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 <polys/weight.h> |
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20 | #include <coeffs/longrat.h> |
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21 | #include <misc/options.h> |
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22 | #include <misc/intvec.h> |
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23 | // #include <???/ideals.h> |
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24 | // #include <???/int64vec.h> |
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25 | #ifndef NDEBUG |
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26 | // #include <???/febase.h> |
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27 | #endif |
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28 | |
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29 | /*************************************************************** |
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30 | * |
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31 | * Completing what needs to be set for the monomial |
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32 | * |
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33 | ***************************************************************/ |
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34 | // this is special for the syz stuff |
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35 | static int* _components = NULL; |
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36 | static long* _componentsShifted = NULL; |
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37 | static int _componentsExternal = 0; |
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38 | |
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39 | BOOLEAN pSetm_error=0; |
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40 | |
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41 | #ifndef NDEBUG |
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42 | # define MYTEST 0 |
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43 | #else /* ifndef NDEBUG */ |
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44 | # define MYTEST 0 |
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45 | #endif /* ifndef NDEBUG */ |
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46 | |
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47 | void p_Setm_General(poly p, const ring r) |
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48 | { |
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49 | p_LmCheckPolyRing(p, r); |
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50 | int pos=0; |
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51 | if (r->typ!=NULL) |
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52 | { |
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53 | loop |
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54 | { |
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55 | long ord=0; |
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56 | sro_ord* o=&(r->typ[pos]); |
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57 | switch(o->ord_typ) |
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58 | { |
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59 | case ro_dp: |
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60 | { |
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61 | int a,e; |
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62 | a=o->data.dp.start; |
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63 | e=o->data.dp.end; |
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64 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
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65 | p->exp[o->data.dp.place]=ord; |
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66 | break; |
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67 | } |
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68 | case ro_wp_neg: |
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69 | ord=POLY_NEGWEIGHT_OFFSET; |
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70 | // no break; |
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71 | case ro_wp: |
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72 | { |
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73 | int a,e; |
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74 | a=o->data.wp.start; |
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75 | e=o->data.wp.end; |
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76 | int *w=o->data.wp.weights; |
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77 | #if 1 |
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78 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r)*w[i-a]; |
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79 | #else |
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80 | long ai; |
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81 | int ei,wi; |
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82 | for(int i=a;i<=e;i++) |
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83 | { |
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84 | ei=p_GetExp(p,i,r); |
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85 | wi=w[i-a]; |
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86 | ai=ei*wi; |
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87 | if (ai/ei!=wi) pSetm_error=TRUE; |
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88 | ord+=ai; |
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89 | if (ord<ai) pSetm_error=TRUE; |
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90 | } |
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91 | #endif |
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92 | p->exp[o->data.wp.place]=ord; |
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93 | break; |
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94 | } |
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95 | case ro_wp64: |
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96 | { |
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97 | int64 ord=0; |
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98 | int a,e; |
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99 | a=o->data.wp64.start; |
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100 | e=o->data.wp64.end; |
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101 | int64 *w=o->data.wp64.weights64; |
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102 | int64 ei,wi,ai; |
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103 | for(int i=a;i<=e;i++) |
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104 | { |
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105 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
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106 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
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107 | ei=(int64)p_GetExp(p,i,r); |
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108 | wi=w[i-a]; |
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109 | ai=ei*wi; |
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110 | if(ei!=0 && ai/ei!=wi) |
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111 | { |
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112 | pSetm_error=TRUE; |
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113 | #if SIZEOF_LONG == 4 |
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114 | Print("ai %lld, wi %lld\n",ai,wi); |
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115 | #else |
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116 | Print("ai %ld, wi %ld\n",ai,wi); |
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117 | #endif |
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118 | } |
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119 | ord+=ai; |
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120 | if (ord<ai) |
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121 | { |
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122 | pSetm_error=TRUE; |
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123 | #if SIZEOF_LONG == 4 |
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124 | Print("ai %lld, ord %lld\n",ai,ord); |
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125 | #else |
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126 | Print("ai %ld, ord %ld\n",ai,ord); |
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127 | #endif |
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128 | } |
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129 | } |
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130 | int64 mask=(int64)0x7fffffff; |
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131 | long a_0=(long)(ord&mask); //2^31 |
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132 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
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133 | |
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134 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
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135 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
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136 | //Print("mask: %d",mask); |
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137 | |
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138 | p->exp[o->data.wp64.place]=a_1; |
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139 | p->exp[o->data.wp64.place+1]=a_0; |
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140 | // if(p_Setm_error) Print("***************************\n |
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141 | // ***************************\n |
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142 | // **WARNING: overflow error**\n |
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143 | // ***************************\n |
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144 | // ***************************\n"); |
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145 | break; |
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146 | } |
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147 | case ro_cp: |
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148 | { |
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149 | int a,e; |
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150 | a=o->data.cp.start; |
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151 | e=o->data.cp.end; |
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152 | int pl=o->data.cp.place; |
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153 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
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154 | break; |
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155 | } |
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156 | case ro_syzcomp: |
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157 | { |
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158 | int c=p_GetComp(p,r); |
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159 | long sc = c; |
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160 | int* Components = (_componentsExternal ? _components : |
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161 | o->data.syzcomp.Components); |
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162 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
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163 | o->data.syzcomp.ShiftedComponents); |
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164 | if (ShiftedComponents != NULL) |
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165 | { |
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166 | assume(Components != NULL); |
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167 | assume(c == 0 || Components[c] != 0); |
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168 | sc = ShiftedComponents[Components[c]]; |
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169 | assume(c == 0 || sc != 0); |
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170 | } |
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171 | p->exp[o->data.syzcomp.place]=sc; |
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172 | break; |
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173 | } |
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174 | case ro_syz: |
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175 | { |
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176 | const unsigned long c = p_GetComp(p, r); |
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177 | const short place = o->data.syz.place; |
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178 | const int limit = o->data.syz.limit; |
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179 | |
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180 | if (c > limit) |
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181 | p->exp[place] = o->data.syz.curr_index; |
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182 | else if (c > 0) |
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183 | { |
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184 | assume( (1 <= c) && (c <= limit) ); |
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185 | p->exp[place]= o->data.syz.syz_index[c]; |
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186 | } |
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187 | else |
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188 | { |
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189 | assume(c == 0); |
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190 | p->exp[place]= 0; |
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191 | } |
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192 | break; |
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193 | } |
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194 | // Prefix for Induced Schreyer ordering |
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195 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
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196 | { |
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197 | assume(p != NULL); |
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198 | |
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199 | #ifndef NDEBUG |
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200 | #if MYTEST |
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201 | Print("p_Setm_General: isTemp ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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202 | #endif |
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203 | #endif |
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204 | int c = p_GetComp(p, r); |
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205 | |
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206 | assume( c >= 0 ); |
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207 | |
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208 | // Let's simulate case ro_syz above.... |
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209 | // Should accumulate (by Suffix) and be a level indicator |
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210 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
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211 | |
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212 | assume( pVarOffset != NULL ); |
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213 | |
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214 | // TODO: Can this be done in the suffix??? |
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215 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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216 | { |
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217 | const int vo = pVarOffset[i]; |
