1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /*************************************************************** |
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5 | * File: p_polys.cc |
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6 | * Purpose: implementation of currRing independent poly procedures |
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7 | * Author: obachman (Olaf Bachmann) |
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8 | * Created: 8/00 |
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9 | * Version: $Id$ |
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10 | *******************************************************************/ |
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11 | |
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12 | #include <ctype.h> |
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13 | |
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14 | #include <misc/auxiliary.h> |
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15 | |
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16 | #include <polys/monomials/ring.h> |
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17 | #include <polys/monomials/p_polys.h> |
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18 | #include <polys/monomials/ring.h> |
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19 | #include <coeffs/longrat.h> |
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20 | // #include <???/ideals.h> |
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21 | // #include <???/int64vec.h> |
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22 | #ifndef NDEBUG |
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23 | // #include <???/febase.h> |
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24 | #endif |
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25 | |
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26 | /*************************************************************** |
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27 | * |
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28 | * Completing what needs to be set for the monomial |
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29 | * |
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30 | ***************************************************************/ |
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31 | // this is special for the syz stuff |
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32 | static int* _components = NULL; |
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33 | static long* _componentsShifted = NULL; |
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34 | static int _componentsExternal = 0; |
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35 | |
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36 | BOOLEAN pSetm_error=0; |
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37 | |
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38 | #ifndef NDEBUG |
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39 | # define MYTEST 0 |
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40 | #else /* ifndef NDEBUG */ |
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41 | # define MYTEST 0 |
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42 | #endif /* ifndef NDEBUG */ |
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43 | |
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44 | void p_Setm_General(poly p, const ring r) |
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45 | { |
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46 | p_LmCheckPolyRing(p, r); |
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47 | int pos=0; |
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48 | if (r->typ!=NULL) |
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49 | { |
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50 | loop |
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51 | { |
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52 | long ord=0; |
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53 | sro_ord* o=&(r->typ[pos]); |
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54 | switch(o->ord_typ) |
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55 | { |
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56 | case ro_dp: |
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57 | { |
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58 | int a,e; |
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59 | a=o->data.dp.start; |
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60 | e=o->data.dp.end; |
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61 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
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62 | p->exp[o->data.dp.place]=ord; |
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63 | break; |
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64 | } |
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65 | case ro_wp_neg: |
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66 | ord=POLY_NEGWEIGHT_OFFSET; |
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67 | // no break; |
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68 | case ro_wp: |
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69 | { |
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70 | int a,e; |
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71 | a=o->data.wp.start; |
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72 | e=o->data.wp.end; |
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73 | int *w=o->data.wp.weights; |
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74 | #if 1 |
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75 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r)*w[i-a]; |
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76 | #else |
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77 | long ai; |
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78 | int ei,wi; |
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79 | for(int i=a;i<=e;i++) |
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80 | { |
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81 | ei=p_GetExp(p,i,r); |
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82 | wi=w[i-a]; |
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83 | ai=ei*wi; |
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84 | if (ai/ei!=wi) pSetm_error=TRUE; |
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85 | ord+=ai; |
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86 | if (ord<ai) pSetm_error=TRUE; |
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87 | } |
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88 | #endif |
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89 | p->exp[o->data.wp.place]=ord; |
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90 | break; |
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91 | } |
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92 | case ro_wp64: |
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93 | { |
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94 | int64 ord=0; |
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95 | int a,e; |
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96 | a=o->data.wp64.start; |
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97 | e=o->data.wp64.end; |
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98 | int64 *w=o->data.wp64.weights64; |
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99 | int64 ei,wi,ai; |
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100 | for(int i=a;i<=e;i++) |
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101 | { |
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102 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
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103 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
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104 | ei=(int64)p_GetExp(p,i,r); |
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105 | wi=w[i-a]; |
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106 | ai=ei*wi; |
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107 | if(ei!=0 && ai/ei!=wi) |
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108 | { |
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109 | pSetm_error=TRUE; |
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110 | #if SIZEOF_LONG == 4 |
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111 | Print("ai %lld, wi %lld\n",ai,wi); |
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112 | #else |
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113 | Print("ai %ld, wi %ld\n",ai,wi); |
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114 | #endif |
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115 | } |
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116 | ord+=ai; |
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117 | if (ord<ai) |
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118 | { |
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119 | pSetm_error=TRUE; |
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120 | #if SIZEOF_LONG == 4 |
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121 | Print("ai %lld, ord %lld\n",ai,ord); |
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122 | #else |
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123 | Print("ai %ld, ord %ld\n",ai,ord); |
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124 | #endif |
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125 | } |
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126 | } |
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127 | int64 mask=(int64)0x7fffffff; |
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128 | long a_0=(long)(ord&mask); //2^31 |
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129 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
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130 | |
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131 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
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132 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
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133 | //Print("mask: %d",mask); |
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134 | |
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135 | p->exp[o->data.wp64.place]=a_1; |
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136 | p->exp[o->data.wp64.place+1]=a_0; |
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137 | // if(p_Setm_error) Print("***************************\n |
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138 | // ***************************\n |
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139 | // **WARNING: overflow error**\n |
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140 | // ***************************\n |
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141 | // ***************************\n"); |
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142 | break; |
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143 | } |
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144 | case ro_cp: |
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145 | { |
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146 | int a,e; |
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147 | a=o->data.cp.start; |
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148 | e=o->data.cp.end; |
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149 | int pl=o->data.cp.place; |
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150 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
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151 | break; |
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152 | } |
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153 | case ro_syzcomp: |
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154 | { |
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155 | int c=p_GetComp(p,r); |
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156 | long sc = c; |
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157 | int* Components = (_componentsExternal ? _components : |
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158 | o->data.syzcomp.Components); |
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159 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
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160 | o->data.syzcomp.ShiftedComponents); |
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161 | if (ShiftedComponents != NULL) |
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162 | { |
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163 | assume(Components != NULL); |
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164 | assume(c == 0 || Components[c] != 0); |
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165 | sc = ShiftedComponents[Components[c]]; |
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166 | assume(c == 0 || sc != 0); |
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167 | } |
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168 | p->exp[o->data.syzcomp.place]=sc; |
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169 | break; |
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170 | } |
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171 | case ro_syz: |
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172 | { |
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173 | const unsigned long c = p_GetComp(p, r); |
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174 | const short place = o->data.syz.place; |
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175 | const int limit = o->data.syz.limit; |
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176 | |
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177 | if (c > limit) |
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178 | p->exp[place] = o->data.syz.curr_index; |
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179 | else if (c > 0) |
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180 | { |
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181 | assume( (1 <= c) && (c <= limit) ); |
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182 | p->exp[place]= o->data.syz.syz_index[c]; |
