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 ring 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 | *******************************************************************/ |
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10 | |
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11 | #include <ctype.h> |
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12 | |
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13 | #include "misc/auxiliary.h" |
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14 | |
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15 | #include "misc/options.h" |
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16 | #include "misc/intvec.h" |
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17 | |
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18 | |
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19 | #include "coeffs/longrat.h" // snumber is needed... |
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20 | #include "coeffs/numbers.h" // ndCopyMap |
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21 | |
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22 | #include "polys/PolyEnumerator.h" |
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23 | |
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24 | #define TRANSEXT_PRIVATES |
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25 | |
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26 | #include "polys/ext_fields/transext.h" |
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27 | #include "polys/ext_fields/algext.h" |
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28 | |
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29 | #include "polys/weight.h" |
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30 | #include "polys/simpleideals.h" |
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31 | |
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32 | #include "ring.h" |
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33 | #include "p_polys.h" |
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34 | |
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35 | #include "polys/templates/p_MemCmp.h" |
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36 | #include "polys/templates/p_MemAdd.h" |
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37 | #include "polys/templates/p_MemCopy.h" |
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38 | |
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39 | |
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40 | #ifdef HAVE_PLURAL |
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41 | #include "nc/nc.h" |
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42 | #include "nc/sca.h" |
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43 | #endif |
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44 | |
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45 | #ifdef HAVE_SHIFTBBA |
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46 | #include "polys/shiftop.h" |
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47 | #endif |
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48 | |
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49 | #include "clapsing.h" |
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50 | |
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51 | /* |
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52 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
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53 | */ |
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54 | poly p_Farey(poly p, number N, const ring r) |
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55 | { |
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56 | poly h=p_Copy(p,r); |
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57 | poly hh=h; |
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58 | while(h!=NULL) |
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59 | { |
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60 | number c=pGetCoeff(h); |
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61 | pSetCoeff0(h,n_Farey(c,N,r->cf)); |
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62 | n_Delete(&c,r->cf); |
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63 | pIter(h); |
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64 | } |
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65 | while((hh!=NULL)&&(n_IsZero(pGetCoeff(hh),r->cf))) |
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66 | { |
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67 | p_LmDelete(&hh,r); |
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68 | } |
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69 | h=hh; |
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70 | while((h!=NULL) && (pNext(h)!=NULL)) |
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71 | { |
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72 | if(n_IsZero(pGetCoeff(pNext(h)),r->cf)) |
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73 | { |
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74 | p_LmDelete(&pNext(h),r); |
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75 | } |
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76 | else pIter(h); |
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77 | } |
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78 | return hh; |
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79 | } |
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80 | /*2 |
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81 | * xx,q: arrays of length 0..rl-1 |
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82 | * xx[i]: SB mod q[i] |
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83 | * assume: char=0 |
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84 | * assume: q[i]!=0 |
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85 | * destroys xx |
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86 | */ |
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87 | poly p_ChineseRemainder(poly *xx, number *x,number *q, int rl, CFArray &inv_cache,const ring R) |
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88 | { |
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89 | poly r,h,hh; |
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90 | int j; |
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91 | poly res_p=NULL; |
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92 | loop |
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93 | { |
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94 | /* search the lead term */ |
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95 | r=NULL; |
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96 | for(j=rl-1;j>=0;j--) |
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97 | { |
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98 | h=xx[j]; |
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99 | if ((h!=NULL) |
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100 | &&((r==NULL)||(p_LmCmp(r,h,R)==-1))) |
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101 | r=h; |
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102 | } |
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103 | /* nothing found -> return */ |
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104 | if (r==NULL) break; |
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105 | /* create the monomial in h */ |
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106 | h=p_Head(r,R); |
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107 | /* collect the coeffs in x[..]*/ |
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108 | for(j=rl-1;j>=0;j--) |
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109 | { |
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110 | hh=xx[j]; |
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111 | if ((hh!=NULL) && (p_LmCmp(h,hh,R)==0)) |
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112 | { |
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113 | x[j]=pGetCoeff(hh); |
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114 | hh=p_LmFreeAndNext(hh,R); |
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115 | xx[j]=hh; |
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116 | } |
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117 | else |
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118 | x[j]=n_Init(0, R->cf); |
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119 | } |
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120 | number n=n_ChineseRemainderSym(x,q,rl,TRUE,inv_cache,R->cf); |
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121 | for(j=rl-1;j>=0;j--) |
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122 | { |
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123 | x[j]=NULL; // n_Init(0...) takes no memory |
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124 | } |
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125 | if (n_IsZero(n,R->cf)) p_Delete(&h,R); |
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126 | else |
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127 | { |
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128 | //Print("new mon:");pWrite(h); |
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129 | p_SetCoeff(h,n,R); |
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130 | pNext(h)=res_p; |
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131 | res_p=h; // building res_p in reverse order! |
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132 | } |
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133 | } |
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134 | res_p=pReverse(res_p); |
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135 | p_Test(res_p, R); |
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136 | return res_p; |
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137 | } |
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138 | /*************************************************************** |
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139 | * |
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140 | * Completing what needs to be set for the monomial |
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141 | * |
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142 | ***************************************************************/ |
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143 | // this is special for the syz stuff |
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144 | STATIC_VAR int* _components = NULL; |
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145 | STATIC_VAR long* _componentsShifted = NULL; |
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146 | STATIC_VAR int _componentsExternal = 0; |
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147 | |
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148 | VAR BOOLEAN pSetm_error=0; |
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149 | |
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150 | #ifndef SING_NDEBUG |
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151 | # define MYTEST 0 |
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152 | #else /* ifndef SING_NDEBUG */ |
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153 | # define MYTEST 0 |
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154 | #endif /* ifndef SING_NDEBUG */ |
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155 | |
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156 | void p_Setm_General(poly p, const ring r) |
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157 | { |
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158 | p_LmCheckPolyRing(p, r); |
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159 | int pos=0; |
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160 | if (r->typ!=NULL) |
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161 | { |
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162 | loop |
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163 | { |
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164 | unsigned long ord=0; |
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165 | sro_ord* o=&(r->typ[pos]); |
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166 | switch(o->ord_typ) |
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167 | { |
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168 | case ro_dp: |
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169 | { |
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170 | int a,e; |
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171 | a=o->data.dp.start; |
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172 | e=o->data.dp.end; |
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173 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
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174 | p->exp[o->data.dp.place]=ord; |
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175 | break; |
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176 | } |
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177 | case ro_wp_neg: |
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178 | ord=POLY_NEGWEIGHT_OFFSET; |
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179 | // no break; |
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180 | case ro_wp: |
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181 | { |
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182 | int a,e; |
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183 | a=o->data.wp.start; |
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184 | e=o->data.wp.end; |
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185 | int *w=o->data.wp.weights; |
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186 | #if 1 |
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187 | for(int i=a;i<=e;i++) ord+=((unsigned long)p_GetExp(p,i,r))*((unsigned long)w[i-a]); |
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188 | #else |
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189 | long ai; |
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190 | int ei,wi; |
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191 | for(int i=a;i<=e;i++) |
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192 | { |
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193 | ei=p_GetExp(p,i,r); |
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194 | wi=w[i-a]; |
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195 | ai=ei*wi; |
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196 | if (ai/ei!=wi) pSetm_error=TRUE; |
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197 | ord+=ai; |
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198 | if (ord<ai) pSetm_error=TRUE; |
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199 | } |
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200 | #endif |
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201 | p->exp[o->data.wp.place]=ord; |
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202 | break; |
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203 | } |
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204 | case ro_am: |
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205 | { |
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206 | ord = POLY_NEGWEIGHT_OFFSET; |
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207 | const short a=o->data.am.start; |
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208 | const short e=o->data.am.end; |
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209 | const int * w=o->data.am.weights; |
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210 | #if 1 |
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211 | for(short i=a; i<=e; i++, w++) |
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212 | ord += ((*w) * p_GetExp(p,i,r)); |
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213 | #else |
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214 | long ai; |
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215 | int ei,wi; |
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216 | for(short i=a;i<=e;i++) |
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217 | { |
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218 | ei=p_GetExp(p,i,r); |
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219 | wi=w[i-a]; |
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220 | ai=ei*wi; |
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221 | if (ai/ei!=wi) pSetm_error=TRUE; |
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222 | ord += ai; |
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223 | if (ord<ai) pSetm_error=TRUE; |
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224 | } |
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225 | #endif |
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226 | const int c = p_GetComp(p,r); |
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227 | |
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228 | const short len_gen= o->data.am.len_gen; |
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229 | |
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230 | if ((c > 0) && (c <= len_gen)) |
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231 | { |
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232 | assume( w == o->data.am.weights_m ); |
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233 | assume( w[0] == len_gen ); |
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234 | ord += w[c]; |
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235 | } |
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236 | |
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237 | p->exp[o->data.am.place] = ord; |
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238 | break; |
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239 | } |
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240 | case ro_wp64: |
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241 | { |
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242 | int64 ord=0; |
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243 | int a,e; |
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244 | a=o->data.wp64.start; |
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245 | e=o->data.wp64.end; |
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246 | int64 *w=o->data.wp64.weights64; |
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247 | int64 ei,wi,ai; |
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248 | for(int i=a;i<=e;i++) |
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249 | { |
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250 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
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251 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
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252 | ei=(int64)p_GetExp(p,i,r); |
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253 | wi=w[i-a]; |
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254 | ai=ei*wi; |
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255 | if(ei!=0 && ai/ei!=wi) |
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256 | { |
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257 | pSetm_error=TRUE; |
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258 | #if SIZEOF_LONG == 4 |
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259 | Print("ai %lld, wi %lld\n",ai,wi); |
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260 | #else |
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261 | Print("ai %ld, wi %ld\n",ai,wi); |
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262 | #endif |
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263 | } |
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264 | ord+=ai; |
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265 | if (ord<ai) |
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266 | { |
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267 | pSetm_error=TRUE; |
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268 | #if SIZEOF_LONG == 4 |
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269 | Print("ai %lld, ord %lld\n",ai,ord); |
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270 | #else |
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271 | Print("ai %ld, ord %ld\n",ai,ord); |
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272 | #endif |
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273 | } |
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274 | } |
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275 | int64 mask=(int64)0x7fffffff; |
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276 | long a_0=(long)(ord&mask); //2^31 |
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277 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
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278 | |
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279 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
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280 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
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281 | //Print("mask: %d",mask); |
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282 | |
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283 | p->exp[o->data.wp64.place]=a_1; |
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284 | p->exp[o->data.wp64.place+1]=a_0; |
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285 | // if(p_Setm_error) PrintS("***************************\n" |
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286 | // "***************************\n" |
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287 | // "**WARNING: overflow error**\n" |
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288 | // "***************************\n" |
