[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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[341696] | 9 | * Version: $Id$ |
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[35aab3] | 10 | *******************************************************************/ |
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| 11 | |
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[9982049] | 12 | |
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[45d2332] | 13 | |
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[22a09d] | 14 | #include "config.h" |
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[6bec87] | 15 | #include <misc/auxiliary.h> |
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[22a09d] | 16 | |
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| 17 | #include <ctype.h> |
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| 18 | #include <omalloc/omalloc.h> |
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[45d2332] | 19 | #include <misc/options.h> |
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| 20 | #include <misc/intvec.h> |
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| 21 | |
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| 22 | #include <coeffs/longrat.h> // ??? |
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[b38d70] | 23 | #include <coeffs/ffields.h> |
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| 24 | |
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| 25 | #define TRANSEXT_PRIVATES |
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| 26 | |
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| 27 | #include "ext_fields/transext.h" |
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| 28 | #include "ext_fields/algext.h" |
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[45d2332] | 29 | |
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[af598e] | 30 | #include "weight.h" |
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| 31 | #include "simpleideals.h" |
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[9982049] | 32 | |
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[af598e] | 33 | #include "monomials/ring.h" |
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| 34 | #include "monomials/p_polys.h" |
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[304ad9b] | 35 | #include <polys/templates/p_MemCmp.h> |
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| 36 | #include <polys/templates/p_MemAdd.h> |
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| 37 | #include <polys/templates/p_MemCopy.h> |
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| 38 | |
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[45d2332] | 39 | |
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[20b794] | 40 | // #include <???/ideals.h> |
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| 41 | // #include <???/int64vec.h> |
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[45d2332] | 42 | |
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[fc5095] | 43 | #ifndef NDEBUG |
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[20b794] | 44 | // #include <???/febase.h> |
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[fc5095] | 45 | #endif |
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[35aab3] | 46 | |
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[45d2332] | 47 | #ifdef HAVE_PLURAL |
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[af598e] | 48 | #include "nc/nc.h" |
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| 49 | #include "nc/sca.h" |
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[45d2332] | 50 | #endif |
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| 51 | |
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[af598e] | 52 | #include "coeffrings.h" |
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[0654122] | 53 | #ifdef HAVE_FACTORY |
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[af598e] | 54 | #include "clapsing.h" |
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[0654122] | 55 | #endif |
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[32d07a5] | 56 | |
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[35aab3] | 57 | /*************************************************************** |
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| 58 | * |
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| 59 | * Completing what needs to be set for the monomial |
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| 60 | * |
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| 61 | ***************************************************************/ |
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| 62 | // this is special for the syz stuff |
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[eb72ba1] | 63 | static int* _components = NULL; |
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| 64 | static long* _componentsShifted = NULL; |
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| 65 | static int _componentsExternal = 0; |
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[35aab3] | 66 | |
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[fc5095] | 67 | BOOLEAN pSetm_error=0; |
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| 68 | |
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[324710] | 69 | #ifndef NDEBUG |
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| 70 | # define MYTEST 0 |
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| 71 | #else /* ifndef NDEBUG */ |
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| 72 | # define MYTEST 0 |
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| 73 | #endif /* ifndef NDEBUG */ |
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| 74 | |
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[33c36d] | 75 | void p_Setm_General(poly p, const ring r) |
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[35aab3] | 76 | { |
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| 77 | p_LmCheckPolyRing(p, r); |
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| 78 | int pos=0; |
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| 79 | if (r->typ!=NULL) |
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| 80 | { |
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| 81 | loop |
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| 82 | { |
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| 83 | long ord=0; |
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| 84 | sro_ord* o=&(r->typ[pos]); |
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| 85 | switch(o->ord_typ) |
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| 86 | { |
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| 87 | case ro_dp: |
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| 88 | { |
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| 89 | int a,e; |
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| 90 | a=o->data.dp.start; |
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| 91 | e=o->data.dp.end; |
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| 92 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
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| 93 | p->exp[o->data.dp.place]=ord; |
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| 94 | break; |
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| 95 | } |
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| 96 | case ro_wp_neg: |
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| 97 | ord=POLY_NEGWEIGHT_OFFSET; |
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| 98 | // no break; |
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| 99 | case ro_wp: |
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| 100 | { |
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| 101 | int a,e; |
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| 102 | a=o->data.wp.start; |
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| 103 | e=o->data.wp.end; |
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| 104 | int *w=o->data.wp.weights; |
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[fc5095] | 105 | #if 1 |
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[35aab3] | 106 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r)*w[i-a]; |
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[fc5095] | 107 | #else |
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| 108 | long ai; |
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| 109 | int ei,wi; |
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| 110 | for(int i=a;i<=e;i++) |
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| 111 | { |
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| 112 | ei=p_GetExp(p,i,r); |
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| 113 | wi=w[i-a]; |
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| 114 | ai=ei*wi; |
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| 115 | if (ai/ei!=wi) pSetm_error=TRUE; |
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| 116 | ord+=ai; |
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| 117 | if (ord<ai) pSetm_error=TRUE; |
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| 118 | } |
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[ab4778] | 119 | #endif |
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[35aab3] | 120 | p->exp[o->data.wp.place]=ord; |
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| 121 | break; |
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| 122 | } |
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[fc5095] | 123 | case ro_wp64: |
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| 124 | { |
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[ab4778] | 125 | int64 ord=0; |
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[fc5095] | 126 | int a,e; |
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| 127 | a=o->data.wp64.start; |
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| 128 | e=o->data.wp64.end; |
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| 129 | int64 *w=o->data.wp64.weights64; |
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| 130 | int64 ei,wi,ai; |
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[2132395] | 131 | for(int i=a;i<=e;i++) |
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[b5d4d1] | 132 | { |
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[fc5095] | 133 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
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| 134 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
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| 135 | ei=(int64)p_GetExp(p,i,r); |
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| 136 | wi=w[i-a]; |
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| 137 | ai=ei*wi; |
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[2132395] | 138 | if(ei!=0 && ai/ei!=wi) |
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[b5d4d1] | 139 | { |
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[fc5095] | 140 | pSetm_error=TRUE; |
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[b5d4d1] | 141 | #if SIZEOF_LONG == 4 |
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[fc5095] | 142 | Print("ai %lld, wi %lld\n",ai,wi); |
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[b5d4d1] | 143 | #else |
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[2132395] | 144 | Print("ai %ld, wi %ld\n",ai,wi); |
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[b5d4d1] | 145 | #endif |
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[fc5095] | 146 | } |
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| 147 | ord+=ai; |
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[2132395] | 148 | if (ord<ai) |
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[b5d4d1] | 149 | { |
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[2132395] | 150 | pSetm_error=TRUE; |
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[b5d4d1] | 151 | #if SIZEOF_LONG == 4 |
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[2132395] | 152 | Print("ai %lld, ord %lld\n",ai,ord); |
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[b5d4d1] | 153 | #else |
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[2132395] | 154 | Print("ai %ld, ord %ld\n",ai,ord); |
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[b5d4d1] | 155 | #endif |
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[fc5095] | 156 | } |
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| 157 | } |
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| 158 | int64 mask=(int64)0x7fffffff; |
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| 159 | long a_0=(long)(ord&mask); //2^31 |
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| 160 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
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| 161 | |
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[ab4778] | 162 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
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| 163 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
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| 164 | //Print("mask: %d",mask); |
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[fc5095] | 165 | |
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| 166 | p->exp[o->data.wp64.place]=a_1; |
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[ab4778] | 167 | p->exp[o->data.wp64.place+1]=a_0; |
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[fc5095] | 168 | // if(p_Setm_error) Print("***************************\n |
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| 169 | // ***************************\n |
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| 170 | // **WARNING: overflow error**\n |