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183 | } |
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184 | else |
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185 | { |
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186 | assume(c == 0); |
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187 | p->exp[place]= 0; |
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188 | } |
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189 | break; |
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190 | } |
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191 | // Prefix for Induced Schreyer ordering |
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192 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
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193 | { |
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194 | assume(p != NULL); |
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195 | |
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196 | #ifndef NDEBUG |
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197 | #if MYTEST |
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198 | Print("p_Setm_General: isTemp ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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199 | #endif |
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200 | #endif |
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201 | int c = p_GetComp(p, r); |
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202 | |
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203 | assume( c >= 0 ); |
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204 | |
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205 | // Let's simulate case ro_syz above.... |
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206 | // Should accumulate (by Suffix) and be a level indicator |
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207 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
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208 | |
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209 | assume( pVarOffset != NULL ); |
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210 | |
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211 | // TODO: Can this be done in the suffix??? |
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212 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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213 | { |
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214 | const int vo = pVarOffset[i]; |
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215 | if( vo != -1) // TODO: optimize: can be done once! |
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216 | { |
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217 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
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218 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
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219 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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220 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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221 | } |
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222 | } |
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223 | |
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224 | #ifndef NDEBUG |
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225 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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226 | { |
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227 | const int vo = pVarOffset[i]; |
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228 | if( vo != -1) // TODO: optimize: can be done once! |
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229 | { |
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230 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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231 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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232 | } |
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233 | } |
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234 | #if MYTEST |
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235 | // if( p->exp[o->data.isTemp.start] > 0 ) |
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236 | // { |
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237 | // PrintS("Initial Value: "); p_DebugPrint(p, r, r, 1); |
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238 | // } |
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239 | #endif |
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240 | #endif |
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241 | break; |
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242 | } |
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243 | |
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244 | // Suffix for Induced Schreyer ordering |
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245 | case ro_is: |
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246 | { |
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247 | #ifndef NDEBUG |
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248 | #if MYTEST |
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249 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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250 | #endif |
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251 | #endif |
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252 | |
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253 | assume(p != NULL); |
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254 | |
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255 | int c = p_GetComp(p, r); |
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256 | |
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257 | assume( c >= 0 ); |
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258 | const ideal F = o->data.is.F; |
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259 | const int limit = o->data.is.limit; |
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260 | |
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261 | if( F != NULL && c > limit ) |
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262 | { |
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263 | #ifndef NDEBUG |
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264 | #if MYTEST |
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265 | Print("p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit); // p_DebugPrint(p, r, r, 1); |
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266 | #endif |
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267 | #endif |
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268 | |
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269 | c -= limit; |
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270 | assume( c > 0 ); |
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271 | c--; |
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272 | |
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273 | assume( c < IDELEMS(F) ); // What about others??? |
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274 | |
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275 | const poly pp = F->m[c]; // get reference monomial!!! |
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276 | |
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277 | #ifndef NDEBUG |
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278 | #if MYTEST |
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279 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
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280 | p_DebugPrint(pp, r, r, 1); |
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281 | #endif |
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282 | #endif |
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283 | |
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284 | |
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285 | assume(pp != NULL); |
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286 | if(pp == NULL) break; |
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287 | |
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288 | const int start = o->data.is.start; |
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289 | const int end = o->data.is.end; |
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290 | |
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291 | assume(start <= end); |
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292 | |
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293 | // const int limit = o->data.is.limit; |
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294 | assume( limit >= 0 ); |
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295 | |
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296 | // const int st = o->data.isTemp.start; |
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297 | |
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298 | if( c > limit ) |
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299 | p->exp[start] = 1; |
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300 | // else |
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301 | // p->exp[start] = 0; |
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302 | |
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303 | |
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304 | #ifndef NDEBUG |
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305 | Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]); |
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306 | #endif |
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307 | |
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308 | |
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309 | for( int i = start; i <= end; i++) // v[0] may be here... |
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310 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
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311 | |
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312 | |
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313 | |
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314 | |
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315 | #ifndef NDEBUG |
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316 | const int* const pVarOffset = o->data.is.pVarOffset; |
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317 | |
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318 | assume( pVarOffset != NULL ); |
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319 | |
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320 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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321 | { |
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322 | const int vo = pVarOffset[i]; |
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323 | if( vo != -1) // TODO: optimize: can be done once! |
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324 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
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325 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
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326 | } |
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327 | // TODO: how to check this for computed values??? |
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328 | #endif |
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329 | } else |
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330 | { |
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331 | const int* const pVarOffset = o->data.is.pVarOffset; |
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332 | |
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333 | // What about v[0] - component: it will be added later by |
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334 | // suffix!!! |
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335 | // TODO: Test it! |
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336 | const int vo = pVarOffset[0]; |
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337 | if( vo != -1 ) |
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338 | p->exp[vo] = c; // initial component v[0]! |
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339 | |
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340 | #ifndef NDEBUG |
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341 | #if MYTEST |
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342 | Print("p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]); |
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343 | p_DebugPrint(p, r, r, 1); |
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344 | #endif |
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345 | #endif |
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346 | } |
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347 | |
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348 | |
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349 | break; |
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350 | } |
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351 | default: |
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352 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
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353 | return; |
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354 | } |
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355 | pos++; |
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356 | if (pos == r->OrdSize) return; |
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357 | } |
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358 | } |
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359 | } |
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360 | |
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361 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
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362 | { |
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363 | _components = Components; |
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364 | _componentsShifted = ShiftedComponents; |