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218 | if( vo != -1) // TODO: optimize: can be done once! |
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219 | { |
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220 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
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221 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
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222 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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223 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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224 | } |
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225 | } |
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226 | #ifndef NDEBUG |
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227 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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228 | { |
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229 | const int vo = pVarOffset[i]; |
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230 | if( vo != -1) // TODO: optimize: can be done once! |
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231 | { |
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232 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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233 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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234 | } |
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235 | } |
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236 | #if MYTEST |
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237 | // if( p->exp[o->data.isTemp.start] > 0 ) |
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238 | // { |
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239 | // PrintS("Initial Value: "); p_DebugPrint(p, r, r, 1); |
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240 | // } |
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241 | #endif |
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242 | #endif |
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243 | break; |
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244 | } |
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245 | |
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246 | // Suffix for Induced Schreyer ordering |
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247 | case ro_is: |
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248 | { |
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249 | #ifndef NDEBUG |
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250 | #if MYTEST |
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251 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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252 | #endif |
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253 | #endif |
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254 | |
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255 | assume(p != NULL); |
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256 | |
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257 | int c = p_GetComp(p, r); |
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258 | |
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259 | assume( c >= 0 ); |
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260 | const ideal F = o->data.is.F; |
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261 | const int limit = o->data.is.limit; |
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262 | |
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263 | if( F != NULL && c > limit ) |
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264 | { |
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265 | #ifndef NDEBUG |
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266 | #if MYTEST |
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267 | 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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268 | #endif |
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269 | #endif |
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270 | |
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271 | c -= limit; |
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272 | assume( c > 0 ); |
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273 | c--; |
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274 | |
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275 | assume( c < IDELEMS(F) ); // What about others??? |
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276 | |
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277 | const poly pp = F->m[c]; // get reference monomial!!! |
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278 | |
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279 | #ifndef NDEBUG |
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280 | #if MYTEST |
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281 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
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282 | p_DebugPrint(pp, r, r, 1); |
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283 | #endif |
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284 | #endif |
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285 | |
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286 | |
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287 | assume(pp != NULL); |
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288 | if(pp == NULL) break; |
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289 | |
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290 | const int start = o->data.is.start; |
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291 | const int end = o->data.is.end; |
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292 | |
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293 | assume(start <= end); |
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294 | |
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295 | // const int limit = o->data.is.limit; |
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296 | assume( limit >= 0 ); |
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297 | |
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298 | // const int st = o->data.isTemp.start; |
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299 | |
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300 | if( c > limit ) |
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301 | p->exp[start] = 1; |
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302 | // else |
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303 | // p->exp[start] = 0; |
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304 | |
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305 | |
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306 | #ifndef NDEBUG |
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307 | Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]); |
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308 | #endif |
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309 | |
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310 | |
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311 | for( int i = start; i <= end; i++) // v[0] may be here... |
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312 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
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313 | |
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314 | |
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315 | |
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316 | |
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317 | #ifndef NDEBUG |
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318 | const int* const pVarOffset = o->data.is.pVarOffset; |
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319 | |
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320 | assume( pVarOffset != NULL ); |
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321 | |
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322 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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323 | { |
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324 | const int vo = pVarOffset[i]; |
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325 | if( vo != -1) // TODO: optimize: can be done once! |
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326 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
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327 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
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328 | } |
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329 | // TODO: how to check this for computed values??? |
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330 | #endif |
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331 | } else |
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332 | { |
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333 | const int* const pVarOffset = o->data.is.pVarOffset; |
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334 | |
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335 | // What about v[0] - component: it will be added later by |
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336 | // suffix!!! |
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337 | // TODO: Test it! |
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338 | const int vo = pVarOffset[0]; |
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339 | if( vo != -1 ) |
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340 | p->exp[vo] = c; // initial component v[0]! |
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341 | |
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342 | #ifndef NDEBUG |
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343 | #if MYTEST |
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344 | 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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345 | p_DebugPrint(p, r, r, 1); |
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346 | #endif |
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347 | #endif |
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348 | } |
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349 | |
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350 | |
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351 | break; |
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352 | } |
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353 | default: |
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354 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
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355 | return; |
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356 | } |
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357 | pos++; |
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358 | if (pos == r->OrdSize) return; |
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359 | } |
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360 | } |
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361 | } |
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362 | |
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363 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
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364 | { |
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365 | _components = Components; |
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366 | _componentsShifted = ShiftedComponents; |
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367 | _componentsExternal = 1; |
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368 | p_Setm_General(p, r); |
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369 | _componentsExternal = 0; |
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370 | } |
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371 | |
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372 | // dummy for lp, ls, etc |
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373 | void p_Setm_Dummy(poly p, const ring r) |
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374 | { |
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375 | p_LmCheckPolyRing(p, r); |
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376 | } |
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377 | |
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378 | // for dp, Dp, ds, etc |
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379 | void p_Setm_TotalDegree(poly p, const ring r) |
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380 | { |
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381 | p_LmCheckPolyRing(p, r); |
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382 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
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383 | } |
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384 | |
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385 | // for wp, Wp, ws, etc |
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386 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
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387 | { |
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388 | p_LmCheckPolyRing(p, r); |
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389 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
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390 | } |
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391 | |
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392 | p_SetmProc p_GetSetmProc(ring r) |
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393 | { |
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394 | // covers lp, rp, ls, |
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395 | if (r->typ == NULL) return p_Setm_Dummy; |
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396 | |
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397 | if (r->OrdSize == 1) |
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398 | { |
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399 | if (r->typ[0].ord_typ == ro_dp && |
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400 | r->typ[0].data.dp.start == 1 && |
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401 | r->typ[0].data.dp.end == r->N && |
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402 | r->typ[0].data.dp.place == r->pOrdIndex) |
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403 | return p_Setm_TotalDegree; |
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404 | if (r->typ[0].ord_typ == ro_wp && |
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405 | r->typ[0].data.wp.start == 1 && |
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406 | r->typ[0].data.wp.end == r->N && |
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407 | r->typ[0].data.wp.place == r->pOrdIndex && |
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408 | r->typ[0].data.wp.weights == r->firstwv) |
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409 | return p_Setm_WFirstTotalDegree; |
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410 | } |
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411 | return p_Setm_General; |
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412 | } |
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413 | |
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414 | |
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415 | /* -------------------------------------------------------------------*/ |