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| 171 | // ***************************\n |
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| 172 | // ***************************\n"); |
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| 173 | break; |
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| 174 | } |
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[35aab3] | 175 | case ro_cp: |
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| 176 | { |
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| 177 | int a,e; |
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| 178 | a=o->data.cp.start; |
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| 179 | e=o->data.cp.end; |
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| 180 | int pl=o->data.cp.place; |
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| 181 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
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| 182 | break; |
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| 183 | } |
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| 184 | case ro_syzcomp: |
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| 185 | { |
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| 186 | int c=p_GetComp(p,r); |
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| 187 | long sc = c; |
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[eb72ba1] | 188 | int* Components = (_componentsExternal ? _components : |
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[35aab3] | 189 | o->data.syzcomp.Components); |
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[eb72ba1] | 190 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
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[35aab3] | 191 | o->data.syzcomp.ShiftedComponents); |
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| 192 | if (ShiftedComponents != NULL) |
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| 193 | { |
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| 194 | assume(Components != NULL); |
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| 195 | assume(c == 0 || Components[c] != 0); |
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| 196 | sc = ShiftedComponents[Components[c]]; |
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| 197 | assume(c == 0 || sc != 0); |
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| 198 | } |
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| 199 | p->exp[o->data.syzcomp.place]=sc; |
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| 200 | break; |
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| 201 | } |
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| 202 | case ro_syz: |
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| 203 | { |
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[273fed] | 204 | const unsigned long c = p_GetComp(p, r); |
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| 205 | const short place = o->data.syz.place; |
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| 206 | const int limit = o->data.syz.limit; |
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| 207 | |
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| 208 | if (c > limit) |
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| 209 | p->exp[place] = o->data.syz.curr_index; |
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[35aab3] | 210 | else if (c > 0) |
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[273fed] | 211 | { |
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| 212 | assume( (1 <= c) && (c <= limit) ); |
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| 213 | p->exp[place]= o->data.syz.syz_index[c]; |
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| 214 | } |
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[35aab3] | 215 | else |
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| 216 | { |
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| 217 | assume(c == 0); |
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[273fed] | 218 | p->exp[place]= 0; |
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[35aab3] | 219 | } |
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| 220 | break; |
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| 221 | } |
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[645a19] | 222 | // Prefix for Induced Schreyer ordering |
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| 223 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
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| 224 | { |
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| 225 | assume(p != NULL); |
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| 226 | |
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| 227 | #ifndef NDEBUG |
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| 228 | #if MYTEST |
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[273fed] | 229 | Print("p_Setm_General: isTemp ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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[645a19] | 230 | #endif |
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| 231 | #endif |
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| 232 | int c = p_GetComp(p, r); |
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| 233 | |
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| 234 | assume( c >= 0 ); |
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| 235 | |
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| 236 | // Let's simulate case ro_syz above.... |
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| 237 | // Should accumulate (by Suffix) and be a level indicator |
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| 238 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
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| 239 | |
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| 240 | assume( pVarOffset != NULL ); |
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| 241 | |
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| 242 | // TODO: Can this be done in the suffix??? |
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| 243 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 244 | { |
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| 245 | const int vo = pVarOffset[i]; |
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| 246 | if( vo != -1) // TODO: optimize: can be done once! |
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| 247 | { |
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[5cb9ec] | 248 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
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| 249 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
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| 250 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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| 251 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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[645a19] | 252 | } |
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| 253 | } |
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| 254 | #ifndef NDEBUG |
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| 255 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 256 | { |
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| 257 | const int vo = pVarOffset[i]; |
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| 258 | if( vo != -1) // TODO: optimize: can be done once! |
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| 259 | { |
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[5cb9ec] | 260 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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| 261 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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[645a19] | 262 | } |
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| 263 | } |
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| 264 | #if MYTEST |
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[1b816a3] | 265 | // if( p->exp[o->data.isTemp.start] > 0 ) |
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| 266 | // { |
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| 267 | // PrintS("Initial Value: "); p_DebugPrint(p, r, r, 1); |
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| 268 | // } |
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[645a19] | 269 | #endif |
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| 270 | #endif |
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| 271 | break; |
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| 272 | } |
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| 273 | |
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| 274 | // Suffix for Induced Schreyer ordering |
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| 275 | case ro_is: |
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| 276 | { |
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[273fed] | 277 | #ifndef NDEBUG |
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| 278 | #if MYTEST |
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| 279 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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| 280 | #endif |
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| 281 | #endif |
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| 282 | |
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[645a19] | 283 | assume(p != NULL); |
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| 284 | |
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| 285 | int c = p_GetComp(p, r); |
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| 286 | |
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| 287 | assume( c >= 0 ); |
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| 288 | const ideal F = o->data.is.F; |
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| 289 | const int limit = o->data.is.limit; |
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| 290 | |
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| 291 | if( F != NULL && c > limit ) |
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| 292 | { |
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| 293 | #ifndef NDEBUG |
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| 294 | #if MYTEST |
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[6e66d2] | 295 | 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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[645a19] | 296 | #endif |
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| 297 | #endif |
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| 298 | |
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| 299 | c -= limit; |
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| 300 | assume( c > 0 ); |
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| 301 | c--; |
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| 302 | |
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| 303 | assume( c < IDELEMS(F) ); // What about others??? |
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| 304 | |
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| 305 | const poly pp = F->m[c]; // get reference monomial!!! |
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| 306 | |
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| 307 | #ifndef NDEBUG |
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| 308 | #if MYTEST |
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| 309 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
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| 310 | p_DebugPrint(pp, r, r, 1); |
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| 311 | #endif |
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| 312 | #endif |
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| 313 | |
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| 314 | |
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[6e66d2] | 315 | assume(pp != NULL); |
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[645a19] | 316 | if(pp == NULL) break; |
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| 317 | |
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| 318 | const int start = o->data.is.start; |
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| 319 | const int end = o->data.is.end; |
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| 320 | |
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| 321 | assume(start <= end); |
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[6e66d2] | 322 | |
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| 323 | // const int limit = o->data.is.limit; |
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| 324 | assume( limit >= 0 ); |
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| 325 | |
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| 326 | // const int st = o->data.isTemp.start; |
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| 327 | |
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| 328 | if( c > limit ) |
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| 329 | p->exp[start] = 1; |
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| 330 | // else |
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| 331 | // p->exp[start] = 0; |
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| 332 | |
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| 333 | |
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| 334 | #ifndef NDEBUG |
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[a41623] | 335 | Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]); |
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[6e66d2] | 336 | #endif |
