[35aab3] | 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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[45d2332] | 6 | * Purpose: implementation of ring independent poly procedures? |
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[35aab3] | 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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[9982049] | 11 | |
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[45d2332] | 12 | |
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[22a09d] | 13 | #include "config.h" |
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[6bec87] | 14 | #include <misc/auxiliary.h> |
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[22a09d] | 15 | |
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| 16 | #include <ctype.h> |
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| 17 | #include <omalloc/omalloc.h> |
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[45d2332] | 18 | #include <misc/options.h> |
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| 19 | #include <misc/intvec.h> |
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| 20 | |
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| 21 | #include <coeffs/longrat.h> // ??? |
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[b38d70] | 22 | #include <coeffs/ffields.h> |
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| 23 | |
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[975db18] | 24 | #include <polys/PolyEnumerator.h> |
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| 25 | |
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[b38d70] | 26 | #define TRANSEXT_PRIVATES |
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| 27 | |
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[805d0b1] | 28 | #include <polys/ext_fields/transext.h> |
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| 29 | #include <polys/ext_fields/algext.h> |
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[45d2332] | 30 | |
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[805d0b1] | 31 | #include <polys/weight.h> |
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| 32 | #include <polys/simpleideals.h> |
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| 33 | |
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| 34 | #include "ring.h" |
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| 35 | #include "p_polys.h" |
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[9982049] | 36 | |
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[304ad9b] | 37 | #include <polys/templates/p_MemCmp.h> |
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| 38 | #include <polys/templates/p_MemAdd.h> |
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| 39 | #include <polys/templates/p_MemCopy.h> |
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| 40 | |
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[45d2332] | 41 | |
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[20b794] | 42 | // #include <???/ideals.h> |
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| 43 | // #include <???/int64vec.h> |
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[45d2332] | 44 | |
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[fc5095] | 45 | #ifndef NDEBUG |
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[20b794] | 46 | // #include <???/febase.h> |
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[fc5095] | 47 | #endif |
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[35aab3] | 48 | |
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[45d2332] | 49 | #ifdef HAVE_PLURAL |
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[af598e] | 50 | #include "nc/nc.h" |
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| 51 | #include "nc/sca.h" |
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[45d2332] | 52 | #endif |
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| 53 | |
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[af598e] | 54 | #include "coeffrings.h" |
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[0654122] | 55 | #ifdef HAVE_FACTORY |
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[af598e] | 56 | #include "clapsing.h" |
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[0654122] | 57 | #endif |
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[32d07a5] | 58 | |
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[35aab3] | 59 | /*************************************************************** |
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| 60 | * |
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| 61 | * Completing what needs to be set for the monomial |
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| 62 | * |
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| 63 | ***************************************************************/ |
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| 64 | // this is special for the syz stuff |
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[eb72ba1] | 65 | static int* _components = NULL; |
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| 66 | static long* _componentsShifted = NULL; |
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| 67 | static int _componentsExternal = 0; |
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[35aab3] | 68 | |
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[fc5095] | 69 | BOOLEAN pSetm_error=0; |
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| 70 | |
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[324710] | 71 | #ifndef NDEBUG |
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| 72 | # define MYTEST 0 |
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| 73 | #else /* ifndef NDEBUG */ |
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| 74 | # define MYTEST 0 |
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| 75 | #endif /* ifndef NDEBUG */ |
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| 76 | |
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[33c36d] | 77 | void p_Setm_General(poly p, const ring r) |
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[35aab3] | 78 | { |
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| 79 | p_LmCheckPolyRing(p, r); |
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| 80 | int pos=0; |
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| 81 | if (r->typ!=NULL) |
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| 82 | { |
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| 83 | loop |
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| 84 | { |
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| 85 | long ord=0; |
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| 86 | sro_ord* o=&(r->typ[pos]); |
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| 87 | switch(o->ord_typ) |
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| 88 | { |
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| 89 | case ro_dp: |
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| 90 | { |
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| 91 | int a,e; |
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| 92 | a=o->data.dp.start; |
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| 93 | e=o->data.dp.end; |
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| 94 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
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| 95 | p->exp[o->data.dp.place]=ord; |
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| 96 | break; |
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| 97 | } |
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| 98 | case ro_wp_neg: |
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| 99 | ord=POLY_NEGWEIGHT_OFFSET; |
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| 100 | // no break; |
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| 101 | case ro_wp: |
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| 102 | { |
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| 103 | int a,e; |
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| 104 | a=o->data.wp.start; |
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| 105 | e=o->data.wp.end; |
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| 106 | int *w=o->data.wp.weights; |
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[fc5095] | 107 | #if 1 |
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[35aab3] | 108 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r)*w[i-a]; |
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[fc5095] | 109 | #else |
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| 110 | long ai; |
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| 111 | int ei,wi; |
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| 112 | for(int i=a;i<=e;i++) |
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| 113 | { |
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| 114 | ei=p_GetExp(p,i,r); |
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| 115 | wi=w[i-a]; |
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| 116 | ai=ei*wi; |
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| 117 | if (ai/ei!=wi) pSetm_error=TRUE; |
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| 118 | ord+=ai; |
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| 119 | if (ord<ai) pSetm_error=TRUE; |
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| 120 | } |
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[ab4778] | 121 | #endif |
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[35aab3] | 122 | p->exp[o->data.wp.place]=ord; |
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| 123 | break; |
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| 124 | } |
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[f93c5e9] | 125 | case ro_am: |
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| 126 | { |
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[3a8a0d9] | 127 | ord = POLY_NEGWEIGHT_OFFSET; |
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| 128 | const short a=o->data.am.start; |
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| 129 | const short e=o->data.am.end; |
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| 130 | const int * w=o->data.am.weights; |
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[f93c5e9] | 131 | #if 1 |
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[3a8a0d9] | 132 | for(short i=a; i<=e; i++, w++) |
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| 133 | ord += ((*w) * p_GetExp(p,i,r)); |
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[f93c5e9] | 134 | #else |
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| 135 | long ai; |
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| 136 | int ei,wi; |
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[3a8a0d9] | 137 | for(short i=a;i<=e;i++) |
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[f93c5e9] | 138 | { |
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| 139 | ei=p_GetExp(p,i,r); |
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| 140 | wi=w[i-a]; |
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| 141 | ai=ei*wi; |
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| 142 | if (ai/ei!=wi) pSetm_error=TRUE; |
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[3a8a0d9] | 143 | ord += ai; |
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[f93c5e9] | 144 | if (ord<ai) pSetm_error=TRUE; |
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| 145 | } |
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| 146 | #endif |
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[3a8a0d9] | 147 | const int c = p_GetComp(p,r); |
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| 148 | |
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| 149 | const short len_gen= o->data.am.len_gen; |
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| 150 | |
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| 151 | if ((c > 0) && (c <= len_gen)) |
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[f93c5e9] | 152 | { |
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[599813] | 153 | assume( w == o->data.am.weights_m ); |
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| 154 | assume( w[0] == len_gen ); |
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| 155 | ord += w[c]; |
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[f93c5e9] | 156 | } |
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[3a8a0d9] | 157 | |
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| 158 | p->exp[o->data.am.place] = ord; |
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[f93c5e9] | 159 | break; |
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| 160 | } |
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[fc5095] | 161 | case ro_wp64: |
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| 162 | { |
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[ab4778] | 163 | int64 ord=0; |
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[fc5095] | 164 | int a,e; |
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| 165 | a=o->data.wp64.start; |
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| 166 | e=o->data.wp64.end; |
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| 167 | int64 *w=o->data.wp64.weights64; |
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| 168 | int64 ei,wi,ai; |
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[2132395] | 169 | for(int i=a;i<=e;i++) |
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[b5d4d1] | 170 | { |
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[fc5095] | 171 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
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| 172 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
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| 173 | ei=(int64)p_GetExp(p,i,r); |
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| 174 | wi=w[i-a]; |
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| 175 | ai=ei*wi; |
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[2132395] | 176 | if(ei!=0 && ai/ei!=wi) |
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[b5d4d1] | 177 | { |
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[fc5095] | 178 | pSetm_error=TRUE; |
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[b5d4d1] | 179 | #if SIZEOF_LONG == 4 |
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[fc5095] | 180 | Print("ai %lld, wi %lld\n",ai,wi); |
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[b5d4d1] | 181 | #else |
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[2132395] | 182 | Print("ai %ld, wi %ld\n",ai,wi); |
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[b5d4d1] | 183 | #endif |
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[fc5095] | 184 | } |
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| 185 | ord+=ai; |
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[2132395] | 186 | if (ord<ai) |
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[b5d4d1] | 187 | { |
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[2132395] | 188 | pSetm_error=TRUE; |
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[b5d4d1] | 189 | #if SIZEOF_LONG == 4 |
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[2132395] | 190 | Print("ai %lld, ord %lld\n",ai,ord); |
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[b5d4d1] | 191 | #else |
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[2132395] | 192 | Print("ai %ld, ord %ld\n",ai,ord); |
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[b5d4d1] | 193 | #endif |
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[fc5095] | 194 | } |
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| 195 | } |
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| 196 | int64 mask=(int64)0x7fffffff; |
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| 197 | long a_0=(long)(ord&mask); //2^31 |
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| 198 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
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| 199 | |
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[ab4778] | 200 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
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| 201 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
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| 202 | //Print("mask: %d",mask); |
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[fc5095] | 203 | |
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| 204 | p->exp[o->data.wp64.place]=a_1; |
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[ab4778] | 205 | p->exp[o->data.wp64.place+1]=a_0; |
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[fc5095] | 206 | // if(p_Setm_error) Print("***************************\n |
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| 207 | // ***************************\n |
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| 208 | // **WARNING: overflow error**\n |
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| 209 | // ***************************\n |
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| 210 | // ***************************\n"); |
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| 211 | break; |
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| 212 | } |
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[35aab3] | 213 | case ro_cp: |
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| 214 | { |
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| 215 | int a,e; |
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| 216 | a=o->data.cp.start; |
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| 217 | e=o->data.cp.end; |
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| 218 | int pl=o->data.cp.place; |
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| 219 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
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| 220 | break; |
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| 221 | } |
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| 222 | case ro_syzcomp: |
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| 223 | { |
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| 224 | int c=p_GetComp(p,r); |
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| 225 | long sc = c; |
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[eb72ba1] | 226 | int* Components = (_componentsExternal ? _components : |
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[35aab3] | 227 | o->data.syzcomp.Components); |
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[eb72ba1] | 228 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
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[35aab3] | 229 | o->data.syzcomp.ShiftedComponents); |
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| 230 | if (ShiftedComponents != NULL) |
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| 231 | { |
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| 232 | assume(Components != NULL); |
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| 233 | assume(c == 0 || Components[c] != 0); |
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| 234 | sc = ShiftedComponents[Components[c]]; |
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| 235 | assume(c == 0 || sc != 0); |
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| 236 | } |
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| 237 | p->exp[o->data.syzcomp.place]=sc; |
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| 238 | break; |
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| 239 | } |
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| 240 | case ro_syz: |
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| 241 | { |
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[273fed] | 242 | const unsigned long c = p_GetComp(p, r); |
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| 243 | const short place = o->data.syz.place; |