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416 | /* several possibilities for pFDeg: the degree of the head term */ |
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417 | |
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418 | /* comptible with ordering */ |
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419 | long p_Deg(poly a, const ring r) |
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420 | { |
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421 | p_LmCheckPolyRing(a, r); |
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422 | assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); |
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423 | return p_GetOrder(a, r); |
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424 | } |
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425 | |
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426 | // p_WTotalDegree for weighted orderings |
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427 | // whose first block covers all variables |
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428 | long p_WFirstTotalDegree(poly p, const ring r) |
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429 | { |
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430 | int i; |
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431 | long sum = 0; |
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432 | |
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433 | for (i=1; i<= r->firstBlockEnds; i++) |
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434 | { |
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435 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
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436 | } |
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437 | return sum; |
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438 | } |
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439 | |
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440 | /*2 |
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441 | * compute the degree of the leading monomial of p |
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442 | * with respect to weigths from the ordering |
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443 | * the ordering is not compatible with degree so do not use p->Order |
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444 | */ |
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445 | long p_WTotaldegree(poly p, const ring r) |
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446 | { |
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447 | p_LmCheckPolyRing(p, r); |
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448 | int i, k; |
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449 | long j =0; |
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450 | |
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451 | // iterate through each block: |
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452 | for (i=0;r->order[i]!=0;i++) |
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453 | { |
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454 | int b0=r->block0[i]; |
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455 | int b1=r->block1[i]; |
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456 | switch(r->order[i]) |
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457 | { |
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458 | case ringorder_M: |
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459 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
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460 | { // in jedem block: |
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461 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
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462 | } |
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463 | break; |
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464 | case ringorder_wp: |
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465 | case ringorder_ws: |
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466 | case ringorder_Wp: |
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467 | case ringorder_Ws: |
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468 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
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469 | { // in jedem block: |
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470 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
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471 | } |
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472 | break; |
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473 | case ringorder_lp: |
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474 | case ringorder_ls: |
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475 | case ringorder_rs: |
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476 | case ringorder_dp: |
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477 | case ringorder_ds: |
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478 | case ringorder_Dp: |
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479 | case ringorder_Ds: |
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480 | case ringorder_rp: |
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481 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
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482 | { |
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483 | j+= p_GetExp(p,k,r); |
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484 | } |
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485 | break; |
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486 | case ringorder_a64: |
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487 | { |
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488 | int64* w=(int64*)r->wvhdl[i]; |
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489 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
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490 | { |
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491 | //there should be added a line which checks if w[k]>2^31 |
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492 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
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493 | } |
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494 | //break; |
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495 | return j; |
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496 | } |
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497 | case ringorder_c: |
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498 | case ringorder_C: |
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499 | case ringorder_S: |
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500 | case ringorder_s: |
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501 | case ringorder_IS: |
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502 | case ringorder_aa: |
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503 | break; |
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504 | case ringorder_a: |
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505 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
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506 | { // only one line |
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507 | j+= p_GetExp(p,k, r)*r->wvhdl[i][ k- b0 /*r->block0[i]*/]; |
---|
508 | } |
---|
509 | //break; |
---|
510 | return j; |
---|
511 | |
---|
512 | #ifndef NDEBUG |
---|
513 | default: |
---|
514 | Print("missing order %d in p_WTotaldegree\n",r->order[i]); |
---|
515 | break; |
---|
516 | #endif |
---|
517 | } |
---|
518 | } |
---|
519 | return j; |
---|
520 | } |
---|
521 | |
---|
522 | long p_DegW(poly p, const short *w, const ring R) |
---|
523 | { |
---|
524 | long r=~0L; |
---|
525 | |
---|
526 | while (p!=NULL) |
---|
527 | { |
---|
528 | long t=totaldegreeWecart_IV(p,R,w); |
---|
529 | if (t>r) r=t; |
---|
530 | pIter(p); |
---|
531 | } |
---|
532 | return r; |
---|
533 | } |
---|
534 | |
---|
535 | int p_Weight(int i, const ring r) |
---|
536 | { |
---|
537 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
538 | { |
---|
539 | return 1; |
---|
540 | } |
---|
541 | return r->firstwv[i-1]; |
---|
542 | } |
---|
543 | |
---|
544 | long p_WDegree(poly p, const ring r) |
---|
545 | { |
---|
546 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
547 | p_LmCheckPolyRing(p, r); |
---|
548 | int i; |
---|
549 | long j =0; |
---|
550 | |
---|
551 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
552 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
553 | |
---|
554 | for (;i<=r->N;i++) |
---|
555 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
556 | |
---|
557 | return j; |
---|
558 | } |
---|
559 | |
---|
560 | |
---|
561 | /* ---------------------------------------------------------------------*/ |
---|
562 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
563 | /* compute in l also the pLength of p */ |
---|
564 | |
---|
565 | /*2 |
---|
566 | * compute the length of a polynomial (in l) |
---|
567 | * and the degree of the monomial with maximal degree: the last one |
---|
568 | */ |
---|
569 | long pLDeg0(poly p,int *l, const ring r) |
---|
570 | { |
---|
571 | p_CheckPolyRing(p, r); |
---|
572 | long k= p_GetComp(p, r); |
---|
573 | int ll=1; |
---|
574 | |
---|
575 | if (k > 0) |
---|
576 | { |
---|
577 | while ((pNext(p)!=NULL) && (p_GetComp(pNext(p), r)==k)) |
---|
578 | { |
---|
579 | pIter(p); |
---|
580 | ll++; |
---|
581 | } |
---|
582 | } |
---|
583 | else |
---|
584 | { |
---|
585 | while (pNext(p)!=NULL) |
---|
586 | { |
---|
587 | pIter(p); |
---|
588 | ll++; |
---|
589 | } |
---|
590 | } |
---|
591 | *l=ll; |
---|
592 | return r->pFDeg(p, r); |
---|
593 | } |
---|
594 | |
---|
595 | /*2 |
---|
596 | * compute the length of a polynomial (in l) |
---|
597 | * and the degree of the monomial with maximal degree: the last one |
---|
598 | * but search in all components before syzcomp |
---|
599 | */ |
---|
600 | long pLDeg0c(poly p,int *l, const ring r) |
---|
601 | { |
---|
602 | assume(p!=NULL); |
---|
603 | #ifdef PDEBUG |
---|
604 | _p_Test(p,r,PDEBUG); |
---|
605 | #endif |
---|
606 | p_CheckPolyRing(p, r); |
---|
607 | long o; |
---|
608 | int ll=1; |
---|
609 | |
---|
610 | if (! rIsSyzIndexRing(r)) |
---|
611 | { |
---|
612 | while (pNext(p) != NULL) |
---|
613 | { |
---|
614 | pIter(p); |
---|
615 | ll++; |
---|
616 | } |
---|
617 | o = r->pFDeg(p, r); |
---|
618 | } |
---|
619 | else |
---|
620 | { |
---|
621 | int curr_limit = rGetCurrSyzLimit(r); |
---|
622 | poly pp = p; |
---|
623 | while ((p=pNext(p))!=NULL) |
---|
624 | { |
---|
625 | if (p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
626 | ll++; |
---|
627 | else break; |
---|
628 | pp = p; |
---|
629 | } |
---|
630 | #ifdef PDEBUG |
---|
631 | _p_Test(pp,r,PDEBUG); |
---|
632 | #endif |
---|
633 | o = r->pFDeg(pp, r); |
---|
634 | } |
---|
635 | *l=ll; |
---|
636 | return o; |
---|
637 | } |
---|
638 | |
---|
639 | /*2 |
---|
640 | * compute the length of a polynomial (in l) |
---|
641 | * and the degree of the monomial with maximal degree: the first one |
---|
642 | * this works for the polynomial case with degree orderings |
---|
643 | * (both c,dp and dp,c) |
---|
644 | */ |
---|
645 | long pLDegb(poly p,int *l, const ring r) |
---|
646 | { |
---|
647 | p_CheckPolyRing(p, r); |
---|
648 | long k= p_GetComp(p, r); |
---|
649 | long o = r->pFDeg(p, r); |
---|
650 | int ll=1; |
---|
651 | |
---|
652 | if (k != 0) |
---|
653 | { |
---|
654 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
655 | { |
---|
656 | ll++; |
---|
657 | } |
---|
658 | } |
---|
659 | else |
---|
660 | { |
---|
661 | while ((p=pNext(p)) !=NULL) |
---|
662 | { |
---|
663 | ll++; |
---|
664 | } |
---|
665 | } |
---|
666 | *l=ll; |
---|
667 | return o; |
---|
668 | } |
---|
669 | |
---|
670 | /*2 |
---|
671 | * compute the length of a polynomial (in l) |
---|
672 | * and the degree of the monomial with maximal degree: |
---|
673 | * this is NOT the last one, we have to look for it |
---|
674 | */ |
---|
675 | long pLDeg1(poly p,int *l, const ring r) |
---|
676 | { |
---|
677 | p_CheckPolyRing(p, r); |
---|
678 | long k= p_GetComp(p, r); |
---|
679 | int ll=1; |
---|
680 | long t,max; |
---|
681 | |
---|
682 | max=r->pFDeg(p, r); |
---|
683 | if (k > 0) |
---|
684 | { |
---|
685 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
686 | { |
---|
687 | t=r->pFDeg(p, r); |
---|
688 | if (t>max) max=t; |
---|
689 | ll++; |
---|
690 | } |
---|
691 | } |
---|
692 | else |
---|
693 | { |
---|
694 | while ((p=pNext(p))!=NULL) |
---|
695 | { |
---|
696 | t=r->pFDeg(p, r); |
---|
697 | if (t>max) max=t; |
---|
698 | ll++; |
---|
699 | } |
---|
700 | } |
---|
701 | *l=ll; |
---|
702 | return max; |
---|
703 | } |
---|
704 | |
---|
705 | /*2 |
---|
706 | * compute the length of a polynomial (in l) |
---|
707 | * and the degree of the monomial with maximal degree: |
---|
708 | * this is NOT the last one, we have to look for it |
---|
709 | * in all components |
---|
710 | */ |
---|
711 | long pLDeg1c(poly p,int *l, const ring r) |
---|
712 | { |
---|
713 | p_CheckPolyRing(p, r); |
---|
714 | int ll=1; |
---|
715 | long t,max; |
---|
716 | |
---|
717 | max=r->pFDeg(p, r); |
---|
718 | if (rIsSyzIndexRing(r)) |
---|
719 | { |
---|
720 | long limit = rGetCurrSyzLimit(r); |
---|
721 | while ((p=pNext(p))!=NULL) |
---|
722 | { |
---|
723 | if (p_GetComp(p, r)<=limit) |
---|
724 | { |
---|
725 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
726 | ll++; |
---|
727 | } |
---|
728 | else break; |
---|
729 | } |
---|
730 | } |
---|
731 | else |
---|
732 | { |
---|
733 | while ((p=pNext(p))!=NULL) |
---|
734 | { |
---|
735 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
736 | ll++; |
---|
737 | } |
---|
738 | } |
---|
739 | *l=ll; |
---|
740 | return max; |
---|
741 | } |
---|
742 | |
---|
743 | // like pLDeg1, only pFDeg == pDeg |
---|
744 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
745 | { |
---|
746 | assume(r->pFDeg == pDeg); |
---|
747 | p_CheckPolyRing(p, r); |
---|
748 | long k= p_GetComp(p, r); |
---|
749 | int ll=1; |
---|
750 | long t,max; |
---|
751 | |
---|
752 | max=p_GetOrder(p, r); |
---|
753 | if (k > 0) |
---|
754 | { |
---|
755 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
756 | { |
---|
757 | t=p_GetOrder(p, r); |
---|
758 | if (t>max) max=t; |
---|
759 | ll++; |
---|
760 | } |
---|
761 | } |
---|
762 | else |
---|
763 | { |
---|
764 | while ((p=pNext(p))!=NULL) |
---|
765 | { |
---|
766 | t=p_GetOrder(p, r); |
---|
767 | if (t>max) max=t; |
---|
768 | ll++; |
---|
769 | } |
---|
770 | } |
---|
771 | *l=ll; |
---|
772 | return max; |
---|
773 | } |
---|
774 | |
---|
775 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
776 | { |
---|
777 | assume(r->pFDeg == pDeg); |
---|
778 | p_CheckPolyRing(p, r); |
---|
779 | int ll=1; |
---|
780 | long t,max; |
---|
781 | |
---|
782 | max=p_GetOrder(p, r); |
---|
783 | if (rIsSyzIndexRing(r)) |
---|
784 | { |
---|
785 | long limit = rGetCurrSyzLimit(r); |
---|
786 | while ((p=pNext(p))!=NULL) |
---|
787 | { |
---|
788 | if (p_GetComp(p, r)<=limit) |
---|
789 | { |
---|
790 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
791 | ll++; |
---|
792 | } |
---|
793 | else break; |
---|
794 | } |
---|
795 | } |
---|
796 | else |
---|
797 | { |
---|
798 | while ((p=pNext(p))!=NULL) |
---|
799 | { |
---|
800 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
801 | ll++; |
---|
802 | } |
---|
803 | } |
---|
804 | *l=ll; |
---|
805 | return max; |
---|
806 | } |
---|
807 | |
---|
808 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
809 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
810 | { |
---|
811 | p_CheckPolyRing(p, r); |
---|
812 | long k= p_GetComp(p, r); |
---|
813 | int ll=1; |
---|
814 | long t,max; |
---|
815 | |