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| 337 | |
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[645a19] | 338 | |
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| 339 | for( int i = start; i <= end; i++) // v[0] may be here... |
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| 340 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
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| 341 | |
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[6e66d2] | 342 | |
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| 343 | |
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| 344 | |
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[645a19] | 345 | #ifndef NDEBUG |
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| 346 | const int* const pVarOffset = o->data.is.pVarOffset; |
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| 347 | |
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| 348 | assume( pVarOffset != NULL ); |
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| 349 | |
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| 350 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 351 | { |
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| 352 | const int vo = pVarOffset[i]; |
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| 353 | if( vo != -1) // TODO: optimize: can be done once! |
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[5cb9ec] | 354 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
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| 355 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
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[645a19] | 356 | } |
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| 357 | // TODO: how to check this for computed values??? |
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| 358 | #endif |
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| 359 | } else |
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| 360 | { |
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| 361 | const int* const pVarOffset = o->data.is.pVarOffset; |
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| 362 | |
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| 363 | // What about v[0] - component: it will be added later by |
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| 364 | // suffix!!! |
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| 365 | // TODO: Test it! |
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| 366 | const int vo = pVarOffset[0]; |
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| 367 | if( vo != -1 ) |
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| 368 | p->exp[vo] = c; // initial component v[0]! |
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[6e66d2] | 369 | |
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| 370 | #ifndef NDEBUG |
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| 371 | #if MYTEST |
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| 372 | Print("p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]); |
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| 373 | p_DebugPrint(p, r, r, 1); |
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| 374 | #endif |
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| 375 | #endif |
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[645a19] | 376 | } |
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[6e66d2] | 377 | |
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[645a19] | 378 | |
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| 379 | break; |
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| 380 | } |
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[35aab3] | 381 | default: |
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| 382 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
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| 383 | return; |
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| 384 | } |
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| 385 | pos++; |
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| 386 | if (pos == r->OrdSize) return; |
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| 387 | } |
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| 388 | } |
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| 389 | } |
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| 390 | |
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| 391 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
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| 392 | { |
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[eb72ba1] | 393 | _components = Components; |
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| 394 | _componentsShifted = ShiftedComponents; |
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| 395 | _componentsExternal = 1; |
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[35aab3] | 396 | p_Setm_General(p, r); |
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[eb72ba1] | 397 | _componentsExternal = 0; |
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[35aab3] | 398 | } |
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| 399 | |
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| 400 | // dummy for lp, ls, etc |
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[33c36d] | 401 | void p_Setm_Dummy(poly p, const ring r) |
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[35aab3] | 402 | { |
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| 403 | p_LmCheckPolyRing(p, r); |
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| 404 | } |
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| 405 | |
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| 406 | // for dp, Dp, ds, etc |
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[33c36d] | 407 | void p_Setm_TotalDegree(poly p, const ring r) |
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[35aab3] | 408 | { |
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| 409 | p_LmCheckPolyRing(p, r); |
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[99bdcf] | 410 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
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[35aab3] | 411 | } |
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| 412 | |
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| 413 | // for wp, Wp, ws, etc |
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[33c36d] | 414 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
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[35aab3] | 415 | { |
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| 416 | p_LmCheckPolyRing(p, r); |
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[19ae652] | 417 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
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[35aab3] | 418 | } |
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| 419 | |
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| 420 | p_SetmProc p_GetSetmProc(ring r) |
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| 421 | { |
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[ab4778] | 422 | // covers lp, rp, ls, |
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[35aab3] | 423 | if (r->typ == NULL) return p_Setm_Dummy; |
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| 424 | |
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| 425 | if (r->OrdSize == 1) |
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| 426 | { |
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[ab4778] | 427 | if (r->typ[0].ord_typ == ro_dp && |
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[35aab3] | 428 | r->typ[0].data.dp.start == 1 && |
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| 429 | r->typ[0].data.dp.end == r->N && |
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| 430 | r->typ[0].data.dp.place == r->pOrdIndex) |
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| 431 | return p_Setm_TotalDegree; |
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[ab4778] | 432 | if (r->typ[0].ord_typ == ro_wp && |
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[35aab3] | 433 | r->typ[0].data.wp.start == 1 && |
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| 434 | r->typ[0].data.wp.end == r->N && |
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| 435 | r->typ[0].data.wp.place == r->pOrdIndex && |
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| 436 | r->typ[0].data.wp.weights == r->firstwv) |
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| 437 | return p_Setm_WFirstTotalDegree; |
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| 438 | } |
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| 439 | return p_Setm_General; |
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| 440 | } |
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| 441 | |
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| 442 | |
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| 443 | /* -------------------------------------------------------------------*/ |
---|
| 444 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
[b5d4d1] | 445 | |
---|
| 446 | /* comptible with ordering */ |
---|
[bf183f] | 447 | long p_Deg(poly a, const ring r) |
---|
[35aab3] | 448 | { |
---|
| 449 | p_LmCheckPolyRing(a, r); |
---|
[19ae652] | 450 | assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); |
---|
[35aab3] | 451 | return p_GetOrder(a, r); |
---|
| 452 | } |
---|
| 453 | |
---|
[19ae652] | 454 | // p_WTotalDegree for weighted orderings |
---|
[35aab3] | 455 | // whose first block covers all variables |
---|
[19ae652] | 456 | long p_WFirstTotalDegree(poly p, const ring r) |
---|
[35aab3] | 457 | { |
---|
| 458 | int i; |
---|
| 459 | long sum = 0; |
---|
[ab4778] | 460 | |
---|
[35aab3] | 461 | for (i=1; i<= r->firstBlockEnds; i++) |
---|
| 462 | { |
---|
| 463 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 464 | } |
---|
| 465 | return sum; |
---|
| 466 | } |
---|
| 467 | |
---|
| 468 | /*2 |
---|
| 469 | * compute the degree of the leading monomial of p |
---|
| 470 | * with respect to weigths from the ordering |
---|
| 471 | * the ordering is not compatible with degree so do not use p->Order |
---|
| 472 | */ |
---|
[19ae652] | 473 | long p_WTotaldegree(poly p, const ring r) |
---|
[35aab3] | 474 | { |
---|
| 475 | p_LmCheckPolyRing(p, r); |
---|
| 476 | int i, k; |
---|
| 477 | long j =0; |
---|
| 478 | |
---|
| 479 | // iterate through each block: |
---|
| 480 | for (i=0;r->order[i]!=0;i++) |
---|
| 481 | { |
---|
[ab4778] | 482 | int b0=r->block0[i]; |
---|
| 483 | int b1=r->block1[i]; |
---|
[35aab3] | 484 | switch(r->order[i]) |
---|
| 485 | { |
---|
[3e0a7b] | 486 | case ringorder_M: |
---|
[ab4778] | 487 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
| 488 | { // in jedem block: |
---|
| 489 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
---|
| 490 | } |
---|
| 491 | break; |
---|
[35aab3] | 492 | case ringorder_wp: |
---|
| 493 | case ringorder_ws: |
---|
| 494 | case ringorder_Wp: |
---|
| 495 | case ringorder_Ws: |
---|
[ab4778] | 496 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 497 | { // in jedem block: |
---|
[ab4778] | 498 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
---|
[35aab3] | 499 | } |
---|
| 500 | break; |
---|
| 501 | case ringorder_lp: |
---|
| 502 | case ringorder_ls: |
---|
[e519c5c] | 503 | case ringorder_rs: |
---|
[35aab3] | 504 | case ringorder_dp: |
---|
| 505 | case ringorder_ds: |
---|
| 506 | case ringorder_Dp: |
---|
| 507 | case ringorder_Ds: |
---|
| 508 | case ringorder_rp: |
---|
[ab4778] | 509 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 510 | { |
---|
| 511 | j+= p_GetExp(p,k,r); |
---|
| 512 | } |
---|
| 513 | break; |
---|
[fc5095] | 514 | case ringorder_a64: |
---|
| 515 | { |
---|
| 516 | int64* w=(int64*)r->wvhdl[i]; |
---|
[ab4778] | 517 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
---|
| 518 | { |
---|
[fc5095] | 519 | //there should be added a line which checks if w[k]>2^31 |
---|
| 520 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
---|
| 521 | } |
---|
| 522 | //break; |
---|
| 523 | return j; |
---|
| 524 | } |
---|
[35aab3] | 525 | case ringorder_c: |
---|
| 526 | case ringorder_C: |
---|
| 527 | case ringorder_S: |
---|
| 528 | case ringorder_s: |
---|
[645a19] | 529 | case ringorder_IS: |
---|
[35aab3] | 530 | case ringorder_aa: |
---|
| 531 | break; |
---|
| 532 | case ringorder_a: |
---|
[ab4778] | 533 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 534 | { // only one line |
---|
[ab4778] | 535 | j+= p_GetExp(p,k, r)*r->wvhdl[i][ k- b0 /*r->block0[i]*/]; |
---|
[35aab3] | 536 | } |
---|
[fc5095] | 537 | //break; |
---|
[35aab3] | 538 | return j; |
---|
[fc5095] | 539 | |
---|
[35aab3] | 540 | #ifndef NDEBUG |
---|
| 541 | default: |
---|
[19ae652] | 542 | Print("missing order %d in p_WTotaldegree\n",r->order[i]); |
---|
[35aab3] | 543 | break; |
---|
| 544 | #endif |
---|
| 545 | } |
---|
| 546 | } |
---|
| 547 | return j; |
---|
| 548 | } |
---|
| 549 | |
---|
[ba0fc3] | 550 | long p_DegW(poly p, const short *w, const ring R) |
---|
| 551 | { |
---|
| 552 | long r=~0L; |
---|
| 553 | |
---|
| 554 | while (p!=NULL) |
---|
| 555 | { |
---|
| 556 | long t=totaldegreeWecart_IV(p,R,w); |
---|
| 557 | if (t>r) r=t; |
---|
| 558 | pIter(p); |
---|
| 559 | } |
---|
| 560 | return r; |
---|
| 561 | } |
---|
| 562 | |
---|
[bf183f] | 563 | int p_Weight(int i, const ring r) |
---|
[35aab3] | 564 | { |
---|
| 565 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
| 566 | { |
---|
| 567 | return 1; |
---|
| 568 | } |
---|
| 569 | return r->firstwv[i-1]; |
---|
| 570 | } |
---|
| 571 | |
---|
[bf183f] | 572 | long p_WDegree(poly p, const ring r) |