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| 244 | const int limit = o->data.syz.limit; |
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[f93c5e9] | 245 | |
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[273fed] | 246 | if (c > limit) |
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| 247 | p->exp[place] = o->data.syz.curr_index; |
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[35aab3] | 248 | else if (c > 0) |
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[273fed] | 249 | { |
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| 250 | assume( (1 <= c) && (c <= limit) ); |
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| 251 | p->exp[place]= o->data.syz.syz_index[c]; |
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| 252 | } |
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[35aab3] | 253 | else |
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| 254 | { |
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| 255 | assume(c == 0); |
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[273fed] | 256 | p->exp[place]= 0; |
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[35aab3] | 257 | } |
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| 258 | break; |
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| 259 | } |
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[645a19] | 260 | // Prefix for Induced Schreyer ordering |
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| 261 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
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| 262 | { |
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| 263 | assume(p != NULL); |
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| 264 | |
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| 265 | #ifndef NDEBUG |
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| 266 | #if MYTEST |
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[5c0183] | 267 | Print("p_Setm_General: ro_isTemp ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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[645a19] | 268 | #endif |
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| 269 | #endif |
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| 270 | int c = p_GetComp(p, r); |
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| 271 | |
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| 272 | assume( c >= 0 ); |
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| 273 | |
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| 274 | // Let's simulate case ro_syz above.... |
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| 275 | // Should accumulate (by Suffix) and be a level indicator |
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| 276 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
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| 277 | |
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| 278 | assume( pVarOffset != NULL ); |
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| 279 | |
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| 280 | // TODO: Can this be done in the suffix??? |
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| 281 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 282 | { |
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| 283 | const int vo = pVarOffset[i]; |
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| 284 | if( vo != -1) // TODO: optimize: can be done once! |
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| 285 | { |
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[5cb9ec] | 286 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
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| 287 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
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| 288 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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| 289 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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[645a19] | 290 | } |
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| 291 | } |
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| 292 | #ifndef NDEBUG |
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| 293 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 294 | { |
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| 295 | const int vo = pVarOffset[i]; |
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| 296 | if( vo != -1) // TODO: optimize: can be done once! |
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| 297 | { |
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[5cb9ec] | 298 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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| 299 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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[645a19] | 300 | } |
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| 301 | } |
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| 302 | #if MYTEST |
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[1b816a3] | 303 | // if( p->exp[o->data.isTemp.start] > 0 ) |
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[5c0183] | 304 | PrintS("after Values: "); p_DebugPrint(p, r, r, 1); |
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[645a19] | 305 | #endif |
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| 306 | #endif |
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| 307 | break; |
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| 308 | } |
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| 309 | |
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| 310 | // Suffix for Induced Schreyer ordering |
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| 311 | case ro_is: |
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| 312 | { |
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[273fed] | 313 | #ifndef NDEBUG |
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| 314 | #if MYTEST |
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| 315 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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| 316 | #endif |
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| 317 | #endif |
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| 318 | |
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[645a19] | 319 | assume(p != NULL); |
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| 320 | |
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| 321 | int c = p_GetComp(p, r); |
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| 322 | |
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| 323 | assume( c >= 0 ); |
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| 324 | const ideal F = o->data.is.F; |
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| 325 | const int limit = o->data.is.limit; |
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[e4f491] | 326 | assume( limit >= 0 ); |
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[5c0183] | 327 | const int start = o->data.is.start; |
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[645a19] | 328 | |
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| 329 | if( F != NULL && c > limit ) |
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| 330 | { |
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| 331 | #ifndef NDEBUG |
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| 332 | #if MYTEST |
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[6e66d2] | 333 | Print("p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit); // p_DebugPrint(p, r, r, 1); |
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[5c0183] | 334 | PrintS("preComputed Values: "); |
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| 335 | p_DebugPrint(p, r, r, 1); |
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[645a19] | 336 | #endif |
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| 337 | #endif |
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[e4f491] | 338 | // if( c > limit ) // BUG??? |
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| 339 | p->exp[start] = 1; |
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| 340 | // else |
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| 341 | // p->exp[start] = 0; |
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| 342 | |
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[645a19] | 343 | |
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| 344 | c -= limit; |
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| 345 | assume( c > 0 ); |
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| 346 | c--; |
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| 347 | |
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[e4f491] | 348 | if( c >= IDELEMS(F) ) |
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| 349 | break; |
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| 350 | |
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[de0a2a] | 351 | assume( c < IDELEMS(F) ); // What about others??? |
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| 352 | |
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[645a19] | 353 | const poly pp = F->m[c]; // get reference monomial!!! |
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| 354 | |
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[de0a2a] | 355 | if(pp == NULL) |
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| 356 | break; |
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| 357 | |
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[e4f491] | 358 | assume(pp != NULL); |
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| 359 | |
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[645a19] | 360 | #ifndef NDEBUG |
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| 361 | #if MYTEST |
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[f93c5e9] | 362 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
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[645a19] | 363 | p_DebugPrint(pp, r, r, 1); |
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| 364 | #endif |
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| 365 | #endif |
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| 366 | |
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| 367 | const int end = o->data.is.end; |
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| 368 | assume(start <= end); |
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[6e66d2] | 369 | |
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| 370 | |
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[f93c5e9] | 371 | // const int st = o->data.isTemp.start; |
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[5c0183] | 372 | |
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[6e66d2] | 373 | #ifndef NDEBUG |
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[5c0183] | 374 | Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]); |
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[e4f491] | 375 | #endif |
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[5c0183] | 376 | |
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| 377 | // p_ExpVectorAdd(p, pp, r); |
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[645a19] | 378 | |
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| 379 | for( int i = start; i <= end; i++) // v[0] may be here... |
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| 380 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
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| 381 | |
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[5c0183] | 382 | // p_MemAddAdjust(p, ri); |
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| 383 | if (r->NegWeightL_Offset != NULL) |
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| 384 | { |
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| 385 | for (int i=r->NegWeightL_Size-1; i>=0; i--) |
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| 386 | { |
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| 387 | const int _i = r->NegWeightL_Offset[i]; |
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| 388 | if( start <= _i && _i <= end ) |
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| 389 | p->exp[_i] -= POLY_NEGWEIGHT_OFFSET; |
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| 390 | } |
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| 391 | } |
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| 392 | |
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[6e66d2] | 393 | |
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[645a19] | 394 | #ifndef NDEBUG |
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| 395 | const int* const pVarOffset = o->data.is.pVarOffset; |
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| 396 | |
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| 397 | assume( pVarOffset != NULL ); |
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| 398 | |
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| 399 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 400 | { |
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| 401 | const int vo = pVarOffset[i]; |
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| 402 | if( vo != -1) // TODO: optimize: can be done once! |
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[5cb9ec] | 403 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
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| 404 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
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[645a19] | 405 | } |
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| 406 | // TODO: how to check this for computed values??? |
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[5c0183] | 407 | #if MYTEST |
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| 408 | PrintS("Computed Values: "); p_DebugPrint(p, r, r, 1); |
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| 409 | #endif |
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[645a19] | 410 | #endif |
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| 411 | } else |
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| 412 | { |
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[5c0183] | 413 | p->exp[start] = 0; //!!!!????? where????? |
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[f93c5e9] | 414 | |
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[645a19] | 415 | const int* const pVarOffset = o->data.is.pVarOffset; |
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| 416 | |
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| 417 | // What about v[0] - component: it will be added later by |
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| 418 | // suffix!!! |
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| 419 | // TODO: Test it! |
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| 420 | const int vo = pVarOffset[0]; |
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| 421 | if( vo != -1 ) |
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| 422 | p->exp[vo] = c; // initial component v[0]! |
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[6e66d2] | 423 | |
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| 424 | #ifndef NDEBUG |
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| 425 | #if MYTEST |
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[5c0183] | 426 | 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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[6e66d2] | 427 | p_DebugPrint(p, r, r, 1); |
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[5c0183] | 428 | #endif |
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| 429 | #endif |
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[645a19] | 430 | } |
---|
| 431 | |
---|
| 432 | break; |
---|
| 433 | } |
---|
[35aab3] | 434 | default: |
---|
| 435 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
---|
| 436 | return; |
---|
| 437 | } |
---|
| 438 | pos++; |
---|
| 439 | if (pos == r->OrdSize) return; |
---|
| 440 | } |
---|
| 441 | } |
---|
| 442 | } |
---|
| 443 | |
---|
| 444 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
---|
| 445 | { |
---|
[eb72ba1] | 446 | _components = Components; |
---|
| 447 | _componentsShifted = ShiftedComponents; |
---|
| 448 | _componentsExternal = 1; |
---|
[35aab3] | 449 | p_Setm_General(p, r); |
---|
[eb72ba1] | 450 | _componentsExternal = 0; |
---|
[35aab3] | 451 | } |
---|
| 452 | |
---|
| 453 | // dummy for lp, ls, etc |
---|
[33c36d] | 454 | void p_Setm_Dummy(poly p, const ring r) |
---|
[35aab3] | 455 | { |
---|
| 456 | p_LmCheckPolyRing(p, r); |
---|
| 457 | } |
---|
| 458 | |
---|
| 459 | // for dp, Dp, ds, etc |
---|
[33c36d] | 460 | void p_Setm_TotalDegree(poly p, const ring r) |
---|
[35aab3] | 461 | { |
---|
| 462 | p_LmCheckPolyRing(p, r); |
---|
[99bdcf] | 463 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
---|
[35aab3] | 464 | } |
---|
| 465 | |
---|
| 466 | // for wp, Wp, ws, etc |
---|
[33c36d] | 467 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
---|
[35aab3] | 468 | { |
---|
| 469 | p_LmCheckPolyRing(p, r); |
---|
[19ae652] | 470 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 471 | } |
---|
| 472 | |
---|
| 473 | p_SetmProc p_GetSetmProc(ring r) |
---|
| 474 | { |
---|
[ab4778] | 475 | // covers lp, rp, ls, |
---|
[35aab3] | 476 | if (r->typ == NULL) return p_Setm_Dummy; |
---|
| 477 | |
---|
| 478 | if (r->OrdSize == 1) |
---|
| 479 | { |
---|
[ab4778] | 480 | if (r->typ[0].ord_typ == ro_dp && |
---|
[35aab3] | 481 | r->typ[0].data.dp.start == 1 && |
---|
| 482 | r->typ[0].data.dp.end == r->N && |
---|
| 483 | r->typ[0].data.dp.place == r->pOrdIndex) |
---|
| 484 | return p_Setm_TotalDegree; |
---|
[ab4778] | 485 | if (r->typ[0].ord_typ == ro_wp && |
---|
[35aab3] | 486 | r->typ[0].data.wp.start == 1 && |
---|
| 487 | r->typ[0].data.wp.end == r->N && |
---|
| 488 | r->typ[0].data.wp.place == r->pOrdIndex && |
---|
| 489 | r->typ[0].data.wp.weights == r->firstwv) |
---|
| 490 | return p_Setm_WFirstTotalDegree; |
---|
| 491 | } |
---|
| 492 | return p_Setm_General; |
---|
| 493 | } |
---|
| 494 | |
---|
| 495 | |
---|
| 496 | /* -------------------------------------------------------------------*/ |
---|
| 497 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
[b5d4d1] | 498 | |
---|
| 499 | /* comptible with ordering */ |
---|
[bf183f] | 500 | long p_Deg(poly a, const ring r) |
---|
[35aab3] | 501 | { |
---|
| 502 | p_LmCheckPolyRing(a, r); |
---|
[74f51f] | 503 | // assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); // WRONG assume! |
---|
[35aab3] | 504 | return p_GetOrder(a, r); |
---|
| 505 | } |
---|
| 506 | |
---|
[19ae652] | 507 | // p_WTotalDegree for weighted orderings |
---|
[35aab3] | 508 | // whose first block covers all variables |
---|
[19ae652] | 509 | long p_WFirstTotalDegree(poly p, const ring r) |
---|
[35aab3] | 510 | { |
---|
| 511 | int i; |
---|
| 512 | long sum = 0; |
---|
[ab4778] | 513 | |
---|
[35aab3] | 514 | for (i=1; i<= r->firstBlockEnds; i++) |
---|
| 515 | { |
---|
| 516 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 517 | } |
---|
| 518 | return sum; |
---|
| 519 | } |
---|
| 520 | |
---|
| 521 | /*2 |
---|
| 522 | * compute the degree of the leading monomial of p |
---|
| 523 | * with respect to weigths from the ordering |
---|
| 524 | * the ordering is not compatible with degree so do not use p->Order |
---|
| 525 | */ |
---|
[19ae652] | 526 | long p_WTotaldegree(poly p, const ring r) |
---|
[35aab3] | 527 | { |
---|
| 528 | p_LmCheckPolyRing(p, r); |
---|
| 529 | int i, k; |
---|
[f93c5e9] | 530 | int pIS = 0; |
---|
[35aab3] | 531 | long j =0; |
---|
| 532 | |
---|
| 533 | // iterate through each block: |
---|
| 534 | for (i=0;r->order[i]!=0;i++) |
---|
| 535 | { |
---|
[ab4778] | 536 | int b0=r->block0[i]; |
---|
| 537 | int b1=r->block1[i]; |
---|