---|
816 | max=p_Totaldegree(p, r); |
---|
817 | if (k > 0) |
---|
818 | { |
---|
819 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
820 | { |
---|
821 | t=p_Totaldegree(p, r); |
---|
822 | if (t>max) max=t; |
---|
823 | ll++; |
---|
824 | } |
---|
825 | } |
---|
826 | else |
---|
827 | { |
---|
828 | while ((p=pNext(p))!=NULL) |
---|
829 | { |
---|
830 | t=p_Totaldegree(p, r); |
---|
831 | if (t>max) max=t; |
---|
832 | ll++; |
---|
833 | } |
---|
834 | } |
---|
835 | *l=ll; |
---|
836 | return max; |
---|
837 | } |
---|
838 | |
---|
839 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
840 | { |
---|
841 | p_CheckPolyRing(p, r); |
---|
842 | int ll=1; |
---|
843 | long t,max; |
---|
844 | |
---|
845 | max=p_Totaldegree(p, r); |
---|
846 | if (rIsSyzIndexRing(r)) |
---|
847 | { |
---|
848 | long limit = rGetCurrSyzLimit(r); |
---|
849 | while ((p=pNext(p))!=NULL) |
---|
850 | { |
---|
851 | if (p_GetComp(p, r)<=limit) |
---|
852 | { |
---|
853 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
854 | ll++; |
---|
855 | } |
---|
856 | else break; |
---|
857 | } |
---|
858 | } |
---|
859 | else |
---|
860 | { |
---|
861 | while ((p=pNext(p))!=NULL) |
---|
862 | { |
---|
863 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
864 | ll++; |
---|
865 | } |
---|
866 | } |
---|
867 | *l=ll; |
---|
868 | return max; |
---|
869 | } |
---|
870 | |
---|
871 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
872 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
873 | { |
---|
874 | p_CheckPolyRing(p, r); |
---|
875 | long k= p_GetComp(p, r); |
---|
876 | int ll=1; |
---|
877 | long t,max; |
---|
878 | |
---|
879 | max=p_WFirstTotalDegree(p, r); |
---|
880 | if (k > 0) |
---|
881 | { |
---|
882 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
883 | { |
---|
884 | t=p_WFirstTotalDegree(p, r); |
---|
885 | if (t>max) max=t; |
---|
886 | ll++; |
---|
887 | } |
---|
888 | } |
---|
889 | else |
---|
890 | { |
---|
891 | while ((p=pNext(p))!=NULL) |
---|
892 | { |
---|
893 | t=p_WFirstTotalDegree(p, r); |
---|
894 | if (t>max) max=t; |
---|
895 | ll++; |
---|
896 | } |
---|
897 | } |
---|
898 | *l=ll; |
---|
899 | return max; |
---|
900 | } |
---|
901 | |
---|
902 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
903 | { |
---|
904 | p_CheckPolyRing(p, r); |
---|
905 | int ll=1; |
---|
906 | long t,max; |
---|
907 | |
---|
908 | max=p_WFirstTotalDegree(p, r); |
---|
909 | if (rIsSyzIndexRing(r)) |
---|
910 | { |
---|
911 | long limit = rGetCurrSyzLimit(r); |
---|
912 | while ((p=pNext(p))!=NULL) |
---|
913 | { |
---|
914 | if (p_GetComp(p, r)<=limit) |
---|
915 | { |
---|
916 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
917 | ll++; |
---|
918 | } |
---|
919 | else break; |
---|
920 | } |
---|
921 | } |
---|
922 | else |
---|
923 | { |
---|
924 | while ((p=pNext(p))!=NULL) |
---|
925 | { |
---|
926 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
927 | ll++; |
---|
928 | } |
---|
929 | } |
---|
930 | *l=ll; |
---|
931 | return max; |
---|
932 | } |
---|
933 | |
---|
934 | /*************************************************************** |
---|
935 | * |
---|
936 | * Maximal Exponent business |
---|
937 | * |
---|
938 | ***************************************************************/ |
---|
939 | |
---|
940 | static inline unsigned long |
---|
941 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
942 | unsigned long number_of_exp) |
---|
943 | { |
---|
944 | const unsigned long bitmask = r->bitmask; |
---|
945 | unsigned long ml1 = l1 & bitmask; |
---|
946 | unsigned long ml2 = l2 & bitmask; |
---|
947 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
948 | unsigned long j = number_of_exp - 1; |
---|
949 | |
---|
950 | if (j > 0) |
---|
951 | { |
---|
952 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
953 | while (1) |
---|
954 | { |
---|
955 | ml1 = l1 & mask; |
---|
956 | ml2 = l2 & mask; |
---|
957 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
958 | j--; |
---|
959 | if (j == 0) break; |
---|
960 | mask = mask << r->BitsPerExp; |
---|
961 | } |
---|
962 | } |
---|
963 | return max; |
---|
964 | } |
---|
965 | |
---|
966 | static inline unsigned long |
---|
967 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
968 | { |
---|
969 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
970 | } |
---|
971 | |
---|
972 | poly p_GetMaxExpP(poly p, const ring r) |
---|
973 | { |
---|
974 | p_CheckPolyRing(p, r); |
---|
975 | if (p == NULL) return p_Init(r); |
---|
976 | poly max = p_LmInit(p, r); |
---|
977 | pIter(p); |
---|
978 | if (p == NULL) return max; |
---|
979 | int i, offset; |
---|
980 | unsigned long l_p, l_max; |
---|
981 | unsigned long divmask = r->divmask; |
---|
982 | |
---|
983 | do |
---|
984 | { |
---|
985 | offset = r->VarL_Offset[0]; |
---|
986 | l_p = p->exp[offset]; |
---|
987 | l_max = max->exp[offset]; |
---|
988 | // do the divisibility trick to find out whether l has an exponent |
---|
989 | if (l_p > l_max || |
---|
990 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
991 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
992 | |
---|
993 | for (i=1; i<r->VarL_Size; i++) |
---|
994 | { |
---|
995 | offset = r->VarL_Offset[i]; |
---|
996 | l_p = p->exp[offset]; |
---|
997 | l_max = max->exp[offset]; |
---|
998 | // do the divisibility trick to find out whether l has an exponent |
---|
999 | if (l_p > l_max || |
---|
1000 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1001 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
1002 | } |
---|
1003 | pIter(p); |
---|
1004 | } |
---|
1005 | while (p != NULL); |
---|
1006 | return max; |
---|
1007 | } |
---|
1008 | |
---|
1009 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
1010 | { |
---|
1011 | unsigned long l_p, divmask = r->divmask; |
---|
1012 | int i; |
---|
1013 | |
---|
1014 | while (p != NULL) |
---|
1015 | { |
---|
1016 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
1017 | if (l_p > l_max || |
---|
1018 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1019 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
1020 | for (i=1; i<r->VarL_Size; i++) |
---|
1021 | { |
---|
1022 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
1023 | // do the divisibility trick to find out whether l has an exponent |
---|
1024 | if (l_p > l_max || |
---|
1025 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1026 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
1027 | } |
---|
1028 | pIter(p); |
---|
1029 | } |
---|
1030 | return l_max; |
---|
1031 | } |
---|
1032 | |
---|
1033 | |
---|
1034 | |
---|
1035 | |
---|
1036 | /*************************************************************** |
---|
1037 | * |
---|
1038 | * Misc things |
---|
1039 | * |
---|
1040 | ***************************************************************/ |
---|
1041 | // returns TRUE, if all monoms have the same component |
---|
1042 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
1043 | { |
---|
1044 | if(p!=NULL) |
---|
1045 | { |
---|
1046 | long i = p_GetComp(p, r); |
---|
1047 | while (pNext(p)!=NULL) |
---|
1048 | { |
---|
1049 | pIter(p); |
---|
1050 | if(i != p_GetComp(p, r)) return FALSE; |
---|
1051 | } |
---|
1052 | } |
---|
1053 | return TRUE; |
---|
1054 | } |
---|
1055 | |
---|
1056 | /*2 |
---|
1057 | *test if a monomial /head term is a pure power |
---|
1058 | */ |
---|
1059 | int p_IsPurePower(const poly p, const ring r) |
---|
1060 | { |
---|
1061 | int i,k=0; |
---|
1062 | |
---|
1063 | for (i=r->N;i;i--) |
---|
1064 | { |
---|
1065 | if (p_GetExp(p,i, r)!=0) |
---|
1066 | { |
---|
1067 | if(k!=0) return 0; |
---|
1068 | k=i; |
---|
1069 | } |
---|
1070 | } |
---|
1071 | return k; |
---|
1072 | } |
---|
1073 | |
---|
1074 | /*2 |
---|
1075 | *test if a polynomial is univariate |
---|
1076 | * return -1 for constant, |
---|
1077 | * 0 for not univariate,s |
---|
1078 | * i if dep. on var(i) |
---|
1079 | */ |
---|
1080 | int p_IsUnivariate(poly p, const ring r) |
---|
1081 | { |
---|
1082 | int i,k=-1; |
---|
1083 | |
---|
1084 | while (p!=NULL) |
---|
1085 | { |
---|
1086 | for (i=r->N;i;i--) |
---|
1087 | { |
---|
1088 | if (p_GetExp(p,i, r)!=0) |
---|
1089 | { |
---|
1090 | if((k!=-1)&&(k!=i)) return 0; |
---|
1091 | k=i; |
---|
1092 | } |
---|
1093 | } |
---|
1094 | pIter(p); |
---|
1095 | } |
---|
1096 | return k; |
---|
1097 | } |
---|
1098 | |
---|
1099 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
1100 | int p_GetVariables(poly p, int * e, const ring r) |
---|
1101 | { |
---|
1102 | int i; |
---|
1103 | int n=0; |
---|
1104 | while(p!=NULL) |
---|
1105 | { |
---|
1106 | n=0; |
---|
1107 | for(i=r->N; i>0; i--) |
---|
1108 | { |
---|
1109 | if(e[i]==0) |
---|
1110 | { |
---|
1111 | if (p_GetExp(p,i,r)>0) |
---|
1112 | { |
---|
1113 | e[i]=1; |
---|
1114 | n++; |
---|
1115 | } |
---|
1116 | } |
---|
1117 | else |
---|
1118 | n++; |
---|
1119 | } |
---|
1120 | if (n==r->N) break; |
---|
1121 | pIter(p); |
---|
1122 | } |
---|
1123 | return n; |
---|
1124 | } |
---|
1125 | |
---|
1126 | |
---|
1127 | /*2 |
---|
1128 | * returns a polynomial representing the integer i |
---|
1129 | */ |
---|
1130 | poly p_ISet(int i, const ring r) |
---|
1131 | { |
---|
1132 | poly rc = NULL; |
---|
1133 | if (i!=0) |
---|
1134 | { |
---|
1135 | rc = p_Init(r); |
---|
1136 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
1137 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
1138 | p_LmDelete(&rc,r); |
---|
1139 | } |
---|
1140 | return rc; |
---|
1141 | } |
---|
1142 | |
---|
1143 | /*2 |
---|
1144 | * an optimized version of p_ISet for the special case 1 |
---|
1145 | */ |
---|
1146 | poly p_One(const ring r) |
---|
1147 | { |
---|
1148 | poly rc = p_Init(r); |
---|
1149 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
1150 | return rc; |
---|
1151 | } |
---|
1152 | |
---|
1153 | void p_Split(poly p, poly *h) |
---|
1154 | { |
---|
1155 | *h=pNext(p); |
---|
1156 | pNext(p)=NULL; |
---|
1157 | } |
---|
1158 | |
---|
1159 | /*2 |
---|
1160 | * pair has no common factor ? or is no polynomial |
---|
1161 | */ |
---|
1162 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
1163 | { |
---|
1164 | |
---|
1165 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
1166 | return FALSE; |
---|
1167 | int i = rVar(r); |
---|
1168 | loop |
---|
1169 | { |
---|
1170 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
1171 | return FALSE; |
---|
1172 | i--; |
---|
1173 | if (i == 0) |
---|
1174 | return TRUE; |
---|
1175 | } |
---|
1176 | } |
---|
1177 | |
---|
1178 | /*2 |
---|
1179 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
1180 | */ |
---|
1181 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
1182 | { |
---|
1183 | if (r==NULL) { rc=NULL;return st;} |
---|
1184 | int i,j; |
---|
1185 | rc = p_Init(r); |
---|
1186 | const char *s = r->cf->cfRead(st,&(rc->coef),r->cf); |
---|
1187 | if (s==st) |
---|
1188 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
1189 | { |
---|
1190 | j = r_IsRingVar(s,r); |
---|
1191 | if (j >= 0) |
---|
1192 | { |
---|
1193 | p_IncrExp(rc,1+j,r); |
---|
1194 | while (*s!='\0') s++; |
---|
1195 | goto done; |
---|
1196 | } |
---|
1197 | } |
---|
1198 | while (*s!='\0') |
---|
1199 | { |
---|
1200 | char ss[2]; |
---|
1201 | ss[0] = *s++; |
---|
1202 | ss[1] = '\0'; |
---|
1203 | j = r_IsRingVar(ss,r); |
---|
1204 | if (j >= 0) |
---|
1205 | { |
---|
1206 | const char *s_save=s; |
---|
1207 | s = eati(s,&i); |
---|
1208 | if (((unsigned long)i) > r->bitmask) |
---|
1209 | { |
---|
1210 | // exponent to large: it is not a monomial |
---|
1211 | p_LmDelete(&rc,r); |
---|
1212 | return s_save; |
---|
1213 | } |
---|
1214 | p_AddExp(rc,1+j, (long)i, r); |
---|
1215 | } |
---|
1216 | else |
---|
1217 | { |
---|
1218 | // 1st char of is not a varname |
---|
1219 | p_LmDelete(&rc,r); |
---|
1220 | s--; |
---|
1221 | return s; |
---|
1222 | } |
---|
1223 | } |
---|
1224 | done: |
---|
1225 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
1226 | else |
---|
1227 | { |
---|
1228 | #ifdef HAVE_PLURAL |
---|
1229 | // in super-commutative ring |
---|
1230 | // squares of anti-commutative variables are zeroes! |
---|
1231 | if(rIsSCA(r)) |
---|
1232 | { |
---|
1233 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
1234 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
1235 | |
---|
1236 | assume(rc != NULL); |
---|
1237 | |
---|
1238 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
1239 | if( p_GetExp(rc, k, r) > 1 ) |
---|
1240 | { |
---|
1241 | p_LmDelete(&rc, r); |
---|
1242 | goto finish; |
---|
1243 | } |
---|
1244 | } |
---|
1245 | #endif |
---|
1246 | |
---|
1247 | p_Setm(rc,r); |
---|
1248 | } |
---|
1249 | finish: |
---|
1250 | return s; |
---|
1251 | } |
---|
1252 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
1253 | { |
---|
1254 | poly p; |
---|
1255 | const char *s=p_Read(st,p,r); |
---|
1256 | if (*s!='\0') |
---|
1257 | { |
---|
1258 | if ((s!=st)&&isdigit(st[0])) |
---|
1259 | { |
---|
1260 | errorreported=TRUE; |
---|
1261 | } |
---|
1262 | ok=FALSE; |
---|
1263 | p_Delete(&p,r); |
---|
1264 | return NULL; |
---|
1265 | } |
---|
1266 | #ifdef PDEBUG |
---|
1267 | _p_Test(p,r,PDEBUG); |
---|
1268 | #endif |
---|
1269 | ok=!errorreported; |
---|
1270 | return p; |
---|
1271 | } |
---|
1272 | |
---|
1273 | /*2 |
---|
1274 | * returns a polynomial representing the number n |
---|
1275 | * destroys n |
---|
1276 | */ |
---|
1277 | poly p_NSet(number n, const ring r) |
---|
1278 | { |
---|
1279 | if (n_IsZero(n,r->cf)) |
---|
1280 | { |
---|
1281 | n_Delete(&n, r->cf); |
---|
1282 | return NULL; |
---|
1283 | } |
---|
1284 | else |
---|
1285 | { |
---|
1286 | poly rc = p_Init(r); |
---|
1287 | pSetCoeff0(rc,n); |
---|
1288 | return rc; |
---|
1289 | } |
---|
1290 | } |
---|
1291 | /*2 |
---|
1292 | * assumes that the head term of b is a multiple of the head term of a |
---|
1293 | * and return the multiplicant *m |
---|
1294 | * Frank's observation: If LM(b) = LM(a)*m, then we may actually set |
---|
1295 | * negative(!) exponents in the below loop. I suspect that the correct |
---|
1296 | * comment should be "assumes that LM(a) = LM(b)*m, for some monomial m..." |
---|
1297 | */ |
---|
1298 | poly p_Divide(poly a, poly b, const ring r) |
---|
1299 | { |
---|
1300 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
1301 | int i; |
---|
1302 | poly result = p_Init(r); |
---|
1303 | |
---|
1304 | for(i=(int)r->N; i; i--) |
---|
1305 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
1306 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
1307 | p_Setm(result,r); |
---|
1308 | return result; |
---|
1309 | } |
---|
1310 | |
---|
1311 | #ifdef HAVE_RINGS //TODO Oliver |
---|
1312 | |
---|
1313 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
1314 | { |
---|
1315 | pAssume(!n_IsZero(n,r)); |
---|
1316 | p_Test(p, r); |
---|
1317 | |
---|
1318 | poly q = p; |
---|
1319 | while (p != NULL) |
---|
1320 | { |
---|
1321 | number nc = pGetCoeff(p); |
---|
1322 | pSetCoeff0(p, n_Div(nc, n, r->cf)); |
---|
1323 | n_Delete(&nc, r->cf); |
---|
1324 | pIter(p); |
---|
1325 | } |
---|
1326 | p_Test(q, r); |
---|
1327 | return q; |
---|
1328 | } |
---|
1329 | #endif |
---|
1330 | |
---|
1331 | /*2 |
---|
1332 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
1333 | * assumes that b is not NULL |
---|
1334 | */ |
---|
1335 | poly p_DivideM(poly a, poly b, const ring r) |
---|
1336 | { |
---|
1337 | if (a==NULL) return NULL; |
---|
1338 | poly result=a; |
---|
1339 | poly prev=NULL; |
---|
1340 | int i; |
---|
1341 | #ifdef HAVE_RINGS |
---|
1342 | number inv=pGetCoeff(b); |
---|
1343 | #else |
---|
1344 | number inv=n_Invers(pGetCoeff(b),r->cf); |
---|
1345 | #endif |
---|
1346 | |
---|
1347 | while (a!=NULL) |
---|
1348 | { |
---|
1349 | if (p_DivisibleBy(b,a,r)) |
---|
1350 | { |
---|
1351 | for(i=(int)r->N; i; i--) |
---|
1352 | p_SubExp(a,i, p_GetExp(b,i,r),r); |
---|
1353 | p_SubComp(a, p_GetComp(b,r),r); |
---|
1354 | p_Setm(a,r); |
---|
1355 | prev=a; |
---|
1356 | pIter(a); |
---|
1357 | } |