---|
[35aab3] | 573 | { |
---|
[99bdcf] | 574 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
[35aab3] | 575 | p_LmCheckPolyRing(p, r); |
---|
[9f73e80] | 576 | int i; |
---|
[35aab3] | 577 | long j =0; |
---|
| 578 | |
---|
| 579 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
| 580 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 581 | |
---|
| 582 | for (;i<=r->N;i++) |
---|
[8a8c9e] | 583 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
[35aab3] | 584 | |
---|
| 585 | return j; |
---|
| 586 | } |
---|
| 587 | |
---|
| 588 | |
---|
| 589 | /* ---------------------------------------------------------------------*/ |
---|
| 590 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
| 591 | /* compute in l also the pLength of p */ |
---|
| 592 | |
---|
| 593 | /*2 |
---|
| 594 | * compute the length of a polynomial (in l) |
---|
| 595 | * and the degree of the monomial with maximal degree: the last one |
---|
| 596 | */ |
---|
[107986] | 597 | long pLDeg0(poly p,int *l, const ring r) |
---|
[35aab3] | 598 | { |
---|
| 599 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 600 | long k= p_GetComp(p, r); |
---|
[35aab3] | 601 | int ll=1; |
---|
| 602 | |
---|
| 603 | if (k > 0) |
---|
| 604 | { |
---|
| 605 | while ((pNext(p)!=NULL) && (p_GetComp(pNext(p), r)==k)) |
---|
| 606 | { |
---|
| 607 | pIter(p); |
---|
| 608 | ll++; |
---|
| 609 | } |
---|
| 610 | } |
---|
| 611 | else |
---|
| 612 | { |
---|
| 613 | while (pNext(p)!=NULL) |
---|
| 614 | { |
---|
| 615 | pIter(p); |
---|
| 616 | ll++; |
---|
| 617 | } |
---|
| 618 | } |
---|
| 619 | *l=ll; |
---|
| 620 | return r->pFDeg(p, r); |
---|
| 621 | } |
---|
| 622 | |
---|
| 623 | /*2 |
---|
| 624 | * compute the length of a polynomial (in l) |
---|
| 625 | * and the degree of the monomial with maximal degree: the last one |
---|
| 626 | * but search in all components before syzcomp |
---|
| 627 | */ |
---|
[107986] | 628 | long pLDeg0c(poly p,int *l, const ring r) |
---|
[35aab3] | 629 | { |
---|
| 630 | assume(p!=NULL); |
---|
| 631 | #ifdef PDEBUG |
---|
| 632 | _p_Test(p,r,PDEBUG); |
---|
| 633 | #endif |
---|
| 634 | p_CheckPolyRing(p, r); |
---|
| 635 | long o; |
---|
| 636 | int ll=1; |
---|
| 637 | |
---|
| 638 | if (! rIsSyzIndexRing(r)) |
---|
| 639 | { |
---|
[ab4778] | 640 | while (pNext(p) != NULL) |
---|
[35aab3] | 641 | { |
---|
| 642 | pIter(p); |
---|
| 643 | ll++; |
---|
| 644 | } |
---|
| 645 | o = r->pFDeg(p, r); |
---|
| 646 | } |
---|
| 647 | else |
---|
| 648 | { |
---|
| 649 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 650 | poly pp = p; |
---|
| 651 | while ((p=pNext(p))!=NULL) |
---|
| 652 | { |
---|
| 653 | if (p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
| 654 | ll++; |
---|
| 655 | else break; |
---|
| 656 | pp = p; |
---|
| 657 | } |
---|
| 658 | #ifdef PDEBUG |
---|
| 659 | _p_Test(pp,r,PDEBUG); |
---|
| 660 | #endif |
---|
| 661 | o = r->pFDeg(pp, r); |
---|
| 662 | } |
---|
| 663 | *l=ll; |
---|
| 664 | return o; |
---|
| 665 | } |
---|
| 666 | |
---|
| 667 | /*2 |
---|
| 668 | * compute the length of a polynomial (in l) |
---|
| 669 | * and the degree of the monomial with maximal degree: the first one |
---|
| 670 | * this works for the polynomial case with degree orderings |
---|
| 671 | * (both c,dp and dp,c) |
---|
| 672 | */ |
---|
[107986] | 673 | long pLDegb(poly p,int *l, const ring r) |
---|
[35aab3] | 674 | { |
---|
| 675 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 676 | long k= p_GetComp(p, r); |
---|
[35aab3] | 677 | long o = r->pFDeg(p, r); |
---|
| 678 | int ll=1; |
---|
| 679 | |
---|
| 680 | if (k != 0) |
---|
| 681 | { |
---|
| 682 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 683 | { |
---|
| 684 | ll++; |
---|
| 685 | } |
---|
| 686 | } |
---|
| 687 | else |
---|
| 688 | { |
---|
| 689 | while ((p=pNext(p)) !=NULL) |
---|
| 690 | { |
---|
| 691 | ll++; |
---|
| 692 | } |
---|
| 693 | } |
---|
| 694 | *l=ll; |
---|
| 695 | return o; |
---|
| 696 | } |
---|
| 697 | |
---|
| 698 | /*2 |
---|
| 699 | * compute the length of a polynomial (in l) |
---|
| 700 | * and the degree of the monomial with maximal degree: |
---|
| 701 | * this is NOT the last one, we have to look for it |
---|
| 702 | */ |
---|
[107986] | 703 | long pLDeg1(poly p,int *l, const ring r) |
---|
[35aab3] | 704 | { |
---|
| 705 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 706 | long k= p_GetComp(p, r); |
---|
[35aab3] | 707 | int ll=1; |
---|
| 708 | long t,max; |
---|
| 709 | |
---|
| 710 | max=r->pFDeg(p, r); |
---|
| 711 | if (k > 0) |
---|
| 712 | { |
---|
| 713 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 714 | { |
---|
| 715 | t=r->pFDeg(p, r); |
---|
| 716 | if (t>max) max=t; |
---|
| 717 | ll++; |
---|
| 718 | } |
---|
| 719 | } |
---|
| 720 | else |
---|
| 721 | { |
---|
| 722 | while ((p=pNext(p))!=NULL) |
---|
| 723 | { |
---|
| 724 | t=r->pFDeg(p, r); |
---|
| 725 | if (t>max) max=t; |
---|
| 726 | ll++; |
---|
| 727 | } |
---|
| 728 | } |
---|
| 729 | *l=ll; |
---|
| 730 | return max; |
---|
| 731 | } |
---|
| 732 | |
---|
| 733 | /*2 |
---|
| 734 | * compute the length of a polynomial (in l) |
---|
| 735 | * and the degree of the monomial with maximal degree: |
---|
| 736 | * this is NOT the last one, we have to look for it |
---|
| 737 | * in all components |
---|
| 738 | */ |
---|
[107986] | 739 | long pLDeg1c(poly p,int *l, const ring r) |
---|
[35aab3] | 740 | { |
---|
| 741 | p_CheckPolyRing(p, r); |
---|
| 742 | int ll=1; |
---|
| 743 | long t,max; |
---|
| 744 | |
---|
| 745 | max=r->pFDeg(p, r); |
---|
| 746 | if (rIsSyzIndexRing(r)) |
---|
| 747 | { |
---|
| 748 | long limit = rGetCurrSyzLimit(r); |
---|
| 749 | while ((p=pNext(p))!=NULL) |
---|
| 750 | { |
---|
| 751 | if (p_GetComp(p, r)<=limit) |
---|
| 752 | { |
---|
| 753 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 754 | ll++; |
---|
| 755 | } |
---|
| 756 | else break; |
---|
| 757 | } |
---|
| 758 | } |
---|
| 759 | else |
---|
| 760 | { |
---|
| 761 | while ((p=pNext(p))!=NULL) |
---|
| 762 | { |
---|
| 763 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 764 | ll++; |
---|
| 765 | } |
---|
| 766 | } |
---|
| 767 | *l=ll; |
---|
| 768 | return max; |
---|
| 769 | } |
---|
| 770 | |
---|
| 771 | // like pLDeg1, only pFDeg == pDeg |
---|
[107986] | 772 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 773 | { |
---|
[45d2332] | 774 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 775 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 776 | long k= p_GetComp(p, r); |
---|
[35aab3] | 777 | int ll=1; |
---|
| 778 | long t,max; |
---|
| 779 | |
---|
[b5d4d1] | 780 | max=p_GetOrder(p, r); |
---|
[35aab3] | 781 | if (k > 0) |
---|
| 782 | { |
---|
| 783 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 784 | { |
---|
[b5d4d1] | 785 | t=p_GetOrder(p, r); |
---|
[35aab3] | 786 | if (t>max) max=t; |
---|
| 787 | ll++; |
---|
| 788 | } |
---|
| 789 | } |
---|
| 790 | else |
---|
| 791 | { |
---|
| 792 | while ((p=pNext(p))!=NULL) |
---|
| 793 | { |
---|
[b5d4d1] | 794 | t=p_GetOrder(p, r); |
---|
[35aab3] | 795 | if (t>max) max=t; |
---|
| 796 | ll++; |
---|
| 797 | } |
---|
| 798 | } |
---|
| 799 | *l=ll; |
---|
| 800 | return max; |
---|
| 801 | } |
---|
| 802 | |
---|
[107986] | 803 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 804 | { |
---|
[45d2332] | 805 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 806 | p_CheckPolyRing(p, r); |
---|
| 807 | int ll=1; |
---|
| 808 | long t,max; |
---|
| 809 | |
---|
[b5d4d1] | 810 | max=p_GetOrder(p, r); |
---|
[35aab3] | 811 | if (rIsSyzIndexRing(r)) |
---|
| 812 | { |
---|
| 813 | long limit = rGetCurrSyzLimit(r); |
---|
| 814 | while ((p=pNext(p))!=NULL) |
---|
| 815 | { |
---|
| 816 | if (p_GetComp(p, r)<=limit) |
---|
| 817 | { |
---|
[b5d4d1] | 818 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 819 | ll++; |
---|
| 820 | } |
---|
| 821 | else break; |
---|
| 822 | } |
---|
| 823 | } |
---|
| 824 | else |
---|
| 825 | { |
---|
| 826 | while ((p=pNext(p))!=NULL) |
---|
| 827 | { |
---|
[b5d4d1] | 828 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 829 | ll++; |
---|
| 830 | } |
---|
| 831 | } |
---|
| 832 | *l=ll; |
---|
| 833 | return max; |
---|
| 834 | } |
---|
| 835 | |
---|
| 836 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
[107986] | 837 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 838 | { |
---|
| 839 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 840 | long k= p_GetComp(p, r); |
---|
[35aab3] | 841 | int ll=1; |
---|
| 842 | long t,max; |
---|
| 843 | |
---|
[99bdcf] | 844 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 845 | if (k > 0) |
---|
| 846 | { |
---|
| 847 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 848 | { |
---|
[99bdcf] | 849 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 850 | if (t>max) max=t; |
---|
| 851 | ll++; |
---|
| 852 | } |
---|
| 853 | } |
---|
| 854 | else |
---|
| 855 | { |
---|
| 856 | while ((p=pNext(p))!=NULL) |
---|
| 857 | { |
---|
[99bdcf] | 858 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 859 | if (t>max) max=t; |
---|
| 860 | ll++; |
---|
| 861 | } |
---|
| 862 | } |
---|
| 863 | *l=ll; |
---|
| 864 | return max; |
---|
| 865 | } |
---|
| 866 | |
---|
[107986] | 867 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 868 | { |
---|
| 869 | p_CheckPolyRing(p, r); |
---|
| 870 | int ll=1; |
---|
| 871 | long t,max; |
---|
| 872 | |
---|
[99bdcf] | 873 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 874 | if (rIsSyzIndexRing(r)) |
---|
| 875 | { |
---|
| 876 | long limit = rGetCurrSyzLimit(r); |
---|
| 877 | while ((p=pNext(p))!=NULL) |
---|
| 878 | { |
---|
| 879 | if (p_GetComp(p, r)<=limit) |
---|
| 880 | { |
---|
[99bdcf] | 881 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 882 | ll++; |
---|
| 883 | } |
---|
| 884 | else break; |
---|
| 885 | } |
---|
| 886 | } |
---|
| 887 | else |
---|
| 888 | { |
---|
| 889 | while ((p=pNext(p))!=NULL) |
---|
| 890 | { |
---|
[99bdcf] | 891 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 892 | ll++; |
---|
| 893 | } |
---|
| 894 | } |
---|
| 895 | *l=ll; |
---|
| 896 | return max; |
---|
| 897 | } |
---|
| 898 | |
---|
[19ae652] | 899 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
[107986] | 900 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 901 | { |
---|
| 902 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 903 | long k= p_GetComp(p, r); |
---|
[35aab3] | 904 | int ll=1; |
---|
| 905 | long t,max; |
---|
| 906 | |
---|
[19ae652] | 907 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 908 | if (k > 0) |
---|
| 909 | { |
---|
| 910 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 911 | { |
---|
[19ae652] | 912 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 913 | if (t>max) max=t; |
---|
| 914 | ll++; |
---|
| 915 | } |
---|
| 916 | } |
---|
| 917 | else |
---|
| 918 | { |
---|
| 919 | while ((p=pNext(p))!=NULL) |
---|
| 920 | { |
---|
[19ae652] | 921 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 922 | if (t>max) max=t; |
---|
| 923 | ll++; |
---|
| 924 | } |
---|
| 925 | } |
---|
| 926 | *l=ll; |
---|
| 927 | return max; |
---|
| 928 | } |
---|
| 929 | |
---|
[107986] | 930 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 931 | { |
---|
| 932 | p_CheckPolyRing(p, r); |
---|
| 933 | int ll=1; |
---|
| 934 | long t,max; |
---|
| 935 | |
---|
[19ae652] | 936 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 937 | if (rIsSyzIndexRing(r)) |
---|
| 938 | { |
---|
| 939 | long limit = rGetCurrSyzLimit(r); |
---|
| 940 | while ((p=pNext(p))!=NULL) |
---|
| 941 | { |
---|
| 942 | if (p_GetComp(p, r)<=limit) |
---|
| 943 | { |
---|
[99bdcf] | 944 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 945 | ll++; |
---|
| 946 | } |
---|
| 947 | else break; |
---|
| 948 | } |
---|
| 949 | } |
---|
| 950 | else |
---|
| 951 | { |
---|
| 952 | while ((p=pNext(p))!=NULL) |
---|
| 953 | { |
---|
[99bdcf] | 954 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 955 | ll++; |
---|
| 956 | } |
---|
| 957 | } |
---|
| 958 | *l=ll; |
---|
| 959 | return max; |
---|
| 960 | } |
---|
| 961 | |
---|
| 962 | /*************************************************************** |
---|
| 963 | * |
---|
| 964 | * Maximal Exponent business |
---|
| 965 | * |
---|
| 966 | ***************************************************************/ |
---|
| 967 | |
---|
[ab4778] | 968 | static inline unsigned long |
---|
[107986] | 969 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
[35aab3] | 970 | unsigned long number_of_exp) |
---|
| 971 | { |
---|
| 972 | const unsigned long bitmask = r->bitmask; |
---|
| 973 | unsigned long ml1 = l1 & bitmask; |
---|
| 974 | unsigned long ml2 = l2 & bitmask; |
---|
| 975 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
| 976 | unsigned long j = number_of_exp - 1; |
---|
| 977 | |
---|
| 978 | if (j > 0) |
---|
| 979 | { |
---|
| 980 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
| 981 | while (1) |
---|
| 982 | { |
---|
| 983 | ml1 = l1 & mask; |
---|
| 984 | ml2 = l2 & mask; |
---|
| 985 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
| 986 | j--; |
---|
| 987 | if (j == 0) break; |
---|
| 988 | mask = mask << r->BitsPerExp; |
---|
| 989 | } |
---|
| 990 | } |
---|
| 991 | return max; |
---|
| 992 | } |
---|
| 993 | |
---|
| 994 | static inline unsigned long |
---|
[107986] | 995 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
[35aab3] | 996 | { |
---|
| 997 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
| 998 | } |
---|
| 999 | |
---|
[107986] | 1000 | poly p_GetMaxExpP(poly p, const ring r) |
---|
[35aab3] | 1001 | { |
---|
| 1002 | p_CheckPolyRing(p, r); |
---|
| 1003 | if (p == NULL) return p_Init(r); |
---|
| 1004 | poly max = p_LmInit(p, r); |
---|
| 1005 | pIter(p); |
---|
| 1006 | if (p == NULL) return max; |