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289 | // "***************************\n"); |
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290 | break; |
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291 | } |
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292 | case ro_cp: |
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293 | { |
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294 | int a,e; |
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295 | a=o->data.cp.start; |
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296 | e=o->data.cp.end; |
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297 | int pl=o->data.cp.place; |
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298 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
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299 | break; |
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300 | } |
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301 | case ro_syzcomp: |
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302 | { |
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303 | long c=__p_GetComp(p,r); |
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304 | long sc = c; |
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305 | int* Components = (_componentsExternal ? _components : |
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306 | o->data.syzcomp.Components); |
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307 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
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308 | o->data.syzcomp.ShiftedComponents); |
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309 | if (ShiftedComponents != NULL) |
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310 | { |
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311 | assume(Components != NULL); |
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312 | assume(c == 0 || Components[c] != 0); |
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313 | sc = ShiftedComponents[Components[c]]; |
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314 | assume(c == 0 || sc != 0); |
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315 | } |
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316 | p->exp[o->data.syzcomp.place]=sc; |
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317 | break; |
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318 | } |
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319 | case ro_syz: |
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320 | { |
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321 | const unsigned long c = __p_GetComp(p, r); |
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322 | const short place = o->data.syz.place; |
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323 | const int limit = o->data.syz.limit; |
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324 | |
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325 | if (c > (unsigned long)limit) |
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326 | p->exp[place] = o->data.syz.curr_index; |
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327 | else if (c > 0) |
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328 | { |
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329 | assume( (1 <= c) && (c <= (unsigned long)limit) ); |
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330 | p->exp[place]= o->data.syz.syz_index[c]; |
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331 | } |
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332 | else |
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333 | { |
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334 | assume(c == 0); |
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335 | p->exp[place]= 0; |
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336 | } |
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337 | break; |
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338 | } |
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339 | // Prefix for Induced Schreyer ordering |
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340 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
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341 | { |
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342 | assume(p != NULL); |
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343 | |
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344 | #ifndef SING_NDEBUG |
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345 | #if MYTEST |
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346 | Print("p_Setm_General: ro_isTemp ord: pos: %d, p: ", pos); p_wrp(p, r); |
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347 | #endif |
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348 | #endif |
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349 | int c = p_GetComp(p, r); |
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350 | |
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351 | assume( c >= 0 ); |
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352 | |
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353 | // Let's simulate case ro_syz above.... |
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354 | // Should accumulate (by Suffix) and be a level indicator |
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355 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
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356 | |
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357 | assume( pVarOffset != NULL ); |
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358 | |
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359 | // TODO: Can this be done in the suffix??? |
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360 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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361 | { |
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362 | const int vo = pVarOffset[i]; |
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363 | if( vo != -1) // TODO: optimize: can be done once! |
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364 | { |
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365 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
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366 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
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367 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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368 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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369 | } |
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370 | } |
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371 | #ifndef SING_NDEBUG |
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372 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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373 | { |
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374 | const int vo = pVarOffset[i]; |
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375 | if( vo != -1) // TODO: optimize: can be done once! |
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376 | { |
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377 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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378 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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379 | } |
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380 | } |
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381 | #if MYTEST |
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382 | // if( p->exp[o->data.isTemp.start] > 0 ) |
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383 | PrintS("after Values: "); p_wrp(p, r); |
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384 | #endif |
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385 | #endif |
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386 | break; |
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387 | } |
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388 | |
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389 | // Suffix for Induced Schreyer ordering |
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390 | case ro_is: |
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391 | { |
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392 | #ifndef SING_NDEBUG |
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393 | #if MYTEST |
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394 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_wrp(p, r); |
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395 | #endif |
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396 | #endif |
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397 | |
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398 | assume(p != NULL); |
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399 | |
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400 | int c = p_GetComp(p, r); |
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401 | |
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402 | assume( c >= 0 ); |
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403 | const ideal F = o->data.is.F; |
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404 | const int limit = o->data.is.limit; |
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405 | assume( limit >= 0 ); |
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406 | const int start = o->data.is.start; |
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407 | |
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408 | if( F != NULL && c > limit ) |
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409 | { |
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410 | #ifndef SING_NDEBUG |
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411 | #if MYTEST |
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412 | Print("p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit); |
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413 | PrintS("preComputed Values: "); |
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414 | p_wrp(p, r); |
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415 | #endif |
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416 | #endif |
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417 | // if( c > limit ) // BUG??? |
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418 | p->exp[start] = 1; |
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419 | // else |
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420 | // p->exp[start] = 0; |
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421 | |
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422 | |
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423 | c -= limit; |
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424 | assume( c > 0 ); |
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425 | c--; |
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426 | |
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427 | if( c >= IDELEMS(F) ) |
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428 | break; |
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429 | |
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430 | assume( c < IDELEMS(F) ); // What about others??? |
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431 | |
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432 | const poly pp = F->m[c]; // get reference monomial!!! |
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433 | |
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434 | if(pp == NULL) |
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435 | break; |
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436 | |
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437 | assume(pp != NULL); |
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438 | |
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439 | #ifndef SING_NDEBUG |
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440 | #if MYTEST |
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441 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
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442 | p_wrp(pp, r); |
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443 | #endif |
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444 | #endif |
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445 | |
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446 | const int end = o->data.is.end; |
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447 | assume(start <= end); |
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448 | |
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449 | |
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450 | // const int st = o->data.isTemp.start; |
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451 | |
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452 | #ifndef SING_NDEBUG |
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453 | #if MYTEST |
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454 | Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]); |
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455 | #endif |
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456 | #endif |
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457 | |
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458 | // p_ExpVectorAdd(p, pp, r); |
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459 | |
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460 | for( int i = start; i <= end; i++) // v[0] may be here... |
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461 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
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462 | |
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463 | // p_MemAddAdjust(p, ri); |
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464 | if (r->NegWeightL_Offset != NULL) |
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465 | { |
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466 | for (int i=r->NegWeightL_Size-1; i>=0; i--) |
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467 | { |
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468 | const int _i = r->NegWeightL_Offset[i]; |
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469 | if( start <= _i && _i <= end ) |
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470 | p->exp[_i] -= POLY_NEGWEIGHT_OFFSET; |
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471 | } |
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472 | } |
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473 | |
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474 | |
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475 | #ifndef SING_NDEBUG |
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476 | const int* const pVarOffset = o->data.is.pVarOffset; |
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477 | |
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478 | assume( pVarOffset != NULL ); |
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479 | |
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480 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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481 | { |
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482 | const int vo = pVarOffset[i]; |
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483 | if( vo != -1) // TODO: optimize: can be done once! |
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484 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
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485 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
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486 | } |
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487 | // TODO: how to check this for computed values??? |
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488 | #if MYTEST |
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489 | PrintS("Computed Values: "); p_wrp(p, r); |
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490 | #endif |
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491 | #endif |
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492 | } else |
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493 | { |
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494 | p->exp[start] = 0; //!!!!????? where????? |
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495 | |
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496 | const int* const pVarOffset = o->data.is.pVarOffset; |
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497 | |
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498 | // What about v[0] - component: it will be added later by |
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499 | // suffix!!! |
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500 | // TODO: Test it! |
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501 | const int vo = pVarOffset[0]; |
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502 | if( vo != -1 ) |
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503 | p->exp[vo] = c; // initial component v[0]! |
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504 | |
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505 | #ifndef SING_NDEBUG |
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506 | #if MYTEST |
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507 | Print("ELSE p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]); |
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508 | p_wrp(p, r); |
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509 | #endif |
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510 | #endif |
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511 | } |
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512 | |
---|
513 | break; |
---|
514 | } |
---|
515 | default: |
---|
516 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
---|
517 | return; |
---|
518 | } |
---|
519 | pos++; |
---|
520 | if (pos == r->OrdSize) return; |
---|
521 | } |
---|
522 | } |
---|
523 | } |
---|
524 | |
---|
525 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
---|
526 | { |
---|
527 | _components = Components; |
---|
528 | _componentsShifted = ShiftedComponents; |
---|
529 | _componentsExternal = 1; |
---|
530 | p_Setm_General(p, r); |
---|
531 | _componentsExternal = 0; |
---|
532 | } |
---|
533 | |
---|
534 | // dummy for lp, ls, etc |
---|
535 | void p_Setm_Dummy(poly p, const ring r) |
---|
536 | { |
---|
537 | p_LmCheckPolyRing(p, r); |
---|
538 | } |
---|
539 | |
---|
540 | // for dp, Dp, ds, etc |
---|
541 | void p_Setm_TotalDegree(poly p, const ring r) |
---|
542 | { |
---|
543 | p_LmCheckPolyRing(p, r); |
---|
544 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
---|
545 | } |
---|
546 | |
---|
547 | // for wp, Wp, ws, etc |
---|
548 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
---|
549 | { |
---|
550 | p_LmCheckPolyRing(p, r); |
---|
551 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
---|
552 | } |
---|
553 | |
---|
554 | p_SetmProc p_GetSetmProc(const ring r) |
---|
555 | { |
---|
556 | // covers lp, rp, ls, |
---|
557 | if (r->typ == NULL) return p_Setm_Dummy; |
---|
558 | |
---|
559 | if (r->OrdSize == 1) |
---|
560 | { |
---|
561 | if (r->typ[0].ord_typ == ro_dp && |
---|
562 | r->typ[0].data.dp.start == 1 && |
---|
563 | r->typ[0].data.dp.end == r->N && |
---|
564 | r->typ[0].data.dp.place == r->pOrdIndex) |
---|
565 | return p_Setm_TotalDegree; |
---|
566 | if (r->typ[0].ord_typ == ro_wp && |
---|
567 | r->typ[0].data.wp.start == 1 && |
---|
568 | r->typ[0].data.wp.end == r->N && |
---|
569 | r->typ[0].data.wp.place == r->pOrdIndex && |
---|
570 | r->typ[0].data.wp.weights == r->firstwv) |
---|
571 | return p_Setm_WFirstTotalDegree; |
---|
572 | } |
---|
573 | return p_Setm_General; |
---|
574 | } |
---|
575 | |
---|
576 | |
---|
577 | /* -------------------------------------------------------------------*/ |
---|
578 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
579 | |
---|
580 | /* comptible with ordering */ |
---|
581 | long p_Deg(poly a, const ring r) |
---|
582 | { |
---|
583 | p_LmCheckPolyRing(a, r); |
---|
584 | // assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); // WRONG assume! |
---|
585 | return p_GetOrder(a, r); |
---|
586 | } |
---|
587 | |
---|
588 | // p_WTotalDegree for weighted orderings |
---|
589 | // whose first block covers all variables |
---|
590 | long p_WFirstTotalDegree(poly p, const ring r) |
---|
591 | { |
---|
592 | int i; |
---|
593 | long sum = 0; |
---|
594 | |
---|
595 | for (i=1; i<= r->firstBlockEnds; i++) |
---|
596 | { |
---|
597 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
598 | } |
---|
599 | return sum; |
---|
600 | } |
---|
601 | |
---|
602 | /*2 |
---|
603 | * compute the degree of the leading monomial of p |
---|
604 | * with respect to weigths from the ordering |
---|
605 | * the ordering is not compatible with degree so do not use p->Order |
---|
606 | */ |
---|
607 | long p_WTotaldegree(poly p, const ring r) |
---|
608 | { |
---|
609 | p_LmCheckPolyRing(p, r); |
---|
610 | int i, k; |
---|
611 | long j =0; |
---|
612 | |
---|
613 | // iterate through each block: |
---|
614 | for (i=0;r->order[i]!=0;i++) |
---|
615 | { |
---|
616 | int b0=r->block0[i]; |
---|
617 | int b1=r->block1[i]; |
---|
618 | switch(r->order[i]) |
---|
619 | { |
---|
620 | case ringorder_M: |
---|
621 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
622 | { // in jedem block: |
---|
623 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
---|
624 | } |
---|
625 | break; |
---|
626 | case ringorder_am: |
---|
627 | b1=si_min(b1,r->N); |
---|
628 | /* no break, continue as ringorder_a*/ |
---|
629 | case ringorder_a: |
---|
630 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
631 | { // only one line |
---|