[35aab3] | 538 | switch(r->order[i]) |
---|
| 539 | { |
---|
[3e0a7b] | 540 | case ringorder_M: |
---|
[ab4778] | 541 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
| 542 | { // in jedem block: |
---|
| 543 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
---|
| 544 | } |
---|
| 545 | break; |
---|
[35aab3] | 546 | case ringorder_wp: |
---|
| 547 | case ringorder_ws: |
---|
| 548 | case ringorder_Wp: |
---|
| 549 | case ringorder_Ws: |
---|
[ab4778] | 550 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 551 | { // in jedem block: |
---|
[ab4778] | 552 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
---|
[35aab3] | 553 | } |
---|
| 554 | break; |
---|
| 555 | case ringorder_lp: |
---|
| 556 | case ringorder_ls: |
---|
[e519c5c] | 557 | case ringorder_rs: |
---|
[35aab3] | 558 | case ringorder_dp: |
---|
| 559 | case ringorder_ds: |
---|
| 560 | case ringorder_Dp: |
---|
| 561 | case ringorder_Ds: |
---|
| 562 | case ringorder_rp: |
---|
[ab4778] | 563 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 564 | { |
---|
| 565 | j+= p_GetExp(p,k,r); |
---|
| 566 | } |
---|
| 567 | break; |
---|
[fc5095] | 568 | case ringorder_a64: |
---|
| 569 | { |
---|
| 570 | int64* w=(int64*)r->wvhdl[i]; |
---|
[ab4778] | 571 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
---|
| 572 | { |
---|
[fc5095] | 573 | //there should be added a line which checks if w[k]>2^31 |
---|
| 574 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
---|
| 575 | } |
---|
| 576 | //break; |
---|
| 577 | return j; |
---|
| 578 | } |
---|
[35aab3] | 579 | case ringorder_c: |
---|
| 580 | case ringorder_C: |
---|
| 581 | case ringorder_S: |
---|
| 582 | case ringorder_s: |
---|
| 583 | case ringorder_aa: |
---|
[74f51f] | 584 | case ringorder_IS: |
---|
| 585 | break; |
---|
[35aab3] | 586 | case ringorder_a: |
---|
[ab4778] | 587 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 588 | { // only one line |
---|
[ab4778] | 589 | j+= p_GetExp(p,k, r)*r->wvhdl[i][ k- b0 /*r->block0[i]*/]; |
---|
[35aab3] | 590 | } |
---|
[fc5095] | 591 | //break; |
---|
[35aab3] | 592 | return j; |
---|
[fc5095] | 593 | |
---|
[35aab3] | 594 | #ifndef NDEBUG |
---|
| 595 | default: |
---|
[19ae652] | 596 | Print("missing order %d in p_WTotaldegree\n",r->order[i]); |
---|
[35aab3] | 597 | break; |
---|
| 598 | #endif |
---|
| 599 | } |
---|
| 600 | } |
---|
| 601 | return j; |
---|
| 602 | } |
---|
| 603 | |
---|
[ba0fc3] | 604 | long p_DegW(poly p, const short *w, const ring R) |
---|
| 605 | { |
---|
| 606 | long r=~0L; |
---|
| 607 | |
---|
| 608 | while (p!=NULL) |
---|
| 609 | { |
---|
| 610 | long t=totaldegreeWecart_IV(p,R,w); |
---|
| 611 | if (t>r) r=t; |
---|
| 612 | pIter(p); |
---|
| 613 | } |
---|
| 614 | return r; |
---|
| 615 | } |
---|
| 616 | |
---|
[bf183f] | 617 | int p_Weight(int i, const ring r) |
---|
[35aab3] | 618 | { |
---|
| 619 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
| 620 | { |
---|
| 621 | return 1; |
---|
| 622 | } |
---|
| 623 | return r->firstwv[i-1]; |
---|
| 624 | } |
---|
| 625 | |
---|
[bf183f] | 626 | long p_WDegree(poly p, const ring r) |
---|
[35aab3] | 627 | { |
---|
[99bdcf] | 628 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
[35aab3] | 629 | p_LmCheckPolyRing(p, r); |
---|
[9f73e80] | 630 | int i; |
---|
[35aab3] | 631 | long j =0; |
---|
| 632 | |
---|
| 633 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
| 634 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 635 | |
---|
| 636 | for (;i<=r->N;i++) |
---|
[8a8c9e] | 637 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
[35aab3] | 638 | |
---|
| 639 | return j; |
---|
| 640 | } |
---|
| 641 | |
---|
| 642 | |
---|
| 643 | /* ---------------------------------------------------------------------*/ |
---|
| 644 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
| 645 | /* compute in l also the pLength of p */ |
---|
| 646 | |
---|
| 647 | /*2 |
---|
| 648 | * compute the length of a polynomial (in l) |
---|
| 649 | * and the degree of the monomial with maximal degree: the last one |
---|
| 650 | */ |
---|
[107986] | 651 | long pLDeg0(poly p,int *l, const ring r) |
---|
[35aab3] | 652 | { |
---|
| 653 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 654 | long k= p_GetComp(p, r); |
---|
[35aab3] | 655 | int ll=1; |
---|
| 656 | |
---|
| 657 | if (k > 0) |
---|
| 658 | { |
---|
| 659 | while ((pNext(p)!=NULL) && (p_GetComp(pNext(p), r)==k)) |
---|
| 660 | { |
---|
| 661 | pIter(p); |
---|
| 662 | ll++; |
---|
| 663 | } |
---|
| 664 | } |
---|
| 665 | else |
---|
| 666 | { |
---|
| 667 | while (pNext(p)!=NULL) |
---|
| 668 | { |
---|
| 669 | pIter(p); |
---|
| 670 | ll++; |
---|
| 671 | } |
---|
| 672 | } |
---|
| 673 | *l=ll; |
---|
| 674 | return r->pFDeg(p, r); |
---|
| 675 | } |
---|
| 676 | |
---|
| 677 | /*2 |
---|
| 678 | * compute the length of a polynomial (in l) |
---|
| 679 | * and the degree of the monomial with maximal degree: the last one |
---|
| 680 | * but search in all components before syzcomp |
---|
| 681 | */ |
---|
[107986] | 682 | long pLDeg0c(poly p,int *l, const ring r) |
---|
[35aab3] | 683 | { |
---|
| 684 | assume(p!=NULL); |
---|
| 685 | #ifdef PDEBUG |
---|
| 686 | _p_Test(p,r,PDEBUG); |
---|
| 687 | #endif |
---|
| 688 | p_CheckPolyRing(p, r); |
---|
| 689 | long o; |
---|
| 690 | int ll=1; |
---|
| 691 | |
---|
| 692 | if (! rIsSyzIndexRing(r)) |
---|
| 693 | { |
---|
[ab4778] | 694 | while (pNext(p) != NULL) |
---|
[35aab3] | 695 | { |
---|
| 696 | pIter(p); |
---|
| 697 | ll++; |
---|
| 698 | } |
---|
| 699 | o = r->pFDeg(p, r); |
---|
| 700 | } |
---|
| 701 | else |
---|
| 702 | { |
---|
| 703 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 704 | poly pp = p; |
---|
| 705 | while ((p=pNext(p))!=NULL) |
---|
| 706 | { |
---|
| 707 | if (p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
| 708 | ll++; |
---|
| 709 | else break; |
---|
| 710 | pp = p; |
---|
| 711 | } |
---|
| 712 | #ifdef PDEBUG |
---|
| 713 | _p_Test(pp,r,PDEBUG); |
---|
| 714 | #endif |
---|
| 715 | o = r->pFDeg(pp, r); |
---|
| 716 | } |
---|
| 717 | *l=ll; |
---|
| 718 | return o; |
---|
| 719 | } |
---|
| 720 | |
---|
| 721 | /*2 |
---|
| 722 | * compute the length of a polynomial (in l) |
---|
| 723 | * and the degree of the monomial with maximal degree: the first one |
---|
| 724 | * this works for the polynomial case with degree orderings |
---|
| 725 | * (both c,dp and dp,c) |
---|
| 726 | */ |
---|
[107986] | 727 | long pLDegb(poly p,int *l, const ring r) |
---|
[35aab3] | 728 | { |
---|
| 729 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 730 | long k= p_GetComp(p, r); |
---|
[35aab3] | 731 | long o = r->pFDeg(p, r); |
---|
| 732 | int ll=1; |
---|
| 733 | |
---|
| 734 | if (k != 0) |
---|
| 735 | { |
---|
| 736 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 737 | { |
---|
| 738 | ll++; |
---|
| 739 | } |
---|
| 740 | } |
---|
| 741 | else |
---|
| 742 | { |
---|
| 743 | while ((p=pNext(p)) !=NULL) |
---|
| 744 | { |
---|
| 745 | ll++; |
---|
| 746 | } |
---|
| 747 | } |
---|
| 748 | *l=ll; |
---|
| 749 | return o; |
---|
| 750 | } |
---|
| 751 | |
---|
| 752 | /*2 |
---|
| 753 | * compute the length of a polynomial (in l) |
---|
| 754 | * and the degree of the monomial with maximal degree: |
---|
| 755 | * this is NOT the last one, we have to look for it |
---|
| 756 | */ |
---|
[107986] | 757 | long pLDeg1(poly p,int *l, const ring r) |
---|
[35aab3] | 758 | { |
---|
| 759 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 760 | long k= p_GetComp(p, r); |
---|
[35aab3] | 761 | int ll=1; |
---|
| 762 | long t,max; |
---|
| 763 | |
---|
| 764 | max=r->pFDeg(p, r); |
---|
| 765 | if (k > 0) |
---|
| 766 | { |
---|
| 767 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 768 | { |
---|
| 769 | t=r->pFDeg(p, r); |
---|
| 770 | if (t>max) max=t; |
---|
| 771 | ll++; |
---|
| 772 | } |
---|
| 773 | } |
---|
| 774 | else |
---|
| 775 | { |
---|
| 776 | while ((p=pNext(p))!=NULL) |
---|
| 777 | { |
---|
| 778 | t=r->pFDeg(p, r); |
---|
| 779 | if (t>max) max=t; |
---|
| 780 | ll++; |
---|
| 781 | } |
---|
| 782 | } |
---|
| 783 | *l=ll; |
---|
| 784 | return max; |
---|
| 785 | } |
---|
| 786 | |
---|
| 787 | /*2 |
---|
| 788 | * compute the length of a polynomial (in l) |
---|
| 789 | * and the degree of the monomial with maximal degree: |
---|
| 790 | * this is NOT the last one, we have to look for it |
---|
| 791 | * in all components |
---|
| 792 | */ |
---|
[107986] | 793 | long pLDeg1c(poly p,int *l, const ring r) |
---|
[35aab3] | 794 | { |
---|
| 795 | p_CheckPolyRing(p, r); |
---|
| 796 | int ll=1; |
---|
| 797 | long t,max; |
---|
| 798 | |
---|
| 799 | max=r->pFDeg(p, r); |
---|
| 800 | if (rIsSyzIndexRing(r)) |
---|
| 801 | { |
---|
| 802 | long limit = rGetCurrSyzLimit(r); |
---|
| 803 | while ((p=pNext(p))!=NULL) |
---|
| 804 | { |
---|
| 805 | if (p_GetComp(p, r)<=limit) |
---|
| 806 | { |
---|
| 807 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 808 | ll++; |
---|
| 809 | } |
---|
| 810 | else break; |
---|
| 811 | } |
---|
| 812 | } |
---|
| 813 | else |
---|
| 814 | { |
---|
| 815 | while ((p=pNext(p))!=NULL) |
---|
| 816 | { |
---|
| 817 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 818 | ll++; |
---|
| 819 | } |
---|
| 820 | } |
---|
| 821 | *l=ll; |
---|
| 822 | return max; |
---|
| 823 | } |
---|
| 824 | |
---|
| 825 | // like pLDeg1, only pFDeg == pDeg |
---|
[107986] | 826 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 827 | { |
---|
[45d2332] | 828 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 829 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 830 | long k= p_GetComp(p, r); |
---|
[35aab3] | 831 | int ll=1; |
---|
| 832 | long t,max; |
---|
| 833 | |
---|
[b5d4d1] | 834 | max=p_GetOrder(p, r); |
---|
[35aab3] | 835 | if (k > 0) |
---|
| 836 | { |
---|
| 837 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 838 | { |
---|
[b5d4d1] | 839 | t=p_GetOrder(p, r); |
---|
[35aab3] | 840 | if (t>max) max=t; |
---|
| 841 | ll++; |
---|
| 842 | } |
---|
| 843 | } |
---|
| 844 | else |
---|
| 845 | { |
---|
| 846 | while ((p=pNext(p))!=NULL) |
---|
| 847 | { |
---|
[b5d4d1] | 848 | t=p_GetOrder(p, r); |
---|
[35aab3] | 849 | if (t>max) max=t; |
---|
| 850 | ll++; |
---|
| 851 | } |
---|
| 852 | } |
---|
| 853 | *l=ll; |
---|
| 854 | return max; |
---|
| 855 | } |
---|
| 856 | |
---|
[107986] | 857 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 858 | { |
---|
[45d2332] | 859 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 860 | p_CheckPolyRing(p, r); |
---|
| 861 | int ll=1; |
---|
| 862 | long t,max; |
---|
| 863 | |
---|
[b5d4d1] | 864 | max=p_GetOrder(p, r); |
---|
[35aab3] | 865 | if (rIsSyzIndexRing(r)) |
---|
| 866 | { |
---|
| 867 | long limit = rGetCurrSyzLimit(r); |
---|
| 868 | while ((p=pNext(p))!=NULL) |
---|
| 869 | { |
---|
| 870 | if (p_GetComp(p, r)<=limit) |
---|
| 871 | { |
---|
[b5d4d1] | 872 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 873 | ll++; |
---|
| 874 | } |
---|
| 875 | else break; |
---|
| 876 | } |
---|
| 877 | } |
---|
| 878 | else |
---|
| 879 | { |
---|
| 880 | while ((p=pNext(p))!=NULL) |
---|
| 881 | { |
---|
[b5d4d1] | 882 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 883 | ll++; |
---|
| 884 | } |
---|
| 885 | } |
---|
| 886 | *l=ll; |
---|
| 887 | return max; |
---|
| 888 | } |
---|
| 889 | |
---|
| 890 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
[107986] | 891 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 892 | { |
---|
| 893 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 894 | long k= p_GetComp(p, r); |
---|
[35aab3] | 895 | int ll=1; |
---|
| 896 | long t,max; |
---|
| 897 | |
---|
[99bdcf] | 898 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 899 | if (k > 0) |
---|
| 900 | { |
---|
| 901 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 902 | { |
---|
[99bdcf] | 903 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 904 | if (t>max) max=t; |
---|
| 905 | ll++; |
---|
| 906 | } |
---|
| 907 | } |
---|
| 908 | else |
---|
| 909 | { |
---|
| 910 | while ((p=pNext(p))!=NULL) |
---|
| 911 | { |
---|
[99bdcf] | 912 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 913 | if (t>max) max=t; |
---|
| 914 | ll++; |
---|
| 915 | } |
---|
| 916 | } |
---|
| 917 | *l=ll; |
---|
| 918 | return max; |
---|
| 919 | } |
---|
| 920 | |
---|
[107986] | 921 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 922 | { |
---|
| 923 | p_CheckPolyRing(p, r); |
---|
| 924 | int ll=1; |
---|
| 925 | long t,max; |
---|
| 926 | |
---|
[99bdcf] | 927 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 928 | if (rIsSyzIndexRing(r)) |
---|
| 929 | { |
---|
| 930 | long limit = rGetCurrSyzLimit(r); |
---|
| 931 | while ((p=pNext(p))!=NULL) |
---|
| 932 | { |
---|
| 933 | if (p_GetComp(p, r)<=limit) |
---|
| 934 | { |
---|
[99bdcf] | 935 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 936 | ll++; |
---|
| 937 | } |
---|
| 938 | else break; |
---|
| 939 | } |
---|
| 940 | } |
---|
| 941 | else |
---|
| 942 | { |
---|
| 943 | while ((p=pNext(p))!=NULL) |
---|
| 944 | { |
---|
[99bdcf] | 945 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 946 | ll++; |
---|
| 947 | } |
---|
| 948 | } |
---|
| 949 | *l=ll; |
---|
| 950 | return max; |
---|
| 951 | } |
---|
| 952 | |
---|
[19ae652] | 953 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
[107986] | 954 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 955 | { |
---|
| 956 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 957 | long k= p_GetComp(p, r); |
---|
[35aab3] | 958 | int ll=1; |
---|
| 959 | long t,max; |
---|
| 960 | |
---|
[19ae652] | 961 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 962 | if (k > 0) |
---|
| 963 | { |
---|
| 964 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 965 | { |
---|
[19ae652] | 966 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 967 | if (t>max) max=t; |
---|
| 968 | ll++; |
---|
| 969 | } |
---|
| 970 | } |
---|
| 971 | else |
---|
| 972 | { |
---|
| 973 | while ((p=pNext(p))!=NULL) |
---|
| 974 | { |
---|
[19ae652] | 975 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 976 | if (t>max) max=t; |
---|
| 977 | ll++; |
---|
| 978 | } |
---|
| 979 | } |
---|
| 980 | *l=ll; |
---|
| 981 | return max; |
---|
| 982 | } |
---|
| 983 | |
---|
[107986] | 984 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 985 | { |
---|
| 986 | p_CheckPolyRing(p, r); |
---|
| 987 | int ll=1; |
---|
| 988 | long t,max; |
---|
| 989 | |
---|
[19ae652] | 990 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 991 | if (rIsSyzIndexRing(r)) |
---|
| 992 | { |
---|
| 993 | long limit = rGetCurrSyzLimit(r); |
---|
| 994 | while ((p=pNext(p))!=NULL) |
---|
| 995 | { |
---|
| 996 | if (p_GetComp(p, r)<=limit) |
---|
| 997 | { |
---|
[99bdcf] | 998 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 999 | ll++; |
---|
| 1000 | } |
---|
| 1001 | else break; |
---|
| 1002 | } |
---|
| 1003 | } |
---|
| 1004 | else |
---|
| 1005 | { |
---|
| 1006 | while ((p=pNext(p))!=NULL) |
---|
| 1007 | { |
---|
[99bdcf] | 1008 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 1009 | ll++; |
---|
| 1010 | } |
---|
| 1011 | } |
---|
| 1012 | *l=ll; |
---|
| 1013 | return max; |
---|
| 1014 | } |
---|
| 1015 | |
---|
| 1016 | /*************************************************************** |
---|
| 1017 | * |
---|
| 1018 | * Maximal Exponent business |
---|
| 1019 | * |
---|
| 1020 | ***************************************************************/ |
---|
| 1021 | |
---|
[ab4778] | 1022 | static inline unsigned long |
---|
[107986] | 1023 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
[35aab3] | 1024 | unsigned long number_of_exp) |
---|
| 1025 | { |
---|
| 1026 | const unsigned long bitmask = r->bitmask; |
---|
| 1027 | unsigned long ml1 = l1 & bitmask; |
---|
| 1028 | unsigned long ml2 = l2 & bitmask; |
---|
| 1029 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
| 1030 | unsigned long j = number_of_exp - 1; |
---|
| 1031 | |
---|
| 1032 | if (j > 0) |
---|
| 1033 | { |
---|
| 1034 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
| 1035 | while (1) |
---|
| 1036 | { |
---|
| 1037 | ml1 = l1 & mask; |
---|
| 1038 | ml2 = l2 & mask; |
---|
| 1039 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
| 1040 | j--; |
---|
| 1041 | if (j == 0) break; |
---|
| 1042 | mask = mask << r->BitsPerExp; |
---|
| 1043 | } |
---|
| 1044 | } |
---|
| 1045 | return max; |
---|
| 1046 | } |
---|
| 1047 | |
---|
| 1048 | static inline unsigned long |
---|
[107986] | 1049 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
[35aab3] | 1050 | { |
---|
| 1051 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
| 1052 | } |
---|
| 1053 | |
---|
[107986] | 1054 | poly p_GetMaxExpP(poly p, const ring r) |
---|
[35aab3] | 1055 | { |
---|
| 1056 | p_CheckPolyRing(p, r); |
---|
| 1057 | if (p == NULL) return p_Init(r); |
---|
| 1058 | poly max = p_LmInit(p, r); |
---|
| 1059 | pIter(p); |
---|
| 1060 | if (p == NULL) return max; |
---|
| 1061 | int i, offset; |
---|
| 1062 | unsigned long l_p, l_max; |
---|
| 1063 | unsigned long divmask = r->divmask; |
---|
[ab4778] | 1064 | |
---|
[35aab3] | 1065 | do |
---|
| 1066 | { |
---|
| 1067 | offset = r->VarL_Offset[0]; |
---|
| 1068 | l_p = p->exp[offset]; |
---|
| 1069 | l_max = max->exp[offset]; |
---|
| 1070 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1071 | if (l_p > l_max || |
---|
[35aab3] | 1072 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1073 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1074 | |
---|
| 1075 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1076 | { |
---|
| 1077 | offset = r->VarL_Offset[i]; |
---|
| 1078 | l_p = p->exp[offset]; |
---|
| 1079 | l_max = max->exp[offset]; |
---|
| 1080 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1081 | if (l_p > l_max || |
---|
[35aab3] | 1082 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1083 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1084 | } |
---|
| 1085 | pIter(p); |
---|
| 1086 | } |
---|
| 1087 | while (p != NULL); |
---|
| 1088 | return max; |
---|
| 1089 | } |
---|
| 1090 | |
---|
[107986] | 1091 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
[35aab3] | 1092 | { |
---|
| 1093 | unsigned long l_p, divmask = r->divmask; |
---|
| 1094 | int i; |
---|
[ab4778] | 1095 | |
---|
[35aab3] | 1096 | while (p != NULL) |
---|
| 1097 | { |
---|
| 1098 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
| 1099 | if (l_p > l_max || |
---|
| 1100 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1101 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1102 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1103 | { |
---|
| 1104 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
| 1105 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1106 | if (l_p > l_max || |
---|
[35aab3] | 1107 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1108 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1109 | } |
---|
| 1110 | pIter(p); |
---|
| 1111 | } |
---|
| 1112 | return l_max; |
---|
| 1113 | } |
---|
| 1114 | |
---|
[fc5095] | 1115 | |
---|
| 1116 | |
---|
[ab4778] | 1117 | |
---|
[35aab3] | 1118 | /*************************************************************** |
---|
| 1119 | * |
---|
| 1120 | * Misc things |
---|
| 1121 | * |
---|
| 1122 | ***************************************************************/ |
---|
| 1123 | // returns TRUE, if all monoms have the same component |
---|
[107986] | 1124 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
[35aab3] | 1125 | { |
---|
| 1126 | if(p!=NULL) |
---|
| 1127 | { |
---|
| 1128 | long i = p_GetComp(p, r); |
---|
| 1129 | while (pNext(p)!=NULL) |
---|
| 1130 | { |
---|
| 1131 | pIter(p); |
---|
| 1132 | if(i != p_GetComp(p, r)) return FALSE; |
---|
| 1133 | } |
---|
| 1134 | } |
---|
| 1135 | return TRUE; |
---|
| 1136 | } |
---|
| 1137 | |
---|
| 1138 | /*2 |
---|
| 1139 | *test if a monomial /head term is a pure power |
---|
| 1140 | */ |
---|
| 1141 | int p_IsPurePower(const poly p, const ring r) |
---|
| 1142 | { |
---|
| 1143 | int i,k=0; |