---|
1358 | else |
---|
1359 | { |
---|
1360 | if (prev==NULL) |
---|
1361 | { |
---|
1362 | p_LmDelete(&result,r); |
---|
1363 | a=result; |
---|
1364 | } |
---|
1365 | else |
---|
1366 | { |
---|
1367 | p_LmDelete(&pNext(prev),r); |
---|
1368 | a=pNext(prev); |
---|
1369 | } |
---|
1370 | } |
---|
1371 | } |
---|
1372 | #ifdef HAVE_RINGS |
---|
1373 | if (n_IsUnit(inv,r->cf)) |
---|
1374 | { |
---|
1375 | inv = n_Invers(inv,r->cf); |
---|
1376 | p_Mult_nn(result,inv,r); |
---|
1377 | n_Delete(&inv, r->cf); |
---|
1378 | } |
---|
1379 | else |
---|
1380 | { |
---|
1381 | p_Div_nn(result,inv,r); |
---|
1382 | } |
---|
1383 | #else |
---|
1384 | p_Mult_nn(result,inv,r); |
---|
1385 | n_Delete(&inv, r->cf); |
---|
1386 | #endif |
---|
1387 | p_Delete(&b, r); |
---|
1388 | return result; |
---|
1389 | } |
---|
1390 | |
---|
1391 | /*2 |
---|
1392 | * returns the LCM of the head terms of a and b in *m |
---|
1393 | */ |
---|
1394 | void p_Lcm(poly a, poly b, poly m, const ring r) |
---|
1395 | { |
---|
1396 | int i; |
---|
1397 | for (i=rVar(r); i; i--) |
---|
1398 | { |
---|
1399 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
1400 | } |
---|
1401 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
1402 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
1403 | } |
---|
1404 | |
---|
1405 | /*2 |
---|
1406 | * returns the partial differentiate of a by the k-th variable |
---|
1407 | * does not destroy the input |
---|
1408 | */ |
---|
1409 | poly p_Diff(poly a, int k, const ring r) |
---|
1410 | { |
---|
1411 | poly res, f, last; |
---|
1412 | number t; |
---|
1413 | |
---|
1414 | last = res = NULL; |
---|
1415 | while (a!=NULL) |
---|
1416 | { |
---|
1417 | if (p_GetExp(a,k,r)!=0) |
---|
1418 | { |
---|
1419 | f = p_LmInit(a,r); |
---|
1420 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
1421 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
1422 | n_Delete(&t,r->cf); |
---|
1423 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
1424 | p_LmDelete(&f,r); |
---|
1425 | else |
---|
1426 | { |
---|
1427 | p_DecrExp(f,k,r); |
---|
1428 | p_Setm(f,r); |
---|
1429 | if (res==NULL) |
---|
1430 | { |
---|
1431 | res=last=f; |
---|
1432 | } |
---|
1433 | else |
---|
1434 | { |
---|
1435 | pNext(last)=f; |
---|
1436 | last=f; |
---|
1437 | } |
---|
1438 | } |
---|
1439 | } |
---|
1440 | pIter(a); |
---|
1441 | } |
---|
1442 | return res; |
---|
1443 | } |
---|
1444 | |
---|
1445 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
1446 | { |
---|
1447 | int i,j,s; |
---|
1448 | number n,h,hh; |
---|
1449 | poly p=p_One(r); |
---|
1450 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
1451 | for(i=rVar(r);i>0;i--) |
---|
1452 | { |
---|
1453 | s=p_GetExp(b,i,r); |
---|
1454 | if (s<p_GetExp(a,i,r)) |
---|
1455 | { |
---|
1456 | n_Delete(&n,r->cf); |
---|
1457 | p_LmDelete(&p,r); |
---|
1458 | return NULL; |
---|
1459 | } |
---|
1460 | if (multiply) |
---|
1461 | { |
---|
1462 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
1463 | { |
---|
1464 | h = n_Init(s,r->cf); |
---|
1465 | hh=n_Mult(n,h,r->cf); |
---|
1466 | n_Delete(&h,r->cf); |
---|
1467 | n_Delete(&n,r->cf); |
---|
1468 | n=hh; |
---|
1469 | s--; |
---|
1470 | } |
---|
1471 | p_SetExp(p,i,s,r); |
---|
1472 | } |
---|
1473 | else |
---|
1474 | { |
---|
1475 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
1476 | } |
---|
1477 | } |
---|
1478 | p_Setm(p,r); |
---|
1479 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
1480 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
1481 | return p; |
---|
1482 | } |
---|
1483 | |
---|
1484 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
1485 | { |
---|
1486 | poly result=NULL; |
---|
1487 | poly h; |
---|
1488 | for(;a!=NULL;pIter(a)) |
---|
1489 | { |
---|
1490 | for(h=b;h!=NULL;pIter(h)) |
---|
1491 | { |
---|
1492 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
1493 | } |
---|
1494 | } |
---|
1495 | return result; |
---|
1496 | } |
---|
1497 | /*2 |
---|
1498 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
1499 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
1500 | */ |
---|
1501 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
1502 | { |
---|
1503 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
1504 | } |
---|
1505 | |
---|
1506 | /*3 |
---|
1507 | * compute for a monomial m |
---|
1508 | * the power m^exp, exp > 1 |
---|
1509 | * destroys p |
---|
1510 | */ |
---|
1511 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
1512 | { |
---|
1513 | int i; |
---|
1514 | |
---|
1515 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
1516 | { |
---|
1517 | number x, y; |
---|
1518 | y = pGetCoeff(p); |
---|
1519 | n_Power(y,exp,&x,r->cf); |
---|
1520 | n_Delete(&y,r->cf); |
---|
1521 | pSetCoeff0(p,x); |
---|
1522 | } |
---|
1523 | for (i=rVar(r); i!=0; i--) |
---|
1524 | { |
---|
1525 | p_MultExp(p,i, exp,r); |
---|
1526 | } |
---|
1527 | p_Setm(p,r); |
---|
1528 | return p; |
---|
1529 | } |
---|
1530 | |
---|
1531 | /*3 |
---|
1532 | * compute for monomials p*q |
---|
1533 | * destroys p, keeps q |
---|
1534 | */ |
---|
1535 | static void p_MonMult(poly p, poly q, const ring r) |
---|
1536 | { |
---|
1537 | number x, y; |
---|
1538 | int i; |
---|
1539 | |
---|
1540 | y = pGetCoeff(p); |
---|
1541 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
1542 | n_Delete(&y,r->cf); |
---|
1543 | pSetCoeff0(p,x); |
---|
1544 | //for (i=pVariables; i!=0; i--) |
---|
1545 | //{ |
---|
1546 | // pAddExp(p,i, pGetExp(q,i)); |
---|
1547 | //} |
---|
1548 | //p->Order += q->Order; |
---|
1549 | p_ExpVectorAdd(p,q,r); |
---|
1550 | } |
---|
1551 | |
---|
1552 | /*3 |
---|
1553 | * compute for monomials p*q |
---|
1554 | * keeps p, q |
---|
1555 | */ |
---|
1556 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
1557 | { |
---|
1558 | number x; |
---|
1559 | int i; |
---|
1560 | poly r = p_Init(rr); |
---|
1561 | |
---|
1562 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
1563 | pSetCoeff0(r,x); |
---|
1564 | p_ExpVectorSum(r,p, q, rr); |
---|
1565 | return r; |
---|
1566 | } |
---|
1567 | |
---|
1568 | /*3 |
---|
1569 | * create binomial coef. |
---|
1570 | */ |
---|
1571 | static number* pnBin(int exp, const ring r) |
---|
1572 | { |
---|
1573 | int e, i, h; |
---|
1574 | number x, y, *bin=NULL; |
---|
1575 | |
---|
1576 | x = n_Init(exp,r->cf); |
---|
1577 | if (n_IsZero(x,r->cf)) |
---|
1578 | { |
---|
1579 | n_Delete(&x,r->cf); |
---|
1580 | return bin; |
---|
1581 | } |
---|
1582 | h = (exp >> 1) + 1; |
---|
1583 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
1584 | bin[1] = x; |
---|
1585 | if (exp < 4) |
---|
1586 | return bin; |
---|
1587 | i = exp - 1; |
---|
1588 | for (e=2; e<h; e++) |
---|
1589 | { |
---|
1590 | x = n_Init(i,r->cf); |
---|
1591 | i--; |
---|
1592 | y = n_Mult(x,bin[e-1],r->cf); |
---|
1593 | n_Delete(&x,r->cf); |
---|
1594 | x = n_Init(e,r->cf); |
---|
1595 | bin[e] = n_IntDiv(y,x,r->cf); |
---|
1596 | n_Delete(&x,r->cf); |
---|
1597 | n_Delete(&y,r->cf); |
---|
1598 | } |
---|
1599 | return bin; |
---|
1600 | } |
---|
1601 | |
---|
1602 | static void pnFreeBin(number *bin, int exp,const coeffs r) |
---|
1603 | { |
---|
1604 | int e, h = (exp >> 1) + 1; |
---|
1605 | |
---|
1606 | if (bin[1] != NULL) |
---|
1607 | { |
---|
1608 | for (e=1; e<h; e++) |
---|
1609 | n_Delete(&(bin[e]),r); |
---|
1610 | } |
---|
1611 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
---|
1612 | } |
---|
1613 | |
---|
1614 | /* |
---|
1615 | * compute for a poly p = head+tail, tail is monomial |
---|
1616 | * (head + tail)^exp, exp > 1 |
---|
1617 | * with binomial coef. |
---|
1618 | */ |
---|
1619 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
1620 | { |
---|
1621 | int eh, e; |
---|
1622 | long al; |
---|
1623 | poly *a; |
---|
1624 | poly tail, b, res, h; |
---|
1625 | number x; |
---|
1626 | number *bin = pnBin(exp,r); |
---|
1627 | |
---|
1628 | tail = pNext(p); |
---|
1629 | if (bin == NULL) |
---|
1630 | { |
---|
1631 | p_MonPower(p,exp,r); |
---|
1632 | p_MonPower(tail,exp,r); |
---|
1633 | #ifdef PDEBUG |
---|
1634 | p_Test(p,r); |
---|
1635 | #endif |
---|
1636 | return p; |
---|
1637 | } |
---|
1638 | eh = exp >> 1; |
---|
1639 | al = (exp + 1) * sizeof(poly); |
---|
1640 | a = (poly *)omAlloc(al); |
---|
1641 | a[1] = p; |
---|
1642 | for (e=1; e<exp; e++) |
---|
1643 | { |
---|
1644 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
1645 | } |
---|
1646 | res = a[exp]; |
---|
1647 | b = p_Head(tail,r); |
---|
1648 | for (e=exp-1; e>eh; e--) |
---|
1649 | { |
---|
1650 | h = a[e]; |
---|
1651 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
1652 | p_SetCoeff(h,x,r); |
---|
1653 | p_MonMult(h,b,r); |
---|
1654 | res = pNext(res) = h; |
---|
1655 | p_MonMult(b,tail,r); |
---|
1656 | } |
---|
1657 | for (e=eh; e!=0; e--) |
---|
1658 | { |
---|
1659 | h = a[e]; |
---|
1660 | x = n_Mult(bin[e],pGetCoeff(h),r->cf); |
---|
1661 | p_SetCoeff(h,x,r); |
---|
1662 | p_MonMult(h,b,r); |
---|
1663 | res = pNext(res) = h; |
---|
1664 | p_MonMult(b,tail,r); |
---|
1665 | } |
---|
1666 | p_LmDelete(&tail,r); |
---|
1667 | pNext(res) = b; |
---|
1668 | pNext(b) = NULL; |
---|
1669 | res = a[exp]; |
---|
1670 | omFreeSize((ADDRESS)a, al); |
---|
1671 | pnFreeBin(bin, exp, r->cf); |
---|
1672 | // tail=res; |
---|
1673 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
1674 | // { |
---|
1675 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
1676 | // { |
---|
1677 | // pLmDelete(&pNext(tail)); |
---|
1678 | // } |
---|
1679 | // else |
---|
1680 | // pIter(tail); |
---|
1681 | // } |
---|
1682 | #ifdef PDEBUG |
---|
1683 | p_Test(res,r); |
---|
1684 | #endif |
---|
1685 | return res; |
---|
1686 | } |
---|
1687 | |
---|
1688 | static poly p_Pow(poly p, int i, const ring r) |
---|
1689 | { |
---|
1690 | poly rc = p_Copy(p,r); |
---|
1691 | i -= 2; |
---|
1692 | do |
---|
1693 | { |
---|
1694 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
1695 | p_Normalize(rc,r); |
---|
1696 | i--; |
---|
1697 | } |
---|
1698 | while (i != 0); |
---|
1699 | return p_Mult_q(rc,p,r); |
---|
1700 | } |
---|
1701 | |
---|
1702 | /*2 |
---|
1703 | * returns the i-th power of p |
---|
1704 | * p will be destroyed |
---|
1705 | */ |
---|
1706 | poly p_Power(poly p, int i, const ring r) |
---|
1707 | { |
---|
1708 | poly rc=NULL; |
---|
1709 | |
---|
1710 | if (i==0) |
---|
1711 | { |
---|
1712 | p_Delete(&p,r); |
---|
1713 | return p_One(r); |
---|
1714 | } |
---|
1715 | |
---|
1716 | if(p!=NULL) |
---|
1717 | { |
---|
1718 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask))) |
---|
1719 | { |
---|
1720 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
1721 | return NULL; |
---|
1722 | } |
---|
1723 | switch (i) |
---|
1724 | { |
---|
1725 | // cannot happen, see above |
---|
1726 | // case 0: |
---|
1727 | // { |
---|
1728 | // rc=pOne(); |
---|
1729 | // pDelete(&p); |
---|
1730 | // break; |
---|
1731 | // } |
---|
1732 | case 1: |
---|
1733 | rc=p; |
---|
1734 | break; |
---|
1735 | case 2: |
---|
1736 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
1737 | break; |
---|
1738 | default: |
---|
1739 | if (i < 0) |
---|
1740 | { |
---|
1741 | p_Delete(&p,r); |
---|
1742 | return NULL; |
---|
1743 | } |
---|
1744 | else |
---|
1745 | { |
---|
1746 | #ifdef HAVE_PLURAL |
---|
1747 | if (rIsPluralRing(r)) /* in the NC case nothing helps :-( */ |
---|
1748 | { |
---|
1749 | int j=i; |
---|
1750 | rc = p_Copy(p,r); |
---|
1751 | while (j>1) |
---|
1752 | { |
---|
1753 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
1754 | j--; |
---|
1755 | } |
---|
1756 | p_Delete(&p,r); |
---|
1757 | return rc; |
---|
1758 | } |
---|
1759 | #endif |
---|
1760 | rc = pNext(p); |
---|
1761 | if (rc == NULL) |
---|
1762 | return p_MonPower(p,i,r); |
---|
1763 | /* else: binom ?*/ |
---|
1764 | int char_p=rChar(r); |
---|
1765 | if ((pNext(rc) != NULL) |
---|
1766 | #ifdef HAVE_RINGS |
---|
1767 | || rField_is_Ring(r) |
---|
1768 | #endif |
---|
1769 | ) |
---|
1770 | return p_Pow(p,i,r); |
---|
1771 | if ((char_p==0) || (i<=char_p)) |
---|
1772 | return p_TwoMonPower(p,i,r); |
---|
1773 | poly p_p=p_TwoMonPower(p_Copy(p,r),char_p,r); |
---|
1774 | return p_Mult_q(p_Power(p,i-char_p,r),p_p,r); |
---|
1775 | } |
---|
1776 | /*end default:*/ |
---|
1777 | } |
---|
1778 | } |
---|
1779 | return rc; |
---|
1780 | } |
---|
1781 | |
---|
1782 | /* --------------------------------------------------------------------------------*/ |
---|
1783 | /* content suff */ |
---|
1784 | |
---|
1785 | static number p_InitContent(poly ph, const ring r); |
---|
1786 | static number p_InitContent_a(poly ph, const ring r); |
---|
1787 | |
---|
1788 | void p_Content(poly ph, const ring r) |
---|
1789 | { |
---|
1790 | #ifdef HAVE_RINGS |
---|
1791 | if (rField_is_Ring(r)) |
---|
1792 | { |
---|
1793 | if ((ph!=NULL) && rField_has_Units(r)) |
---|
1794 | { |
---|
1795 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
1796 | if (!n_IsOne(k,r->cf)) |
---|
1797 | { |
---|
1798 | number tmpGMP = k; |
---|
1799 | k = n_Invers(k,r->cf); |
---|
1800 | n_Delete(&tmpGMP,r->cf); |
---|
1801 | poly h = pNext(ph); |
---|
1802 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
1803 | while (h != NULL) |
---|
1804 | { |
---|
1805 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
1806 | pIter(h); |
---|
1807 | } |
---|
1808 | } |
---|
1809 | n_Delete(&k,r->cf); |
---|
1810 | } |
---|
1811 | return; |
---|
1812 | } |
---|
1813 | #endif |
---|
1814 | number h,d; |
---|
1815 | poly p; |
---|
1816 | |
---|
1817 | if(TEST_OPT_CONTENTSB) return; |
---|
1818 | if(pNext(ph)==NULL) |
---|
1819 | { |
---|
1820 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
1821 | } |
---|
1822 | else |
---|
1823 | { |
---|
1824 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
1825 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
1826 | if (rField_is_Q(r)) |
---|
1827 | { |
---|
1828 | h=p_InitContent(ph,r); |
---|
1829 | p=ph; |
---|
1830 | } |
---|
1831 | else if ((rField_is_Extension(r)) |
---|
1832 | && ((rPar(r)>1)||(r->minpoly==NULL))) |
---|
1833 | { |
---|
1834 | h=p_InitContent_a(ph,r); |
---|
1835 | p=ph; |
---|
1836 | } |
---|
1837 | else |
---|
1838 | { |
---|
1839 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
1840 | p = pNext(ph); |
---|
1841 | } |
---|
1842 | while (p!=NULL) |
---|
1843 | { |
---|
1844 | n_Normalize(pGetCoeff(p),r->cf); |
---|
1845 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
1846 | n_Delete(&h,r->cf); |
---|
1847 | h = d; |
---|
1848 | if(n_IsOne(h,r->cf)) |
---|
1849 | { |
---|
1850 | break; |
---|
1851 | } |
---|
1852 | pIter(p); |
---|
1853 | } |
---|
1854 | p = ph; |
---|
1855 | //number tmp; |
---|
1856 | if(!n_IsOne(h,r->cf)) |
---|
1857 | { |
---|
1858 | while (p!=NULL) |
---|
1859 | { |
---|
1860 | //d = nDiv(pGetCoeff(p),h); |
---|
1861 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
1862 | //if (!nEqual(d,tmp)) |
---|
1863 | //{ |
---|
1864 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
1865 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
1866 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
1867 | //} |
---|
1868 | //nDelete(&tmp); |
---|
1869 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
1870 | p_SetCoeff(p,d,r); |
---|
1871 | pIter(p); |
---|
1872 | } |
---|
1873 | } |
---|
1874 | n_Delete(&h,r->cf); |
---|
1875 | #ifdef HAVE_FACTORY |
---|
1876 | if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
1877 | { |
---|
1878 | singclap_divide_content(ph); |
---|
1879 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
1880 | } |
---|
1881 | #endif |
---|
1882 | if (rField_is_Q_a(r)) |
---|
1883 | { |
---|
1884 | number hzz = nlInit(1, r->cf); |
---|
1885 | h = nlInit(1, r->cf); |
---|
1886 | p=ph; |
---|
1887 | Werror("longalg missing"); |
---|
1888 | #if 0 |
---|
1889 | while (p!=NULL) |
---|
1890 | { // each monom: coeff in Q_a |
---|
1891 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
1892 | poly c_n=c_n_n->z; |
---|
1893 | while (c_n!=NULL) |
---|