632 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
---|
633 | } |
---|
634 | return j*r->OrdSgn; |
---|
635 | case ringorder_wp: |
---|
636 | case ringorder_ws: |
---|
637 | case ringorder_Wp: |
---|
638 | case ringorder_Ws: |
---|
639 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
640 | { // in jedem block: |
---|
641 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
---|
642 | } |
---|
643 | break; |
---|
644 | case ringorder_lp: |
---|
645 | case ringorder_ls: |
---|
646 | case ringorder_rs: |
---|
647 | case ringorder_dp: |
---|
648 | case ringorder_ds: |
---|
649 | case ringorder_Dp: |
---|
650 | case ringorder_Ds: |
---|
651 | case ringorder_rp: |
---|
652 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
653 | { |
---|
654 | j+= p_GetExp(p,k,r); |
---|
655 | } |
---|
656 | break; |
---|
657 | case ringorder_a64: |
---|
658 | { |
---|
659 | int64* w=(int64*)r->wvhdl[i]; |
---|
660 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
---|
661 | { |
---|
662 | //there should be added a line which checks if w[k]>2^31 |
---|
663 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
---|
664 | } |
---|
665 | //break; |
---|
666 | return j; |
---|
667 | } |
---|
668 | case ringorder_c: /* nothing to do*/ |
---|
669 | case ringorder_C: /* nothing to do*/ |
---|
670 | case ringorder_S: /* nothing to do*/ |
---|
671 | case ringorder_s: /* nothing to do*/ |
---|
672 | case ringorder_IS: /* nothing to do */ |
---|
673 | case ringorder_unspec: /* to make clang happy, does not occur*/ |
---|
674 | case ringorder_no: /* to make clang happy, does not occur*/ |
---|
675 | case ringorder_L: /* to make clang happy, does not occur*/ |
---|
676 | case ringorder_aa: /* ignored by p_WTotaldegree*/ |
---|
677 | break; |
---|
678 | /* no default: all orderings covered */ |
---|
679 | } |
---|
680 | } |
---|
681 | return j; |
---|
682 | } |
---|
683 | |
---|
684 | long p_DegW(poly p, const short *w, const ring R) |
---|
685 | { |
---|
686 | p_Test(p, R); |
---|
687 | assume( w != NULL ); |
---|
688 | long r=-LONG_MAX; |
---|
689 | |
---|
690 | while (p!=NULL) |
---|
691 | { |
---|
692 | long t=totaldegreeWecart_IV(p,R,w); |
---|
693 | if (t>r) r=t; |
---|
694 | pIter(p); |
---|
695 | } |
---|
696 | return r; |
---|
697 | } |
---|
698 | |
---|
699 | int p_Weight(int i, const ring r) |
---|
700 | { |
---|
701 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
702 | { |
---|
703 | return 1; |
---|
704 | } |
---|
705 | return r->firstwv[i-1]; |
---|
706 | } |
---|
707 | |
---|
708 | long p_WDegree(poly p, const ring r) |
---|
709 | { |
---|
710 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
711 | p_LmCheckPolyRing(p, r); |
---|
712 | int i; |
---|
713 | long j =0; |
---|
714 | |
---|
715 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
716 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
717 | |
---|
718 | for (;i<=rVar(r);i++) |
---|
719 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
720 | |
---|
721 | return j; |
---|
722 | } |
---|
723 | |
---|
724 | |
---|
725 | /* ---------------------------------------------------------------------*/ |
---|
726 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
727 | /* compute in l also the pLength of p */ |
---|
728 | |
---|
729 | /*2 |
---|
730 | * compute the length of a polynomial (in l) |
---|
731 | * and the degree of the monomial with maximal degree: the last one |
---|
732 | */ |
---|
733 | long pLDeg0(poly p,int *l, const ring r) |
---|
734 | { |
---|
735 | p_CheckPolyRing(p, r); |
---|
736 | long k= p_GetComp(p, r); |
---|
737 | int ll=1; |
---|
738 | |
---|
739 | if (k > 0) |
---|
740 | { |
---|
741 | while ((pNext(p)!=NULL) && (__p_GetComp(pNext(p), r)==k)) |
---|
742 | { |
---|
743 | pIter(p); |
---|
744 | ll++; |
---|
745 | } |
---|
746 | } |
---|
747 | else |
---|
748 | { |
---|
749 | while (pNext(p)!=NULL) |
---|
750 | { |
---|
751 | pIter(p); |
---|
752 | ll++; |
---|
753 | } |
---|
754 | } |
---|
755 | *l=ll; |
---|
756 | return r->pFDeg(p, r); |
---|
757 | } |
---|
758 | |
---|
759 | /*2 |
---|
760 | * compute the length of a polynomial (in l) |
---|
761 | * and the degree of the monomial with maximal degree: the last one |
---|
762 | * but search in all components before syzcomp |
---|
763 | */ |
---|
764 | long pLDeg0c(poly p,int *l, const ring r) |
---|
765 | { |
---|
766 | assume(p!=NULL); |
---|
767 | p_Test(p,r); |
---|
768 | p_CheckPolyRing(p, r); |
---|
769 | long o; |
---|
770 | int ll=1; |
---|
771 | |
---|
772 | if (! rIsSyzIndexRing(r)) |
---|
773 | { |
---|
774 | while (pNext(p) != NULL) |
---|
775 | { |
---|
776 | pIter(p); |
---|
777 | ll++; |
---|
778 | } |
---|
779 | o = r->pFDeg(p, r); |
---|
780 | } |
---|
781 | else |
---|
782 | { |
---|
783 | int curr_limit = rGetCurrSyzLimit(r); |
---|
784 | poly pp = p; |
---|
785 | while ((p=pNext(p))!=NULL) |
---|
786 | { |
---|
787 | if (__p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
788 | ll++; |
---|
789 | else break; |
---|
790 | pp = p; |
---|
791 | } |
---|
792 | p_Test(pp,r); |
---|
793 | o = r->pFDeg(pp, r); |
---|
794 | } |
---|
795 | *l=ll; |
---|
796 | return o; |
---|
797 | } |
---|
798 | |
---|
799 | /*2 |
---|
800 | * compute the length of a polynomial (in l) |
---|
801 | * and the degree of the monomial with maximal degree: the first one |
---|
802 | * this works for the polynomial case with degree orderings |
---|
803 | * (both c,dp and dp,c) |
---|
804 | */ |
---|
805 | long pLDegb(poly p,int *l, const ring r) |
---|
806 | { |
---|
807 | p_CheckPolyRing(p, r); |
---|
808 | long k= p_GetComp(p, r); |
---|
809 | long o = r->pFDeg(p, r); |
---|
810 | int ll=1; |
---|
811 | |
---|
812 | if (k != 0) |
---|
813 | { |
---|
814 | while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k)) |
---|
815 | { |
---|
816 | ll++; |
---|
817 | } |
---|
818 | } |
---|
819 | else |
---|
820 | { |
---|
821 | while ((p=pNext(p)) !=NULL) |
---|
822 | { |
---|
823 | ll++; |
---|
824 | } |
---|
825 | } |
---|
826 | *l=ll; |
---|
827 | return o; |
---|
828 | } |
---|
829 | |
---|
830 | /*2 |
---|
831 | * compute the length of a polynomial (in l) |
---|
832 | * and the degree of the monomial with maximal degree: |
---|
833 | * this is NOT the last one, we have to look for it |
---|
834 | */ |
---|
835 | long pLDeg1(poly p,int *l, const ring r) |
---|
836 | { |
---|
837 | p_CheckPolyRing(p, r); |
---|
838 | long k= p_GetComp(p, r); |
---|
839 | int ll=1; |
---|
840 | long t,max; |
---|
841 | |
---|
842 | max=r->pFDeg(p, r); |
---|
843 | if (k > 0) |
---|
844 | { |
---|
845 | while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k)) |
---|
846 | { |
---|
847 | t=r->pFDeg(p, r); |
---|
848 | if (t>max) max=t; |
---|
849 | ll++; |
---|
850 | } |
---|
851 | } |
---|
852 | else |
---|
853 | { |
---|
854 | while ((p=pNext(p))!=NULL) |
---|
855 | { |
---|
856 | t=r->pFDeg(p, r); |
---|
857 | if (t>max) max=t; |
---|
858 | ll++; |
---|
859 | } |
---|
860 | } |
---|
861 | *l=ll; |
---|
862 | return max; |
---|
863 | } |
---|
864 | |
---|
865 | /*2 |
---|
866 | * compute the length of a polynomial (in l) |
---|
867 | * and the degree of the monomial with maximal degree: |
---|
868 | * this is NOT the last one, we have to look for it |
---|
869 | * in all components |
---|
870 | */ |
---|
871 | long pLDeg1c(poly p,int *l, const ring r) |
---|
872 | { |
---|
873 | p_CheckPolyRing(p, r); |
---|
874 | int ll=1; |
---|
875 | long t,max; |
---|
876 | |
---|
877 | max=r->pFDeg(p, r); |
---|
878 | if (rIsSyzIndexRing(r)) |
---|
879 | { |
---|
880 | long limit = rGetCurrSyzLimit(r); |
---|
881 | while ((p=pNext(p))!=NULL) |
---|
882 | { |
---|
883 | if (__p_GetComp(p, r)<=limit) |
---|
884 | { |
---|
885 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
886 | ll++; |
---|
887 | } |
---|
888 | else break; |
---|
889 | } |
---|
890 | } |
---|
891 | else |
---|
892 | { |
---|
893 | while ((p=pNext(p))!=NULL) |
---|
894 | { |
---|
895 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
896 | ll++; |
---|
897 | } |
---|
898 | } |
---|
899 | *l=ll; |
---|
900 | return max; |
---|
901 | } |
---|
902 | |
---|
903 | // like pLDeg1, only pFDeg == pDeg |
---|
904 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
905 | { |
---|
906 | assume(r->pFDeg == p_Deg); |
---|
907 | p_CheckPolyRing(p, r); |
---|
908 | long k= p_GetComp(p, r); |
---|
909 | int ll=1; |
---|
910 | long t,max; |
---|
911 | |
---|
912 | max=p_GetOrder(p, r); |
---|
913 | if (k > 0) |
---|
914 | { |
---|
915 | while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k)) |
---|
916 | { |
---|
917 | t=p_GetOrder(p, r); |
---|
918 | if (t>max) max=t; |
---|
919 | ll++; |
---|
920 | } |
---|
921 | } |
---|
922 | else |
---|
923 | { |
---|
924 | while ((p=pNext(p))!=NULL) |
---|
925 | { |
---|
926 | t=p_GetOrder(p, r); |
---|
927 | if (t>max) max=t; |
---|
928 | ll++; |
---|
929 | } |
---|
930 | } |
---|
931 | *l=ll; |
---|
932 | return max; |
---|
933 | } |
---|
934 | |
---|
935 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
936 | { |
---|
937 | assume(r->pFDeg == p_Deg); |
---|
938 | p_CheckPolyRing(p, r); |
---|
939 | int ll=1; |
---|
940 | long t,max; |
---|
941 | |
---|
942 | max=p_GetOrder(p, r); |
---|
943 | if (rIsSyzIndexRing(r)) |
---|
944 | { |
---|
945 | long limit = rGetCurrSyzLimit(r); |
---|
946 | while ((p=pNext(p))!=NULL) |
---|
947 | { |
---|
948 | if (__p_GetComp(p, r)<=limit) |
---|
949 | { |
---|
950 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
951 | ll++; |
---|
952 | } |
---|
953 | else break; |
---|
954 | } |
---|
955 | } |
---|
956 | else |
---|
957 | { |
---|
958 | while ((p=pNext(p))!=NULL) |
---|
959 | { |
---|
960 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
961 | ll++; |
---|
962 | } |
---|
963 | } |
---|
964 | *l=ll; |
---|
965 | return max; |
---|
966 | } |
---|
967 | |
---|
968 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
969 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
970 | { |
---|
971 | p_CheckPolyRing(p, r); |
---|
972 | long k= p_GetComp(p, r); |
---|
973 | int ll=1; |
---|
974 | long t,max; |
---|
975 | |
---|
976 | max=p_Totaldegree(p, r); |
---|
977 | if (k > 0) |
---|
978 | { |
---|
979 | while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k)) |
---|
980 | { |
---|
981 | t=p_Totaldegree(p, r); |
---|
982 | if (t>max) max=t; |
---|
983 | ll++; |
---|
984 | } |
---|
985 | } |
---|
986 | else |
---|
987 | { |
---|
988 | while ((p=pNext(p))!=NULL) |
---|
989 | { |
---|
990 | t=p_Totaldegree(p, r); |
---|
991 | if (t>max) max=t; |
---|
992 | ll++; |
---|
993 | } |
---|
994 | } |
---|
995 | *l=ll; |
---|
996 | return max; |
---|
997 | } |
---|
998 | |
---|
999 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
1000 | { |
---|
1001 | p_CheckPolyRing(p, r); |
---|
1002 | int ll=1; |
---|
1003 | long t,max; |
---|
1004 | |
---|
1005 | max=p_Totaldegree(p, r); |
---|
1006 | if (rIsSyzIndexRing(r)) |
---|
1007 | { |
---|
1008 | long limit = rGetCurrSyzLimit(r); |
---|
1009 | while ((p=pNext(p))!=NULL) |
---|
1010 | { |
---|
1011 | if (__p_GetComp(p, r)<=limit) |
---|
1012 | { |
---|
1013 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
1014 | ll++; |
---|
1015 | } |
---|
1016 | else break; |
---|
1017 | } |
---|
1018 | } |
---|
1019 | else |
---|
1020 | { |
---|
1021 | while ((p=pNext(p))!=NULL) |
---|
1022 | { |
---|
1023 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
1024 | ll++; |
---|
1025 | } |
---|
1026 | } |
---|
1027 | *l=ll; |
---|
1028 | return max; |
---|
1029 | } |
---|
1030 | |
---|
1031 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
1032 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
1033 | { |
---|
1034 | p_CheckPolyRing(p, r); |
---|
1035 | long k= p_GetComp(p, r); |
---|
1036 | int ll=1; |
---|
1037 | long t,max; |
---|
1038 | |
---|
1039 | max=p_WFirstTotalDegree(p, r); |
---|
1040 | if (k > 0) |
---|
1041 | { |
---|
1042 | while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k)) |
---|
1043 | { |
---|
1044 | t=p_WFirstTotalDegree(p, r); |
---|
1045 | if (t>max) max=t; |
---|
1046 | ll++; |
---|
1047 | } |
---|
1048 | } |
---|
1049 | else |
---|
1050 | { |
---|
1051 | while ((p=pNext(p))!=NULL) |
---|
1052 | { |
---|
1053 | t=p_WFirstTotalDegree(p, r); |
---|
1054 | if (t>max) max=t; |
---|
1055 | ll++; |
---|
1056 | } |
---|
1057 | } |
---|
1058 | *l=ll; |
---|
1059 | return max; |
---|
1060 | } |
---|
1061 | |
---|
1062 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
1063 | { |
---|
1064 | p_CheckPolyRing(p, r); |
---|
1065 | int ll=1; |
---|
1066 | long t,max; |
---|
1067 | |
---|
1068 | max=p_WFirstTotalDegree(p, r); |
---|
1069 | if (rIsSyzIndexRing(r)) |
---|
1070 | { |
---|
1071 | long limit = rGetCurrSyzLimit(r); |
---|
1072 | while ((p=pNext(p))!=NULL) |
---|
1073 | { |
---|
1074 | if (__p_GetComp(p, r)<=limit) |
---|
1075 | { |
---|
1076 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
1077 | ll++; |
---|
1078 | } |
---|
1079 | else break; |
---|
1080 | } |
---|
1081 | } |
---|
1082 | else |
---|
1083 | { |
---|
1084 | while ((p=pNext(p))!=NULL) |
---|
1085 | { |
---|
1086 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
1087 | ll++; |
---|
1088 | } |
---|
1089 | } |
---|
1090 | *l=ll; |
---|
1091 | return max; |
---|
1092 | } |
---|
1093 | |
---|
1094 | /*************************************************************** |
---|
1095 | * |
---|
1096 | * Maximal Exponent business |
---|
1097 | * |
---|
1098 | ***************************************************************/ |
---|
1099 | |
---|
1100 | static inline unsigned long |
---|
1101 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
1102 | unsigned long number_of_exp) |
---|
1103 | { |
---|
1104 | const unsigned long bitmask = r->bitmask; |
---|
1105 | unsigned long ml1 = l1 & bitmask; |
---|
1106 | unsigned long ml2 = l2 & bitmask; |
---|
1107 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
1108 | unsigned long j = number_of_exp - 1; |
---|
1109 | |
---|
1110 | if (j > 0) |
---|
1111 | { |
---|
1112 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
1113 | while (1) |
---|
1114 | { |
---|
1115 | ml1 = l1 & mask; |
---|
1116 | ml2 = l2 & mask; |
---|
1117 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
1118 | j--; |
---|
1119 | if (j == 0) break; |
---|
1120 | mask = mask << r->BitsPerExp; |
---|
1121 | } |
---|
1122 | } |
---|
1123 | return max; |
---|
1124 | } |
---|
1125 | |
---|
1126 | static inline unsigned long |
---|
1127 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
1128 | { |
---|
1129 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
1130 | } |
---|
1131 | |
---|
1132 | poly p_GetMaxExpP(poly p, const ring r) |
---|
1133 | { |
---|
1134 | p_CheckPolyRing(p, r); |
---|
1135 | if (p == NULL) return p_Init(r); |
---|
1136 | poly max = p_LmInit(p, r); |
---|
1137 | pIter(p); |
---|
1138 | if (p == NULL) return max; |
---|
1139 | int i, offset; |
---|
1140 | unsigned long l_p, l_max; |
---|
1141 | unsigned long divmask = r->divmask; |
---|
1142 | |
---|
1143 | do |
---|
1144 | { |
---|
1145 | offset = r->VarL_Offset[0]; |
---|
1146 | l_p = p->exp[offset]; |
---|
1147 | l_max = max->exp[offset]; |
---|
1148 | // do the divisibility trick to find out whether l has an exponent |
---|
1149 | if (l_p > l_max || |
---|
1150 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1151 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
1152 | |
---|
1153 | for (i=1; i<r->VarL_Size; i++) |
---|
1154 | { |
---|
1155 | offset = r->VarL_Offset[i]; |
---|
1156 | l_p = p->exp[offset]; |
---|
1157 | l_max = max->exp[offset]; |
---|
1158 | // do the divisibility trick to find out whether l has an exponent |
---|
1159 | if (l_p > l_max || |
---|
1160 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1161 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
1162 | } |
---|
1163 | pIter(p); |
---|
1164 | } |
---|
1165 | while (p != NULL); |
---|
1166 | return max; |
---|
1167 | } |
---|
1168 | |
---|
1169 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
1170 | { |
---|
1171 | unsigned long l_p, divmask = r->divmask; |
---|
1172 | int i; |
---|
1173 | |
---|
1174 | while (p != NULL) |
---|
1175 | { |
---|
1176 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
1177 | if (l_p > l_max || |
---|
1178 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1179 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
1180 | for (i=1; i<r->VarL_Size; i++) |
---|
1181 | { |
---|
1182 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
1183 | // do the divisibility trick to find out whether l has an exponent |
---|
1184 | if (l_p > l_max || |
---|
1185 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1186 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
1187 | } |
---|
1188 | pIter(p); |
---|
1189 | } |
---|
1190 | return l_max; |
---|
1191 | } |
---|
1192 | |
---|
1193 | |
---|
1194 | |
---|
1195 | |
---|
1196 | /*************************************************************** |
---|
1197 | * |
---|
1198 | * Misc things |
---|
1199 | * |
---|
1200 | ***************************************************************/ |
---|
1201 | // returns TRUE, if all monoms have the same component |
---|
1202 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
1203 | { |
---|
1204 | if(p!=NULL) |
---|
1205 | { |
---|
1206 | long i = p_GetComp(p, r); |
---|
1207 | while (pNext(p)!=NULL) |
---|
1208 | { |
---|
1209 | pIter(p); |
---|
1210 | if(i != p_GetComp(p, r)) return FALSE; |
---|
1211 | } |
---|
1212 | } |
---|
1213 | return TRUE; |
---|
1214 | } |
---|
1215 | |
---|
1216 | /*2 |
---|
1217 | *test if a monomial /head term is a pure power, |
---|
1218 | * i.e. depends on only one variable |
---|
1219 | */ |
---|
1220 | int p_IsPurePower(const poly p, const ring r) |
---|
1221 | { |
---|
1222 | int i,k=0; |
---|
1223 | |
---|
1224 | for (i=r->N;i;i--) |
---|
1225 | { |
---|
1226 | if (p_GetExp(p,i, r)!=0) |
---|
1227 | { |
---|
1228 | if(k!=0) return 0; |
---|
1229 | k=i; |
---|
1230 | } |
---|
1231 | } |
---|
1232 | return k; |
---|
1233 | } |
---|
1234 | |
---|
1235 | /*2 |
---|
1236 | *test if a polynomial is univariate |
---|
1237 | * return -1 for constant, |
---|
1238 | * 0 for not univariate,s |
---|
1239 | * i if dep. on var(i) |
---|
1240 | */ |
---|
1241 | int p_IsUnivariate(poly p, const ring r) |
---|
1242 | { |
---|
1243 | int i,k=-1; |
---|
1244 | |
---|
1245 | while (p!=NULL) |
---|
1246 | { |
---|
1247 | for (i=r->N;i;i--) |
---|
1248 | { |
---|
1249 | if (p_GetExp(p,i, r)!=0) |
---|
1250 | { |
---|
1251 | if((k!=-1)&&(k!=i)) return 0; |
---|
1252 | k=i; |
---|
1253 | } |
---|
1254 | } |
---|
1255 | pIter(p); |
---|
1256 | } |
---|
1257 | return k; |
---|
1258 | } |
---|
1259 | |
---|
1260 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
1261 | int p_GetVariables(poly p, int * e, const ring r) |
---|
1262 | { |
---|
1263 | int i; |
---|
1264 | int n=0; |
---|
1265 | while(p!=NULL) |
---|
1266 | { |
---|
1267 | n=0; |
---|
1268 | for(i=r->N; i>0; i--) |
---|
1269 | { |
---|
1270 | if(e[i]==0) |
---|
1271 | { |
---|
1272 | if (p_GetExp(p,i,r)>0) |
---|
1273 | { |
---|
1274 | e[i]=1; |
---|
1275 | n++; |
---|
1276 | } |
---|
1277 | } |
---|
1278 | else |
---|
1279 | n++; |
---|
1280 | } |
---|
1281 | if (n==r->N) break; |
---|
1282 | pIter(p); |
---|
1283 | } |
---|
1284 | return n; |
---|
1285 | } |
---|
1286 | |
---|
1287 | |
---|
1288 | /*2 |
---|
1289 | * returns a polynomial representing the integer i |
---|
1290 | */ |
---|
1291 | poly p_ISet(long i, const ring r) |
---|
1292 | { |
---|
1293 | poly rc = NULL; |
---|
1294 | if (i!=0) |
---|
1295 | { |
---|
1296 | rc = p_Init(r); |
---|
1297 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
1298 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
1299 | p_LmDelete(&rc,r); |
---|
1300 | } |
---|
1301 | return rc; |
---|
1302 | } |
---|
1303 | |
---|
1304 | /*2 |
---|
1305 | * an optimized version of p_ISet for the special case 1 |
---|
1306 | */ |
---|
1307 | poly p_One(const ring r) |
---|
1308 | { |
---|
1309 | poly rc = p_Init(r); |
---|
1310 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
1311 | return rc; |
---|
1312 | } |
---|
1313 | |
---|
1314 | void p_Split(poly p, poly *h) |
---|
1315 | { |
---|
1316 | *h=pNext(p); |
---|
1317 | pNext(p)=NULL; |
---|
1318 | } |
---|
1319 | |
---|
1320 | /*2 |
---|
1321 | * pair has no common factor ? or is no polynomial |
---|
1322 | */ |
---|
1323 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
1324 | { |
---|
1325 | |
---|
1326 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
1327 | return FALSE; |
---|
1328 | int i = rVar(r); |
---|
1329 | loop |
---|
1330 | { |
---|
1331 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
1332 | return FALSE; |
---|
1333 | i--; |
---|
1334 | if (i == 0) |
---|
1335 | return TRUE; |
---|
1336 | } |
---|
1337 | } |
---|
1338 | |
---|
1339 | BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r) |
---|
1340 | { |
---|
1341 | |
---|
1342 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
1343 | return FALSE; |
---|
1344 | int i = rVar(r); |
---|
1345 | loop |
---|
1346 | { |
---|
1347 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
1348 | return FALSE; |
---|
1349 | i--; |
---|
1350 | if (i == 0) { |
---|
1351 | if (n_DivBy(pGetCoeff(p1), pGetCoeff(p2), r->cf) || |
---|
1352 | n_DivBy(pGetCoeff(p2), pGetCoeff(p1), r->cf)) { |
---|
1353 | return FALSE; |
---|
1354 | } else { |
---|
1355 | return TRUE; |
---|
1356 | } |
---|
1357 | } |
---|
1358 | } |
---|
1359 | } |
---|
1360 | |
---|
1361 | /*2 |
---|
1362 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
1363 | */ |
---|
1364 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
1365 | { |
---|
1366 | if (r==NULL) { rc=NULL;return st;} |
---|
1367 | int i,j; |
---|
1368 | rc = p_Init(r); |
---|
1369 | const char *s = n_Read(st,&(p_GetCoeff(rc, r)),r->cf); |
---|
1370 | if (s==st) |
---|
1371 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
1372 | { |
---|
1373 | j = r_IsRingVar(s,r->names,r->N); |
---|
1374 | if (j >= 0) |
---|
1375 | { |
---|
1376 | p_IncrExp(rc,1+j,r); |
---|
1377 | while (*s!='\0') s++; |
---|
1378 | goto done; |
---|
1379 | } |
---|
1380 | } |
---|
1381 | while (*s!='\0') |
---|
1382 | { |
---|
1383 | char ss[2]; |
---|
1384 | ss[0] = *s++; |
---|
