
1268 | { |
---|
1269 | qq = pInit(); |
---|
1270 | number n=nMap(pGetCoeff(p)); |
---|
1271 | if ((currRing->minpoly!=NULL) |
---|
1272 | && ((rField_is_Zp_a()) || (rField_is_Q_a()))) |
---|
1273 | { |
---|
1274 | nNormalize(n); |
---|
1275 | } |
---|
1276 | pGetCoeff(qq)=n; |
---|
1277 | // coef may be zero: pTest(qq); |
---|
1278 | } |
---|
1279 | else |
---|
1280 | { |
---|
1281 | qq=pOne(); |
---|
1282 | aq=naPermNumber(pGetCoeff(p),par_perm,OldPar, oldRing); |
---|
1283 | if ((currRing->minpoly!=NULL) |
---|
1284 | && ((rField_is_Zp_a()) || (rField_is_Q_a()))) |
---|
1285 | { |
---|
1286 | poly tmp=aq; |
---|
1287 | while (tmp!=NULL) |
---|
1288 | { |
---|
1289 | number n=pGetCoeff(tmp); |
---|
1290 | nNormalize(n); |
---|
1291 | pGetCoeff(tmp)=n; |
---|
1292 | pIter(tmp); |
---|
1293 | } |
---|
1294 | } |
---|
1295 | pTest(aq); |
---|
1296 | } |
---|
1297 | if (rRing_has_Comp(currRing)) pSetComp(qq, p_GetComp(p,oldRing)); |
---|
1298 | if (nIsZero(pGetCoeff(qq))) |
---|
1299 | { |
---|
1300 | pDeleteLm(&qq); |
---|
1301 | } |
---|
1302 | else |
---|
1303 | { |
---|
1304 | int i; |
---|
1305 | int mapped_to_par=0; |
---|
1306 | for(i=1; i<=OldpVariables; i++) |
---|
1307 | { |
---|
1308 | int e=p_GetExp(p,i,oldRing); |
---|
1309 | if (e!=0) |
---|
1310 | { |
---|
1311 | if (perm==NULL) |
---|
1312 | { |
---|
1313 | pSetExp(qq,i, e); |
---|
1314 | } |
---|
1315 | else if (perm[i]>0) |
---|
1316 | pAddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/); |
---|
1317 | else if (perm[i]<0) |
---|
1318 | { |
---|
1319 | if (rField_is_GF()) |
---|
1320 | { |
---|
1321 | number c=pGetCoeff(qq); |
---|
1322 | number ee=nfPar(1); |
---|
1323 | number eee;nfPower(ee,e,&eee); //nfDelete(ee,currRing); |
---|
1324 | ee=nfMult(c,eee); |
---|
1325 | //nfDelete(c,currRing);nfDelete(eee,currRing); |
---|
1326 | pSetCoeff0(qq,ee); |
---|
1327 | } |
---|
1328 | else |
---|
1329 | { |
---|
1330 | lnumber c=(lnumber)pGetCoeff(qq); |
---|
1331 | if (c->z->next==NULL) |
---|
1332 | napAddExp(c->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/); |
---|
1333 | else /* more difficult: we have really to multiply: */ |
---|
1334 | { |
---|
1335 | lnumber mmc=(lnumber)naInit(1); |
---|
1336 | napSetExp(mmc->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/); |
---|
1337 | napSetm(mmc->z); |
---|
1338 | pGetCoeff(qq)=naMult((number)c,(number)mmc); |
---|
1339 | nDelete((number *)&c); |
---|
1340 | nDelete((number *)&mmc); |
---|
1341 | } |
---|
1342 | mapped_to_par=1; |
---|
1343 | } |
---|
1344 | } |
---|
1345 | else |
---|
1346 | { |
---|
1347 | /* this variable maps to 0 !*/ |
---|
1348 | pDeleteLm(&qq); |
---|
1349 | break; |
---|
1350 | } |
---|
1351 | } |
---|
1352 | } |
---|
1353 | if (mapped_to_par |
---|
1354 | && (currRing->minpoly!=NULL)) |
---|
1355 | { |
---|
1356 | number n=pGetCoeff(qq); |
---|
1357 | nNormalize(n); |
---|
1358 | pGetCoeff(qq)=n; |
---|
1359 | } |
---|
1360 | } |
---|
1361 | pIter(p); |
---|
1362 | #if 1 |
---|
1363 | if (qq!=NULL) |