---|
| 1144 | |
---|
| 1145 | for (i=r->N;i;i--) |
---|
| 1146 | { |
---|
| 1147 | if (p_GetExp(p,i, r)!=0) |
---|
| 1148 | { |
---|
| 1149 | if(k!=0) return 0; |
---|
| 1150 | k=i; |
---|
| 1151 | } |
---|
| 1152 | } |
---|
| 1153 | return k; |
---|
| 1154 | } |
---|
| 1155 | |
---|
[2f0d83f] | 1156 | /*2 |
---|
| 1157 | *test if a polynomial is univariate |
---|
| 1158 | * return -1 for constant, |
---|
| 1159 | * 0 for not univariate,s |
---|
| 1160 | * i if dep. on var(i) |
---|
| 1161 | */ |
---|
| 1162 | int p_IsUnivariate(poly p, const ring r) |
---|
| 1163 | { |
---|
| 1164 | int i,k=-1; |
---|
| 1165 | |
---|
| 1166 | while (p!=NULL) |
---|
| 1167 | { |
---|
| 1168 | for (i=r->N;i;i--) |
---|
| 1169 | { |
---|
| 1170 | if (p_GetExp(p,i, r)!=0) |
---|
| 1171 | { |
---|
| 1172 | if((k!=-1)&&(k!=i)) return 0; |
---|
| 1173 | k=i; |
---|
| 1174 | } |
---|
| 1175 | } |
---|
| 1176 | pIter(p); |
---|
| 1177 | } |
---|
| 1178 | return k; |
---|
| 1179 | } |
---|
| 1180 | |
---|
[3931bf] | 1181 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
[f46646] | 1182 | int p_GetVariables(poly p, int * e, const ring r) |
---|
[3931bf] | 1183 | { |
---|
| 1184 | int i; |
---|
[f46646] | 1185 | int n=0; |
---|
[3931bf] | 1186 | while(p!=NULL) |
---|
| 1187 | { |
---|
[f46646] | 1188 | n=0; |
---|
[95450e] | 1189 | for(i=r->N; i>0; i--) |
---|
[3931bf] | 1190 | { |
---|
| 1191 | if(e[i]==0) |
---|
| 1192 | { |
---|
| 1193 | if (p_GetExp(p,i,r)>0) |
---|
[f46646] | 1194 | { |
---|
[3931bf] | 1195 | e[i]=1; |
---|
[f46646] | 1196 | n++; |
---|
| 1197 | } |
---|
[3931bf] | 1198 | } |
---|
[f46646] | 1199 | else |
---|
| 1200 | n++; |
---|
[3931bf] | 1201 | } |
---|
[f46646] | 1202 | if (n==r->N) break; |
---|
[3931bf] | 1203 | pIter(p); |
---|
| 1204 | } |
---|
[f46646] | 1205 | return n; |
---|
[3931bf] | 1206 | } |
---|
| 1207 | |
---|
| 1208 | |
---|
[35aab3] | 1209 | /*2 |
---|
| 1210 | * returns a polynomial representing the integer i |
---|
| 1211 | */ |
---|
[2f3764] | 1212 | poly p_ISet(long i, const ring r) |
---|
[35aab3] | 1213 | { |
---|
| 1214 | poly rc = NULL; |
---|
| 1215 | if (i!=0) |
---|
| 1216 | { |
---|
| 1217 | rc = p_Init(r); |
---|
[8a8c9e] | 1218 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
| 1219 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
[fb82895] | 1220 | p_LmDelete(&rc,r); |
---|
[35aab3] | 1221 | } |
---|
| 1222 | return rc; |
---|
| 1223 | } |
---|
| 1224 | |
---|
[1c33e0d] | 1225 | /*2 |
---|
| 1226 | * an optimized version of p_ISet for the special case 1 |
---|
| 1227 | */ |
---|
[5bc4103] | 1228 | poly p_One(const ring r) |
---|
[1c33e0d] | 1229 | { |
---|
| 1230 | poly rc = p_Init(r); |
---|
[8a8c9e] | 1231 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
[1c33e0d] | 1232 | return rc; |
---|
| 1233 | } |
---|
| 1234 | |
---|
[f34215] | 1235 | void p_Split(poly p, poly *h) |
---|
| 1236 | { |
---|
| 1237 | *h=pNext(p); |
---|
| 1238 | pNext(p)=NULL; |
---|
| 1239 | } |
---|
| 1240 | |
---|
| 1241 | /*2 |
---|
| 1242 | * pair has no common factor ? or is no polynomial |
---|
| 1243 | */ |
---|
| 1244 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
| 1245 | { |
---|
| 1246 | |
---|
| 1247 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
| 1248 | return FALSE; |
---|
| 1249 | int i = rVar(r); |
---|
| 1250 | loop |
---|
| 1251 | { |
---|
| 1252 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
| 1253 | return FALSE; |
---|
| 1254 | i--; |
---|
| 1255 | if (i == 0) |
---|
| 1256 | return TRUE; |
---|
| 1257 | } |
---|
| 1258 | } |
---|
| 1259 | |
---|
| 1260 | /*2 |
---|
| 1261 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
| 1262 | */ |
---|
| 1263 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
| 1264 | { |
---|
| 1265 | if (r==NULL) { rc=NULL;return st;} |
---|
| 1266 | int i,j; |
---|
| 1267 | rc = p_Init(r); |
---|
[8a8c9e] | 1268 | const char *s = r->cf->cfRead(st,&(rc->coef),r->cf); |
---|
[f34215] | 1269 | if (s==st) |
---|
| 1270 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
| 1271 | { |
---|
| 1272 | j = r_IsRingVar(s,r); |
---|
| 1273 | if (j >= 0) |
---|
| 1274 | { |
---|
| 1275 | p_IncrExp(rc,1+j,r); |
---|
| 1276 | while (*s!='\0') s++; |
---|
| 1277 | goto done; |
---|
| 1278 | } |
---|
| 1279 | } |
---|
| 1280 | while (*s!='\0') |
---|
| 1281 | { |
---|
| 1282 | char ss[2]; |
---|
| 1283 | ss[0] = *s++; |
---|
| 1284 | ss[1] = '\0'; |
---|
| 1285 | j = r_IsRingVar(ss,r); |
---|
| 1286 | if (j >= 0) |
---|
| 1287 | { |
---|
| 1288 | const char *s_save=s; |
---|
| 1289 | s = eati(s,&i); |
---|
| 1290 | if (((unsigned long)i) > r->bitmask) |
---|
| 1291 | { |
---|
| 1292 | // exponent to large: it is not a monomial |
---|
| 1293 | p_LmDelete(&rc,r); |
---|
| 1294 | return s_save; |
---|
| 1295 | } |
---|
| 1296 | p_AddExp(rc,1+j, (long)i, r); |
---|
| 1297 | } |
---|
| 1298 | else |
---|
| 1299 | { |
---|
| 1300 | // 1st char of is not a varname |
---|
[d0340f] | 1301 | // We return the parsed polynomial nevertheless. This is needed when |
---|
| 1302 | // we are parsing coefficients in a rational function field. |
---|
[f34215] | 1303 | s--; |
---|
| 1304 | return s; |
---|
| 1305 | } |
---|
| 1306 | } |
---|
| 1307 | done: |
---|
[8a8c9e] | 1308 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
[f34215] | 1309 | else |
---|
| 1310 | { |
---|
| 1311 | #ifdef HAVE_PLURAL |
---|
| 1312 | // in super-commutative ring |
---|
| 1313 | // squares of anti-commutative variables are zeroes! |
---|
| 1314 | if(rIsSCA(r)) |
---|
| 1315 | { |
---|
| 1316 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
| 1317 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
| 1318 | |
---|
| 1319 | assume(rc != NULL); |
---|
| 1320 | |
---|
| 1321 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
| 1322 | if( p_GetExp(rc, k, r) > 1 ) |
---|
| 1323 | { |
---|
| 1324 | p_LmDelete(&rc, r); |
---|
| 1325 | goto finish; |
---|
| 1326 | } |
---|
| 1327 | } |
---|
| 1328 | #endif |
---|
[71ba5b8] | 1329 | |
---|
[f34215] | 1330 | p_Setm(rc,r); |
---|
| 1331 | } |
---|
[71ba5b8] | 1332 | finish: |
---|
[f34215] | 1333 | return s; |
---|
| 1334 | } |
---|
| 1335 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
| 1336 | { |
---|
| 1337 | poly p; |
---|
| 1338 | const char *s=p_Read(st,p,r); |
---|
| 1339 | if (*s!='\0') |
---|
| 1340 | { |
---|
| 1341 | if ((s!=st)&&isdigit(st[0])) |
---|
| 1342 | { |
---|
| 1343 | errorreported=TRUE; |
---|
| 1344 | } |
---|
| 1345 | ok=FALSE; |
---|
| 1346 | p_Delete(&p,r); |
---|
| 1347 | return NULL; |
---|
| 1348 | } |
---|
| 1349 | #ifdef PDEBUG |
---|
| 1350 | _p_Test(p,r,PDEBUG); |
---|
| 1351 | #endif |
---|
| 1352 | ok=!errorreported; |
---|
| 1353 | return p; |
---|
| 1354 | } |
---|
| 1355 | |
---|
[35aab3] | 1356 | /*2 |
---|
| 1357 | * returns a polynomial representing the number n |
---|
| 1358 | * destroys n |
---|
| 1359 | */ |
---|
[107986] | 1360 | poly p_NSet(number n, const ring r) |
---|
[35aab3] | 1361 | { |
---|
[8a8c9e] | 1362 | if (n_IsZero(n,r->cf)) |
---|
[35aab3] | 1363 | { |
---|
[8a8c9e] | 1364 | n_Delete(&n, r->cf); |
---|
[35aab3] | 1365 | return NULL; |
---|
| 1366 | } |
---|
| 1367 | else |
---|
| 1368 | { |
---|
| 1369 | poly rc = p_Init(r); |
---|
| 1370 | pSetCoeff0(rc,n); |
---|
| 1371 | return rc; |
---|
| 1372 | } |
---|
| 1373 | } |
---|
[fb4075b] | 1374 | /*2 |
---|
[e5d267] | 1375 | * assumes that LM(a) = LM(b)*m, for some monomial m, |
---|
| 1376 | * returns the multiplicant m, |
---|
| 1377 | * leaves a and b unmodified |
---|
[fb4075b] | 1378 | */ |
---|
| 1379 | poly p_Divide(poly a, poly b, const ring r) |
---|
| 1380 | { |
---|
| 1381 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
| 1382 | int i; |
---|
[8a8c9e] | 1383 | poly result = p_Init(r); |
---|
[fb4075b] | 1384 | |
---|
| 1385 | for(i=(int)r->N; i; i--) |
---|
| 1386 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
| 1387 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
| 1388 | p_Setm(result,r); |
---|
| 1389 | return result; |
---|
| 1390 | } |
---|
| 1391 | |
---|
[8a8c9e] | 1392 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
| 1393 | { |
---|
[45d2332] | 1394 | pAssume(!n_IsZero(n,r->cf)); |
---|
[8a8c9e] | 1395 | p_Test(p, r); |
---|
| 1396 | |
---|
| 1397 | poly q = p; |
---|
| 1398 | while (p != NULL) |
---|
| 1399 | { |
---|
| 1400 | number nc = pGetCoeff(p); |
---|
| 1401 | pSetCoeff0(p, n_Div(nc, n, r->cf)); |
---|
| 1402 | n_Delete(&nc, r->cf); |
---|
| 1403 | pIter(p); |
---|
| 1404 | } |
---|
| 1405 | p_Test(q, r); |
---|
| 1406 | return q; |
---|
| 1407 | } |
---|
| 1408 | |
---|
[fb4075b] | 1409 | /*2 |
---|
| 1410 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
[e432a0] | 1411 | * assumes that b is not NULL, destroyes b |
---|
[fb4075b] | 1412 | */ |
---|
| 1413 | poly p_DivideM(poly a, poly b, const ring r) |
---|
| 1414 | { |
---|
[e432a0] | 1415 | if (a==NULL) { p_Delete(&b,r); return NULL; } |
---|
[fb4075b] | 1416 | poly result=a; |
---|
| 1417 | poly prev=NULL; |
---|
| 1418 | int i; |
---|
| 1419 | #ifdef HAVE_RINGS |
---|
| 1420 | number inv=pGetCoeff(b); |
---|
| 1421 | #else |
---|
| 1422 | number inv=n_Invers(pGetCoeff(b),r->cf); |
---|
| 1423 | #endif |
---|
| 1424 | |
---|
| 1425 | while (a!=NULL) |
---|
| 1426 | { |
---|
| 1427 | if (p_DivisibleBy(b,a,r)) |
---|
| 1428 | { |
---|
| 1429 | for(i=(int)r->N; i; i--) |
---|
| 1430 | p_SubExp(a,i, p_GetExp(b,i,r),r); |
---|
| 1431 | p_SubComp(a, p_GetComp(b,r),r); |
---|
| 1432 | p_Setm(a,r); |
---|
| 1433 | prev=a; |
---|
| 1434 | pIter(a); |
---|
| 1435 | } |
---|
| 1436 | else |
---|
| 1437 | { |
---|
| 1438 | if (prev==NULL) |
---|
| 1439 | { |
---|
[8a8c9e] | 1440 | p_LmDelete(&result,r); |
---|
[fb4075b] | 1441 | a=result; |
---|
| 1442 | } |
---|
| 1443 | else |
---|
| 1444 | { |
---|
[8a8c9e] | 1445 | p_LmDelete(&pNext(prev),r); |
---|
[fb4075b] | 1446 | a=pNext(prev); |
---|
| 1447 | } |
---|
| 1448 | } |
---|
| 1449 | } |
---|
| 1450 | #ifdef HAVE_RINGS |
---|
| 1451 | if (n_IsUnit(inv,r->cf)) |
---|
| 1452 | { |
---|
| 1453 | inv = n_Invers(inv,r->cf); |
---|
| 1454 | p_Mult_nn(result,inv,r); |
---|
| 1455 | n_Delete(&inv, r->cf); |
---|
| 1456 | } |
---|
| 1457 | else |
---|
| 1458 | { |
---|
| 1459 | p_Div_nn(result,inv,r); |
---|
| 1460 | } |
---|
| 1461 | #else |
---|
| 1462 | p_Mult_nn(result,inv,r); |
---|
| 1463 | n_Delete(&inv, r->cf); |
---|
| 1464 | #endif |
---|
| 1465 | p_Delete(&b, r); |
---|
| 1466 | return result; |
---|
| 1467 | } |
---|
[35aab3] | 1468 | |
---|
[3d0808] | 1469 | #ifdef HAVE_RINGS |
---|
| 1470 | /* TRUE iff LT(f) | LT(g) */ |
---|
| 1471 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
| 1472 | { |
---|
| 1473 | int exponent; |
---|
| 1474 | for(int i = (int)rVar(r); i>0; i--) |
---|
| 1475 | { |
---|
| 1476 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
| 1477 | if (exponent < 0) return FALSE; |
---|
| 1478 | } |
---|
| 1479 | return n_DivBy(pGetCoeff(g), pGetCoeff(f), r->cf); |
---|
| 1480 | } |
---|
| 1481 | #endif |
---|
| 1482 | |
---|
[a7ee69] | 1483 | /*2 |
---|
| 1484 | * returns the LCM of the head terms of a and b in *m |
---|
| 1485 | */ |
---|
| 1486 | void p_Lcm(poly a, poly b, poly m, const ring r) |
---|
| 1487 | { |
---|
| 1488 | int i; |
---|
| 1489 | for (i=rVar(r); i; i--) |
---|
| 1490 | { |
---|
| 1491 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
| 1492 | } |
---|
| 1493 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
| 1494 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
| 1495 | } |
---|
| 1496 | |
---|
[f0b01f] | 1497 | /* assumes that p and divisor are univariate polynomials in r, |
---|
[ba2359] | 1498 | mentioning the same variable; |
---|
| 1499 | assumes divisor != NULL; |
---|
[f0b01f] | 1500 | p may be NULL; |
---|
[ba2359] | 1501 | assumes a global monomial ordering in r; |
---|
[f0b01f] | 1502 | performs polynomial division of p by divisor: |
---|
| 1503 | - afterwards p contains the remainder of the division, i.e., |
---|
| 1504 | p_before = result * divisor + p_afterwards; |
---|
[ba2359] | 1505 | - if needResult == TRUE, then the method computes and returns 'result', |
---|
| 1506 | otherwise NULL is returned (This parametrization can be used when |
---|
| 1507 | one is only interested in the remainder of the division. In this |
---|
[f0b01f] | 1508 | case, the method will be slightly faster.) |
---|
| 1509 | leaves divisor unmodified */ |
---|
| 1510 | poly p_PolyDiv(poly &p, poly divisor, BOOLEAN needResult, ring r) |
---|
[ba2359] | 1511 | { |
---|
| 1512 | assume(divisor != NULL); |
---|
[f0b01f] | 1513 | if (p == NULL) return NULL; |
---|
[f93c5e9] | 1514 | |
---|
[69fb9d0] | 1515 | poly result = NULL; |
---|
[f0b01f] | 1516 | number divisorLC = p_GetCoeff(divisor, r); |
---|
| 1517 | int divisorLE = p_GetExp(divisor, 1, r); |
---|
[c28ecf] | 1518 | while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r))) |
---|
[69fb9d0] | 1519 | { |
---|
[f0b01f] | 1520 | /* determine t = LT(p) / LT(divisor) */ |
---|
[69fb9d0] | 1521 | poly t = p_ISet(1, r); |
---|
[f0b01f] | 1522 | number c = n_Div(p_GetCoeff(p, r), divisorLC, r->cf); |
---|
[69fb9d0] | 1523 | p_SetCoeff(t, c, r); |
---|
[f0b01f] | 1524 | int e = p_GetExp(p, 1, r) - divisorLE; |
---|
[69fb9d0] | 1525 | p_SetExp(t, 1, e, r); |
---|
| 1526 | p_Setm(t, r); |
---|
[f0b01f] | 1527 | if (needResult) result = p_Add_q(result, p_Copy(t, r), r); |
---|
| 1528 | p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r); |
---|
[69fb9d0] | 1529 | } |
---|
| 1530 | return result; |
---|
| 1531 | } |
---|
| 1532 | |
---|
[c28ecf] | 1533 | /* returns NULL if p == NULL, otherwise makes p monic by dividing |
---|
| 1534 | by its leading coefficient (only done if this is not already 1); |
---|
| 1535 | this assumes that we are over a ground field so that division |
---|
| 1536 | is well-defined; |
---|
| 1537 | modifies p */ |
---|
[90aec7] | 1538 | void p_Monic(poly p, const ring r) |
---|
[c28ecf] | 1539 | { |
---|
| 1540 | if (p == NULL) return; |
---|
[90aec7] | 1541 | number n = n_Init(1, r->cf); |
---|
| 1542 | if (p->next==NULL) { p_SetCoeff(p,n,r); return; } |
---|
[c28ecf] | 1543 | poly pp = p; |
---|
| 1544 | number lc = p_GetCoeff(p, r); |
---|
| 1545 | if (n_IsOne(lc, r->cf)) return; |
---|
[cfb500] | 1546 | number lcInverse = n_Invers(lc, r->cf); |
---|
| 1547 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
[90aec7] | 1548 | pIter(p); |
---|
[c28ecf] | 1549 | while (p != NULL) |
---|
| 1550 | { |
---|
[cfb500] | 1551 | number n = n_Mult(p_GetCoeff(p, r), lcInverse, r->cf); |
---|
[90aec7] | 1552 | n_Normalize(n,r->cf); |
---|
[cfb500] | 1553 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
[05f61f] | 1554 | pIter(p); |
---|
[c28ecf] | 1555 | } |
---|
[cfb500] | 1556 | n_Delete(&lcInverse, r->cf); |
---|
[c28ecf] | 1557 | p = pp; |
---|
| 1558 | } |
---|
| 1559 | |
---|
[69fb9d0] | 1560 | /* see p_Gcd; |
---|
[f0b01f] | 1561 | additional assumption: deg(p) >= deg(q); |
---|
| 1562 | must destroy p and q (unless one of them is returned) */ |
---|
| 1563 | poly p_GcdHelper(poly &p, poly &q, ring r) |
---|
[69fb9d0] | 1564 | { |
---|
[c28ecf] | 1565 | if (q == NULL) |
---|
| 1566 | { |
---|
| 1567 | /* We have to make p monic before we return it, so that if the |
---|
| 1568 | gcd is a unit in the ground field, we will actually return 1. */ |
---|
| 1569 | p_Monic(p, r); |
---|
| 1570 | return p; |
---|
| 1571 | } |
---|
[69fb9d0] | 1572 | else |
---|
| 1573 | { |
---|
[f0b01f] | 1574 | p_PolyDiv(p, q, FALSE, r); |
---|
[69fb9d0] | 1575 | return p_GcdHelper(q, p, r); |
---|
| 1576 | } |
---|
[ba2359] | 1577 | } |
---|
| 1578 | |
---|
| 1579 | /* assumes that p and q are univariate polynomials in r, |
---|
| 1580 | mentioning the same variable; |
---|
| 1581 | assumes a global monomial ordering in r; |
---|
| 1582 | assumes that not both p and q are NULL; |
---|
[69fb9d0] | 1583 | returns the gcd of p and q; |
---|
| 1584 | leaves p and q unmodified */ |
---|
[ba2359] | 1585 | poly p_Gcd(poly p, poly q, ring r) |
---|
| 1586 | { |
---|
| 1587 | assume((p != NULL) || (q != NULL)); |
---|
[f93c5e9] | 1588 | |
---|
[69fb9d0] | 1589 | poly a = p; poly b = q; |
---|
| 1590 | if (p_Deg(a, r) < p_Deg(b, r)) { a = q; b = p; } |
---|
| 1591 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
[f0b01f] | 1592 | return p_GcdHelper(a, b, r); |
---|
[69fb9d0] | 1593 | } |
---|
| 1594 | |
---|
| 1595 | /* see p_ExtGcd; |
---|
[f0b01f] | 1596 | additional assumption: deg(p) >= deg(q); |
---|
| 1597 | must destroy p and q (unless one of them is returned) */ |
---|
| 1598 | poly p_ExtGcdHelper(poly &p, poly &pFactor, poly &q, poly &qFactor, |
---|
[69fb9d0] | 1599 | ring r) |
---|
| 1600 | { |
---|
| 1601 | if (q == NULL) |
---|
| 1602 | { |
---|
[c28ecf] | 1603 | qFactor = NULL; |
---|
| 1604 | pFactor = p_ISet(1, r); |
---|
| 1605 | p_SetCoeff(pFactor, n_Invers(p_GetCoeff(p, r), r->cf), r); |
---|
| 1606 | p_Monic(p, r); |
---|
| 1607 | return p; |
---|
[69fb9d0] | 1608 | } |
---|
| 1609 | else |
---|
| 1610 | { |
---|
[f0b01f] | 1611 | poly pDivQ = p_PolyDiv(p, q, TRUE, r); |
---|
[c28ecf] | 1612 | poly ppFactor = NULL; poly qqFactor = NULL; |
---|
| 1613 | poly theGcd = p_ExtGcdHelper(q, qqFactor, p, ppFactor, r); |
---|
| 1614 | pFactor = ppFactor; |
---|
| 1615 | qFactor = p_Add_q(qqFactor, |
---|
| 1616 | p_Neg(p_Mult_q(pDivQ, p_Copy(ppFactor, r), r), r), |
---|
[f0b01f] | 1617 | r); |
---|
[69fb9d0] | 1618 | return theGcd; |
---|
| 1619 | } |
---|
[ba2359] | 1620 | } |
---|
| 1621 | |
---|
| 1622 | /* assumes that p and q are univariate polynomials in r, |
---|
| 1623 | mentioning the same variable; |
---|
| 1624 | assumes a global monomial ordering in r; |
---|
| 1625 | assumes that not both p and q are NULL; |
---|
| 1626 | returns the gcd of p and q; |
---|
[f0b01f] | 1627 | moreover, afterwards pFactor and qFactor contain appropriate |
---|
| 1628 | factors such that gcd(p, q) = p * pFactor + q * qFactor; |
---|
[69fb9d0] | 1629 | leaves p and q unmodified */ |
---|
[f0b01f] | 1630 | poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r) |
---|
[ba2359] | 1631 | { |
---|
[f93c5e9] | 1632 | assume((p != NULL) || (q != NULL)); |
---|
[c28ecf] | 1633 | poly a = p; poly b = q; BOOLEAN aCorrespondsToP = TRUE; |
---|
[69fb9d0] | 1634 | if (p_Deg(a, r) < p_Deg(b, r)) |
---|
[c28ecf] | 1635 | { a = q; b = p; aCorrespondsToP = FALSE; } |
---|
[69fb9d0] | 1636 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
[c28ecf] | 1637 | poly aFactor = NULL; poly bFactor = NULL; |
---|
| 1638 | poly theGcd = p_ExtGcdHelper(a, aFactor, b, bFactor, r); |
---|
| 1639 | if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; } |
---|
| 1640 | else { pFactor = bFactor; qFactor = aFactor; } |
---|
| 1641 | return theGcd; |
---|
[ba2359] | 1642 | } |
---|
| 1643 | |
---|
[ac0bd6] | 1644 | /*2 |
---|
| 1645 | * returns the partial differentiate of a by the k-th variable |
---|
| 1646 | * does not destroy the input |
---|
| 1647 | */ |
---|
| 1648 | poly p_Diff(poly a, int k, const ring r) |
---|
| 1649 | { |
---|
| 1650 | poly res, f, last; |
---|
| 1651 | number t; |
---|
| 1652 | |
---|
| 1653 | last = res = NULL; |
---|
| 1654 | while (a!=NULL) |
---|
| 1655 | { |
---|
| 1656 | if (p_GetExp(a,k,r)!=0) |
---|
| 1657 | { |
---|
| 1658 | f = p_LmInit(a,r); |
---|
| 1659 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
| 1660 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
| 1661 | n_Delete(&t,r->cf); |
---|
| 1662 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
| 1663 | p_LmDelete(&f,r); |
---|
| 1664 | else |
---|
| 1665 | { |
---|
| 1666 | p_DecrExp(f,k,r); |
---|
| 1667 | p_Setm(f,r); |
---|
| 1668 | if (res==NULL) |
---|
| 1669 | { |
---|
| 1670 | res=last=f; |
---|
| 1671 | } |
---|
| 1672 | else |
---|
| 1673 | { |
---|
| 1674 | pNext(last)=f; |
---|
| 1675 | last=f; |
---|
| 1676 | } |
---|
| 1677 | } |
---|
| 1678 | } |
---|
| 1679 | pIter(a); |
---|
| 1680 | } |
---|
| 1681 | return res; |
---|
| 1682 | } |
---|
[5162db] | 1683 | |
---|
[8a8c9e] | 1684 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