1385 | ss[1] = '\0'; |
---|
1386 | j = r_IsRingVar(ss,r->names,r->N); |
---|
1387 | if (j >= 0) |
---|
1388 | { |
---|
1389 | const char *s_save=s; |
---|
1390 | s = eati(s,&i); |
---|
1391 | if (((unsigned long)i) > r->bitmask/2) |
---|
1392 | { |
---|
1393 | // exponent to large: it is not a monomial |
---|
1394 | p_LmDelete(&rc,r); |
---|
1395 | return s_save; |
---|
1396 | } |
---|
1397 | p_AddExp(rc,1+j, (long)i, r); |
---|
1398 | } |
---|
1399 | else |
---|
1400 | { |
---|
1401 | // 1st char of is not a varname |
---|
1402 | // We return the parsed polynomial nevertheless. This is needed when |
---|
1403 | // we are parsing coefficients in a rational function field. |
---|
1404 | s--; |
---|
1405 | break; |
---|
1406 | } |
---|
1407 | } |
---|
1408 | done: |
---|
1409 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
1410 | else |
---|
1411 | { |
---|
1412 | #ifdef HAVE_PLURAL |
---|
1413 | // in super-commutative ring |
---|
1414 | // squares of anti-commutative variables are zeroes! |
---|
1415 | if(rIsSCA(r)) |
---|
1416 | { |
---|
1417 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
1418 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
1419 | |
---|
1420 | assume(rc != NULL); |
---|
1421 | |
---|
1422 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
1423 | if( p_GetExp(rc, k, r) > 1 ) |
---|
1424 | { |
---|
1425 | p_LmDelete(&rc, r); |
---|
1426 | goto finish; |
---|
1427 | } |
---|
1428 | } |
---|
1429 | #endif |
---|
1430 | |
---|
1431 | p_Setm(rc,r); |
---|
1432 | } |
---|
1433 | finish: |
---|
1434 | return s; |
---|
1435 | } |
---|
1436 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
1437 | { |
---|
1438 | poly p; |
---|
1439 | const char *s=p_Read(st,p,r); |
---|
1440 | if (*s!='\0') |
---|
1441 | { |
---|
1442 | if ((s!=st)&&isdigit(st[0])) |
---|
1443 | { |
---|
1444 | errorreported=TRUE; |
---|
1445 | } |
---|
1446 | ok=FALSE; |
---|
1447 | p_Delete(&p,r); |
---|
1448 | return NULL; |
---|
1449 | } |
---|
1450 | p_Test(p,r); |
---|
1451 | ok=!errorreported; |
---|
1452 | return p; |
---|
1453 | } |
---|
1454 | |
---|
1455 | /*2 |
---|
1456 | * returns a polynomial representing the number n |
---|
1457 | * destroys n |
---|
1458 | */ |
---|
1459 | poly p_NSet(number n, const ring r) |
---|
1460 | { |
---|
1461 | if (n_IsZero(n,r->cf)) |
---|
1462 | { |
---|
1463 | n_Delete(&n, r->cf); |
---|
1464 | return NULL; |
---|
1465 | } |
---|
1466 | else |
---|
1467 | { |
---|
1468 | poly rc = p_Init(r); |
---|
1469 | pSetCoeff0(rc,n); |
---|
1470 | return rc; |
---|
1471 | } |
---|
1472 | } |
---|
1473 | /*2 |
---|
1474 | * assumes that LM(a) = LM(b)*m, for some monomial m, |
---|
1475 | * returns the multiplicant m, |
---|
1476 | * leaves a and b unmodified |
---|
1477 | */ |
---|
1478 | poly p_MDivide(poly a, poly b, const ring r) |
---|
1479 | { |
---|
1480 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
1481 | int i; |
---|
1482 | poly result = p_Init(r); |
---|
1483 | |
---|
1484 | for(i=(int)r->N; i; i--) |
---|
1485 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
1486 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
1487 | p_Setm(result,r); |
---|
1488 | return result; |
---|
1489 | } |
---|
1490 | |
---|
1491 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
1492 | { |
---|
1493 | pAssume(!n_IsZero(n,r->cf)); |
---|
1494 | p_Test(p, r); |
---|
1495 | poly result = p; |
---|
1496 | poly prev = NULL; |
---|
1497 | while (p!=NULL) |
---|
1498 | { |
---|
1499 | number nc = n_Div(pGetCoeff(p),n,r->cf); |
---|
1500 | if (!n_IsZero(nc,r->cf)) |
---|
1501 | { |
---|
1502 | p_SetCoeff(p,nc,r); |
---|
1503 | prev=p; |
---|
1504 | pIter(p); |
---|
1505 | } |
---|
1506 | else |
---|
1507 | { |
---|
1508 | if (prev==NULL) |
---|
1509 | { |
---|
1510 | p_LmDelete(&result,r); |
---|
1511 | p=result; |
---|
1512 | } |
---|
1513 | else |
---|
1514 | { |
---|
1515 | p_LmDelete(&pNext(prev),r); |
---|
1516 | p=pNext(prev); |
---|
1517 | } |
---|
1518 | } |
---|
1519 | } |
---|
1520 | p_Test(result,r); |
---|
1521 | return(result); |
---|
1522 | } |
---|
1523 | |
---|
1524 | poly p_Div_mm(poly p, const poly m, const ring r) |
---|
1525 | { |
---|
1526 | p_Test(p, r); |
---|
1527 | p_Test(m, r); |
---|
1528 | poly result = p; |
---|
1529 | poly prev = NULL; |
---|
1530 | number n=pGetCoeff(m); |
---|
1531 | while (p!=NULL) |
---|
1532 | { |
---|
1533 | number nc = n_Div(pGetCoeff(p),n,r->cf); |
---|
1534 | n_Normalize(nc,r->cf); |
---|
1535 | if (!n_IsZero(nc,r->cf)) |
---|
1536 | { |
---|
1537 | p_SetCoeff(p,nc,r); |
---|
1538 | prev=p; |
---|
1539 | p_ExpVectorSub(p,m,r); |
---|
1540 | pIter(p); |
---|
1541 | } |
---|
1542 | else |
---|
1543 | { |
---|
1544 | if (prev==NULL) |
---|
1545 | { |
---|
1546 | p_LmDelete(&result,r); |
---|
1547 | p=result; |
---|
1548 | } |
---|
1549 | else |
---|
1550 | { |
---|
1551 | p_LmDelete(&pNext(prev),r); |
---|
1552 | p=pNext(prev); |
---|
1553 | } |
---|
1554 | } |
---|
1555 | } |
---|
1556 | p_Test(result,r); |
---|
1557 | return(result); |
---|
1558 | } |
---|
1559 | |
---|
1560 | /*2 |
---|
1561 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
1562 | * assumes that b is not NULL, destroyes b |
---|
1563 | */ |
---|
1564 | poly p_DivideM(poly a, poly b, const ring r) |
---|
1565 | { |
---|
1566 | if (a==NULL) { p_Delete(&b,r); return NULL; } |
---|
1567 | poly result=a; |
---|
1568 | |
---|
1569 | if(!p_IsConstant(b,r)) |
---|
1570 | { |
---|
1571 | if (rIsNCRing(r)) |
---|
1572 | { |
---|
1573 | WerrorS("p_DivideM not implemented for non-commuative rings"); |
---|
1574 | return NULL; |
---|
1575 | } |
---|
1576 | poly prev=NULL; |
---|
1577 | while (a!=NULL) |
---|
1578 | { |
---|
1579 | if (p_DivisibleBy(b,a,r)) |
---|
1580 | { |
---|
1581 | p_ExpVectorSub(a,b,r); |
---|
1582 | prev=a; |
---|
1583 | pIter(a); |
---|
1584 | } |
---|
1585 | else |
---|
1586 | { |
---|
1587 | if (prev==NULL) |
---|
1588 | { |
---|
1589 | p_LmDelete(&result,r); |
---|
1590 | a=result; |
---|
1591 | } |
---|
1592 | else |
---|
1593 | { |
---|
1594 | p_LmDelete(&pNext(prev),r); |
---|
1595 | a=pNext(prev); |
---|
1596 | } |
---|
1597 | } |
---|
1598 | } |
---|
1599 | } |
---|
1600 | if (result!=NULL) |
---|
1601 | { |
---|
1602 | number inv=pGetCoeff(b); |
---|
1603 | //if ((!rField_is_Ring(r)) || n_IsUnit(inv,r->cf)) |
---|
1604 | if (rField_is_Zp(r)) |
---|
1605 | { |
---|
1606 | inv = n_Invers(inv,r->cf); |
---|
1607 | __p_Mult_nn(result,inv,r); |
---|
1608 | n_Delete(&inv, r->cf); |
---|
1609 | } |
---|
1610 | else |
---|
1611 | { |
---|
1612 | result = p_Div_nn(result,inv,r); |
---|
1613 | } |
---|
1614 | } |
---|
1615 | p_Delete(&b, r); |
---|
1616 | return result; |
---|
1617 | } |
---|
1618 | |
---|
1619 | poly pp_DivideM(poly a, poly b, const ring r) |
---|
1620 | { |
---|
1621 | if (a==NULL) { return NULL; } |
---|
1622 | // TODO: better implementation without copying a,b |
---|
1623 | return p_DivideM(p_Copy(a,r),p_Head(b,r),r); |
---|
1624 | } |
---|
1625 | |
---|
1626 | #ifdef HAVE_RINGS |
---|
1627 | /* TRUE iff LT(f) | LT(g) */ |
---|
1628 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
1629 | { |
---|
1630 | int exponent; |
---|
1631 | for(int i = (int)rVar(r); i>0; i--) |
---|
1632 | { |
---|
1633 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
1634 | if (exponent < 0) return FALSE; |
---|
1635 | } |
---|
1636 | return n_DivBy(pGetCoeff(g), pGetCoeff(f), r->cf); |
---|
1637 | } |
---|
1638 | #endif |
---|
1639 | |
---|
1640 | // returns the LCM of the head terms of a and b in *m |
---|
1641 | void p_Lcm(const poly a, const poly b, poly m, const ring r) |
---|
1642 | { |
---|
1643 | for (int i=r->N; i; --i) |
---|
1644 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
1645 | |
---|
1646 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
1647 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
1648 | } |
---|
1649 | |
---|
1650 | poly p_Lcm(const poly a, const poly b, const ring r) |
---|
1651 | { |
---|
1652 | poly m=p_Init(r); |
---|
1653 | p_Lcm(a, b, m, r); |
---|
1654 | p_Setm(m,r); |
---|
1655 | return(m); |
---|
1656 | } |
---|
1657 | |
---|
1658 | #ifdef HAVE_RATGRING |
---|
1659 | /*2 |
---|
1660 | * returns the rational LCM of the head terms of a and b |
---|
1661 | * without coefficient!!! |
---|
1662 | */ |
---|
1663 | poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r) |
---|
1664 | { |
---|
1665 | poly m = // p_One( r); |
---|
1666 | p_Init(r); |
---|
1667 | |
---|
1668 | // const int (currRing->N) = r->N; |
---|
1669 | |
---|
1670 | // for (int i = (currRing->N); i>=r->real_var_start; i--) |
---|
1671 | for (int i = r->real_var_end; i>=r->real_var_start; i--) |
---|
1672 | { |
---|
1673 | const int lExpA = p_GetExp (a, i, r); |
---|
1674 | const int lExpB = p_GetExp (b, i, r); |
---|
1675 | |
---|
1676 | p_SetExp (m, i, si_max(lExpA, lExpB), r); |
---|
1677 | } |
---|
1678 | |
---|
1679 | p_SetComp (m, lCompM, r); |
---|
1680 | p_Setm(m,r); |
---|
1681 | n_New(&(p_GetCoeff(m, r)), r); |
---|
1682 | |
---|
1683 | return(m); |
---|
1684 | }; |
---|
1685 | |
---|
1686 | void p_LmDeleteAndNextRat(poly *p, int ishift, ring r) |
---|
1687 | { |
---|
1688 | /* modifies p*/ |
---|
1689 | // Print("start: "); Print(" "); p_wrp(*p,r); |
---|
1690 | p_LmCheckPolyRing2(*p, r); |
---|
1691 | poly q = p_Head(*p,r); |
---|
1692 | const long cmp = p_GetComp(*p, r); |
---|
1693 | while ( ( (*p)!=NULL ) && ( p_Comp_k_n(*p, q, ishift+1, r) ) && (p_GetComp(*p, r) == cmp) ) |
---|
1694 | { |
---|
1695 | p_LmDelete(p,r); |
---|
1696 | // Print("while: ");p_wrp(*p,r);Print(" "); |
---|
1697 | } |
---|
1698 | // p_wrp(*p,r);Print(" "); |
---|
1699 | // PrintS("end\n"); |
---|
1700 | p_LmDelete(&q,r); |
---|
1701 | } |
---|
1702 | |
---|
1703 | |
---|
1704 | /* returns x-coeff of p, i.e. a poly in x, s.t. corresponding xd-monomials |
---|
1705 | have the same D-part and the component 0 |
---|
1706 | does not destroy p |
---|
1707 | */ |
---|
1708 | poly p_GetCoeffRat(poly p, int ishift, ring r) |
---|
1709 | { |
---|
1710 | poly q = pNext(p); |
---|
1711 | poly res; // = p_Head(p,r); |
---|
1712 | res = p_GetExp_k_n(p, ishift+1, r->N, r); // does pSetm internally |
---|
1713 | p_SetCoeff(res,n_Copy(p_GetCoeff(p,r),r),r); |
---|
1714 | poly s; |
---|
1715 | long cmp = p_GetComp(p, r); |
---|
1716 | while ( (q!= NULL) && (p_Comp_k_n(p, q, ishift+1, r)) && (p_GetComp(q, r) == cmp) ) |
---|
1717 | { |
---|
1718 | s = p_GetExp_k_n(q, ishift+1, r->N, r); |
---|
1719 | p_SetCoeff(s,n_Copy(p_GetCoeff(q,r),r),r); |
---|
1720 | res = p_Add_q(res,s,r); |
---|
1721 | q = pNext(q); |
---|
1722 | } |
---|
1723 | cmp = 0; |
---|
1724 | p_SetCompP(res,cmp,r); |
---|
1725 | return res; |
---|
1726 | } |
---|
1727 | |
---|
1728 | |
---|
1729 | |
---|
1730 | void p_ContentRat(poly &ph, const ring r) |
---|
1731 | // changes ph |
---|
1732 | // for rat coefficients in K(x1,..xN) |
---|
1733 | { |
---|
1734 | // init array of RatLeadCoeffs |
---|
1735 | // poly p_GetCoeffRat(poly p, int ishift, ring r); |
---|
1736 | |
---|
1737 | int len=pLength(ph); |
---|
1738 | poly *C = (poly *)omAlloc0((len+1)*sizeof(poly)); //rat coeffs |
---|
1739 | poly *LM = (poly *)omAlloc0((len+1)*sizeof(poly)); // rat lead terms |
---|
1740 | int *D = (int *)omAlloc0((len+1)*sizeof(int)); //degrees of coeffs |
---|
1741 | int *L = (int *)omAlloc0((len+1)*sizeof(int)); //lengths of coeffs |
---|
1742 | int k = 0; |
---|
1743 | poly p = p_Copy(ph, r); // ph will be needed below |
---|
1744 | int mintdeg = p_Totaldegree(p, r); |
---|
1745 | int minlen = len; |
---|
1746 | int dd = 0; int i; |
---|
1747 | int HasConstantCoef = 0; |
---|
1748 | int is = r->real_var_start - 1; |
---|
1749 | while (p!=NULL) |
---|
1750 | { |
---|
1751 | LM[k] = p_GetExp_k_n(p,1,is, r); // need LmRat istead of p_HeadRat(p, is, currRing); ! |
---|
1752 | C[k] = p_GetCoeffRat(p, is, r); |
---|
1753 | D[k] = p_Totaldegree(C[k], r); |
---|
1754 | mintdeg = si_min(mintdeg,D[k]); |
---|
1755 | L[k] = pLength(C[k]); |
---|
1756 | minlen = si_min(minlen,L[k]); |
---|
1757 | if (p_IsConstant(C[k], r)) |
---|
1758 | { |
---|
1759 | // C[k] = const, so the content will be numerical |
---|
1760 | HasConstantCoef = 1; |
---|
1761 | // smth like goto cleanup and return(pContent(p)); |
---|
1762 | } |
---|
1763 | p_LmDeleteAndNextRat(&p, is, r); |
---|
1764 | k++; |
---|
1765 | } |
---|
1766 | |
---|
1767 | // look for 1 element of minimal degree and of minimal length |
---|
1768 | k--; |
---|
1769 | poly d; |
---|
1770 | int mindeglen = len; |
---|
1771 | if (k<=0) // this poly is not a ratgring poly -> pContent |
---|
1772 | { |
---|
1773 | p_Delete(&C[0], r); |
---|
1774 | p_Delete(&LM[0], r); |
---|
1775 | p_ContentForGB(ph, r); |
---|
1776 | goto cleanup; |
---|
1777 | } |
---|
1778 | |
---|
1779 | int pmindeglen; |
---|
1780 | for(i=0; i<=k; i++) |
---|
1781 | { |
---|
1782 | if (D[i] == mintdeg) |
---|
1783 | { |
---|
1784 | if (L[i] < mindeglen) |
---|
1785 | { |
---|
1786 | mindeglen=L[i]; |
---|
1787 | pmindeglen = i; |
---|
1788 | } |
---|
1789 | } |
---|
1790 | } |
---|
1791 | d = p_Copy(C[pmindeglen], r); |
---|
1792 | // there are dd>=1 mindeg elements |
---|
1793 | // and pmideglen is the coordinate of one of the smallest among them |
---|
1794 | |
---|
1795 | // poly g = singclap_gcd(p_Copy(p,r),p_Copy(q,r)); |
---|
1796 | // return naGcd(d,d2,currRing); |
---|
1797 | |
---|
1798 | // adjoin pContentRat here? |
---|
1799 | for(i=0; i<=k; i++) |
---|
1800 | { |
---|
1801 | d=singclap_gcd(d,p_Copy(C[i], r), r); |
---|
1802 | if (p_Totaldegree(d, r)==0) |
---|
1803 | { |
---|
1804 | // cleanup, pContent, return |
---|
1805 | p_Delete(&d, r); |
---|
1806 | for(;k>=0;k--) |
---|
1807 | { |
---|
1808 | p_Delete(&C[k], r); |
---|
1809 | p_Delete(&LM[k], r); |
---|
1810 | } |
---|
1811 | p_ContentForGB(ph, r); |
---|
1812 | goto cleanup; |
---|
1813 | } |
---|
1814 | } |
---|
1815 | for(i=0; i<=k; i++) |
---|
1816 | { |
---|
1817 | poly h=singclap_pdivide(C[i],d, r); |
---|
1818 | p_Delete(&C[i], r); |
---|
1819 | C[i]=h; |
---|
1820 | } |
---|
1821 | |
---|
1822 | // zusammensetzen, |
---|
1823 | p=NULL; // just to be sure |
---|
1824 | for(i=0; i<=k; i++) |
---|
1825 | { |
---|
1826 | p = p_Add_q(p, p_Mult_q(C[i],LM[i], r), r); |
---|
1827 | C[i]=NULL; LM[i]=NULL; |
---|
1828 | } |
---|
1829 | p_Delete(&ph, r); // do not need it anymore |
---|
1830 | ph = p; |
---|
1831 | // aufraeumen, return |
---|
1832 | cleanup: |
---|
1833 | omFree(C); |
---|
1834 | omFree(LM); |
---|
1835 | omFree(D); |
---|
1836 | omFree(L); |
---|
1837 | } |
---|
1838 | |
---|
1839 | |
---|
1840 | #endif |
---|
1841 | |
---|
1842 | |
---|
1843 | /* assumes that p and divisor are univariate polynomials in r, |
---|
1844 | mentioning the same variable; |
---|
1845 | assumes divisor != NULL; |
---|
1846 | p may be NULL; |
---|
1847 | assumes a global monomial ordering in r; |
---|
1848 | performs polynomial division of p by divisor: |
---|
1849 | - afterwards p contains the remainder of the division, i.e., |
---|
1850 | p_before = result * divisor + p_afterwards; |
---|
1851 | - if needResult == TRUE, then the method computes and returns 'result', |
---|
1852 | otherwise NULL is returned (This parametrization can be used when |
---|
1853 | one is only interested in the remainder of the division. In this |
---|
1854 | case, the method will be slightly faster.) |
---|
1855 | leaves divisor unmodified */ |
---|
1856 | poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r) |
---|
1857 | { |
---|
1858 | assume(divisor != NULL); |
---|
1859 | if (p == NULL) return NULL; |
---|
1860 | |
---|
1861 | poly result = NULL; |
---|
1862 | number divisorLC = p_GetCoeff(divisor, r); |
---|
1863 | int divisorLE = p_GetExp(divisor, 1, r); |
---|
1864 | while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r))) |
---|
1865 | { |
---|
1866 | /* determine t = LT(p) / LT(divisor) */ |
---|
1867 | poly t = p_ISet(1, r); |
---|
1868 | number c = n_Div(p_GetCoeff(p, r), divisorLC, r->cf); |
---|
1869 | n_Normalize(c,r->cf); |
---|
1870 | p_SetCoeff(t, c, r); |
---|
1871 | int e = p_GetExp(p, 1, r) - divisorLE; |
---|
1872 | p_SetExp(t, 1, e, r); |
---|
1873 | p_Setm(t, r); |
---|
1874 | if (needResult) result = p_Add_q(result, p_Copy(t, r), r); |
---|
1875 | p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r); |
---|
1876 | } |
---|
1877 | return result; |
---|
1878 | } |
---|
1879 | |
---|
1880 | /*2 |
---|
1881 | * returns the partial differentiate of a by the k-th variable |
---|
1882 | * does not destroy the input |
---|
1883 | */ |
---|
1884 | poly p_Diff(poly a, int k, const ring r) |
---|
1885 | { |
---|
1886 | poly res, f, last; |
---|
1887 | number t; |
---|
1888 | |
---|
1889 | last = res = NULL; |
---|
1890 | while (a!=NULL) |
---|
1891 | { |
---|
1892 | if (p_GetExp(a,k,r)!=0) |
---|
1893 | { |
---|
1894 | f = p_LmInit(a,r); |
---|
1895 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
1896 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
1897 | n_Delete(&t,r->cf); |
---|
1898 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
1899 | p_LmDelete(&f,r); |
---|
1900 | else |
---|
1901 | { |
---|
1902 | p_DecrExp(f,k,r); |
---|
1903 | p_Setm(f,r); |
---|
1904 | if (res==NULL) |
---|
1905 | { |
---|
1906 | res=last=f; |
---|
1907 | } |
---|
1908 | else |
---|
1909 | { |
---|
1910 | pNext(last)=f; |
---|
1911 | last=f; |
---|
1912 | } |
---|
1913 | } |
---|
1914 | } |
---|
1915 | pIter(a); |
---|
1916 | } |
---|
1917 | return res; |
---|
1918 | } |
---|
1919 | |
---|
1920 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
1921 | { |
---|
1922 | int i,j,s; |
---|
1923 | number n,h,hh; |
---|
1924 | poly p=p_One(r); |
---|
1925 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
1926 | for(i=rVar(r);i>0;i--) |
---|
1927 | { |
---|
1928 | s=p_GetExp(b,i,r); |
---|
1929 | if (s<p_GetExp(a,i,r)) |
---|
1930 | { |
---|
1931 | n_Delete(&n,r->cf); |
---|
1932 | p_LmDelete(&p,r); |
---|
1933 | return NULL; |
---|
1934 | } |
---|
1935 | if (multiply) |
---|
1936 | { |
---|
1937 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
1938 | { |
---|
1939 | h = n_Init(s,r->cf); |
---|
1940 | hh=n_Mult(n,h,r->cf); |
---|
1941 | n_Delete(&h,r->cf); |
---|
1942 | n_Delete(&n,r->cf); |
---|
1943 | n=hh; |
---|
1944 | s--; |
---|
1945 | } |
---|
1946 | p_SetExp(p,i,s,r); |
---|
1947 | } |
---|
1948 | else |
---|
1949 | { |
---|
1950 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
1951 | } |
---|
1952 | } |
---|
1953 | p_Setm(p,r); |
---|
1954 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
1955 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
1956 | return p; |
---|
1957 | } |
---|
1958 | |
---|
1959 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
1960 | { |
---|
1961 | poly result=NULL; |
---|
1962 | poly h; |
---|
1963 | for(;a!=NULL;pIter(a)) |
---|
1964 | { |
---|
1965 | for(h=b;h!=NULL;pIter(h)) |
---|
1966 | { |
---|
1967 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
1968 | } |
---|
1969 | } |
---|
1970 | return result; |
---|
1971 | } |
---|
1972 | /*2 |
---|
1973 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
1974 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
1975 | */ |
---|
1976 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
1977 | { |
---|
1978 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
1979 | } |
---|
1980 | |
---|
1981 | /*3 |
---|
1982 | * compute for a monomial m |
---|
1983 | * the power m^exp, exp > 1 |
---|
1984 | * destroys p |
---|
1985 | */ |
---|
1986 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
1987 | { |
---|
1988 | int i; |
---|
1989 | |
---|
1990 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
1991 | { |
---|
1992 | number x, y; |
---|
1993 | y = pGetCoeff(p); |
---|
1994 | n_Power(y,exp,&x,r->cf); |
---|
1995 | n_Delete(&y,r->cf); |
---|
1996 | pSetCoeff0(p,x); |
---|
1997 | } |
---|
1998 | for (i=rVar(r); i!=0; i--) |
---|
1999 | { |
---|
2000 | p_MultExp(p,i, exp,r); |
---|
2001 | } |
---|
2002 | p_Setm(p,r); |
---|
2003 | return p; |
---|
2004 | } |
---|
2005 | |
---|
2006 | /*3 |
---|
2007 | * compute for monomials p*q |
---|
2008 | * destroys p, keeps q |
---|
2009 | */ |
---|
2010 | static void p_MonMult(poly p, poly q, const ring r) |
---|
2011 | { |
---|
2012 | number x, y; |
---|
2013 | |
---|
2014 | y = pGetCoeff(p); |
---|
2015 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
2016 | n_Delete(&y,r->cf); |
---|
2017 | pSetCoeff0(p,x); |
---|
2018 | //for (int i=pVariables; i!=0; i--) |
---|
2019 | //{ |
---|
2020 | // pAddExp(p,i, pGetExp(q,i)); |
---|
2021 | //} |
---|
2022 | //p->Order += q->Order; |
---|
2023 | p_ExpVectorAdd(p,q,r); |
---|
2024 | } |
---|
2025 | |
---|
2026 | /*3 |
---|
2027 | * compute for monomials p*q |
---|
2028 | * keeps p, q |
---|
2029 | */ |
---|
2030 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
2031 | { |
---|
2032 | number x; |
---|
2033 | poly r = p_Init(rr); |
---|
2034 | |
---|
2035 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
2036 | pSetCoeff0(r,x); |
---|
2037 | p_ExpVectorSum(r,p, q, rr); |
---|
2038 | return r; |
---|
2039 | } |
---|
2040 | |
---|
2041 | /*3 |
---|
2042 | * create binomial coef. |
---|
2043 | */ |
---|
2044 | static number* pnBin(int exp, const ring r) |
---|
2045 | { |
---|
2046 | int e, i, h; |
---|
2047 | number x, y, *bin=NULL; |
---|
2048 | |
---|
2049 | x = n_Init(exp,r->cf); |
---|
2050 | if (n_IsZero(x,r->cf)) |
---|
2051 | { |
---|
2052 | n_Delete(&x,r->cf); |
---|
2053 | return bin; |
---|
2054 | } |
---|
2055 | h = (exp >> 1) + 1; |
---|
2056 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
2057 | bin[1] = x; |
---|
2058 | if (exp < 4) |
---|
2059 | return bin; |
---|
2060 | i = exp - 1; |
---|
2061 | for (e=2; e<h; e++) |
---|
2062 | { |
---|
2063 | x = n_Init(i,r->cf); |
---|
2064 | i--; |
---|
2065 | y = n_Mult(x,bin[e-1],r->cf); |
---|
2066 | n_Delete(&x,r->cf); |
---|
2067 | x = n_Init(e,r->cf); |
---|
2068 | bin[e] = n_ExactDiv(y,x,r->cf); |
---|
2069 | n_Delete(&x,r->cf); |
---|
2070 | n_Delete(&y,r->cf); |
---|
2071 | } |
---|
2072 | return bin; |
---|
2073 | } |
---|
2074 | |
---|
2075 | static void pnFreeBin(number *bin, int exp,const coeffs r) |
---|
2076 | { |
---|
2077 | int e, h = (exp >> 1) + 1; |
---|
2078 | |