---|
1364 | { |
---|
1365 | pSetm(qq); |
---|
1366 | pTest(aq); |
---|
1367 | pTest(qq); |
---|
1368 | if (aq!=NULL) qq=pMult(aq,qq); |
---|
1369 | aq = qq; |
---|
1370 | while (pNext(aq) != NULL) pIter(aq); |
---|
1371 | if (result_last==NULL) |
---|
1372 | { |
---|
1373 | result=qq; |
---|
1374 | } |
---|
1375 | else |
---|
1376 | { |
---|
1377 | pNext(result_last)=qq; |
---|
1378 | } |
---|
1379 | result_last=aq; |
---|
1380 | aq = NULL; |
---|
1381 | } |
---|
1382 | else if (aq!=NULL) |
---|
1383 | { |
---|
1384 | pDelete(&aq); |
---|
1385 | } |
---|
1386 | } |
---|
1387 | result=pSortAdd(result); |
---|
1388 | #else |
---|
1389 | // if (qq!=NULL) |
---|
1390 | // { |
---|
1391 | // pSetm(qq); |
---|
1392 | // pTest(qq); |
---|
1393 | // pTest(aq); |
---|
1394 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
1395 | // aq = qq; |
---|
1396 | // while (pNext(aq) != NULL) pIter(aq); |
---|
1397 | // pNext(aq) = result; |
---|
1398 | // aq = NULL; |
---|
1399 | // result = qq; |
---|
1400 | // } |
---|
1401 | // else if (aq!=NULL) |
---|
1402 | // { |
---|
1403 | // pDelete(&aq); |
---|
1404 | // } |
---|
1405 | //} |
---|
1406 | //p = result; |
---|
1407 | //result = NULL; |
---|
1408 | //while (p != NULL) |
---|
1409 | //{ |
---|
1410 | // qq = p; |
---|
1411 | // pIter(p); |
---|
1412 | // qq->next = NULL; |
---|
1413 | // result = pAdd(result, qq); |
---|
1414 | //} |
---|
1415 | #endif |
---|
1416 | pTest(result); |
---|
1417 | return result; |
---|
1418 | } |
---|
1419 | |
---|
1420 | #if 0 |
---|
1421 | /*2 |
---|
1422 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
1423 | */ |
---|
1424 | poly p_PermPoly (poly p, int * perm, ring oldRing, |
---|
1425 | int *par_perm, int OldPar, ring newRing) |
---|
1426 | { |
---|
1427 | int OldpVariables = oldRing->N; |
---|
1428 | poly result = NULL; |
---|
1429 | poly result_last = NULL; |
---|
1430 | poly aq=NULL; /* the map coefficient */ |
---|
1431 | poly qq; /* the mapped monomial */ |
---|
1432 | |
---|
1433 | while (p != NULL) |
---|
1434 | { |
---|
1435 | if (OldPar==0) |
---|
1436 | { |
---|
1437 | qq = pInit(); |
---|
1438 | number n=newRing->cf->nMap(pGetCoeff(p)); |
---|
1439 | if ((newRing->minpoly!=NULL) |
---|
1440 | && ((rField_is_Zp_a(newRing)) || (rField_is_Q_a(newRing)))) |
---|
1441 | { |
---|
1442 | newRing->cf->nNormalize(n); |
---|
1443 | } |
---|
1444 | pGetCoeff(qq)=n; |
---|
1445 | // coef may be zero: pTest(qq); |
---|
1446 | } |
---|
1447 | else |
---|
1448 | { |
---|
1449 | qq=p_ISet(1, newRing); |
---|
1450 | aq=naPermNumber(pGetCoeff(p),par_perm,OldPar, oldRing); |
---|
1451 | if ((newRing->minpoly!=NULL) |
---|
1452 | && ((rField_is_Zp_a(newRing)) || (rField_is_Q_a(newRing)))) |
---|
1453 | { |
---|
1454 | poly tmp=aq; |
---|
1455 | while (tmp!=NULL) |
---|
1456 | { |
---|
1457 | number n=pGetCoeff(tmp); |
---|
1458 | newRing->cf->nNormalize(n); |
---|
1459 | pGetCoeff(tmp)=n; |
---|
1460 | pIter(tmp); |
---|
1461 | } |
---|
1462 | } |
---|
1463 | //pTest(aq); |