1894 | { // each monom: coeff in Q |
---|
1895 | d=nlLcm(hzz,pGetCoeff(c_n),r->algring->cf); |
---|
1896 | n_Delete(&hzz,r->algring->cf); |
---|
1897 | hzz=d; |
---|
1898 | pIter(c_n); |
---|
1899 | } |
---|
1900 | c_n=c_n_n->n; |
---|
1901 | while (c_n!=NULL) |
---|
1902 | { // each monom: coeff in Q |
---|
1903 | d=nlLcm(h,pGetCoeff(c_n),r->algring->cf); |
---|
1904 | n_Delete(&h,r->algring->cf); |
---|
1905 | h=d; |
---|
1906 | pIter(c_n); |
---|
1907 | } |
---|
1908 | pIter(p); |
---|
1909 | } |
---|
1910 | /* hzz contains the 1/lcm of all denominators in c_n_n->z*/ |
---|
1911 | /* h contains the 1/lcm of all denominators in c_n_n->n*/ |
---|
1912 | number htmp=nlInvers(h,r->algring->cf); |
---|
1913 | number hzztmp=nlInvers(hzz,r->algring->cf); |
---|
1914 | number hh=nlMult(hzz,h,r->algring->cf); |
---|
1915 | nlDelete(&hzz,r->algring->cf); |
---|
1916 | nlDelete(&h,r->algring->cf); |
---|
1917 | number hg=nlGcd(hzztmp,htmp,r->algring->cf); |
---|
1918 | nlDelete(&hzztmp,r->algring->cf); |
---|
1919 | nlDelete(&htmp,r->algring->cf); |
---|
1920 | h=nlMult(hh,hg,r->algring->cf); |
---|
1921 | nlDelete(&hg,r->algring->cf); |
---|
1922 | nlDelete(&hh,r->algring->cf); |
---|
1923 | nlNormalize(h,r->algring->cf); |
---|
1924 | if(!nlIsOne(h,r->algring->cf)) |
---|
1925 | { |
---|
1926 | p=ph; |
---|
1927 | while (p!=NULL) |
---|
1928 | { // each monom: coeff in Q_a |
---|
1929 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
1930 | poly c_n=c_n_n->z; |
---|
1931 | while (c_n!=NULL) |
---|
1932 | { // each monom: coeff in Q |
---|
1933 | d=nlMult(h,pGetCoeff(c_n),r->algring->cf); |
---|
1934 | nlNormalize(d,r->algring->cf); |
---|
1935 | nlDelete(&pGetCoeff(c_n),r->algring->cf); |
---|
1936 | pGetCoeff(c_n)=d; |
---|
1937 | pIter(c_n); |
---|
1938 | } |
---|
1939 | c_n=c_n_n->n; |
---|
1940 | while (c_n!=NULL) |
---|
1941 | { // each monom: coeff in Q |
---|
1942 | d=nlMult(h,pGetCoeff(c_n),r->algring->cf); |
---|
1943 | nlNormalize(d,r->algring->cf); |
---|
1944 | nlDelete(&pGetCoeff(c_n),r->algring->cf); |
---|
1945 | pGetCoeff(c_n)=d; |
---|
1946 | pIter(c_n); |
---|
1947 | } |
---|
1948 | pIter(p); |
---|
1949 | } |
---|
1950 | } |
---|
1951 | nlDelete(&h,r->algring->cf); |
---|
1952 | #endif |
---|
1953 | } |
---|
1954 | } |
---|
1955 | } |
---|
1956 | #if 0 // currently not used |
---|
1957 | void p_SimpleContent(poly ph,int smax, const ring r) |
---|
1958 | { |
---|
1959 | if(TEST_OPT_CONTENTSB) return; |
---|
1960 | if (ph==NULL) return; |
---|
1961 | if (pNext(ph)==NULL) |
---|
1962 | { |
---|
1963 | p_SetCoeff(ph,n_Init(1,r_cf),r); |
---|
1964 | return; |
---|
1965 | } |
---|
1966 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
1967 | { |
---|
1968 | return; |
---|
1969 | } |
---|
1970 | number d=p_InitContent(ph,r); |
---|
1971 | if (nlSize(d,r->cf)<=smax) |
---|
1972 | { |
---|
1973 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
1974 | return; |
---|
1975 | } |
---|
1976 | poly p=ph; |
---|
1977 | number h=d; |
---|
1978 | if (smax==1) smax=2; |
---|
1979 | while (p!=NULL) |
---|
1980 | { |
---|
1981 | #if 0 |
---|
1982 | d=nlGcd(h,pGetCoeff(p),r->cf); |
---|
1983 | nlDelete(&h,r->cf); |
---|
1984 | h = d; |
---|
1985 | #else |
---|
1986 | nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
1987 | #endif |
---|
1988 | if(nlSize(h,r->cf)<smax) |
---|
1989 | { |
---|
1990 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
1991 | return; |
---|
1992 | } |
---|
1993 | pIter(p); |
---|
1994 | } |
---|
1995 | p = ph; |
---|
1996 | if (!nlGreaterZero(pGetCoeff(p),r->cf)) h=nlNeg(h,r->cf); |
---|
1997 | if(nlIsOne(h,r->cf)) return; |
---|
1998 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
1999 | while (p!=NULL) |
---|
2000 | { |
---|
2001 | #if 1 |
---|
2002 | d = nlIntDiv(pGetCoeff(p),h,r->cf); |
---|
2003 | p_SetCoeff(p,d,r); |
---|
2004 | #else |
---|
2005 | nlInpIntDiv(pGetCoeff(p),h,r->cf); |
---|
2006 | #endif |
---|
2007 | pIter(p); |
---|
2008 | } |
---|
2009 | nlDelete(&h,r->cf); |
---|
2010 | } |
---|
2011 | #endif |
---|
2012 | |
---|
2013 | static number p_InitContent(poly ph, const ring r) |
---|
2014 | // only for coefficients in Q |
---|
2015 | #if 0 |
---|
2016 | { |
---|
2017 | assume(!TEST_OPT_CONTENTSB); |
---|
2018 | assume(ph!=NULL); |
---|
2019 | assume(pNext(ph)!=NULL); |
---|
2020 | assume(rField_is_Q(r)); |
---|
2021 | if (pNext(pNext(ph))==NULL) |
---|
2022 | { |
---|
2023 | return nlGetNom(pGetCoeff(pNext(ph)),r->cf); |
---|
2024 | } |
---|
2025 | poly p=ph; |
---|
2026 | number n1=nlGetNom(pGetCoeff(p),r->cf); |
---|
2027 | pIter(p); |
---|
2028 | number n2=nlGetNom(pGetCoeff(p),r->cf); |
---|
2029 | pIter(p); |
---|
2030 | number d; |
---|
2031 | number t; |
---|
2032 | loop |
---|
2033 | { |
---|
2034 | nlNormalize(pGetCoeff(p),r->cf); |
---|
2035 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
2036 | if (nlGreaterZero(t,r->cf)) |
---|
2037 | d=nlAdd(n1,t,r->cf); |
---|
2038 | else |
---|
2039 | d=nlSub(n1,t,r->cf); |
---|
2040 | nlDelete(&t,r->cf); |
---|
2041 | nlDelete(&n1,r->cf); |
---|
2042 | n1=d; |
---|
2043 | pIter(p); |
---|
2044 | if (p==NULL) break; |
---|
2045 | nlNormalize(pGetCoeff(p),r->cf); |
---|
2046 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
2047 | if (nlGreaterZero(t,r->cf)) |
---|
2048 | d=nlAdd(n2,t,r->cf); |
---|
2049 | else |
---|
2050 | d=nlSub(n2,t,r->cf); |
---|
2051 | nlDelete(&t,r->cf); |
---|
2052 | nlDelete(&n2,r->cf); |
---|
2053 | n2=d; |
---|
2054 | pIter(p); |
---|
2055 | if (p==NULL) break; |
---|
2056 | } |
---|
2057 | d=nlGcd(n1,n2,r->cf); |
---|
2058 | nlDelete(&n1,r->cf); |
---|
2059 | nlDelete(&n2,r->cf); |
---|
2060 | return d; |
---|
2061 | } |
---|
2062 | #else |
---|
2063 | { |
---|
2064 | number d=pGetCoeff(ph); |
---|
2065 | if(SR_HDL(d)&SR_INT) return d; |
---|
2066 | int s=mpz_size1(d->z); |
---|
2067 | int s2=-1; |
---|
2068 | number d2; |
---|
2069 | loop |
---|
2070 | { |
---|
2071 | pIter(ph); |
---|
2072 | if(ph==NULL) |
---|
2073 | { |
---|
2074 | if (s2==-1) return nlCopy(d,r->cf); |
---|
2075 | break; |
---|
2076 | } |
---|
2077 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
2078 | { |
---|
2079 | s2=s; |
---|
2080 | d2=d; |
---|
2081 | s=0; |
---|
2082 | d=pGetCoeff(ph); |
---|
2083 | if (s2==0) break; |
---|
2084 | } |
---|
2085 | else |
---|
2086 | if (mpz_size1((pGetCoeff(ph)->z))<=s) |
---|
2087 | { |
---|
2088 | s2=s; |
---|
2089 | d2=d; |
---|
2090 | d=pGetCoeff(ph); |
---|
2091 | s=mpz_size1(d->z); |
---|
2092 | } |
---|
2093 | } |
---|
2094 | return nlGcd(d,d2,r->cf); |
---|
2095 | } |
---|
2096 | #endif |
---|
2097 | |
---|
2098 | number p_InitContent_a(poly ph, const ring r) |
---|
2099 | // only for coefficients in K(a) anf K(a,...) |
---|
2100 | { |
---|
2101 | number d=pGetCoeff(ph); |
---|
2102 | int s=n_ParDeg(d,r->cf); |
---|
2103 | if (s /* n_ParDeg(d)*/ <=1) return n_Copy(d,r->cf); |
---|
2104 | int s2=-1; |
---|
2105 | number d2; |
---|
2106 | int ss; |
---|
2107 | loop |
---|
2108 | { |
---|
2109 | pIter(ph); |
---|
2110 | if(ph==NULL) |
---|
2111 | { |
---|
2112 | if (s2==-1) return n_Copy(d,r->cf); |
---|
2113 | break; |
---|
2114 | } |
---|
2115 | if ((ss=n_ParDeg(pGetCoeff(ph),r->cf))<s) |
---|
2116 | { |
---|
2117 | s2=s; |
---|
2118 | d2=d; |
---|
2119 | s=ss; |
---|
2120 | d=pGetCoeff(ph); |
---|
2121 | if (s2<=1) break; |
---|
2122 | } |
---|
2123 | } |
---|
2124 | return n_Gcd(d,d2,r->cf); |
---|
2125 | } |
---|
2126 | |
---|
2127 | |
---|
2128 | //void pContent(poly ph) |
---|
2129 | //{ |
---|
2130 | // number h,d; |
---|
2131 | // poly p; |
---|
2132 | // |
---|
2133 | // p = ph; |
---|
2134 | // if(pNext(p)==NULL) |
---|
2135 | // { |
---|
2136 | // pSetCoeff(p,nInit(1)); |
---|
2137 | // } |
---|
2138 | // else |
---|
2139 | // { |
---|
2140 | //#ifdef PDEBUG |
---|
2141 | // if (!pTest(p)) return; |
---|
2142 | //#endif |
---|
2143 | // nNormalize(pGetCoeff(p)); |
---|
2144 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
2145 | // { |
---|
2146 | // ph = pNeg(ph); |
---|
2147 | // nNormalize(pGetCoeff(p)); |
---|
2148 | // } |
---|
2149 | // h=pGetCoeff(p); |
---|
2150 | // pIter(p); |
---|
2151 | // while (p!=NULL) |
---|
2152 | // { |
---|
2153 | // nNormalize(pGetCoeff(p)); |
---|
2154 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
2155 | // pIter(p); |
---|
2156 | // } |
---|
2157 | // h=nCopy(h); |
---|
2158 | // p=ph; |
---|
2159 | // while (p!=NULL) |
---|
2160 | // { |
---|
2161 | // d=nGcd(h,pGetCoeff(p)); |
---|
2162 | // nDelete(&h); |
---|
2163 | // h = d; |
---|
2164 | // if(nIsOne(h)) |
---|
2165 | // { |
---|
2166 | // break; |
---|
2167 | // } |
---|
2168 | // pIter(p); |
---|
2169 | // } |
---|
2170 | // p = ph; |
---|
2171 | // //number tmp; |
---|
2172 | // if(!nIsOne(h)) |
---|
2173 | // { |
---|
2174 | // while (p!=NULL) |
---|
2175 | // { |
---|
2176 | // d = nIntDiv(pGetCoeff(p),h); |
---|
2177 | // pSetCoeff(p,d); |
---|
2178 | // pIter(p); |
---|
2179 | // } |
---|
2180 | // } |
---|
2181 | // nDelete(&h); |
---|
2182 | //#ifdef HAVE_FACTORY |
---|
2183 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2184 | // { |
---|
2185 | // pTest(ph); |
---|
2186 | // singclap_divide_content(ph); |
---|
2187 | // pTest(ph); |
---|
2188 | // } |
---|
2189 | //#endif |
---|
2190 | // } |
---|
2191 | //} |
---|
2192 | #if 0 |
---|
2193 | void p_Content(poly ph, const ring r) |
---|
2194 | { |
---|
2195 | number h,d; |
---|
2196 | poly p; |
---|
2197 | |
---|
2198 | if(pNext(ph)==NULL) |
---|
2199 | { |
---|
2200 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
2201 | } |
---|
2202 | else |
---|
2203 | { |
---|
2204 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
2205 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2206 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
2207 | p = pNext(ph); |
---|
2208 | while (p!=NULL) |
---|
2209 | { |
---|
2210 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2211 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
2212 | n_Delete(&h,r->cf); |
---|
2213 | h = d; |
---|
2214 | if(n_IsOne(h,r->cf)) |
---|
2215 | { |
---|
2216 | break; |
---|
2217 | } |
---|
2218 | pIter(p); |
---|
2219 | } |
---|
2220 | p = ph; |
---|
2221 | //number tmp; |
---|
2222 | if(!n_IsOne(h,r->cf)) |
---|
2223 | { |
---|
2224 | while (p!=NULL) |
---|
2225 | { |
---|
2226 | //d = nDiv(pGetCoeff(p),h); |
---|
2227 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
2228 | //if (!nEqual(d,tmp)) |
---|
2229 | //{ |
---|
2230 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
2231 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
2232 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
2233 | //} |
---|
2234 | //nDelete(&tmp); |
---|
2235 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
2236 | p_SetCoeff(p,d,r->cf); |
---|
2237 | pIter(p); |
---|
2238 | } |
---|
2239 | } |
---|
2240 | n_Delete(&h,r->cf); |
---|
2241 | #ifdef HAVE_FACTORY |
---|
2242 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2243 | //{ |
---|
2244 | // singclap_divide_content(ph); |
---|
2245 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
2246 | //} |
---|
2247 | #endif |
---|
2248 | } |
---|
2249 | } |
---|
2250 | #endif |
---|
2251 | /* ---------------------------------------------------------------------------*/ |
---|
2252 | /* cleardenom suff */ |
---|
2253 | poly p_Cleardenom(poly ph, const ring r) |
---|
2254 | { |
---|
2255 | poly start=ph; |
---|
2256 | number d, h; |
---|
2257 | poly p; |
---|
2258 | |
---|
2259 | #ifdef HAVE_RINGS |
---|
2260 | if (rField_is_Ring(r)) |
---|
2261 | { |
---|
2262 | p_Content(ph,r); |
---|
2263 | return start; |
---|
2264 | } |
---|
2265 | #endif |
---|
2266 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) return start; |
---|
2267 | p = ph; |
---|
2268 | if(pNext(p)==NULL) |
---|
2269 | { |
---|
2270 | if (TEST_OPT_CONTENTSB) |
---|
2271 | { |
---|
2272 | number n=n_GetDenom(pGetCoeff(p),r->cf); |
---|
2273 | if (!n_IsOne(n,r->cf)) |
---|
2274 | { |
---|
2275 | number nn=n_Mult(pGetCoeff(p),n,r->cf); |
---|
2276 | n_Normalize(nn,r->cf); |
---|
2277 | p_SetCoeff(p,nn,r); |
---|
2278 | } |
---|
2279 | n_Delete(&n,r->cf); |
---|
2280 | } |
---|
2281 | else |
---|
2282 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
2283 | } |
---|
2284 | else |
---|
2285 | { |
---|
2286 | h = n_Init(1,r->cf); |
---|
2287 | while (p!=NULL) |
---|
2288 | { |
---|
2289 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2290 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2291 | n_Delete(&h,r->cf); |
---|
2292 | h=d; |
---|
2293 | pIter(p); |
---|
2294 | } |
---|
2295 | /* contains the 1/lcm of all denominators */ |
---|
2296 | if(!n_IsOne(h,r->cf)) |
---|
2297 | { |
---|
2298 | p = ph; |
---|
2299 | while (p!=NULL) |
---|
2300 | { |
---|
2301 | /* should be: |
---|
2302 | * number hh; |
---|
2303 | * nGetDenom(p->coef,&hh); |
---|
2304 | * nMult(&h,&hh,&d); |
---|
2305 | * nNormalize(d); |
---|
2306 | * nDelete(&hh); |
---|
2307 | * nMult(d,p->coef,&hh); |
---|
2308 | * nDelete(&d); |
---|
2309 | * nDelete(&(p->coef)); |
---|
2310 | * p->coef =hh; |
---|
2311 | */ |
---|
2312 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2313 | n_Normalize(d,r->cf); |
---|
2314 | p_SetCoeff(p,d,r); |
---|
2315 | pIter(p); |
---|
2316 | } |
---|
2317 | n_Delete(&h,r->cf); |
---|
2318 | if (n_GetChar(r->cf)==1) |
---|
2319 | { |
---|
2320 | loop |
---|
2321 | { |
---|
2322 | h = n_Init(1,r->cf); |
---|
2323 | p=ph; |
---|
2324 | while (p!=NULL) |
---|
2325 | { |
---|
2326 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2327 | n_Delete(&h,r->cf); |
---|
2328 | h=d; |
---|
2329 | pIter(p); |
---|
2330 | } |
---|
2331 | /* contains the 1/lcm of all denominators */ |
---|
2332 | if(!n_IsOne(h,r->cf)) |
---|
2333 | { |
---|
2334 | p = ph; |
---|
2335 | while (p!=NULL) |
---|
2336 | { |
---|
2337 | /* should be: |
---|
2338 | * number hh; |
---|
2339 | * nGetDenom(p->coef,&hh); |
---|
2340 | * nMult(&h,&hh,&d); |
---|
2341 | * nNormalize(d); |
---|
2342 | * nDelete(&hh); |
---|
2343 | * nMult(d,p->coef,&hh); |
---|
2344 | * nDelete(&d); |
---|
2345 | * nDelete(&(p->coef)); |
---|
2346 | * p->coef =hh; |
---|
2347 | */ |
---|
2348 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2349 | n_Normalize(d,r->cf); |
---|
2350 | p_SetCoeff(p,d,r); |
---|
2351 | pIter(p); |
---|
2352 | } |
---|
2353 | n_Delete(&h,r->cf); |
---|
2354 | } |
---|
2355 | else |
---|
2356 | { |
---|
2357 | n_Delete(&h,r->cf); |
---|
2358 | break; |
---|
2359 | } |
---|
2360 | } |
---|
2361 | } |
---|
2362 | } |
---|
2363 | if (h!=NULL) n_Delete(&h,r->cf); |
---|
2364 | |
---|
2365 | p_Content(ph,r); |
---|
2366 | #ifdef HAVE_RATGRING |
---|
2367 | if (rIsRatGRing(r)) |
---|
2368 | { |
---|
2369 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
2370 | pContentRat(ph); |
---|
2371 | start=ph; |
---|
2372 | } |
---|
2373 | #endif |
---|
2374 | } |
---|
2375 | return start; |
---|
2376 | } |
---|
2377 | |
---|
2378 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
2379 | { |
---|
2380 | number d, h; |
---|
2381 | poly p; |
---|
2382 | |
---|
2383 | p = ph; |
---|
2384 | if(pNext(p)==NULL) |
---|
2385 | { |
---|
2386 | c=n_Invers(pGetCoeff(p),r->cf); |
---|
2387 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
2388 | } |
---|
2389 | else |
---|
2390 | { |
---|
2391 | h = n_Init(1,r->cf); |
---|
2392 | while (p!=NULL) |
---|
2393 | { |
---|
2394 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2395 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2396 | n_Delete(&h,r->cf); |
---|
2397 | h=d; |
---|
2398 | pIter(p); |
---|
2399 | } |
---|
2400 | c=h; |
---|
2401 | /* contains the 1/lcm of all denominators */ |
---|
2402 | if(!n_IsOne(h,r->cf)) |
---|
2403 | { |
---|
2404 | p = ph; |
---|
2405 | while (p!=NULL) |
---|
2406 | { |
---|
2407 | /* should be: |
---|
2408 | * number hh; |
---|
2409 | * nGetDenom(p->coef,&hh); |
---|
2410 | * nMult(&h,&hh,&d); |
---|
2411 | * nNormalize(d); |
---|
2412 | * nDelete(&hh); |
---|
2413 | * nMult(d,p->coef,&hh); |
---|