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365 | _componentsExternal = 1; |
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366 | p_Setm_General(p, r); |
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367 | _componentsExternal = 0; |
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368 | } |
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369 | |
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370 | // dummy for lp, ls, etc |
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371 | void p_Setm_Dummy(poly p, const ring r) |
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372 | { |
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373 | p_LmCheckPolyRing(p, r); |
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374 | } |
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375 | |
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376 | // for dp, Dp, ds, etc |
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377 | void p_Setm_TotalDegree(poly p, const ring r) |
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378 | { |
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379 | p_LmCheckPolyRing(p, r); |
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380 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
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381 | } |
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382 | |
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383 | // for wp, Wp, ws, etc |
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384 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
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385 | { |
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386 | p_LmCheckPolyRing(p, r); |
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387 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
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388 | } |
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389 | |
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390 | p_SetmProc p_GetSetmProc(ring r) |
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391 | { |
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392 | // covers lp, rp, ls, |
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393 | if (r->typ == NULL) return p_Setm_Dummy; |
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394 | |
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395 | if (r->OrdSize == 1) |
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396 | { |
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397 | if (r->typ[0].ord_typ == ro_dp && |
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398 | r->typ[0].data.dp.start == 1 && |
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399 | r->typ[0].data.dp.end == r->N && |
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400 | r->typ[0].data.dp.place == r->pOrdIndex) |
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401 | return p_Setm_TotalDegree; |
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402 | if (r->typ[0].ord_typ == ro_wp && |
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403 | r->typ[0].data.wp.start == 1 && |
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404 | r->typ[0].data.wp.end == r->N && |
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405 | r->typ[0].data.wp.place == r->pOrdIndex && |
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406 | r->typ[0].data.wp.weights == r->firstwv) |
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407 | return p_Setm_WFirstTotalDegree; |
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408 | } |
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409 | return p_Setm_General; |
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410 | } |
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411 | |
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412 | |
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413 | /* -------------------------------------------------------------------*/ |
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414 | /* several possibilities for pFDeg: the degree of the head term */ |
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415 | |
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416 | /* comptible with ordering */ |
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417 | long p_Deg(poly a, const ring r) |
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418 | { |
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419 | p_LmCheckPolyRing(a, r); |
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420 | assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); |
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421 | return p_GetOrder(a, r); |
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422 | } |
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423 | |
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424 | // p_WTotalDegree for weighted orderings |
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425 | // whose first block covers all variables |
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426 | long p_WFirstTotalDegree(poly p, const ring r) |
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427 | { |
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428 | int i; |
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429 | long sum = 0; |
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430 | |
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431 | for (i=1; i<= r->firstBlockEnds; i++) |
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432 | { |
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433 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
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434 | } |
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435 | return sum; |
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436 | } |
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437 | |
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438 | /*2 |
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439 | * compute the degree of the leading monomial of p |
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440 | * with respect to weigths from the ordering |
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441 | * the ordering is not compatible with degree so do not use p->Order |
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442 | */ |
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443 | long p_WTotaldegree(poly p, const ring r) |
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444 | { |
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445 | p_LmCheckPolyRing(p, r); |
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446 | int i, k; |
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447 | long j =0; |
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448 | |
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449 | // iterate through each block: |
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450 | for (i=0;r->order[i]!=0;i++) |
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451 | { |
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452 | int b0=r->block0[i]; |
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453 | int b1=r->block1[i]; |
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454 | switch(r->order[i]) |
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455 | { |
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456 | case ringorder_M: |
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457 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
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458 | { // in jedem block: |
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459 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
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460 | } |
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461 | break; |
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462 | case ringorder_wp: |
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463 | case ringorder_ws: |
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464 | case ringorder_Wp: |
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465 | case ringorder_Ws: |
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466 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
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467 | { // in jedem block: |
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468 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
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469 | } |
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470 | break; |
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471 | case ringorder_lp: |
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472 | case ringorder_ls: |
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473 | case ringorder_rs: |
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474 | case ringorder_dp: |
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475 | case ringorder_ds: |
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476 | case ringorder_Dp: |
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477 | case ringorder_Ds: |
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478 | case ringorder_rp: |
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479 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
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480 | { |
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481 | j+= p_GetExp(p,k,r); |
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482 | } |
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483 | break; |
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484 | case ringorder_a64: |
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485 | { |
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486 | int64* w=(int64*)r->wvhdl[i]; |
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487 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
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488 | { |
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489 | //there should be added a line which checks if w[k]>2^31 |
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490 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
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491 | } |
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492 | //break; |
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493 | return j; |
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494 | } |
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495 | case ringorder_c: |
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496 | case ringorder_C: |
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497 | case ringorder_S: |
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498 | case ringorder_s: |
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499 | case ringorder_IS: |
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500 | case ringorder_aa: |
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501 | break; |
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502 | case ringorder_a: |
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503 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
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504 | { // only one line |
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505 | j+= p_GetExp(p,k, r)*r->wvhdl[i][ k- b0 /*r->block0[i]*/]; |
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506 | } |
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507 | //break; |
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508 | return j; |
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509 | |
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510 | #ifndef NDEBUG |
---|
511 | default: |
---|
512 | Print("missing order %d in p_WTotaldegree\n",r->order[i]); |
---|
513 | break; |
---|
514 | #endif |
---|
515 | } |
---|
516 | } |
---|
517 | return j; |
---|
518 | } |
---|
519 | |
---|
520 | int p_Weight(int i, const ring r) |
---|
521 | { |
---|
522 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
523 | { |
---|
524 | return 1; |
---|
525 | } |
---|
526 | return r->firstwv[i-1]; |
---|
527 | } |
---|
528 | |
---|
529 | long p_WDegree(poly p, const ring r) |
---|
530 | { |
---|
531 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
532 | p_LmCheckPolyRing(p, r); |
---|
533 | int i; |
---|
534 | long j =0; |
---|
535 | |
---|
536 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
537 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
538 | |
---|
539 | for (;i<=r->N;i++) |
---|
540 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
541 | |
---|
542 | return j; |
---|
543 | } |
---|
544 | |
---|
545 | |
---|
546 | /* ---------------------------------------------------------------------*/ |
---|
547 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
548 | /* compute in l also the pLength of p */ |
---|
549 | |
---|
550 | /*2 |
---|
551 | * compute the length of a polynomial (in l) |
---|
552 | * and the degree of the monomial with maximal degree: the last one |
---|
553 | */ |
---|
554 | long pLDeg0(poly p,int *l, const ring r) |
---|
555 | { |
---|
556 | p_CheckPolyRing(p, r); |
---|
557 | long k= p_GetComp(p, r); |
---|
558 | int ll=1; |
---|
559 | |
---|
560 | if (k > 0) |
---|
561 | { |
---|
562 | while ((pNext(p)!=NULL) && (p_GetComp(pNext(p), r)==k)) |
---|
563 | { |
---|
564 | pIter(p); |
---|
565 | ll++; |
---|
566 | } |
---|
567 | } |
---|
568 | else |
---|
569 | { |
---|
570 | while (pNext(p)!=NULL) |
---|
571 | { |
---|
572 | pIter(p); |
---|
573 | ll++; |
---|
574 | } |
---|
575 | } |
---|
576 | *l=ll; |
---|
577 | return r->pFDeg(p, r); |
---|
578 | } |
---|
579 | |
---|
580 | /*2 |
---|
581 | * compute the length of a polynomial (in l) |
---|
582 | * and the degree of the monomial with maximal degree: the last one |
---|
583 | * but search in all components before syzcomp |
---|
584 | */ |
---|
585 | long pLDeg0c(poly p,int *l, const ring r) |
---|
586 | { |
---|
587 | assume(p!=NULL); |
---|
588 | #ifdef PDEBUG |
---|
589 | _p_Test(p,r,PDEBUG); |
---|
590 | #endif |
---|
591 | p_CheckPolyRing(p, r); |
---|
592 | long o; |
---|
593 | int ll=1; |
---|
594 | |
---|
595 | if (! rIsSyzIndexRing(r)) |
---|