---|
1464 | } |
---|
1465 | p_SetComp(qq, p_GetComp(p,oldRing), newRing); |
---|
1466 | if (newRing->cf->nIsZero(pGetCoeff(qq))) |
---|
1467 | { |
---|
1468 | p_DeleteLm(&qq, newRing); |
---|
1469 | } |
---|
1470 | else |
---|
1471 | { |
---|
1472 | int i; |
---|
1473 | int mapped_to_par=0; |
---|
1474 | for(i=1; i<=OldpVariables; i++) |
---|
1475 | { |
---|
1476 | int e=p_GetExp(p,i,oldRing); |
---|
1477 | if (e!=0) |
---|
1478 | { |
---|
1479 | if (perm==NULL) |
---|
1480 | { |
---|
1481 | p_SetExp(qq,i, e, newRing); |
---|
1482 | } |
---|
1483 | else if (perm[i]>0) |
---|
1484 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, newRing); |
---|
1485 | else if (perm[i]<0) |
---|
1486 | { |
---|
1487 | lnumber c=(lnumber)pGetCoeff(qq); |
---|
1488 | napAddExp(c->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/); |
---|
1489 | mapped_to_par=1; |
---|
1490 | } |
---|
1491 | else |
---|
1492 | { |
---|
1493 | /* this variable maps to 0 !*/ |
---|
1494 | p_DeleteLm(&qq, newRing); |
---|
1495 | break; |
---|
1496 | } |
---|
1497 | } |
---|
1498 | } |
---|
1499 | if (mapped_to_par |
---|
1500 | && (newRing->minpoly!=NULL)) |
---|
1501 | { |
---|
1502 | number n=pGetCoeff(qq); |
---|
1503 | newRing->cf->nNormalize(n); |
---|
1504 | pGetCoeff(qq)=n; |
---|
1505 | } |
---|
1506 | } |
---|
1507 | pIter(p); |
---|
1508 | if (qq!=NULL) |
---|
1509 | { |
---|
1510 | p_Setm(qq, newRing); |
---|
1511 | //pTest(aq); |
---|
1512 | //pTest(qq); |
---|
1513 | if (aq!=NULL) qq=pMult(aq,qq); |
---|
1514 | aq = qq; |
---|
1515 | while (pNext(aq) != NULL) pIter(aq); |
---|
1516 | if (result_last==NULL) |
---|
1517 | { |
---|
1518 | result=qq; |
---|
1519 | } |
---|
1520 | else |
---|
1521 | { |
---|
1522 | pNext(result_last)=qq; |
---|
1523 | } |
---|
1524 | result_last=aq; |
---|
1525 | aq = NULL; |
---|
1526 | } |
---|
1527 | else if (aq!=NULL) |
---|
1528 | { |
---|
1529 | p_Delete(&aq, newRing); |
---|
1530 | } |
---|
1531 | } |
---|
1532 | result=pOrdPolyMerge(result); |
---|
1533 | //pTest(result); |
---|
1534 | return result; |
---|
1535 | } |
---|
1536 | #endif |
---|
1537 | |
---|
1538 | poly ppJet(poly p, int m) |
---|
1539 | { |
---|
1540 | poly r=NULL; |
---|
1541 | poly t=NULL; |
---|
1542 | |
---|
1543 | while (p!=NULL) |
---|
1544 | { |
---|
1545 | if (pTotaldegree(p)<=m) |
---|
1546 | { |
---|
1547 | if (r==NULL) |
---|
1548 | r=pHead(p); |
---|
1549 | else |
---|
1550 | if (t==NULL) |
---|
1551 | { |
---|
1552 | pNext(r)=pHead(p); |
---|
1553 | t=pNext(r); |
---|
1554 | } |
---|
1555 | else |
---|
1556 | { |
---|
1557 | pNext(t)=pHead(p); |
---|
1558 | pIter(t); |
---|
1559 | } |
---|
1560 | } |
---|
1561 | pIter(p); |
---|
1562 | } |
---|
1563 | return r; |
---|
1564 | } |
---|
1565 | |
---|
1566 | poly pJet(poly p, int m) |
---|
1567 | { |
---|
1568 | poly t=NULL; |
---|
1569 | |
---|
1570 | while((p!=NULL) && (pTotaldegree(p)>m)) pLmDelete(&p); |
---|
1571 | if (p==NULL) return NULL; |
---|
1572 | poly r=p; |
---|
1573 | while (pNext(p)!=NULL) |