---|
2079 | if (bin[1] != NULL) |
---|
2080 | { |
---|
2081 | for (e=1; e<h; e++) |
---|
2082 | n_Delete(&(bin[e]),r); |
---|
2083 | } |
---|
2084 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
---|
2085 | } |
---|
2086 | |
---|
2087 | /* |
---|
2088 | * compute for a poly p = head+tail, tail is monomial |
---|
2089 | * (head + tail)^exp, exp > 1 |
---|
2090 | * with binomial coef. |
---|
2091 | */ |
---|
2092 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
2093 | { |
---|
2094 | int eh, e; |
---|
2095 | long al; |
---|
2096 | poly *a; |
---|
2097 | poly tail, b, res, h; |
---|
2098 | number x; |
---|
2099 | number *bin = pnBin(exp,r); |
---|
2100 | |
---|
2101 | tail = pNext(p); |
---|
2102 | if (bin == NULL) |
---|
2103 | { |
---|
2104 | p_MonPower(p,exp,r); |
---|
2105 | p_MonPower(tail,exp,r); |
---|
2106 | p_Test(p,r); |
---|
2107 | return p; |
---|
2108 | } |
---|
2109 | eh = exp >> 1; |
---|
2110 | al = (exp + 1) * sizeof(poly); |
---|
2111 | a = (poly *)omAlloc(al); |
---|
2112 | a[1] = p; |
---|
2113 | for (e=1; e<exp; e++) |
---|
2114 | { |
---|
2115 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
2116 | } |
---|
2117 | res = a[exp]; |
---|
2118 | b = p_Head(tail,r); |
---|
2119 | for (e=exp-1; e>eh; e--) |
---|
2120 | { |
---|
2121 | h = a[e]; |
---|
2122 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
2123 | p_SetCoeff(h,x,r); |
---|
2124 | p_MonMult(h,b,r); |
---|
2125 | res = pNext(res) = h; |
---|
2126 | p_MonMult(b,tail,r); |
---|
2127 | } |
---|
2128 | for (e=eh; e!=0; e--) |
---|
2129 | { |
---|
2130 | h = a[e]; |
---|
2131 | x = n_Mult(bin[e],pGetCoeff(h),r->cf); |
---|
2132 | p_SetCoeff(h,x,r); |
---|
2133 | p_MonMult(h,b,r); |
---|
2134 | res = pNext(res) = h; |
---|
2135 | p_MonMult(b,tail,r); |
---|
2136 | } |
---|
2137 | p_LmDelete(&tail,r); |
---|
2138 | pNext(res) = b; |
---|
2139 | pNext(b) = NULL; |
---|
2140 | res = a[exp]; |
---|
2141 | omFreeSize((ADDRESS)a, al); |
---|
2142 | pnFreeBin(bin, exp, r->cf); |
---|
2143 | // tail=res; |
---|
2144 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
2145 | // { |
---|
2146 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
2147 | // { |
---|
2148 | // pLmDelete(&pNext(tail)); |
---|
2149 | // } |
---|
2150 | // else |
---|
2151 | // pIter(tail); |
---|
2152 | // } |
---|
2153 | p_Test(res,r); |
---|
2154 | return res; |
---|
2155 | } |
---|
2156 | |
---|
2157 | static poly p_Pow(poly p, int i, const ring r) |
---|
2158 | { |
---|
2159 | poly rc = p_Copy(p,r); |
---|
2160 | i -= 2; |
---|
2161 | do |
---|
2162 | { |
---|
2163 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
2164 | p_Normalize(rc,r); |
---|
2165 | i--; |
---|
2166 | } |
---|
2167 | while (i != 0); |
---|
2168 | return p_Mult_q(rc,p,r); |
---|
2169 | } |
---|
2170 | |
---|
2171 | static poly p_Pow_charp(poly p, int i, const ring r) |
---|
2172 | { |
---|
2173 | //assume char_p == i |
---|
2174 | poly h=p; |
---|
2175 | while(h!=NULL) { p_MonPower(h,i,r);pIter(h);} |
---|
2176 | return p; |
---|
2177 | } |
---|
2178 | |
---|
2179 | /*2 |
---|
2180 | * returns the i-th power of p |
---|
2181 | * p will be destroyed |
---|
2182 | */ |
---|
2183 | poly p_Power(poly p, int i, const ring r) |
---|
2184 | { |
---|
2185 | poly rc=NULL; |
---|
2186 | |
---|
2187 | if (i==0) |
---|
2188 | { |
---|
2189 | p_Delete(&p,r); |
---|
2190 | return p_One(r); |
---|
2191 | } |
---|
2192 | |
---|
2193 | if(p!=NULL) |
---|
2194 | { |
---|
2195 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask)) |
---|
2196 | #ifdef HAVE_SHIFTBBA |
---|
2197 | && (!rIsLPRing(r)) |
---|
2198 | #endif |
---|
2199 | ) |
---|
2200 | { |
---|
2201 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
2202 | return NULL; |
---|
2203 | } |
---|
2204 | switch (i) |
---|
2205 | { |
---|
2206 | // cannot happen, see above |
---|
2207 | // case 0: |
---|
2208 | // { |
---|
2209 | // rc=pOne(); |
---|
2210 | // pDelete(&p); |
---|
2211 | // break; |
---|
2212 | // } |
---|
2213 | case 1: |
---|
2214 | rc=p; |
---|
2215 | break; |
---|
2216 | case 2: |
---|
2217 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
2218 | break; |
---|
2219 | default: |
---|
2220 | if (i < 0) |
---|
2221 | { |
---|
2222 | p_Delete(&p,r); |
---|
2223 | return NULL; |
---|
2224 | } |
---|
2225 | else |
---|
2226 | { |
---|
2227 | #ifdef HAVE_PLURAL |
---|
2228 | if (rIsNCRing(r)) /* in the NC case nothing helps :-( */ |
---|
2229 | { |
---|
2230 | int j=i; |
---|
2231 | rc = p_Copy(p,r); |
---|
2232 | while (j>1) |
---|
2233 | { |
---|
2234 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
2235 | j--; |
---|
2236 | } |
---|
2237 | p_Delete(&p,r); |
---|
2238 | return rc; |
---|
2239 | } |
---|
2240 | #endif |
---|
2241 | rc = pNext(p); |
---|
2242 | if (rc == NULL) |
---|
2243 | return p_MonPower(p,i,r); |
---|
2244 | /* else: binom ?*/ |
---|
2245 | int char_p=rChar(r); |
---|
2246 | if ((char_p>0) && (i>char_p) |
---|
2247 | && ((rField_is_Zp(r,char_p) |
---|
2248 | || (rField_is_Zp_a(r,char_p))))) |
---|
2249 | { |
---|
2250 | poly h=p_Pow_charp(p_Copy(p,r),char_p,r); |
---|
2251 | int rest=i-char_p; |
---|
2252 | while (rest>=char_p) |
---|
2253 | { |
---|
2254 | rest-=char_p; |
---|
2255 | h=p_Mult_q(h,p_Pow_charp(p_Copy(p,r),char_p,r),r); |
---|
2256 | } |
---|
2257 | poly res=h; |
---|
2258 | if (rest>0) |
---|
2259 | res=p_Mult_q(p_Power(p_Copy(p,r),rest,r),h,r); |
---|
2260 | p_Delete(&p,r); |
---|
2261 | return res; |
---|
2262 | } |
---|
2263 | if ((pNext(rc) != NULL) |
---|
2264 | || rField_is_Ring(r) |
---|
2265 | ) |
---|
2266 | return p_Pow(p,i,r); |
---|
2267 | if ((char_p==0) || (i<=char_p)) |
---|
2268 | return p_TwoMonPower(p,i,r); |
---|
2269 | return p_Pow(p,i,r); |
---|
2270 | } |
---|
2271 | /*end default:*/ |
---|
2272 | } |
---|
2273 | } |
---|
2274 | return rc; |
---|
2275 | } |
---|
2276 | |
---|
2277 | /* --------------------------------------------------------------------------------*/ |
---|
2278 | /* content suff */ |
---|
2279 | //number p_InitContent(poly ph, const ring r); |
---|
2280 | |
---|
2281 | void p_Content(poly ph, const ring r) |
---|
2282 | { |
---|
2283 | if (ph==NULL) return; |
---|
2284 | const coeffs cf=r->cf; |
---|
2285 | if (pNext(ph)==NULL) |
---|
2286 | { |
---|
2287 | p_SetCoeff(ph,n_Init(1,cf),r); |
---|
2288 | } |
---|
2289 | if (cf->cfSubringGcd==ndGcd) /* trivial gcd*/ return; |
---|
2290 | number h=p_InitContent(ph,r); /* first guess of a gcd of all coeffs */ |
---|
2291 | poly p; |
---|
2292 | if(n_IsOne(h,cf)) |
---|
2293 | { |
---|
2294 | goto content_finish; |
---|
2295 | } |
---|
2296 | p=ph; |
---|
2297 | // take the SubringGcd of all coeffs |
---|
2298 | while (p!=NULL) |
---|
2299 | { |
---|
2300 | n_Normalize(pGetCoeff(p),cf); |
---|
2301 | number d=n_SubringGcd(h,pGetCoeff(p),cf); |
---|
2302 | n_Delete(&h,cf); |
---|
2303 | h = d; |
---|
2304 | if(n_IsOne(h,cf)) |
---|
2305 | { |
---|
2306 | goto content_finish; |
---|
2307 | } |
---|
2308 | pIter(p); |
---|
2309 | } |
---|
2310 | // if found<>1, divide by it |
---|
2311 | p = ph; |
---|
2312 | while (p!=NULL) |
---|
2313 | { |
---|
2314 | number d = n_ExactDiv(pGetCoeff(p),h,cf); |
---|
2315 | p_SetCoeff(p,d,r); |
---|
2316 | pIter(p); |
---|
2317 | } |
---|
2318 | content_finish: |
---|
2319 | n_Delete(&h,r->cf); |
---|
2320 | // and last: check leading sign: |
---|
2321 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2322 | } |
---|
2323 | |
---|
2324 | #define CLEARENUMERATORS 1 |
---|
2325 | |
---|
2326 | void p_ContentForGB(poly ph, const ring r) |
---|
2327 | { |
---|
2328 | if(TEST_OPT_CONTENTSB) return; |
---|
2329 | assume( ph != NULL ); |
---|
2330 | |
---|
2331 | assume( r != NULL ); assume( r->cf != NULL ); |
---|
2332 | |
---|
2333 | |
---|
2334 | #if CLEARENUMERATORS |
---|
2335 | if( 0 ) |
---|
2336 | { |
---|
2337 | const coeffs C = r->cf; |
---|
2338 | // experimentall (recursive enumerator treatment) of alg. Ext! |
---|
2339 | CPolyCoeffsEnumerator itr(ph); |
---|
2340 | n_ClearContent(itr, r->cf); |
---|
2341 | |
---|
2342 | p_Test(ph, r); n_Test(pGetCoeff(ph), C); |
---|
2343 | assume(n_GreaterZero(pGetCoeff(ph), C)); // ?? |
---|
2344 | |
---|
2345 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2346 | return; |
---|
2347 | } |
---|
2348 | #endif |
---|
2349 | |
---|
2350 | |
---|
2351 | #ifdef HAVE_RINGS |
---|
2352 | if (rField_is_Ring(r)) |
---|
2353 | { |
---|
2354 | if (rField_has_Units(r)) |
---|
2355 | { |
---|
2356 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
2357 | if (!n_IsOne(k,r->cf)) |
---|
2358 | { |
---|
2359 | number tmpGMP = k; |
---|
2360 | k = n_Invers(k,r->cf); |
---|
2361 | n_Delete(&tmpGMP,r->cf); |
---|
2362 | poly h = pNext(ph); |
---|
2363 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
2364 | while (h != NULL) |
---|
2365 | { |
---|
2366 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
2367 | pIter(h); |
---|
2368 | } |
---|
2369 | // assume( n_GreaterZero(pGetCoeff(ph),r->cf) ); |
---|
2370 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2371 | } |
---|
2372 | n_Delete(&k,r->cf); |
---|
2373 | } |
---|
2374 | return; |
---|
2375 | } |
---|
2376 | #endif |
---|
2377 | number h,d; |
---|
2378 | poly p; |
---|
2379 | |
---|
2380 | if(pNext(ph)==NULL) |
---|
2381 | { |
---|
2382 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
2383 | } |
---|
2384 | else |
---|
2385 | { |
---|
2386 | assume( pNext(ph) != NULL ); |
---|
2387 | #if CLEARENUMERATORS |
---|
2388 | if( nCoeff_is_Q(r->cf) ) |
---|
2389 | { |
---|
2390 | // experimentall (recursive enumerator treatment) of alg. Ext! |
---|
2391 | CPolyCoeffsEnumerator itr(ph); |
---|
2392 | n_ClearContent(itr, r->cf); |
---|
2393 | |
---|
2394 | p_Test(ph, r); n_Test(pGetCoeff(ph), r->cf); |
---|
2395 | assume(n_GreaterZero(pGetCoeff(ph), r->cf)); // ?? |
---|
2396 | |
---|
2397 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2398 | return; |
---|
2399 | } |
---|
2400 | #endif |
---|
2401 | |
---|
2402 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
2403 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2404 | if (rField_is_Q(r)||(getCoeffType(r->cf)==n_transExt)) // should not be used anymore if CLEARENUMERATORS is 1 |
---|
2405 | { |
---|
2406 | h=p_InitContent(ph,r); |
---|
2407 | p=ph; |
---|
2408 | } |
---|
2409 | else |
---|
2410 | { |
---|
2411 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
2412 | p = pNext(ph); |
---|
2413 | } |
---|
2414 | while (p!=NULL) |
---|
2415 | { |
---|
2416 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2417 | d=n_SubringGcd(h,pGetCoeff(p),r->cf); |
---|
2418 | n_Delete(&h,r->cf); |
---|
2419 | h = d; |
---|
2420 | if(n_IsOne(h,r->cf)) |
---|
2421 | { |
---|
2422 | break; |
---|
2423 | } |
---|
2424 | pIter(p); |
---|
2425 | } |
---|
2426 | //number tmp; |
---|
2427 | if(!n_IsOne(h,r->cf)) |
---|
2428 | { |
---|
2429 | p = ph; |
---|
2430 | while (p!=NULL) |
---|
2431 | { |
---|
2432 | //d = nDiv(pGetCoeff(p),h); |
---|
2433 | //tmp = nExactDiv(pGetCoeff(p),h); |
---|
2434 | //if (!nEqual(d,tmp)) |
---|
2435 | //{ |
---|
2436 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
2437 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
2438 | // nWrite(tmp);Print(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s); |
---|
2439 | //} |
---|
2440 | //nDelete(&tmp); |
---|
2441 | d = n_ExactDiv(pGetCoeff(p),h,r->cf); |
---|
2442 | p_SetCoeff(p,d,r); |
---|
2443 | pIter(p); |
---|
2444 | } |
---|
2445 | } |
---|
2446 | n_Delete(&h,r->cf); |
---|
2447 | if (rField_is_Q_a(r)) |
---|
2448 | { |
---|
2449 | // special handling for alg. ext.: |
---|
2450 | if (getCoeffType(r->cf)==n_algExt) |
---|
2451 | { |
---|
2452 | h = n_Init(1, r->cf->extRing->cf); |
---|
2453 | p=ph; |
---|
2454 | while (p!=NULL) |
---|
2455 | { // each monom: coeff in Q_a |
---|
2456 | poly c_n_n=(poly)pGetCoeff(p); |
---|
2457 | poly c_n=c_n_n; |
---|
2458 | while (c_n!=NULL) |
---|
2459 | { // each monom: coeff in Q |
---|
2460 | d=n_NormalizeHelper(h,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
2461 | n_Delete(&h,r->cf->extRing->cf); |
---|
2462 | h=d; |
---|
2463 | pIter(c_n); |
---|
2464 | } |
---|
2465 | pIter(p); |
---|
2466 | } |
---|
2467 | /* h contains the 1/lcm of all denominators in c_n_n*/ |
---|
2468 | //n_Normalize(h,r->cf->extRing->cf); |
---|
2469 | if(!n_IsOne(h,r->cf->extRing->cf)) |
---|
2470 | { |
---|
2471 | p=ph; |
---|
2472 | while (p!=NULL) |
---|
2473 | { // each monom: coeff in Q_a |
---|
2474 | poly c_n=(poly)pGetCoeff(p); |
---|
2475 | while (c_n!=NULL) |
---|
2476 | { // each monom: coeff in Q |
---|
2477 | d=n_Mult(h,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
2478 | n_Normalize(d,r->cf->extRing->cf); |
---|
2479 | n_Delete(&pGetCoeff(c_n),r->cf->extRing->cf); |
---|
2480 | pGetCoeff(c_n)=d; |
---|
2481 | pIter(c_n); |
---|
2482 | } |
---|
2483 | pIter(p); |
---|
2484 | } |
---|
2485 | } |
---|
2486 | n_Delete(&h,r->cf->extRing->cf); |
---|
2487 | } |
---|
2488 | /*else |
---|
2489 | { |
---|
2490 | // special handling for rat. functions.: |
---|
2491 | number hzz =NULL; |
---|
2492 | p=ph; |
---|
2493 | while (p!=NULL) |
---|
2494 | { // each monom: coeff in Q_a (Z_a) |
---|
2495 | fraction f=(fraction)pGetCoeff(p); |
---|
2496 | poly c_n=NUM(f); |
---|
2497 | if (hzz==NULL) |
---|
2498 | { |
---|
2499 | hzz=n_Copy(pGetCoeff(c_n),r->cf->extRing->cf); |
---|
2500 | pIter(c_n); |
---|
2501 | } |
---|
2502 | while ((c_n!=NULL)&&(!n_IsOne(hzz,r->cf->extRing->cf))) |
---|
2503 | { // each monom: coeff in Q (Z) |
---|
2504 | d=n_Gcd(hzz,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
2505 | n_Delete(&hzz,r->cf->extRing->cf); |
---|
2506 | hzz=d; |
---|
2507 | pIter(c_n); |
---|
2508 | } |
---|
2509 | pIter(p); |
---|
2510 | } |
---|
2511 | // hzz contains the gcd of all numerators in f |
---|
2512 | h=n_Invers(hzz,r->cf->extRing->cf); |
---|
2513 | n_Delete(&hzz,r->cf->extRing->cf); |
---|
2514 | n_Normalize(h,r->cf->extRing->cf); |
---|
2515 | if(!n_IsOne(h,r->cf->extRing->cf)) |
---|
2516 | { |
---|
2517 | p=ph; |
---|
2518 | while (p!=NULL) |
---|
2519 | { // each monom: coeff in Q_a (Z_a) |
---|
2520 | fraction f=(fraction)pGetCoeff(p); |
---|
2521 | NUM(f)=__p_Mult_nn(NUM(f),h,r->cf->extRing); |
---|
2522 | p_Normalize(NUM(f),r->cf->extRing); |
---|
2523 | pIter(p); |
---|
2524 | } |
---|
2525 | } |
---|
2526 | n_Delete(&h,r->cf->extRing->cf); |
---|
2527 | }*/ |
---|
2528 | } |
---|
2529 | } |
---|
2530 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2531 | } |
---|
2532 | |
---|
2533 | // Not yet? |
---|
2534 | #if 1 // currently only used by Singular/janet |
---|
2535 | void p_SimpleContent(poly ph, int smax, const ring r) |
---|
2536 | { |
---|
2537 | if(TEST_OPT_CONTENTSB) return; |
---|
2538 | if (ph==NULL) return; |
---|
2539 | if (pNext(ph)==NULL) |
---|
2540 | { |
---|
2541 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
2542 | return; |
---|
2543 | } |
---|
2544 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
2545 | { |
---|
2546 | return; |
---|
2547 | } |
---|
2548 | number d=p_InitContent(ph,r); |
---|
2549 | if (n_Size(d,r->cf)<=smax) |
---|
2550 | { |
---|
2551 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
2552 | return; |
---|
2553 | } |
---|
2554 | |
---|
2555 | poly p=ph; |
---|
2556 | number h=d; |
---|
2557 | if (smax==1) smax=2; |
---|
2558 | while (p!=NULL) |
---|
2559 | { |
---|
2560 | #if 0 |
---|
2561 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
2562 | n_Delete(&h,r->cf); |
---|
2563 | h = d; |
---|
2564 | #else |
---|
2565 | STATISTIC(n_Gcd); nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
2566 | #endif |
---|
2567 | if(n_Size(h,r->cf)<smax) |
---|
2568 | { |
---|
2569 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
2570 | return; |
---|
2571 | } |
---|
2572 | pIter(p); |
---|
2573 | } |
---|
2574 | p = ph; |
---|
2575 | if (!n_GreaterZero(pGetCoeff(p),r->cf)) h=n_InpNeg(h,r->cf); |
---|
2576 | if(n_IsOne(h,r->cf)) return; |
---|
2577 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
2578 | while (p!=NULL) |
---|
2579 | { |
---|
2580 | #if 1 |
---|
2581 | d = n_ExactDiv(pGetCoeff(p),h,r->cf); |
---|
2582 | p_SetCoeff(p,d,r); |
---|
2583 | #else |
---|
2584 | STATISTIC(n_ExactDiv); nlInpExactDiv(pGetCoeff(p),h,r->cf); // no such function... ? |
---|
2585 | #endif |
---|
2586 | pIter(p); |
---|
2587 | } |
---|
2588 | n_Delete(&h,r->cf); |
---|
2589 | } |
---|
2590 | #endif |
---|
2591 | |
---|
2592 | number p_InitContent(poly ph, const ring r) |
---|
2593 | // only for coefficients in Q and rational functions |
---|
2594 | #if 0 |
---|
2595 | { |
---|
2596 | assume(!TEST_OPT_CONTENTSB); |
---|
2597 | assume(ph!=NULL); |
---|
2598 | assume(pNext(ph)!=NULL); |
---|
2599 | assume(rField_is_Q(r)); |
---|
2600 | if (pNext(pNext(ph))==NULL) |
---|
2601 | { |
---|
2602 | return n_GetNumerator(pGetCoeff(pNext(ph)),r->cf); |
---|
2603 | } |
---|
2604 | poly p=ph; |
---|
2605 | number n1=n_GetNumerator(pGetCoeff(p),r->cf); |
---|
2606 | pIter(p); |
---|
2607 | number n2=n_GetNumerator(pGetCoeff(p),r->cf); |
---|
2608 | pIter(p); |
---|
2609 | number d; |
---|
2610 | number t; |
---|
2611 | loop |
---|
2612 | { |
---|
2613 | nlNormalize(pGetCoeff(p),r->cf); |
---|
2614 | t=n_GetNumerator(pGetCoeff(p),r->cf); |
---|
2615 | if (nlGreaterZero(t,r->cf)) |
---|
2616 | d=nlAdd(n1,t,r->cf); |
---|
2617 | else |
---|
2618 | d=nlSub(n1,t,r->cf); |
---|
2619 | nlDelete(&t,r->cf); |
---|
2620 | nlDelete(&n1,r->cf); |
---|
2621 | n1=d; |
---|
2622 | pIter(p); |
---|
2623 | if (p==NULL) break; |
---|
2624 | nlNormalize(pGetCoeff(p),r->cf); |
---|
2625 | t=n_GetNumerator(pGetCoeff(p),r->cf); |
---|
2626 | if (nlGreaterZero(t,r->cf)) |
---|
2627 | d=nlAdd(n2,t,r->cf); |
---|
2628 | else |
---|
2629 | d=nlSub(n2,t,r->cf); |
---|
2630 | nlDelete(&t,r->cf); |
---|
2631 | nlDelete(&n2,r->cf); |
---|
2632 | n2=d; |
---|
2633 | pIter(p); |
---|
2634 | if (p==NULL) break; |
---|
2635 | } |
---|
2636 | d=nlGcd(n1,n2,r->cf); |
---|
2637 | nlDelete(&n1,r->cf); |
---|
2638 | nlDelete(&n2,r->cf); |
---|
2639 | return d; |
---|
2640 | } |
---|
2641 | #else |
---|
2642 | { |
---|
2643 | /* ph has al least 2 terms */ |
---|
2644 | number d=pGetCoeff(ph); |
---|
2645 | int s=n_Size(d,r->cf); |
---|
2646 | pIter(ph); |
---|
2647 | number d2=pGetCoeff(ph); |
---|
2648 | int s2=n_Size(d2,r->cf); |
---|
2649 | pIter(ph); |
---|
2650 | if (ph==NULL) |
---|
2651 | { |
---|
2652 | if (s<s2) return n_Copy(d,r->cf); |
---|
2653 | else return n_Copy(d2,r->cf); |
---|
2654 | } |
---|
2655 | do |
---|
2656 | { |
---|
2657 | number nd=pGetCoeff(ph); |
---|
2658 | int ns=n_Size(nd,r->cf); |
---|
2659 | if (ns<=2) |
---|
2660 | { |
---|
2661 | s2=s; |
---|
2662 | d2=d; |
---|
2663 | d=nd; |
---|
2664 | s=ns; |
---|
2665 | break; |
---|
2666 | } |
---|
2667 | else if (ns<s) |
---|
2668 | { |
---|
2669 | s2=s; |
---|
2670 | d2=d; |
---|
2671 | d=nd; |
---|
2672 | s=ns; |
---|
2673 | } |
---|
2674 | pIter(ph); |
---|
2675 | } |
---|
2676 | while(ph!=NULL); |
---|
2677 | return n_SubringGcd(d,d2,r->cf); |
---|
2678 | } |
---|
2679 | #endif |
---|
2680 | |
---|
2681 | //void pContent(poly ph) |
---|
2682 | //{ |
---|
2683 | // number h,d; |
---|
2684 | // poly p; |
---|
2685 | // |
---|
2686 | // p = ph; |
---|
2687 | // if(pNext(p)==NULL) |
---|
2688 | // { |
---|
2689 | // pSetCoeff(p,nInit(1)); |
---|
2690 | // } |
---|
2691 | // else |
---|
2692 | // { |
---|
2693 | //#ifdef PDEBUG |
---|
2694 | // if (!pTest(p)) return; |
---|
2695 | //#endif |
---|
2696 | // nNormalize(pGetCoeff(p)); |
---|
2697 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
2698 | // { |
---|
2699 | // ph = pNeg(ph); |
---|
2700 | // nNormalize(pGetCoeff(p)); |
---|
2701 | // } |
---|
2702 | // h=pGetCoeff(p); |
---|
2703 | // pIter(p); |
---|
2704 | // while (p!=NULL) |
---|
2705 | // { |
---|
2706 | // nNormalize(pGetCoeff(p)); |
---|
2707 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
2708 | // pIter(p); |
---|
2709 | // } |
---|
2710 | // h=nCopy(h); |
---|
2711 | // p=ph; |
---|
2712 | // while (p!=NULL) |
---|
2713 | // { |
---|
2714 | // d=n_Gcd(h,pGetCoeff(p)); |
---|
2715 | // nDelete(&h); |
---|
2716 | // h = d; |
---|
2717 | // if(nIsOne(h)) |
---|
2718 | // { |
---|
2719 | // break; |
---|
2720 | // } |
---|
2721 | // pIter(p); |
---|
2722 | // } |
---|
2723 | // p = ph; |
---|
2724 | // //number tmp; |
---|
2725 | // if(!nIsOne(h)) |
---|
2726 | // { |
---|
2727 | // while (p!=NULL) |
---|
2728 | // { |
---|
2729 | // d = nExactDiv(pGetCoeff(p),h); |
---|
2730 | // pSetCoeff(p,d); |
---|
2731 | // pIter(p); |
---|
2732 | // } |
---|
2733 | // } |
---|
2734 | // nDelete(&h); |
---|
2735 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2736 | // { |
---|
2737 | // pTest(ph); |
---|
2738 | // singclap_divide_content(ph); |
---|
2739 | // pTest(ph); |
---|
2740 | // } |
---|
2741 | // } |
---|
2742 | //} |
---|
2743 | #if 0 |
---|
2744 | void p_Content(poly ph, const ring r) |
---|
2745 | { |
---|
2746 | number h,d; |
---|
2747 | poly p; |
---|
2748 | |
---|
2749 | if(pNext(ph)==NULL) |
---|
2750 | { |
---|
2751 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
2752 | } |
---|
2753 | else |
---|
2754 | { |
---|
2755 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
2756 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2757 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
2758 | p = pNext(ph); |
---|
2759 | while (p!=NULL) |
---|
2760 | { |
---|
2761 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2762 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
2763 | n_Delete(&h,r->cf); |
---|
2764 | h = d; |
---|
2765 | if(n_IsOne(h,r->cf)) |
---|
2766 | { |
---|
2767 | break; |
---|
2768 | } |
---|
2769 | pIter(p); |
---|
2770 | } |
---|
2771 | p = ph; |
---|
2772 | //number tmp; |
---|
2773 | if(!n_IsOne(h,r->cf)) |
---|
2774 | { |
---|
2775 | while (p!=NULL) |
---|
2776 | { |
---|
2777 | //d = nDiv(pGetCoeff(p),h); |
---|
2778 | //tmp = nExactDiv(pGetCoeff(p),h); |
---|
2779 | //if (!nEqual(d,tmp)) |
---|
2780 | //{ |
---|
2781 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
2782 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
2783 | // nWrite(tmp);Print(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s); |
---|