[5162db] | 1685 | { |
---|
| 1686 | int i,j,s; |
---|
| 1687 | number n,h,hh; |
---|
| 1688 | poly p=p_One(r); |
---|
| 1689 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
| 1690 | for(i=rVar(r);i>0;i--) |
---|
| 1691 | { |
---|
| 1692 | s=p_GetExp(b,i,r); |
---|
| 1693 | if (s<p_GetExp(a,i,r)) |
---|
| 1694 | { |
---|
| 1695 | n_Delete(&n,r->cf); |
---|
| 1696 | p_LmDelete(&p,r); |
---|
| 1697 | return NULL; |
---|
| 1698 | } |
---|
| 1699 | if (multiply) |
---|
| 1700 | { |
---|
| 1701 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
| 1702 | { |
---|
| 1703 | h = n_Init(s,r->cf); |
---|
| 1704 | hh=n_Mult(n,h,r->cf); |
---|
| 1705 | n_Delete(&h,r->cf); |
---|
| 1706 | n_Delete(&n,r->cf); |
---|
| 1707 | n=hh; |
---|
| 1708 | s--; |
---|
| 1709 | } |
---|
| 1710 | p_SetExp(p,i,s,r); |
---|
| 1711 | } |
---|
| 1712 | else |
---|
| 1713 | { |
---|
| 1714 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
| 1715 | } |
---|
| 1716 | } |
---|
| 1717 | p_Setm(p,r); |
---|
| 1718 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
| 1719 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
| 1720 | return p; |
---|
| 1721 | } |
---|
| 1722 | |
---|
| 1723 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
| 1724 | { |
---|
| 1725 | poly result=NULL; |
---|
| 1726 | poly h; |
---|
| 1727 | for(;a!=NULL;pIter(a)) |
---|
| 1728 | { |
---|
| 1729 | for(h=b;h!=NULL;pIter(h)) |
---|
| 1730 | { |
---|
| 1731 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
| 1732 | } |
---|
| 1733 | } |
---|
| 1734 | return result; |
---|
| 1735 | } |
---|
[bf183f] | 1736 | /*2 |
---|
| 1737 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
| 1738 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
| 1739 | */ |
---|
| 1740 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
| 1741 | { |
---|
| 1742 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
| 1743 | } |
---|
| 1744 | |
---|
| 1745 | /*3 |
---|
| 1746 | * compute for a monomial m |
---|
| 1747 | * the power m^exp, exp > 1 |
---|
| 1748 | * destroys p |
---|
| 1749 | */ |
---|
| 1750 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
| 1751 | { |
---|
| 1752 | int i; |
---|
| 1753 | |
---|
[8a8c9e] | 1754 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
[bf183f] | 1755 | { |
---|
| 1756 | number x, y; |
---|
| 1757 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1758 | n_Power(y,exp,&x,r->cf); |
---|
| 1759 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1760 | pSetCoeff0(p,x); |
---|
| 1761 | } |
---|
| 1762 | for (i=rVar(r); i!=0; i--) |
---|
| 1763 | { |
---|
| 1764 | p_MultExp(p,i, exp,r); |
---|
| 1765 | } |
---|
| 1766 | p_Setm(p,r); |
---|
| 1767 | return p; |
---|
| 1768 | } |
---|
| 1769 | |
---|
| 1770 | /*3 |
---|
| 1771 | * compute for monomials p*q |
---|
| 1772 | * destroys p, keeps q |
---|
| 1773 | */ |
---|
| 1774 | static void p_MonMult(poly p, poly q, const ring r) |
---|
| 1775 | { |
---|
| 1776 | number x, y; |
---|
| 1777 | |
---|
| 1778 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1779 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
| 1780 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1781 | pSetCoeff0(p,x); |
---|
[abb4787] | 1782 | //for (int i=pVariables; i!=0; i--) |
---|
[bf183f] | 1783 | //{ |
---|
| 1784 | // pAddExp(p,i, pGetExp(q,i)); |
---|
| 1785 | //} |
---|
| 1786 | //p->Order += q->Order; |
---|
| 1787 | p_ExpVectorAdd(p,q,r); |
---|
| 1788 | } |
---|
| 1789 | |
---|
| 1790 | /*3 |
---|
| 1791 | * compute for monomials p*q |
---|
| 1792 | * keeps p, q |
---|
| 1793 | */ |
---|
| 1794 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
| 1795 | { |
---|
| 1796 | number x; |
---|
| 1797 | poly r = p_Init(rr); |
---|
| 1798 | |
---|
[8a8c9e] | 1799 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
[bf183f] | 1800 | pSetCoeff0(r,x); |
---|
| 1801 | p_ExpVectorSum(r,p, q, rr); |
---|
| 1802 | return r; |
---|
| 1803 | } |
---|
| 1804 | |
---|
[5679049] | 1805 | /*3 |
---|
| 1806 | * create binomial coef. |
---|
| 1807 | */ |
---|
| 1808 | static number* pnBin(int exp, const ring r) |
---|
| 1809 | { |
---|
| 1810 | int e, i, h; |
---|
| 1811 | number x, y, *bin=NULL; |
---|
| 1812 | |
---|
| 1813 | x = n_Init(exp,r->cf); |
---|
| 1814 | if (n_IsZero(x,r->cf)) |
---|
| 1815 | { |
---|
| 1816 | n_Delete(&x,r->cf); |
---|
| 1817 | return bin; |
---|
| 1818 | } |
---|
| 1819 | h = (exp >> 1) + 1; |
---|
| 1820 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
| 1821 | bin[1] = x; |
---|
| 1822 | if (exp < 4) |
---|
| 1823 | return bin; |
---|
| 1824 | i = exp - 1; |
---|
| 1825 | for (e=2; e<h; e++) |
---|
| 1826 | { |
---|
| 1827 | x = n_Init(i,r->cf); |
---|
| 1828 | i--; |
---|
| 1829 | y = n_Mult(x,bin[e-1],r->cf); |
---|
| 1830 | n_Delete(&x,r->cf); |
---|
| 1831 | x = n_Init(e,r->cf); |
---|
| 1832 | bin[e] = n_IntDiv(y,x,r->cf); |
---|
| 1833 | n_Delete(&x,r->cf); |
---|
| 1834 | n_Delete(&y,r->cf); |
---|
| 1835 | } |
---|
| 1836 | return bin; |
---|
| 1837 | } |
---|
| 1838 | |
---|
[1389a4] | 1839 | static void pnFreeBin(number *bin, int exp,const coeffs r) |
---|
| 1840 | { |
---|
| 1841 | int e, h = (exp >> 1) + 1; |
---|
| 1842 | |
---|
| 1843 | if (bin[1] != NULL) |
---|
| 1844 | { |
---|
| 1845 | for (e=1; e<h; e++) |
---|
| 1846 | n_Delete(&(bin[e]),r); |
---|
| 1847 | } |
---|
| 1848 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
---|
| 1849 | } |
---|
| 1850 | |
---|
[bf183f] | 1851 | /* |
---|
| 1852 | * compute for a poly p = head+tail, tail is monomial |
---|
| 1853 | * (head + tail)^exp, exp > 1 |
---|
| 1854 | * with binomial coef. |
---|
| 1855 | */ |
---|
| 1856 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
| 1857 | { |
---|
| 1858 | int eh, e; |
---|
| 1859 | long al; |
---|
| 1860 | poly *a; |
---|
| 1861 | poly tail, b, res, h; |
---|
| 1862 | number x; |
---|
[7eb7b5] | 1863 | number *bin = pnBin(exp,r); |
---|
[bf183f] | 1864 | |
---|
| 1865 | tail = pNext(p); |
---|
| 1866 | if (bin == NULL) |
---|
| 1867 | { |
---|
| 1868 | p_MonPower(p,exp,r); |
---|
| 1869 | p_MonPower(tail,exp,r); |
---|
| 1870 | #ifdef PDEBUG |
---|
| 1871 | p_Test(p,r); |
---|
| 1872 | #endif |
---|
| 1873 | return p; |
---|
| 1874 | } |
---|
| 1875 | eh = exp >> 1; |
---|
| 1876 | al = (exp + 1) * sizeof(poly); |
---|
| 1877 | a = (poly *)omAlloc(al); |
---|
| 1878 | a[1] = p; |
---|
| 1879 | for (e=1; e<exp; e++) |
---|
| 1880 | { |
---|
| 1881 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
| 1882 | } |
---|
| 1883 | res = a[exp]; |
---|
| 1884 | b = p_Head(tail,r); |
---|
| 1885 | for (e=exp-1; e>eh; e--) |
---|
| 1886 | { |
---|
| 1887 | h = a[e]; |
---|
[8a8c9e] | 1888 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1889 | p_SetCoeff(h,x,r); |
---|
| 1890 | p_MonMult(h,b,r); |
---|
| 1891 | res = pNext(res) = h; |
---|
| 1892 | p_MonMult(b,tail,r); |
---|
| 1893 | } |
---|
| 1894 | for (e=eh; e!=0; e--) |
---|
| 1895 | { |
---|
| 1896 | h = a[e]; |
---|
[8a8c9e] | 1897 | x = n_Mult(bin[e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1898 | p_SetCoeff(h,x,r); |
---|
| 1899 | p_MonMult(h,b,r); |
---|
| 1900 | res = pNext(res) = h; |
---|
| 1901 | p_MonMult(b,tail,r); |
---|
| 1902 | } |
---|
| 1903 | p_LmDelete(&tail,r); |
---|
| 1904 | pNext(res) = b; |
---|
| 1905 | pNext(b) = NULL; |
---|
| 1906 | res = a[exp]; |
---|
| 1907 | omFreeSize((ADDRESS)a, al); |
---|
[1389a4] | 1908 | pnFreeBin(bin, exp, r->cf); |
---|
[bf183f] | 1909 | // tail=res; |
---|
| 1910 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
| 1911 | // { |
---|
| 1912 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
| 1913 | // { |
---|
| 1914 | // pLmDelete(&pNext(tail)); |
---|
| 1915 | // } |
---|
| 1916 | // else |
---|
| 1917 | // pIter(tail); |
---|
| 1918 | // } |
---|
| 1919 | #ifdef PDEBUG |
---|
| 1920 | p_Test(res,r); |
---|
| 1921 | #endif |
---|
| 1922 | return res; |
---|
| 1923 | } |
---|
| 1924 | |
---|
| 1925 | static poly p_Pow(poly p, int i, const ring r) |
---|
| 1926 | { |
---|
| 1927 | poly rc = p_Copy(p,r); |
---|
| 1928 | i -= 2; |
---|
| 1929 | do |
---|
| 1930 | { |
---|
| 1931 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
| 1932 | p_Normalize(rc,r); |
---|
| 1933 | i--; |
---|
| 1934 | } |
---|
| 1935 | while (i != 0); |
---|
| 1936 | return p_Mult_q(rc,p,r); |
---|
| 1937 | } |
---|
| 1938 | |
---|
| 1939 | /*2 |
---|
| 1940 | * returns the i-th power of p |
---|
| 1941 | * p will be destroyed |
---|
| 1942 | */ |
---|
| 1943 | poly p_Power(poly p, int i, const ring r) |
---|
| 1944 | { |
---|
| 1945 | poly rc=NULL; |
---|
| 1946 | |
---|
| 1947 | if (i==0) |
---|
| 1948 | { |
---|
| 1949 | p_Delete(&p,r); |
---|
| 1950 | return p_One(r); |
---|
| 1951 | } |
---|
| 1952 | |
---|
| 1953 | if(p!=NULL) |
---|
| 1954 | { |
---|
| 1955 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask))) |
---|
| 1956 | { |
---|
| 1957 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
| 1958 | return NULL; |
---|
| 1959 | } |
---|
| 1960 | switch (i) |
---|
| 1961 | { |
---|
| 1962 | // cannot happen, see above |
---|
| 1963 | // case 0: |
---|
| 1964 | // { |
---|
| 1965 | // rc=pOne(); |
---|
| 1966 | // pDelete(&p); |
---|
| 1967 | // break; |
---|
| 1968 | // } |
---|
| 1969 | case 1: |
---|
| 1970 | rc=p; |
---|
| 1971 | break; |
---|
| 1972 | case 2: |
---|
| 1973 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
| 1974 | break; |
---|
| 1975 | default: |
---|
| 1976 | if (i < 0) |
---|
| 1977 | { |
---|
| 1978 | p_Delete(&p,r); |
---|
| 1979 | return NULL; |
---|
| 1980 | } |
---|
| 1981 | else |
---|
| 1982 | { |
---|
| 1983 | #ifdef HAVE_PLURAL |
---|
| 1984 | if (rIsPluralRing(r)) /* in the NC case nothing helps :-( */ |
---|
| 1985 | { |
---|
| 1986 | int j=i; |
---|
| 1987 | rc = p_Copy(p,r); |
---|
| 1988 | while (j>1) |
---|
| 1989 | { |
---|
| 1990 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
| 1991 | j--; |
---|
| 1992 | } |
---|
| 1993 | p_Delete(&p,r); |
---|
| 1994 | return rc; |
---|
| 1995 | } |
---|
| 1996 | #endif |
---|
| 1997 | rc = pNext(p); |
---|
| 1998 | if (rc == NULL) |
---|
| 1999 | return p_MonPower(p,i,r); |
---|
| 2000 | /* else: binom ?*/ |
---|
| 2001 | int char_p=rChar(r); |
---|
| 2002 | if ((pNext(rc) != NULL) |
---|
| 2003 | #ifdef HAVE_RINGS |
---|
| 2004 | || rField_is_Ring(r) |
---|
| 2005 | #endif |
---|
| 2006 | ) |
---|
| 2007 | return p_Pow(p,i,r); |
---|
| 2008 | if ((char_p==0) || (i<=char_p)) |
---|
| 2009 | return p_TwoMonPower(p,i,r); |
---|
[131ab78] | 2010 | return p_Pow(p,i,r); |
---|
[bf183f] | 2011 | } |
---|
| 2012 | /*end default:*/ |
---|
| 2013 | } |
---|
| 2014 | } |
---|
| 2015 | return rc; |
---|
| 2016 | } |
---|
[8d1d30c] | 2017 | |
---|
| 2018 | /* --------------------------------------------------------------------------------*/ |
---|
| 2019 | /* content suff */ |
---|
| 2020 | |
---|
| 2021 | static number p_InitContent(poly ph, const ring r); |
---|
| 2022 | |
---|
| 2023 | void p_Content(poly ph, const ring r) |
---|
| 2024 | { |
---|
[975db18] | 2025 | #if 0 |
---|
| 2026 | if( ph != NULL ) |
---|
| 2027 | { |
---|
| 2028 | CPolyCoeffsEnumerator itr(ph); |
---|
| 2029 | n_ClearContent(itr, r->cf); |
---|
| 2030 | // return; |
---|
| 2031 | } |
---|
| 2032 | #endif |
---|
| 2033 | |
---|
| 2034 | |
---|
[8d1d30c] | 2035 | #ifdef HAVE_RINGS |
---|
| 2036 | if (rField_is_Ring(r)) |
---|
| 2037 | { |
---|
| 2038 | if ((ph!=NULL) && rField_has_Units(r)) |
---|
| 2039 | { |
---|
[8a8c9e] | 2040 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
[8d1d30c] | 2041 | if (!n_IsOne(k,r->cf)) |
---|
| 2042 | { |
---|
| 2043 | number tmpGMP = k; |
---|
| 2044 | k = n_Invers(k,r->cf); |
---|
| 2045 | n_Delete(&tmpGMP,r->cf); |
---|
| 2046 | poly h = pNext(ph); |
---|
| 2047 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
| 2048 | while (h != NULL) |
---|
| 2049 | { |
---|
| 2050 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
| 2051 | pIter(h); |
---|
| 2052 | } |
---|
| 2053 | } |
---|
| 2054 | n_Delete(&k,r->cf); |
---|
| 2055 | } |
---|
| 2056 | return; |
---|
| 2057 | } |
---|
| 2058 | #endif |
---|
| 2059 | number h,d; |
---|
| 2060 | poly p; |
---|
| 2061 | |
---|
| 2062 | if(TEST_OPT_CONTENTSB) return; |
---|
| 2063 | if(pNext(ph)==NULL) |
---|
| 2064 | { |
---|
[8a8c9e] | 2065 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
[8d1d30c] | 2066 | } |
---|
| 2067 | else |
---|
| 2068 | { |
---|
| 2069 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 2070 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8a8c9e] | 2071 | if (rField_is_Q(r)) |
---|
[8d1d30c] | 2072 | { |
---|
| 2073 | h=p_InitContent(ph,r); |
---|
| 2074 | p=ph; |
---|
| 2075 | } |
---|
| 2076 | else |
---|
| 2077 | { |
---|
| 2078 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2079 | p = pNext(ph); |
---|
| 2080 | } |
---|
| 2081 | while (p!=NULL) |
---|
| 2082 | { |
---|
| 2083 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2084 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2085 | n_Delete(&h,r->cf); |
---|
| 2086 | h = d; |
---|
| 2087 | if(n_IsOne(h,r->cf)) |
---|
| 2088 | { |
---|
| 2089 | break; |
---|
| 2090 | } |
---|
| 2091 | pIter(p); |
---|
| 2092 | } |
---|
| 2093 | p = ph; |
---|
| 2094 | //number tmp; |
---|
| 2095 | if(!n_IsOne(h,r->cf)) |
---|
| 2096 | { |
---|
| 2097 | while (p!=NULL) |
---|
| 2098 | { |
---|
| 2099 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2100 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2101 | //if (!nEqual(d,tmp)) |
---|
| 2102 | //{ |
---|
| 2103 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2104 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
| 2105 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
| 2106 | //} |
---|
| 2107 | //nDelete(&tmp); |
---|
| 2108 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2109 | p_SetCoeff(p,d,r); |
---|
| 2110 | pIter(p); |
---|
| 2111 | } |
---|
| 2112 | } |
---|
| 2113 | n_Delete(&h,r->cf); |
---|
| 2114 | #ifdef HAVE_FACTORY |
---|
[aa98be] | 2115 | // if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2116 | // { |
---|
| 2117 | // singclap_divide_content(ph, r); |
---|
| 2118 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2119 | // } |
---|
[8d1d30c] | 2120 | #endif |
---|
| 2121 | if (rField_is_Q_a(r)) |
---|
| 2122 | { |
---|
[aa98be] | 2123 | // we only need special handling for alg. ext. |
---|
| 2124 | if (getCoeffType(r->cf)==n_algExt) |
---|
[8d1d30c] | 2125 | { |
---|
[aa98be] | 2126 | number hzz = n_Init(1, r->cf->extRing->cf); |
---|
[8d1d30c] | 2127 | p=ph; |
---|
| 2128 | while (p!=NULL) |
---|
| 2129 | { // each monom: coeff in Q_a |
---|
[aa98be] | 2130 | poly c_n_n=(poly)pGetCoeff(p); |
---|
| 2131 | poly c_n=c_n_n; |
---|
[8d1d30c] | 2132 | while (c_n!=NULL) |
---|
| 2133 | { // each monom: coeff in Q |
---|
[aa98be] | 2134 | d=n_Lcm(hzz,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2135 | n_Delete(&hzz,r->cf->extRing->cf); |
---|
| 2136 | hzz=d; |
---|
[8d1d30c] | 2137 | pIter(c_n); |
---|
| 2138 | } |
---|
[90aec7] | 2139 | pIter(p); |
---|
[aa98be] | 2140 | } |
---|
| 2141 | /* hzz contains the 1/lcm of all denominators in c_n_n*/ |
---|
| 2142 | h=n_Invers(hzz,r->cf->extRing->cf); |
---|
| 2143 | n_Delete(&hzz,r->cf->extRing->cf); |
---|
| 2144 | n_Normalize(h,r->cf->extRing->cf); |
---|
| 2145 | if(!n_IsOne(h,r->cf->extRing->cf)) |
---|
| 2146 | { |
---|
| 2147 | p=ph; |
---|
| 2148 | while (p!=NULL) |
---|
| 2149 | { // each monom: coeff in Q_a |
---|
| 2150 | poly c_n=(poly)pGetCoeff(p); |
---|
| 2151 | while (c_n!=NULL) |
---|
| 2152 | { // each monom: coeff in Q |
---|
| 2153 | d=n_Mult(h,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2154 | n_Normalize(d,r->cf->extRing->cf); |
---|
| 2155 | n_Delete(&pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2156 | pGetCoeff(c_n)=d; |
---|
| 2157 | pIter(c_n); |
---|
| 2158 | } |
---|
| 2159 | pIter(p); |
---|
[8d1d30c] | 2160 | } |
---|
| 2161 | } |
---|
[aa98be] | 2162 | n_Delete(&h,r->cf->extRing->cf); |
---|
[8d1d30c] | 2163 | } |
---|
| 2164 | } |
---|
| 2165 | } |
---|
[f9a64e] | 2166 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8d1d30c] | 2167 | } |
---|
[e48172] | 2168 | |
---|
| 2169 | // Not yet? |
---|
| 2170 | #if 1 // currently only used by Singular/janet |
---|
| 2171 | void p_SimpleContent(poly ph, int smax, const ring r) |
---|
[8d1d30c] | 2172 | { |
---|
| 2173 | if(TEST_OPT_CONTENTSB) return; |
---|
| 2174 | if (ph==NULL) return; |
---|
| 2175 | if (pNext(ph)==NULL) |
---|
| 2176 | { |
---|
[e48172] | 2177 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
[8d1d30c] | 2178 | return; |
---|
| 2179 | } |
---|
| 2180 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
| 2181 | { |
---|
| 2182 | return; |
---|
| 2183 | } |
---|
| 2184 | number d=p_InitContent(ph,r); |
---|
[e48172] | 2185 | if (n_Size(d,r->cf)<=smax) |
---|
[8d1d30c] | 2186 | { |
---|
| 2187 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
| 2188 | return; |
---|
| 2189 | } |
---|
[e48172] | 2190 | |
---|
[f93c5e9] | 2191 | |
---|
[8d1d30c] | 2192 | poly p=ph; |
---|
| 2193 | number h=d; |
---|
| 2194 | if (smax==1) smax=2; |
---|
| 2195 | while (p!=NULL) |
---|
| 2196 | { |
---|
| 2197 | #if 0 |
---|
| 2198 | d=nlGcd(h,pGetCoeff(p),r->cf); |
---|
| 2199 | nlDelete(&h,r->cf); |
---|
| 2200 | h = d; |
---|
| 2201 | #else |
---|
| 2202 | nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
| 2203 | #endif |
---|
| 2204 | if(nlSize(h,r->cf)<smax) |
---|
| 2205 | { |
---|
| 2206 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
| 2207 | return; |
---|
| 2208 | } |
---|
| 2209 | pIter(p); |
---|
| 2210 | } |
---|
| 2211 | p = ph; |
---|
| 2212 | if (!nlGreaterZero(pGetCoeff(p),r->cf)) h=nlNeg(h,r->cf); |
---|
| 2213 | if(nlIsOne(h,r->cf)) return; |
---|
| 2214 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
| 2215 | while (p!=NULL) |
---|
| 2216 | { |
---|
| 2217 | #if 1 |
---|
| 2218 | d = nlIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2219 | p_SetCoeff(p,d,r); |
---|
| 2220 | #else |
---|
| 2221 | nlInpIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2222 | #endif |
---|
| 2223 | pIter(p); |
---|
| 2224 | } |
---|
| 2225 | nlDelete(&h,r->cf); |
---|
| 2226 | } |
---|
[5698bb] | 2227 | #endif |
---|
[8d1d30c] | 2228 | |
---|
| 2229 | static number p_InitContent(poly ph, const ring r) |
---|
| 2230 | // only for coefficients in Q |
---|
| 2231 | #if 0 |
---|
| 2232 | { |
---|
| 2233 | assume(!TEST_OPT_CONTENTSB); |
---|
| 2234 | assume(ph!=NULL); |
---|
| 2235 | assume(pNext(ph)!=NULL); |
---|
| 2236 | assume(rField_is_Q(r)); |
---|
| 2237 | if (pNext(pNext(ph))==NULL) |
---|
| 2238 | { |
---|
| 2239 | return nlGetNom(pGetCoeff(pNext(ph)),r->cf); |
---|
| 2240 | } |
---|
| 2241 | poly p=ph; |
---|
| 2242 | number n1=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2243 | pIter(p); |
---|
| 2244 | number n2=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2245 | pIter(p); |
---|
| 2246 | number d; |
---|
| 2247 | number t; |
---|
| 2248 | loop |
---|
| 2249 | { |
---|
| 2250 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2251 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2252 | if (nlGreaterZero(t,r->cf)) |
---|
| 2253 | d=nlAdd(n1,t,r->cf); |
---|
| 2254 | else |
---|
| 2255 | d=nlSub(n1,t,r->cf); |
---|
| 2256 | nlDelete(&t,r->cf); |
---|
| 2257 | nlDelete(&n1,r->cf); |
---|
| 2258 | n1=d; |
---|
| 2259 | pIter(p); |
---|
| 2260 | if (p==NULL) break; |
---|
| 2261 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2262 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2263 | if (nlGreaterZero(t,r->cf)) |
---|
| 2264 | d=nlAdd(n2,t,r->cf); |
---|
| 2265 | else |
---|
| 2266 | d=nlSub(n2,t,r->cf); |
---|
| 2267 | nlDelete(&t,r->cf); |
---|
| 2268 | nlDelete(&n2,r->cf); |
---|
| 2269 | n2=d; |
---|
| 2270 | pIter(p); |
---|
| 2271 | if (p==NULL) break; |
---|
| 2272 | } |
---|
| 2273 | d=nlGcd(n1,n2,r->cf); |
---|
| 2274 | nlDelete(&n1,r->cf); |
---|
| 2275 | nlDelete(&n2,r->cf); |
---|
| 2276 | return d; |
---|
| 2277 | } |
---|
| 2278 | #else |
---|
| 2279 | { |
---|
| 2280 | number d=pGetCoeff(ph); |
---|