---|
1574 | { |
---|
1575 | if (pTotaldegree(pNext(p))>m) |
---|
1576 | { |
---|
1577 | pLmDelete(&pNext(p)); |
---|
1578 | } |
---|
1579 | else |
---|
1580 | pIter(p); |
---|
1581 | } |
---|
1582 | return r; |
---|
1583 | } |
---|
1584 | |
---|
1585 | poly ppJetW(poly p, int m, short *w) |
---|
1586 | { |
---|
1587 | poly r=NULL; |
---|
1588 | poly t=NULL; |
---|
1589 | while (p!=NULL) |
---|
1590 | { |
---|
1591 | if (totaldegreeWecart_IV(p,currRing,w)<=m) |
---|
1592 | { |
---|
1593 | if (r==NULL) |
---|
1594 | r=pHead(p); |
---|
1595 | else |
---|
1596 | if (t==NULL) |
---|
1597 | { |
---|
1598 | pNext(r)=pHead(p); |
---|
1599 | t=pNext(r); |
---|
1600 | } |
---|
1601 | else |
---|
1602 | { |
---|
1603 | pNext(t)=pHead(p); |
---|
1604 | pIter(t); |
---|
1605 | } |
---|
1606 | } |
---|
1607 | pIter(p); |
---|
1608 | } |
---|
1609 | return r; |
---|
1610 | } |
---|
1611 | |
---|
1612 | poly pJetW(poly p, int m, short *w) |
---|
1613 | { |
---|
1614 | poly t=NULL; |
---|
1615 | while((p!=NULL) && (totaldegreeWecart_IV(p,currRing,w)>m)) pLmDelete(&p); |
---|
1616 | if (p==NULL) return NULL; |
---|
1617 | poly r=p; |
---|
1618 | while (pNext(p)!=NULL) |
---|
1619 | { |
---|
1620 | if (totaldegreeWecart_IV(pNext(p),currRing,w)>m) |
---|
1621 | { |
---|
1622 | pLmDelete(&pNext(p)); |
---|
1623 | } |
---|
1624 | else |
---|
1625 | pIter(p); |
---|
1626 | } |
---|
1627 | return r; |
---|
1628 | } |
---|
1629 | |
---|
1630 | int pMinDeg(poly p,intvec *w) |
---|
1631 | { |
---|
1632 | if(p==NULL) |
---|
1633 | return -1; |
---|
1634 | int d=-1; |
---|
1635 | while(p!=NULL) |
---|
1636 | { |
---|
1637 | int d0=0; |
---|
1638 | for(int j=0;j<pVariables;j++) |
---|
1639 | if(w==NULL||j>=w->length()) |
---|
1640 | d0+=pGetExp(p,j+1); |
---|
1641 | else |
---|
1642 | d0+=(*w)[j]*pGetExp(p,j+1); |
---|
1643 | if(d0<d||d==-1) |
---|
1644 | d=d0; |
---|
1645 | pIter(p); |
---|
1646 | } |
---|
1647 | return d; |
---|
1648 | } |
---|
1649 | |
---|
1650 | poly pSeries(int n,poly p,poly u, intvec *w) |
---|
1651 | { |
---|
1652 | short *ww=iv2array(w); |
---|
1653 | if(p!=NULL) |
---|
1654 | { |
---|
1655 | if(u==NULL) |
---|
1656 | p=pJetW(p,n,ww); |
---|
1657 | else |
---|
1658 | p=pJetW(pMult(p,pInvers(n-pMinDeg(p,w),u,w)),n,ww); |
---|
1659 | } |
---|
1660 | omFreeSize((ADDRESS)ww,(pVariables+1)*sizeof(short)); |
---|
1661 | return p; |
---|
1662 | } |
---|
1663 | |
---|
1664 | poly pInvers(int n,poly u,intvec *w) |
---|
1665 | { |
---|
1666 | short *ww=iv2array(w); |
---|
1667 | if(n<0) |
---|
1668 | return NULL; |
---|
1669 | number u0=nInvers(pGetCoeff(u)); |
---|
1670 | poly v=pNSet(u0); |
---|
1671 | if(n==0) |
---|
1672 | return v; |
---|
1673 | poly u1=pJetW(pSub(pOne(),pMult_nn(u,u0)),n,ww); |
---|
1674 | if(u1==NULL) |
---|
1675 | return v; |
---|
1676 | poly v1=pMult_nn(pCopy(u1),u0); |
---|
1677 | v=pAdd(v,pCopy(v1)); |
---|
1678 | for(int i=n/pMinDeg(u1,w);i>1;i--) |
---|
1679 | { |
---|
1680 | v1=pJetW(pMult(v1,pCopy(u1)),n,ww); |
---|