596 | { |
---|
597 | while (pNext(p) != NULL) |
---|
598 | { |
---|
599 | pIter(p); |
---|
600 | ll++; |
---|
601 | } |
---|
602 | o = r->pFDeg(p, r); |
---|
603 | } |
---|
604 | else |
---|
605 | { |
---|
606 | int curr_limit = rGetCurrSyzLimit(r); |
---|
607 | poly pp = p; |
---|
608 | while ((p=pNext(p))!=NULL) |
---|
609 | { |
---|
610 | if (p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
611 | ll++; |
---|
612 | else break; |
---|
613 | pp = p; |
---|
614 | } |
---|
615 | #ifdef PDEBUG |
---|
616 | _p_Test(pp,r,PDEBUG); |
---|
617 | #endif |
---|
618 | o = r->pFDeg(pp, r); |
---|
619 | } |
---|
620 | *l=ll; |
---|
621 | return o; |
---|
622 | } |
---|
623 | |
---|
624 | /*2 |
---|
625 | * compute the length of a polynomial (in l) |
---|
626 | * and the degree of the monomial with maximal degree: the first one |
---|
627 | * this works for the polynomial case with degree orderings |
---|
628 | * (both c,dp and dp,c) |
---|
629 | */ |
---|
630 | long pLDegb(poly p,int *l, const ring r) |
---|
631 | { |
---|
632 | p_CheckPolyRing(p, r); |
---|
633 | long k= p_GetComp(p, r); |
---|
634 | long o = r->pFDeg(p, r); |
---|
635 | int ll=1; |
---|
636 | |
---|
637 | if (k != 0) |
---|
638 | { |
---|
639 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
640 | { |
---|
641 | ll++; |
---|
642 | } |
---|
643 | } |
---|
644 | else |
---|
645 | { |
---|
646 | while ((p=pNext(p)) !=NULL) |
---|
647 | { |
---|
648 | ll++; |
---|
649 | } |
---|
650 | } |
---|
651 | *l=ll; |
---|
652 | return o; |
---|
653 | } |
---|
654 | |
---|
655 | /*2 |
---|
656 | * compute the length of a polynomial (in l) |
---|
657 | * and the degree of the monomial with maximal degree: |
---|
658 | * this is NOT the last one, we have to look for it |
---|
659 | */ |
---|
660 | long pLDeg1(poly p,int *l, const ring r) |
---|
661 | { |
---|
662 | p_CheckPolyRing(p, r); |
---|
663 | long k= p_GetComp(p, r); |
---|
664 | int ll=1; |
---|
665 | long t,max; |
---|
666 | |
---|
667 | max=r->pFDeg(p, r); |
---|
668 | if (k > 0) |
---|
669 | { |
---|
670 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
671 | { |
---|
672 | t=r->pFDeg(p, r); |
---|
673 | if (t>max) max=t; |
---|
674 | ll++; |
---|
675 | } |
---|
676 | } |
---|
677 | else |
---|
678 | { |
---|
679 | while ((p=pNext(p))!=NULL) |
---|
680 | { |
---|
681 | t=r->pFDeg(p, r); |
---|
682 | if (t>max) max=t; |
---|
683 | ll++; |
---|
684 | } |
---|
685 | } |
---|
686 | *l=ll; |
---|
687 | return max; |
---|
688 | } |
---|
689 | |
---|
690 | /*2 |
---|
691 | * compute the length of a polynomial (in l) |
---|
692 | * and the degree of the monomial with maximal degree: |
---|
693 | * this is NOT the last one, we have to look for it |
---|
694 | * in all components |
---|
695 | */ |
---|
696 | long pLDeg1c(poly p,int *l, const ring r) |
---|
697 | { |
---|
698 | p_CheckPolyRing(p, r); |
---|
699 | int ll=1; |
---|
700 | long t,max; |
---|
701 | |
---|
702 | max=r->pFDeg(p, r); |
---|
703 | if (rIsSyzIndexRing(r)) |
---|
704 | { |
---|
705 | long limit = rGetCurrSyzLimit(r); |
---|
706 | while ((p=pNext(p))!=NULL) |
---|
707 | { |
---|
708 | if (p_GetComp(p, r)<=limit) |
---|
709 | { |
---|
710 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
711 | ll++; |
---|
712 | } |
---|
713 | else break; |
---|
714 | } |
---|
715 | } |
---|
716 | else |
---|
717 | { |
---|
718 | while ((p=pNext(p))!=NULL) |
---|
719 | { |
---|
720 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
721 | ll++; |
---|
722 | } |
---|
723 | } |
---|
724 | *l=ll; |
---|
725 | return max; |
---|
726 | } |
---|
727 | |
---|
728 | // like pLDeg1, only pFDeg == pDeg |
---|
729 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
730 | { |
---|
731 | assume(r->pFDeg == pDeg); |
---|
732 | p_CheckPolyRing(p, r); |
---|
733 | long k= p_GetComp(p, r); |
---|
734 | int ll=1; |
---|
735 | long t,max; |
---|
736 | |
---|
737 | max=p_GetOrder(p, r); |
---|
738 | if (k > 0) |
---|
739 | { |
---|
740 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
741 | { |
---|
742 | t=p_GetOrder(p, r); |
---|
743 | if (t>max) max=t; |
---|
744 | ll++; |
---|
745 | } |
---|
746 | } |
---|
747 | else |
---|
748 | { |
---|
749 | while ((p=pNext(p))!=NULL) |
---|
750 | { |
---|
751 | t=p_GetOrder(p, r); |
---|
752 | if (t>max) max=t; |
---|
753 | ll++; |
---|
754 | } |
---|
755 | } |
---|
756 | *l=ll; |
---|
757 | return max; |
---|
758 | } |
---|
759 | |
---|
760 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
761 | { |
---|
762 | assume(r->pFDeg == pDeg); |
---|
763 | p_CheckPolyRing(p, r); |
---|
764 | int ll=1; |
---|
765 | long t,max; |
---|
766 | |
---|
767 | max=p_GetOrder(p, r); |
---|
768 | if (rIsSyzIndexRing(r)) |
---|
769 | { |
---|
770 | long limit = rGetCurrSyzLimit(r); |
---|
771 | while ((p=pNext(p))!=NULL) |
---|
772 | { |
---|
773 | if (p_GetComp(p, r)<=limit) |
---|
774 | { |
---|
775 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
776 | ll++; |
---|
777 | } |
---|
778 | else break; |
---|
779 | } |
---|
780 | } |
---|
781 | else |
---|
782 | { |
---|
783 | while ((p=pNext(p))!=NULL) |
---|
784 | { |
---|
785 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
786 | ll++; |
---|
787 | } |
---|
788 | } |
---|
789 | *l=ll; |
---|
790 | return max; |
---|
791 | } |
---|
792 | |
---|
793 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
794 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
795 | { |
---|
796 | p_CheckPolyRing(p, r); |
---|
797 | long k= p_GetComp(p, r); |
---|
798 | int ll=1; |
---|
799 | long t,max; |
---|
800 | |
---|
801 | max=p_Totaldegree(p, r); |
---|
802 | if (k > 0) |
---|
803 | { |
---|
804 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
805 | { |
---|
806 | t=p_Totaldegree(p, r); |
---|
807 | if (t>max) max=t; |
---|
808 | ll++; |
---|
809 | } |
---|
810 | } |
---|
811 | else |
---|
812 | { |
---|
813 | while ((p=pNext(p))!=NULL) |
---|
814 | { |
---|
815 | t=p_Totaldegree(p, r); |
---|
816 | if (t>max) max=t; |
---|
817 | ll++; |
---|
818 | } |
---|
819 | } |
---|
820 | *l=ll; |
---|
821 | return max; |
---|
822 | } |
---|
823 | |
---|
824 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
825 | { |
---|
826 | p_CheckPolyRing(p, r); |
---|
827 | int ll=1; |
---|
828 | long t,max; |
---|
829 | |
---|
830 | max=p_Totaldegree(p, r); |
---|
831 | if (rIsSyzIndexRing(r)) |
---|
832 | { |
---|
833 | long limit = rGetCurrSyzLimit(r); |
---|
834 | while ((p=pNext(p))!=NULL) |
---|
835 | { |
---|
836 | if (p_GetComp(p, r)<=limit) |
---|
837 | { |
---|
838 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
839 | ll++; |
---|
840 | } |
---|
841 | else break; |
---|
842 | } |
---|
843 | } |
---|
844 | else |
---|
845 | { |
---|
846 | while ((p=pNext(p))!=NULL) |
---|
847 | { |
---|
848 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
849 | ll++; |
---|
850 | } |
---|
851 | } |
---|
852 | *l=ll; |
---|
853 | return max; |
---|
854 | } |
---|
855 | |
---|
856 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
857 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
858 | { |
---|
859 | p_CheckPolyRing(p, r); |
---|
860 | long k= p_GetComp(p, r); |
---|
861 | int ll=1; |
---|
862 | long t,max; |
---|
863 | |
---|
864 | max=p_WFirstTotalDegree(p, r); |
---|
865 | if (k > 0) |
---|
866 | { |
---|
867 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
868 | { |
---|
869 | t=p_WFirstTotalDegree(p, r); |
---|
870 | if (t>max) max=t; |
---|
871 | ll++; |
---|
872 | } |
---|
873 | } |
---|
874 | else |
---|
875 | { |
---|
876 | while ((p=pNext(p))!=NULL) |
---|
877 | { |
---|
878 | t=p_WFirstTotalDegree(p, r); |
---|
879 | if (t>max) max=t; |
---|
880 | ll++; |
---|
881 | } |
---|
882 | } |
---|
883 | *l=ll; |
---|
884 | return max; |
---|
885 | } |
---|
886 | |
---|
887 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
888 | { |
---|
889 | p_CheckPolyRing(p, r); |
---|
890 | int ll=1; |
---|
891 | long t,max; |
---|
892 | |
---|
893 | max=p_WFirstTotalDegree(p, r); |
---|
894 | if (rIsSyzIndexRing(r)) |
---|
895 | { |
---|
896 | long limit = rGetCurrSyzLimit(r); |
---|
897 | while ((p=pNext(p))!=NULL) |
---|
898 | { |
---|
899 | if (p_GetComp(p, r)<=limit) |
---|
900 | { |
---|
901 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
902 | ll++; |
---|
903 | } |
---|
904 | else break; |
---|
905 | } |
---|
906 | } |
---|
907 | else |
---|
908 | { |
---|
909 | while ((p=pNext(p))!=NULL) |
---|
910 | { |
---|
911 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
912 | ll++; |
---|
913 | } |
---|
914 | } |
---|
915 | *l=ll; |
---|
916 | return max; |
---|
917 | } |
---|
918 | |
---|
919 | /*************************************************************** |
---|
920 | * |
---|
921 | * Maximal Exponent business |
---|
922 | * |
---|
923 | ***************************************************************/ |
---|
924 | |
---|
925 | static inline unsigned long |
---|
926 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
927 | unsigned long number_of_exp) |
---|
928 | { |
---|
929 | const unsigned long bitmask = r->bitmask; |
---|
930 | unsigned long ml1 = l1 & bitmask; |
---|
931 | unsigned long ml2 = l2 & bitmask; |
---|
932 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
933 | unsigned long j = number_of_exp - 1; |
---|
934 | |
---|
935 | if (j > 0) |
---|
936 | { |
---|
937 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
938 | while (1) |
---|
939 | { |
---|
940 | ml1 = l1 & mask; |
---|
941 | ml2 = l2 & mask; |
---|
942 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
943 | j--; |
---|
944 | if (j == 0) break; |
---|
945 | mask = mask << r->BitsPerExp; |
---|
946 | } |
---|
947 | } |
---|
948 | return max; |
---|
949 | } |
---|
950 | |
---|
951 | static inline unsigned long |
---|
952 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
953 | { |
---|
954 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
955 | } |
---|
956 | |
---|
957 | poly p_GetMaxExpP(poly p, const ring r) |
---|
958 | { |
---|
959 | p_CheckPolyRing(p, r); |
---|
960 | if (p == NULL) return p_Init(r); |
---|
961 | poly max = p_LmInit(p, r); |
---|
962 | pIter(p); |
---|
963 | if (p == NULL) return max; |
---|
964 | int i, offset; |
---|
965 | unsigned long l_p, l_max; |
---|
966 | unsigned long divmask = r->divmask; |
---|
967 | |
---|
968 | do |
---|
969 | { |
---|
970 | offset = r->VarL_Offset[0]; |
---|
971 | l_p = p->exp[offset]; |
---|
972 | l_max = max->exp[offset]; |
---|
973 | // do the divisibility trick to find out whether l has an exponent |
---|
974 | if (l_p > l_max || |
---|
975 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
976 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
977 | |
---|
978 | for (i=1; i<r->VarL_Size; i++) |
---|
979 | { |
---|
980 | offset = r->VarL_Offset[i]; |
---|
981 | l_p = p->exp[offset]; |
---|
982 | l_max = max->exp[offset]; |
---|
983 | // do the divisibility trick to find out whether l has an exponent |
---|
984 | if (l_p > l_max || |
---|
985 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
986 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
987 | } |
---|
988 | pIter(p); |
---|
989 | } |
---|
990 | while (p != NULL); |
---|
991 | return max; |
---|
992 | } |
---|
993 | |
---|
994 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
995 | { |
---|
996 | unsigned long l_p, divmask = r->divmask; |
---|
997 | int i; |
---|
998 | |
---|
999 | while (p != NULL) |
---|
1000 | { |
---|
1001 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
1002 | if (l_p > l_max || |
---|
1003 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1004 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
1005 | for (i=1; i<r->VarL_Size; i++) |
---|
1006 | { |
---|
1007 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
1008 | // do the divisibility trick to find out whether l has an exponent |
---|
1009 | if (l_p > l_max || |
---|
1010 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1011 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
1012 | } |
---|
1013 | pIter(p); |
---|
1014 | } |
---|
1015 | return l_max; |
---|
1016 | } |
---|
1017 | |
---|
1018 | |
---|
1019 | |
---|
1020 | |
---|
1021 | /*************************************************************** |
---|
1022 | * |
---|
1023 | * Misc things |
---|
1024 | * |
---|
1025 | ***************************************************************/ |
---|
1026 | // returns TRUE, if all monoms have the same component |
---|
1027 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
1028 | { |
---|
1029 | if(p!=NULL) |
---|
1030 | { |
---|
1031 | long i = p_GetComp(p, r); |
---|
1032 | while (pNext(p)!=NULL) |
---|
1033 | { |
---|
1034 | pIter(p); |
---|
1035 | if(i != p_GetComp(p, r)) return FALSE; |
---|
1036 | } |
---|
1037 | } |
---|
1038 | return TRUE; |
---|
1039 | } |
---|
1040 | |
---|
1041 | /*2 |
---|
1042 | *test if a monomial /head term is a pure power |
---|
1043 | */ |
---|
1044 | int p_IsPurePower(const poly p, const ring r) |
---|
1045 | { |
---|
1046 | int i,k=0; |
---|
1047 | |
---|
1048 | for (i=r->N;i;i--) |
---|
1049 | { |
---|
1050 | if (p_GetExp(p,i, r)!=0) |
---|
1051 | { |
---|
1052 | if(k!=0) return 0; |
---|
1053 | k=i; |
---|
1054 | } |
---|
1055 | } |
---|
1056 | return k; |
---|
1057 | } |
---|
1058 | |
---|
1059 | /*2 |
---|
1060 | *test if a polynomial is univariate |
---|
1061 | * return -1 for constant, |
---|
1062 | * 0 for not univariate,s |
---|
1063 | * i if dep. on var(i) |
---|
1064 | */ |
---|
1065 | int p_IsUnivariate(poly p, const ring r) |
---|
1066 | { |
---|
1067 | int i,k=-1; |
---|
1068 | |
---|
1069 | while (p!=NULL) |
---|
1070 | { |
---|
1071 | for (i=r->N;i;i--) |
---|
1072 | { |
---|
1073 | if (p_GetExp(p,i, r)!=0) |
---|
1074 | { |
---|
1075 | if((k!=-1)&&(k!=i)) return 0; |
---|
1076 | k=i; |
---|
1077 | } |
---|
1078 | } |
---|
1079 | pIter(p); |
---|
1080 | } |
---|
1081 | return k; |
---|
1082 | } |
---|
1083 | |
---|
1084 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
1085 | int p_GetVariables(poly p, int * e, const ring r) |
---|
1086 | { |
---|
1087 | int i; |
---|
1088 | int n=0; |
---|
1089 | while(p!=NULL) |
---|
1090 | { |
---|
1091 | n=0; |
---|
1092 | for(i=r->N; i>0; i--) |
---|
1093 | { |
---|
1094 | if(e[i]==0) |
---|
1095 | { |
---|
1096 | if (p_GetExp(p,i,r)>0) |
---|
1097 | { |
---|
1098 | e[i]=1; |
---|
1099 | n++; |
---|
1100 | } |
---|
1101 | } |
---|
1102 | else |
---|
1103 | n++; |
---|
1104 | } |
---|
1105 | if (n==r->N) break; |
---|
1106 | pIter(p); |
---|
1107 | } |
---|
1108 | return n; |
---|
1109 | } |
---|
1110 | |
---|