| 2281 | if(SR_HDL(d)&SR_INT) return d; |
---|
| 2282 | int s=mpz_size1(d->z); |
---|
| 2283 | int s2=-1; |
---|
| 2284 | number d2; |
---|
| 2285 | loop |
---|
| 2286 | { |
---|
| 2287 | pIter(ph); |
---|
| 2288 | if(ph==NULL) |
---|
| 2289 | { |
---|
| 2290 | if (s2==-1) return nlCopy(d,r->cf); |
---|
| 2291 | break; |
---|
| 2292 | } |
---|
| 2293 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
| 2294 | { |
---|
| 2295 | s2=s; |
---|
| 2296 | d2=d; |
---|
| 2297 | s=0; |
---|
| 2298 | d=pGetCoeff(ph); |
---|
| 2299 | if (s2==0) break; |
---|
| 2300 | } |
---|
| 2301 | else |
---|
| 2302 | if (mpz_size1((pGetCoeff(ph)->z))<=s) |
---|
| 2303 | { |
---|
| 2304 | s2=s; |
---|
| 2305 | d2=d; |
---|
| 2306 | d=pGetCoeff(ph); |
---|
| 2307 | s=mpz_size1(d->z); |
---|
| 2308 | } |
---|
| 2309 | } |
---|
| 2310 | return nlGcd(d,d2,r->cf); |
---|
| 2311 | } |
---|
| 2312 | #endif |
---|
| 2313 | |
---|
| 2314 | //void pContent(poly ph) |
---|
| 2315 | //{ |
---|
| 2316 | // number h,d; |
---|
| 2317 | // poly p; |
---|
| 2318 | // |
---|
| 2319 | // p = ph; |
---|
| 2320 | // if(pNext(p)==NULL) |
---|
| 2321 | // { |
---|
| 2322 | // pSetCoeff(p,nInit(1)); |
---|
| 2323 | // } |
---|
| 2324 | // else |
---|
| 2325 | // { |
---|
| 2326 | //#ifdef PDEBUG |
---|
| 2327 | // if (!pTest(p)) return; |
---|
| 2328 | //#endif |
---|
| 2329 | // nNormalize(pGetCoeff(p)); |
---|
| 2330 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
| 2331 | // { |
---|
| 2332 | // ph = pNeg(ph); |
---|
| 2333 | // nNormalize(pGetCoeff(p)); |
---|
| 2334 | // } |
---|
| 2335 | // h=pGetCoeff(p); |
---|
| 2336 | // pIter(p); |
---|
| 2337 | // while (p!=NULL) |
---|
| 2338 | // { |
---|
| 2339 | // nNormalize(pGetCoeff(p)); |
---|
| 2340 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
| 2341 | // pIter(p); |
---|
| 2342 | // } |
---|
| 2343 | // h=nCopy(h); |
---|
| 2344 | // p=ph; |
---|
| 2345 | // while (p!=NULL) |
---|
| 2346 | // { |
---|
[32d07a5] | 2347 | // d=n_Gcd(h,pGetCoeff(p)); |
---|
[8d1d30c] | 2348 | // nDelete(&h); |
---|
| 2349 | // h = d; |
---|
| 2350 | // if(nIsOne(h)) |
---|
| 2351 | // { |
---|
| 2352 | // break; |
---|
| 2353 | // } |
---|
| 2354 | // pIter(p); |
---|
| 2355 | // } |
---|
| 2356 | // p = ph; |
---|
| 2357 | // //number tmp; |
---|
| 2358 | // if(!nIsOne(h)) |
---|
| 2359 | // { |
---|
| 2360 | // while (p!=NULL) |
---|
| 2361 | // { |
---|
| 2362 | // d = nIntDiv(pGetCoeff(p),h); |
---|
| 2363 | // pSetCoeff(p,d); |
---|
| 2364 | // pIter(p); |
---|
| 2365 | // } |
---|
| 2366 | // } |
---|
| 2367 | // nDelete(&h); |
---|
| 2368 | //#ifdef HAVE_FACTORY |
---|
| 2369 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2370 | // { |
---|
| 2371 | // pTest(ph); |
---|
| 2372 | // singclap_divide_content(ph); |
---|
| 2373 | // pTest(ph); |
---|
| 2374 | // } |
---|
| 2375 | //#endif |
---|
| 2376 | // } |
---|
| 2377 | //} |
---|
| 2378 | #if 0 |
---|
| 2379 | void p_Content(poly ph, const ring r) |
---|
| 2380 | { |
---|
| 2381 | number h,d; |
---|
| 2382 | poly p; |
---|
| 2383 | |
---|
| 2384 | if(pNext(ph)==NULL) |
---|
| 2385 | { |
---|
| 2386 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
| 2387 | } |
---|
| 2388 | else |
---|
| 2389 | { |
---|
| 2390 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 2391 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2392 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2393 | p = pNext(ph); |
---|
| 2394 | while (p!=NULL) |
---|
| 2395 | { |
---|
| 2396 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2397 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2398 | n_Delete(&h,r->cf); |
---|
| 2399 | h = d; |
---|
| 2400 | if(n_IsOne(h,r->cf)) |
---|
| 2401 | { |
---|
| 2402 | break; |
---|
| 2403 | } |
---|
| 2404 | pIter(p); |
---|
| 2405 | } |
---|
| 2406 | p = ph; |
---|
| 2407 | //number tmp; |
---|
| 2408 | if(!n_IsOne(h,r->cf)) |
---|
| 2409 | { |
---|
| 2410 | while (p!=NULL) |
---|
| 2411 | { |
---|
| 2412 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2413 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2414 | //if (!nEqual(d,tmp)) |
---|
| 2415 | //{ |
---|
| 2416 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2417 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
| 2418 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
| 2419 | //} |
---|
| 2420 | //nDelete(&tmp); |
---|
| 2421 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2422 | p_SetCoeff(p,d,r->cf); |
---|
| 2423 | pIter(p); |
---|
| 2424 | } |
---|
| 2425 | } |
---|
| 2426 | n_Delete(&h,r->cf); |
---|
| 2427 | #ifdef HAVE_FACTORY |
---|
| 2428 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2429 | //{ |
---|
| 2430 | // singclap_divide_content(ph); |
---|
| 2431 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
| 2432 | //} |
---|
| 2433 | #endif |
---|
| 2434 | } |
---|
| 2435 | } |
---|
| 2436 | #endif |
---|
[fbf8a6] | 2437 | /* ---------------------------------------------------------------------------*/ |
---|
| 2438 | /* cleardenom suff */ |
---|
[8d1d30c] | 2439 | poly p_Cleardenom(poly ph, const ring r) |
---|
| 2440 | { |
---|
| 2441 | poly start=ph; |
---|
[975db18] | 2442 | |
---|
| 2443 | #if 0 |
---|
| 2444 | if( ph != NULL ) |
---|
| 2445 | { |
---|
| 2446 | CPolyCoeffsEnumerator itr(ph); |
---|
| 2447 | n_ClearDenominators(itr, r->cf); |
---|
| 2448 | // return start; |
---|
| 2449 | } |
---|
| 2450 | #endif |
---|
| 2451 | |
---|
[8d1d30c] | 2452 | number d, h; |
---|
| 2453 | poly p; |
---|
| 2454 | |
---|
| 2455 | #ifdef HAVE_RINGS |
---|
| 2456 | if (rField_is_Ring(r)) |
---|
| 2457 | { |
---|
| 2458 | p_Content(ph,r); |
---|
| 2459 | return start; |
---|
| 2460 | } |
---|
| 2461 | #endif |
---|
| 2462 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) return start; |
---|
| 2463 | p = ph; |
---|
| 2464 | if(pNext(p)==NULL) |
---|
| 2465 | { |
---|
| 2466 | if (TEST_OPT_CONTENTSB) |
---|
| 2467 | { |
---|
| 2468 | number n=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2469 | if (!n_IsOne(n,r->cf)) |
---|
| 2470 | { |
---|
| 2471 | number nn=n_Mult(pGetCoeff(p),n,r->cf); |
---|
| 2472 | n_Normalize(nn,r->cf); |
---|
| 2473 | p_SetCoeff(p,nn,r); |
---|
| 2474 | } |
---|
| 2475 | n_Delete(&n,r->cf); |
---|
| 2476 | } |
---|
| 2477 | else |
---|
| 2478 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
| 2479 | } |
---|
| 2480 | else |
---|
| 2481 | { |
---|
| 2482 | h = n_Init(1,r->cf); |
---|
| 2483 | while (p!=NULL) |
---|
| 2484 | { |
---|
[8a8c9e] | 2485 | n_Normalize(pGetCoeff(p),r->cf); |
---|
[8d1d30c] | 2486 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2487 | n_Delete(&h,r->cf); |
---|
| 2488 | h=d; |
---|
| 2489 | pIter(p); |
---|
| 2490 | } |
---|
| 2491 | /* contains the 1/lcm of all denominators */ |
---|
| 2492 | if(!n_IsOne(h,r->cf)) |
---|
| 2493 | { |
---|
| 2494 | p = ph; |
---|
| 2495 | while (p!=NULL) |
---|
| 2496 | { |
---|
| 2497 | /* should be: |
---|
| 2498 | * number hh; |
---|
| 2499 | * nGetDenom(p->coef,&hh); |
---|
| 2500 | * nMult(&h,&hh,&d); |
---|
| 2501 | * nNormalize(d); |
---|
| 2502 | * nDelete(&hh); |
---|
| 2503 | * nMult(d,p->coef,&hh); |
---|
| 2504 | * nDelete(&d); |
---|
| 2505 | * nDelete(&(p->coef)); |
---|
| 2506 | * p->coef =hh; |
---|
| 2507 | */ |
---|
| 2508 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2509 | n_Normalize(d,r->cf); |
---|
| 2510 | p_SetCoeff(p,d,r); |
---|
| 2511 | pIter(p); |
---|
| 2512 | } |
---|
| 2513 | n_Delete(&h,r->cf); |
---|
[5679049] | 2514 | if (n_GetChar(r->cf)==1) |
---|
[8d1d30c] | 2515 | { |
---|
| 2516 | loop |
---|
| 2517 | { |
---|
| 2518 | h = n_Init(1,r->cf); |
---|
| 2519 | p=ph; |
---|
| 2520 | while (p!=NULL) |
---|
| 2521 | { |
---|
| 2522 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2523 | n_Delete(&h,r->cf); |
---|
| 2524 | h=d; |
---|
| 2525 | pIter(p); |
---|
| 2526 | } |
---|
| 2527 | /* contains the 1/lcm of all denominators */ |
---|
| 2528 | if(!n_IsOne(h,r->cf)) |
---|
| 2529 | { |
---|
| 2530 | p = ph; |
---|
| 2531 | while (p!=NULL) |
---|
| 2532 | { |
---|
| 2533 | /* should be: |
---|
| 2534 | * number hh; |
---|
| 2535 | * nGetDenom(p->coef,&hh); |
---|
| 2536 | * nMult(&h,&hh,&d); |
---|
| 2537 | * nNormalize(d); |
---|
| 2538 | * nDelete(&hh); |
---|
| 2539 | * nMult(d,p->coef,&hh); |
---|
| 2540 | * nDelete(&d); |
---|
| 2541 | * nDelete(&(p->coef)); |
---|
| 2542 | * p->coef =hh; |
---|
| 2543 | */ |
---|
| 2544 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2545 | n_Normalize(d,r->cf); |
---|
| 2546 | p_SetCoeff(p,d,r); |
---|
| 2547 | pIter(p); |
---|
| 2548 | } |
---|
| 2549 | n_Delete(&h,r->cf); |
---|
| 2550 | } |
---|
| 2551 | else |
---|
| 2552 | { |
---|
| 2553 | n_Delete(&h,r->cf); |
---|
| 2554 | break; |
---|
| 2555 | } |
---|
| 2556 | } |
---|
| 2557 | } |
---|
| 2558 | } |
---|
| 2559 | if (h!=NULL) n_Delete(&h,r->cf); |
---|
[71ba5b8] | 2560 | |
---|
[8d1d30c] | 2561 | p_Content(ph,r); |
---|
| 2562 | #ifdef HAVE_RATGRING |
---|
| 2563 | if (rIsRatGRing(r)) |
---|
| 2564 | { |
---|
| 2565 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
| 2566 | pContentRat(ph); |
---|
| 2567 | start=ph; |
---|
| 2568 | } |
---|
| 2569 | #endif |
---|
| 2570 | } |
---|
| 2571 | return start; |
---|
| 2572 | } |
---|
| 2573 | |
---|
| 2574 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
| 2575 | { |
---|
[975db18] | 2576 | #if 0 |
---|
| 2577 | if( ph != NULL ) |
---|
| 2578 | { |
---|
| 2579 | CPolyCoeffsEnumerator itr(ph); |
---|
| 2580 | n_ClearDenominators(itr, c, r->cf); |
---|
| 2581 | // return; |
---|
| 2582 | } |
---|
| 2583 | #endif |
---|
| 2584 | |
---|
[8d1d30c] | 2585 | number d, h; |
---|
| 2586 | poly p; |
---|
| 2587 | |
---|
| 2588 | p = ph; |
---|
| 2589 | if(pNext(p)==NULL) |
---|
| 2590 | { |
---|
| 2591 | c=n_Invers(pGetCoeff(p),r->cf); |
---|
| 2592 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
| 2593 | } |
---|
| 2594 | else |
---|
| 2595 | { |
---|
| 2596 | h = n_Init(1,r->cf); |
---|
| 2597 | while (p!=NULL) |
---|
| 2598 | { |
---|
| 2599 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2600 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2601 | n_Delete(&h,r->cf); |
---|
| 2602 | h=d; |
---|
| 2603 | pIter(p); |
---|
| 2604 | } |
---|
| 2605 | c=h; |
---|
| 2606 | /* contains the 1/lcm of all denominators */ |
---|
| 2607 | if(!n_IsOne(h,r->cf)) |
---|
| 2608 | { |
---|
| 2609 | p = ph; |
---|
| 2610 | while (p!=NULL) |
---|
| 2611 | { |
---|
| 2612 | /* should be: |
---|
| 2613 | * number hh; |
---|
| 2614 | * nGetDenom(p->coef,&hh); |
---|
| 2615 | * nMult(&h,&hh,&d); |
---|
| 2616 | * nNormalize(d); |
---|
| 2617 | * nDelete(&hh); |
---|
| 2618 | * nMult(d,p->coef,&hh); |
---|
| 2619 | * nDelete(&d); |
---|
| 2620 | * nDelete(&(p->coef)); |
---|
| 2621 | * p->coef =hh; |
---|
| 2622 | */ |
---|
| 2623 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2624 | n_Normalize(d,r->cf); |
---|
| 2625 | p_SetCoeff(p,d,r); |
---|
| 2626 | pIter(p); |
---|
| 2627 | } |
---|
| 2628 | if (rField_is_Q_a(r)) |
---|
| 2629 | { |
---|
| 2630 | loop |
---|
| 2631 | { |
---|
| 2632 | h = n_Init(1,r->cf); |
---|
| 2633 | p=ph; |
---|
| 2634 | while (p!=NULL) |
---|
| 2635 | { |
---|
| 2636 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2637 | n_Delete(&h,r->cf); |
---|
| 2638 | h=d; |
---|
| 2639 | pIter(p); |
---|
| 2640 | } |
---|
| 2641 | /* contains the 1/lcm of all denominators */ |
---|
| 2642 | if(!n_IsOne(h,r->cf)) |
---|
| 2643 | { |
---|
| 2644 | p = ph; |
---|
| 2645 | while (p!=NULL) |
---|
| 2646 | { |
---|
| 2647 | /* should be: |
---|
| 2648 | * number hh; |
---|
| 2649 | * nGetDenom(p->coef,&hh); |
---|
| 2650 | * nMult(&h,&hh,&d); |
---|
| 2651 | * nNormalize(d); |
---|
| 2652 | * nDelete(&hh); |
---|
| 2653 | * nMult(d,p->coef,&hh); |
---|
| 2654 | * nDelete(&d); |
---|
| 2655 | * nDelete(&(p->coef)); |
---|
| 2656 | * p->coef =hh; |
---|
| 2657 | */ |
---|
| 2658 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2659 | n_Normalize(d,r->cf); |
---|
| 2660 | p_SetCoeff(p,d,r); |
---|
| 2661 | pIter(p); |
---|
| 2662 | } |
---|
| 2663 | number t=n_Mult(c,h,r->cf); |
---|
| 2664 | n_Delete(&c,r->cf); |
---|
| 2665 | c=t; |
---|
| 2666 | } |
---|
| 2667 | else |
---|
| 2668 | { |
---|
| 2669 | break; |
---|
| 2670 | } |
---|
| 2671 | n_Delete(&h,r->cf); |
---|
| 2672 | } |
---|
| 2673 | } |
---|
| 2674 | } |
---|
| 2675 | } |
---|
| 2676 | } |
---|
| 2677 | |
---|
| 2678 | number p_GetAllDenom(poly ph, const ring r) |
---|
| 2679 | { |
---|
| 2680 | number d=n_Init(1,r->cf); |
---|
| 2681 | poly p = ph; |
---|
| 2682 | |
---|
| 2683 | while (p!=NULL) |
---|
| 2684 | { |
---|
| 2685 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2686 | if (!n_IsOne(h,r->cf)) |
---|
| 2687 | { |
---|
| 2688 | number dd=n_Mult(d,h,r->cf); |
---|
| 2689 | n_Delete(&d,r->cf); |
---|
| 2690 | d=dd; |
---|
| 2691 | } |
---|
| 2692 | n_Delete(&h,r->cf); |
---|
| 2693 | pIter(p); |
---|
| 2694 | } |
---|
| 2695 | return d; |
---|
| 2696 | } |
---|
| 2697 | |
---|
[fbf8a6] | 2698 | int p_Size(poly p, const ring r) |
---|
| 2699 | { |
---|
| 2700 | int count = 0; |
---|
| 2701 | while ( p != NULL ) |
---|
| 2702 | { |
---|
| 2703 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
| 2704 | pIter( p ); |
---|
| 2705 | } |
---|
| 2706 | return count; |
---|
| 2707 | } |
---|
| 2708 | |
---|
[4e8ef90] | 2709 | /*2 |
---|
| 2710 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
| 2711 | *assume: deg(var(varnum))==1 |
---|
| 2712 | */ |
---|
| 2713 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
| 2714 | { |
---|
| 2715 | pFDegProc deg; |
---|
[5679049] | 2716 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2717 | deg=p_Totaldegree; |
---|
| 2718 | else |
---|
[9765f3] | 2719 | deg=r->pFDeg; |
---|
[4e8ef90] | 2720 | |
---|
| 2721 | poly q=NULL, qn; |
---|
| 2722 | int o,ii; |
---|
| 2723 | sBucket_pt bp; |
---|
| 2724 | |
---|
| 2725 | if (p!=NULL) |
---|
| 2726 | { |
---|
| 2727 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
| 2728 | { |
---|
| 2729 | return NULL; |
---|
| 2730 | } |
---|
| 2731 | o=deg(p,r); |
---|
| 2732 | q=pNext(p); |
---|
| 2733 | while (q != NULL) |
---|
| 2734 | { |
---|
| 2735 | ii=deg(q,r); |
---|
| 2736 | if (ii>o) o=ii; |
---|
| 2737 | pIter(q); |
---|
| 2738 | } |
---|
| 2739 | q = p_Copy(p,r); |
---|
| 2740 | bp = sBucketCreate(r); |
---|
| 2741 | while (q != NULL) |
---|
| 2742 | { |
---|
| 2743 | ii = o-deg(q,r); |
---|
| 2744 | if (ii!=0) |
---|
| 2745 | { |
---|
| 2746 | p_AddExp(q,varnum, (long)ii,r); |
---|
| 2747 | p_Setm(q,r); |
---|
| 2748 | } |
---|
| 2749 | qn = pNext(q); |
---|
| 2750 | pNext(q) = NULL; |
---|
| 2751 | sBucket_Add_p(bp, q, 1); |
---|
| 2752 | q = qn; |
---|
| 2753 | } |
---|
| 2754 | sBucketDestroyAdd(bp, &q, &ii); |
---|
| 2755 | } |
---|
| 2756 | return q; |
---|
| 2757 | } |
---|
| 2758 | |
---|
| 2759 | /*2 |
---|
| 2760 | *tests if p is homogeneous with respect to the actual weigths |
---|
| 2761 | */ |
---|
| 2762 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
| 2763 | { |
---|
| 2764 | poly qp=p; |
---|
| 2765 | int o; |
---|
| 2766 | |
---|
| 2767 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
| 2768 | pFDegProc d; |
---|
[5679049] | 2769 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2770 | d=p_Totaldegree; |
---|
[71ba5b8] | 2771 | else |
---|
[9765f3] | 2772 | d=r->pFDeg; |
---|
[8a8c9e] | 2773 | o = d(p,r); |
---|
[4e8ef90] | 2774 | do |
---|
| 2775 | { |
---|
| 2776 | if (d(qp,r) != o) return FALSE; |
---|
| 2777 | pIter(qp); |
---|
| 2778 | } |
---|
| 2779 | while (qp != NULL); |
---|
| 2780 | return TRUE; |
---|
| 2781 | } |
---|
| 2782 | |
---|
[cd246b] | 2783 | /*----------utilities for syzygies--------------*/ |
---|
| 2784 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
| 2785 | { |
---|
| 2786 | poly q=p,qq; |
---|
| 2787 | int i; |
---|
| 2788 | |
---|
| 2789 | while (q!=NULL) |
---|
| 2790 | { |
---|
| 2791 | if (p_LmIsConstantComp(q,r)) |
---|
| 2792 | { |
---|
| 2793 | i = p_GetComp(q,r); |
---|
| 2794 | qq = p; |
---|
| 2795 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2796 | if (qq == q) |
---|
| 2797 | { |
---|
| 2798 | *k = i; |
---|
| 2799 | return TRUE; |
---|
| 2800 | } |
---|
| 2801 | else |
---|
| 2802 | pIter(q); |
---|
| 2803 | } |
---|
| 2804 | else pIter(q); |
---|
| 2805 | } |
---|
| 2806 | return FALSE; |
---|
| 2807 | } |
---|
| 2808 | |
---|
| 2809 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
| 2810 | { |
---|
| 2811 | poly q=p,qq; |
---|
| 2812 | int i,j=0; |
---|
| 2813 | |
---|
| 2814 | *len = 0; |
---|
| 2815 | while (q!=NULL) |
---|
| 2816 | { |
---|
| 2817 | if (p_LmIsConstantComp(q,r)) |
---|
| 2818 | { |
---|
| 2819 | i = p_GetComp(q,r); |
---|
| 2820 | qq = p; |
---|
| 2821 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2822 | if (qq == q) |
---|
| 2823 | { |
---|
| 2824 | j = 0; |
---|
| 2825 | while (qq!=NULL) |
---|
| 2826 | { |
---|
| 2827 | if (p_GetComp(qq,r)==i) j++; |
---|
| 2828 | pIter(qq); |
---|
| 2829 | } |
---|
| 2830 | if ((*len == 0) || (j<*len)) |
---|
| 2831 | { |
---|
| 2832 | *len = j; |
---|
| 2833 | *k = i; |
---|
| 2834 | } |
---|
| 2835 | } |
---|
| 2836 | } |
---|
| 2837 | pIter(q); |
---|
| 2838 | } |
---|
| 2839 | } |
---|
| 2840 | |
---|
| 2841 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
| 2842 | { |
---|
| 2843 | poly q = *p; |
---|
| 2844 | |
---|
| 2845 | if (q==NULL) return NULL; |
---|
| 2846 | |
---|
| 2847 | poly qq=NULL,result = NULL; |
---|
| 2848 | |
---|
| 2849 | if (p_GetComp(q,r)==k) |
---|
| 2850 | { |
---|
| 2851 | result = q; /* *p */ |
---|
| 2852 | while ((q!=NULL) && (p_GetComp(q,r)==k)) |
---|
| 2853 | { |
---|
| 2854 | p_SetComp(q,0,r); |
---|
| 2855 | p_SetmComp(q,r); |
---|
| 2856 | qq = q; |
---|
| 2857 | pIter(q); |
---|
| 2858 | } |
---|
| 2859 | *p = q; |
---|
| 2860 | pNext(qq) = NULL; |
---|
| 2861 | } |
---|
| 2862 | if (q==NULL) return result; |
---|
| 2863 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2864 | while (pNext(q)!=NULL) |
---|
| 2865 | { |
---|
| 2866 | if (p_GetComp(pNext(q),r)==k) |
---|
| 2867 | { |
---|
| 2868 | if (result==NULL) |
---|
| 2869 | { |
---|
| 2870 | result = pNext(q); |
---|
| 2871 | qq = result; |
---|
| 2872 | } |
---|
| 2873 | else |
---|
| 2874 | { |
---|
| 2875 | pNext(qq) = pNext(q); |
---|
| 2876 | pIter(qq); |
---|
| 2877 | } |
---|
| 2878 | pNext(q) = pNext(pNext(q)); |
---|
| 2879 | pNext(qq) =NULL; |
---|
| 2880 | p_SetComp(qq,0,r); |
---|
| 2881 | p_SetmComp(qq,r); |
---|
| 2882 | } |
---|
| 2883 | else |
---|
| 2884 | { |
---|
| 2885 | pIter(q); |
---|
| 2886 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2887 | } |
---|
| 2888 | } |
---|
| 2889 | return result; |
---|
| 2890 | } |
---|
[74021a] | 2891 | |
---|
| 2892 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
| 2893 | { |
---|
| 2894 | poly q = *p,qq=NULL,result = NULL; |
---|
| 2895 | |
---|
| 2896 | if (q==NULL) return NULL; |
---|
| 2897 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
| 2898 | if (p_GetComp(q,r)==k) |
---|
| 2899 | { |
---|
| 2900 | result = q; |
---|
| 2901 | do |
---|
| 2902 | { |
---|
| 2903 | p_SetComp(q,0,r); |
---|
| 2904 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2905 | qq = q; |
---|
| 2906 | pIter(q); |
---|
| 2907 | } |
---|
| 2908 | while ((q!=NULL) && (p_GetComp(q,r)==k)); |
---|
| 2909 | *p = q; |
---|
| 2910 | pNext(qq) = NULL; |
---|
| 2911 | } |
---|
| 2912 | if (q==NULL) return result; |
---|
| 2913 | if (p_GetComp(q,r) > k) |
---|
| 2914 | { |
---|
| 2915 | p_SubComp(q,1,r); |
---|
| 2916 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2917 | } |
---|
| 2918 | poly pNext_q; |
---|
| 2919 | while ((pNext_q=pNext(q))!=NULL) |
---|
| 2920 | { |
---|
| 2921 | if (p_GetComp(pNext_q,r)==k) |
---|
| 2922 | { |
---|
| 2923 | if (result==NULL) |
---|
| 2924 | { |
---|
| 2925 | result = pNext_q; |
---|
| 2926 | qq = result; |
---|
| 2927 | } |
---|
| 2928 | else |
---|
| 2929 | { |
---|
| 2930 | pNext(qq) = pNext_q; |
---|
| 2931 | pIter(qq); |
---|
| 2932 | } |
---|
| 2933 | pNext(q) = pNext(pNext_q); |
---|