---|
| 1007 | int i, offset; |
---|
| 1008 | unsigned long l_p, l_max; |
---|
| 1009 | unsigned long divmask = r->divmask; |
---|
[ab4778] | 1010 | |
---|
[35aab3] | 1011 | do |
---|
| 1012 | { |
---|
| 1013 | offset = r->VarL_Offset[0]; |
---|
| 1014 | l_p = p->exp[offset]; |
---|
| 1015 | l_max = max->exp[offset]; |
---|
| 1016 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1017 | if (l_p > l_max || |
---|
[35aab3] | 1018 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1019 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1020 | |
---|
| 1021 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1022 | { |
---|
| 1023 | offset = r->VarL_Offset[i]; |
---|
| 1024 | l_p = p->exp[offset]; |
---|
| 1025 | l_max = max->exp[offset]; |
---|
| 1026 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1027 | if (l_p > l_max || |
---|
[35aab3] | 1028 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1029 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1030 | } |
---|
| 1031 | pIter(p); |
---|
| 1032 | } |
---|
| 1033 | while (p != NULL); |
---|
| 1034 | return max; |
---|
| 1035 | } |
---|
| 1036 | |
---|
[107986] | 1037 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
[35aab3] | 1038 | { |
---|
| 1039 | unsigned long l_p, divmask = r->divmask; |
---|
| 1040 | int i; |
---|
[ab4778] | 1041 | |
---|
[35aab3] | 1042 | while (p != NULL) |
---|
| 1043 | { |
---|
| 1044 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
| 1045 | if (l_p > l_max || |
---|
| 1046 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1047 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1048 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1049 | { |
---|
| 1050 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
| 1051 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1052 | if (l_p > l_max || |
---|
[35aab3] | 1053 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1054 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1055 | } |
---|
| 1056 | pIter(p); |
---|
| 1057 | } |
---|
| 1058 | return l_max; |
---|
| 1059 | } |
---|
| 1060 | |
---|
[fc5095] | 1061 | |
---|
| 1062 | |
---|
[ab4778] | 1063 | |
---|
[35aab3] | 1064 | /*************************************************************** |
---|
| 1065 | * |
---|
| 1066 | * Misc things |
---|
| 1067 | * |
---|
| 1068 | ***************************************************************/ |
---|
| 1069 | // returns TRUE, if all monoms have the same component |
---|
[107986] | 1070 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
[35aab3] | 1071 | { |
---|
| 1072 | if(p!=NULL) |
---|
| 1073 | { |
---|
| 1074 | long i = p_GetComp(p, r); |
---|
| 1075 | while (pNext(p)!=NULL) |
---|
| 1076 | { |
---|
| 1077 | pIter(p); |
---|
| 1078 | if(i != p_GetComp(p, r)) return FALSE; |
---|
| 1079 | } |
---|
| 1080 | } |
---|
| 1081 | return TRUE; |
---|
| 1082 | } |
---|
| 1083 | |
---|
| 1084 | /*2 |
---|
| 1085 | *test if a monomial /head term is a pure power |
---|
| 1086 | */ |
---|
| 1087 | int p_IsPurePower(const poly p, const ring r) |
---|
| 1088 | { |
---|
| 1089 | int i,k=0; |
---|
| 1090 | |
---|
| 1091 | for (i=r->N;i;i--) |
---|
| 1092 | { |
---|
| 1093 | if (p_GetExp(p,i, r)!=0) |
---|
| 1094 | { |
---|
| 1095 | if(k!=0) return 0; |
---|
| 1096 | k=i; |
---|
| 1097 | } |
---|
| 1098 | } |
---|
| 1099 | return k; |
---|
| 1100 | } |
---|
| 1101 | |
---|
[2f0d83f] | 1102 | /*2 |
---|
| 1103 | *test if a polynomial is univariate |
---|
| 1104 | * return -1 for constant, |
---|
| 1105 | * 0 for not univariate,s |
---|
| 1106 | * i if dep. on var(i) |
---|
| 1107 | */ |
---|
| 1108 | int p_IsUnivariate(poly p, const ring r) |
---|
| 1109 | { |
---|
| 1110 | int i,k=-1; |
---|
| 1111 | |
---|
| 1112 | while (p!=NULL) |
---|
| 1113 | { |
---|
| 1114 | for (i=r->N;i;i--) |
---|
| 1115 | { |
---|
| 1116 | if (p_GetExp(p,i, r)!=0) |
---|
| 1117 | { |
---|
| 1118 | if((k!=-1)&&(k!=i)) return 0; |
---|
| 1119 | k=i; |
---|
| 1120 | } |
---|
| 1121 | } |
---|
| 1122 | pIter(p); |
---|
| 1123 | } |
---|
| 1124 | return k; |
---|
| 1125 | } |
---|
| 1126 | |
---|
[3931bf] | 1127 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
[f46646] | 1128 | int p_GetVariables(poly p, int * e, const ring r) |
---|
[3931bf] | 1129 | { |
---|
| 1130 | int i; |
---|
[f46646] | 1131 | int n=0; |
---|
[3931bf] | 1132 | while(p!=NULL) |
---|
| 1133 | { |
---|
[f46646] | 1134 | n=0; |
---|
[95450e] | 1135 | for(i=r->N; i>0; i--) |
---|
[3931bf] | 1136 | { |
---|
| 1137 | if(e[i]==0) |
---|
| 1138 | { |
---|
| 1139 | if (p_GetExp(p,i,r)>0) |
---|
[f46646] | 1140 | { |
---|
[3931bf] | 1141 | e[i]=1; |
---|
[f46646] | 1142 | n++; |
---|
| 1143 | } |
---|
[3931bf] | 1144 | } |
---|
[f46646] | 1145 | else |
---|
| 1146 | n++; |
---|
[3931bf] | 1147 | } |
---|
[f46646] | 1148 | if (n==r->N) break; |
---|
[3931bf] | 1149 | pIter(p); |
---|
| 1150 | } |
---|
[f46646] | 1151 | return n; |
---|
[3931bf] | 1152 | } |
---|
| 1153 | |
---|
| 1154 | |
---|
[35aab3] | 1155 | /*2 |
---|
| 1156 | * returns a polynomial representing the integer i |
---|
| 1157 | */ |
---|
[107986] | 1158 | poly p_ISet(int i, const ring r) |
---|
[35aab3] | 1159 | { |
---|
| 1160 | poly rc = NULL; |
---|
| 1161 | if (i!=0) |
---|
| 1162 | { |
---|
| 1163 | rc = p_Init(r); |
---|
[8a8c9e] | 1164 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
| 1165 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
[fb82895] | 1166 | p_LmDelete(&rc,r); |
---|
[35aab3] | 1167 | } |
---|
| 1168 | return rc; |
---|
| 1169 | } |
---|
| 1170 | |
---|
[1c33e0d] | 1171 | /*2 |
---|
| 1172 | * an optimized version of p_ISet for the special case 1 |
---|
| 1173 | */ |
---|
[5bc4103] | 1174 | poly p_One(const ring r) |
---|
[1c33e0d] | 1175 | { |
---|
| 1176 | poly rc = p_Init(r); |
---|
[8a8c9e] | 1177 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
[1c33e0d] | 1178 | return rc; |
---|
| 1179 | } |
---|
| 1180 | |
---|
[f34215] | 1181 | void p_Split(poly p, poly *h) |
---|
| 1182 | { |
---|
| 1183 | *h=pNext(p); |
---|
| 1184 | pNext(p)=NULL; |
---|
| 1185 | } |
---|
| 1186 | |
---|
| 1187 | /*2 |
---|
| 1188 | * pair has no common factor ? or is no polynomial |
---|
| 1189 | */ |
---|
| 1190 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
| 1191 | { |
---|
| 1192 | |
---|
| 1193 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
| 1194 | return FALSE; |
---|
| 1195 | int i = rVar(r); |
---|
| 1196 | loop |
---|
| 1197 | { |
---|
| 1198 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
| 1199 | return FALSE; |
---|
| 1200 | i--; |
---|
| 1201 | if (i == 0) |
---|
| 1202 | return TRUE; |
---|
| 1203 | } |
---|
| 1204 | } |
---|
| 1205 | |
---|
| 1206 | /*2 |
---|
| 1207 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
| 1208 | */ |
---|
| 1209 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
| 1210 | { |
---|
| 1211 | if (r==NULL) { rc=NULL;return st;} |
---|
| 1212 | int i,j; |
---|
| 1213 | rc = p_Init(r); |
---|
[8a8c9e] | 1214 | const char *s = r->cf->cfRead(st,&(rc->coef),r->cf); |
---|
[f34215] | 1215 | if (s==st) |
---|
| 1216 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
| 1217 | { |
---|
| 1218 | j = r_IsRingVar(s,r); |
---|
| 1219 | if (j >= 0) |
---|
| 1220 | { |
---|
| 1221 | p_IncrExp(rc,1+j,r); |
---|
| 1222 | while (*s!='\0') s++; |
---|
| 1223 | goto done; |
---|
| 1224 | } |
---|
| 1225 | } |
---|
| 1226 | while (*s!='\0') |
---|
| 1227 | { |
---|
| 1228 | char ss[2]; |
---|
| 1229 | ss[0] = *s++; |
---|
| 1230 | ss[1] = '\0'; |
---|
| 1231 | j = r_IsRingVar(ss,r); |
---|
| 1232 | if (j >= 0) |
---|
| 1233 | { |
---|
| 1234 | const char *s_save=s; |
---|
| 1235 | s = eati(s,&i); |
---|
| 1236 | if (((unsigned long)i) > r->bitmask) |
---|
| 1237 | { |
---|
| 1238 | // exponent to large: it is not a monomial |
---|
| 1239 | p_LmDelete(&rc,r); |
---|
| 1240 | return s_save; |
---|
| 1241 | } |
---|
| 1242 | p_AddExp(rc,1+j, (long)i, r); |
---|
| 1243 | } |
---|
| 1244 | else |
---|
| 1245 | { |
---|
| 1246 | // 1st char of is not a varname |
---|
[d0340f] | 1247 | // We return the parsed polynomial nevertheless. This is needed when |
---|
| 1248 | // we are parsing coefficients in a rational function field. |
---|
[f34215] | 1249 | s--; |
---|
| 1250 | return s; |
---|
| 1251 | } |
---|
| 1252 | } |
---|
| 1253 | done: |
---|
[8a8c9e] | 1254 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
[f34215] | 1255 | else |
---|
| 1256 | { |
---|
| 1257 | #ifdef HAVE_PLURAL |
---|
| 1258 | // in super-commutative ring |
---|
| 1259 | // squares of anti-commutative variables are zeroes! |
---|
| 1260 | if(rIsSCA(r)) |
---|
| 1261 | { |
---|
| 1262 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
| 1263 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
| 1264 | |
---|
| 1265 | assume(rc != NULL); |
---|
| 1266 | |
---|
| 1267 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
| 1268 | if( p_GetExp(rc, k, r) > 1 ) |
---|
| 1269 | { |
---|
| 1270 | p_LmDelete(&rc, r); |
---|
| 1271 | goto finish; |
---|
| 1272 | } |
---|
| 1273 | } |
---|
| 1274 | #endif |
---|
[71ba5b8] | 1275 | |
---|
[f34215] | 1276 | p_Setm(rc,r); |
---|
| 1277 | } |
---|
[71ba5b8] | 1278 | finish: |
---|
[f34215] | 1279 | return s; |
---|
| 1280 | } |
---|
| 1281 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
| 1282 | { |
---|
| 1283 | poly p; |
---|
| 1284 | const char *s=p_Read(st,p,r); |
---|
| 1285 | if (*s!='\0') |
---|
| 1286 | { |
---|
| 1287 | if ((s!=st)&&isdigit(st[0])) |
---|
| 1288 | { |
---|
| 1289 | errorreported=TRUE; |
---|
| 1290 | } |
---|
| 1291 | ok=FALSE; |
---|
| 1292 | p_Delete(&p,r); |
---|
| 1293 | return NULL; |
---|
| 1294 | } |
---|
| 1295 | #ifdef PDEBUG |
---|
| 1296 | _p_Test(p,r,PDEBUG); |
---|
| 1297 | #endif |
---|
| 1298 | ok=!errorreported; |
---|
| 1299 | return p; |
---|
| 1300 | } |
---|
| 1301 | |
---|
[35aab3] | 1302 | /*2 |
---|
| 1303 | * returns a polynomial representing the number n |
---|
| 1304 | * destroys n |
---|
| 1305 | */ |
---|
[107986] | 1306 | poly p_NSet(number n, const ring r) |
---|
[35aab3] | 1307 | { |
---|
[8a8c9e] | 1308 | if (n_IsZero(n,r->cf)) |
---|
[35aab3] | 1309 | { |
---|
[8a8c9e] | 1310 | n_Delete(&n, r->cf); |
---|
[35aab3] | 1311 | return NULL; |
---|
| 1312 | } |
---|
| 1313 | else |
---|
| 1314 | { |
---|
| 1315 | poly rc = p_Init(r); |
---|
| 1316 | pSetCoeff0(rc,n); |
---|
| 1317 | return rc; |
---|
| 1318 | } |
---|
| 1319 | } |
---|
[fb4075b] | 1320 | /*2 |
---|
[e5d267] | 1321 | * assumes that LM(a) = LM(b)*m, for some monomial m, |
---|
| 1322 | * returns the multiplicant m, |
---|
| 1323 | * leaves a and b unmodified |
---|
[fb4075b] | 1324 | */ |
---|
| 1325 | poly p_Divide(poly a, poly b, const ring r) |
---|
| 1326 | { |
---|
| 1327 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
| 1328 | int i; |
---|
[8a8c9e] | 1329 | poly result = p_Init(r); |
---|
[fb4075b] | 1330 | |
---|
| 1331 | for(i=(int)r->N; i; i--) |
---|
| 1332 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
| 1333 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
| 1334 | p_Setm(result,r); |
---|
| 1335 | return result; |
---|
| 1336 | } |
---|
| 1337 | |
---|
[8a8c9e] | 1338 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
| 1339 | { |
---|
[45d2332] | 1340 | pAssume(!n_IsZero(n,r->cf)); |
---|
[8a8c9e] | 1341 | p_Test(p, r); |
---|
| 1342 | |
---|
| 1343 | poly q = p; |
---|
| 1344 | while (p != NULL) |
---|
| 1345 | { |
---|
| 1346 | number nc = pGetCoeff(p); |
---|
| 1347 | pSetCoeff0(p, n_Div(nc, n, r->cf)); |
---|
| 1348 | n_Delete(&nc, r->cf); |
---|
| 1349 | pIter(p); |
---|
| 1350 | } |
---|
| 1351 | p_Test(q, r); |
---|
| 1352 | return q; |
---|
| 1353 | } |
---|
| 1354 | |
---|
[fb4075b] | 1355 | /*2 |
---|
| 1356 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
[e432a0] | 1357 | * assumes that b is not NULL, destroyes b |
---|
[fb4075b] | 1358 | */ |
---|
| 1359 | poly p_DivideM(poly a, poly b, const ring r) |
---|
| 1360 | { |
---|
[e432a0] | 1361 | if (a==NULL) { p_Delete(&b,r); return NULL; } |
---|
[fb4075b] | 1362 | poly result=a; |
---|
| 1363 | poly prev=NULL; |
---|
| 1364 | int i; |
---|
| 1365 | #ifdef HAVE_RINGS |
---|
| 1366 | number inv=pGetCoeff(b); |
---|
| 1367 | #else |
---|
| 1368 | number inv=n_Invers(pGetCoeff(b),r->cf); |
---|
| 1369 | #endif |
---|
| 1370 | |
---|
| 1371 | while (a!=NULL) |
---|
| 1372 | { |
---|
| 1373 | if (p_DivisibleBy(b,a,r)) |
---|
| 1374 | { |
---|
| 1375 | for(i=(int)r->N; i; i--) |
---|
| 1376 | p_SubExp(a,i, p_GetExp(b,i,r),r); |
---|
| 1377 | p_SubComp(a, p_GetComp(b,r),r); |
---|
| 1378 | p_Setm(a,r); |
---|
| 1379 | prev=a; |
---|
| 1380 | pIter(a); |
---|
| 1381 | } |
---|
| 1382 | else |
---|
| 1383 | { |
---|
| 1384 | if (prev==NULL) |
---|
| 1385 | { |
---|
[8a8c9e] | 1386 | p_LmDelete(&result,r); |
---|
[fb4075b] | 1387 | a=result; |
---|
| 1388 | } |
---|
| 1389 | else |
---|
| 1390 | { |
---|
[8a8c9e] | 1391 | p_LmDelete(&pNext(prev),r); |
---|
[fb4075b] | 1392 | a=pNext(prev); |
---|
| 1393 | } |
---|
| 1394 | } |
---|
| 1395 | } |
---|
| 1396 | #ifdef HAVE_RINGS |
---|
| 1397 | if (n_IsUnit(inv,r->cf)) |
---|
| 1398 | { |
---|
| 1399 | inv = n_Invers(inv,r->cf); |
---|
| 1400 | p_Mult_nn(result,inv,r); |
---|
| 1401 | n_Delete(&inv, r->cf); |
---|
| 1402 | } |
---|
| 1403 | else |
---|
| 1404 | { |
---|
| 1405 | p_Div_nn(result,inv,r); |
---|
| 1406 | } |
---|
| 1407 | #else |
---|
| 1408 | p_Mult_nn(result,inv,r); |
---|
| 1409 | n_Delete(&inv, r->cf); |
---|
| 1410 | #endif |
---|
| 1411 | p_Delete(&b, r); |
---|
| 1412 | return result; |
---|
| 1413 | } |
---|
[35aab3] | 1414 | |
---|
[3d0808] | 1415 | #ifdef HAVE_RINGS |
---|
| 1416 | /* TRUE iff LT(f) | LT(g) */ |
---|
| 1417 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
| 1418 | { |
---|
| 1419 | int exponent; |
---|
| 1420 | for(int i = (int)rVar(r); i>0; i--) |