2414 | * nDelete(&d); |
---|
2415 | * nDelete(&(p->coef)); |
---|
2416 | * p->coef =hh; |
---|
2417 | */ |
---|
2418 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2419 | n_Normalize(d,r->cf); |
---|
2420 | p_SetCoeff(p,d,r); |
---|
2421 | pIter(p); |
---|
2422 | } |
---|
2423 | if (rField_is_Q_a(r)) |
---|
2424 | { |
---|
2425 | loop |
---|
2426 | { |
---|
2427 | h = n_Init(1,r->cf); |
---|
2428 | p=ph; |
---|
2429 | while (p!=NULL) |
---|
2430 | { |
---|
2431 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2432 | n_Delete(&h,r->cf); |
---|
2433 | h=d; |
---|
2434 | pIter(p); |
---|
2435 | } |
---|
2436 | /* contains the 1/lcm of all denominators */ |
---|
2437 | if(!n_IsOne(h,r->cf)) |
---|
2438 | { |
---|
2439 | p = ph; |
---|
2440 | while (p!=NULL) |
---|
2441 | { |
---|
2442 | /* should be: |
---|
2443 | * number hh; |
---|
2444 | * nGetDenom(p->coef,&hh); |
---|
2445 | * nMult(&h,&hh,&d); |
---|
2446 | * nNormalize(d); |
---|
2447 | * nDelete(&hh); |
---|
2448 | * nMult(d,p->coef,&hh); |
---|
2449 | * nDelete(&d); |
---|
2450 | * nDelete(&(p->coef)); |
---|
2451 | * p->coef =hh; |
---|
2452 | */ |
---|
2453 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2454 | n_Normalize(d,r->cf); |
---|
2455 | p_SetCoeff(p,d,r); |
---|
2456 | pIter(p); |
---|
2457 | } |
---|
2458 | number t=n_Mult(c,h,r->cf); |
---|
2459 | n_Delete(&c,r->cf); |
---|
2460 | c=t; |
---|
2461 | } |
---|
2462 | else |
---|
2463 | { |
---|
2464 | break; |
---|
2465 | } |
---|
2466 | n_Delete(&h,r->cf); |
---|
2467 | } |
---|
2468 | } |
---|
2469 | } |
---|
2470 | } |
---|
2471 | } |
---|
2472 | |
---|
2473 | number p_GetAllDenom(poly ph, const ring r) |
---|
2474 | { |
---|
2475 | number d=n_Init(1,r->cf); |
---|
2476 | poly p = ph; |
---|
2477 | |
---|
2478 | while (p!=NULL) |
---|
2479 | { |
---|
2480 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
2481 | if (!n_IsOne(h,r->cf)) |
---|
2482 | { |
---|
2483 | number dd=n_Mult(d,h,r->cf); |
---|
2484 | n_Delete(&d,r->cf); |
---|
2485 | d=dd; |
---|
2486 | } |
---|
2487 | n_Delete(&h,r->cf); |
---|
2488 | pIter(p); |
---|
2489 | } |
---|
2490 | return d; |
---|
2491 | } |
---|
2492 | |
---|
2493 | int p_Size(poly p, const ring r) |
---|
2494 | { |
---|
2495 | int count = 0; |
---|
2496 | while ( p != NULL ) |
---|
2497 | { |
---|
2498 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
2499 | pIter( p ); |
---|
2500 | } |
---|
2501 | return count; |
---|
2502 | } |
---|
2503 | |
---|
2504 | /*2 |
---|
2505 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
2506 | *assume: deg(var(varnum))==1 |
---|
2507 | */ |
---|
2508 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
2509 | { |
---|
2510 | pFDegProc deg; |
---|
2511 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
2512 | deg=p_Totaldegree; |
---|
2513 | else |
---|
2514 | deg=pFDeg; |
---|
2515 | |
---|
2516 | poly q=NULL, qn; |
---|
2517 | int o,ii; |
---|
2518 | sBucket_pt bp; |
---|
2519 | |
---|
2520 | if (p!=NULL) |
---|
2521 | { |
---|
2522 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
2523 | { |
---|
2524 | return NULL; |
---|
2525 | } |
---|
2526 | o=deg(p,r); |
---|
2527 | q=pNext(p); |
---|
2528 | while (q != NULL) |
---|
2529 | { |
---|
2530 | ii=deg(q,r); |
---|
2531 | if (ii>o) o=ii; |
---|
2532 | pIter(q); |
---|
2533 | } |
---|
2534 | q = p_Copy(p,r); |
---|
2535 | bp = sBucketCreate(r); |
---|
2536 | while (q != NULL) |
---|
2537 | { |
---|
2538 | ii = o-deg(q,r); |
---|
2539 | if (ii!=0) |
---|
2540 | { |
---|
2541 | p_AddExp(q,varnum, (long)ii,r); |
---|
2542 | p_Setm(q,r); |
---|
2543 | } |
---|
2544 | qn = pNext(q); |
---|
2545 | pNext(q) = NULL; |
---|
2546 | sBucket_Add_p(bp, q, 1); |
---|
2547 | q = qn; |
---|
2548 | } |
---|
2549 | sBucketDestroyAdd(bp, &q, &ii); |
---|
2550 | } |
---|
2551 | return q; |
---|
2552 | } |
---|
2553 | |
---|
2554 | /*2 |
---|
2555 | *tests if p is homogeneous with respect to the actual weigths |
---|
2556 | */ |
---|
2557 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
2558 | { |
---|
2559 | poly qp=p; |
---|
2560 | int o; |
---|
2561 | |
---|
2562 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
2563 | pFDegProc d; |
---|
2564 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
2565 | d=p_Totaldegree; |
---|
2566 | else |
---|
2567 | d=pFDeg; |
---|
2568 | o = d(p,r); |
---|
2569 | do |
---|
2570 | { |
---|
2571 | if (d(qp,r) != o) return FALSE; |
---|
2572 | pIter(qp); |
---|
2573 | } |
---|
2574 | while (qp != NULL); |
---|
2575 | return TRUE; |
---|
2576 | } |
---|
2577 | |
---|
2578 | /*----------utilities for syzygies--------------*/ |
---|
2579 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
2580 | { |
---|
2581 | poly q=p,qq; |
---|
2582 | int i; |
---|
2583 | |
---|
2584 | while (q!=NULL) |
---|
2585 | { |
---|
2586 | if (p_LmIsConstantComp(q,r)) |
---|
2587 | { |
---|
2588 | i = p_GetComp(q,r); |
---|
2589 | qq = p; |
---|
2590 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
2591 | if (qq == q) |
---|
2592 | { |
---|
2593 | *k = i; |
---|
2594 | return TRUE; |
---|
2595 | } |
---|
2596 | else |
---|
2597 | pIter(q); |
---|
2598 | } |
---|
2599 | else pIter(q); |
---|
2600 | } |
---|
2601 | return FALSE; |
---|
2602 | } |
---|
2603 | |
---|
2604 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
2605 | { |
---|
2606 | poly q=p,qq; |
---|
2607 | int i,j=0; |
---|
2608 | |
---|
2609 | *len = 0; |
---|
2610 | while (q!=NULL) |
---|
2611 | { |
---|
2612 | if (p_LmIsConstantComp(q,r)) |
---|
2613 | { |
---|
2614 | i = p_GetComp(q,r); |
---|
2615 | qq = p; |
---|
2616 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
2617 | if (qq == q) |
---|
2618 | { |
---|
2619 | j = 0; |
---|
2620 | while (qq!=NULL) |
---|
2621 | { |
---|
2622 | if (p_GetComp(qq,r)==i) j++; |
---|
2623 | pIter(qq); |
---|
2624 | } |
---|
2625 | if ((*len == 0) || (j<*len)) |
---|
2626 | { |
---|
2627 | *len = j; |
---|
2628 | *k = i; |
---|
2629 | } |
---|
2630 | } |
---|
2631 | } |
---|
2632 | pIter(q); |
---|
2633 | } |
---|
2634 | } |
---|
2635 | |
---|
2636 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
2637 | { |
---|
2638 | poly q = *p; |
---|
2639 | |
---|
2640 | if (q==NULL) return NULL; |
---|
2641 | |
---|
2642 | poly qq=NULL,result = NULL; |
---|
2643 | |
---|
2644 | if (p_GetComp(q,r)==k) |
---|
2645 | { |
---|
2646 | result = q; /* *p */ |
---|
2647 | while ((q!=NULL) && (p_GetComp(q,r)==k)) |
---|
2648 | { |
---|
2649 | p_SetComp(q,0,r); |
---|
2650 | p_SetmComp(q,r); |
---|
2651 | qq = q; |
---|
2652 | pIter(q); |
---|
2653 | } |
---|
2654 | *p = q; |
---|
2655 | pNext(qq) = NULL; |
---|
2656 | } |
---|
2657 | if (q==NULL) return result; |
---|
2658 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2659 | while (pNext(q)!=NULL) |
---|
2660 | { |
---|
2661 | if (p_GetComp(pNext(q),r)==k) |
---|
2662 | { |
---|
2663 | if (result==NULL) |
---|
2664 | { |
---|
2665 | result = pNext(q); |
---|
2666 | qq = result; |
---|
2667 | } |
---|
2668 | else |
---|
2669 | { |
---|
2670 | pNext(qq) = pNext(q); |
---|
2671 | pIter(qq); |
---|
2672 | } |
---|
2673 | pNext(q) = pNext(pNext(q)); |
---|
2674 | pNext(qq) =NULL; |
---|
2675 | p_SetComp(qq,0,r); |
---|
2676 | p_SetmComp(qq,r); |
---|
2677 | } |
---|
2678 | else |
---|
2679 | { |
---|
2680 | pIter(q); |
---|
2681 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2682 | } |
---|
2683 | } |
---|
2684 | return result; |
---|
2685 | } |
---|
2686 | |
---|
2687 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
2688 | { |
---|
2689 | poly q = *p,qq=NULL,result = NULL; |
---|
2690 | |
---|
2691 | if (q==NULL) return NULL; |
---|
2692 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
2693 | if (p_GetComp(q,r)==k) |
---|
2694 | { |
---|
2695 | result = q; |
---|
2696 | do |
---|
2697 | { |
---|
2698 | p_SetComp(q,0,r); |
---|
2699 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2700 | qq = q; |
---|
2701 | pIter(q); |
---|
2702 | } |
---|
2703 | while ((q!=NULL) && (p_GetComp(q,r)==k)); |
---|
2704 | *p = q; |
---|
2705 | pNext(qq) = NULL; |
---|
2706 | } |
---|
2707 | if (q==NULL) return result; |
---|
2708 | if (p_GetComp(q,r) > k) |
---|
2709 | { |
---|
2710 | p_SubComp(q,1,r); |
---|
2711 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2712 | } |
---|
2713 | poly pNext_q; |
---|
2714 | while ((pNext_q=pNext(q))!=NULL) |
---|
2715 | { |
---|
2716 | if (p_GetComp(pNext_q,r)==k) |
---|
2717 | { |
---|
2718 | if (result==NULL) |
---|
2719 | { |
---|
2720 | result = pNext_q; |
---|
2721 | qq = result; |
---|
2722 | } |
---|
2723 | else |
---|
2724 | { |
---|
2725 | pNext(qq) = pNext_q; |
---|
2726 | pIter(qq); |
---|
2727 | } |
---|
2728 | pNext(q) = pNext(pNext_q); |
---|
2729 | pNext(qq) =NULL; |
---|
2730 | p_SetComp(qq,0,r); |
---|
2731 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
2732 | } |
---|
2733 | else |
---|
2734 | { |
---|
2735 | /*pIter(q);*/ q=pNext_q; |
---|
2736 | if (p_GetComp(q,r) > k) |
---|
2737 | { |
---|
2738 | p_SubComp(q,1,r); |
---|
2739 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2740 | } |
---|
2741 | } |
---|
2742 | } |
---|
2743 | return result; |
---|
2744 | } |
---|
2745 | |
---|
2746 | // Splits *p into two polys: *q which consists of all monoms with |
---|
2747 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
2748 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
2749 | { |
---|
2750 | spolyrec pp, qq; |
---|
2751 | poly p, q, p_prev; |
---|
2752 | int l = 0; |
---|
2753 | |
---|
2754 | #ifdef HAVE_ASSUME |
---|
2755 | int lp = pLength(*r_p); |
---|
2756 | #endif |
---|
2757 | |
---|
2758 | pNext(&pp) = *r_p; |
---|
2759 | p = *r_p; |
---|
2760 | p_prev = &pp; |
---|
2761 | q = &qq; |
---|
2762 | |
---|
2763 | while(p != NULL) |
---|
2764 | { |
---|
2765 | while (p_GetComp(p,r) == comp) |
---|
2766 | { |
---|
2767 | pNext(q) = p; |
---|
2768 | pIter(q); |
---|
2769 | p_SetComp(p, 0,r); |
---|
2770 | p_SetmComp(p,r); |
---|
2771 | pIter(p); |
---|
2772 | l++; |
---|
2773 | if (p == NULL) |
---|
2774 | { |
---|
2775 | pNext(p_prev) = NULL; |
---|
2776 | goto Finish; |
---|
2777 | } |
---|
2778 | } |
---|
2779 | pNext(p_prev) = p; |
---|
2780 | p_prev = p; |
---|
2781 | pIter(p); |
---|
2782 | } |
---|
2783 | |
---|
2784 | Finish: |
---|
2785 | pNext(q) = NULL; |
---|
2786 | *r_p = pNext(&pp); |
---|
2787 | *r_q = pNext(&qq); |
---|
2788 | *lq = l; |
---|
2789 | #ifdef HAVE_ASSUME |
---|
2790 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
2791 | #endif |
---|
2792 | p_Test(*r_p,r); |
---|
2793 | p_Test(*r_q,r); |
---|
2794 | } |
---|
2795 | |
---|
2796 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
2797 | { |
---|
2798 | poly q; |
---|
2799 | |
---|
2800 | while ((*p!=NULL) && (p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
2801 | if (*p==NULL) return; |
---|
2802 | q = *p; |
---|
2803 | if (p_GetComp(q,r)>k) |
---|
2804 | { |
---|
2805 | p_SubComp(q,1,r); |
---|
2806 | p_SetmComp(q,r); |
---|
2807 | } |
---|
2808 | while (pNext(q)!=NULL) |
---|
2809 | { |
---|
2810 | if (p_GetComp(pNext(q),r)==k) |
---|
2811 | p_LmDelete(&(pNext(q)),r); |
---|
2812 | else |
---|
2813 | { |
---|
2814 | pIter(q); |
---|
2815 | if (p_GetComp(q,r)>k) |
---|
2816 | { |
---|
2817 | p_SubComp(q,1,r); |
---|
2818 | p_SetmComp(q,r); |
---|
2819 | } |
---|
2820 | } |
---|
2821 | } |
---|
2822 | } |
---|
2823 | /* -------------------------------------------------------- */ |
---|
2824 | /*2 |
---|
2825 | * change all global variables to fit the description of the new ring |
---|
2826 | */ |
---|
2827 | |
---|
2828 | void p_SetGlobals(const ring r, BOOLEAN complete) |
---|
2829 | { |
---|
2830 | int i; |
---|
2831 | if (r->ppNoether!=NULL) p_Delete(&r->ppNoether,r); |
---|
2832 | |
---|
2833 | if (complete) |
---|
2834 | { |
---|
2835 | test &= ~ TEST_RINGDEP_OPTS; |
---|
2836 | test |= r->options; |
---|
2837 | } |
---|
2838 | } |
---|
2839 | // |
---|
2840 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
2841 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
2842 | // only uses pFDeg (and not pDeg, or pTotalDegree, etc) |
---|
2843 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
2844 | { |
---|
2845 | assume(new_FDeg != NULL); |
---|
2846 | r->pFDeg = new_FDeg; |
---|
2847 | |
---|
2848 | if (new_lDeg == NULL) |
---|
2849 | new_lDeg = r->pLDegOrig; |
---|
2850 | |
---|
2851 | r->pLDeg = new_lDeg; |
---|
2852 | } |
---|
2853 | |
---|
2854 | // restores pFDeg and pLDeg: |
---|
2855 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
2856 | { |
---|
2857 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
2858 | r->pFDeg = old_FDeg; |
---|
2859 | r->pLDeg = old_lDeg; |
---|
2860 | } |
---|
2861 | |
---|
2862 | /*-------- several access procedures to monomials -------------------- */ |
---|
2863 | /* |
---|
2864 | * the module weights for std |
---|
2865 | */ |
---|
2866 | static pFDegProc pOldFDeg; |
---|
2867 | static pLDegProc pOldLDeg; |
---|
2868 | static intvec * pModW; |
---|
2869 | static BOOLEAN pOldLexOrder; |
---|
2870 | |
---|
2871 | static long pModDeg(poly p, ring r) |
---|
2872 | { |
---|
2873 | long d=pOldFDeg(p, r); |
---|
2874 | int c=p_GetComp(p, r); |
---|
2875 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
2876 | return d; |
---|
2877 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
2878 | } |
---|
2879 | |
---|
2880 | void p_SetModDeg(intvec *w, ring r) |
---|
2881 | { |
---|
2882 | if (w!=NULL) |
---|
2883 | { |
---|
2884 | r->pModW = w; |
---|
2885 | pOldFDeg = r->pFDeg; |
---|
2886 | pOldLDeg = r->pLDeg; |
---|
2887 | pOldLexOrder = r->pLexOrder; |
---|
2888 | pSetDegProcs(r,pModDeg); |
---|
2889 | r->pLexOrder = TRUE; |
---|
2890 | } |
---|
2891 | else |
---|
2892 | { |
---|
2893 | r->pModW = NULL; |
---|
2894 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
2895 | r->pLexOrder = pOldLexOrder; |
---|
2896 | } |
---|
2897 | } |
---|
2898 | |
---|
2899 | /*2 |
---|
2900 | * handle memory request for sets of polynomials (ideals) |
---|
2901 | * l is the length of *p, increment is the difference (may be negative) |
---|
2902 | */ |
---|
2903 | void pEnlargeSet(poly* *p, int l, int increment) |
---|
2904 | { |
---|
2905 | poly* h; |
---|
2906 | |
---|
2907 | h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
2908 | if (increment>0) |
---|
2909 | { |
---|
2910 | //for (i=l; i<l+increment; i++) |
---|
2911 | // h[i]=NULL; |
---|
2912 | memset(&(h[l]),0,increment*sizeof(poly)); |
---|
2913 | } |
---|
2914 | *p=h; |
---|
2915 | } |
---|
2916 | |
---|
2917 | /*2 |
---|
2918 | *divides p1 by its leading coefficient |
---|
2919 | */ |
---|
2920 | void p_Norm(poly p1, const ring r) |
---|
2921 | { |
---|
2922 | #ifdef HAVE_RINGS |
---|
2923 | if (rField_is_Ring(r)) |
---|
2924 | { |
---|
2925 | if (!nIsUnit(pGetCoeff(p1))) return; |
---|
2926 | // Werror("p_Norm not possible in the case of coefficient rings."); |
---|
2927 | } |
---|
2928 | else |
---|
2929 | #endif |
---|
2930 | if (p1!=NULL) |
---|
2931 | { |
---|
2932 | if (pNext(p1)==NULL) |
---|
2933 | { |
---|
2934 | p_SetCoeff(p1,n_Init(1,r->cf),r); |
---|
2935 | return; |
---|
2936 | } |
---|
2937 | poly h; |
---|
2938 | if (!n_IsOne(pGetCoeff(p1),r->cf)) |
---|
2939 | { |
---|
2940 | number k, c; |
---|
2941 | n_Normalize(pGetCoeff(p1),r->cf); |
---|
2942 | k = pGetCoeff(p1); |
---|
2943 | c = n_Init(1,r->cf); |
---|
2944 | pSetCoeff0(p1,c); |
---|
2945 | h = pNext(p1); |
---|
2946 | while (h!=NULL) |
---|
2947 | { |
---|
2948 | c=n_Div(pGetCoeff(h),k,r->cf); |
---|
2949 | // no need to normalize: Z/p, R |
---|
2950 | // normalize already in nDiv: Q_a, Z/p_a |
---|
2951 | // remains: Q |
---|
2952 | if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) n_Normalize(c,r->cf); |
---|
2953 | p_SetCoeff(h,c,r); |
---|
2954 | pIter(h); |
---|
2955 | } |
---|
2956 | n_Delete(&k,r->cf); |
---|
2957 | } |
---|
2958 | else |
---|
2959 | { |
---|
2960 | //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE |
---|
2961 | { |
---|
2962 | h = pNext(p1); |
---|
2963 | while (h!=NULL) |
---|
2964 | { |