2784 | //} |
---|
2785 | //nDelete(&tmp); |
---|
2786 | d = n_ExactDiv(pGetCoeff(p),h,r->cf); |
---|
2787 | p_SetCoeff(p,d,r->cf); |
---|
2788 | pIter(p); |
---|
2789 | } |
---|
2790 | } |
---|
2791 | n_Delete(&h,r->cf); |
---|
2792 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2793 | //{ |
---|
2794 | // singclap_divide_content(ph); |
---|
2795 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
2796 | //} |
---|
2797 | } |
---|
2798 | } |
---|
2799 | #endif |
---|
2800 | /* ---------------------------------------------------------------------------*/ |
---|
2801 | /* cleardenom suff */ |
---|
2802 | poly p_Cleardenom(poly p, const ring r) |
---|
2803 | { |
---|
2804 | if( p == NULL ) |
---|
2805 | return NULL; |
---|
2806 | |
---|
2807 | assume( r != NULL ); assume( r->cf != NULL ); const coeffs C = r->cf; |
---|
2808 | |
---|
2809 | #if CLEARENUMERATORS |
---|
2810 | if( 0 ) |
---|
2811 | { |
---|
2812 | CPolyCoeffsEnumerator itr(p); |
---|
2813 | n_ClearDenominators(itr, C); |
---|
2814 | n_ClearContent(itr, C); // divide out the content |
---|
2815 | p_Test(p, r); n_Test(pGetCoeff(p), C); |
---|
2816 | assume(n_GreaterZero(pGetCoeff(p), C)); // ?? |
---|
2817 | // if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r); |
---|
2818 | return p; |
---|
2819 | } |
---|
2820 | #endif |
---|
2821 | |
---|
2822 | number d, h; |
---|
2823 | |
---|
2824 | if (rField_is_Ring(r)) |
---|
2825 | { |
---|
2826 | p_ContentForGB(p,r); |
---|
2827 | if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r); |
---|
2828 | return p; |
---|
2829 | } |
---|
2830 | |
---|
2831 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) |
---|
2832 | { |
---|
2833 | if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r); |
---|
2834 | return p; |
---|
2835 | } |
---|
2836 | |
---|
2837 | assume(p != NULL); |
---|
2838 | |
---|
2839 | if(pNext(p)==NULL) |
---|
2840 | { |
---|
2841 | if (!TEST_OPT_CONTENTSB |
---|
2842 | && !rField_is_Ring(r)) |
---|
2843 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
2844 | else if(!n_GreaterZero(pGetCoeff(p),C)) |
---|
2845 | p = p_Neg(p,r); |
---|
2846 | return p; |
---|
2847 | } |
---|
2848 | |
---|
2849 | assume(pNext(p)!=NULL); |
---|
2850 | poly start=p; |
---|
2851 | |
---|
2852 | #if 0 && CLEARENUMERATORS |
---|
2853 | //CF: does not seem to work that well.. |
---|
2854 | |
---|
2855 | if( nCoeff_is_Q(C) || nCoeff_is_Q_a(C) ) |
---|
2856 | { |
---|
2857 | CPolyCoeffsEnumerator itr(p); |
---|
2858 | n_ClearDenominators(itr, C); |
---|
2859 | n_ClearContent(itr, C); // divide out the content |
---|
2860 | p_Test(p, r); n_Test(pGetCoeff(p), C); |
---|
2861 | assume(n_GreaterZero(pGetCoeff(p), C)); // ?? |
---|
2862 | // if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r); |
---|
2863 | return start; |
---|
2864 | } |
---|
2865 | #endif |
---|
2866 | |
---|
2867 | if(1) |
---|
2868 | { |
---|
2869 | // get lcm of all denominators ---------------------------------- |
---|
2870 | h = n_Init(1,r->cf); |
---|
2871 | while (p!=NULL) |
---|
2872 | { |
---|
2873 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2874 | d=n_NormalizeHelper(h,pGetCoeff(p),r->cf); |
---|
2875 | n_Delete(&h,r->cf); |
---|
2876 | h=d; |
---|
2877 | pIter(p); |
---|
2878 | } |
---|
2879 | /* h now contains the 1/lcm of all denominators */ |
---|
2880 | if(!n_IsOne(h,r->cf)) |
---|
2881 | { |
---|
2882 | // multiply by the lcm of all denominators |
---|
2883 | p = start; |
---|
2884 | while (p!=NULL) |
---|
2885 | { |
---|
2886 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2887 | n_Normalize(d,r->cf); |
---|
2888 | p_SetCoeff(p,d,r); |
---|
2889 | pIter(p); |
---|
2890 | } |
---|
2891 | } |
---|
2892 | n_Delete(&h,r->cf); |
---|
2893 | p=start; |
---|
2894 | |
---|
2895 | p_ContentForGB(p,r); |
---|
2896 | #ifdef HAVE_RATGRING |
---|
2897 | if (rIsRatGRing(r)) |
---|
2898 | { |
---|
2899 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
2900 | p_ContentRat(p, r); |
---|
2901 | start=p; |
---|
2902 | } |
---|
2903 | #endif |
---|
2904 | } |
---|
2905 | |
---|
2906 | if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r); |
---|
2907 | |
---|
2908 | return start; |
---|
2909 | } |
---|
2910 | |
---|
2911 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
2912 | { |
---|
2913 | const coeffs C = r->cf; |
---|
2914 | number d, h; |
---|
2915 | |
---|
2916 | assume( ph != NULL ); |
---|
2917 | |
---|
2918 | poly p = ph; |
---|
2919 | |
---|
2920 | #if CLEARENUMERATORS |
---|
2921 | if( 0 ) |
---|
2922 | { |
---|
2923 | CPolyCoeffsEnumerator itr(ph); |
---|
2924 | |
---|
2925 | n_ClearDenominators(itr, d, C); // multiply with common denom. d |
---|
2926 | n_ClearContent(itr, h, C); // divide by the content h |
---|
2927 | |
---|
2928 | c = n_Div(d, h, C); // d/h |
---|
2929 | |
---|
2930 | n_Delete(&d, C); |
---|
2931 | n_Delete(&h, C); |
---|
2932 | |
---|
2933 | n_Test(c, C); |
---|
2934 | |
---|
2935 | p_Test(ph, r); n_Test(pGetCoeff(ph), C); |
---|
2936 | assume(n_GreaterZero(pGetCoeff(ph), C)); // ?? |
---|
2937 | /* |
---|
2938 | if(!n_GreaterZero(pGetCoeff(ph),C)) |
---|
2939 | { |
---|
2940 | ph = p_Neg(ph,r); |
---|
2941 | c = n_InpNeg(c, C); |
---|
2942 | } |
---|
2943 | */ |
---|
2944 | return; |
---|
2945 | } |
---|
2946 | #endif |
---|
2947 | |
---|
2948 | |
---|
2949 | if( pNext(p) == NULL ) |
---|
2950 | { |
---|
2951 | if(!TEST_OPT_CONTENTSB) |
---|
2952 | { |
---|
2953 | c=n_Invers(pGetCoeff(p), C); |
---|
2954 | p_SetCoeff(p, n_Init(1, C), r); |
---|
2955 | } |
---|
2956 | else |
---|
2957 | { |
---|
2958 | c=n_Init(1,C); |
---|
2959 | } |
---|
2960 | |
---|
2961 | if(!n_GreaterZero(pGetCoeff(ph),C)) |
---|
2962 | { |
---|
2963 | ph = p_Neg(ph,r); |
---|
2964 | c = n_InpNeg(c, C); |
---|
2965 | } |
---|
2966 | |
---|
2967 | return; |
---|
2968 | } |
---|
2969 | if (TEST_OPT_CONTENTSB) { c=n_Init(1,C); return; } |
---|
2970 | |
---|
2971 | assume( pNext(p) != NULL ); |
---|
2972 | |
---|
2973 | #if CLEARENUMERATORS |
---|
2974 | if( nCoeff_is_Q(C) || nCoeff_is_Q_a(C) ) |
---|
2975 | { |
---|
2976 | CPolyCoeffsEnumerator itr(ph); |
---|
2977 | |
---|
2978 | n_ClearDenominators(itr, d, C); // multiply with common denom. d |
---|
2979 | n_ClearContent(itr, h, C); // divide by the content h |
---|
2980 | |
---|
2981 | c = n_Div(d, h, C); // d/h |
---|
2982 | |
---|
2983 | n_Delete(&d, C); |
---|
2984 | n_Delete(&h, C); |
---|
2985 | |
---|
2986 | n_Test(c, C); |
---|
2987 | |
---|
2988 | p_Test(ph, r); n_Test(pGetCoeff(ph), C); |
---|
2989 | assume(n_GreaterZero(pGetCoeff(ph), C)); // ?? |
---|
2990 | /* |
---|
2991 | if(!n_GreaterZero(pGetCoeff(ph),C)) |
---|
2992 | { |
---|
2993 | ph = p_Neg(ph,r); |
---|
2994 | c = n_InpNeg(c, C); |
---|
2995 | } |
---|
2996 | */ |
---|
2997 | return; |
---|
2998 | } |
---|
2999 | #endif |
---|
3000 | |
---|
3001 | |
---|
3002 | |
---|
3003 | |
---|
3004 | if(1) |
---|
3005 | { |
---|
3006 | h = n_Init(1,r->cf); |
---|
3007 | while (p!=NULL) |
---|
3008 | { |
---|
3009 | n_Normalize(pGetCoeff(p),r->cf); |
---|
3010 | d=n_NormalizeHelper(h,pGetCoeff(p),r->cf); |
---|
3011 | n_Delete(&h,r->cf); |
---|
3012 | h=d; |
---|
3013 | pIter(p); |
---|
3014 | } |
---|
3015 | c=h; |
---|
3016 | /* contains the 1/lcm of all denominators */ |
---|
3017 | if(!n_IsOne(h,r->cf)) |
---|
3018 | { |
---|
3019 | p = ph; |
---|
3020 | while (p!=NULL) |
---|
3021 | { |
---|
3022 | /* should be: // NOTE: don't use ->coef!!!! |
---|
3023 | * number hh; |
---|
3024 | * nGetDenom(p->coef,&hh); |
---|
3025 | * nMult(&h,&hh,&d); |
---|
3026 | * nNormalize(d); |
---|
3027 | * nDelete(&hh); |
---|
3028 | * nMult(d,p->coef,&hh); |
---|
3029 | * nDelete(&d); |
---|
3030 | * nDelete(&(p->coef)); |
---|
3031 | * p->coef =hh; |
---|
3032 | */ |
---|
3033 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
3034 | n_Normalize(d,r->cf); |
---|
3035 | p_SetCoeff(p,d,r); |
---|
3036 | pIter(p); |
---|
3037 | } |
---|
3038 | if (rField_is_Q_a(r)) |
---|
3039 | { |
---|
3040 | loop |
---|
3041 | { |
---|
3042 | h = n_Init(1,r->cf); |
---|
3043 | p=ph; |
---|
3044 | while (p!=NULL) |
---|
3045 | { |
---|
3046 | d=n_NormalizeHelper(h,pGetCoeff(p),r->cf); |
---|
3047 | n_Delete(&h,r->cf); |
---|
3048 | h=d; |
---|
3049 | pIter(p); |
---|
3050 | } |
---|
3051 | /* contains the 1/lcm of all denominators */ |
---|
3052 | if(!n_IsOne(h,r->cf)) |
---|
3053 | { |
---|
3054 | p = ph; |
---|
3055 | while (p!=NULL) |
---|
3056 | { |
---|
3057 | /* should be: // NOTE: don't use ->coef!!!! |
---|
3058 | * number hh; |
---|
3059 | * nGetDenom(p->coef,&hh); |
---|
3060 | * nMult(&h,&hh,&d); |
---|
3061 | * nNormalize(d); |
---|
3062 | * nDelete(&hh); |
---|
3063 | * nMult(d,p->coef,&hh); |
---|
3064 | * nDelete(&d); |
---|
3065 | * nDelete(&(p->coef)); |
---|
3066 | * p->coef =hh; |
---|
3067 | */ |
---|
3068 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
3069 | n_Normalize(d,r->cf); |
---|
3070 | p_SetCoeff(p,d,r); |
---|
3071 | pIter(p); |
---|
3072 | } |
---|
3073 | number t=n_Mult(c,h,r->cf); |
---|
3074 | n_Delete(&c,r->cf); |
---|
3075 | c=t; |
---|
3076 | } |
---|
3077 | else |
---|
3078 | { |
---|
3079 | break; |
---|
3080 | } |
---|
3081 | n_Delete(&h,r->cf); |
---|
3082 | } |
---|
3083 | } |
---|
3084 | } |
---|
3085 | } |
---|
3086 | |
---|
3087 | if(!n_GreaterZero(pGetCoeff(ph),C)) |
---|
3088 | { |
---|
3089 | ph = p_Neg(ph,r); |
---|
3090 | c = n_InpNeg(c, C); |
---|
3091 | } |
---|
3092 | |
---|
3093 | } |
---|
3094 | |
---|
3095 | // normalization: for poly over Q: make poly primitive, integral |
---|
3096 | // Qa make poly integral with leading |
---|
3097 | // coefficient minimal in N |
---|
3098 | // Q(t) make poly primitive, integral |
---|
3099 | |
---|
3100 | void p_ProjectiveUnique(poly ph, const ring r) |
---|
3101 | { |
---|
3102 | if( ph == NULL ) |
---|
3103 | return; |
---|
3104 | |
---|
3105 | assume( r != NULL ); assume( r->cf != NULL ); |
---|
3106 | const coeffs C = r->cf; |
---|
3107 | |
---|
3108 | number h; |
---|
3109 | poly p; |
---|
3110 | |
---|
3111 | if (nCoeff_is_Ring(C)) |
---|
3112 | { |
---|
3113 | p_ContentForGB(ph,r); |
---|
3114 | if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r); |
---|
3115 | assume( n_GreaterZero(pGetCoeff(ph),C) ); |
---|
3116 | return; |
---|
3117 | } |
---|
3118 | |
---|
3119 | if (nCoeff_is_Zp(C) && TEST_OPT_INTSTRATEGY) |
---|
3120 | { |
---|
3121 | assume( n_GreaterZero(pGetCoeff(ph),C) ); |
---|
3122 | if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r); |
---|
3123 | return; |
---|
3124 | } |
---|
3125 | p = ph; |
---|
3126 | |
---|
3127 | assume(p != NULL); |
---|
3128 | |
---|
3129 | if(pNext(p)==NULL) // a monomial |
---|
3130 | { |
---|
3131 | p_SetCoeff(p, n_Init(1, C), r); |
---|
3132 | return; |
---|
3133 | } |
---|
3134 | |
---|
3135 | assume(pNext(p)!=NULL); |
---|
3136 | |
---|
3137 | if(!nCoeff_is_Q(C) && !nCoeff_is_transExt(C)) |
---|
3138 | { |
---|
3139 | h = p_GetCoeff(p, C); |
---|
3140 | number hInv = n_Invers(h, C); |
---|
3141 | pIter(p); |
---|
3142 | while (p!=NULL) |
---|
3143 | { |
---|
3144 | p_SetCoeff(p, n_Mult(p_GetCoeff(p, C), hInv, C), r); |
---|
3145 | pIter(p); |
---|
3146 | } |
---|
3147 | n_Delete(&hInv, C); |
---|
3148 | p = ph; |
---|
3149 | p_SetCoeff(p, n_Init(1, C), r); |
---|
3150 | } |
---|
3151 | |
---|
3152 | p_Cleardenom(ph, r); //removes also Content |
---|
3153 | |
---|
3154 | |
---|
3155 | /* normalize ph over a transcendental extension s.t. |
---|
3156 | lead (ph) is > 0 if extRing->cf == Q |
---|
3157 | or lead (ph) is monic if extRing->cf == Zp*/ |
---|
3158 | if (nCoeff_is_transExt(C)) |
---|
3159 | { |
---|
3160 | p= ph; |
---|
3161 | h= p_GetCoeff (p, C); |
---|
3162 | fraction f = (fraction) h; |
---|
3163 | number n=p_GetCoeff (NUM (f),C->extRing->cf); |
---|
3164 | if (rField_is_Q (C->extRing)) |
---|
3165 | { |
---|
3166 | if (!n_GreaterZero(n,C->extRing->cf)) |
---|
3167 | { |
---|
3168 | p=p_Neg (p,r); |
---|
3169 | } |
---|
3170 | } |
---|
3171 | else if (rField_is_Zp(C->extRing)) |
---|
3172 | { |
---|
3173 | if (!n_IsOne (n, C->extRing->cf)) |
---|
3174 | { |
---|
3175 | n=n_Invers (n,C->extRing->cf); |
---|
3176 | nMapFunc nMap; |
---|
3177 | nMap= n_SetMap (C->extRing->cf, C); |
---|
3178 | number ninv= nMap (n,C->extRing->cf, C); |
---|
3179 | p=__p_Mult_nn (p, ninv, r); |
---|
3180 | n_Delete (&ninv, C); |
---|
3181 | n_Delete (&n, C->extRing->cf); |
---|
3182 | } |
---|
3183 | } |
---|
3184 | p= ph; |
---|
3185 | } |
---|
3186 | |
---|
3187 | return; |
---|
3188 | } |
---|
3189 | |
---|
3190 | #if 0 /*unused*/ |
---|
3191 | number p_GetAllDenom(poly ph, const ring r) |
---|
3192 | { |
---|
3193 | number d=n_Init(1,r->cf); |
---|
3194 | poly p = ph; |
---|
3195 | |
---|
3196 | while (p!=NULL) |
---|
3197 | { |
---|
3198 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
3199 | if (!n_IsOne(h,r->cf)) |
---|
3200 | { |
---|
3201 | number dd=n_Mult(d,h,r->cf); |
---|
3202 | n_Delete(&d,r->cf); |
---|
3203 | d=dd; |
---|
3204 | } |
---|
3205 | n_Delete(&h,r->cf); |
---|
3206 | pIter(p); |
---|
3207 | } |
---|
3208 | return d; |
---|
3209 | } |
---|
3210 | #endif |
---|
3211 | |
---|
3212 | int p_Size(poly p, const ring r) |
---|
3213 | { |
---|
3214 | int count = 0; |
---|
3215 | if (r->cf->has_simple_Alloc) |
---|
3216 | return pLength(p); |
---|
3217 | while ( p != NULL ) |
---|
3218 | { |
---|
3219 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
3220 | pIter( p ); |
---|
3221 | } |
---|
3222 | return count; |
---|
3223 | } |
---|
3224 | |
---|
3225 | /*2 |
---|
3226 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
3227 | *assume: deg(var(varnum))==1 |
---|
3228 | */ |
---|
3229 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
3230 | { |
---|
3231 | pFDegProc deg; |
---|
3232 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
3233 | deg=p_Totaldegree; |
---|
3234 | else |
---|
3235 | deg=r->pFDeg; |
---|
3236 | |
---|
3237 | poly q=NULL, qn; |
---|
3238 | int o,ii; |
---|
3239 | sBucket_pt bp; |
---|
3240 | |
---|
3241 | if (p!=NULL) |
---|
3242 | { |
---|
3243 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
3244 | { |
---|
3245 | return NULL; |
---|
3246 | } |
---|
3247 | o=deg(p,r); |
---|
3248 | q=pNext(p); |
---|
3249 | while (q != NULL) |
---|
3250 | { |
---|
3251 | ii=deg(q,r); |
---|
3252 | if (ii>o) o=ii; |
---|
3253 | pIter(q); |
---|
3254 | } |
---|
3255 | q = p_Copy(p,r); |
---|
3256 | bp = sBucketCreate(r); |
---|
3257 | while (q != NULL) |
---|
3258 | { |
---|
3259 | ii = o-deg(q,r); |
---|
3260 | if (ii!=0) |
---|
3261 | { |
---|
3262 | p_AddExp(q,varnum, (long)ii,r); |
---|
3263 | p_Setm(q,r); |
---|
3264 | } |
---|
3265 | qn = pNext(q); |
---|
3266 | pNext(q) = NULL; |
---|
3267 | sBucket_Add_m(bp, q); |
---|
3268 | q = qn; |
---|
3269 | } |
---|
3270 | sBucketDestroyAdd(bp, &q, &ii); |
---|
3271 | } |
---|
3272 | return q; |
---|
3273 | } |
---|
3274 | |
---|
3275 | /*2 |
---|
3276 | *tests if p is homogeneous with respect to the actual weigths |
---|
3277 | */ |
---|
3278 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
3279 | { |
---|
3280 | poly qp=p; |
---|
3281 | int o; |
---|
3282 | |
---|
3283 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
3284 | pFDegProc d; |
---|
3285 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
3286 | d=p_Totaldegree; |
---|
3287 | else |
---|
3288 | d=r->pFDeg; |
---|
3289 | o = d(p,r); |
---|
3290 | do |
---|
3291 | { |
---|
3292 | if (d(qp,r) != o) return FALSE; |
---|
3293 | pIter(qp); |
---|
3294 | } |
---|
3295 | while (qp != NULL); |
---|
3296 | return TRUE; |
---|
3297 | } |
---|
3298 | |
---|
3299 | /*----------utilities for syzygies--------------*/ |
---|
3300 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
3301 | { |
---|
3302 | poly q=p,qq; |
---|
3303 | int i; |
---|
3304 | |
---|
3305 | while (q!=NULL) |
---|
3306 | { |
---|
3307 | if (p_LmIsConstantComp(q,r)) |
---|
3308 | { |
---|
3309 | i = __p_GetComp(q,r); |
---|
3310 | qq = p; |
---|
3311 | while ((qq != q) && (__p_GetComp(qq,r) != i)) pIter(qq); |
---|
3312 | if (qq == q) |
---|
3313 | { |
---|
3314 | *k = i; |
---|
3315 | return TRUE; |
---|
3316 | } |
---|
3317 | } |
---|
3318 | pIter(q); |
---|
3319 | } |
---|
3320 | return FALSE; |
---|
3321 | } |
---|
3322 | |
---|
3323 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
3324 | { |
---|
3325 | poly q=p,qq; |
---|
3326 | int i,j=0; |
---|
3327 | |
---|
3328 | *len = 0; |
---|
3329 | while (q!=NULL) |
---|
3330 | { |
---|
3331 | if (p_LmIsConstantComp(q,r)) |
---|
3332 | { |
---|
3333 | i = __p_GetComp(q,r); |
---|
3334 | qq = p; |
---|
3335 | while ((qq != q) && (__p_GetComp(qq,r) != i)) pIter(qq); |
---|
3336 | if (qq == q) |
---|
3337 | { |
---|
3338 | j = 0; |
---|
3339 | while (qq!=NULL) |
---|
3340 | { |
---|
3341 | if (__p_GetComp(qq,r)==i) j++; |
---|
3342 | pIter(qq); |
---|
3343 | } |
---|
3344 | if ((*len == 0) || (j<*len)) |
---|
3345 | { |
---|
3346 | *len = j; |
---|
3347 | *k = i; |
---|
3348 | } |
---|
3349 | } |
---|
3350 | } |
---|
3351 | pIter(q); |
---|
3352 | } |
---|
3353 | } |
---|
3354 | |
---|
3355 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
3356 | { |
---|
3357 | poly q = *p; |
---|
3358 | |
---|
3359 | if (q==NULL) return NULL; |
---|
3360 | |
---|
3361 | poly qq=NULL,result = NULL; |
---|
3362 | |
---|
3363 | if (__p_GetComp(q,r)==k) |
---|
3364 | { |
---|
3365 | result = q; /* *p */ |
---|
3366 | while ((q!=NULL) && (__p_GetComp(q,r)==k)) |
---|
3367 | { |
---|
3368 | p_SetComp(q,0,r); |
---|
3369 | p_SetmComp(q,r); |
---|
3370 | qq = q; |
---|
3371 | pIter(q); |
---|
3372 | } |
---|
3373 | *p = q; |
---|
3374 | pNext(qq) = NULL; |
---|
3375 | } |
---|
3376 | if (q==NULL) return result; |
---|
3377 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
3378 | while (pNext(q)!=NULL) |
---|
3379 | { |
---|
3380 | if (__p_GetComp(pNext(q),r)==k) |
---|
3381 | { |
---|
3382 | if (result==NULL) |
---|
3383 | { |
---|
3384 | result = pNext(q); |
---|
3385 | qq = result; |
---|
3386 | } |
---|
3387 | else |
---|
3388 | { |
---|
3389 | pNext(qq) = pNext(q); |
---|
3390 | pIter(qq); |
---|
3391 | } |
---|
3392 | pNext(q) = pNext(pNext(q)); |
---|
3393 | pNext(qq) =NULL; |
---|
3394 | p_SetComp(qq,0,r); |
---|
3395 | p_SetmComp(qq,r); |
---|
3396 | } |
---|
3397 | else |
---|
3398 | { |
---|
3399 | pIter(q); |
---|
3400 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
3401 | } |
---|
3402 | } |
---|
3403 | return result; |
---|
3404 | } |
---|
3405 | |
---|
3406 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
3407 | { |
---|
3408 | poly q = *p,qq=NULL,result = NULL; |
---|
3409 | |
---|
3410 | if (q==NULL) return NULL; |
---|
3411 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
3412 | if (__p_GetComp(q,r)==k) |
---|
3413 | { |
---|
3414 | result = q; |
---|
3415 | do |
---|
3416 | { |
---|
3417 | p_SetComp(q,0,r); |
---|
3418 | if (use_setmcomp) p_SetmComp(q,r); |
---|
3419 | qq = q; |
---|
3420 | pIter(q); |
---|
3421 | } |
---|
3422 | while ((q!=NULL) && (__p_GetComp(q,r)==k)); |
---|
3423 | *p = q; |
---|
3424 | pNext(qq) = NULL; |
---|
3425 | } |
---|
3426 | if (q==NULL) return result; |
---|
3427 | if (__p_GetComp(q,r) > k) |
---|
3428 | { |
---|
3429 | p_SubComp(q,1,r); |
---|
3430 | if (use_setmcomp) p_SetmComp(q,r); |
---|
3431 | } |
---|
3432 | poly pNext_q; |
---|
3433 | while ((pNext_q=pNext(q))!=NULL) |
---|
3434 | { |
---|
3435 | if (__p_GetComp(pNext_q,r)==k) |
---|
3436 | { |
---|
3437 | if (result==NULL) |
---|
3438 | { |
---|
3439 | result = pNext_q; |
---|
3440 | qq = result; |
---|
3441 | } |
---|
3442 | else |
---|
3443 | { |
---|
3444 | pNext(qq) = pNext_q; |
---|
3445 | pIter(qq); |
---|
3446 | } |
---|
3447 | pNext(q) = pNext(pNext_q); |
---|
3448 | pNext(qq) =NULL; |
---|
3449 | p_SetComp(qq,0,r); |
---|
3450 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
3451 | } |
---|
3452 | else |
---|
3453 | { |
---|
3454 | /*pIter(q);*/ q=pNext_q; |
---|
3455 | if (__p_GetComp(q,r) > k) |
---|
3456 | { |
---|
3457 | p_SubComp(q,1,r); |
---|
3458 | if (use_setmcomp) p_SetmComp(q,r); |
---|
3459 | } |
---|
3460 | } |
---|
3461 | } |
---|
3462 | return result; |
---|
3463 | } |
---|
3464 | |
---|
3465 | // Splits *p into two polys: *q which consists of all monoms with |
---|
3466 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
3467 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
3468 | { |
---|
3469 | spolyrec pp, qq; |
---|
3470 | poly p, q, p_prev; |
---|
3471 | int l = 0; |
---|
3472 | |
---|
3473 | #ifndef SING_NDEBUG |
---|
3474 | int lp = pLength(*r_p); |
---|
3475 | #endif |
---|
3476 | |
---|
3477 | pNext(&pp) = *r_p; |
---|
3478 | p = *r_p; |
---|
3479 | p_prev = &pp; |
---|
3480 | q = &qq; |
---|
3481 | |
---|
3482 | while(p != NULL) |
---|
3483 | { |
---|
3484 | while (__p_GetComp(p,r) == comp) |
---|
3485 | { |
---|
3486 | pNext(q) = p; |
---|
3487 | pIter(q); |
---|
3488 | p_SetComp(p, 0,r); |
---|
3489 | p_SetmComp(p,r); |
---|
3490 | pIter(p); |
---|
3491 | l++; |
---|
3492 | if (p == NULL) |
---|
3493 | { |
---|
3494 | pNext(p_prev) = NULL; |
---|
3495 | goto Finish; |
---|
3496 | } |
---|
3497 | } |
---|
3498 | pNext(p_prev) = p; |
---|
3499 | p_prev = p; |
---|
3500 | pIter(p); |
---|
3501 | } |
---|
3502 | |
---|
3503 | Finish: |
---|
3504 | pNext(q) = NULL; |
---|
3505 | *r_p = pNext(&pp); |
---|
3506 | *r_q = pNext(&qq); |
---|
3507 | *lq = l; |
---|
3508 | #ifndef SING_NDEBUG |
---|
3509 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
3510 | #endif |
---|
3511 | p_Test(*r_p,r); |
---|
3512 | p_Test(*r_q,r); |
---|
3513 | } |
---|
3514 | |
---|
3515 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
3516 | { |
---|
3517 | poly q; |
---|
3518 | |
---|
3519 | while ((*p!=NULL) && (__p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
3520 | if (*p==NULL) return; |
---|
3521 | q = *p; |
---|
3522 | if (__p_GetComp(q,r)>k) |
---|
3523 | { |
---|
3524 | p_SubComp(q,1,r); |
---|
3525 | p_SetmComp(q,r); |
---|
3526 | } |
---|
3527 | while (pNext(q)!=NULL) |
---|
3528 | { |
---|
3529 | if (__p_GetComp(pNext(q),r)==k) |
---|
3530 | p_LmDelete(&(pNext(q)),r); |
---|
3531 | else |
---|
3532 | { |
---|
3533 | pIter(q); |
---|
3534 | if (__p_GetComp(q,r)>k) |
---|
3535 | { |
---|
3536 | p_SubComp(q,1,r); |
---|
3537 | p_SetmComp(q,r); |