---|
| 1421 | { |
---|
| 1422 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
| 1423 | if (exponent < 0) return FALSE; |
---|
| 1424 | } |
---|
| 1425 | return n_DivBy(pGetCoeff(g), pGetCoeff(f), r->cf); |
---|
| 1426 | } |
---|
| 1427 | #endif |
---|
| 1428 | |
---|
[a7ee69] | 1429 | /*2 |
---|
| 1430 | * returns the LCM of the head terms of a and b in *m |
---|
| 1431 | */ |
---|
| 1432 | void p_Lcm(poly a, poly b, poly m, const ring r) |
---|
| 1433 | { |
---|
| 1434 | int i; |
---|
| 1435 | for (i=rVar(r); i; i--) |
---|
| 1436 | { |
---|
| 1437 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
| 1438 | } |
---|
| 1439 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
| 1440 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
| 1441 | } |
---|
| 1442 | |
---|
[f0b01f] | 1443 | /* assumes that p and divisor are univariate polynomials in r, |
---|
[ba2359] | 1444 | mentioning the same variable; |
---|
| 1445 | assumes divisor != NULL; |
---|
[f0b01f] | 1446 | p may be NULL; |
---|
[ba2359] | 1447 | assumes a global monomial ordering in r; |
---|
[f0b01f] | 1448 | performs polynomial division of p by divisor: |
---|
| 1449 | - afterwards p contains the remainder of the division, i.e., |
---|
| 1450 | p_before = result * divisor + p_afterwards; |
---|
[ba2359] | 1451 | - if needResult == TRUE, then the method computes and returns 'result', |
---|
| 1452 | otherwise NULL is returned (This parametrization can be used when |
---|
| 1453 | one is only interested in the remainder of the division. In this |
---|
[f0b01f] | 1454 | case, the method will be slightly faster.) |
---|
| 1455 | leaves divisor unmodified */ |
---|
| 1456 | poly p_PolyDiv(poly &p, poly divisor, BOOLEAN needResult, ring r) |
---|
[ba2359] | 1457 | { |
---|
| 1458 | assume(divisor != NULL); |
---|
[f0b01f] | 1459 | if (p == NULL) return NULL; |
---|
[ba2359] | 1460 | |
---|
[69fb9d0] | 1461 | poly result = NULL; |
---|
[f0b01f] | 1462 | number divisorLC = p_GetCoeff(divisor, r); |
---|
| 1463 | int divisorLE = p_GetExp(divisor, 1, r); |
---|
[c28ecf] | 1464 | while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r))) |
---|
[69fb9d0] | 1465 | { |
---|
[f0b01f] | 1466 | /* determine t = LT(p) / LT(divisor) */ |
---|
[69fb9d0] | 1467 | poly t = p_ISet(1, r); |
---|
[f0b01f] | 1468 | number c = n_Div(p_GetCoeff(p, r), divisorLC, r->cf); |
---|
[69fb9d0] | 1469 | p_SetCoeff(t, c, r); |
---|
[f0b01f] | 1470 | int e = p_GetExp(p, 1, r) - divisorLE; |
---|
[69fb9d0] | 1471 | p_SetExp(t, 1, e, r); |
---|
| 1472 | p_Setm(t, r); |
---|
[f0b01f] | 1473 | if (needResult) result = p_Add_q(result, p_Copy(t, r), r); |
---|
| 1474 | p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r); |
---|
[69fb9d0] | 1475 | } |
---|
| 1476 | return result; |
---|
| 1477 | } |
---|
| 1478 | |
---|
[c28ecf] | 1479 | /* returns NULL if p == NULL, otherwise makes p monic by dividing |
---|
| 1480 | by its leading coefficient (only done if this is not already 1); |
---|
| 1481 | this assumes that we are over a ground field so that division |
---|
| 1482 | is well-defined; |
---|
| 1483 | modifies p */ |
---|
[90aec7] | 1484 | void p_Monic(poly p, const ring r) |
---|
[c28ecf] | 1485 | { |
---|
| 1486 | if (p == NULL) return; |
---|
[90aec7] | 1487 | number n = n_Init(1, r->cf); |
---|
| 1488 | if (p->next==NULL) { p_SetCoeff(p,n,r); return; } |
---|
[c28ecf] | 1489 | poly pp = p; |
---|
| 1490 | number lc = p_GetCoeff(p, r); |
---|
| 1491 | if (n_IsOne(lc, r->cf)) return; |
---|
[cfb500] | 1492 | number lcInverse = n_Invers(lc, r->cf); |
---|
| 1493 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
[90aec7] | 1494 | pIter(p); |
---|
[c28ecf] | 1495 | while (p != NULL) |
---|
| 1496 | { |
---|
[cfb500] | 1497 | number n = n_Mult(p_GetCoeff(p, r), lcInverse, r->cf); |
---|
[90aec7] | 1498 | n_Normalize(n,r->cf); |
---|
[cfb500] | 1499 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
[c28ecf] | 1500 | p = pIter(p); |
---|
| 1501 | } |
---|
[cfb500] | 1502 | n_Delete(&lcInverse, r->cf); |
---|
[c28ecf] | 1503 | p = pp; |
---|
| 1504 | } |
---|
| 1505 | |
---|
[69fb9d0] | 1506 | /* see p_Gcd; |
---|
[f0b01f] | 1507 | additional assumption: deg(p) >= deg(q); |
---|
| 1508 | must destroy p and q (unless one of them is returned) */ |
---|
| 1509 | poly p_GcdHelper(poly &p, poly &q, ring r) |
---|
[69fb9d0] | 1510 | { |
---|
[c28ecf] | 1511 | if (q == NULL) |
---|
| 1512 | { |
---|
| 1513 | /* We have to make p monic before we return it, so that if the |
---|
| 1514 | gcd is a unit in the ground field, we will actually return 1. */ |
---|
| 1515 | p_Monic(p, r); |
---|
| 1516 | return p; |
---|
| 1517 | } |
---|
[69fb9d0] | 1518 | else |
---|
| 1519 | { |
---|
[f0b01f] | 1520 | p_PolyDiv(p, q, FALSE, r); |
---|
[69fb9d0] | 1521 | return p_GcdHelper(q, p, r); |
---|
| 1522 | } |
---|
[ba2359] | 1523 | } |
---|
| 1524 | |
---|
| 1525 | /* assumes that p and q are univariate polynomials in r, |
---|
| 1526 | mentioning the same variable; |
---|
| 1527 | assumes a global monomial ordering in r; |
---|
| 1528 | assumes that not both p and q are NULL; |
---|
[69fb9d0] | 1529 | returns the gcd of p and q; |
---|
| 1530 | leaves p and q unmodified */ |
---|
[ba2359] | 1531 | poly p_Gcd(poly p, poly q, ring r) |
---|
| 1532 | { |
---|
| 1533 | assume((p != NULL) || (q != NULL)); |
---|
| 1534 | |
---|
[69fb9d0] | 1535 | poly a = p; poly b = q; |
---|
| 1536 | if (p_Deg(a, r) < p_Deg(b, r)) { a = q; b = p; } |
---|
| 1537 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
[f0b01f] | 1538 | return p_GcdHelper(a, b, r); |
---|
[69fb9d0] | 1539 | } |
---|
| 1540 | |
---|
| 1541 | /* see p_ExtGcd; |
---|
[f0b01f] | 1542 | additional assumption: deg(p) >= deg(q); |
---|
| 1543 | must destroy p and q (unless one of them is returned) */ |
---|
| 1544 | poly p_ExtGcdHelper(poly &p, poly &pFactor, poly &q, poly &qFactor, |
---|
[69fb9d0] | 1545 | ring r) |
---|
| 1546 | { |
---|
| 1547 | if (q == NULL) |
---|
| 1548 | { |
---|
[c28ecf] | 1549 | qFactor = NULL; |
---|
| 1550 | pFactor = p_ISet(1, r); |
---|
| 1551 | p_SetCoeff(pFactor, n_Invers(p_GetCoeff(p, r), r->cf), r); |
---|
| 1552 | p_Monic(p, r); |
---|
| 1553 | return p; |
---|
[69fb9d0] | 1554 | } |
---|
| 1555 | else |
---|
| 1556 | { |
---|
[f0b01f] | 1557 | poly pDivQ = p_PolyDiv(p, q, TRUE, r); |
---|
[c28ecf] | 1558 | poly ppFactor = NULL; poly qqFactor = NULL; |
---|
| 1559 | poly theGcd = p_ExtGcdHelper(q, qqFactor, p, ppFactor, r); |
---|
| 1560 | pFactor = ppFactor; |
---|
| 1561 | qFactor = p_Add_q(qqFactor, |
---|
| 1562 | p_Neg(p_Mult_q(pDivQ, p_Copy(ppFactor, r), r), r), |
---|
[f0b01f] | 1563 | r); |
---|
[69fb9d0] | 1564 | return theGcd; |
---|
| 1565 | } |
---|
[ba2359] | 1566 | } |
---|
| 1567 | |
---|
| 1568 | /* assumes that p and q are univariate polynomials in r, |
---|
| 1569 | mentioning the same variable; |
---|
| 1570 | assumes a global monomial ordering in r; |
---|
| 1571 | assumes that not both p and q are NULL; |
---|
| 1572 | returns the gcd of p and q; |
---|
[f0b01f] | 1573 | moreover, afterwards pFactor and qFactor contain appropriate |
---|
| 1574 | factors such that gcd(p, q) = p * pFactor + q * qFactor; |
---|
[69fb9d0] | 1575 | leaves p and q unmodified */ |
---|
[f0b01f] | 1576 | poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r) |
---|
[ba2359] | 1577 | { |
---|
[f0b01f] | 1578 | assume((p != NULL) || (q != NULL)); |
---|
[c28ecf] | 1579 | poly a = p; poly b = q; BOOLEAN aCorrespondsToP = TRUE; |
---|
[69fb9d0] | 1580 | if (p_Deg(a, r) < p_Deg(b, r)) |
---|
[c28ecf] | 1581 | { a = q; b = p; aCorrespondsToP = FALSE; } |
---|
[69fb9d0] | 1582 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
[c28ecf] | 1583 | poly aFactor = NULL; poly bFactor = NULL; |
---|
| 1584 | poly theGcd = p_ExtGcdHelper(a, aFactor, b, bFactor, r); |
---|
| 1585 | if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; } |
---|
| 1586 | else { pFactor = bFactor; qFactor = aFactor; } |
---|
| 1587 | return theGcd; |
---|
[ba2359] | 1588 | } |
---|
| 1589 | |
---|
[ac0bd6] | 1590 | /*2 |
---|
| 1591 | * returns the partial differentiate of a by the k-th variable |
---|
| 1592 | * does not destroy the input |
---|
| 1593 | */ |
---|
| 1594 | poly p_Diff(poly a, int k, const ring r) |
---|
| 1595 | { |
---|
| 1596 | poly res, f, last; |
---|
| 1597 | number t; |
---|
| 1598 | |
---|
| 1599 | last = res = NULL; |
---|
| 1600 | while (a!=NULL) |
---|
| 1601 | { |
---|
| 1602 | if (p_GetExp(a,k,r)!=0) |
---|
| 1603 | { |
---|
| 1604 | f = p_LmInit(a,r); |
---|
| 1605 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
| 1606 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
| 1607 | n_Delete(&t,r->cf); |
---|
| 1608 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
| 1609 | p_LmDelete(&f,r); |
---|
| 1610 | else |
---|
| 1611 | { |
---|
| 1612 | p_DecrExp(f,k,r); |
---|
| 1613 | p_Setm(f,r); |
---|
| 1614 | if (res==NULL) |
---|
| 1615 | { |
---|
| 1616 | res=last=f; |
---|
| 1617 | } |
---|
| 1618 | else |
---|
| 1619 | { |
---|
| 1620 | pNext(last)=f; |
---|
| 1621 | last=f; |
---|
| 1622 | } |
---|
| 1623 | } |
---|
| 1624 | } |
---|
| 1625 | pIter(a); |
---|
| 1626 | } |
---|
| 1627 | return res; |
---|
| 1628 | } |
---|
[5162db] | 1629 | |
---|
[8a8c9e] | 1630 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
[5162db] | 1631 | { |
---|
| 1632 | int i,j,s; |
---|
| 1633 | number n,h,hh; |
---|
| 1634 | poly p=p_One(r); |
---|
| 1635 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
| 1636 | for(i=rVar(r);i>0;i--) |
---|
| 1637 | { |
---|
| 1638 | s=p_GetExp(b,i,r); |
---|
| 1639 | if (s<p_GetExp(a,i,r)) |
---|
| 1640 | { |
---|
| 1641 | n_Delete(&n,r->cf); |
---|
| 1642 | p_LmDelete(&p,r); |
---|
| 1643 | return NULL; |
---|
| 1644 | } |
---|
| 1645 | if (multiply) |
---|
| 1646 | { |
---|
| 1647 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
| 1648 | { |
---|
| 1649 | h = n_Init(s,r->cf); |
---|
| 1650 | hh=n_Mult(n,h,r->cf); |
---|
| 1651 | n_Delete(&h,r->cf); |
---|
| 1652 | n_Delete(&n,r->cf); |
---|
| 1653 | n=hh; |
---|
| 1654 | s--; |
---|
| 1655 | } |
---|
| 1656 | p_SetExp(p,i,s,r); |
---|
| 1657 | } |
---|
| 1658 | else |
---|
| 1659 | { |
---|
| 1660 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
| 1661 | } |
---|
| 1662 | } |
---|
| 1663 | p_Setm(p,r); |
---|
| 1664 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
| 1665 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
| 1666 | return p; |
---|
| 1667 | } |
---|
| 1668 | |
---|
| 1669 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
| 1670 | { |
---|
| 1671 | poly result=NULL; |
---|
| 1672 | poly h; |
---|
| 1673 | for(;a!=NULL;pIter(a)) |
---|
| 1674 | { |
---|
| 1675 | for(h=b;h!=NULL;pIter(h)) |
---|
| 1676 | { |
---|
| 1677 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
| 1678 | } |
---|
| 1679 | } |
---|
| 1680 | return result; |
---|
| 1681 | } |
---|
[bf183f] | 1682 | /*2 |
---|
| 1683 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
| 1684 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
| 1685 | */ |
---|
| 1686 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
| 1687 | { |
---|
| 1688 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
| 1689 | } |
---|
| 1690 | |
---|
| 1691 | /*3 |
---|
| 1692 | * compute for a monomial m |
---|
| 1693 | * the power m^exp, exp > 1 |
---|
| 1694 | * destroys p |
---|
| 1695 | */ |
---|
| 1696 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
| 1697 | { |
---|
| 1698 | int i; |
---|
| 1699 | |
---|
[8a8c9e] | 1700 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
[bf183f] | 1701 | { |
---|
| 1702 | number x, y; |
---|
| 1703 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1704 | n_Power(y,exp,&x,r->cf); |
---|
| 1705 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1706 | pSetCoeff0(p,x); |
---|
| 1707 | } |
---|
| 1708 | for (i=rVar(r); i!=0; i--) |
---|
| 1709 | { |
---|
| 1710 | p_MultExp(p,i, exp,r); |
---|
| 1711 | } |
---|
| 1712 | p_Setm(p,r); |
---|
| 1713 | return p; |
---|
| 1714 | } |
---|
| 1715 | |
---|
| 1716 | /*3 |
---|
| 1717 | * compute for monomials p*q |
---|
| 1718 | * destroys p, keeps q |
---|
| 1719 | */ |
---|
| 1720 | static void p_MonMult(poly p, poly q, const ring r) |
---|
| 1721 | { |
---|
| 1722 | number x, y; |
---|
| 1723 | |
---|
| 1724 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1725 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
| 1726 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1727 | pSetCoeff0(p,x); |
---|
[abb4787] | 1728 | //for (int i=pVariables; i!=0; i--) |
---|
[bf183f] | 1729 | //{ |
---|
| 1730 | // pAddExp(p,i, pGetExp(q,i)); |
---|
| 1731 | //} |
---|
| 1732 | //p->Order += q->Order; |
---|
| 1733 | p_ExpVectorAdd(p,q,r); |
---|
| 1734 | } |
---|
| 1735 | |
---|
| 1736 | /*3 |
---|
| 1737 | * compute for monomials p*q |
---|
| 1738 | * keeps p, q |
---|
| 1739 | */ |
---|
| 1740 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
| 1741 | { |
---|
| 1742 | number x; |
---|
| 1743 | poly r = p_Init(rr); |
---|
| 1744 | |
---|
[8a8c9e] | 1745 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
[bf183f] | 1746 | pSetCoeff0(r,x); |
---|
| 1747 | p_ExpVectorSum(r,p, q, rr); |
---|
| 1748 | return r; |
---|
| 1749 | } |
---|
| 1750 | |
---|
[5679049] | 1751 | /*3 |
---|
| 1752 | * create binomial coef. |
---|
| 1753 | */ |
---|
| 1754 | static number* pnBin(int exp, const ring r) |
---|
| 1755 | { |
---|
| 1756 | int e, i, h; |
---|
| 1757 | number x, y, *bin=NULL; |
---|
| 1758 | |
---|
| 1759 | x = n_Init(exp,r->cf); |
---|
| 1760 | if (n_IsZero(x,r->cf)) |
---|
| 1761 | { |
---|
| 1762 | n_Delete(&x,r->cf); |
---|
| 1763 | return bin; |
---|
| 1764 | } |
---|
| 1765 | h = (exp >> 1) + 1; |
---|
| 1766 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
| 1767 | bin[1] = x; |
---|
| 1768 | if (exp < 4) |