1111 | |
---|
1112 | /*2 |
---|
1113 | * returns a polynomial representing the integer i |
---|
1114 | */ |
---|
1115 | poly p_ISet(int i, const ring r) |
---|
1116 | { |
---|
1117 | poly rc = NULL; |
---|
1118 | if (i!=0) |
---|
1119 | { |
---|
1120 | rc = p_Init(r); |
---|
1121 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
1122 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
1123 | p_LmDelete(&rc,r); |
---|
1124 | } |
---|
1125 | return rc; |
---|
1126 | } |
---|
1127 | |
---|
1128 | /*2 |
---|
1129 | * an optimized version of p_ISet for the special case 1 |
---|
1130 | */ |
---|
1131 | poly p_One(const ring r) |
---|
1132 | { |
---|
1133 | poly rc = p_Init(r); |
---|
1134 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
1135 | return rc; |
---|
1136 | } |
---|
1137 | |
---|
1138 | void p_Split(poly p, poly *h) |
---|
1139 | { |
---|
1140 | *h=pNext(p); |
---|
1141 | pNext(p)=NULL; |
---|
1142 | } |
---|
1143 | |
---|
1144 | /*2 |
---|
1145 | * pair has no common factor ? or is no polynomial |
---|
1146 | */ |
---|
1147 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
1148 | { |
---|
1149 | |
---|
1150 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
1151 | return FALSE; |
---|
1152 | int i = rVar(r); |
---|
1153 | loop |
---|
1154 | { |
---|
1155 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
1156 | return FALSE; |
---|
1157 | i--; |
---|
1158 | if (i == 0) |
---|
1159 | return TRUE; |
---|
1160 | } |
---|
1161 | } |
---|
1162 | |
---|
1163 | /*2 |
---|
1164 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
1165 | */ |
---|
1166 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
1167 | { |
---|
1168 | if (r==NULL) { rc=NULL;return st;} |
---|
1169 | int i,j; |
---|
1170 | rc = p_Init(r); |
---|
1171 | const char *s = r->cf->cfRead(st,&(rc->coef),r->cf); |
---|
1172 | if (s==st) |
---|
1173 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
1174 | { |
---|
1175 | j = r_IsRingVar(s,r); |
---|
1176 | if (j >= 0) |
---|
1177 | { |
---|
1178 | p_IncrExp(rc,1+j,r); |
---|
1179 | while (*s!='\0') s++; |
---|
1180 | goto done; |
---|
1181 | } |
---|
1182 | } |
---|
1183 | while (*s!='\0') |
---|
1184 | { |
---|
1185 | char ss[2]; |
---|
1186 | ss[0] = *s++; |
---|
1187 | ss[1] = '\0'; |
---|
1188 | j = r_IsRingVar(ss,r); |
---|
1189 | if (j >= 0) |
---|
1190 | { |
---|
1191 | const char *s_save=s; |
---|
1192 | s = eati(s,&i); |
---|
1193 | if (((unsigned long)i) > r->bitmask) |
---|
1194 | { |
---|
1195 | // exponent to large: it is not a monomial |
---|
1196 | p_LmDelete(&rc,r); |
---|
1197 | return s_save; |
---|
1198 | } |
---|
1199 | p_AddExp(rc,1+j, (long)i, r); |
---|
1200 | } |
---|
1201 | else |
---|
1202 | { |
---|
1203 | // 1st char of is not a varname |
---|
1204 | p_LmDelete(&rc,r); |
---|
1205 | s--; |
---|
1206 | return s; |
---|
1207 | } |
---|
1208 | } |
---|
1209 | done: |
---|
1210 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
1211 | else |
---|
1212 | { |
---|
1213 | #ifdef HAVE_PLURAL |
---|
1214 | // in super-commutative ring |
---|
1215 | // squares of anti-commutative variables are zeroes! |
---|
1216 | if(rIsSCA(r)) |
---|
1217 | { |
---|
1218 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
1219 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
1220 | |
---|
1221 | assume(rc != NULL); |
---|
1222 | |
---|
1223 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
1224 | if( p_GetExp(rc, k, r) > 1 ) |
---|
1225 | { |
---|
1226 | p_LmDelete(&rc, r); |
---|
1227 | goto finish; |
---|
1228 | } |
---|
1229 | } |
---|
1230 | #endif |
---|
1231 | |
---|
1232 | p_Setm(rc,r); |
---|
1233 | } |
---|
1234 | finish: |
---|
1235 | return s; |
---|
1236 | } |
---|
1237 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
1238 | { |
---|
1239 | poly p; |
---|
1240 | const char *s=p_Read(st,p,r); |
---|
1241 | if (*s!='\0') |
---|
1242 | { |
---|
1243 | if ((s!=st)&&isdigit(st[0])) |
---|
1244 | { |
---|
1245 | errorreported=TRUE; |
---|
1246 | } |
---|
1247 | ok=FALSE; |
---|
1248 | p_Delete(&p,r); |
---|
1249 | return NULL; |
---|
1250 | } |
---|
1251 | #ifdef PDEBUG |
---|
1252 | _p_Test(p,r,PDEBUG); |
---|
1253 | #endif |
---|
1254 | ok=!errorreported; |
---|
1255 | return p; |
---|
1256 | } |
---|
1257 | |
---|
1258 | /*2 |
---|
1259 | * returns a polynomial representing the number n |
---|
1260 | * destroys n |
---|
1261 | */ |
---|
1262 | poly p_NSet(number n, const ring r) |
---|
1263 | { |
---|
1264 | if (n_IsZero(n,r->cf)) |
---|
1265 | { |
---|
1266 | n_Delete(&n, r->cf); |
---|
1267 | return NULL; |
---|
1268 | } |
---|
1269 | else |
---|
1270 | { |
---|
1271 | poly rc = p_Init(r); |
---|
1272 | pSetCoeff0(rc,n); |
---|
1273 | return rc; |
---|
1274 | } |
---|
1275 | } |
---|
1276 | /*2 |
---|
1277 | * assumes that the head term of b is a multiple of the head term of a |
---|
1278 | * and return the multiplicant *m |
---|
1279 | * Frank's observation: If LM(b) = LM(a)*m, then we may actually set |
---|
1280 | * negative(!) exponents in the below loop. I suspect that the correct |
---|
1281 | * comment should be "assumes that LM(a) = LM(b)*m, for some monomial m..." |
---|
1282 | */ |
---|
1283 | poly p_Divide(poly a, poly b, const ring r) |
---|
1284 | { |
---|
1285 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
1286 | int i; |
---|
1287 | poly result = p_Init(r); |
---|
1288 | |
---|
1289 | for(i=(int)r->N; i; i--) |
---|
1290 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
1291 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
1292 | p_Setm(result,r); |
---|
1293 | return result; |
---|
1294 | } |
---|
1295 | |
---|
1296 | #ifdef HAVE_RINGS //TODO Oliver |
---|
1297 | |
---|
1298 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
1299 | { |
---|
1300 | pAssume(!n_IsZero(n,r)); |
---|
1301 | p_Test(p, r); |
---|
1302 | |
---|
1303 | poly q = p; |
---|
1304 | while (p != NULL) |
---|
1305 | { |
---|
1306 | number nc = pGetCoeff(p); |
---|
1307 | pSetCoeff0(p, n_Div(nc, n, r->cf)); |
---|
1308 | n_Delete(&nc, r->cf); |
---|
1309 | pIter(p); |
---|
1310 | } |
---|
1311 | p_Test(q, r); |
---|
1312 | return q; |
---|
1313 | } |
---|
1314 | #endif |
---|
1315 | |
---|
1316 | /*2 |
---|
1317 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
1318 | * assumes that b is not NULL |
---|
1319 | */ |
---|
1320 | poly p_DivideM(poly a, poly b, const ring r) |
---|
1321 | { |
---|
1322 | if (a==NULL) return NULL; |
---|
1323 | poly result=a; |
---|
1324 | poly prev=NULL; |
---|
1325 | int i; |
---|
1326 | #ifdef HAVE_RINGS |
---|
1327 | number inv=pGetCoeff(b); |
---|
1328 | #else |
---|
1329 | number inv=n_Invers(pGetCoeff(b),r->cf); |
---|
1330 | #endif |
---|
1331 | |
---|
1332 | while (a!=NULL) |
---|
1333 | { |
---|
1334 | if (p_DivisibleBy(b,a,r)) |
---|
1335 | { |
---|
1336 | for(i=(int)r->N; i; i--) |
---|
1337 | p_SubExp(a,i, p_GetExp(b,i,r),r); |
---|
1338 | p_SubComp(a, p_GetComp(b,r),r); |
---|
1339 | p_Setm(a,r); |
---|
1340 | prev=a; |
---|
1341 | pIter(a); |
---|
1342 | } |
---|
1343 | else |
---|
1344 | { |
---|
1345 | if (prev==NULL) |
---|
1346 | { |
---|
1347 | p_LmDelete(&result,r); |
---|
1348 | a=result; |
---|
1349 | } |
---|
1350 | else |
---|
1351 | { |
---|
1352 | p_LmDelete(&pNext(prev),r); |
---|
1353 | a=pNext(prev); |
---|
1354 | } |
---|
1355 | } |
---|
1356 | } |
---|
1357 | #ifdef HAVE_RINGS |
---|
1358 | if (n_IsUnit(inv,r->cf)) |
---|
1359 | { |
---|
1360 | inv = n_Invers(inv,r->cf); |
---|
1361 | p_Mult_nn(result,inv,r); |
---|
1362 | n_Delete(&inv, r->cf); |
---|
1363 | } |
---|
1364 | else |
---|
1365 | { |
---|
1366 | p_Div_nn(result,inv,r); |
---|
1367 | } |
---|
1368 | #else |
---|
1369 | p_Mult_nn(result,inv,r); |
---|
1370 | n_Delete(&inv, r->cf); |
---|
1371 | #endif |
---|
1372 | p_Delete(&b, r); |
---|
1373 | return result; |
---|
1374 | } |
---|
1375 | |
---|
1376 | /*2 |
---|
1377 | * returns the LCM of the head terms of a and b in *m |
---|
1378 | */ |
---|
1379 | void p_Lcm(poly a, poly b, poly m, const ring r) |
---|
1380 | { |
---|
1381 | int i; |
---|
1382 | for (i=rVar(r); i; i--) |
---|
1383 | { |
---|
1384 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
1385 | } |
---|
1386 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
1387 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
1388 | } |
---|
1389 | |
---|
1390 | /*2 |
---|
1391 | * returns the partial differentiate of a by the k-th variable |
---|
1392 | * does not destroy the input |
---|
1393 | */ |
---|
1394 | poly p_Diff(poly a, int k, const ring r) |
---|
1395 | { |
---|
1396 | poly res, f, last; |
---|
1397 | number t; |
---|
1398 | |
---|
1399 | last = res = NULL; |
---|
1400 | while (a!=NULL) |
---|
1401 | { |
---|
1402 | if (p_GetExp(a,k,r)!=0) |
---|
1403 | { |
---|
1404 | f = p_LmInit(a,r); |
---|
1405 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
1406 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
1407 | n_Delete(&t,r->cf); |
---|
1408 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
1409 | p_LmDelete(&f,r); |
---|
1410 | else |
---|
1411 | { |
---|
1412 | p_DecrExp(f,k,r); |
---|
1413 | p_Setm(f,r); |
---|
1414 | if (res==NULL) |
---|
1415 | { |
---|
1416 | res=last=f; |
---|
1417 | } |
---|
1418 | else |
---|
1419 | { |
---|
1420 | pNext(last)=f; |
---|
1421 | last=f; |
---|
1422 | } |
---|
1423 | } |
---|
1424 | } |
---|
1425 | pIter(a); |
---|
1426 | } |
---|
1427 | return res; |
---|
1428 | } |
---|
1429 | |
---|
1430 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
1431 | { |
---|
1432 | int i,j,s; |
---|
1433 | number n,h,hh; |
---|
1434 | poly p=p_One(r); |
---|
1435 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
1436 | for(i=rVar(r);i>0;i--) |
---|
1437 | { |
---|
1438 | s=p_GetExp(b,i,r); |
---|
1439 | if (s<p_GetExp(a,i,r)) |
---|
1440 | { |
---|
1441 | n_Delete(&n,r->cf); |
---|
1442 | p_LmDelete(&p,r); |
---|
1443 | return NULL; |
---|
1444 | } |
---|
1445 | if (multiply) |
---|
1446 | { |
---|
1447 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
1448 | { |
---|
1449 | h = n_Init(s,r->cf); |
---|
1450 | hh=n_Mult(n,h,r->cf); |
---|
1451 | n_Delete(&h,r->cf); |
---|
1452 | n_Delete(&n,r->cf); |
---|
1453 | n=hh; |
---|
1454 | s--; |
---|
1455 | } |
---|
1456 | p_SetExp(p,i,s,r); |
---|
1457 | } |
---|
1458 | else |
---|
1459 | { |
---|
1460 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
1461 | } |
---|
1462 | } |
---|
1463 | p_Setm(p,r); |
---|
1464 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
1465 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
1466 | return p; |
---|
1467 | } |
---|
1468 | |
---|
1469 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
1470 | { |
---|
1471 | poly result=NULL; |
---|
1472 | poly h; |
---|
1473 | for(;a!=NULL;pIter(a)) |
---|
1474 | { |
---|
1475 | for(h=b;h!=NULL;pIter(h)) |
---|
1476 | { |
---|
1477 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
1478 | } |
---|
1479 | } |
---|
1480 | return result; |
---|
1481 | } |
---|
1482 | /*2 |
---|
1483 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
1484 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
1485 | */ |
---|
1486 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
1487 | { |
---|
1488 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
1489 | } |
---|
1490 | |
---|
1491 | /*3 |
---|
1492 | * compute for a monomial m |
---|
1493 | * the power m^exp, exp > 1 |
---|
1494 | * destroys p |
---|
1495 | */ |
---|
1496 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
1497 | { |
---|
1498 | int i; |
---|
1499 | |
---|
1500 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
1501 | { |
---|
1502 | number x, y; |
---|
1503 | y = pGetCoeff(p); |
---|
1504 | n_Power(y,exp,&x,r->cf); |
---|
1505 | n_Delete(&y,r->cf); |
---|
1506 | pSetCoeff0(p,x); |
---|
1507 | } |
---|
1508 | for (i=rVar(r); i!=0; i--) |
---|
1509 | { |
---|
1510 | p_MultExp(p,i, exp,r); |
---|
1511 | } |
---|
1512 | p_Setm(p,r); |
---|
1513 | return p; |
---|
1514 | } |
---|
1515 | |
---|
1516 | /*3 |
---|
1517 | * compute for monomials p*q |
---|
1518 | * destroys p, keeps q |
---|
1519 | */ |
---|
1520 | static void p_MonMult(poly p, poly q, const ring r) |
---|
1521 | { |
---|
1522 | number x, y; |
---|
1523 | int i; |
---|
1524 | |
---|
1525 | y = pGetCoeff(p); |
---|
1526 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
1527 | n_Delete(&y,r->cf); |
---|
1528 | pSetCoeff0(p,x); |
---|
1529 | //for (i=pVariables; i!=0; i--) |
---|
1530 | //{ |
---|
1531 | // pAddExp(p,i, pGetExp(q,i)); |
---|
1532 | //} |
---|
1533 | //p->Order += q->Order; |
---|
1534 | p_ExpVectorAdd(p,q,r); |
---|
1535 | } |
---|
1536 | |
---|
1537 | /*3 |
---|
1538 | * compute for monomials p*q |
---|
1539 | * keeps p, q |
---|
1540 | */ |
---|
1541 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
1542 | { |
---|
1543 | number x; |
---|
1544 | int i; |
---|
1545 | poly r = p_Init(rr); |
---|
1546 | |
---|
1547 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
1548 | pSetCoeff0(r,x); |
---|
1549 | p_ExpVectorSum(r,p, q, rr); |
---|
1550 | return r; |
---|
1551 | } |
---|
1552 | |
---|
1553 | /*3 |
---|
1554 | * create binomial coef. |
---|
1555 | */ |
---|
1556 | static number* pnBin(int exp, const ring r) |
---|
1557 | { |
---|
1558 | int e, i, h; |
---|
1559 | number x, y, *bin=NULL; |
---|
1560 | |
---|
1561 | x = n_Init(exp,r->cf); |
---|
1562 | if (n_IsZero(x,r->cf)) |
---|
1563 | { |
---|
1564 | n_Delete(&x,r->cf); |
---|
1565 | return bin; |
---|
1566 | } |
---|
1567 | h = (exp >> 1) + 1; |
---|
1568 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
1569 | bin[1] = x; |
---|
1570 | if (exp < 4) |
---|
1571 | return bin; |
---|
1572 | i = exp - 1; |
---|
1573 | for (e=2; e<h; e++) |
---|
1574 | { |
---|
1575 | x = n_Init(i,r->cf); |
---|
1576 | i--; |
---|
1577 | y = n_Mult(x,bin[e-1],r->cf); |
---|
1578 | n_Delete(&x,r->cf); |
---|
1579 | x = n_Init(e,r->cf); |
---|
1580 | bin[e] = n_IntDiv(y,x,r->cf); |
---|
1581 | n_Delete(&x,r->cf); |
---|
1582 | n_Delete(&y,r->cf); |
---|
1583 | } |
---|
1584 | return bin; |
---|
1585 | } |
---|
1586 | |
---|
1587 | /* |
---|
1588 | * compute for a poly p = head+tail, tail is monomial |
---|
1589 | * (head + tail)^exp, exp > 1 |
---|
1590 | * with binomial coef. |
---|
1591 | */ |
---|
1592 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
1593 | { |
---|
1594 | int eh, e; |
---|
1595 | long al; |
---|
1596 | poly *a; |
---|
1597 | poly tail, b, res, h; |
---|
1598 | number x; |
---|
1599 | number *bin = pnBin(exp); |
---|
1600 | |
---|
1601 | tail = pNext(p); |