---|
2965 | n_Normalize(pGetCoeff(h),r->cf); |
---|
2966 | pIter(h); |
---|
2967 | } |
---|
2968 | } |
---|
2969 | } |
---|
2970 | } |
---|
2971 | } |
---|
2972 | |
---|
2973 | /*2 |
---|
2974 | *normalize all coefficients |
---|
2975 | */ |
---|
2976 | void p_Normalize(poly p,const ring r) |
---|
2977 | { |
---|
2978 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
2979 | while (p!=NULL) |
---|
2980 | { |
---|
2981 | #ifdef LDEBUG |
---|
2982 | if (currRing==r) {nTest(pGetCoeff(p));} |
---|
2983 | #endif |
---|
2984 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2985 | pIter(p); |
---|
2986 | } |
---|
2987 | } |
---|
2988 | |
---|
2989 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
2990 | // Poly with Exp(n) != 0 is reversed |
---|
2991 | static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r) |
---|
2992 | { |
---|
2993 | if (p == NULL) |
---|
2994 | { |
---|
2995 | *non_zero = NULL; |
---|
2996 | *zero = NULL; |
---|
2997 | return; |
---|
2998 | } |
---|
2999 | spolyrec sz; |
---|
3000 | poly z, n_z, next; |
---|
3001 | z = &sz; |
---|
3002 | n_z = NULL; |
---|
3003 | |
---|
3004 | while(p != NULL) |
---|
3005 | { |
---|
3006 | next = pNext(p); |
---|
3007 | if (p_GetExp(p, n,r) == 0) |
---|
3008 | { |
---|
3009 | pNext(z) = p; |
---|
3010 | pIter(z); |
---|
3011 | } |
---|
3012 | else |
---|
3013 | { |
---|
3014 | pNext(p) = n_z; |
---|
3015 | n_z = p; |
---|
3016 | } |
---|
3017 | p = next; |
---|
3018 | } |
---|
3019 | pNext(z) = NULL; |
---|
3020 | *zero = pNext(&sz); |
---|
3021 | *non_zero = n_z; |
---|
3022 | } |
---|
3023 | /*3 |
---|
3024 | * substitute the n-th variable by 1 in p |
---|
3025 | * destroy p |
---|
3026 | */ |
---|
3027 | static poly p_Subst1 (poly p,int n, const ring r) |
---|
3028 | { |
---|
3029 | poly qq=NULL, result = NULL; |
---|
3030 | poly zero=NULL, non_zero=NULL; |
---|
3031 | |
---|
3032 | // reverse, so that add is likely to be linear |
---|
3033 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
3034 | |
---|
3035 | while (non_zero != NULL) |
---|
3036 | { |
---|
3037 | assume(p_GetExp(non_zero, n,r) != 0); |
---|
3038 | qq = non_zero; |
---|
3039 | pIter(non_zero); |
---|
3040 | qq->next = NULL; |
---|
3041 | p_SetExp(qq,n,0,r); |
---|
3042 | p_Setm(qq,r); |
---|
3043 | result = p_Add_q(result,qq,r); |
---|
3044 | } |
---|
3045 | p = p_Add_q(result, zero,r); |
---|
3046 | p_Test(p,r); |
---|
3047 | return p; |
---|
3048 | } |
---|
3049 | |
---|
3050 | /*3 |
---|
3051 | * substitute the n-th variable by number e in p |
---|
3052 | * destroy p |
---|
3053 | */ |
---|
3054 | static poly p_Subst2 (poly p,int n, number e, const ring r) |
---|
3055 | { |
---|
3056 | assume( ! n_IsZero(e,r->cf) ); |
---|
3057 | poly qq,result = NULL; |
---|
3058 | number nn, nm; |
---|
3059 | poly zero, non_zero; |
---|
3060 | |
---|
3061 | // reverse, so that add is likely to be linear |
---|
3062 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
3063 | |
---|
3064 | while (non_zero != NULL) |
---|
3065 | { |
---|
3066 | assume(p_GetExp(non_zero, nm,r) != 0); |
---|
3067 | qq = non_zero; |
---|
3068 | pIter(non_zero); |
---|
3069 | qq->next = NULL; |
---|
3070 | n_Power(e, p_GetExp(qq, n, r), &nn,r->cf); |
---|
3071 | nm = n_Mult(nn, pGetCoeff(qq),r->cf); |
---|
3072 | #ifdef HAVE_RINGS |
---|
3073 | if (n_IsZero(nm,r->cf)) |
---|
3074 | { |
---|
3075 | p_LmFree(&qq,r); |
---|
3076 | n_Delete(&nm,r->cf); |
---|
3077 | } |
---|
3078 | else |
---|
3079 | #endif |
---|
3080 | { |
---|
3081 | p_SetCoeff(qq, nm,r); |
---|
3082 | p_SetExp(qq, n, 0,r); |
---|
3083 | p_Setm(qq,r); |
---|
3084 | result = p_Add_q(result,qq,r); |
---|
3085 | } |
---|
3086 | n_Delete(&nn,r->cf); |
---|
3087 | } |
---|
3088 | p = p_Add_q(result, zero,r); |
---|
3089 | p_Test(p,r); |
---|
3090 | return p; |
---|
3091 | } |
---|
3092 | |
---|
3093 | |
---|
3094 | /* delete monoms whose n-th exponent is different from zero */ |
---|
3095 | static poly p_Subst0(poly p, int n, const ring r) |
---|
3096 | { |
---|
3097 | spolyrec res; |
---|
3098 | poly h = &res; |
---|
3099 | pNext(h) = p; |
---|
3100 | |
---|
3101 | while (pNext(h)!=NULL) |
---|
3102 | { |
---|
3103 | if (p_GetExp(pNext(h),n,r)!=0) |
---|
3104 | { |
---|
3105 | p_LmDelete(&pNext(h),r); |
---|
3106 | } |
---|
3107 | else |
---|
3108 | { |
---|
3109 | pIter(h); |
---|
3110 | } |
---|
3111 | } |
---|
3112 | p_Test(pNext(&res),r); |
---|
3113 | return pNext(&res); |
---|
3114 | } |
---|
3115 | |
---|
3116 | /*2 |
---|
3117 | * substitute the n-th variable by e in p |
---|
3118 | * destroy p |
---|
3119 | */ |
---|
3120 | poly p_Subst(poly p, int n, poly e, const ring r) |
---|
3121 | { |
---|
3122 | if (e == NULL) return p_Subst0(p, n,r); |
---|
3123 | |
---|
3124 | if (p_IsConstant(e,r)) |
---|
3125 | { |
---|
3126 | if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r); |
---|
3127 | else return p_Subst2(p, n, pGetCoeff(e),r); |
---|
3128 | } |
---|
3129 | |
---|
3130 | #ifdef HAVE_PLURAL |
---|
3131 | if (rIsPluralRing(r)) |
---|
3132 | { |
---|
3133 | return nc_pSubst(p,n,e,r); |
---|
3134 | } |
---|
3135 | #endif |
---|
3136 | |
---|
3137 | int exponent,i; |
---|
3138 | poly h, res, m; |
---|
3139 | int *me,*ee; |
---|
3140 | number nu,nu1; |
---|
3141 | |
---|
3142 | me=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
3143 | ee=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
3144 | if (e!=NULL) p_GetExpV(e,ee,r); |
---|
3145 | res=NULL; |
---|
3146 | h=p; |
---|
3147 | while (h!=NULL) |
---|
3148 | { |
---|
3149 | if ((e!=NULL) || (p_GetExp(h,n,r)==0)) |
---|
3150 | { |
---|
3151 | m=p_Head(h,r); |
---|
3152 | p_GetExpV(m,me,r); |
---|
3153 | exponent=me[n]; |
---|
3154 | me[n]=0; |
---|
3155 | for(i=rVar(r);i>0;i--) |
---|
3156 | me[i]+=exponent*ee[i]; |
---|
3157 | p_SetExpV(m,me,r); |
---|
3158 | if (e!=NULL) |
---|
3159 | { |
---|
3160 | n_Power(pGetCoeff(e),exponent,&nu,r->cf); |
---|
3161 | nu1=n_Mult(pGetCoeff(m),nu,r->cf); |
---|
3162 | n_Delete(&nu,r->cf); |
---|
3163 | p_SetCoeff(m,nu1,r); |
---|
3164 | } |
---|
3165 | res=p_Add_q(res,m,r); |
---|
3166 | } |
---|
3167 | p_LmDelete(&h,r); |
---|
3168 | } |
---|
3169 | omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int)); |
---|
3170 | omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int)); |
---|
3171 | return res; |
---|
3172 | } |
---|
3173 | /*2 |
---|
3174 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
3175 | */ |
---|
3176 | poly p_PermPoly (poly p, int * perm, const ring oldRing, const ring dst, |
---|
3177 | nMapFunc nMap, int *par_perm, int OldPar) |
---|
3178 | { |
---|
3179 | int OldpVariables = oldRing->N; |
---|
3180 | poly result = NULL; |
---|
3181 | poly result_last = NULL; |
---|
3182 | poly aq=NULL; /* the map coefficient */ |
---|
3183 | poly qq; /* the mapped monomial */ |
---|
3184 | |
---|
3185 | while (p != NULL) |
---|
3186 | { |
---|
3187 | if ((OldPar==0)||(rField_is_GF(oldRing))) |
---|
3188 | { |
---|
3189 | qq = p_Init(dst); |
---|
3190 | number n=nMap(pGetCoeff(p),oldRing->cf,dst->cf); |
---|
3191 | if ((dst->minpoly!=NULL) |
---|
3192 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
3193 | { |
---|
3194 | n_Normalize(n,dst->cf); |
---|
3195 | } |
---|
3196 | pGetCoeff(qq)=n; |
---|
3197 | // coef may be zero: pTest(qq); |
---|
3198 | } |
---|
3199 | else |
---|
3200 | { |
---|
3201 | qq=p_One(dst); |
---|
3202 | WerrorS("longalg missing"); |
---|
3203 | #if 0 |
---|
3204 | aq=naPermNumber(pGetCoeff(p),par_perm,OldPar, oldRing); |
---|
3205 | if ((dst->minpoly!=NULL) |
---|
3206 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
3207 | { |
---|
3208 | poly tmp=aq; |
---|
3209 | while (tmp!=NULL) |
---|
3210 | { |
---|
3211 | number n=pGetCoeff(tmp); |
---|
3212 | n_Normalize(n,dst->cf); |
---|
3213 | pGetCoeff(tmp)=n; |
---|
3214 | pIter(tmp); |
---|
3215 | } |
---|
3216 | } |
---|
3217 | p_Test(aq,dst); |
---|
3218 | #endif |
---|
3219 | } |
---|
3220 | if (rRing_has_Comp(dst)) p_SetComp(qq, p_GetComp(p,oldRing),dst); |
---|
3221 | if (n_IsZero(pGetCoeff(qq),dst->cf)) |
---|
3222 | { |
---|
3223 | p_LmDelete(&qq,dst); |
---|
3224 | } |
---|
3225 | else |
---|
3226 | { |
---|
3227 | int i; |
---|
3228 | int mapped_to_par=0; |
---|
3229 | for(i=1; i<=OldpVariables; i++) |
---|
3230 | { |
---|
3231 | int e=p_GetExp(p,i,oldRing); |
---|
3232 | if (e!=0) |
---|
3233 | { |
---|
3234 | if (perm==NULL) |
---|
3235 | { |
---|
3236 | p_SetExp(qq,i, e, dst); |
---|
3237 | } |
---|
3238 | else if (perm[i]>0) |
---|
3239 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
3240 | else if (perm[i]<0) |
---|
3241 | { |
---|
3242 | if (rField_is_GF(dst)) |
---|
3243 | { |
---|
3244 | number c=pGetCoeff(qq); |
---|
3245 | number ee=n_Par(1,dst->cf); |
---|
3246 | number eee;n_Power(ee,e,&eee,dst->cf); //nfDelete(ee,dst); |
---|
3247 | ee=n_Mult(c,eee,dst->cf); |
---|
3248 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
3249 | pSetCoeff0(qq,ee); |
---|
3250 | } |
---|
3251 | else |
---|
3252 | { |
---|
3253 | WerrorS("longalg missing"); |
---|
3254 | #if 0 |
---|
3255 | lnumber c=(lnumber)pGetCoeff(qq); |
---|
3256 | if (c->z->next==NULL) |
---|
3257 | p_AddExp(c->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->algring); |
---|
3258 | else /* more difficult: we have really to multiply: */ |
---|
3259 | { |
---|
3260 | lnumber mmc=(lnumber)naInit(1,dst); |
---|
3261 | p_SetExp(mmc->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->algring); |
---|
3262 | p_Setm(mmc->z,dst->algring->cf); |
---|
3263 | pGetCoeff(qq)=n_Mult((number)c,(number)mmc,dst->cf); |
---|
3264 | n_Delete((number *)&c,dst->cf); |
---|
3265 | n_Delete((number *)&mmc,dst->cf); |
---|
3266 | } |
---|
3267 | mapped_to_par=1; |
---|
3268 | #endif |
---|
3269 | } |
---|
3270 | } |
---|
3271 | else |
---|
3272 | { |
---|
3273 | /* this variable maps to 0 !*/ |
---|
3274 | p_LmDelete(&qq,dst); |
---|
3275 | break; |
---|
3276 | } |
---|
3277 | } |
---|
3278 | } |
---|
3279 | if (mapped_to_par |
---|
3280 | && (dst->minpoly!=NULL)) |
---|
3281 | { |
---|
3282 | number n=pGetCoeff(qq); |
---|
3283 | n_Normalize(n,dst->cf); |
---|
3284 | pGetCoeff(qq)=n; |
---|
3285 | } |
---|
3286 | } |
---|
3287 | pIter(p); |
---|
3288 | #if 1 |
---|
3289 | if (qq!=NULL) |
---|
3290 | { |
---|
3291 | p_Setm(qq,dst); |
---|
3292 | p_Test(aq,dst); |
---|
3293 | p_Test(qq,dst); |
---|
3294 | if (aq!=NULL) qq=p_Mult_q(aq,qq,dst); |
---|
3295 | aq = qq; |
---|
3296 | while (pNext(aq) != NULL) pIter(aq); |
---|
3297 | if (result_last==NULL) |
---|
3298 | { |
---|
3299 | result=qq; |
---|
3300 | } |
---|
3301 | else |
---|
3302 | { |
---|
3303 | pNext(result_last)=qq; |
---|
3304 | } |
---|
3305 | result_last=aq; |
---|
3306 | aq = NULL; |
---|
3307 | } |
---|
3308 | else if (aq!=NULL) |
---|
3309 | { |
---|
3310 | p_Delete(&aq,dst); |
---|
3311 | } |
---|
3312 | } |
---|
3313 | result=p_SortAdd(result,dst); |
---|
3314 | #else |
---|
3315 | // if (qq!=NULL) |
---|
3316 | // { |
---|
3317 | // pSetm(qq); |
---|
3318 | // pTest(qq); |
---|
3319 | // pTest(aq); |
---|
3320 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
3321 | // aq = qq; |
---|
3322 | // while (pNext(aq) != NULL) pIter(aq); |
---|
3323 | // pNext(aq) = result; |
---|
3324 | // aq = NULL; |
---|
3325 | // result = qq; |
---|
3326 | // } |
---|
3327 | // else if (aq!=NULL) |
---|
3328 | // { |
---|
3329 | // pDelete(&aq); |
---|
3330 | // } |
---|
3331 | //} |
---|
3332 | //p = result; |
---|
3333 | //result = NULL; |
---|
3334 | //while (p != NULL) |
---|
3335 | //{ |
---|
3336 | // qq = p; |
---|
3337 | // pIter(p); |
---|
3338 | // qq->next = NULL; |
---|
3339 | // result = pAdd(result, qq); |
---|
3340 | //} |
---|
3341 | #endif |
---|
3342 | p_Test(result,dst); |
---|
3343 | return result; |
---|
3344 | } |
---|
3345 | /************************************************************** |
---|
3346 | * |
---|
3347 | * Jet |
---|
3348 | * |
---|
3349 | **************************************************************/ |
---|
3350 | |
---|
3351 | poly pp_Jet(poly p, int m, const ring R) |
---|
3352 | { |
---|
3353 | poly r=NULL; |
---|
3354 | poly t=NULL; |
---|
3355 | |
---|
3356 | while (p!=NULL) |
---|
3357 | { |
---|
3358 | if (p_Totaldegree(p,R)<=m) |
---|
3359 | { |
---|
3360 | if (r==NULL) |
---|
3361 | r=p_Head(p,R); |
---|
3362 | else |
---|
3363 | if (t==NULL) |
---|
3364 | { |
---|
3365 | pNext(r)=p_Head(p,R); |
---|
3366 | t=pNext(r); |
---|
3367 | } |
---|
3368 | else |
---|
3369 | { |
---|
3370 | pNext(t)=p_Head(p,R); |
---|
3371 | pIter(t); |
---|
3372 | } |
---|
3373 | } |
---|
3374 | pIter(p); |
---|
3375 | } |
---|
3376 | return r; |
---|
3377 | } |
---|
3378 | |
---|
3379 | poly p_Jet(poly p, int m,const ring R) |
---|
3380 | { |
---|
3381 | poly t=NULL; |
---|
3382 | |
---|
3383 | while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R); |
---|
3384 | if (p==NULL) return NULL; |
---|
3385 | poly r=p; |
---|
3386 | while (pNext(p)!=NULL) |
---|
3387 | { |
---|
3388 | if (p_Totaldegree(pNext(p),R)>m) |
---|
3389 | { |
---|
3390 | p_LmDelete(&pNext(p),R); |
---|
3391 | } |
---|
3392 | else |
---|
3393 | pIter(p); |
---|
3394 | } |
---|
3395 | return r; |
---|
3396 | } |
---|
3397 | |
---|
3398 | poly pp_JetW(poly p, int m, short *w, const ring R) |
---|
3399 | { |
---|
3400 | poly r=NULL; |
---|
3401 | poly t=NULL; |
---|
3402 | while (p!=NULL) |
---|
3403 | { |
---|
3404 | if (totaldegreeWecart_IV(p,R,w)<=m) |
---|
3405 | { |
---|
3406 | if (r==NULL) |
---|
3407 | r=p_Head(p,R); |
---|
3408 | else |
---|
3409 | if (t==NULL) |
---|
3410 | { |
---|
3411 | pNext(r)=p_Head(p,R); |
---|
3412 | t=pNext(r); |
---|
3413 | } |
---|
3414 | else |
---|
3415 | { |
---|
3416 | pNext(t)=p_Head(p,R); |
---|
3417 | pIter(t); |
---|
3418 | } |
---|
3419 | } |
---|
3420 | pIter(p); |
---|
3421 | } |
---|
3422 | return r; |
---|
3423 | } |
---|
3424 | |
---|
3425 | poly p_JetW(poly p, int m, short *w, const ring R) |
---|
3426 | { |
---|
3427 | poly t=NULL; |
---|
3428 | while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R); |
---|
3429 | if (p==NULL) return NULL; |
---|
3430 | poly r=p; |
---|
3431 | while (pNext(p)!=NULL) |
---|
3432 | { |
---|
3433 | if (totaldegreeWecart_IV(pNext(p),R,w)>m) |
---|
3434 | { |
---|
3435 | p_LmDelete(&pNext(p),R); |
---|
3436 | } |
---|
3437 | else |
---|
3438 | pIter(p); |
---|
3439 | } |
---|
3440 | return r; |
---|
3441 | } |
---|
3442 | |
---|
3443 | /*************************************************************/ |
---|
3444 | int p_MinDeg(poly p,intvec *w, const ring R) |
---|
3445 | { |
---|
3446 | if(p==NULL) |
---|
3447 | return -1; |
---|
3448 | int d=-1; |
---|
3449 | while(p!=NULL) |
---|
3450 | { |
---|
3451 | int d0=0; |
---|
3452 | for(int j=0;j<rVar(R);j++) |
---|
3453 | if(w==NULL||j>=w->length()) |
---|
3454 | d0+=p_GetExp(p,j+1,R); |
---|
3455 | else |
---|
3456 | d0+=(*w)[j]*p_GetExp(p,j+1,R); |
---|
3457 | if(d0<d||d==-1) |
---|
3458 | d=d0; |
---|
3459 | pIter(p); |
---|
3460 | } |
---|
3461 | return d; |
---|
3462 | } |
---|
3463 | |
---|
3464 | /*************************************************************** |
---|
3465 | * |
---|
3466 | * p_ShallowDelete |
---|
3467 | * |
---|
3468 | ***************************************************************/ |
---|
3469 | #undef LINKAGE |
---|
3470 | #define LINKAGE |
---|
3471 | #undef p_Delete__T |
---|
3472 | #define p_Delete__T p_ShallowDelete |
---|
3473 | #undef n_Delete__T |
---|
3474 | #define n_Delete__T(n, r) ((void)0) |
---|
3475 | |
---|
3476 | #include <polys/templates/p_Delete__T.cc> |
---|
3477 | |
---|
3478 | #ifdef HAVE_RINGS |
---|
3479 | /* TRUE iff LT(f) | LT(g) */ |
---|
3480 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
3481 | { |
---|
3482 | int exponent; |
---|
3483 | for(int i = (int)r->N; i; i--) |
---|
3484 | { |
---|
3485 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
3486 | if (exponent < 0) return FALSE; |
---|
3487 | } |
---|
3488 | return n_DivBy(p_GetCoeff(g,r), p_GetCoeff(f,r),r->cf); |
---|
3489 | } |
---|
3490 | #endif |
---|