---|
3538 | } |
---|
3539 | } |
---|
3540 | } |
---|
3541 | } |
---|
3542 | |
---|
3543 | poly p_Vec2Poly(poly v, int k, const ring r) |
---|
3544 | { |
---|
3545 | poly h; |
---|
3546 | poly res=NULL; |
---|
3547 | |
---|
3548 | while (v!=NULL) |
---|
3549 | { |
---|
3550 | if (__p_GetComp(v,r)==k) |
---|
3551 | { |
---|
3552 | h=p_Head(v,r); |
---|
3553 | p_SetComp(h,0,r); |
---|
3554 | pNext(h)=res;res=h; |
---|
3555 | } |
---|
3556 | pIter(v); |
---|
3557 | } |
---|
3558 | if (res!=NULL) res=pReverse(res); |
---|
3559 | return res; |
---|
3560 | } |
---|
3561 | |
---|
3562 | /// vector to already allocated array (len>=p_MaxComp(v,r)) |
---|
3563 | // also used for p_Vec2Polys |
---|
3564 | void p_Vec2Array(poly v, poly *p, int len, const ring r) |
---|
3565 | { |
---|
3566 | poly h; |
---|
3567 | int k; |
---|
3568 | |
---|
3569 | for(int i=len-1;i>=0;i--) p[i]=NULL; |
---|
3570 | while (v!=NULL) |
---|
3571 | { |
---|
3572 | h=p_Head(v,r); |
---|
3573 | k=__p_GetComp(h,r); |
---|
3574 | if (k>len) { Werror("wrong rank:%d, should be %d",len,k); } |
---|
3575 | else |
---|
3576 | { |
---|
3577 | p_SetComp(h,0,r); |
---|
3578 | p_Setm(h,r); |
---|
3579 | pNext(h)=p[k-1];p[k-1]=h; |
---|
3580 | } |
---|
3581 | pIter(v); |
---|
3582 | } |
---|
3583 | for(int i=len-1;i>=0;i--) |
---|
3584 | { |
---|
3585 | if (p[i]!=NULL) p[i]=pReverse(p[i]); |
---|
3586 | } |
---|
3587 | } |
---|
3588 | |
---|
3589 | /*2 |
---|
3590 | * convert a vector to a set of polys, |
---|
3591 | * allocates the polyset, (entries 0..(*len)-1) |
---|
3592 | * the vector will not be changed |
---|
3593 | */ |
---|
3594 | void p_Vec2Polys(poly v, poly* *p, int *len, const ring r) |
---|
3595 | { |
---|
3596 | poly h; |
---|
3597 | int k; |
---|
3598 | |
---|
3599 | *len=p_MaxComp(v,r); |
---|
3600 | if (*len==0) *len=1; |
---|
3601 | *p=(poly*)omAlloc((*len)*sizeof(poly)); |
---|
3602 | p_Vec2Array(v,*p,*len,r); |
---|
3603 | } |
---|
3604 | |
---|
3605 | // |
---|
3606 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
3607 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
3608 | // only uses pFDeg (and not p_Deg, or pTotalDegree, etc) |
---|
3609 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
3610 | { |
---|
3611 | assume(new_FDeg != NULL); |
---|
3612 | r->pFDeg = new_FDeg; |
---|
3613 | |
---|
3614 | if (new_lDeg == NULL) |
---|
3615 | new_lDeg = r->pLDegOrig; |
---|
3616 | |
---|
3617 | r->pLDeg = new_lDeg; |
---|
3618 | } |
---|
3619 | |
---|
3620 | // restores pFDeg and pLDeg: |
---|
3621 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
3622 | { |
---|
3623 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
3624 | r->pFDeg = old_FDeg; |
---|
3625 | r->pLDeg = old_lDeg; |
---|
3626 | } |
---|
3627 | |
---|
3628 | /*-------- several access procedures to monomials -------------------- */ |
---|
3629 | /* |
---|
3630 | * the module weights for std |
---|
3631 | */ |
---|
3632 | STATIC_VAR pFDegProc pOldFDeg; |
---|
3633 | STATIC_VAR pLDegProc pOldLDeg; |
---|
3634 | STATIC_VAR BOOLEAN pOldLexOrder; |
---|
3635 | |
---|
3636 | static long pModDeg(poly p, ring r) |
---|
3637 | { |
---|
3638 | long d=pOldFDeg(p, r); |
---|
3639 | int c=__p_GetComp(p, r); |
---|
3640 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
3641 | return d; |
---|
3642 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
3643 | } |
---|
3644 | |
---|
3645 | void p_SetModDeg(intvec *w, ring r) |
---|
3646 | { |
---|
3647 | if (w!=NULL) |
---|
3648 | { |
---|
3649 | r->pModW = w; |
---|
3650 | pOldFDeg = r->pFDeg; |
---|
3651 | pOldLDeg = r->pLDeg; |
---|
3652 | pOldLexOrder = r->pLexOrder; |
---|
3653 | pSetDegProcs(r,pModDeg); |
---|
3654 | r->pLexOrder = TRUE; |
---|
3655 | } |
---|
3656 | else |
---|
3657 | { |
---|
3658 | r->pModW = NULL; |
---|
3659 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
3660 | r->pLexOrder = pOldLexOrder; |
---|
3661 | } |
---|
3662 | } |
---|
3663 | |
---|
3664 | /*2 |
---|
3665 | * handle memory request for sets of polynomials (ideals) |
---|
3666 | * l is the length of *p, increment is the difference (may be negative) |
---|
3667 | */ |
---|
3668 | void pEnlargeSet(poly* *p, int l, int increment) |
---|
3669 | { |
---|
3670 | poly* h; |
---|
3671 | |
---|
3672 | if (*p==NULL) |
---|
3673 | { |
---|
3674 | if (increment==0) return; |
---|
3675 | h=(poly*)omAlloc0(increment*sizeof(poly)); |
---|
3676 | } |
---|
3677 | else |
---|
3678 | { |
---|
3679 | h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
3680 | if (increment>0) |
---|
3681 | { |
---|
3682 | memset(&(h[l]),0,increment*sizeof(poly)); |
---|
3683 | } |
---|
3684 | } |
---|
3685 | *p=h; |
---|
3686 | } |
---|
3687 | |
---|
3688 | /*2 |
---|
3689 | *divides p1 by its leading coefficient |
---|
3690 | */ |
---|
3691 | void p_Norm(poly p1, const ring r) |
---|
3692 | { |
---|
3693 | if (rField_is_Ring(r)) |
---|
3694 | { |
---|
3695 | if (!n_IsUnit(pGetCoeff(p1), r->cf)) return; |
---|
3696 | // Werror("p_Norm not possible in the case of coefficient rings."); |
---|
3697 | } |
---|
3698 | else if (p1!=NULL) |
---|
3699 | { |
---|
3700 | if (pNext(p1)==NULL) |
---|
3701 | { |
---|
3702 | p_SetCoeff(p1,n_Init(1,r->cf),r); |
---|
3703 | return; |
---|
3704 | } |
---|
3705 | poly h; |
---|
3706 | if (!n_IsOne(pGetCoeff(p1),r->cf)) |
---|
3707 | { |
---|
3708 | number k, c; |
---|
3709 | n_Normalize(pGetCoeff(p1),r->cf); |
---|
3710 | k = pGetCoeff(p1); |
---|
3711 | c = n_Init(1,r->cf); |
---|
3712 | pSetCoeff0(p1,c); |
---|
3713 | h = pNext(p1); |
---|
3714 | while (h!=NULL) |
---|
3715 | { |
---|
3716 | c=n_Div(pGetCoeff(h),k,r->cf); |
---|
3717 | // no need to normalize: Z/p, R |
---|
3718 | // normalize already in nDiv: Q_a, Z/p_a |
---|
3719 | // remains: Q |
---|
3720 | if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) n_Normalize(c,r->cf); |
---|
3721 | p_SetCoeff(h,c,r); |
---|
3722 | pIter(h); |
---|
3723 | } |
---|
3724 | n_Delete(&k,r->cf); |
---|
3725 | } |
---|
3726 | else |
---|
3727 | { |
---|
3728 | //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE |
---|
3729 | { |
---|
3730 | h = pNext(p1); |
---|
3731 | while (h!=NULL) |
---|
3732 | { |
---|
3733 | n_Normalize(pGetCoeff(h),r->cf); |
---|
3734 | pIter(h); |
---|
3735 | } |
---|
3736 | } |
---|
3737 | } |
---|
3738 | } |
---|
3739 | } |
---|
3740 | |
---|
3741 | /*2 |
---|
3742 | *normalize all coefficients |
---|
3743 | */ |
---|
3744 | void p_Normalize(poly p,const ring r) |
---|
3745 | { |
---|
3746 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
3747 | while (p!=NULL) |
---|
3748 | { |
---|
3749 | // no test befor n_Normalize: n_Normalize should fix problems |
---|
3750 | n_Normalize(pGetCoeff(p),r->cf); |
---|
3751 | pIter(p); |
---|
3752 | } |
---|
3753 | } |
---|
3754 | |
---|
3755 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
3756 | // Poly with Exp(n) != 0 is reversed |
---|
3757 | static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r) |
---|
3758 | { |
---|
3759 | if (p == NULL) |
---|
3760 | { |
---|
3761 | *non_zero = NULL; |
---|
3762 | *zero = NULL; |
---|
3763 | return; |
---|
3764 | } |
---|
3765 | spolyrec sz; |
---|
3766 | poly z, n_z, next; |
---|
3767 | z = &sz; |
---|
3768 | n_z = NULL; |
---|
3769 | |
---|
3770 | while(p != NULL) |
---|
3771 | { |
---|
3772 | next = pNext(p); |
---|
3773 | if (p_GetExp(p, n,r) == 0) |
---|
3774 | { |
---|
3775 | pNext(z) = p; |
---|
3776 | pIter(z); |
---|
3777 | } |
---|
3778 | else |
---|
3779 | { |
---|
3780 | pNext(p) = n_z; |
---|
3781 | n_z = p; |
---|
3782 | } |
---|
3783 | p = next; |
---|
3784 | } |
---|
3785 | pNext(z) = NULL; |
---|
3786 | *zero = pNext(&sz); |
---|
3787 | *non_zero = n_z; |
---|
3788 | } |
---|
3789 | /*3 |
---|
3790 | * substitute the n-th variable by 1 in p |
---|
3791 | * destroy p |
---|
3792 | */ |
---|
3793 | static poly p_Subst1 (poly p,int n, const ring r) |
---|
3794 | { |
---|
3795 | poly qq=NULL, result = NULL; |
---|
3796 | poly zero=NULL, non_zero=NULL; |
---|
3797 | |
---|
3798 | // reverse, so that add is likely to be linear |
---|
3799 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
3800 | |
---|
3801 | while (non_zero != NULL) |
---|
3802 | { |
---|
3803 | assume(p_GetExp(non_zero, n,r) != 0); |
---|
3804 | qq = non_zero; |
---|
3805 | pIter(non_zero); |
---|
3806 | qq->next = NULL; |
---|
3807 | p_SetExp(qq,n,0,r); |
---|
3808 | p_Setm(qq,r); |
---|
3809 | result = p_Add_q(result,qq,r); |
---|
3810 | } |
---|
3811 | p = p_Add_q(result, zero,r); |
---|
3812 | p_Test(p,r); |
---|
3813 | return p; |
---|
3814 | } |
---|
3815 | |
---|
3816 | /*3 |
---|
3817 | * substitute the n-th variable by number e in p |
---|
3818 | * destroy p |
---|
3819 | */ |
---|
3820 | static poly p_Subst2 (poly p,int n, number e, const ring r) |
---|
3821 | { |
---|
3822 | assume( ! n_IsZero(e,r->cf) ); |
---|
3823 | poly qq,result = NULL; |
---|
3824 | number nn, nm; |
---|
3825 | poly zero, non_zero; |
---|
3826 | |
---|
3827 | // reverse, so that add is likely to be linear |
---|
3828 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
3829 | |
---|
3830 | while (non_zero != NULL) |
---|
3831 | { |
---|
3832 | assume(p_GetExp(non_zero, n, r) != 0); |
---|
3833 | qq = non_zero; |
---|
3834 | pIter(non_zero); |
---|
3835 | qq->next = NULL; |
---|
3836 | n_Power(e, p_GetExp(qq, n, r), &nn,r->cf); |
---|
3837 | nm = n_Mult(nn, pGetCoeff(qq),r->cf); |
---|
3838 | #ifdef HAVE_RINGS |
---|
3839 | if (n_IsZero(nm,r->cf)) |
---|
3840 | { |
---|
3841 | p_LmFree(&qq,r); |
---|
3842 | n_Delete(&nm,r->cf); |
---|
3843 | } |
---|
3844 | else |
---|
3845 | #endif |
---|
3846 | { |
---|
3847 | p_SetCoeff(qq, nm,r); |
---|
3848 | p_SetExp(qq, n, 0,r); |
---|
3849 | p_Setm(qq,r); |
---|
3850 | result = p_Add_q(result,qq,r); |
---|
3851 | } |
---|
3852 | n_Delete(&nn,r->cf); |
---|
3853 | } |
---|
3854 | p = p_Add_q(result, zero,r); |
---|
3855 | p_Test(p,r); |
---|
3856 | return p; |
---|
3857 | } |
---|
3858 | |
---|
3859 | |
---|
3860 | /* delete monoms whose n-th exponent is different from zero */ |
---|
3861 | static poly p_Subst0(poly p, int n, const ring r) |
---|
3862 | { |
---|
3863 | spolyrec res; |
---|
3864 | poly h = &res; |
---|
3865 | pNext(h) = p; |
---|
3866 | |
---|
3867 | while (pNext(h)!=NULL) |
---|
3868 | { |
---|
3869 | if (p_GetExp(pNext(h),n,r)!=0) |
---|
3870 | { |
---|
3871 | p_LmDelete(&pNext(h),r); |
---|
3872 | } |
---|
3873 | else |
---|
3874 | { |
---|
3875 | pIter(h); |
---|
3876 | } |
---|
3877 | } |
---|
3878 | p_Test(pNext(&res),r); |
---|
3879 | return pNext(&res); |
---|
3880 | } |
---|
3881 | |
---|
3882 | /*2 |
---|
3883 | * substitute the n-th variable by e in p |
---|
3884 | * destroy p |
---|
3885 | */ |
---|
3886 | poly p_Subst(poly p, int n, poly e, const ring r) |
---|
3887 | { |
---|
3888 | #ifdef HAVE_SHIFTBBA |
---|
3889 | // also don't even use p_Subst0 for Letterplace |
---|
3890 | if (rIsLPRing(r)) |
---|
3891 | { |
---|
3892 | poly subst = p_LPSubst(p, n, e, r); |
---|
3893 | p_Delete(&p, r); |
---|
3894 | return subst; |
---|
3895 | } |
---|
3896 | #endif |
---|
3897 | |
---|
3898 | if (e == NULL) return p_Subst0(p, n,r); |
---|
3899 | |
---|
3900 | if (p_IsConstant(e,r)) |
---|
3901 | { |
---|
3902 | if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r); |
---|
3903 | else return p_Subst2(p, n, pGetCoeff(e),r); |
---|
3904 | } |
---|
3905 | |
---|
3906 | #ifdef HAVE_PLURAL |
---|
3907 | if (rIsPluralRing(r)) |
---|
3908 | { |
---|
3909 | return nc_pSubst(p,n,e,r); |
---|
3910 | } |
---|
3911 | #endif |
---|
3912 | |
---|
3913 | int exponent,i; |
---|
3914 | poly h, res, m; |
---|
3915 | int *me,*ee; |
---|
3916 | number nu,nu1; |
---|
3917 | |
---|
3918 | me=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
3919 | ee=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
3920 | if (e!=NULL) p_GetExpV(e,ee,r); |
---|
3921 | res=NULL; |
---|
3922 | h=p; |
---|
3923 | while (h!=NULL) |
---|
3924 | { |
---|
3925 | if ((e!=NULL) || (p_GetExp(h,n,r)==0)) |
---|
3926 | { |
---|
3927 | m=p_Head(h,r); |
---|
3928 | p_GetExpV(m,me,r); |
---|
3929 | exponent=me[n]; |
---|
3930 | me[n]=0; |
---|
3931 | for(i=rVar(r);i>0;i--) |
---|
3932 | me[i]+=exponent*ee[i]; |
---|
3933 | p_SetExpV(m,me,r); |
---|
3934 | if (e!=NULL) |
---|
3935 | { |
---|
3936 | n_Power(pGetCoeff(e),exponent,&nu,r->cf); |
---|
3937 | nu1=n_Mult(pGetCoeff(m),nu,r->cf); |
---|
3938 | n_Delete(&nu,r->cf); |
---|
3939 | p_SetCoeff(m,nu1,r); |
---|
3940 | } |
---|
3941 | res=p_Add_q(res,m,r); |
---|
3942 | } |
---|
3943 | p_LmDelete(&h,r); |
---|
3944 | } |
---|
3945 | omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int)); |
---|
3946 | omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int)); |
---|
3947 | return res; |
---|
3948 | } |
---|
3949 | |
---|
3950 | /*2 |
---|
3951 | * returns a re-ordered convertion of a number as a polynomial, |
---|
3952 | * with permutation of parameters |
---|
3953 | * NOTE: this only works for Frank's alg. & trans. fields |
---|
3954 | */ |
---|
3955 | poly n_PermNumber(const number z, const int *par_perm, const int , const ring src, const ring dst) |
---|
3956 | { |
---|
3957 | #if 0 |
---|
3958 | PrintS("\nSource Ring: \n"); |
---|
3959 | rWrite(src); |
---|
3960 | |
---|
3961 | if(0) |
---|
3962 | { |
---|
3963 | number zz = n_Copy(z, src->cf); |
---|
3964 | PrintS("z: "); n_Write(zz, src); |
---|
3965 | n_Delete(&zz, src->cf); |
---|
3966 | } |
---|
3967 | |
---|
3968 | PrintS("\nDestination Ring: \n"); |
---|
3969 | rWrite(dst); |
---|
3970 | |
---|
3971 | /*Print("\nOldPar: %d\n", OldPar); |
---|
3972 | for( int i = 1; i <= OldPar; i++ ) |
---|
3973 | { |
---|
3974 | Print("par(%d) -> par/var (%d)\n", i, par_perm[i-1]); |
---|
3975 | }*/ |
---|
3976 | #endif |
---|
3977 | if( z == NULL ) |
---|
3978 | return NULL; |
---|
3979 | |
---|
3980 | const coeffs srcCf = src->cf; |
---|
3981 | assume( srcCf != NULL ); |
---|
3982 | |
---|
3983 | assume( !nCoeff_is_GF(srcCf) ); |
---|
3984 | assume( src->cf->extRing!=NULL ); |
---|
3985 | |
---|
3986 | poly zz = NULL; |
---|
3987 | |
---|
3988 | const ring srcExtRing = srcCf->extRing; |
---|
3989 | assume( srcExtRing != NULL ); |
---|
3990 | |
---|
3991 | const coeffs dstCf = dst->cf; |
---|
3992 | assume( dstCf != NULL ); |
---|
3993 | |
---|
3994 | if( nCoeff_is_algExt(srcCf) ) // nCoeff_is_GF(srcCf)? |
---|
3995 | { |
---|
3996 | zz = (poly) z; |
---|
3997 | if( zz == NULL ) return NULL; |
---|
3998 | } |
---|
3999 | else if (nCoeff_is_transExt(srcCf)) |
---|
4000 | { |
---|
4001 | assume( !IS0(z) ); |
---|
4002 | |
---|
4003 | zz = NUM((fraction)z); |
---|
4004 | p_Test (zz, srcExtRing); |
---|
4005 | |
---|
4006 | if( zz == NULL ) return NULL; |
---|
4007 | if( !DENIS1((fraction)z) ) |
---|
4008 | { |
---|
4009 | if (!p_IsConstant(DEN((fraction)z),srcExtRing)) |
---|
4010 | WarnS("Not defined: Cannot map a rational fraction and make a polynomial out of it! Ignoring the denominator."); |
---|
4011 | } |
---|
4012 | } |
---|
4013 | else |
---|
4014 | { |
---|
4015 | assume (FALSE); |
---|
4016 | WerrorS("Number permutation is not implemented for this data yet!"); |
---|
4017 | return NULL; |
---|
4018 | } |
---|
4019 | |
---|
4020 | assume( zz != NULL ); |
---|
4021 | p_Test (zz, srcExtRing); |
---|
4022 | |
---|
4023 | nMapFunc nMap = n_SetMap(srcExtRing->cf, dstCf); |
---|
4024 | |
---|
4025 | assume( nMap != NULL ); |
---|
4026 | |
---|
4027 | poly qq; |
---|
4028 | if ((par_perm == NULL) && (rPar(dst) != 0 && rVar (srcExtRing) > 0)) |
---|
4029 | { |
---|
4030 | int* perm; |
---|
4031 | perm=(int *)omAlloc0((rVar(srcExtRing)+1)*sizeof(int)); |
---|
4032 | for(int i=si_min(rVar(srcExtRing),rPar(dst));i>0;i--) |
---|
4033 | perm[i]=-i; |
---|
4034 | qq = p_PermPoly(zz, perm, srcExtRing, dst, nMap, NULL, rVar(srcExtRing)-1); |
---|
4035 | omFreeSize ((ADDRESS)perm, (rVar(srcExtRing)+1)*sizeof(int)); |
---|
4036 | } |
---|
4037 | else |
---|
4038 | qq = p_PermPoly(zz, par_perm-1, srcExtRing, dst, nMap, NULL, rVar (srcExtRing)-1); |
---|
4039 | |
---|
4040 | if(nCoeff_is_transExt(srcCf) |
---|
4041 | && (!DENIS1((fraction)z)) |
---|
4042 | && p_IsConstant(DEN((fraction)z),srcExtRing)) |
---|
4043 | { |
---|
4044 | number n=nMap(pGetCoeff(DEN((fraction)z)),srcExtRing->cf, dstCf); |
---|
4045 | qq=p_Div_nn(qq,n,dst); |
---|
4046 | n_Delete(&n,dstCf); |
---|
4047 | p_Normalize(qq,dst); |
---|
4048 | } |
---|
4049 | p_Test (qq, dst); |
---|
4050 | |
---|
4051 | return qq; |
---|
4052 | } |
---|
4053 | |
---|
4054 | |
---|
4055 | /*2 |
---|
4056 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
4057 | */ |
---|
4058 | poly p_PermPoly (poly p, const int * perm, const ring oldRing, const ring dst, |
---|
4059 | nMapFunc nMap, const int *par_perm, int OldPar, BOOLEAN use_mult) |
---|
4060 | { |
---|
4061 | #if 0 |
---|
4062 | p_Test(p, oldRing); |
---|
4063 | PrintS("p_PermPoly::p: "); p_Write(p, oldRing, oldRing); |
---|
4064 | #endif |
---|
4065 | const int OldpVariables = rVar(oldRing); |
---|
4066 | poly result = NULL; |
---|
4067 | poly result_last = NULL; |
---|
4068 | poly aq = NULL; /* the map coefficient */ |
---|
4069 | poly qq; /* the mapped monomial */ |
---|
4070 | assume(dst != NULL); |
---|
4071 | assume(dst->cf != NULL); |
---|
4072 | #ifdef HAVE_PLURAL |
---|
4073 | poly tmp_mm=p_One(dst); |
---|
4074 | #endif |
---|
4075 | while (p != NULL) |
---|
4076 | { |
---|
4077 | // map the coefficient |
---|
4078 | if ( ((OldPar == 0) || (par_perm == NULL) || rField_is_GF(oldRing) || (nMap==ndCopyMap)) |
---|
4079 | && (nMap != NULL) ) |
---|
4080 | { |
---|
4081 | qq = p_Init(dst); |
---|
4082 | assume( nMap != NULL ); |
---|
4083 | number n = nMap(p_GetCoeff(p, oldRing), oldRing->cf, dst->cf); |
---|
4084 | n_Test (n,dst->cf); |
---|
4085 | if ( nCoeff_is_algExt(dst->cf) ) |
---|
4086 | n_Normalize(n, dst->cf); |
---|
4087 | p_GetCoeff(qq, dst) = n;// Note: n can be a ZERO!!! |
---|
4088 | } |
---|
4089 | else |
---|
4090 | { |
---|
4091 | qq = p_One(dst); |
---|
4092 | // aq = naPermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing); // no dst??? |
---|
4093 | // poly n_PermNumber(const number z, const int *par_perm, const int P, const ring src, const ring dst) |
---|
4094 | aq = n_PermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing, dst); |
---|
4095 | p_Test(aq, dst); |
---|
4096 | if ( nCoeff_is_algExt(dst->cf) ) |
---|
4097 | p_Normalize(aq,dst); |
---|
4098 | if (aq == NULL) |
---|
4099 | p_SetCoeff(qq, n_Init(0, dst->cf),dst); // Very dirty trick!!! |
---|
4100 | p_Test(aq, dst); |
---|
4101 | } |
---|
4102 | if (rRing_has_Comp(dst)) |
---|
4103 | p_SetComp(qq, p_GetComp(p, oldRing), dst); |
---|
4104 | if ( n_IsZero(pGetCoeff(qq), dst->cf) ) |
---|
4105 | { |
---|
4106 | p_LmDelete(&qq,dst); |
---|
4107 | qq = NULL; |
---|
4108 | } |
---|
4109 | else |
---|
4110 | { |
---|
4111 | // map pars: |
---|
4112 | int mapped_to_par = 0; |
---|
4113 | for(int i = 1; i <= OldpVariables; i++) |
---|
4114 | { |
---|
4115 | int e = p_GetExp(p, i, oldRing); |
---|
4116 | if (e != 0) |
---|
4117 | { |
---|
4118 | if (perm==NULL) |
---|
4119 | p_SetExp(qq, i, e, dst); |
---|
4120 | else if (perm[i]>0) |
---|
4121 | { |
---|
4122 | #ifdef HAVE_PLURAL |
---|
4123 | if(use_mult) |
---|
4124 | { |
---|
4125 | p_SetExp(tmp_mm,perm[i],e,dst); |
---|
4126 | p_Setm(tmp_mm,dst); |
---|
4127 | qq=p_Mult_mm(qq,tmp_mm,dst); |
---|
4128 | p_SetExp(tmp_mm,perm[i],0,dst); |
---|
4129 | |
---|
4130 | } |
---|
4131 | else |
---|
4132 | #endif |
---|
4133 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
4134 | } |
---|
4135 | else if (perm[i]<0) |
---|
4136 | { |
---|
4137 | number c = p_GetCoeff(qq, dst); |
---|
4138 | if (rField_is_GF(dst)) |
---|
4139 | { |
---|
4140 | assume( dst->cf->extRing == NULL ); |
---|
4141 | number ee = n_Param(1, dst); |
---|
4142 | number eee; |
---|
4143 | n_Power(ee, e, &eee, dst->cf); //nfDelete(ee,dst); |
---|
4144 | ee = n_Mult(c, eee, dst->cf); |
---|
4145 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
4146 | pSetCoeff0(qq,ee); |
---|
4147 | } |
---|
4148 | else if (nCoeff_is_Extension(dst->cf)) |
---|
4149 | { |
---|
4150 | const int par = -perm[i]; |
---|
4151 | assume( par > 0 ); |
---|
4152 | // WarnS("longalg missing 3"); |
---|
4153 | #if 1 |
---|
4154 | const coeffs C = dst->cf; |
---|
4155 | assume( C != NULL ); |
---|
4156 | const ring R = C->extRing; |
---|
4157 | assume( R != NULL ); |
---|
4158 | assume( par <= rVar(R) ); |
---|
4159 | poly pcn; // = (number)c |
---|
4160 | assume( !n_IsZero(c, C) ); |
---|
4161 | if( nCoeff_is_algExt(C) ) |
---|
4162 | pcn = (poly) c; |
---|
4163 | else // nCoeff_is_transExt(C) |
---|
4164 | pcn = NUM((fraction)c); |
---|
4165 | if (pNext(pcn) == NULL) // c->z |
---|
4166 | p_AddExp(pcn, -perm[i], e, R); |
---|
4167 | else /* more difficult: we have really to multiply: */ |
---|
4168 | { |
---|
4169 | poly mmc = p_ISet(1, R); |
---|
4170 | p_SetExp(mmc, -perm[i], e, R); |
---|
4171 | p_Setm(mmc, R); |
---|
4172 | number nnc; |
---|
4173 | // convert back to a number: number nnc = mmc; |
---|
4174 | if( nCoeff_is_algExt(C) ) |
---|
4175 | nnc = (number) mmc; |
---|
4176 | else // nCoeff_is_transExt(C) |
---|
4177 | nnc = ntInit(mmc, C); |
---|
4178 | p_GetCoeff(qq, dst) = n_Mult((number)c, nnc, C); |
---|
4179 | n_Delete((number *)&c, C); |
---|
4180 | n_Delete((number *)&nnc, C); |
---|
4181 | } |
---|
4182 | mapped_to_par=1; |
---|
4183 | #endif |
---|
4184 | } |
---|
4185 | } |
---|
4186 | else |
---|
4187 | { |
---|
4188 | /* this variable maps to 0 !*/ |
---|
4189 | p_LmDelete(&qq, dst); |
---|
4190 | break; |
---|
4191 | } |
---|
4192 | } |
---|
4193 | } |
---|
4194 | if ( mapped_to_par && (qq!= NULL) && nCoeff_is_algExt(dst->cf) ) |
---|
4195 | { |
---|
4196 | number n = p_GetCoeff(qq, dst); |
---|
4197 | n_Normalize(n, dst->cf); |
---|
4198 | p_GetCoeff(qq, dst) = n; |
---|
4199 | } |
---|
4200 | } |
---|
4201 | pIter(p); |
---|
4202 | |
---|
4203 | #if 0 |
---|
4204 | p_Test(aq,dst); |
---|
4205 | PrintS("aq: "); p_Write(aq, dst, dst); |
---|
4206 | #endif |
---|
4207 | |
---|
4208 | |
---|
4209 | #if 1 |
---|
4210 | if (qq!=NULL) |
---|
4211 | { |
---|
4212 | p_Setm(qq,dst); |
---|
4213 | |
---|
4214 | p_Test(aq,dst); |
---|
4215 | p_Test(qq,dst); |
---|
4216 | |