| 2934 | pNext(qq) =NULL; |
---|
| 2935 | p_SetComp(qq,0,r); |
---|
| 2936 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
| 2937 | } |
---|
| 2938 | else |
---|
| 2939 | { |
---|
| 2940 | /*pIter(q);*/ q=pNext_q; |
---|
| 2941 | if (p_GetComp(q,r) > k) |
---|
| 2942 | { |
---|
| 2943 | p_SubComp(q,1,r); |
---|
| 2944 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2945 | } |
---|
| 2946 | } |
---|
| 2947 | } |
---|
| 2948 | return result; |
---|
| 2949 | } |
---|
| 2950 | |
---|
| 2951 | // Splits *p into two polys: *q which consists of all monoms with |
---|
| 2952 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
| 2953 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
| 2954 | { |
---|
| 2955 | spolyrec pp, qq; |
---|
| 2956 | poly p, q, p_prev; |
---|
| 2957 | int l = 0; |
---|
| 2958 | |
---|
| 2959 | #ifdef HAVE_ASSUME |
---|
| 2960 | int lp = pLength(*r_p); |
---|
| 2961 | #endif |
---|
| 2962 | |
---|
| 2963 | pNext(&pp) = *r_p; |
---|
| 2964 | p = *r_p; |
---|
| 2965 | p_prev = &pp; |
---|
| 2966 | q = &qq; |
---|
| 2967 | |
---|
| 2968 | while(p != NULL) |
---|
| 2969 | { |
---|
| 2970 | while (p_GetComp(p,r) == comp) |
---|
| 2971 | { |
---|
| 2972 | pNext(q) = p; |
---|
| 2973 | pIter(q); |
---|
| 2974 | p_SetComp(p, 0,r); |
---|
| 2975 | p_SetmComp(p,r); |
---|
| 2976 | pIter(p); |
---|
| 2977 | l++; |
---|
| 2978 | if (p == NULL) |
---|
| 2979 | { |
---|
| 2980 | pNext(p_prev) = NULL; |
---|
| 2981 | goto Finish; |
---|
| 2982 | } |
---|
| 2983 | } |
---|
| 2984 | pNext(p_prev) = p; |
---|
| 2985 | p_prev = p; |
---|
| 2986 | pIter(p); |
---|
| 2987 | } |
---|
| 2988 | |
---|
| 2989 | Finish: |
---|
| 2990 | pNext(q) = NULL; |
---|
| 2991 | *r_p = pNext(&pp); |
---|
| 2992 | *r_q = pNext(&qq); |
---|
| 2993 | *lq = l; |
---|
| 2994 | #ifdef HAVE_ASSUME |
---|
| 2995 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
| 2996 | #endif |
---|
| 2997 | p_Test(*r_p,r); |
---|
| 2998 | p_Test(*r_q,r); |
---|
| 2999 | } |
---|
| 3000 | |
---|
| 3001 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
| 3002 | { |
---|
| 3003 | poly q; |
---|
| 3004 | |
---|
| 3005 | while ((*p!=NULL) && (p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
| 3006 | if (*p==NULL) return; |
---|
| 3007 | q = *p; |
---|
| 3008 | if (p_GetComp(q,r)>k) |
---|
| 3009 | { |
---|
| 3010 | p_SubComp(q,1,r); |
---|
| 3011 | p_SetmComp(q,r); |
---|
| 3012 | } |
---|
| 3013 | while (pNext(q)!=NULL) |
---|
| 3014 | { |
---|
| 3015 | if (p_GetComp(pNext(q),r)==k) |
---|
| 3016 | p_LmDelete(&(pNext(q)),r); |
---|
| 3017 | else |
---|
| 3018 | { |
---|
| 3019 | pIter(q); |
---|
| 3020 | if (p_GetComp(q,r)>k) |
---|
| 3021 | { |
---|
| 3022 | p_SubComp(q,1,r); |
---|
| 3023 | p_SetmComp(q,r); |
---|
| 3024 | } |
---|
| 3025 | } |
---|
| 3026 | } |
---|
| 3027 | } |
---|
[dd693a] | 3028 | |
---|
| 3029 | /*2 |
---|
| 3030 | * convert a vector to a set of polys, |
---|
| 3031 | * allocates the polyset, (entries 0..(*len)-1) |
---|
| 3032 | * the vector will not be changed |
---|
| 3033 | */ |
---|
| 3034 | void p_Vec2Polys(poly v, poly* *p, int *len, const ring r) |
---|
| 3035 | { |
---|
| 3036 | poly h; |
---|
| 3037 | int k; |
---|
| 3038 | |
---|
| 3039 | *len=p_MaxComp(v,r); |
---|
| 3040 | if (*len==0) *len=1; |
---|
| 3041 | *p=(poly*)omAlloc0((*len)*sizeof(poly)); |
---|
| 3042 | while (v!=NULL) |
---|
| 3043 | { |
---|
| 3044 | h=p_Head(v,r); |
---|
| 3045 | k=p_GetComp(h,r); |
---|
| 3046 | p_SetComp(h,0,r); |
---|
| 3047 | (*p)[k-1]=p_Add_q((*p)[k-1],h,r); |
---|
| 3048 | pIter(v); |
---|
| 3049 | } |
---|
| 3050 | } |
---|
| 3051 | |
---|
[949e57] | 3052 | // |
---|
| 3053 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
| 3054 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
[45d2332] | 3055 | // only uses pFDeg (and not p_Deg, or pTotalDegree, etc) |
---|
[949e57] | 3056 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
| 3057 | { |
---|
| 3058 | assume(new_FDeg != NULL); |
---|
| 3059 | r->pFDeg = new_FDeg; |
---|
| 3060 | |
---|
| 3061 | if (new_lDeg == NULL) |
---|
| 3062 | new_lDeg = r->pLDegOrig; |
---|
| 3063 | |
---|
| 3064 | r->pLDeg = new_lDeg; |
---|
| 3065 | } |
---|
| 3066 | |
---|
| 3067 | // restores pFDeg and pLDeg: |
---|
| 3068 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
| 3069 | { |
---|
| 3070 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
| 3071 | r->pFDeg = old_FDeg; |
---|
| 3072 | r->pLDeg = old_lDeg; |
---|
| 3073 | } |
---|
| 3074 | |
---|
[5bc2461] | 3075 | /*-------- several access procedures to monomials -------------------- */ |
---|
| 3076 | /* |
---|
| 3077 | * the module weights for std |
---|
| 3078 | */ |
---|
| 3079 | static pFDegProc pOldFDeg; |
---|
| 3080 | static pLDegProc pOldLDeg; |
---|
| 3081 | static BOOLEAN pOldLexOrder; |
---|
| 3082 | |
---|
[8a8c9e] | 3083 | static long pModDeg(poly p, ring r) |
---|
[5bc2461] | 3084 | { |
---|
| 3085 | long d=pOldFDeg(p, r); |
---|
| 3086 | int c=p_GetComp(p, r); |
---|
| 3087 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
| 3088 | return d; |
---|
| 3089 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
| 3090 | } |
---|
| 3091 | |
---|
| 3092 | void p_SetModDeg(intvec *w, ring r) |
---|
| 3093 | { |
---|
| 3094 | if (w!=NULL) |
---|
| 3095 | { |
---|
| 3096 | r->pModW = w; |
---|
| 3097 | pOldFDeg = r->pFDeg; |
---|
| 3098 | pOldLDeg = r->pLDeg; |
---|
| 3099 | pOldLexOrder = r->pLexOrder; |
---|
| 3100 | pSetDegProcs(r,pModDeg); |
---|
| 3101 | r->pLexOrder = TRUE; |
---|
| 3102 | } |
---|
| 3103 | else |
---|
| 3104 | { |
---|
| 3105 | r->pModW = NULL; |
---|
[5679049] | 3106 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
[5bc2461] | 3107 | r->pLexOrder = pOldLexOrder; |
---|
| 3108 | } |
---|
| 3109 | } |
---|
| 3110 | |
---|
[c6a3eb2] | 3111 | /*2 |
---|
| 3112 | * handle memory request for sets of polynomials (ideals) |
---|
| 3113 | * l is the length of *p, increment is the difference (may be negative) |
---|
| 3114 | */ |
---|
| 3115 | void pEnlargeSet(poly* *p, int l, int increment) |
---|
| 3116 | { |
---|
| 3117 | poly* h; |
---|
| 3118 | |
---|
| 3119 | h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
| 3120 | if (increment>0) |
---|
| 3121 | { |
---|
| 3122 | //for (i=l; i<l+increment; i++) |
---|
| 3123 | // h[i]=NULL; |
---|
| 3124 | memset(&(h[l]),0,increment*sizeof(poly)); |
---|
| 3125 | } |
---|
| 3126 | *p=h; |
---|
| 3127 | } |
---|
| 3128 | |
---|
[71ba5b8] | 3129 | /*2 |
---|
| 3130 | *divides p1 by its leading coefficient |
---|
| 3131 | */ |
---|
| 3132 | void p_Norm(poly p1, const ring r) |
---|
| 3133 | { |
---|
| 3134 | #ifdef HAVE_RINGS |
---|
| 3135 | if (rField_is_Ring(r)) |
---|
| 3136 | { |
---|
[45d2332] | 3137 | if (!n_IsUnit(pGetCoeff(p1), r->cf)) return; |
---|
[71ba5b8] | 3138 | // Werror("p_Norm not possible in the case of coefficient rings."); |
---|
| 3139 | } |
---|
| 3140 | else |
---|
| 3141 | #endif |
---|
| 3142 | if (p1!=NULL) |
---|
| 3143 | { |
---|
| 3144 | if (pNext(p1)==NULL) |
---|
| 3145 | { |
---|
| 3146 | p_SetCoeff(p1,n_Init(1,r->cf),r); |
---|
| 3147 | return; |
---|
| 3148 | } |
---|
| 3149 | poly h; |
---|
| 3150 | if (!n_IsOne(pGetCoeff(p1),r->cf)) |
---|
| 3151 | { |
---|
| 3152 | number k, c; |
---|
| 3153 | n_Normalize(pGetCoeff(p1),r->cf); |
---|
| 3154 | k = pGetCoeff(p1); |
---|
| 3155 | c = n_Init(1,r->cf); |
---|
| 3156 | pSetCoeff0(p1,c); |
---|
| 3157 | h = pNext(p1); |
---|
| 3158 | while (h!=NULL) |
---|
| 3159 | { |
---|
| 3160 | c=n_Div(pGetCoeff(h),k,r->cf); |
---|
| 3161 | // no need to normalize: Z/p, R |
---|
| 3162 | // normalize already in nDiv: Q_a, Z/p_a |
---|
| 3163 | // remains: Q |
---|
| 3164 | if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) n_Normalize(c,r->cf); |
---|
| 3165 | p_SetCoeff(h,c,r); |
---|
| 3166 | pIter(h); |
---|
| 3167 | } |
---|
| 3168 | n_Delete(&k,r->cf); |
---|
| 3169 | } |
---|
| 3170 | else |
---|
| 3171 | { |
---|
| 3172 | //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE |
---|
| 3173 | { |
---|
| 3174 | h = pNext(p1); |
---|
| 3175 | while (h!=NULL) |
---|
| 3176 | { |
---|
| 3177 | n_Normalize(pGetCoeff(h),r->cf); |
---|
| 3178 | pIter(h); |
---|
| 3179 | } |
---|
| 3180 | } |
---|
| 3181 | } |
---|
| 3182 | } |
---|
| 3183 | } |
---|
| 3184 | |
---|
| 3185 | /*2 |
---|
| 3186 | *normalize all coefficients |
---|
| 3187 | */ |
---|
| 3188 | void p_Normalize(poly p,const ring r) |
---|
| 3189 | { |
---|
| 3190 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
| 3191 | while (p!=NULL) |
---|
| 3192 | { |
---|
| 3193 | #ifdef LDEBUG |
---|
[45d2332] | 3194 | n_Test(pGetCoeff(p), r->cf); |
---|
[71ba5b8] | 3195 | #endif |
---|
| 3196 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 3197 | pIter(p); |
---|
| 3198 | } |
---|
| 3199 | } |
---|
| 3200 | |
---|
| 3201 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
| 3202 | // Poly with Exp(n) != 0 is reversed |
---|
| 3203 | static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r) |
---|
| 3204 | { |
---|
| 3205 | if (p == NULL) |
---|
| 3206 | { |
---|
| 3207 | *non_zero = NULL; |
---|
| 3208 | *zero = NULL; |
---|
| 3209 | return; |
---|
| 3210 | } |
---|
| 3211 | spolyrec sz; |
---|
| 3212 | poly z, n_z, next; |
---|
| 3213 | z = &sz; |
---|
| 3214 | n_z = NULL; |
---|
| 3215 | |
---|
| 3216 | while(p != NULL) |
---|
| 3217 | { |
---|
| 3218 | next = pNext(p); |
---|
| 3219 | if (p_GetExp(p, n,r) == 0) |
---|
| 3220 | { |
---|
| 3221 | pNext(z) = p; |
---|
| 3222 | pIter(z); |
---|
| 3223 | } |
---|
| 3224 | else |
---|
| 3225 | { |
---|
| 3226 | pNext(p) = n_z; |
---|
| 3227 | n_z = p; |
---|
| 3228 | } |
---|
| 3229 | p = next; |
---|
| 3230 | } |
---|
| 3231 | pNext(z) = NULL; |
---|
| 3232 | *zero = pNext(&sz); |
---|
| 3233 | *non_zero = n_z; |
---|
| 3234 | } |
---|
| 3235 | /*3 |
---|
| 3236 | * substitute the n-th variable by 1 in p |
---|
| 3237 | * destroy p |
---|
| 3238 | */ |
---|
| 3239 | static poly p_Subst1 (poly p,int n, const ring r) |
---|
| 3240 | { |
---|
| 3241 | poly qq=NULL, result = NULL; |
---|
| 3242 | poly zero=NULL, non_zero=NULL; |
---|
| 3243 | |
---|
| 3244 | // reverse, so that add is likely to be linear |
---|
| 3245 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3246 | |
---|
| 3247 | while (non_zero != NULL) |
---|
| 3248 | { |
---|
| 3249 | assume(p_GetExp(non_zero, n,r) != 0); |
---|
| 3250 | qq = non_zero; |
---|
| 3251 | pIter(non_zero); |
---|
| 3252 | qq->next = NULL; |
---|
| 3253 | p_SetExp(qq,n,0,r); |
---|
| 3254 | p_Setm(qq,r); |
---|
| 3255 | result = p_Add_q(result,qq,r); |
---|
| 3256 | } |
---|
| 3257 | p = p_Add_q(result, zero,r); |
---|
| 3258 | p_Test(p,r); |
---|
| 3259 | return p; |
---|
| 3260 | } |
---|
| 3261 | |
---|
| 3262 | /*3 |
---|
| 3263 | * substitute the n-th variable by number e in p |
---|
| 3264 | * destroy p |
---|
| 3265 | */ |
---|
| 3266 | static poly p_Subst2 (poly p,int n, number e, const ring r) |
---|
| 3267 | { |
---|
| 3268 | assume( ! n_IsZero(e,r->cf) ); |
---|
| 3269 | poly qq,result = NULL; |
---|
| 3270 | number nn, nm; |
---|
| 3271 | poly zero, non_zero; |
---|
| 3272 | |
---|
| 3273 | // reverse, so that add is likely to be linear |
---|
| 3274 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3275 | |
---|
| 3276 | while (non_zero != NULL) |
---|
| 3277 | { |
---|
[45d2332] | 3278 | assume(p_GetExp(non_zero, n, r) != 0); |
---|
[71ba5b8] | 3279 | qq = non_zero; |
---|
| 3280 | pIter(non_zero); |
---|
| 3281 | qq->next = NULL; |
---|
| 3282 | n_Power(e, p_GetExp(qq, n, r), &nn,r->cf); |
---|
| 3283 | nm = n_Mult(nn, pGetCoeff(qq),r->cf); |
---|
| 3284 | #ifdef HAVE_RINGS |
---|
| 3285 | if (n_IsZero(nm,r->cf)) |
---|
| 3286 | { |
---|
| 3287 | p_LmFree(&qq,r); |
---|
| 3288 | n_Delete(&nm,r->cf); |
---|
| 3289 | } |
---|
| 3290 | else |
---|
| 3291 | #endif |
---|
| 3292 | { |
---|
| 3293 | p_SetCoeff(qq, nm,r); |
---|
| 3294 | p_SetExp(qq, n, 0,r); |
---|
| 3295 | p_Setm(qq,r); |
---|
| 3296 | result = p_Add_q(result,qq,r); |
---|
| 3297 | } |
---|
| 3298 | n_Delete(&nn,r->cf); |
---|
| 3299 | } |
---|
| 3300 | p = p_Add_q(result, zero,r); |
---|
| 3301 | p_Test(p,r); |
---|
| 3302 | return p; |
---|
| 3303 | } |
---|
| 3304 | |
---|
| 3305 | |
---|
| 3306 | /* delete monoms whose n-th exponent is different from zero */ |
---|
| 3307 | static poly p_Subst0(poly p, int n, const ring r) |
---|
| 3308 | { |
---|
| 3309 | spolyrec res; |
---|
| 3310 | poly h = &res; |
---|
| 3311 | pNext(h) = p; |
---|
| 3312 | |
---|
| 3313 | while (pNext(h)!=NULL) |
---|
| 3314 | { |
---|
| 3315 | if (p_GetExp(pNext(h),n,r)!=0) |
---|
| 3316 | { |
---|
| 3317 | p_LmDelete(&pNext(h),r); |
---|
| 3318 | } |
---|
| 3319 | else |
---|
| 3320 | { |
---|
| 3321 | pIter(h); |
---|
| 3322 | } |
---|
| 3323 | } |
---|
| 3324 | p_Test(pNext(&res),r); |
---|
| 3325 | return pNext(&res); |
---|
| 3326 | } |
---|
| 3327 | |
---|
| 3328 | /*2 |
---|
| 3329 | * substitute the n-th variable by e in p |
---|
| 3330 | * destroy p |
---|
| 3331 | */ |
---|
| 3332 | poly p_Subst(poly p, int n, poly e, const ring r) |
---|
| 3333 | { |
---|
| 3334 | if (e == NULL) return p_Subst0(p, n,r); |
---|
| 3335 | |
---|
| 3336 | if (p_IsConstant(e,r)) |
---|
| 3337 | { |
---|
| 3338 | if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r); |
---|
| 3339 | else return p_Subst2(p, n, pGetCoeff(e),r); |
---|
| 3340 | } |
---|
| 3341 | |
---|
| 3342 | #ifdef HAVE_PLURAL |
---|
| 3343 | if (rIsPluralRing(r)) |
---|
| 3344 | { |
---|
| 3345 | return nc_pSubst(p,n,e,r); |
---|
| 3346 | } |
---|
| 3347 | #endif |
---|
| 3348 | |
---|
| 3349 | int exponent,i; |
---|
| 3350 | poly h, res, m; |
---|
| 3351 | int *me,*ee; |
---|
| 3352 | number nu,nu1; |
---|
| 3353 | |
---|
| 3354 | me=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3355 | ee=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3356 | if (e!=NULL) p_GetExpV(e,ee,r); |
---|
| 3357 | res=NULL; |
---|
| 3358 | h=p; |
---|
| 3359 | while (h!=NULL) |
---|
| 3360 | { |
---|
| 3361 | if ((e!=NULL) || (p_GetExp(h,n,r)==0)) |
---|
| 3362 | { |
---|
| 3363 | m=p_Head(h,r); |
---|
| 3364 | p_GetExpV(m,me,r); |
---|
| 3365 | exponent=me[n]; |
---|
| 3366 | me[n]=0; |
---|
| 3367 | for(i=rVar(r);i>0;i--) |
---|
| 3368 | me[i]+=exponent*ee[i]; |
---|
| 3369 | p_SetExpV(m,me,r); |
---|
| 3370 | if (e!=NULL) |
---|
| 3371 | { |
---|
| 3372 | n_Power(pGetCoeff(e),exponent,&nu,r->cf); |
---|
| 3373 | nu1=n_Mult(pGetCoeff(m),nu,r->cf); |
---|
| 3374 | n_Delete(&nu,r->cf); |
---|
| 3375 | p_SetCoeff(m,nu1,r); |
---|
| 3376 | } |
---|
| 3377 | res=p_Add_q(res,m,r); |
---|
| 3378 | } |
---|
| 3379 | p_LmDelete(&h,r); |
---|
| 3380 | } |
---|
| 3381 | omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int)); |
---|
| 3382 | omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int)); |
---|
| 3383 | return res; |
---|
| 3384 | } |
---|
[83a1714] | 3385 | |
---|
| 3386 | /*2 |
---|
[f93c5e9] | 3387 | * returns a re-ordered convertion of a number as a polynomial, |
---|
[83a1714] | 3388 | * with permutation of parameters |
---|
| 3389 | * NOTE: this only works for Frank's alg. & trans. fields |
---|
| 3390 | */ |
---|
[2d2e40] | 3391 | poly n_PermNumber(const number z, const int *par_perm, const int , const ring src, const ring dst) |
---|
[83a1714] | 3392 | { |
---|
| 3393 | #if 0 |
---|
| 3394 | PrintS("\nSource Ring: \n"); |
---|
| 3395 | rWrite(src); |
---|
| 3396 | |
---|
| 3397 | if(0) |
---|
| 3398 | { |
---|
| 3399 | number zz = n_Copy(z, src->cf); |
---|
[ce1f78] | 3400 | PrintS("z: "); n_Write(zz, src); |
---|
[83a1714] | 3401 | n_Delete(&zz, src->cf); |
---|
| 3402 | } |
---|
[f93c5e9] | 3403 | |
---|
[83a1714] | 3404 | PrintS("\nDestination Ring: \n"); |
---|
| 3405 | rWrite(dst); |
---|
[f93c5e9] | 3406 | |
---|
[83a1714] | 3407 | Print("\nOldPar: %d\n", OldPar); |
---|
| 3408 | for( int i = 1; i <= OldPar; i++ ) |
---|
| 3409 | { |
---|
| 3410 | Print("par(%d) -> par/var (%d)\n", i, par_perm[i-1]); |
---|
| 3411 | } |
---|
| 3412 | #endif |
---|
| 3413 | if( z == NULL ) |
---|
| 3414 | return NULL; |
---|
[f93c5e9] | 3415 | |
---|
[83a1714] | 3416 | const coeffs srcCf = src->cf; |
---|
| 3417 | assume( srcCf != NULL ); |
---|
| 3418 | |
---|
| 3419 | assume( !nCoeff_is_GF(srcCf) ); |
---|
| 3420 | assume( rField_is_Extension(src) ); |
---|
[f93c5e9] | 3421 | |
---|
[83a1714] | 3422 | poly zz = NULL; |
---|
[f93c5e9] | 3423 | |
---|
[83a1714] | 3424 | const ring srcExtRing = srcCf->extRing; |
---|
| 3425 | assume( srcExtRing != NULL ); |
---|
[f93c5e9] | 3426 | |
---|
[83a1714] | 3427 | const coeffs dstCf = dst->cf; |
---|
| 3428 | assume( dstCf != NULL ); |
---|
| 3429 | |
---|
| 3430 | if( nCoeff_is_algExt(srcCf) ) // nCoeff_is_GF(srcCf)? |
---|
| 3431 | { |
---|
| 3432 | zz = (poly) z; |
---|
| 3433 | |
---|
| 3434 | if( zz == NULL ) |
---|
| 3435 | return NULL; |
---|
[f93c5e9] | 3436 | |
---|
| 3437 | } else if (nCoeff_is_transExt(srcCf)) |
---|
| 3438 | { |
---|
[83a1714] | 3439 | assume( !IS0(z) ); |
---|
[f93c5e9] | 3440 | |
---|
[83a1714] | 3441 | zz = NUM(z); |
---|
| 3442 | p_Test (zz, srcExtRing); |
---|
[f93c5e9] | 3443 | |
---|
[83a1714] | 3444 | if( zz == NULL ) |
---|
| 3445 | return NULL; |
---|
[f93c5e9] | 3446 | |
---|
[90f57e] | 3447 | //if( !DENIS1(z) ) |
---|
| 3448 | //WarnS("Not implemented yet: Cannot permute a rational fraction and make a polynomial out of it! Ignorring the denumerator."); |
---|
[83a1714] | 3449 | } else |
---|
| 3450 | { |
---|
[f93c5e9] | 3451 | assume (FALSE); |
---|
| 3452 | Werror("Number permutation is not implemented for this data yet!"); |
---|
| 3453 | return NULL; |
---|
[83a1714] | 3454 | } |
---|
[f93c5e9] | 3455 | |
---|
[83a1714] | 3456 | assume( zz != NULL ); |
---|
| 3457 | p_Test (zz, srcExtRing); |
---|
| 3458 | |
---|
[f93c5e9] | 3459 | |
---|
[83a1714] | 3460 | nMapFunc nMap = n_SetMap(srcExtRing->cf, dstCf); |
---|
[f93c5e9] | 3461 | |
---|
[83a1714] | 3462 | assume( nMap != NULL ); |
---|
[f93c5e9] | 3463 | |
---|
[83a1714] | 3464 | poly qq = p_PermPoly(zz, par_perm - 1, srcExtRing, dst, nMap, NULL, rVar(srcExtRing) ); |
---|
| 3465 | // poly p_PermPoly (poly p, int * perm, const ring oldRing, const ring dst, nMapFunc nMap, int *par_perm, int OldPar) |
---|
[f93c5e9] | 3466 | |
---|
[83a1714] | 3467 | // assume( FALSE ); WarnS("longalg missing 2"); |
---|
[f93c5e9] | 3468 | |
---|
[83a1714] | 3469 | return qq; |
---|
| 3470 | } |
---|
| 3471 | |
---|
| 3472 | |
---|
[deca086] | 3473 | /*2 |
---|
| 3474 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
| 3475 | */ |
---|
[83a1714] | 3476 | poly p_PermPoly (poly p, const int * perm, const ring oldRing, const ring dst, |
---|
| 3477 | nMapFunc nMap, const int *par_perm, int OldPar) |
---|
[deca086] | 3478 | { |
---|
[83a1714] | 3479 | #if 0 |
---|
| 3480 | p_Test(p, oldRing); |
---|
| 3481 | PrintS("\np_PermPoly::p: "); p_Write(p, oldRing, oldRing); PrintLn(); |
---|
| 3482 | #endif |
---|
[f93c5e9] | 3483 | |
---|
[b38d70] | 3484 | const int OldpVariables = rVar(oldRing); |
---|
[deca086] | 3485 | poly result = NULL; |
---|
| 3486 | poly result_last = NULL; |
---|
[83a1714] | 3487 | poly aq = NULL; /* the map coefficient */ |
---|
[deca086] | 3488 | poly qq; /* the mapped monomial */ |
---|
| 3489 | |
---|
[bcfd11a] | 3490 | assume(dst != NULL); |
---|
| 3491 | assume(dst->cf != NULL); |
---|
| 3492 | |
---|
[deca086] | 3493 | while (p != NULL) |
---|
| 3494 | { |
---|
[b38d70] | 3495 | // map the coefficient |
---|
[83a1714] | 3496 | if ( ((OldPar == 0) || (par_perm == NULL) || rField_is_GF(oldRing)) && (nMap != NULL) ) |
---|
[deca086] | 3497 | { |
---|
| 3498 | qq = p_Init(dst); |
---|
[83a1714] | 3499 | assume( nMap != NULL ); |
---|
[b38d70] | 3500 | number n = nMap(p_GetCoeff(p, oldRing), oldRing->cf, dst->cf); |
---|
[f93c5e9] | 3501 | |
---|
[bcfd11a] | 3502 | if ( nCoeff_is_algExt(dst->cf) ) |
---|
[b38d70] | 3503 | n_Normalize(n, dst->cf); |
---|
[f93c5e9] | 3504 | |
---|
[9e26458] | 3505 | p_GetCoeff(qq, dst) = n;// Note: n can be a ZERO!!! |
---|
| 3506 | // coef may be zero: |
---|
| 3507 | // p_Test(qq, dst); |
---|
[deca086] | 3508 | } |