1681 | v=pAdd(v,pCopy(v1)); |
---|
1682 | } |
---|
1683 | pDelete(&u1); |
---|
1684 | pDelete(&v1); |
---|
1685 | omFreeSize((ADDRESS)ww,(pVariables+1)*sizeof(short)); |
---|
1686 | return v; |
---|
1687 | } |
---|
1688 | |
---|
1689 | long pDegW(poly p, const short *w) |
---|
1690 | { |
---|
1691 | long r=-LONG_MAX; |
---|
1692 | |
---|
1693 | while (p!=NULL) |
---|
1694 | { |
---|
1695 | long t=totaldegreeWecart_IV(p,currRing,w); |
---|
1696 | if (t>r) r=t; |
---|
1697 | pIter(p); |
---|
1698 | } |
---|
1699 | return r; |
---|
1700 | } |
---|
1701 | |
---|
1702 | /*-----------type conversions ----------------------------*/ |
---|
1703 | /*2 |
---|
1704 | * input: a set of polys (len elements: p[0]..p[len-1]) |
---|
1705 | * output: a vector |
---|
1706 | * p will not be changed |
---|
1707 | */ |
---|
1708 | poly pPolys2Vec(polyset p, int len) |
---|
1709 | { |
---|
1710 | poly v=NULL; |
---|
1711 | poly h; |
---|
1712 | int i; |
---|
1713 | |
---|
1714 | for (i=len-1; i>=0; i--) |
---|
1715 | { |
---|
1716 | if (p[i]) |
---|
1717 | { |
---|
1718 | h=pCopy(p[i]); |
---|
1719 | pSetCompP(h,i+1); |
---|
1720 | v=pAdd(v,h); |
---|
1721 | } |
---|
1722 | } |
---|
1723 | return v; |
---|
1724 | } |
---|
1725 | |
---|
1726 | /*2 |
---|
1727 | * convert a vector to a set of polys, |
---|
1728 | * allocates the polyset, (entries 0..(*len)-1) |
---|
1729 | * the vector will not be changed |
---|
1730 | */ |
---|
1731 | void pVec2Polys(poly v, polyset *p, int *len) |
---|
1732 | { |
---|
1733 | poly h; |
---|
1734 | int k; |
---|
1735 | |
---|
1736 | *len=pMaxComp(v); |
---|
1737 | if (*len==0) *len=1; |
---|
1738 | *p=(polyset)omAlloc0((*len)*sizeof(poly)); |
---|
1739 | while (v!=NULL) |
---|
1740 | { |
---|
1741 | h=pHead(v); |
---|
1742 | k=pGetComp(h); |
---|
1743 | pSetComp(h,0); |
---|
1744 | (*p)[k-1]=pAdd((*p)[k-1],h); |
---|
1745 | pIter(v); |
---|
1746 | } |
---|
1747 | } |
---|
1748 | |
---|
1749 | int p_Var(poly m,const ring r) |
---|
1750 | { |
---|
1751 | if (m==NULL) return 0; |
---|
1752 | if (pNext(m)!=NULL) return 0; |
---|
1753 | int i,e=0; |
---|
1754 | for (i=r->N; i>0; i--) |
---|
1755 | { |
---|
1756 | if (p_GetExp(m,i,r)==1) |
---|
1757 | { |
---|
1758 | if (e==0) e=i; |
---|
1759 | else return 0; |
---|
1760 | } |
---|
1761 | } |
---|
1762 | return e; |
---|
1763 | } |
---|
1764 | |
---|
1765 | /*----------utilities for syzygies--------------*/ |
---|
1766 | //BOOLEAN pVectorHasUnitM(poly p, int * k) |
---|
1767 | //{ |
---|
1768 | // while (p!=NULL) |
---|
1769 | // { |
---|
1770 | // if (pLmIsConstantComp(p)) |
---|
1771 | // { |
---|
1772 | // *k = pGetComp(p); |
---|
1773 | // return TRUE; |
---|
1774 | // } |
---|
1775 | // else pIter(p); |
---|
1776 | // } |
---|
1777 | // return FALSE; |
---|
1778 | //} |
---|
1779 | |
---|
1780 | BOOLEAN pVectorHasUnitB(poly p, int * k) |
---|
1781 | { |
---|
1782 | poly q=p,qq; |
---|
1783 | int i; |
---|
1784 | |
---|
1785 | while (q!=NULL) |
---|
1786 | { |
---|
1787 | if (pLmIsConstantComp(q)) |