---|
1602 | if (bin == NULL) |
---|
1603 | { |
---|
1604 | p_MonPower(p,exp,r); |
---|
1605 | p_MonPower(tail,exp,r); |
---|
1606 | #ifdef PDEBUG |
---|
1607 | p_Test(p,r); |
---|
1608 | #endif |
---|
1609 | return p; |
---|
1610 | } |
---|
1611 | eh = exp >> 1; |
---|
1612 | al = (exp + 1) * sizeof(poly); |
---|
1613 | a = (poly *)omAlloc(al); |
---|
1614 | a[1] = p; |
---|
1615 | for (e=1; e<exp; e++) |
---|
1616 | { |
---|
1617 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
1618 | } |
---|
1619 | res = a[exp]; |
---|
1620 | b = p_Head(tail,r); |
---|
1621 | for (e=exp-1; e>eh; e--) |
---|
1622 | { |
---|
1623 | h = a[e]; |
---|
1624 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
1625 | p_SetCoeff(h,x,r); |
---|
1626 | p_MonMult(h,b,r); |
---|
1627 | res = pNext(res) = h; |
---|
1628 | p_MonMult(b,tail,r); |
---|
1629 | } |
---|
1630 | for (e=eh; e!=0; e--) |
---|
1631 | { |
---|
1632 | h = a[e]; |
---|
1633 | x = n_Mult(bin[e],pGetCoeff(h),r->cf); |
---|
1634 | p_SetCoeff(h,x,r); |
---|
1635 | p_MonMult(h,b,r); |
---|
1636 | res = pNext(res) = h; |
---|
1637 | p_MonMult(b,tail,r); |
---|
1638 | } |
---|
1639 | p_LmDelete(&tail,r); |
---|
1640 | pNext(res) = b; |
---|
1641 | pNext(b) = NULL; |
---|
1642 | res = a[exp]; |
---|
1643 | omFreeSize((ADDRESS)a, al); |
---|
1644 | pnFreeBin(bin, exp); |
---|
1645 | // tail=res; |
---|
1646 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
1647 | // { |
---|
1648 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
1649 | // { |
---|
1650 | // pLmDelete(&pNext(tail)); |
---|
1651 | // } |
---|
1652 | // else |
---|
1653 | // pIter(tail); |
---|
1654 | // } |
---|
1655 | #ifdef PDEBUG |
---|
1656 | p_Test(res,r); |
---|
1657 | #endif |
---|
1658 | return res; |
---|
1659 | } |
---|
1660 | |
---|
1661 | static poly p_Pow(poly p, int i, const ring r) |
---|
1662 | { |
---|
1663 | poly rc = p_Copy(p,r); |
---|
1664 | i -= 2; |
---|
1665 | do |
---|
1666 | { |
---|
1667 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
1668 | p_Normalize(rc,r); |
---|
1669 | i--; |
---|
1670 | } |
---|
1671 | while (i != 0); |
---|
1672 | return p_Mult_q(rc,p,r); |
---|
1673 | } |
---|
1674 | |
---|
1675 | /*2 |
---|
1676 | * returns the i-th power of p |
---|
1677 | * p will be destroyed |
---|
1678 | */ |
---|
1679 | poly p_Power(poly p, int i, const ring r) |
---|
1680 | { |
---|
1681 | poly rc=NULL; |
---|
1682 | |
---|
1683 | if (i==0) |
---|
1684 | { |
---|
1685 | p_Delete(&p,r); |
---|
1686 | return p_One(r); |
---|
1687 | } |
---|
1688 | |
---|
1689 | if(p!=NULL) |
---|
1690 | { |
---|
1691 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask))) |
---|
1692 | { |
---|
1693 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
1694 | return NULL; |
---|
1695 | } |
---|
1696 | switch (i) |
---|
1697 | { |
---|
1698 | // cannot happen, see above |
---|
1699 | // case 0: |
---|
1700 | // { |
---|
1701 | // rc=pOne(); |
---|
1702 | // pDelete(&p); |
---|
1703 | // break; |
---|
1704 | // } |
---|
1705 | case 1: |
---|
1706 | rc=p; |
---|
1707 | break; |
---|
1708 | case 2: |
---|
1709 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
1710 | break; |
---|
1711 | default: |
---|
1712 | if (i < 0) |
---|
1713 | { |
---|
1714 | p_Delete(&p,r); |
---|
1715 | return NULL; |
---|
1716 | } |
---|
1717 | else |
---|
1718 | { |
---|
1719 | #ifdef HAVE_PLURAL |
---|
1720 | if (rIsPluralRing(r)) /* in the NC case nothing helps :-( */ |
---|
1721 | { |
---|
1722 | int j=i; |
---|
1723 | rc = p_Copy(p,r); |
---|
1724 | while (j>1) |
---|
1725 | { |
---|
1726 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
1727 | j--; |
---|
1728 | } |
---|
1729 | p_Delete(&p,r); |
---|
1730 | return rc; |
---|
1731 | } |
---|
1732 | #endif |
---|
1733 | rc = pNext(p); |
---|
1734 | if (rc == NULL) |
---|
1735 | return p_MonPower(p,i,r); |
---|
1736 | /* else: binom ?*/ |
---|
1737 | int char_p=rChar(r); |
---|
1738 | if ((pNext(rc) != NULL) |
---|
1739 | #ifdef HAVE_RINGS |
---|
1740 | || rField_is_Ring(r) |
---|
1741 | #endif |
---|
1742 | ) |
---|
1743 | return p_Pow(p,i,r); |
---|
1744 | if ((char_p==0) || (i<=char_p)) |
---|
1745 | return p_TwoMonPower(p,i,r); |
---|
1746 | poly p_p=p_TwoMonPower(p_Copy(p,r),char_p,r); |
---|
1747 | return p_Mult_q(p_Power(p,i-char_p,r),p_p,r); |
---|
1748 | } |
---|
1749 | /*end default:*/ |
---|
1750 | } |
---|
1751 | } |
---|
1752 | return rc; |
---|
1753 | } |
---|
1754 | |
---|
1755 | /* --------------------------------------------------------------------------------*/ |
---|
1756 | /* content suff */ |
---|
1757 | |
---|
1758 | static number p_InitContent(poly ph, const ring r); |
---|
1759 | static number p_InitContent_a(poly ph, const ring r); |
---|
1760 | |
---|
1761 | void p_Content(poly ph, const ring r) |
---|
1762 | { |
---|
1763 | #ifdef HAVE_RINGS |
---|
1764 | if (rField_is_Ring(r)) |
---|
1765 | { |
---|
1766 | if ((ph!=NULL) && rField_has_Units(r)) |
---|
1767 | { |
---|
1768 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
1769 | if (!n_IsOne(k,r->cf)) |
---|
1770 | { |
---|
1771 | number tmpGMP = k; |
---|
1772 | k = n_Invers(k,r->cf); |
---|
1773 | n_Delete(&tmpGMP,r->cf); |
---|
1774 | poly h = pNext(ph); |
---|
1775 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
1776 | while (h != NULL) |
---|
1777 | { |
---|
1778 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
1779 | pIter(h); |
---|
1780 | } |
---|
1781 | } |
---|
1782 | n_Delete(&k,r->cf); |
---|
1783 | } |
---|
1784 | return; |
---|
1785 | } |
---|
1786 | #endif |
---|
1787 | number h,d; |
---|
1788 | poly p; |
---|
1789 | |
---|
1790 | if(TEST_OPT_CONTENTSB) return; |
---|
1791 | if(pNext(ph)==NULL) |
---|
1792 | { |
---|
1793 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
1794 | } |
---|
1795 | else |
---|
1796 | { |
---|
1797 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
1798 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
1799 | if (rField_is_Q(r)) |
---|
1800 | { |
---|
1801 | h=p_InitContent(ph,r); |
---|
1802 | p=ph; |
---|
1803 | } |
---|
1804 | else if ((rField_is_Extension(r)) |
---|
1805 | && ((rPar(r)>1)||(r->minpoly==NULL))) |
---|
1806 | { |
---|
1807 | h=p_InitContent_a(ph,r); |
---|
1808 | p=ph; |
---|
1809 | } |
---|
1810 | else |
---|
1811 | { |
---|
1812 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
1813 | p = pNext(ph); |
---|
1814 | } |
---|
1815 | while (p!=NULL) |
---|
1816 | { |
---|
1817 | n_Normalize(pGetCoeff(p),r->cf); |
---|
1818 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
1819 | n_Delete(&h,r->cf); |
---|
1820 | h = d; |
---|
1821 | if(n_IsOne(h,r->cf)) |
---|
1822 | { |
---|
1823 | break; |
---|
1824 | } |
---|
1825 | pIter(p); |
---|
1826 | } |
---|
1827 | p = ph; |
---|
1828 | //number tmp; |
---|
1829 | if(!n_IsOne(h,r->cf)) |
---|
1830 | { |
---|
1831 | while (p!=NULL) |
---|
1832 | { |
---|
1833 | //d = nDiv(pGetCoeff(p),h); |
---|
1834 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
1835 | //if (!nEqual(d,tmp)) |
---|
1836 | //{ |
---|
1837 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
1838 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
1839 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
1840 | //} |
---|
1841 | //nDelete(&tmp); |
---|
1842 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
1843 | p_SetCoeff(p,d,r); |
---|
1844 | pIter(p); |
---|
1845 | } |
---|
1846 | } |
---|
1847 | n_Delete(&h,r->cf); |
---|
1848 | #ifdef HAVE_FACTORY |
---|
1849 | if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
1850 | { |
---|
1851 | singclap_divide_content(ph); |
---|
1852 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
1853 | } |
---|
1854 | #endif |
---|
1855 | if (rField_is_Q_a(r)) |
---|
1856 | { |
---|
1857 | number hzz = nlInit(1, r->cf); |
---|
1858 | h = nlInit(1, r->cf); |
---|
1859 | p=ph; |
---|
1860 | while (p!=NULL) |
---|
1861 | { // each monom: coeff in Q_a |
---|
1862 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
1863 | poly c_n=c_n_n->z; |
---|
1864 | while (c_n!=NULL) |
---|
1865 | { // each monom: coeff in Q |
---|
1866 | d=nlLcm(hzz,pGetCoeff(c_n),r->algring->cf); |
---|
1867 | n_Delete(&hzz,r->algring->cf); |
---|
1868 | hzz=d; |
---|
1869 | pIter(c_n); |
---|
1870 | } |
---|
1871 | c_n=c_n_n->n; |
---|
1872 | while (c_n!=NULL) |
---|
1873 | { // each monom: coeff in Q |
---|
1874 | d=nlLcm(h,pGetCoeff(c_n),r->algring->cf); |
---|
1875 | n_Delete(&h,r->algring->cf); |
---|
1876 | h=d; |
---|
1877 | pIter(c_n); |
---|
1878 | } |
---|
1879 | pIter(p); |
---|
1880 | } |
---|
1881 | /* hzz contains the 1/lcm of all denominators in c_n_n->z*/ |
---|
1882 | /* h contains the 1/lcm of all denominators in c_n_n->n*/ |
---|
1883 | number htmp=nlInvers(h,r->algring->cf); |
---|
1884 | number hzztmp=nlInvers(hzz,r->algring->cf); |
---|
1885 | number hh=nlMult(hzz,h,r->algring->cf); |
---|
1886 | nlDelete(&hzz,r->algring->cf); |
---|
1887 | nlDelete(&h,r->algring->cf); |
---|
1888 | number hg=nlGcd(hzztmp,htmp,r->algring->cf); |
---|
1889 | nlDelete(&hzztmp,r->algring->cf); |
---|
1890 | nlDelete(&htmp,r->algring->cf); |
---|
1891 | h=nlMult(hh,hg,r->algring->cf); |
---|
1892 | nlDelete(&hg,r->algring->cf); |
---|
1893 | nlDelete(&hh,r->algring->cf); |
---|
1894 | nlNormalize(h,r->algring->cf); |
---|
1895 | if(!nlIsOne(h,r->algring->cf)) |
---|
1896 | { |
---|
1897 | p=ph; |
---|
1898 | while (p!=NULL) |
---|
1899 | { // each monom: coeff in Q_a |
---|
1900 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
1901 | poly c_n=c_n_n->z; |
---|
1902 | while (c_n!=NULL) |
---|
1903 | { // each monom: coeff in Q |
---|
1904 | d=nlMult(h,pGetCoeff(c_n),r->algring->cf); |
---|
1905 | nlNormalize(d,r->algring->cf); |
---|
1906 | nlDelete(&pGetCoeff(c_n),r->algring->cf); |
---|
1907 | pGetCoeff(c_n)=d; |
---|
1908 | pIter(c_n); |
---|
1909 | } |
---|
1910 | c_n=c_n_n->n; |
---|
1911 | while (c_n!=NULL) |
---|
1912 | { // each monom: coeff in Q |
---|
1913 | d=nlMult(h,pGetCoeff(c_n),r->algring->cf); |
---|
1914 | nlNormalize(d,r->algring->cf); |
---|
1915 | nlDelete(&pGetCoeff(c_n),r->algring->cf); |
---|
1916 | pGetCoeff(c_n)=d; |
---|
1917 | pIter(c_n); |
---|
1918 | } |
---|
1919 | pIter(p); |
---|
1920 | } |
---|
1921 | } |
---|
1922 | nlDelete(&h,r->algring->cf); |
---|
1923 | } |
---|
1924 | } |
---|
1925 | } |
---|
1926 | #if 0 // currently not used |
---|
1927 | void p_SimpleContent(poly ph,int smax, const ring r) |
---|
1928 | { |
---|
1929 | if(TEST_OPT_CONTENTSB) return; |
---|
1930 | if (ph==NULL) return; |
---|
1931 | if (pNext(ph)==NULL) |
---|
1932 | { |
---|
1933 | p_SetCoeff(ph,n_Init(1,r_cf),r); |
---|
1934 | return; |
---|
1935 | } |
---|
1936 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
1937 | { |
---|
1938 | return; |
---|
1939 | } |
---|
1940 | number d=p_InitContent(ph,r); |
---|
1941 | if (nlSize(d,r->cf)<=smax) |
---|
1942 | { |
---|
1943 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
1944 | return; |
---|
1945 | } |
---|
1946 | poly p=ph; |
---|
1947 | number h=d; |
---|
1948 | if (smax==1) smax=2; |
---|
1949 | while (p!=NULL) |
---|
1950 | { |
---|
1951 | #if 0 |
---|
1952 | d=nlGcd(h,pGetCoeff(p),r->cf); |
---|
1953 | nlDelete(&h,r->cf); |
---|
1954 | h = d; |
---|
1955 | #else |
---|
1956 | nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
1957 | #endif |
---|
1958 | if(nlSize(h,r->cf)<smax) |
---|
1959 | { |
---|
1960 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
1961 | return; |
---|
1962 | } |
---|
1963 | pIter(p); |
---|
1964 | } |
---|
1965 | p = ph; |
---|
1966 | if (!nlGreaterZero(pGetCoeff(p),r->cf)) h=nlNeg(h,r->cf); |
---|
1967 | if(nlIsOne(h,r->cf)) return; |
---|
1968 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
1969 | while (p!=NULL) |
---|
1970 | { |
---|
1971 | #if 1 |
---|
1972 | d = nlIntDiv(pGetCoeff(p),h,r->cf); |
---|
1973 | p_SetCoeff(p,d,r); |
---|
1974 | #else |
---|
1975 | nlInpIntDiv(pGetCoeff(p),h,r->cf); |
---|
1976 | #endif |
---|
1977 | pIter(p); |
---|
1978 | } |
---|
1979 | nlDelete(&h,r->cf); |
---|
1980 | } |
---|
1981 | #endif |
---|
1982 | |
---|
1983 | static number p_InitContent(poly ph, const ring r) |
---|
1984 | // only for coefficients in Q |
---|
1985 | #if 0 |
---|
1986 | { |
---|
1987 | assume(!TEST_OPT_CONTENTSB); |
---|
1988 | assume(ph!=NULL); |
---|
1989 | assume(pNext(ph)!=NULL); |
---|
1990 | assume(rField_is_Q(r)); |
---|
1991 | if (pNext(pNext(ph))==NULL) |
---|
1992 | { |
---|
1993 | return nlGetNom(pGetCoeff(pNext(ph)),r->cf); |
---|
1994 | } |
---|
1995 | poly p=ph; |
---|
1996 | number n1=nlGetNom(pGetCoeff(p),r->cf); |
---|
1997 | pIter(p); |
---|
1998 | number n2=nlGetNom(pGetCoeff(p),r->cf); |
---|
1999 | pIter(p); |
---|
2000 | number d; |
---|
2001 | number t; |
---|
2002 | loop |
---|
2003 | { |
---|
2004 | nlNormalize(pGetCoeff(p),r->cf); |
---|
2005 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
2006 | if (nlGreaterZero(t,r->cf)) |
---|
2007 | d=nlAdd(n1,t,r->cf); |
---|
2008 | else |
---|
2009 | d=nlSub(n1,t,r->cf); |
---|
2010 | nlDelete(&t,r->cf); |
---|
2011 | nlDelete(&n1,r->cf); |
---|
2012 | n1=d; |
---|
2013 | pIter(p); |
---|
2014 | if (p==NULL) break; |
---|
2015 | nlNormalize(pGetCoeff(p),r->cf); |
---|
2016 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
2017 | if (nlGreaterZero(t,r->cf)) |
---|
2018 | d=nlAdd(n2,t,r->cf); |
---|
2019 | else |
---|
2020 | d=nlSub(n2,t,r->cf); |
---|
2021 | nlDelete(&t,r->cf); |
---|
2022 | nlDelete(&n2,r->cf); |
---|
2023 | n2=d; |
---|
2024 | pIter(p); |
---|
2025 | if (p==NULL) break; |
---|
2026 | } |
---|
2027 | d=nlGcd(n1,n2,r->cf); |
---|
2028 | nlDelete(&n1,r->cf); |
---|
2029 | nlDelete(&n2,r->cf); |
---|
2030 | return d; |
---|
2031 | } |
---|
2032 | #else |
---|
2033 | { |
---|
2034 | number d=pGetCoeff(ph); |
---|
2035 | if(SR_HDL(d)&SR_INT) return d; |
---|
2036 | int s=mpz_size1(d->z); |
---|
2037 | int s2=-1; |
---|
2038 | number d2; |
---|
2039 | loop |
---|
2040 | { |
---|
2041 | pIter(ph); |
---|
2042 | if(ph==NULL) |
---|
2043 | { |
---|
2044 | if (s2==-1) return nlCopy(d,r->cf); |
---|
2045 | break; |
---|
2046 | } |
---|
2047 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
2048 | { |
---|
2049 | s2=s; |
---|
2050 | d2=d; |
---|
2051 | s=0; |
---|
2052 | d=pGetCoeff(ph); |
---|
2053 | if (s2==0) break; |
---|
2054 | } |
---|
2055 | else |
---|
2056 | if (mpz_size1((pGetCoeff(ph)->z))<=s) |
---|
2057 | { |
---|
2058 | s2=s; |
---|
2059 | d2=d; |
---|
2060 | d=pGetCoeff(ph); |
---|
2061 | s=mpz_size1(d->z); |
---|
2062 | } |
---|
2063 | } |
---|