---|
| 3509 | else |
---|
| 3510 | { |
---|
[f93c5e9] | 3511 | qq = p_One(dst); |
---|
[83a1714] | 3512 | |
---|
| 3513 | // aq = naPermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing); // no dst??? |
---|
| 3514 | // poly n_PermNumber(const number z, const int *par_perm, const int P, const ring src, const ring dst) |
---|
| 3515 | aq = n_PermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing, dst); |
---|
| 3516 | |
---|
| 3517 | p_Test(aq, dst); |
---|
[f93c5e9] | 3518 | |
---|
[bcfd11a] | 3519 | if ( nCoeff_is_algExt(dst->cf) ) |
---|
[1f414c8] | 3520 | p_Normalize(aq,dst); |
---|
[bcfd11a] | 3521 | |
---|
[83a1714] | 3522 | if (aq == NULL) |
---|
[f93c5e9] | 3523 | p_SetCoeff(qq, n_Init(0, dst->cf),dst); // Very dirty trick!!! |
---|
| 3524 | |
---|
[b38d70] | 3525 | p_Test(aq, dst); |
---|
[deca086] | 3526 | } |
---|
[f93c5e9] | 3527 | |
---|
| 3528 | if (rRing_has_Comp(dst)) |
---|
[b38d70] | 3529 | p_SetComp(qq, p_GetComp(p, oldRing), dst); |
---|
| 3530 | |
---|
| 3531 | if ( n_IsZero(pGetCoeff(qq), dst->cf) ) |
---|
[deca086] | 3532 | { |
---|
| 3533 | p_LmDelete(&qq,dst); |
---|
[b38d70] | 3534 | qq = NULL; |
---|
[f93c5e9] | 3535 | } |
---|
[deca086] | 3536 | else |
---|
| 3537 | { |
---|
[b38d70] | 3538 | // map pars: |
---|
| 3539 | int mapped_to_par = 0; |
---|
| 3540 | for(int i = 1; i <= OldpVariables; i++) |
---|
[deca086] | 3541 | { |
---|
[b38d70] | 3542 | int e = p_GetExp(p, i, oldRing); |
---|
| 3543 | if (e != 0) |
---|
[deca086] | 3544 | { |
---|
| 3545 | if (perm==NULL) |
---|
[b38d70] | 3546 | p_SetExp(qq, i, e, dst); |
---|
[deca086] | 3547 | else if (perm[i]>0) |
---|
| 3548 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
| 3549 | else if (perm[i]<0) |
---|
| 3550 | { |
---|
[b38d70] | 3551 | number c = p_GetCoeff(qq, dst); |
---|
[deca086] | 3552 | if (rField_is_GF(dst)) |
---|
| 3553 | { |
---|
[7fee876] | 3554 | assume( dst->cf->extRing == NULL ); |
---|
| 3555 | number ee = n_Param(1, dst); |
---|
[b38d70] | 3556 | |
---|
[f93c5e9] | 3557 | number eee; |
---|
| 3558 | n_Power(ee, e, &eee, dst->cf); //nfDelete(ee,dst); |
---|
| 3559 | |
---|
[b38d70] | 3560 | ee = n_Mult(c, eee, dst->cf); |
---|
[8a8c9e] | 3561 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
[deca086] | 3562 | pSetCoeff0(qq,ee); |
---|
| 3563 | } |
---|
[b38d70] | 3564 | else if (nCoeff_is_Extension(dst->cf)) |
---|
[deca086] | 3565 | { |
---|
[f93c5e9] | 3566 | const int par = -perm[i]; |
---|
| 3567 | assume( par > 0 ); |
---|
[83a1714] | 3568 | |
---|
[b38d70] | 3569 | // WarnS("longalg missing 3"); |
---|
| 3570 | #if 1 |
---|
[f93c5e9] | 3571 | const coeffs C = dst->cf; |
---|
| 3572 | assume( C != NULL ); |
---|
| 3573 | |
---|
| 3574 | const ring R = C->extRing; |
---|
| 3575 | assume( R != NULL ); |
---|
| 3576 | |
---|
| 3577 | assume( par <= rVar(R) ); |
---|
| 3578 | |
---|
| 3579 | poly pcn; // = (number)c |
---|
| 3580 | |
---|
| 3581 | assume( !n_IsZero(c, C) ); |
---|
| 3582 | |
---|
| 3583 | if( nCoeff_is_algExt(C) ) |
---|
| 3584 | pcn = (poly) c; |
---|
| 3585 | else // nCoeff_is_transExt(C) |
---|
| 3586 | pcn = NUM(c); |
---|
| 3587 | |
---|
[b38d70] | 3588 | if (pNext(pcn) == NULL) // c->z |
---|
| 3589 | p_AddExp(pcn, -perm[i], e, R); |
---|
[deca086] | 3590 | else /* more difficult: we have really to multiply: */ |
---|
| 3591 | { |
---|
[b38d70] | 3592 | poly mmc = p_ISet(1, R); |
---|
| 3593 | p_SetExp(mmc, -perm[i], e, R); |
---|
| 3594 | p_Setm(mmc, R); |
---|
[f93c5e9] | 3595 | |
---|
| 3596 | number nnc; |
---|
| 3597 | // convert back to a number: number nnc = mmc; |
---|
| 3598 | if( nCoeff_is_algExt(C) ) |
---|
| 3599 | nnc = (number) mmc; |
---|
| 3600 | else // nCoeff_is_transExt(C) |
---|
| 3601 | nnc = ntInit(mmc, C); |
---|
| 3602 | |
---|
[b38d70] | 3603 | p_GetCoeff(qq, dst) = n_Mult((number)c, nnc, C); |
---|
| 3604 | n_Delete((number *)&c, C); |
---|
| 3605 | n_Delete((number *)&nnc, C); |
---|
[deca086] | 3606 | } |
---|
[f93c5e9] | 3607 | |
---|
[deca086] | 3608 | mapped_to_par=1; |
---|
[1f414c8] | 3609 | #endif |
---|
[deca086] | 3610 | } |
---|
| 3611 | } |
---|
| 3612 | else |
---|
| 3613 | { |
---|
| 3614 | /* this variable maps to 0 !*/ |
---|
[b38d70] | 3615 | p_LmDelete(&qq, dst); |
---|
[deca086] | 3616 | break; |
---|
| 3617 | } |
---|
| 3618 | } |
---|
| 3619 | } |
---|
[bcfd11a] | 3620 | if ( mapped_to_par && nCoeff_is_algExt(dst->cf) ) |
---|
[deca086] | 3621 | { |
---|
[b38d70] | 3622 | number n = p_GetCoeff(qq, dst); |
---|
[bcfd11a] | 3623 | n_Normalize(n, dst->cf); |
---|
[b38d70] | 3624 | p_GetCoeff(qq, dst) = n; |
---|
[deca086] | 3625 | } |
---|
| 3626 | } |
---|
| 3627 | pIter(p); |
---|
[f93c5e9] | 3628 | |
---|
[83a1714] | 3629 | #if 0 |
---|
| 3630 | p_Test(aq,dst); |
---|
| 3631 | PrintS("\naq: "); p_Write(aq, dst, dst); PrintLn(); |
---|
| 3632 | #endif |
---|
[f93c5e9] | 3633 | |
---|
[b38d70] | 3634 | |
---|
[deca086] | 3635 | #if 1 |
---|
| 3636 | if (qq!=NULL) |
---|
| 3637 | { |
---|
| 3638 | p_Setm(qq,dst); |
---|
[f93c5e9] | 3639 | |
---|
[deca086] | 3640 | p_Test(aq,dst); |
---|
| 3641 | p_Test(qq,dst); |
---|
[f93c5e9] | 3642 | |
---|
[83a1714] | 3643 | #if 0 |
---|
| 3644 | p_Test(qq,dst); |
---|
| 3645 | PrintS("\nqq: "); p_Write(qq, dst, dst); PrintLn(); |
---|
| 3646 | #endif |
---|
[f93c5e9] | 3647 | |
---|
| 3648 | if (aq!=NULL) |
---|
| 3649 | qq=p_Mult_q(aq,qq,dst); |
---|
| 3650 | |
---|
[deca086] | 3651 | aq = qq; |
---|
[f93c5e9] | 3652 | |
---|
[deca086] | 3653 | while (pNext(aq) != NULL) pIter(aq); |
---|
[f93c5e9] | 3654 | |
---|
[deca086] | 3655 | if (result_last==NULL) |
---|
| 3656 | { |
---|
| 3657 | result=qq; |
---|
| 3658 | } |
---|
| 3659 | else |
---|
| 3660 | { |
---|
| 3661 | pNext(result_last)=qq; |
---|
| 3662 | } |
---|
| 3663 | result_last=aq; |
---|
| 3664 | aq = NULL; |
---|
| 3665 | } |
---|
| 3666 | else if (aq!=NULL) |
---|
| 3667 | { |
---|
| 3668 | p_Delete(&aq,dst); |
---|
| 3669 | } |
---|
| 3670 | } |
---|
[f93c5e9] | 3671 | |
---|
[deca086] | 3672 | result=p_SortAdd(result,dst); |
---|
| 3673 | #else |
---|
| 3674 | // if (qq!=NULL) |
---|
| 3675 | // { |
---|
| 3676 | // pSetm(qq); |
---|
| 3677 | // pTest(qq); |
---|
| 3678 | // pTest(aq); |
---|
| 3679 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
| 3680 | // aq = qq; |
---|
| 3681 | // while (pNext(aq) != NULL) pIter(aq); |
---|
| 3682 | // pNext(aq) = result; |
---|
| 3683 | // aq = NULL; |
---|
| 3684 | // result = qq; |
---|
| 3685 | // } |
---|
| 3686 | // else if (aq!=NULL) |
---|
| 3687 | // { |
---|
| 3688 | // pDelete(&aq); |
---|
| 3689 | // } |
---|
| 3690 | //} |
---|
| 3691 | //p = result; |
---|
| 3692 | //result = NULL; |
---|
| 3693 | //while (p != NULL) |
---|
| 3694 | //{ |
---|
| 3695 | // qq = p; |
---|
| 3696 | // pIter(p); |
---|
| 3697 | // qq->next = NULL; |
---|
| 3698 | // result = pAdd(result, qq); |
---|
| 3699 | //} |
---|
| 3700 | #endif |
---|
| 3701 | p_Test(result,dst); |
---|
[f93c5e9] | 3702 | |
---|
[83a1714] | 3703 | #if 0 |
---|
| 3704 | p_Test(result,dst); |
---|
| 3705 | PrintS("\nresult: "); p_Write(result,dst,dst); PrintLn(); |
---|
| 3706 | #endif |
---|
[deca086] | 3707 | return result; |
---|
| 3708 | } |
---|
[f550e86] | 3709 | /************************************************************** |
---|
| 3710 | * |
---|
| 3711 | * Jet |
---|
| 3712 | * |
---|
| 3713 | **************************************************************/ |
---|
| 3714 | |
---|
| 3715 | poly pp_Jet(poly p, int m, const ring R) |
---|
| 3716 | { |
---|
| 3717 | poly r=NULL; |
---|
| 3718 | poly t=NULL; |
---|
| 3719 | |
---|
| 3720 | while (p!=NULL) |
---|
| 3721 | { |
---|
| 3722 | if (p_Totaldegree(p,R)<=m) |
---|
| 3723 | { |
---|
| 3724 | if (r==NULL) |
---|
| 3725 | r=p_Head(p,R); |
---|
| 3726 | else |
---|
| 3727 | if (t==NULL) |
---|
| 3728 | { |
---|
| 3729 | pNext(r)=p_Head(p,R); |
---|
| 3730 | t=pNext(r); |
---|
| 3731 | } |
---|
| 3732 | else |
---|
| 3733 | { |
---|
| 3734 | pNext(t)=p_Head(p,R); |
---|
| 3735 | pIter(t); |
---|
| 3736 | } |
---|
| 3737 | } |
---|
| 3738 | pIter(p); |
---|
| 3739 | } |
---|
| 3740 | return r; |
---|
| 3741 | } |
---|
| 3742 | |
---|
| 3743 | poly p_Jet(poly p, int m,const ring R) |
---|
| 3744 | { |
---|
| 3745 | while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R); |
---|
| 3746 | if (p==NULL) return NULL; |
---|
| 3747 | poly r=p; |
---|
| 3748 | while (pNext(p)!=NULL) |
---|
| 3749 | { |
---|
| 3750 | if (p_Totaldegree(pNext(p),R)>m) |
---|
| 3751 | { |
---|
| 3752 | p_LmDelete(&pNext(p),R); |
---|
| 3753 | } |
---|
| 3754 | else |
---|
| 3755 | pIter(p); |
---|
| 3756 | } |
---|
| 3757 | return r; |
---|
| 3758 | } |
---|
| 3759 | |
---|
| 3760 | poly pp_JetW(poly p, int m, short *w, const ring R) |
---|
| 3761 | { |
---|
| 3762 | poly r=NULL; |
---|
| 3763 | poly t=NULL; |
---|
| 3764 | while (p!=NULL) |
---|
| 3765 | { |
---|
| 3766 | if (totaldegreeWecart_IV(p,R,w)<=m) |
---|
| 3767 | { |
---|
| 3768 | if (r==NULL) |
---|
| 3769 | r=p_Head(p,R); |
---|
| 3770 | else |
---|
| 3771 | if (t==NULL) |
---|
| 3772 | { |
---|
| 3773 | pNext(r)=p_Head(p,R); |
---|
| 3774 | t=pNext(r); |
---|
| 3775 | } |
---|
| 3776 | else |
---|
| 3777 | { |
---|
| 3778 | pNext(t)=p_Head(p,R); |
---|
| 3779 | pIter(t); |
---|
| 3780 | } |
---|
| 3781 | } |
---|
| 3782 | pIter(p); |
---|
| 3783 | } |
---|
| 3784 | return r; |
---|
| 3785 | } |
---|
| 3786 | |
---|
| 3787 | poly p_JetW(poly p, int m, short *w, const ring R) |
---|
| 3788 | { |
---|
| 3789 | while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R); |
---|
| 3790 | if (p==NULL) return NULL; |
---|
| 3791 | poly r=p; |
---|
| 3792 | while (pNext(p)!=NULL) |
---|
| 3793 | { |
---|
| 3794 | if (totaldegreeWecart_IV(pNext(p),R,w)>m) |
---|
| 3795 | { |
---|
| 3796 | p_LmDelete(&pNext(p),R); |
---|
| 3797 | } |
---|
| 3798 | else |
---|
| 3799 | pIter(p); |
---|
| 3800 | } |
---|
| 3801 | return r; |
---|
| 3802 | } |
---|
[5c39a9] | 3803 | |
---|
[ba0fc3] | 3804 | /*************************************************************/ |
---|
| 3805 | int p_MinDeg(poly p,intvec *w, const ring R) |
---|
| 3806 | { |
---|
| 3807 | if(p==NULL) |
---|
| 3808 | return -1; |
---|
| 3809 | int d=-1; |
---|
| 3810 | while(p!=NULL) |
---|
| 3811 | { |
---|
| 3812 | int d0=0; |
---|
| 3813 | for(int j=0;j<rVar(R);j++) |
---|
| 3814 | if(w==NULL||j>=w->length()) |
---|
| 3815 | d0+=p_GetExp(p,j+1,R); |
---|
| 3816 | else |
---|
| 3817 | d0+=(*w)[j]*p_GetExp(p,j+1,R); |
---|
| 3818 | if(d0<d||d==-1) |
---|
| 3819 | d=d0; |
---|
| 3820 | pIter(p); |
---|
| 3821 | } |
---|
| 3822 | return d; |
---|
| 3823 | } |
---|
| 3824 | |
---|
[a4081e5] | 3825 | /***************************************************************/ |
---|
| 3826 | |
---|
| 3827 | poly p_Series(int n,poly p,poly u, intvec *w, const ring R) |
---|
| 3828 | { |
---|
| 3829 | short *ww=iv2array(w,R); |
---|
| 3830 | if(p!=NULL) |
---|
| 3831 | { |
---|
| 3832 | if(u==NULL) |
---|
| 3833 | p=p_JetW(p,n,ww,R); |
---|
| 3834 | else |
---|
| 3835 | p=p_JetW(p_Mult_q(p,p_Invers(n-p_MinDeg(p,w,R),u,w,R),R),n,ww,R); |
---|
| 3836 | } |
---|
| 3837 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3838 | return p; |
---|
| 3839 | } |
---|
| 3840 | |
---|
| 3841 | poly p_Invers(int n,poly u,intvec *w, const ring R) |
---|
| 3842 | { |
---|
| 3843 | if(n<0) |
---|
| 3844 | return NULL; |
---|
| 3845 | number u0=n_Invers(pGetCoeff(u),R->cf); |
---|
| 3846 | poly v=p_NSet(u0,R); |
---|
| 3847 | if(n==0) |
---|
| 3848 | return v; |
---|
| 3849 | short *ww=iv2array(w,R); |
---|
| 3850 | poly u1=p_JetW(p_Sub(p_One(R),p_Mult_nn(u,u0,R),R),n,ww,R); |
---|
| 3851 | if(u1==NULL) |
---|
| 3852 | { |
---|
| 3853 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3854 | return v; |
---|
| 3855 | } |
---|
| 3856 | poly v1=p_Mult_nn(p_Copy(u1,R),u0,R); |
---|
| 3857 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3858 | for(int i=n/p_MinDeg(u1,w,R);i>1;i--) |
---|
| 3859 | { |
---|
| 3860 | v1=p_JetW(p_Mult_q(v1,p_Copy(u1,R),R),n,ww,R); |
---|
| 3861 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3862 | } |
---|
| 3863 | p_Delete(&u1,R); |
---|
| 3864 | p_Delete(&v1,R); |
---|
| 3865 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3866 | return v; |
---|
| 3867 | } |
---|
| 3868 | |
---|
[7dce2d7] | 3869 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r) |
---|
| 3870 | { |
---|
| 3871 | while ((p1 != NULL) && (p2 != NULL)) |
---|
| 3872 | { |
---|
| 3873 | if (! p_LmEqual(p1, p2,r)) |
---|
| 3874 | return FALSE; |
---|
| 3875 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r )) |
---|
| 3876 | return FALSE; |
---|
| 3877 | pIter(p1); |
---|
| 3878 | pIter(p2); |
---|
| 3879 | } |
---|
| 3880 | return (p1==p2); |
---|
| 3881 | } |
---|
[32d07a5] | 3882 | |
---|
[55e2df0] | 3883 | static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r1, const ring r2) |
---|
| 3884 | { |
---|
| 3885 | assume( r1 == r2 || rSamePolyRep(r1, r2) ); |
---|
| 3886 | |
---|
| 3887 | p_LmCheckPolyRing1(p1, r1); |
---|
| 3888 | p_LmCheckPolyRing1(p2, r2); |
---|
| 3889 | |
---|
| 3890 | int i = r1->ExpL_Size; |
---|
| 3891 | |
---|
| 3892 | assume( r1->ExpL_Size == r2->ExpL_Size ); |
---|
| 3893 | |
---|
| 3894 | unsigned long *ep = p1->exp; |
---|
| 3895 | unsigned long *eq = p2->exp; |
---|
| 3896 | |
---|
| 3897 | do |
---|
| 3898 | { |
---|
| 3899 | i--; |
---|
| 3900 | if (ep[i] != eq[i]) return FALSE; |
---|
| 3901 | } |
---|
| 3902 | while (i); |
---|
| 3903 | |
---|
| 3904 | return TRUE; |
---|
| 3905 | } |
---|
| 3906 | |
---|
| 3907 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r1, const ring r2) |
---|
| 3908 | { |
---|
| 3909 | assume( r1 == r2 || rSamePolyRep(r1, r2) ); // will be used in rEqual! |
---|
| 3910 | assume( r1->cf == r2->cf ); |
---|
| 3911 | |
---|
| 3912 | while ((p1 != NULL) && (p2 != NULL)) |
---|
| 3913 | { |
---|
| 3914 | // returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !! |
---|
| 3915 | // #define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r) |
---|
| 3916 | |
---|
| 3917 | if (! p_ExpVectorEqual(p1, p2, r1, r2)) |
---|
| 3918 | return FALSE; |
---|
| 3919 | |
---|
| 3920 | if (! n_Equal(p_GetCoeff(p1,r1), p_GetCoeff(p2,r2), r1->cf )) |
---|
| 3921 | return FALSE; |
---|
| 3922 | |
---|
| 3923 | pIter(p1); |
---|
| 3924 | pIter(p2); |
---|
| 3925 | } |
---|
| 3926 | return (p1==p2); |
---|
| 3927 | } |
---|
| 3928 | |
---|
[32d07a5] | 3929 | /*2 |
---|
| 3930 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
| 3931 | *assume p1 != NULL and p2 != NULL |
---|
| 3932 | */ |
---|
| 3933 | BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r) |
---|
| 3934 | { |
---|
| 3935 | number n,nn; |
---|
| 3936 | pAssume(p1 != NULL && p2 != NULL); |
---|
| 3937 | |
---|
| 3938 | if (!p_LmEqual(p1,p2,r)) //compare leading mons |
---|
| 3939 | return FALSE; |
---|
| 3940 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
---|
| 3941 | return FALSE; |
---|
| 3942 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
---|
| 3943 | return FALSE; |
---|
| 3944 | if (pLength(p1) != pLength(p2)) |
---|
| 3945 | return FALSE; |
---|
| 3946 | #ifdef HAVE_RINGS |
---|
| 3947 | if (rField_is_Ring(r)) |
---|
| 3948 | { |
---|
| 3949 | if (!n_DivBy(p_GetCoeff(p1, r), p_GetCoeff(p2, r), r)) return FALSE; |
---|
| 3950 | } |
---|
| 3951 | #endif |
---|
| 3952 | n=n_Div(p_GetCoeff(p1,r),p_GetCoeff(p2,r),r); |
---|
| 3953 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
| 3954 | { |
---|
| 3955 | if ( ! p_LmEqual(p1, p2,r)) |
---|
| 3956 | { |
---|
| 3957 | n_Delete(&n, r); |
---|
| 3958 | return FALSE; |
---|
| 3959 | } |
---|
| 3960 | if (!n_Equal(p_GetCoeff(p1, r), nn = n_Mult(p_GetCoeff(p2, r),n, r), r)) |
---|
| 3961 | { |
---|
| 3962 | n_Delete(&n, r); |
---|
| 3963 | n_Delete(&nn, r); |
---|
| 3964 | return FALSE; |
---|
| 3965 | } |
---|
| 3966 | n_Delete(&nn, r); |
---|
| 3967 | pIter(p1); |
---|
| 3968 | pIter(p2); |
---|
| 3969 | } |
---|
| 3970 | n_Delete(&n, r); |
---|
| 3971 | return TRUE; |
---|
| 3972 | } |
---|
| 3973 | |
---|
[1fdb6e] | 3974 | /*2 |
---|
| 3975 | * returns the length of a (numbers of monomials) |
---|
| 3976 | * respect syzComp |
---|
| 3977 | */ |
---|
| 3978 | poly p_Last(poly a, int &l, const ring r) |
---|
| 3979 | { |
---|
| 3980 | if (a == NULL) |
---|
| 3981 | { |
---|
| 3982 | l = 0; |
---|
| 3983 | return NULL; |
---|
| 3984 | } |
---|
| 3985 | l = 1; |
---|
| 3986 | if (! rIsSyzIndexRing(r)) |
---|
| 3987 | { |
---|
| 3988 | while (pNext(a)!=NULL) |
---|
| 3989 | { |
---|
| 3990 | pIter(a); |
---|
| 3991 | l++; |
---|
| 3992 | } |
---|
| 3993 | } |
---|
| 3994 | else |
---|
| 3995 | { |
---|
| 3996 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 3997 | poly pp = a; |
---|
| 3998 | while ((a=pNext(a))!=NULL) |
---|
| 3999 | { |
---|
| 4000 | if (p_GetComp(a,r)<=curr_limit/*syzComp*/) |
---|
| 4001 | l++; |
---|
| 4002 | else break; |
---|
| 4003 | pp = a; |
---|
| 4004 | } |
---|
| 4005 | a=pp; |
---|
| 4006 | } |
---|
| 4007 | return a; |
---|
| 4008 | } |
---|
[32d07a5] | 4009 | |
---|
[73ad0c] | 4010 | int p_Var(poly m,const ring r) |
---|
| 4011 | { |
---|
| 4012 | if (m==NULL) return 0; |
---|
| 4013 | if (pNext(m)!=NULL) return 0; |
---|
| 4014 | int i,e=0; |
---|
| 4015 | for (i=rVar(r); i>0; i--) |
---|
| 4016 | { |
---|
| 4017 | int exp=p_GetExp(m,i,r); |
---|
| 4018 | if (exp==1) |
---|
| 4019 | { |
---|
| 4020 | if (e==0) e=i; |
---|
| 4021 | else return 0; |
---|
| 4022 | } |
---|
| 4023 | else if (exp!=0) |
---|
| 4024 | { |
---|
| 4025 | return 0; |
---|
| 4026 | } |
---|
| 4027 | } |
---|
| 4028 | return e; |
---|
| 4029 | } |
---|
| 4030 | |
---|
| 4031 | /*2 |
---|
| 4032 | *the minimal index of used variables - 1 |
---|
| 4033 | */ |
---|
| 4034 | int p_LowVar (poly p, const ring r) |
---|
| 4035 | { |
---|
| 4036 | int k,l,lex; |
---|
| 4037 | |
---|
| 4038 | if (p == NULL) return -1; |
---|
| 4039 | |
---|
| 4040 | k = 32000;/*a very large dummy value*/ |
---|
| 4041 | while (p != NULL) |
---|
| 4042 | { |
---|
| 4043 | l = 1; |
---|
| 4044 | lex = p_GetExp(p,l,r); |
---|
| 4045 | while ((l < (rVar(r))) && (lex == 0)) |
---|
| 4046 | { |
---|
| 4047 | l++; |
---|
| 4048 | lex = p_GetExp(p,l,r); |
---|
| 4049 | } |
---|
| 4050 | l--; |
---|
| 4051 | if (l < k) k = l; |
---|
| 4052 | pIter(p); |
---|
| 4053 | } |
---|
| 4054 | return k; |
---|
| 4055 | } |
---|
| 4056 | |
---|
[b7cfaf] | 4057 | /*2 |
---|
| 4058 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
| 4059 | */ |
---|
| 4060 | void p_Shift (poly * p,int i, const ring r) |
---|
| 4061 | { |
---|
| 4062 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
| 4063 | int j = p_MaxComp(*p,r),k = p_MinComp(*p,r); |
---|
| 4064 | |
---|
| 4065 | if (j+i < 0) return ; |
---|
| 4066 | while (qp1 != NULL) |
---|
| 4067 | { |
---|
| 4068 | if ((p_GetComp(qp1,r)+i > 0) || ((j == -i) && (j == k))) |
---|
| 4069 | { |
---|
| 4070 | p_AddComp(qp1,i,r); |
---|
| 4071 | p_SetmComp(qp1,r); |
---|
| 4072 | qp2 = qp1; |
---|
| 4073 | pIter(qp1); |
---|
| 4074 | } |
---|
| 4075 | else |
---|
| 4076 | { |
---|
| 4077 | if (qp2 == *p) |
---|
| 4078 | { |
---|
| 4079 | pIter(*p); |
---|
| 4080 | p_LmDelete(&qp2,r); |
---|
| 4081 | qp2 = *p; |
---|
| 4082 | qp1 = *p; |
---|
| 4083 | } |
---|
| 4084 | else |
---|
| 4085 | { |
---|
| 4086 | qp2->next = qp1->next; |
---|
| 4087 | if (qp1!=NULL) p_LmDelete(&qp1,r); |
---|
| 4088 | qp1 = qp2->next; |
---|
| 4089 | } |
---|
| 4090 | } |
---|
| 4091 | } |
---|
| 4092 | } |
---|
[50c414] | 4093 | /*************************************************************** |
---|
| 4094 | * |
---|
| 4095 | * p_ShallowDelete |
---|
| 4096 | * |
---|
| 4097 | ***************************************************************/ |
---|
| 4098 | #undef LINKAGE |
---|
| 4099 | #define LINKAGE |
---|
[38500a] | 4100 | #undef p_Delete__T |
---|
| 4101 | #define p_Delete__T p_ShallowDelete |
---|
[35eaf8] | 4102 | #undef n_Delete__T |
---|
| 4103 | #define n_Delete__T(n, r) ((void)0) |
---|
[50c414] | 4104 | |
---|
[20b794] | 4105 | #include <polys/templates/p_Delete__T.cc> |
---|
[50c414] | 4106 | |
---|