---|
| 1769 | return bin; |
---|
| 1770 | i = exp - 1; |
---|
| 1771 | for (e=2; e<h; e++) |
---|
| 1772 | { |
---|
| 1773 | x = n_Init(i,r->cf); |
---|
| 1774 | i--; |
---|
| 1775 | y = n_Mult(x,bin[e-1],r->cf); |
---|
| 1776 | n_Delete(&x,r->cf); |
---|
| 1777 | x = n_Init(e,r->cf); |
---|
| 1778 | bin[e] = n_IntDiv(y,x,r->cf); |
---|
| 1779 | n_Delete(&x,r->cf); |
---|
| 1780 | n_Delete(&y,r->cf); |
---|
| 1781 | } |
---|
| 1782 | return bin; |
---|
| 1783 | } |
---|
| 1784 | |
---|
[1389a4] | 1785 | static void pnFreeBin(number *bin, int exp,const coeffs r) |
---|
| 1786 | { |
---|
| 1787 | int e, h = (exp >> 1) + 1; |
---|
| 1788 | |
---|
| 1789 | if (bin[1] != NULL) |
---|
| 1790 | { |
---|
| 1791 | for (e=1; e<h; e++) |
---|
| 1792 | n_Delete(&(bin[e]),r); |
---|
| 1793 | } |
---|
| 1794 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
---|
| 1795 | } |
---|
| 1796 | |
---|
[bf183f] | 1797 | /* |
---|
| 1798 | * compute for a poly p = head+tail, tail is monomial |
---|
| 1799 | * (head + tail)^exp, exp > 1 |
---|
| 1800 | * with binomial coef. |
---|
| 1801 | */ |
---|
| 1802 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
| 1803 | { |
---|
| 1804 | int eh, e; |
---|
| 1805 | long al; |
---|
| 1806 | poly *a; |
---|
| 1807 | poly tail, b, res, h; |
---|
| 1808 | number x; |
---|
[7eb7b5] | 1809 | number *bin = pnBin(exp,r); |
---|
[bf183f] | 1810 | |
---|
| 1811 | tail = pNext(p); |
---|
| 1812 | if (bin == NULL) |
---|
| 1813 | { |
---|
| 1814 | p_MonPower(p,exp,r); |
---|
| 1815 | p_MonPower(tail,exp,r); |
---|
| 1816 | #ifdef PDEBUG |
---|
| 1817 | p_Test(p,r); |
---|
| 1818 | #endif |
---|
| 1819 | return p; |
---|
| 1820 | } |
---|
| 1821 | eh = exp >> 1; |
---|
| 1822 | al = (exp + 1) * sizeof(poly); |
---|
| 1823 | a = (poly *)omAlloc(al); |
---|
| 1824 | a[1] = p; |
---|
| 1825 | for (e=1; e<exp; e++) |
---|
| 1826 | { |
---|
| 1827 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
| 1828 | } |
---|
| 1829 | res = a[exp]; |
---|
| 1830 | b = p_Head(tail,r); |
---|
| 1831 | for (e=exp-1; e>eh; e--) |
---|
| 1832 | { |
---|
| 1833 | h = a[e]; |
---|
[8a8c9e] | 1834 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1835 | p_SetCoeff(h,x,r); |
---|
| 1836 | p_MonMult(h,b,r); |
---|
| 1837 | res = pNext(res) = h; |
---|
| 1838 | p_MonMult(b,tail,r); |
---|
| 1839 | } |
---|
| 1840 | for (e=eh; e!=0; e--) |
---|
| 1841 | { |
---|
| 1842 | h = a[e]; |
---|
[8a8c9e] | 1843 | x = n_Mult(bin[e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1844 | p_SetCoeff(h,x,r); |
---|
| 1845 | p_MonMult(h,b,r); |
---|
| 1846 | res = pNext(res) = h; |
---|
| 1847 | p_MonMult(b,tail,r); |
---|
| 1848 | } |
---|
| 1849 | p_LmDelete(&tail,r); |
---|
| 1850 | pNext(res) = b; |
---|
| 1851 | pNext(b) = NULL; |
---|
| 1852 | res = a[exp]; |
---|
| 1853 | omFreeSize((ADDRESS)a, al); |
---|
[1389a4] | 1854 | pnFreeBin(bin, exp, r->cf); |
---|
[bf183f] | 1855 | // tail=res; |
---|
| 1856 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
| 1857 | // { |
---|
| 1858 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
| 1859 | // { |
---|
| 1860 | // pLmDelete(&pNext(tail)); |
---|
| 1861 | // } |
---|
| 1862 | // else |
---|
| 1863 | // pIter(tail); |
---|
| 1864 | // } |
---|
| 1865 | #ifdef PDEBUG |
---|
| 1866 | p_Test(res,r); |
---|
| 1867 | #endif |
---|
| 1868 | return res; |
---|
| 1869 | } |
---|
| 1870 | |
---|
| 1871 | static poly p_Pow(poly p, int i, const ring r) |
---|
| 1872 | { |
---|
| 1873 | poly rc = p_Copy(p,r); |
---|
| 1874 | i -= 2; |
---|
| 1875 | do |
---|
| 1876 | { |
---|
| 1877 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
| 1878 | p_Normalize(rc,r); |
---|
| 1879 | i--; |
---|
| 1880 | } |
---|
| 1881 | while (i != 0); |
---|
| 1882 | return p_Mult_q(rc,p,r); |
---|
| 1883 | } |
---|
| 1884 | |
---|
| 1885 | /*2 |
---|
| 1886 | * returns the i-th power of p |
---|
| 1887 | * p will be destroyed |
---|
| 1888 | */ |
---|
| 1889 | poly p_Power(poly p, int i, const ring r) |
---|
| 1890 | { |
---|
| 1891 | poly rc=NULL; |
---|
| 1892 | |
---|
| 1893 | if (i==0) |
---|
| 1894 | { |
---|
| 1895 | p_Delete(&p,r); |
---|
| 1896 | return p_One(r); |
---|
| 1897 | } |
---|
| 1898 | |
---|
| 1899 | if(p!=NULL) |
---|
| 1900 | { |
---|
| 1901 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask))) |
---|
| 1902 | { |
---|
| 1903 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
| 1904 | return NULL; |
---|
| 1905 | } |
---|
| 1906 | switch (i) |
---|
| 1907 | { |
---|
| 1908 | // cannot happen, see above |
---|
| 1909 | // case 0: |
---|
| 1910 | // { |
---|
| 1911 | // rc=pOne(); |
---|
| 1912 | // pDelete(&p); |
---|
| 1913 | // break; |
---|
| 1914 | // } |
---|
| 1915 | case 1: |
---|
| 1916 | rc=p; |
---|
| 1917 | break; |
---|
| 1918 | case 2: |
---|
| 1919 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
| 1920 | break; |
---|
| 1921 | default: |
---|
| 1922 | if (i < 0) |
---|
| 1923 | { |
---|
| 1924 | p_Delete(&p,r); |
---|
| 1925 | return NULL; |
---|
| 1926 | } |
---|
| 1927 | else |
---|
| 1928 | { |
---|
| 1929 | #ifdef HAVE_PLURAL |
---|
| 1930 | if (rIsPluralRing(r)) /* in the NC case nothing helps :-( */ |
---|
| 1931 | { |
---|
| 1932 | int j=i; |
---|
| 1933 | rc = p_Copy(p,r); |
---|
| 1934 | while (j>1) |
---|
| 1935 | { |
---|
| 1936 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
| 1937 | j--; |
---|
| 1938 | } |
---|
| 1939 | p_Delete(&p,r); |
---|
| 1940 | return rc; |
---|
| 1941 | } |
---|
| 1942 | #endif |
---|
| 1943 | rc = pNext(p); |
---|
| 1944 | if (rc == NULL) |
---|
| 1945 | return p_MonPower(p,i,r); |
---|
| 1946 | /* else: binom ?*/ |
---|
| 1947 | int char_p=rChar(r); |
---|
| 1948 | if ((pNext(rc) != NULL) |
---|
| 1949 | #ifdef HAVE_RINGS |
---|
| 1950 | || rField_is_Ring(r) |
---|
| 1951 | #endif |
---|
| 1952 | ) |
---|
| 1953 | return p_Pow(p,i,r); |
---|
| 1954 | if ((char_p==0) || (i<=char_p)) |
---|
| 1955 | return p_TwoMonPower(p,i,r); |
---|
| 1956 | poly p_p=p_TwoMonPower(p_Copy(p,r),char_p,r); |
---|
| 1957 | return p_Mult_q(p_Power(p,i-char_p,r),p_p,r); |
---|
| 1958 | } |
---|
| 1959 | /*end default:*/ |
---|
| 1960 | } |
---|
| 1961 | } |
---|
| 1962 | return rc; |
---|
| 1963 | } |
---|
[8d1d30c] | 1964 | |
---|
| 1965 | /* --------------------------------------------------------------------------------*/ |
---|
| 1966 | /* content suff */ |
---|
| 1967 | |
---|
| 1968 | static number p_InitContent(poly ph, const ring r); |
---|
| 1969 | |
---|
| 1970 | void p_Content(poly ph, const ring r) |
---|
| 1971 | { |
---|
| 1972 | #ifdef HAVE_RINGS |
---|
| 1973 | if (rField_is_Ring(r)) |
---|
| 1974 | { |
---|
| 1975 | if ((ph!=NULL) && rField_has_Units(r)) |
---|
| 1976 | { |
---|
[8a8c9e] | 1977 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
[8d1d30c] | 1978 | if (!n_IsOne(k,r->cf)) |
---|
| 1979 | { |
---|
| 1980 | number tmpGMP = k; |
---|
| 1981 | k = n_Invers(k,r->cf); |
---|
| 1982 | n_Delete(&tmpGMP,r->cf); |
---|
| 1983 | poly h = pNext(ph); |
---|
| 1984 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
| 1985 | while (h != NULL) |
---|
| 1986 | { |
---|
| 1987 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
| 1988 | pIter(h); |
---|
| 1989 | } |
---|
| 1990 | } |
---|
| 1991 | n_Delete(&k,r->cf); |
---|
| 1992 | } |
---|
| 1993 | return; |
---|
| 1994 | } |
---|
| 1995 | #endif |
---|
| 1996 | number h,d; |
---|
| 1997 | poly p; |
---|
| 1998 | |
---|
| 1999 | if(TEST_OPT_CONTENTSB) return; |
---|
| 2000 | if(pNext(ph)==NULL) |
---|
| 2001 | { |
---|
[8a8c9e] | 2002 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
[8d1d30c] | 2003 | } |
---|
| 2004 | else |
---|
| 2005 | { |
---|
| 2006 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 2007 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8a8c9e] | 2008 | if (rField_is_Q(r)) |
---|
[8d1d30c] | 2009 | { |
---|
| 2010 | h=p_InitContent(ph,r); |
---|
| 2011 | p=ph; |
---|
| 2012 | } |
---|
| 2013 | else |
---|
| 2014 | { |
---|
| 2015 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2016 | p = pNext(ph); |
---|
| 2017 | } |
---|
| 2018 | while (p!=NULL) |
---|
| 2019 | { |
---|
| 2020 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2021 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2022 | n_Delete(&h,r->cf); |
---|
| 2023 | h = d; |
---|
| 2024 | if(n_IsOne(h,r->cf)) |
---|
| 2025 | { |
---|
| 2026 | break; |
---|
| 2027 | } |
---|
| 2028 | pIter(p); |
---|
| 2029 | } |
---|
| 2030 | p = ph; |
---|
| 2031 | //number tmp; |
---|
| 2032 | if(!n_IsOne(h,r->cf)) |
---|
| 2033 | { |
---|
| 2034 | while (p!=NULL) |
---|
| 2035 | { |
---|
| 2036 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2037 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2038 | //if (!nEqual(d,tmp)) |
---|
| 2039 | //{ |
---|
| 2040 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2041 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
| 2042 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
| 2043 | //} |
---|
| 2044 | //nDelete(&tmp); |
---|
| 2045 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2046 | p_SetCoeff(p,d,r); |
---|
| 2047 | pIter(p); |
---|
| 2048 | } |
---|
| 2049 | } |
---|
| 2050 | n_Delete(&h,r->cf); |
---|
| 2051 | #ifdef HAVE_FACTORY |
---|
[aa98be] | 2052 | // if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2053 | // { |
---|
| 2054 | // singclap_divide_content(ph, r); |
---|
| 2055 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2056 | // } |
---|
[8d1d30c] | 2057 | #endif |
---|
| 2058 | if (rField_is_Q_a(r)) |
---|
| 2059 | { |
---|
[aa98be] | 2060 | // we only need special handling for alg. ext. |
---|
| 2061 | if (getCoeffType(r->cf)==n_algExt) |
---|
[8d1d30c] | 2062 | { |
---|
[aa98be] | 2063 | number hzz = n_Init(1, r->cf->extRing->cf); |
---|
[8d1d30c] | 2064 | p=ph; |
---|
| 2065 | while (p!=NULL) |
---|
| 2066 | { // each monom: coeff in Q_a |
---|
[aa98be] | 2067 | poly c_n_n=(poly)pGetCoeff(p); |
---|
| 2068 | poly c_n=c_n_n; |
---|
[8d1d30c] | 2069 | while (c_n!=NULL) |
---|
| 2070 | { // each monom: coeff in Q |
---|
[aa98be] | 2071 | d=n_Lcm(hzz,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2072 | n_Delete(&hzz,r->cf->extRing->cf); |
---|
| 2073 | hzz=d; |
---|
[8d1d30c] | 2074 | pIter(c_n); |
---|
| 2075 | } |
---|
[90aec7] | 2076 | pIter(p); |
---|
[aa98be] | 2077 | } |
---|
| 2078 | /* hzz contains the 1/lcm of all denominators in c_n_n*/ |
---|
| 2079 | h=n_Invers(hzz,r->cf->extRing->cf); |
---|
| 2080 | n_Delete(&hzz,r->cf->extRing->cf); |
---|
| 2081 | n_Normalize(h,r->cf->extRing->cf); |
---|
| 2082 | if(!n_IsOne(h,r->cf->extRing->cf)) |
---|
| 2083 | { |
---|
| 2084 | p=ph; |
---|
| 2085 | while (p!=NULL) |
---|
| 2086 | { // each monom: coeff in Q_a |
---|
| 2087 | poly c_n=(poly)pGetCoeff(p); |
---|
| 2088 | while (c_n!=NULL) |
---|
| 2089 | { // each monom: coeff in Q |
---|
| 2090 | d=n_Mult(h,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2091 | n_Normalize(d,r->cf->extRing->cf); |
---|
| 2092 | n_Delete(&pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2093 | pGetCoeff(c_n)=d; |
---|
| 2094 | pIter(c_n); |
---|
| 2095 | } |
---|
| 2096 | pIter(p); |
---|
[8d1d30c] | 2097 | } |
---|
| 2098 | } |
---|
[aa98be] | 2099 | n_Delete(&h,r->cf->extRing->cf); |
---|
[8d1d30c] | 2100 | } |
---|
| 2101 | } |
---|
| 2102 | } |
---|
[f9a64e] | 2103 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8d1d30c] | 2104 | } |
---|
[e48172] | 2105 | |
---|
| 2106 | // Not yet? |
---|
| 2107 | #if 1 // currently only used by Singular/janet |
---|
| 2108 | void p_SimpleContent(poly ph, int smax, const ring r) |
---|
[8d1d30c] | 2109 | { |
---|
| 2110 | if(TEST_OPT_CONTENTSB) return; |
---|
| 2111 | if (ph==NULL) return; |
---|
| 2112 | if (pNext(ph)==NULL) |
---|
| 2113 | { |
---|
[e48172] | 2114 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
[8d1d30c] | 2115 | return; |
---|
| 2116 | } |
---|
| 2117 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
| 2118 | { |
---|
| 2119 | return; |
---|
| 2120 | } |
---|
| 2121 | number d=p_InitContent(ph,r); |
---|
[e48172] | 2122 | if (n_Size(d,r->cf)<=smax) |
---|
[8d1d30c] | 2123 | { |
---|
| 2124 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
| 2125 | return; |
---|
| 2126 | } |
---|
[e48172] | 2127 | |
---|
| 2128 | |
---|
[8d1d30c] | 2129 | poly p=ph; |
---|
| 2130 | number h=d; |
---|
| 2131 | if (smax==1) smax=2; |
---|
| 2132 | while (p!=NULL) |
---|
| 2133 | { |
---|
| 2134 | #if 0 |
---|
| 2135 | d=nlGcd(h,pGetCoeff(p),r->cf); |
---|
| 2136 | nlDelete(&h,r->cf); |
---|
| 2137 | h = d; |
---|
| 2138 | #else |
---|
| 2139 | nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
| 2140 | #endif |
---|
| 2141 | if(nlSize(h,r->cf)<smax) |
---|
| 2142 | { |
---|
| 2143 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
| 2144 | return; |
---|
| 2145 | } |
---|
| 2146 | pIter(p); |
---|
| 2147 | } |
---|
| 2148 | p = ph; |
---|
| 2149 | if (!nlGreaterZero(pGetCoeff(p),r->cf)) h=nlNeg(h,r->cf); |
---|
| 2150 | if(nlIsOne(h,r->cf)) return; |
---|
| 2151 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
| 2152 | while (p!=NULL) |
---|
| 2153 | { |
---|
| 2154 | #if 1 |
---|
| 2155 | d = nlIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2156 | p_SetCoeff(p,d,r); |
---|
| 2157 | #else |
---|
| 2158 | nlInpIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2159 | #endif |
---|
| 2160 | pIter(p); |
---|
| 2161 | } |
---|
| 2162 | nlDelete(&h,r->cf); |
---|
| 2163 | } |
---|
[5698bb] | 2164 | #endif |
---|
[8d1d30c] | 2165 | |
---|
| 2166 | static number p_InitContent(poly ph, const ring r) |
---|
| 2167 | // only for coefficients in Q |
---|
| 2168 | #if 0 |
---|
| 2169 | { |
---|
| 2170 | assume(!TEST_OPT_CONTENTSB); |
---|
| 2171 | assume(ph!=NULL); |
---|
| 2172 | assume(pNext(ph)!=NULL); |
---|
| 2173 | assume(rField_is_Q(r)); |
---|