2064 | return nlGcd(d,d2,r->cf); |
---|
2065 | } |
---|
2066 | #endif |
---|
2067 | |
---|
2068 | number p_InitContent_a(poly ph, const ring r) |
---|
2069 | // only for coefficients in K(a) anf K(a,...) |
---|
2070 | { |
---|
2071 | number d=pGetCoeff(ph); |
---|
2072 | int s=naParDeg(d); |
---|
2073 | if (s /* naParDeg(d)*/ <=1) return naCopy(d); |
---|
2074 | int s2=-1; |
---|
2075 | number d2; |
---|
2076 | int ss; |
---|
2077 | loop |
---|
2078 | { |
---|
2079 | pIter(ph); |
---|
2080 | if(ph==NULL) |
---|
2081 | { |
---|
2082 | if (s2==-1) return naCopy(d); |
---|
2083 | break; |
---|
2084 | } |
---|
2085 | if ((ss=naParDeg(pGetCoeff(ph)))<s) |
---|
2086 | { |
---|
2087 | s2=s; |
---|
2088 | d2=d; |
---|
2089 | s=ss; |
---|
2090 | d=pGetCoeff(ph); |
---|
2091 | if (s2<=1) break; |
---|
2092 | } |
---|
2093 | } |
---|
2094 | return naGcd(d,d2,r->cf); |
---|
2095 | } |
---|
2096 | |
---|
2097 | |
---|
2098 | //void pContent(poly ph) |
---|
2099 | //{ |
---|
2100 | // number h,d; |
---|
2101 | // poly p; |
---|
2102 | // |
---|
2103 | // p = ph; |
---|
2104 | // if(pNext(p)==NULL) |
---|
2105 | // { |
---|
2106 | // pSetCoeff(p,nInit(1)); |
---|
2107 | // } |
---|
2108 | // else |
---|
2109 | // { |
---|
2110 | //#ifdef PDEBUG |
---|
2111 | // if (!pTest(p)) return; |
---|
2112 | //#endif |
---|
2113 | // nNormalize(pGetCoeff(p)); |
---|
2114 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
2115 | // { |
---|
2116 | // ph = pNeg(ph); |
---|
2117 | // nNormalize(pGetCoeff(p)); |
---|
2118 | // } |
---|
2119 | // h=pGetCoeff(p); |
---|
2120 | // pIter(p); |
---|
2121 | // while (p!=NULL) |
---|
2122 | // { |
---|
2123 | // nNormalize(pGetCoeff(p)); |
---|
2124 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
2125 | // pIter(p); |
---|
2126 | // } |
---|
2127 | // h=nCopy(h); |
---|
2128 | // p=ph; |
---|
2129 | // while (p!=NULL) |
---|
2130 | // { |
---|
2131 | // d=nGcd(h,pGetCoeff(p)); |
---|
2132 | // nDelete(&h); |
---|
2133 | // h = d; |
---|
2134 | // if(nIsOne(h)) |
---|
2135 | // { |
---|
2136 | // break; |
---|
2137 | // } |
---|
2138 | // pIter(p); |
---|
2139 | // } |
---|
2140 | // p = ph; |
---|
2141 | // //number tmp; |
---|
2142 | // if(!nIsOne(h)) |
---|
2143 | // { |
---|
2144 | // while (p!=NULL) |
---|
2145 | // { |
---|
2146 | // d = nIntDiv(pGetCoeff(p),h); |
---|
2147 | // pSetCoeff(p,d); |
---|
2148 | // pIter(p); |
---|
2149 | // } |
---|
2150 | // } |
---|
2151 | // nDelete(&h); |
---|
2152 | //#ifdef HAVE_FACTORY |
---|
2153 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2154 | // { |
---|
2155 | // pTest(ph); |
---|
2156 | // singclap_divide_content(ph); |
---|
2157 | // pTest(ph); |
---|
2158 | // } |
---|
2159 | //#endif |
---|
2160 | // } |
---|
2161 | //} |
---|
2162 | #if 0 |
---|
2163 | void p_Content(poly ph, const ring r) |
---|
2164 | { |
---|
2165 | number h,d; |
---|
2166 | poly p; |
---|
2167 | |
---|
2168 | if(pNext(ph)==NULL) |
---|
2169 | { |
---|
2170 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
2171 | } |
---|
2172 | else |
---|
2173 | { |
---|
2174 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
2175 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2176 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
2177 | p = pNext(ph); |
---|
2178 | while (p!=NULL) |
---|
2179 | { |
---|
2180 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2181 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
2182 | n_Delete(&h,r->cf); |
---|
2183 | h = d; |
---|
2184 | if(n_IsOne(h,r->cf)) |
---|
2185 | { |
---|
2186 | break; |
---|
2187 | } |
---|
2188 | pIter(p); |
---|
2189 | } |
---|
2190 | p = ph; |
---|
2191 | //number tmp; |
---|
2192 | if(!n_IsOne(h,r->cf)) |
---|
2193 | { |
---|
2194 | while (p!=NULL) |
---|
2195 | { |
---|
2196 | //d = nDiv(pGetCoeff(p),h); |
---|
2197 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
2198 | //if (!nEqual(d,tmp)) |
---|
2199 | //{ |
---|
2200 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
2201 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
2202 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
2203 | //} |
---|
2204 | //nDelete(&tmp); |
---|
2205 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
2206 | p_SetCoeff(p,d,r->cf); |
---|
2207 | pIter(p); |
---|
2208 | } |
---|
2209 | } |
---|
2210 | n_Delete(&h,r->cf); |
---|
2211 | #ifdef HAVE_FACTORY |
---|
2212 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2213 | //{ |
---|
2214 | // singclap_divide_content(ph); |
---|
2215 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
2216 | //} |
---|
2217 | #endif |
---|
2218 | } |
---|
2219 | } |
---|
2220 | #endif |
---|
2221 | /* ---------------------------------------------------------------------------*/ |
---|
2222 | /* cleardenom suff */ |
---|
2223 | poly p_Cleardenom(poly ph, const ring r) |
---|
2224 | { |
---|
2225 | poly start=ph; |
---|
2226 | number d, h; |
---|
2227 | poly p; |
---|
2228 | |
---|
2229 | #ifdef HAVE_RINGS |
---|
2230 | if (rField_is_Ring(r)) |
---|
2231 | { |
---|
2232 | p_Content(ph,r); |
---|
2233 | return start; |
---|
2234 | } |
---|
2235 | #endif |
---|
2236 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) return start; |
---|
2237 | p = ph; |
---|
2238 | if(pNext(p)==NULL) |
---|
2239 | { |
---|
2240 | if (TEST_OPT_CONTENTSB) |
---|
2241 | { |
---|
2242 | number n=n_GetDenom(pGetCoeff(p),r->cf); |
---|
2243 | if (!n_IsOne(n,r->cf)) |
---|
2244 | { |
---|
2245 | number nn=n_Mult(pGetCoeff(p),n,r->cf); |
---|
2246 | n_Normalize(nn,r->cf); |
---|
2247 | p_SetCoeff(p,nn,r); |
---|
2248 | } |
---|
2249 | n_Delete(&n,r->cf); |
---|
2250 | } |
---|
2251 | else |
---|
2252 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
2253 | } |
---|
2254 | else |
---|
2255 | { |
---|
2256 | h = n_Init(1,r->cf); |
---|
2257 | while (p!=NULL) |
---|
2258 | { |
---|
2259 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2260 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2261 | n_Delete(&h,r->cf); |
---|
2262 | h=d; |
---|
2263 | pIter(p); |
---|
2264 | } |
---|
2265 | /* contains the 1/lcm of all denominators */ |
---|
2266 | if(!n_IsOne(h,r->cf)) |
---|
2267 | { |
---|
2268 | p = ph; |
---|
2269 | while (p!=NULL) |
---|
2270 | { |
---|
2271 | /* should be: |
---|
2272 | * number hh; |
---|
2273 | * nGetDenom(p->coef,&hh); |
---|
2274 | * nMult(&h,&hh,&d); |
---|
2275 | * nNormalize(d); |
---|
2276 | * nDelete(&hh); |
---|
2277 | * nMult(d,p->coef,&hh); |
---|
2278 | * nDelete(&d); |
---|
2279 | * nDelete(&(p->coef)); |
---|
2280 | * p->coef =hh; |
---|
2281 | */ |
---|
2282 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2283 | n_Normalize(d,r->cf); |
---|
2284 | p_SetCoeff(p,d,r); |
---|
2285 | pIter(p); |
---|
2286 | } |
---|
2287 | n_Delete(&h,r->cf); |
---|
2288 | if (n_GetChar(r->cf)==1) |
---|
2289 | { |
---|
2290 | loop |
---|
2291 | { |
---|
2292 | h = n_Init(1,r->cf); |
---|
2293 | p=ph; |
---|
2294 | while (p!=NULL) |
---|
2295 | { |
---|
2296 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2297 | n_Delete(&h,r->cf); |
---|
2298 | h=d; |
---|
2299 | pIter(p); |
---|
2300 | } |
---|
2301 | /* contains the 1/lcm of all denominators */ |
---|
2302 | if(!n_IsOne(h,r->cf)) |
---|
2303 | { |
---|
2304 | p = ph; |
---|
2305 | while (p!=NULL) |
---|
2306 | { |
---|
2307 | /* should be: |
---|
2308 | * number hh; |
---|
2309 | * nGetDenom(p->coef,&hh); |
---|
2310 | * nMult(&h,&hh,&d); |
---|
2311 | * nNormalize(d); |
---|
2312 | * nDelete(&hh); |
---|
2313 | * nMult(d,p->coef,&hh); |
---|
2314 | * nDelete(&d); |
---|
2315 | * nDelete(&(p->coef)); |
---|
2316 | * p->coef =hh; |
---|
2317 | */ |
---|
2318 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2319 | n_Normalize(d,r->cf); |
---|
2320 | p_SetCoeff(p,d,r); |
---|
2321 | pIter(p); |
---|
2322 | } |
---|
2323 | n_Delete(&h,r->cf); |
---|
2324 | } |
---|
2325 | else |
---|
2326 | { |
---|
2327 | n_Delete(&h,r->cf); |
---|
2328 | break; |
---|
2329 | } |
---|
2330 | } |
---|
2331 | } |
---|
2332 | } |
---|
2333 | if (h!=NULL) n_Delete(&h,r->cf); |
---|
2334 | |
---|
2335 | p_Content(ph,r); |
---|
2336 | #ifdef HAVE_RATGRING |
---|
2337 | if (rIsRatGRing(r)) |
---|
2338 | { |
---|
2339 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
2340 | pContentRat(ph); |
---|
2341 | start=ph; |
---|
2342 | } |
---|
2343 | #endif |
---|
2344 | } |
---|
2345 | return start; |
---|
2346 | } |
---|
2347 | |
---|
2348 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
2349 | { |
---|
2350 | number d, h; |
---|
2351 | poly p; |
---|
2352 | |
---|
2353 | p = ph; |
---|
2354 | if(pNext(p)==NULL) |
---|
2355 | { |
---|
2356 | c=n_Invers(pGetCoeff(p),r->cf); |
---|
2357 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
2358 | } |
---|
2359 | else |
---|
2360 | { |
---|
2361 | h = n_Init(1,r->cf); |
---|
2362 | while (p!=NULL) |
---|
2363 | { |
---|
2364 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2365 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2366 | n_Delete(&h,r->cf); |
---|
2367 | h=d; |
---|
2368 | pIter(p); |
---|
2369 | } |
---|
2370 | c=h; |
---|
2371 | /* contains the 1/lcm of all denominators */ |
---|
2372 | if(!n_IsOne(h,r->cf)) |
---|
2373 | { |
---|
2374 | p = ph; |
---|
2375 | while (p!=NULL) |
---|
2376 | { |
---|
2377 | /* should be: |
---|
2378 | * number hh; |
---|
2379 | * nGetDenom(p->coef,&hh); |
---|
2380 | * nMult(&h,&hh,&d); |
---|
2381 | * nNormalize(d); |
---|
2382 | * nDelete(&hh); |
---|
2383 | * nMult(d,p->coef,&hh); |
---|
2384 | * nDelete(&d); |
---|
2385 | * nDelete(&(p->coef)); |
---|
2386 | * p->coef =hh; |
---|
2387 | */ |
---|
2388 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2389 | n_Normalize(d,r->cf); |
---|
2390 | p_SetCoeff(p,d,r); |
---|
2391 | pIter(p); |
---|
2392 | } |
---|
2393 | if (rField_is_Q_a(r)) |
---|
2394 | { |
---|
2395 | loop |
---|
2396 | { |
---|
2397 | h = n_Init(1,r->cf); |
---|
2398 | p=ph; |
---|
2399 | while (p!=NULL) |
---|
2400 | { |
---|
2401 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2402 | n_Delete(&h,r->cf); |
---|
2403 | h=d; |
---|
2404 | pIter(p); |
---|
2405 | } |
---|
2406 | /* contains the 1/lcm of all denominators */ |
---|
2407 | if(!n_IsOne(h,r->cf)) |
---|
2408 | { |
---|
2409 | p = ph; |
---|
2410 | while (p!=NULL) |
---|
2411 | { |
---|
2412 | /* should be: |
---|
2413 | * number hh; |
---|
2414 | * nGetDenom(p->coef,&hh); |
---|
2415 | * nMult(&h,&hh,&d); |
---|
2416 | * nNormalize(d); |
---|
2417 | * nDelete(&hh); |
---|
2418 | * nMult(d,p->coef,&hh); |
---|
2419 | * nDelete(&d); |
---|
2420 | * nDelete(&(p->coef)); |
---|
2421 | * p->coef =hh; |
---|
2422 | */ |
---|
2423 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2424 | n_Normalize(d,r->cf); |
---|
2425 | p_SetCoeff(p,d,r); |
---|
2426 | pIter(p); |
---|
2427 | } |
---|
2428 | number t=n_Mult(c,h,r->cf); |
---|
2429 | n_Delete(&c,r->cf); |
---|
2430 | c=t; |
---|
2431 | } |
---|
2432 | else |
---|
2433 | { |
---|
2434 | break; |
---|
2435 | } |
---|
2436 | n_Delete(&h,r->cf); |
---|
2437 | } |
---|
2438 | } |
---|
2439 | } |
---|
2440 | } |
---|
2441 | } |
---|
2442 | |
---|
2443 | number p_GetAllDenom(poly ph, const ring r) |
---|
2444 | { |
---|
2445 | number d=n_Init(1,r->cf); |
---|
2446 | poly p = ph; |
---|
2447 | |
---|
2448 | while (p!=NULL) |
---|
2449 | { |
---|
2450 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
2451 | if (!n_IsOne(h,r->cf)) |
---|
2452 | { |
---|
2453 | number dd=n_Mult(d,h,r->cf); |
---|
2454 | n_Delete(&d,r->cf); |
---|
2455 | d=dd; |
---|
2456 | } |
---|
2457 | n_Delete(&h,r->cf); |
---|
2458 | pIter(p); |
---|
2459 | } |
---|
2460 | return d; |
---|
2461 | } |
---|
2462 | |
---|
2463 | int p_Size(poly p, const ring r) |
---|
2464 | { |
---|
2465 | int count = 0; |
---|
2466 | while ( p != NULL ) |
---|
2467 | { |
---|
2468 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
2469 | pIter( p ); |
---|
2470 | } |
---|
2471 | return count; |
---|
2472 | } |
---|
2473 | |
---|
2474 | /*2 |
---|
2475 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
2476 | *assume: deg(var(varnum))==1 |
---|
2477 | */ |
---|
2478 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
2479 | { |
---|
2480 | pFDegProc deg; |
---|
2481 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
2482 | deg=p_Totaldegree; |
---|
2483 | else |
---|
2484 | deg=pFDeg; |
---|
2485 | |
---|
2486 | poly q=NULL, qn; |
---|
2487 | int o,ii; |
---|
2488 | sBucket_pt bp; |
---|
2489 | |
---|
2490 | if (p!=NULL) |
---|
2491 | { |
---|
2492 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
2493 | { |
---|
2494 | return NULL; |
---|
2495 | } |
---|
2496 | o=deg(p,r); |
---|
2497 | q=pNext(p); |
---|
2498 | while (q != NULL) |
---|
2499 | { |
---|
2500 | ii=deg(q,r); |
---|
2501 | if (ii>o) o=ii; |
---|
2502 | pIter(q); |
---|
2503 | } |
---|
2504 | q = p_Copy(p,r); |
---|
2505 | bp = sBucketCreate(r); |
---|
2506 | while (q != NULL) |
---|
2507 | { |
---|
2508 | ii = o-deg(q,r); |
---|
2509 | if (ii!=0) |
---|
2510 | { |
---|
2511 | p_AddExp(q,varnum, (long)ii,r); |
---|
2512 | p_Setm(q,r); |
---|
2513 | } |
---|
2514 | qn = pNext(q); |
---|
2515 | pNext(q) = NULL; |
---|
2516 | sBucket_Add_p(bp, q, 1); |
---|
2517 | q = qn; |
---|
2518 | } |
---|
2519 | sBucketDestroyAdd(bp, &q, &ii); |
---|
2520 | } |
---|
2521 | return q; |
---|
2522 | } |
---|
2523 | |
---|
2524 | /*2 |
---|
2525 | *tests if p is homogeneous with respect to the actual weigths |
---|
2526 | */ |
---|
2527 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
2528 | { |
---|
2529 | poly qp=p; |
---|
2530 | int o; |
---|
2531 | |
---|
2532 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
2533 | pFDegProc d; |
---|
2534 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
2535 | d=p_Totaldegree; |
---|
2536 | else |
---|
2537 | d=pFDeg; |
---|
2538 | o = d(p,r); |
---|
2539 | do |
---|
2540 | { |
---|
2541 | if (d(qp,r) != o) return FALSE; |
---|
2542 | pIter(qp); |
---|
2543 | } |
---|
2544 | while (qp != NULL); |
---|
2545 | return TRUE; |
---|
2546 | } |
---|
2547 | |
---|
2548 | /*----------utilities for syzygies--------------*/ |
---|
2549 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
2550 | { |
---|
2551 | poly q=p,qq; |
---|
2552 | int i; |
---|
2553 | |
---|
2554 | while (q!=NULL) |
---|
2555 | { |
---|
2556 | if (p_LmIsConstantComp(q,r)) |
---|
2557 | { |
---|
2558 | i = p_GetComp(q,r); |
---|
2559 | qq = p; |
---|
2560 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
2561 | if (qq == q) |
---|
2562 | { |
---|
2563 | *k = i; |
---|
2564 | return TRUE; |
---|