---|
4217 | #if 0 |
---|
4218 | PrintS("qq: "); p_Write(qq, dst, dst); |
---|
4219 | #endif |
---|
4220 | |
---|
4221 | if (aq!=NULL) |
---|
4222 | qq=p_Mult_q(aq,qq,dst); |
---|
4223 | aq = qq; |
---|
4224 | while (pNext(aq) != NULL) pIter(aq); |
---|
4225 | if (result_last==NULL) |
---|
4226 | { |
---|
4227 | result=qq; |
---|
4228 | } |
---|
4229 | else |
---|
4230 | { |
---|
4231 | pNext(result_last)=qq; |
---|
4232 | } |
---|
4233 | result_last=aq; |
---|
4234 | aq = NULL; |
---|
4235 | } |
---|
4236 | else if (aq!=NULL) |
---|
4237 | { |
---|
4238 | p_Delete(&aq,dst); |
---|
4239 | } |
---|
4240 | } |
---|
4241 | result=p_SortAdd(result,dst); |
---|
4242 | #else |
---|
4243 | // if (qq!=NULL) |
---|
4244 | // { |
---|
4245 | // pSetm(qq); |
---|
4246 | // pTest(qq); |
---|
4247 | // pTest(aq); |
---|
4248 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
4249 | // aq = qq; |
---|
4250 | // while (pNext(aq) != NULL) pIter(aq); |
---|
4251 | // pNext(aq) = result; |
---|
4252 | // aq = NULL; |
---|
4253 | // result = qq; |
---|
4254 | // } |
---|
4255 | // else if (aq!=NULL) |
---|
4256 | // { |
---|
4257 | // pDelete(&aq); |
---|
4258 | // } |
---|
4259 | //} |
---|
4260 | //p = result; |
---|
4261 | //result = NULL; |
---|
4262 | //while (p != NULL) |
---|
4263 | //{ |
---|
4264 | // qq = p; |
---|
4265 | // pIter(p); |
---|
4266 | // qq->next = NULL; |
---|
4267 | // result = pAdd(result, qq); |
---|
4268 | //} |
---|
4269 | #endif |
---|
4270 | p_Test(result,dst); |
---|
4271 | #if 0 |
---|
4272 | p_Test(result,dst); |
---|
4273 | PrintS("result: "); p_Write(result,dst,dst); |
---|
4274 | #endif |
---|
4275 | #ifdef HAVE_PLURAL |
---|
4276 | p_LmDelete(&tmp_mm,dst); |
---|
4277 | #endif |
---|
4278 | return result; |
---|
4279 | } |
---|
4280 | /************************************************************** |
---|
4281 | * |
---|
4282 | * Jet |
---|
4283 | * |
---|
4284 | **************************************************************/ |
---|
4285 | |
---|
4286 | poly pp_Jet(poly p, int m, const ring R) |
---|
4287 | { |
---|
4288 | poly r=NULL; |
---|
4289 | poly t=NULL; |
---|
4290 | |
---|
4291 | while (p!=NULL) |
---|
4292 | { |
---|
4293 | if (p_Totaldegree(p,R)<=m) |
---|
4294 | { |
---|
4295 | if (r==NULL) |
---|
4296 | r=p_Head(p,R); |
---|
4297 | else |
---|
4298 | if (t==NULL) |
---|
4299 | { |
---|
4300 | pNext(r)=p_Head(p,R); |
---|
4301 | t=pNext(r); |
---|
4302 | } |
---|
4303 | else |
---|
4304 | { |
---|
4305 | pNext(t)=p_Head(p,R); |
---|
4306 | pIter(t); |
---|
4307 | } |
---|
4308 | } |
---|
4309 | pIter(p); |
---|
4310 | } |
---|
4311 | return r; |
---|
4312 | } |
---|
4313 | |
---|
4314 | poly p_Jet(poly p, int m,const ring R) |
---|
4315 | { |
---|
4316 | while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R); |
---|
4317 | if (p==NULL) return NULL; |
---|
4318 | poly r=p; |
---|
4319 | while (pNext(p)!=NULL) |
---|
4320 | { |
---|
4321 | if (p_Totaldegree(pNext(p),R)>m) |
---|
4322 | { |
---|
4323 | p_LmDelete(&pNext(p),R); |
---|
4324 | } |
---|
4325 | else |
---|
4326 | pIter(p); |
---|
4327 | } |
---|
4328 | return r; |
---|
4329 | } |
---|
4330 | |
---|
4331 | poly pp_JetW(poly p, int m, short *w, const ring R) |
---|
4332 | { |
---|
4333 | poly r=NULL; |
---|
4334 | poly t=NULL; |
---|
4335 | while (p!=NULL) |
---|
4336 | { |
---|
4337 | if (totaldegreeWecart_IV(p,R,w)<=m) |
---|
4338 | { |
---|
4339 | if (r==NULL) |
---|
4340 | r=p_Head(p,R); |
---|
4341 | else |
---|
4342 | if (t==NULL) |
---|
4343 | { |
---|
4344 | pNext(r)=p_Head(p,R); |
---|
4345 | t=pNext(r); |
---|
4346 | } |
---|
4347 | else |
---|
4348 | { |
---|
4349 | pNext(t)=p_Head(p,R); |
---|
4350 | pIter(t); |
---|
4351 | } |
---|
4352 | } |
---|
4353 | pIter(p); |
---|
4354 | } |
---|
4355 | return r; |
---|
4356 | } |
---|
4357 | |
---|
4358 | poly p_JetW(poly p, int m, short *w, const ring R) |
---|
4359 | { |
---|
4360 | while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R); |
---|
4361 | if (p==NULL) return NULL; |
---|
4362 | poly r=p; |
---|
4363 | while (pNext(p)!=NULL) |
---|
4364 | { |
---|
4365 | if (totaldegreeWecart_IV(pNext(p),R,w)>m) |
---|
4366 | { |
---|
4367 | p_LmDelete(&pNext(p),R); |
---|
4368 | } |
---|
4369 | else |
---|
4370 | pIter(p); |
---|
4371 | } |
---|
4372 | return r; |
---|
4373 | } |
---|
4374 | |
---|
4375 | /*************************************************************/ |
---|
4376 | int p_MinDeg(poly p,intvec *w, const ring R) |
---|
4377 | { |
---|
4378 | if(p==NULL) |
---|
4379 | return -1; |
---|
4380 | int d=-1; |
---|
4381 | while(p!=NULL) |
---|
4382 | { |
---|
4383 | int d0=0; |
---|
4384 | for(int j=0;j<rVar(R);j++) |
---|
4385 | if(w==NULL||j>=w->length()) |
---|
4386 | d0+=p_GetExp(p,j+1,R); |
---|
4387 | else |
---|
4388 | d0+=(*w)[j]*p_GetExp(p,j+1,R); |
---|
4389 | if(d0<d||d==-1) |
---|
4390 | d=d0; |
---|
4391 | pIter(p); |
---|
4392 | } |
---|
4393 | return d; |
---|
4394 | } |
---|
4395 | |
---|
4396 | /***************************************************************/ |
---|
4397 | static poly p_Invers(int n,poly u,intvec *w, const ring R) |
---|
4398 | { |
---|
4399 | if(n<0) |
---|
4400 | return NULL; |
---|
4401 | number u0=n_Invers(pGetCoeff(u),R->cf); |
---|
4402 | poly v=p_NSet(u0,R); |
---|
4403 | if(n==0) |
---|
4404 | return v; |
---|
4405 | short *ww=iv2array(w,R); |
---|
4406 | poly u1=p_JetW(p_Sub(p_One(R),__p_Mult_nn(u,u0,R),R),n,ww,R); |
---|
4407 | if(u1==NULL) |
---|
4408 | { |
---|
4409 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
4410 | return v; |
---|
4411 | } |
---|
4412 | poly v1=__p_Mult_nn(p_Copy(u1,R),u0,R); |
---|
4413 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
4414 | for(int i=n/p_MinDeg(u1,w,R);i>1;i--) |
---|
4415 | { |
---|
4416 | v1=p_JetW(p_Mult_q(v1,p_Copy(u1,R),R),n,ww,R); |
---|
4417 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
4418 | } |
---|
4419 | p_Delete(&u1,R); |
---|
4420 | p_Delete(&v1,R); |
---|
4421 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
4422 | return v; |
---|
4423 | } |
---|
4424 | |
---|
4425 | |
---|
4426 | poly p_Series(int n,poly p,poly u, intvec *w, const ring R) |
---|
4427 | { |
---|
4428 | short *ww=iv2array(w,R); |
---|
4429 | if(p!=NULL) |
---|
4430 | { |
---|
4431 | if(u==NULL) |
---|
4432 | p=p_JetW(p,n,ww,R); |
---|
4433 | else |
---|
4434 | p=p_JetW(p_Mult_q(p,p_Invers(n-p_MinDeg(p,w,R),u,w,R),R),n,ww,R); |
---|
4435 | } |
---|
4436 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
4437 | return p; |
---|
4438 | } |
---|
4439 | |
---|
4440 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r) |
---|
4441 | { |
---|
4442 | while ((p1 != NULL) && (p2 != NULL)) |
---|
4443 | { |
---|
4444 | if (! p_LmEqual(p1, p2,r)) |
---|
4445 | return FALSE; |
---|
4446 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r->cf )) |
---|
4447 | return FALSE; |
---|
4448 | pIter(p1); |
---|
4449 | pIter(p2); |
---|
4450 | } |
---|
4451 | return (p1==p2); |
---|
4452 | } |
---|
4453 | |
---|
4454 | static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r1, const ring r2) |
---|
4455 | { |
---|
4456 | assume( r1 == r2 || rSamePolyRep(r1, r2) ); |
---|
4457 | |
---|
4458 | p_LmCheckPolyRing1(p1, r1); |
---|
4459 | p_LmCheckPolyRing1(p2, r2); |
---|
4460 | |
---|
4461 | int i = r1->ExpL_Size; |
---|
4462 | |
---|
4463 | assume( r1->ExpL_Size == r2->ExpL_Size ); |
---|
4464 | |
---|
4465 | unsigned long *ep = p1->exp; |
---|
4466 | unsigned long *eq = p2->exp; |
---|
4467 | |
---|
4468 | do |
---|
4469 | { |
---|
4470 | i--; |
---|
4471 | if (ep[i] != eq[i]) return FALSE; |
---|
4472 | } |
---|
4473 | while (i); |
---|
4474 | |
---|
4475 | return TRUE; |
---|
4476 | } |
---|
4477 | |
---|
4478 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r1, const ring r2) |
---|
4479 | { |
---|
4480 | assume( r1 == r2 || rSamePolyRep(r1, r2) ); // will be used in rEqual! |
---|
4481 | assume( r1->cf == r2->cf ); |
---|
4482 | |
---|
4483 | while ((p1 != NULL) && (p2 != NULL)) |
---|
4484 | { |
---|
4485 | // returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !! |
---|
4486 | // #define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r) |
---|
4487 | |
---|
4488 | if (! p_ExpVectorEqual(p1, p2, r1, r2)) |
---|
4489 | return FALSE; |
---|
4490 | |
---|
4491 | if (! n_Equal(p_GetCoeff(p1,r1), p_GetCoeff(p2,r2), r1->cf )) |
---|
4492 | return FALSE; |
---|
4493 | |
---|
4494 | pIter(p1); |
---|
4495 | pIter(p2); |
---|
4496 | } |
---|
4497 | return (p1==p2); |
---|
4498 | } |
---|
4499 | |
---|
4500 | /*2 |
---|
4501 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
4502 | *assume p1 != NULL and p2 != NULL |
---|
4503 | */ |
---|
4504 | BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r) |
---|
4505 | { |
---|
4506 | number n,nn; |
---|
4507 | pAssume(p1 != NULL && p2 != NULL); |
---|
4508 | |
---|
4509 | if (!p_LmEqual(p1,p2,r)) //compare leading mons |
---|
4510 | return FALSE; |
---|
4511 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
---|
4512 | return FALSE; |
---|
4513 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
---|
4514 | return FALSE; |
---|
4515 | if (pLength(p1) != pLength(p2)) |
---|
4516 | return FALSE; |
---|
4517 | #ifdef HAVE_RINGS |
---|
4518 | if (rField_is_Ring(r)) |
---|
4519 | { |
---|
4520 | if (!n_DivBy(pGetCoeff(p1), pGetCoeff(p2), r->cf)) return FALSE; |
---|
4521 | } |
---|
4522 | #endif |
---|
4523 | n=n_Div(pGetCoeff(p1),pGetCoeff(p2),r->cf); |
---|
4524 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
4525 | { |
---|
4526 | if ( ! p_LmEqual(p1, p2,r)) |
---|
4527 | { |
---|
4528 | n_Delete(&n, r->cf); |
---|
4529 | return FALSE; |
---|
4530 | } |
---|
4531 | if (!n_Equal(pGetCoeff(p1), nn = n_Mult(pGetCoeff(p2),n, r->cf), r->cf)) |
---|
4532 | { |
---|
4533 | n_Delete(&n, r->cf); |
---|
4534 | n_Delete(&nn, r->cf); |
---|
4535 | return FALSE; |
---|
4536 | } |
---|
4537 | n_Delete(&nn, r->cf); |
---|
4538 | pIter(p1); |
---|
4539 | pIter(p2); |
---|
4540 | } |
---|
4541 | n_Delete(&n, r->cf); |
---|
4542 | return TRUE; |
---|
4543 | } |
---|
4544 | |
---|
4545 | /*2 |
---|
4546 | * returns the length of a (numbers of monomials) |
---|
4547 | * respect syzComp |
---|
4548 | */ |
---|
4549 | poly p_Last(const poly p, int &l, const ring r) |
---|
4550 | { |
---|
4551 | if (p == NULL) |
---|
4552 | { |
---|
4553 | l = 0; |
---|
4554 | return NULL; |
---|
4555 | } |
---|
4556 | l = 1; |
---|
4557 | poly a = p; |
---|
4558 | if (! rIsSyzIndexRing(r)) |
---|
4559 | { |
---|
4560 | poly next = pNext(a); |
---|
4561 | while (next!=NULL) |
---|
4562 | { |
---|
4563 | a = next; |
---|
4564 | next = pNext(a); |
---|
4565 | l++; |
---|
4566 | } |
---|
4567 | } |
---|
4568 | else |
---|
4569 | { |
---|
4570 | int curr_limit = rGetCurrSyzLimit(r); |
---|
4571 | poly pp = a; |
---|
4572 | while ((a=pNext(a))!=NULL) |
---|
4573 | { |
---|
4574 | if (__p_GetComp(a,r)<=curr_limit/*syzComp*/) |
---|
4575 | l++; |
---|
4576 | else break; |
---|
4577 | pp = a; |
---|
4578 | } |
---|
4579 | a=pp; |
---|
4580 | } |
---|
4581 | return a; |
---|
4582 | } |
---|
4583 | |
---|
4584 | int p_Var(poly m,const ring r) |
---|
4585 | { |
---|
4586 | if (m==NULL) return 0; |
---|
4587 | if (pNext(m)!=NULL) return 0; |
---|
4588 | int i,e=0; |
---|
4589 | for (i=rVar(r); i>0; i--) |
---|
4590 | { |
---|
4591 | int exp=p_GetExp(m,i,r); |
---|
4592 | if (exp==1) |
---|
4593 | { |
---|
4594 | if (e==0) e=i; |
---|
4595 | else return 0; |
---|
4596 | } |
---|
4597 | else if (exp!=0) |
---|
4598 | { |
---|
4599 | return 0; |
---|
4600 | } |
---|
4601 | } |
---|
4602 | return e; |
---|
4603 | } |
---|
4604 | |
---|
4605 | /*2 |
---|
4606 | *the minimal index of used variables - 1 |
---|
4607 | */ |
---|
4608 | int p_LowVar (poly p, const ring r) |
---|
4609 | { |
---|
4610 | int k,l,lex; |
---|
4611 | |
---|
4612 | if (p == NULL) return -1; |
---|
4613 | |
---|
4614 | k = 32000;/*a very large dummy value*/ |
---|
4615 | while (p != NULL) |
---|
4616 | { |
---|
4617 | l = 1; |
---|
4618 | lex = p_GetExp(p,l,r); |
---|
4619 | while ((l < (rVar(r))) && (lex == 0)) |
---|
4620 | { |
---|
4621 | l++; |
---|
4622 | lex = p_GetExp(p,l,r); |
---|
4623 | } |
---|
4624 | l--; |
---|
4625 | if (l < k) k = l; |
---|
4626 | pIter(p); |
---|
4627 | } |
---|
4628 | return k; |
---|
4629 | } |
---|
4630 | |
---|
4631 | /*2 |
---|
4632 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
4633 | */ |
---|
4634 | void p_Shift (poly * p,int i, const ring r) |
---|
4635 | { |
---|
4636 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
4637 | int j = p_MaxComp(*p,r),k = p_MinComp(*p,r); |
---|
4638 | |
---|
4639 | if (j+i < 0) return ; |
---|
4640 | BOOLEAN toPoly= ((j == -i) && (j == k)); |
---|
4641 | while (qp1 != NULL) |
---|
4642 | { |
---|
4643 | if (toPoly || (__p_GetComp(qp1,r)+i > 0)) |
---|
4644 | { |
---|
4645 | p_AddComp(qp1,i,r); |
---|
4646 | p_SetmComp(qp1,r); |
---|
4647 | qp2 = qp1; |
---|
4648 | pIter(qp1); |
---|
4649 | } |
---|
4650 | else |
---|
4651 | { |
---|
4652 | if (qp2 == *p) |
---|
4653 | { |
---|
4654 | pIter(*p); |
---|
4655 | p_LmDelete(&qp2,r); |
---|
4656 | qp2 = *p; |
---|
4657 | qp1 = *p; |
---|
4658 | } |
---|
4659 | else |
---|
4660 | { |
---|
4661 | qp2->next = qp1->next; |
---|
4662 | if (qp1!=NULL) p_LmDelete(&qp1,r); |
---|
4663 | qp1 = qp2->next; |
---|
4664 | } |
---|
4665 | } |
---|
4666 | } |
---|
4667 | } |
---|
4668 | |
---|
4669 | /*************************************************************** |
---|
4670 | * |
---|
4671 | * Storage Managament Routines |
---|
4672 | * |
---|
4673 | ***************************************************************/ |
---|
4674 | |
---|
4675 | |
---|
4676 | static inline unsigned long GetBitFields(const long e, |
---|
4677 | const unsigned int s, const unsigned int n) |
---|
4678 | { |
---|
4679 | #define Sy_bit_L(x) (((unsigned long)1L)<<(x)) |
---|
4680 | unsigned int i = 0; |
---|
4681 | unsigned long ev = 0L; |
---|
4682 | assume(n > 0 && s < BIT_SIZEOF_LONG); |
---|
4683 | do |
---|
4684 | { |
---|
4685 | assume(s+i < BIT_SIZEOF_LONG); |
---|
4686 | if (e > (long) i) ev |= Sy_bit_L(s+i); |
---|
4687 | else break; |
---|
4688 | i++; |
---|
4689 | } |
---|
4690 | while (i < n); |
---|
4691 | return ev; |
---|
4692 | } |
---|
4693 | |
---|
4694 | // Short Exponent Vectors are used for fast divisibility tests |
---|
4695 | // ShortExpVectors "squeeze" an exponent vector into one word as follows: |
---|
4696 | // Let n = BIT_SIZEOF_LONG / pVariables. |
---|
4697 | // If n == 0 (i.e. pVariables > BIT_SIZE_OF_LONG), let m == the number |
---|
4698 | // of non-zero exponents. If (m>BIT_SIZEOF_LONG), then sev = ~0, else |
---|
4699 | // first m bits of sev are set to 1. |
---|
4700 | // Otherwise (i.e. pVariables <= BIT_SIZE_OF_LONG) |
---|
4701 | // represented by a bit-field of length n (resp. n+1 for some |
---|
4702 | // exponents). If the value of an exponent is greater or equal to n, then |
---|
4703 | // all of its respective n bits are set to 1. If the value of an exponent |
---|
4704 | // is smaller than n, say m, then only the first m bits of the respective |
---|
4705 | // n bits are set to 1, the others are set to 0. |
---|
4706 | // This way, we have: |
---|
4707 | // exp1 / exp2 ==> (ev1 & ~ev2) == 0, i.e., |
---|
4708 | // if (ev1 & ~ev2) then exp1 does not divide exp2 |
---|
4709 | unsigned long p_GetShortExpVector(const poly p, const ring r) |
---|
4710 | { |
---|
4711 | assume(p != NULL); |
---|
4712 | unsigned long ev = 0; // short exponent vector |
---|
4713 | unsigned int n = BIT_SIZEOF_LONG / r->N; // number of bits per exp |
---|
4714 | unsigned int m1; // highest bit which is filled with (n+1) |
---|
4715 | int i=0,j=1; |
---|
4716 | |
---|
4717 | if (n == 0) |
---|
4718 | { |
---|
4719 | if (r->N <2*BIT_SIZEOF_LONG) |
---|
4720 | { |
---|
4721 | n=1; |
---|
4722 | m1=0; |
---|
4723 | } |
---|
4724 | else |
---|
4725 | { |
---|
4726 | for (; j<=r->N; j++) |
---|
4727 | { |
---|
4728 | if (p_GetExp(p,j,r) > 0) i++; |
---|
4729 | if (i == BIT_SIZEOF_LONG) break; |
---|
4730 | } |
---|
4731 | if (i>0) |
---|
4732 | ev = ~(0UL) >> (BIT_SIZEOF_LONG - i); |
---|
4733 | return ev; |
---|
4734 | } |
---|
4735 | } |
---|
4736 | else |
---|
4737 | { |
---|
4738 | m1 = (n+1)*(BIT_SIZEOF_LONG - n*r->N); |
---|
4739 | } |
---|
4740 | |
---|
4741 | n++; |
---|
4742 | while (i<m1) |
---|
4743 | { |
---|
4744 | ev |= GetBitFields(p_GetExp(p, j,r), i, n); |
---|
4745 | i += n; |
---|
4746 | j++; |
---|
4747 | } |
---|
4748 | |
---|
4749 | n--; |
---|
4750 | while (i<BIT_SIZEOF_LONG) |
---|
4751 | { |
---|
4752 | ev |= GetBitFields(p_GetExp(p, j,r), i, n); |
---|
4753 | i += n; |
---|
4754 | j++; |
---|
4755 | } |
---|
4756 | return ev; |
---|
4757 | } |
---|
4758 | |
---|
4759 | |
---|
4760 | /// p_GetShortExpVector of p * pp |
---|
4761 | unsigned long p_GetShortExpVector(const poly p, const poly pp, const ring r) |
---|
4762 | { |
---|
4763 | assume(p != NULL); |
---|
4764 | assume(pp != NULL); |
---|
4765 | |
---|
4766 | unsigned long ev = 0; // short exponent vector |
---|
4767 | unsigned int n = BIT_SIZEOF_LONG / r->N; // number of bits per exp |
---|
4768 | unsigned int m1; // highest bit which is filled with (n+1) |
---|
4769 | int j=1; |
---|
4770 | unsigned long i = 0L; |
---|
4771 | |
---|
4772 | if (n == 0) |
---|
4773 | { |
---|
4774 | if (r->N <2*BIT_SIZEOF_LONG) |
---|
4775 | { |
---|
4776 | n=1; |
---|
4777 | m1=0; |
---|
4778 | } |
---|
4779 | else |
---|
4780 | { |
---|
4781 | for (; j<=r->N; j++) |
---|
4782 | { |
---|
4783 | if (p_GetExp(p,j,r) > 0 || p_GetExp(pp,j,r) > 0) i++; |
---|
4784 | if (i == BIT_SIZEOF_LONG) break; |
---|
4785 | } |
---|
4786 | if (i>0) |
---|
4787 | ev = ~(0UL) >> (BIT_SIZEOF_LONG - i); |
---|
4788 | return ev; |
---|
4789 | } |
---|
4790 | } |
---|
4791 | else |
---|
4792 | { |
---|
4793 | m1 = (n+1)*(BIT_SIZEOF_LONG - n*r->N); |
---|
4794 | } |
---|
4795 | |
---|
4796 | n++; |
---|
4797 | while (i<m1) |
---|
4798 | { |
---|
4799 | ev |= GetBitFields(p_GetExp(p, j,r) + p_GetExp(pp, j,r), i, n); |
---|
4800 | i += n; |
---|
4801 | j++; |
---|
4802 | } |
---|
4803 | |
---|
4804 | n--; |
---|
4805 | while (i<BIT_SIZEOF_LONG) |
---|
4806 | { |
---|
4807 | ev |= GetBitFields(p_GetExp(p, j,r) + p_GetExp(pp, j,r), i, n); |
---|
4808 | i += n; |
---|
4809 | j++; |
---|
4810 | } |
---|
4811 | return ev; |
---|
4812 | } |
---|
4813 | |
---|
4814 | |
---|
4815 | |
---|
4816 | /*************************************************************** |
---|
4817 | * |
---|
4818 | * p_ShallowDelete |
---|
4819 | * |
---|
4820 | ***************************************************************/ |
---|
4821 | #undef LINKAGE |
---|
4822 | #define LINKAGE |
---|
4823 | #undef p_Delete__T |
---|
4824 | #define p_Delete__T p_ShallowDelete |
---|
4825 | #undef n_Delete__T |
---|
4826 | #define n_Delete__T(n, r) do {} while (0) |
---|
4827 | |
---|
4828 | #include "polys/templates/p_Delete__T.cc" |
---|
4829 | |
---|
4830 | /***************************************************************/ |
---|
4831 | /* |
---|
4832 | * compare a and b |
---|
4833 | */ |
---|
4834 | int p_Compare(const poly a, const poly b, const ring R) |
---|
4835 | { |
---|
4836 | int r=p_Cmp(a,b,R); |
---|
4837 | if ((r==0)&&(a!=NULL)) |
---|
4838 | { |
---|
4839 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
---|
4840 | /* compare lead coeffs */ |
---|
4841 | r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
---|
4842 | n_Delete(&h,R->cf); |
---|
4843 | } |
---|
4844 | else if (a==NULL) |
---|
4845 | { |
---|
4846 | if (b==NULL) |
---|
4847 | { |
---|
4848 | /* compare 0, 0 */ |
---|
4849 | r=0; |
---|
4850 | } |
---|
4851 | else if(p_IsConstant(b,R)) |
---|
4852 | { |
---|
4853 | /* compare 0, const */ |
---|
4854 | r = 1-2*n_GreaterZero(pGetCoeff(b),R->cf); /* -1: <, 1: > */ |
---|
4855 | } |
---|
4856 | } |
---|
4857 | else if (b==NULL) |
---|
4858 | { |
---|
4859 | if (p_IsConstant(a,R)) |
---|
4860 | { |
---|
4861 | /* compare const, 0 */ |
---|
4862 | r = -1+2*n_GreaterZero(pGetCoeff(a),R->cf); /* -1: <, 1: > */ |
---|
4863 | } |
---|
4864 | } |
---|
4865 | return(r); |
---|
4866 | } |
---|
4867 | |
---|
4868 | poly p_GcdMon(poly f, poly g, const ring r) |
---|
4869 | { |
---|
4870 | assume(f!=NULL); |
---|
4871 | assume(g!=NULL); |
---|
4872 | assume(pNext(f)==NULL); |
---|
4873 | poly G=p_Head(f,r); |
---|
4874 | poly h=g; |
---|
4875 | int *mf=(int*)omAlloc((r->N+1)*sizeof(int)); |
---|
4876 | p_GetExpV(f,mf,r); |
---|
4877 | int *mh=(int*)omAlloc((r->N+1)*sizeof(int)); |
---|
4878 | BOOLEAN const_mon; |
---|
4879 | BOOLEAN one_coeff=n_IsOne(pGetCoeff(G),r->cf); |
---|
4880 | loop |
---|
4881 | { |
---|
4882 | if (h==NULL) break; |
---|
4883 | if(!one_coeff) |
---|
4884 | { |
---|
4885 | number n=n_SubringGcd(pGetCoeff(G),pGetCoeff(h),r->cf); |
---|
4886 | one_coeff=n_IsOne(n,r->cf); |
---|
4887 | p_SetCoeff(G,n,r); |
---|
4888 | } |
---|
4889 | p_GetExpV(h,mh,r); |
---|
4890 | const_mon=TRUE; |
---|
4891 | for(unsigned j=r->N;j!=0;j--) |
---|
4892 | { |
---|
4893 | if (mh[j]<mf[j]) mf[j]=mh[j]; |
---|
4894 | if (mf[j]>0) const_mon=FALSE; |
---|
4895 | } |
---|
4896 | if (one_coeff && const_mon) break; |
---|
4897 | pIter(h); |
---|
4898 | } |
---|
4899 | mf[0]=0; |
---|
4900 | p_SetExpV(G,mf,r); // included is p_SetComp, p_Setm |
---|
4901 | omFreeSize(mf,(r->N+1)*sizeof(int)); |
---|
4902 | omFreeSize(mh,(r->N+1)*sizeof(int)); |
---|
4903 | return G; |
---|
4904 | } |
---|
4905 | |
---|
4906 | poly p_CopyPowerProduct(poly p, const ring r) |
---|
4907 | { |
---|
4908 | if (p == NULL) return NULL; |
---|
4909 | p_LmCheckPolyRing1(p, r); |
---|
4910 | poly np; |
---|
4911 | omTypeAllocBin(poly, np, r->PolyBin); |
---|
4912 | p_SetRingOfLm(np, r); |
---|
4913 | memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long)); |
---|
4914 | pNext(np) = NULL; |
---|
4915 | pSetCoeff0(np, n_Init(1, r->cf)); |
---|
4916 | return np; |
---|
4917 | } |
---|
4918 | |
---|
4919 | int p_MaxExpPerVar(poly p, int i, const ring r) |
---|
4920 | { |
---|
4921 | int m=0; |
---|
4922 | while(p!=NULL) |
---|
4923 | { |
---|
4924 | int mm=p_GetExp(p,i,r); |
---|
4925 | if (mm>m) m=mm; |
---|
4926 | pIter(p); |
---|
4927 | } |
---|
4928 | return m; |
---|
4929 | } |
---|
4930 | |
---|