---|
1788 | { |
---|
1789 | i = pGetComp(q); |
---|
1790 | qq = p; |
---|
1791 | while ((qq != q) && (pGetComp(qq) != i)) pIter(qq); |
---|
1792 | if (qq == q) |
---|
1793 | { |
---|
1794 | *k = i; |
---|
1795 | return TRUE; |
---|
1796 | } |
---|
1797 | else |
---|
1798 | pIter(q); |
---|
1799 | } |
---|
1800 | else pIter(q); |
---|
1801 | } |
---|
1802 | return FALSE; |
---|
1803 | } |
---|
1804 | |
---|
1805 | void pVectorHasUnit(poly p, int * k, int * len) |
---|
1806 | { |
---|
1807 | poly q=p,qq; |
---|
1808 | int i,j=0; |
---|
1809 | |
---|
1810 | *len = 0; |
---|
1811 | while (q!=NULL) |
---|
1812 | { |
---|
1813 | if (pLmIsConstantComp(q)) |
---|
1814 | { |
---|
1815 | i = pGetComp(q); |
---|
1816 | qq = p; |
---|
1817 | while ((qq != q) && (pGetComp(qq) != i)) pIter(qq); |
---|
1818 | if (qq == q) |
---|
1819 | { |
---|
1820 | j = 0; |
---|
1821 | while (qq!=NULL) |
---|
1822 | { |
---|
1823 | if (pGetComp(qq)==i) j++; |
---|
1824 | pIter(qq); |
---|
1825 | } |
---|
1826 | if ((*len == 0) || (j<*len)) |
---|
1827 | { |
---|
1828 | *len = j; |
---|
1829 | *k = i; |
---|
1830 | } |
---|
1831 | } |
---|
1832 | } |
---|
1833 | pIter(q); |
---|
1834 | } |
---|
1835 | } |
---|
1836 | |
---|
1837 | /*2 |
---|
1838 | * returns TRUE if p1 = p2 |
---|
1839 | */ |
---|
1840 | BOOLEAN p_EqualPolys(poly p1,poly p2, ring r) |
---|
1841 | { |
---|
1842 | while ((p1 != NULL) && (p2 != NULL)) |
---|
1843 | { |
---|
1844 | if (! p_LmEqual(p1, p2,r)) |
---|
1845 | return FALSE; |
---|
1846 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r )) |
---|
1847 | return FALSE; |
---|
1848 | pIter(p1); |
---|
1849 | pIter(p2); |
---|
1850 | } |
---|
1851 | return (p1==p2); |
---|
1852 | } |
---|
1853 | |
---|
1854 | /*2 |
---|
1855 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
1856 | *assume p1 != NULL and p2 != NULL |
---|
1857 | */ |
---|
1858 | BOOLEAN pComparePolys(poly p1,poly p2) |
---|
1859 | { |
---|
1860 | number n,nn; |
---|
1861 | int i; |
---|
1862 | pAssume(p1 != NULL && p2 != NULL); |
---|
1863 | |
---|
1864 | if (!pLmEqual(p1,p2)) //compare leading mons |
---|
1865 | return FALSE; |
---|
1866 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
---|
1867 | return FALSE; |
---|
1868 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
---|
1869 | return FALSE; |
---|
1870 | if (pLength(p1) != pLength(p2)) |
---|
1871 | return FALSE; |
---|
1872 | n=nDiv(pGetCoeff(p1),pGetCoeff(p2)); |
---|
1873 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
1874 | { |
---|
1875 | if ( ! pLmEqual(p1, p2)) |
---|
1876 | { |
---|
1877 | nDelete(&n); |
---|
1878 | return FALSE; |
---|
1879 | } |
---|
1880 | if (!nEqual(pGetCoeff(p1),nn=nMult(pGetCoeff(p2),n))) |
---|
1881 | { |
---|
1882 | nDelete(&n); |
---|
1883 | nDelete(&nn); |
---|
1884 | return FALSE; |
---|
1885 | } |
---|
1886 | nDelete(&nn); |
---|
1887 | pIter(p1); |
---|
1888 | pIter(p2); |
---|
1889 | } |
---|
1890 | nDelete(&n); |
---|
1891 | return TRUE; |
---|
1892 | } |
---|