2565 | } |
---|
2566 | else |
---|
2567 | pIter(q); |
---|
2568 | } |
---|
2569 | else pIter(q); |
---|
2570 | } |
---|
2571 | return FALSE; |
---|
2572 | } |
---|
2573 | |
---|
2574 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
2575 | { |
---|
2576 | poly q=p,qq; |
---|
2577 | int i,j=0; |
---|
2578 | |
---|
2579 | *len = 0; |
---|
2580 | while (q!=NULL) |
---|
2581 | { |
---|
2582 | if (p_LmIsConstantComp(q,r)) |
---|
2583 | { |
---|
2584 | i = p_GetComp(q,r); |
---|
2585 | qq = p; |
---|
2586 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
2587 | if (qq == q) |
---|
2588 | { |
---|
2589 | j = 0; |
---|
2590 | while (qq!=NULL) |
---|
2591 | { |
---|
2592 | if (p_GetComp(qq,r)==i) j++; |
---|
2593 | pIter(qq); |
---|
2594 | } |
---|
2595 | if ((*len == 0) || (j<*len)) |
---|
2596 | { |
---|
2597 | *len = j; |
---|
2598 | *k = i; |
---|
2599 | } |
---|
2600 | } |
---|
2601 | } |
---|
2602 | pIter(q); |
---|
2603 | } |
---|
2604 | } |
---|
2605 | |
---|
2606 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
2607 | { |
---|
2608 | poly q = *p; |
---|
2609 | |
---|
2610 | if (q==NULL) return NULL; |
---|
2611 | |
---|
2612 | poly qq=NULL,result = NULL; |
---|
2613 | |
---|
2614 | if (p_GetComp(q,r)==k) |
---|
2615 | { |
---|
2616 | result = q; /* *p */ |
---|
2617 | while ((q!=NULL) && (p_GetComp(q,r)==k)) |
---|
2618 | { |
---|
2619 | p_SetComp(q,0,r); |
---|
2620 | p_SetmComp(q,r); |
---|
2621 | qq = q; |
---|
2622 | pIter(q); |
---|
2623 | } |
---|
2624 | *p = q; |
---|
2625 | pNext(qq) = NULL; |
---|
2626 | } |
---|
2627 | if (q==NULL) return result; |
---|
2628 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2629 | while (pNext(q)!=NULL) |
---|
2630 | { |
---|
2631 | if (p_GetComp(pNext(q),r)==k) |
---|
2632 | { |
---|
2633 | if (result==NULL) |
---|
2634 | { |
---|
2635 | result = pNext(q); |
---|
2636 | qq = result; |
---|
2637 | } |
---|
2638 | else |
---|
2639 | { |
---|
2640 | pNext(qq) = pNext(q); |
---|
2641 | pIter(qq); |
---|
2642 | } |
---|
2643 | pNext(q) = pNext(pNext(q)); |
---|
2644 | pNext(qq) =NULL; |
---|
2645 | p_SetComp(qq,0,r); |
---|
2646 | p_SetmComp(qq,r); |
---|
2647 | } |
---|
2648 | else |
---|
2649 | { |
---|
2650 | pIter(q); |
---|
2651 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2652 | } |
---|
2653 | } |
---|
2654 | return result; |
---|
2655 | } |
---|
2656 | |
---|
2657 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
2658 | { |
---|
2659 | poly q = *p,qq=NULL,result = NULL; |
---|
2660 | |
---|
2661 | if (q==NULL) return NULL; |
---|
2662 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
2663 | if (p_GetComp(q,r)==k) |
---|
2664 | { |
---|
2665 | result = q; |
---|
2666 | do |
---|
2667 | { |
---|
2668 | p_SetComp(q,0,r); |
---|
2669 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2670 | qq = q; |
---|
2671 | pIter(q); |
---|
2672 | } |
---|
2673 | while ((q!=NULL) && (p_GetComp(q,r)==k)); |
---|
2674 | *p = q; |
---|
2675 | pNext(qq) = NULL; |
---|
2676 | } |
---|
2677 | if (q==NULL) return result; |
---|
2678 | if (p_GetComp(q,r) > k) |
---|
2679 | { |
---|
2680 | p_SubComp(q,1,r); |
---|
2681 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2682 | } |
---|
2683 | poly pNext_q; |
---|
2684 | while ((pNext_q=pNext(q))!=NULL) |
---|
2685 | { |
---|
2686 | if (p_GetComp(pNext_q,r)==k) |
---|
2687 | { |
---|
2688 | if (result==NULL) |
---|
2689 | { |
---|
2690 | result = pNext_q; |
---|
2691 | qq = result; |
---|
2692 | } |
---|
2693 | else |
---|
2694 | { |
---|
2695 | pNext(qq) = pNext_q; |
---|
2696 | pIter(qq); |
---|
2697 | } |
---|
2698 | pNext(q) = pNext(pNext_q); |
---|
2699 | pNext(qq) =NULL; |
---|
2700 | p_SetComp(qq,0,r); |
---|
2701 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
2702 | } |
---|
2703 | else |
---|
2704 | { |
---|
2705 | /*pIter(q);*/ q=pNext_q; |
---|
2706 | if (p_GetComp(q,r) > k) |
---|
2707 | { |
---|
2708 | p_SubComp(q,1,r); |
---|
2709 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2710 | } |
---|
2711 | } |
---|
2712 | } |
---|
2713 | return result; |
---|
2714 | } |
---|
2715 | |
---|
2716 | // Splits *p into two polys: *q which consists of all monoms with |
---|
2717 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
2718 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
2719 | { |
---|
2720 | spolyrec pp, qq; |
---|
2721 | poly p, q, p_prev; |
---|
2722 | int l = 0; |
---|
2723 | |
---|
2724 | #ifdef HAVE_ASSUME |
---|
2725 | int lp = pLength(*r_p); |
---|
2726 | #endif |
---|
2727 | |
---|
2728 | pNext(&pp) = *r_p; |
---|
2729 | p = *r_p; |
---|
2730 | p_prev = &pp; |
---|
2731 | q = &qq; |
---|
2732 | |
---|
2733 | while(p != NULL) |
---|
2734 | { |
---|
2735 | while (p_GetComp(p,r) == comp) |
---|
2736 | { |
---|
2737 | pNext(q) = p; |
---|
2738 | pIter(q); |
---|
2739 | p_SetComp(p, 0,r); |
---|
2740 | p_SetmComp(p,r); |
---|
2741 | pIter(p); |
---|
2742 | l++; |
---|
2743 | if (p == NULL) |
---|
2744 | { |
---|
2745 | pNext(p_prev) = NULL; |
---|
2746 | goto Finish; |
---|
2747 | } |
---|
2748 | } |
---|
2749 | pNext(p_prev) = p; |
---|
2750 | p_prev = p; |
---|
2751 | pIter(p); |
---|
2752 | } |
---|
2753 | |
---|
2754 | Finish: |
---|
2755 | pNext(q) = NULL; |
---|
2756 | *r_p = pNext(&pp); |
---|
2757 | *r_q = pNext(&qq); |
---|
2758 | *lq = l; |
---|
2759 | #ifdef HAVE_ASSUME |
---|
2760 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
2761 | #endif |
---|
2762 | p_Test(*r_p,r); |
---|
2763 | p_Test(*r_q,r); |
---|
2764 | } |
---|
2765 | |
---|
2766 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
2767 | { |
---|
2768 | poly q; |
---|
2769 | |
---|
2770 | while ((*p!=NULL) && (p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
2771 | if (*p==NULL) return; |
---|
2772 | q = *p; |
---|
2773 | if (p_GetComp(q,r)>k) |
---|
2774 | { |
---|
2775 | p_SubComp(q,1,r); |
---|
2776 | p_SetmComp(q,r); |
---|
2777 | } |
---|
2778 | while (pNext(q)!=NULL) |
---|
2779 | { |
---|
2780 | if (p_GetComp(pNext(q),r)==k) |
---|
2781 | p_LmDelete(&(pNext(q)),r); |
---|
2782 | else |
---|
2783 | { |
---|
2784 | pIter(q); |
---|
2785 | if (p_GetComp(q,r)>k) |
---|
2786 | { |
---|
2787 | p_SubComp(q,1,r); |
---|
2788 | p_SetmComp(q,r); |
---|
2789 | } |
---|
2790 | } |
---|
2791 | } |
---|
2792 | } |
---|
2793 | /* -------------------------------------------------------- */ |
---|
2794 | /*2 |
---|
2795 | * change all global variables to fit the description of the new ring |
---|
2796 | */ |
---|
2797 | |
---|
2798 | void p_SetGlobals(const ring r, BOOLEAN complete) |
---|
2799 | { |
---|
2800 | int i; |
---|
2801 | if (r->ppNoether!=NULL) p_Delete(&r->ppNoether,r); |
---|
2802 | |
---|
2803 | if (complete) |
---|
2804 | { |
---|
2805 | test &= ~ TEST_RINGDEP_OPTS; |
---|
2806 | test |= r->options; |
---|
2807 | } |
---|
2808 | } |
---|
2809 | // |
---|
2810 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
2811 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
2812 | // only uses pFDeg (and not pDeg, or pTotalDegree, etc) |
---|
2813 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
2814 | { |
---|
2815 | assume(new_FDeg != NULL); |
---|
2816 | r->pFDeg = new_FDeg; |
---|
2817 | |
---|
2818 | if (new_lDeg == NULL) |
---|
2819 | new_lDeg = r->pLDegOrig; |
---|
2820 | |
---|
2821 | r->pLDeg = new_lDeg; |
---|
2822 | } |
---|
2823 | |
---|
2824 | // restores pFDeg and pLDeg: |
---|
2825 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
2826 | { |
---|
2827 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
2828 | r->pFDeg = old_FDeg; |
---|
2829 | r->pLDeg = old_lDeg; |
---|
2830 | } |
---|
2831 | |
---|
2832 | /*-------- several access procedures to monomials -------------------- */ |
---|
2833 | /* |
---|
2834 | * the module weights for std |
---|
2835 | */ |
---|
2836 | static pFDegProc pOldFDeg; |
---|
2837 | static pLDegProc pOldLDeg; |
---|
2838 | static intvec * pModW; |
---|
2839 | static BOOLEAN pOldLexOrder; |
---|
2840 | |
---|
2841 | static long pModDeg(poly p, ring r) |
---|
2842 | { |
---|
2843 | long d=pOldFDeg(p, r); |
---|
2844 | int c=p_GetComp(p, r); |
---|
2845 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
2846 | return d; |
---|
2847 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
2848 | } |
---|
2849 | |
---|
2850 | void p_SetModDeg(intvec *w, ring r) |
---|
2851 | { |
---|
2852 | if (w!=NULL) |
---|
2853 | { |
---|
2854 | r->pModW = w; |
---|
2855 | pOldFDeg = r->pFDeg; |
---|
2856 | pOldLDeg = r->pLDeg; |
---|
2857 | pOldLexOrder = r->pLexOrder; |
---|
2858 | pSetDegProcs(r,pModDeg); |
---|
2859 | r->pLexOrder = TRUE; |
---|
2860 | } |
---|
2861 | else |
---|
2862 | { |
---|
2863 | r->pModW = NULL; |
---|
2864 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
2865 | r->pLexOrder = pOldLexOrder; |
---|
2866 | } |
---|
2867 | } |
---|
2868 | |
---|
2869 | /*2 |
---|
2870 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
2871 | */ |
---|
2872 | poly p_PermPoly (poly p, int * perm, const ring oldRing, const ring dst, |
---|
2873 | nMapFunc nMap, int *par_perm, int OldPar) |
---|
2874 | { |
---|
2875 | int OldpVariables = oldRing->N; |
---|
2876 | poly result = NULL; |
---|
2877 | poly result_last = NULL; |
---|
2878 | poly aq=NULL; /* the map coefficient */ |
---|
2879 | poly qq; /* the mapped monomial */ |
---|
2880 | |
---|
2881 | while (p != NULL) |
---|
2882 | { |
---|
2883 | if ((OldPar==0)||(rField_is_GF(oldRing))) |
---|
2884 | { |
---|
2885 | qq = p_Init(dst); |
---|
2886 | number n=nMap(pGetCoeff(p),dst->cf); |
---|
2887 | if ((dst->minpoly!=NULL) |
---|
2888 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
2889 | { |
---|
2890 | n_Normalize(n,dst->cf); |
---|
2891 | } |
---|
2892 | pGetCoeff(qq)=n; |
---|
2893 | // coef may be zero: pTest(qq); |
---|
2894 | } |
---|
2895 | else |
---|
2896 | { |
---|
2897 | qq=p_One(dst); |
---|
2898 | aq=naPermNumber(pGetCoeff(p),par_perm,OldPar, oldRing); |
---|
2899 | if ((dst->minpoly!=NULL) |
---|
2900 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
2901 | { |
---|
2902 | poly tmp=aq; |
---|
2903 | while (tmp!=NULL) |
---|
2904 | { |
---|
2905 | number n=pGetCoeff(tmp); |
---|
2906 | n_Normalize(n,dst->cf); |
---|
2907 | pGetCoeff(tmp)=n; |
---|
2908 | pIter(tmp); |
---|
2909 | } |
---|
2910 | } |
---|
2911 | pTest(aq); |
---|
2912 | } |
---|
2913 | if (rRing_has_Comp(dst)) p_SetComp(qq, p_GetComp(p,oldRing),dst); |
---|
2914 | if (n_IsZero(pGetCoeff(qq),dst->cf)) |
---|
2915 | { |
---|
2916 | p_LmDelete(&qq,dst); |
---|
2917 | } |
---|
2918 | else |
---|
2919 | { |
---|
2920 | int i; |
---|
2921 | int mapped_to_par=0; |
---|
2922 | for(i=1; i<=OldpVariables; i++) |
---|
2923 | { |
---|
2924 | int e=p_GetExp(p,i,oldRing); |
---|
2925 | if (e!=0) |
---|
2926 | { |
---|
2927 | if (perm==NULL) |
---|
2928 | { |
---|
2929 | p_SetExp(qq,i, e, dst); |
---|
2930 | } |
---|
2931 | else if (perm[i]>0) |
---|
2932 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
2933 | else if (perm[i]<0) |
---|
2934 | { |
---|
2935 | if (rField_is_GF(dst)) |
---|
2936 | { |
---|
2937 | number c=pGetCoeff(qq); |
---|
2938 | number ee=nfPar(1); |
---|
2939 | number eee;nfPower(ee,e,&eee); //nfDelete(ee,dst); |
---|
2940 | ee=nfMult(c,eee); |
---|
2941 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
2942 | pSetCoeff0(qq,ee); |
---|
2943 | } |
---|
2944 | else |
---|
2945 | { |
---|
2946 | lnumber c=(lnumber)pGetCoeff(qq); |
---|
2947 | if (c->z->next==NULL) |
---|
2948 | p_AddExp(c->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->algring); |
---|
2949 | else /* more difficult: we have really to multiply: */ |
---|
2950 | { |
---|
2951 | lnumber mmc=(lnumber)naInit(1,dst); |
---|
2952 | napSetExp(mmc->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/); |
---|
2953 | napSetm(mmc->z); |
---|
2954 | pGetCoeff(qq)=naMult((number)c,(number)mmc); |
---|
2955 | n_Delete((number *)&c,dst->cf); |
---|
2956 | n_Delete((number *)&mmc,dst->cf); |
---|
2957 | } |
---|
2958 | mapped_to_par=1; |
---|
2959 | } |
---|
2960 | } |
---|
2961 | else |
---|
2962 | { |
---|
2963 | /* this variable maps to 0 !*/ |
---|
2964 | p_LmDelete(&qq,dst); |
---|
2965 | break; |
---|
2966 | } |
---|
2967 | } |
---|
2968 | } |
---|
2969 | if (mapped_to_par |
---|
2970 | && (dst->minpoly!=NULL)) |
---|
2971 | { |
---|
2972 | number n=pGetCoeff(qq); |
---|
2973 | n_Normalize(n,dst->cf); |
---|
2974 | pGetCoeff(qq)=n; |
---|
2975 | } |
---|
2976 | } |
---|
2977 | pIter(p); |
---|
2978 | #if 1 |
---|
2979 | if (qq!=NULL) |
---|
2980 | { |
---|
2981 | p_Setm(qq,dst); |
---|
2982 | p_Test(aq,dst); |
---|
2983 | p_Test(qq,dst); |
---|
2984 | if (aq!=NULL) qq=p_Mult_q(aq,qq,dst); |
---|
2985 | aq = qq; |
---|
2986 | while (pNext(aq) != NULL) pIter(aq); |
---|
2987 | if (result_last==NULL) |
---|
2988 | { |
---|
2989 | result=qq; |
---|
2990 | } |
---|
2991 | else |
---|
2992 | { |
---|
2993 | pNext(result_last)=qq; |
---|
2994 | } |
---|
2995 | result_last=aq; |
---|
2996 | aq = NULL; |
---|
2997 | } |
---|
2998 | else if (aq!=NULL) |
---|
2999 | { |
---|
3000 | p_Delete(&aq,dst); |
---|
3001 | } |
---|
3002 | } |
---|
3003 | result=p_SortAdd(result,dst); |
---|
3004 | #else |
---|
3005 | // if (qq!=NULL) |
---|
3006 | // { |
---|
3007 | // pSetm(qq); |
---|
3008 | // pTest(qq); |
---|
3009 | // pTest(aq); |
---|
3010 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
3011 | // aq = qq; |
---|
3012 | // while (pNext(aq) != NULL) pIter(aq); |
---|
3013 | // pNext(aq) = result; |
---|
3014 | // aq = NULL; |
---|
3015 | // result = qq; |
---|
3016 | // } |
---|
3017 | // else if (aq!=NULL) |
---|
3018 | // { |
---|
3019 | // pDelete(&aq); |
---|
3020 | // } |
---|
3021 | //} |
---|
3022 | //p = result; |
---|
3023 | //result = NULL; |
---|
3024 | //while (p != NULL) |
---|
3025 | //{ |
---|
3026 | // qq = p; |
---|
3027 | // pIter(p); |
---|
3028 | // qq->next = NULL; |
---|
3029 | // result = pAdd(result, qq); |
---|
3030 | //} |
---|
3031 | #endif |
---|
3032 | p_Test(result,dst); |
---|
3033 | return result; |
---|
3034 | } |
---|
3035 | |
---|
3036 | /*************************************************************** |
---|
3037 | * |
---|
3038 | * p_ShallowDelete |
---|
3039 | * |
---|
3040 | ***************************************************************/ |
---|
3041 | #undef LINKAGE |
---|
3042 | #define LINKAGE |
---|
3043 | #undef p_Delete |
---|
3044 | #define p_Delete p_ShallowDelete |
---|
3045 | #undef n_Delete |
---|
3046 | #define n_Delete(n, r) ((void)0) |
---|
3047 | |
---|
3048 | #include <polys/templates/p_Delete__T.cc> |
---|
3049 | |
---|