| 2174 | if (pNext(pNext(ph))==NULL) |
---|
| 2175 | { |
---|
| 2176 | return nlGetNom(pGetCoeff(pNext(ph)),r->cf); |
---|
| 2177 | } |
---|
| 2178 | poly p=ph; |
---|
| 2179 | number n1=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2180 | pIter(p); |
---|
| 2181 | number n2=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2182 | pIter(p); |
---|
| 2183 | number d; |
---|
| 2184 | number t; |
---|
| 2185 | loop |
---|
| 2186 | { |
---|
| 2187 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2188 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2189 | if (nlGreaterZero(t,r->cf)) |
---|
| 2190 | d=nlAdd(n1,t,r->cf); |
---|
| 2191 | else |
---|
| 2192 | d=nlSub(n1,t,r->cf); |
---|
| 2193 | nlDelete(&t,r->cf); |
---|
| 2194 | nlDelete(&n1,r->cf); |
---|
| 2195 | n1=d; |
---|
| 2196 | pIter(p); |
---|
| 2197 | if (p==NULL) break; |
---|
| 2198 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2199 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2200 | if (nlGreaterZero(t,r->cf)) |
---|
| 2201 | d=nlAdd(n2,t,r->cf); |
---|
| 2202 | else |
---|
| 2203 | d=nlSub(n2,t,r->cf); |
---|
| 2204 | nlDelete(&t,r->cf); |
---|
| 2205 | nlDelete(&n2,r->cf); |
---|
| 2206 | n2=d; |
---|
| 2207 | pIter(p); |
---|
| 2208 | if (p==NULL) break; |
---|
| 2209 | } |
---|
| 2210 | d=nlGcd(n1,n2,r->cf); |
---|
| 2211 | nlDelete(&n1,r->cf); |
---|
| 2212 | nlDelete(&n2,r->cf); |
---|
| 2213 | return d; |
---|
| 2214 | } |
---|
| 2215 | #else |
---|
| 2216 | { |
---|
| 2217 | number d=pGetCoeff(ph); |
---|
| 2218 | if(SR_HDL(d)&SR_INT) return d; |
---|
| 2219 | int s=mpz_size1(d->z); |
---|
| 2220 | int s2=-1; |
---|
| 2221 | number d2; |
---|
| 2222 | loop |
---|
| 2223 | { |
---|
| 2224 | pIter(ph); |
---|
| 2225 | if(ph==NULL) |
---|
| 2226 | { |
---|
| 2227 | if (s2==-1) return nlCopy(d,r->cf); |
---|
| 2228 | break; |
---|
| 2229 | } |
---|
| 2230 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
| 2231 | { |
---|
| 2232 | s2=s; |
---|
| 2233 | d2=d; |
---|
| 2234 | s=0; |
---|
| 2235 | d=pGetCoeff(ph); |
---|
| 2236 | if (s2==0) break; |
---|
| 2237 | } |
---|
| 2238 | else |
---|
| 2239 | if (mpz_size1((pGetCoeff(ph)->z))<=s) |
---|
| 2240 | { |
---|
| 2241 | s2=s; |
---|
| 2242 | d2=d; |
---|
| 2243 | d=pGetCoeff(ph); |
---|
| 2244 | s=mpz_size1(d->z); |
---|
| 2245 | } |
---|
| 2246 | } |
---|
| 2247 | return nlGcd(d,d2,r->cf); |
---|
| 2248 | } |
---|
| 2249 | #endif |
---|
| 2250 | |
---|
| 2251 | //void pContent(poly ph) |
---|
| 2252 | //{ |
---|
| 2253 | // number h,d; |
---|
| 2254 | // poly p; |
---|
| 2255 | // |
---|
| 2256 | // p = ph; |
---|
| 2257 | // if(pNext(p)==NULL) |
---|
| 2258 | // { |
---|
| 2259 | // pSetCoeff(p,nInit(1)); |
---|
| 2260 | // } |
---|
| 2261 | // else |
---|
| 2262 | // { |
---|
| 2263 | //#ifdef PDEBUG |
---|
| 2264 | // if (!pTest(p)) return; |
---|
| 2265 | //#endif |
---|
| 2266 | // nNormalize(pGetCoeff(p)); |
---|
| 2267 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
| 2268 | // { |
---|
| 2269 | // ph = pNeg(ph); |
---|
| 2270 | // nNormalize(pGetCoeff(p)); |
---|
| 2271 | // } |
---|
| 2272 | // h=pGetCoeff(p); |
---|
| 2273 | // pIter(p); |
---|
| 2274 | // while (p!=NULL) |
---|
| 2275 | // { |
---|
| 2276 | // nNormalize(pGetCoeff(p)); |
---|
| 2277 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
| 2278 | // pIter(p); |
---|
| 2279 | // } |
---|
| 2280 | // h=nCopy(h); |
---|
| 2281 | // p=ph; |
---|
| 2282 | // while (p!=NULL) |
---|
| 2283 | // { |
---|
[32d07a5] | 2284 | // d=n_Gcd(h,pGetCoeff(p)); |
---|
[8d1d30c] | 2285 | // nDelete(&h); |
---|
| 2286 | // h = d; |
---|
| 2287 | // if(nIsOne(h)) |
---|
| 2288 | // { |
---|
| 2289 | // break; |
---|
| 2290 | // } |
---|
| 2291 | // pIter(p); |
---|
| 2292 | // } |
---|
| 2293 | // p = ph; |
---|
| 2294 | // //number tmp; |
---|
| 2295 | // if(!nIsOne(h)) |
---|
| 2296 | // { |
---|
| 2297 | // while (p!=NULL) |
---|
| 2298 | // { |
---|
| 2299 | // d = nIntDiv(pGetCoeff(p),h); |
---|
| 2300 | // pSetCoeff(p,d); |
---|
| 2301 | // pIter(p); |
---|
| 2302 | // } |
---|
| 2303 | // } |
---|
| 2304 | // nDelete(&h); |
---|
| 2305 | //#ifdef HAVE_FACTORY |
---|
| 2306 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2307 | // { |
---|
| 2308 | // pTest(ph); |
---|
| 2309 | // singclap_divide_content(ph); |
---|
| 2310 | // pTest(ph); |
---|
| 2311 | // } |
---|
| 2312 | //#endif |
---|
| 2313 | // } |
---|
| 2314 | //} |
---|
| 2315 | #if 0 |
---|
| 2316 | void p_Content(poly ph, const ring r) |
---|
| 2317 | { |
---|
| 2318 | number h,d; |
---|
| 2319 | poly p; |
---|
| 2320 | |
---|
| 2321 | if(pNext(ph)==NULL) |
---|
| 2322 | { |
---|
| 2323 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
| 2324 | } |
---|
| 2325 | else |
---|
| 2326 | { |
---|
| 2327 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 2328 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2329 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2330 | p = pNext(ph); |
---|
| 2331 | while (p!=NULL) |
---|
| 2332 | { |
---|
| 2333 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2334 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2335 | n_Delete(&h,r->cf); |
---|
| 2336 | h = d; |
---|
| 2337 | if(n_IsOne(h,r->cf)) |
---|
| 2338 | { |
---|
| 2339 | break; |
---|
| 2340 | } |
---|
| 2341 | pIter(p); |
---|
| 2342 | } |
---|
| 2343 | p = ph; |
---|
| 2344 | //number tmp; |
---|
| 2345 | if(!n_IsOne(h,r->cf)) |
---|
| 2346 | { |
---|
| 2347 | while (p!=NULL) |
---|
| 2348 | { |
---|
| 2349 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2350 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2351 | //if (!nEqual(d,tmp)) |
---|
| 2352 | //{ |
---|
| 2353 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2354 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
| 2355 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
| 2356 | //} |
---|
| 2357 | //nDelete(&tmp); |
---|
| 2358 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2359 | p_SetCoeff(p,d,r->cf); |
---|
| 2360 | pIter(p); |
---|
| 2361 | } |
---|
| 2362 | } |
---|
| 2363 | n_Delete(&h,r->cf); |
---|
| 2364 | #ifdef HAVE_FACTORY |
---|
| 2365 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2366 | //{ |
---|
| 2367 | // singclap_divide_content(ph); |
---|
| 2368 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
| 2369 | //} |
---|
| 2370 | #endif |
---|
| 2371 | } |
---|
| 2372 | } |
---|
| 2373 | #endif |
---|
[fbf8a6] | 2374 | /* ---------------------------------------------------------------------------*/ |
---|
| 2375 | /* cleardenom suff */ |
---|
[8d1d30c] | 2376 | poly p_Cleardenom(poly ph, const ring r) |
---|
| 2377 | { |
---|
| 2378 | poly start=ph; |
---|
| 2379 | number d, h; |
---|
| 2380 | poly p; |
---|
| 2381 | |
---|
| 2382 | #ifdef HAVE_RINGS |
---|
| 2383 | if (rField_is_Ring(r)) |
---|
| 2384 | { |
---|
| 2385 | p_Content(ph,r); |
---|
| 2386 | return start; |
---|
| 2387 | } |
---|
| 2388 | #endif |
---|
| 2389 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) return start; |
---|
| 2390 | p = ph; |
---|
| 2391 | if(pNext(p)==NULL) |
---|
| 2392 | { |
---|
| 2393 | if (TEST_OPT_CONTENTSB) |
---|
| 2394 | { |
---|
| 2395 | number n=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2396 | if (!n_IsOne(n,r->cf)) |
---|
| 2397 | { |
---|
| 2398 | number nn=n_Mult(pGetCoeff(p),n,r->cf); |
---|
| 2399 | n_Normalize(nn,r->cf); |
---|
| 2400 | p_SetCoeff(p,nn,r); |
---|
| 2401 | } |
---|
| 2402 | n_Delete(&n,r->cf); |
---|
| 2403 | } |
---|
| 2404 | else |
---|
| 2405 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
| 2406 | } |
---|
| 2407 | else |
---|
| 2408 | { |
---|
| 2409 | h = n_Init(1,r->cf); |
---|
| 2410 | while (p!=NULL) |
---|
| 2411 | { |
---|
[8a8c9e] | 2412 | n_Normalize(pGetCoeff(p),r->cf); |
---|
[8d1d30c] | 2413 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2414 | n_Delete(&h,r->cf); |
---|
| 2415 | h=d; |
---|
| 2416 | pIter(p); |
---|
| 2417 | } |
---|
| 2418 | /* contains the 1/lcm of all denominators */ |
---|
| 2419 | if(!n_IsOne(h,r->cf)) |
---|
| 2420 | { |
---|
| 2421 | p = ph; |
---|
| 2422 | while (p!=NULL) |
---|
| 2423 | { |
---|
| 2424 | /* should be: |
---|
| 2425 | * number hh; |
---|
| 2426 | * nGetDenom(p->coef,&hh); |
---|
| 2427 | * nMult(&h,&hh,&d); |
---|
| 2428 | * nNormalize(d); |
---|
| 2429 | * nDelete(&hh); |
---|
| 2430 | * nMult(d,p->coef,&hh); |
---|
| 2431 | * nDelete(&d); |
---|
| 2432 | * nDelete(&(p->coef)); |
---|
| 2433 | * p->coef =hh; |
---|
| 2434 | */ |
---|
| 2435 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2436 | n_Normalize(d,r->cf); |
---|
| 2437 | p_SetCoeff(p,d,r); |
---|
| 2438 | pIter(p); |
---|
| 2439 | } |
---|
| 2440 | n_Delete(&h,r->cf); |
---|
[5679049] | 2441 | if (n_GetChar(r->cf)==1) |
---|
[8d1d30c] | 2442 | { |
---|
| 2443 | loop |
---|
| 2444 | { |
---|
| 2445 | h = n_Init(1,r->cf); |
---|
| 2446 | p=ph; |
---|
| 2447 | while (p!=NULL) |
---|
| 2448 | { |
---|
| 2449 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2450 | n_Delete(&h,r->cf); |
---|
| 2451 | h=d; |
---|
| 2452 | pIter(p); |
---|
| 2453 | } |
---|
| 2454 | /* contains the 1/lcm of all denominators */ |
---|
| 2455 | if(!n_IsOne(h,r->cf)) |
---|
| 2456 | { |
---|
| 2457 | p = ph; |
---|
| 2458 | while (p!=NULL) |
---|
| 2459 | { |
---|
| 2460 | /* should be: |
---|
| 2461 | * number hh; |
---|
| 2462 | * nGetDenom(p->coef,&hh); |
---|
| 2463 | * nMult(&h,&hh,&d); |
---|
| 2464 | * nNormalize(d); |
---|
| 2465 | * nDelete(&hh); |
---|
| 2466 | * nMult(d,p->coef,&hh); |
---|
| 2467 | * nDelete(&d); |
---|
| 2468 | * nDelete(&(p->coef)); |
---|
| 2469 | * p->coef =hh; |
---|
| 2470 | */ |
---|
| 2471 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2472 | n_Normalize(d,r->cf); |
---|
| 2473 | p_SetCoeff(p,d,r); |
---|
| 2474 | pIter(p); |
---|
| 2475 | } |
---|
| 2476 | n_Delete(&h,r->cf); |
---|
| 2477 | } |
---|
| 2478 | else |
---|
| 2479 | { |
---|
| 2480 | n_Delete(&h,r->cf); |
---|
| 2481 | break; |
---|
| 2482 | } |
---|
| 2483 | } |
---|
| 2484 | } |
---|
| 2485 | } |
---|
| 2486 | if (h!=NULL) n_Delete(&h,r->cf); |
---|
[71ba5b8] | 2487 | |
---|
[8d1d30c] | 2488 | p_Content(ph,r); |
---|
| 2489 | #ifdef HAVE_RATGRING |
---|
| 2490 | if (rIsRatGRing(r)) |
---|
| 2491 | { |
---|
| 2492 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
| 2493 | pContentRat(ph); |
---|
| 2494 | start=ph; |
---|
| 2495 | } |
---|
| 2496 | #endif |
---|
| 2497 | } |
---|
| 2498 | return start; |
---|
| 2499 | } |
---|
| 2500 | |
---|
| 2501 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
| 2502 | { |
---|
| 2503 | number d, h; |
---|
| 2504 | poly p; |
---|
| 2505 | |
---|
| 2506 | p = ph; |
---|
| 2507 | if(pNext(p)==NULL) |
---|
| 2508 | { |
---|
| 2509 | c=n_Invers(pGetCoeff(p),r->cf); |
---|
| 2510 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
| 2511 | } |
---|
| 2512 | else |
---|
| 2513 | { |
---|
| 2514 | h = n_Init(1,r->cf); |
---|
| 2515 | while (p!=NULL) |
---|
| 2516 | { |
---|
| 2517 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2518 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2519 | n_Delete(&h,r->cf); |
---|
| 2520 | h=d; |
---|
| 2521 | pIter(p); |
---|
| 2522 | } |
---|
| 2523 | c=h; |
---|
| 2524 | /* contains the 1/lcm of all denominators */ |
---|
| 2525 | if(!n_IsOne(h,r->cf)) |
---|
| 2526 | { |
---|
| 2527 | p = ph; |
---|
| 2528 | while (p!=NULL) |
---|
| 2529 | { |
---|
| 2530 | /* should be: |
---|
| 2531 | * number hh; |
---|
| 2532 | * nGetDenom(p->coef,&hh); |
---|
| 2533 | * nMult(&h,&hh,&d); |
---|
| 2534 | * nNormalize(d); |
---|
| 2535 | * nDelete(&hh); |
---|
| 2536 | * nMult(d,p->coef,&hh); |
---|
| 2537 | * nDelete(&d); |
---|
| 2538 | * nDelete(&(p->coef)); |
---|
| 2539 | * p->coef =hh; |
---|
| 2540 | */ |
---|
| 2541 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2542 | n_Normalize(d,r->cf); |
---|
| 2543 | p_SetCoeff(p,d,r); |
---|
| 2544 | pIter(p); |
---|
| 2545 | } |
---|
| 2546 | if (rField_is_Q_a(r)) |
---|
| 2547 | { |
---|
| 2548 | loop |
---|
| 2549 | { |
---|
| 2550 | h = n_Init(1,r->cf); |
---|
| 2551 | p=ph; |
---|
| 2552 | while (p!=NULL) |
---|
| 2553 | { |
---|
| 2554 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2555 | n_Delete(&h,r->cf); |
---|
| 2556 | h=d; |
---|
| 2557 | pIter(p); |
---|
| 2558 | } |
---|
| 2559 | /* contains the 1/lcm of all denominators */ |
---|
| 2560 | if(!n_IsOne(h,r->cf)) |
---|
| 2561 | { |
---|
| 2562 | p = ph; |
---|
| 2563 | while (p!=NULL) |
---|
| 2564 | { |
---|
| 2565 | /* should be: |
---|
| 2566 | * number hh; |
---|
| 2567 | * nGetDenom(p->coef,&hh); |
---|
| 2568 | * nMult(&h,&hh,&d); |
---|
| 2569 | * nNormalize(d); |
---|
| 2570 | * nDelete(&hh); |
---|
| 2571 | * nMult(d,p->coef,&hh); |
---|
| 2572 | * nDelete(&d); |
---|
| 2573 | * nDelete(&(p->coef)); |
---|
| 2574 | * p->coef =hh; |
---|
| 2575 | */ |
---|
| 2576 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2577 | n_Normalize(d,r->cf); |
---|
| 2578 | p_SetCoeff(p,d,r); |
---|
| 2579 | pIter(p); |
---|
| 2580 | } |
---|
| 2581 | number t=n_Mult(c,h,r->cf); |
---|
| 2582 | n_Delete(&c,r->cf); |
---|
| 2583 | c=t; |
---|
| 2584 | } |
---|
| 2585 | else |
---|
| 2586 | { |
---|
| 2587 | break; |
---|
| 2588 | } |
---|
| 2589 | n_Delete(&h,r->cf); |
---|
| 2590 | } |
---|
| 2591 | } |
---|
| 2592 | } |
---|
| 2593 | } |
---|
| 2594 | } |
---|
| 2595 | |
---|
| 2596 | number p_GetAllDenom(poly ph, const ring r) |
---|
| 2597 | { |
---|
| 2598 | number d=n_Init(1,r->cf); |
---|
| 2599 | poly p = ph; |
---|
| 2600 | |
---|
| 2601 | while (p!=NULL) |
---|
| 2602 | { |
---|
| 2603 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2604 | if (!n_IsOne(h,r->cf)) |
---|
| 2605 | { |
---|
| 2606 | number dd=n_Mult(d,h,r->cf); |
---|
| 2607 | n_Delete(&d,r->cf); |
---|
| 2608 | d=dd; |
---|
| 2609 | } |
---|
| 2610 | n_Delete(&h,r->cf); |
---|
| 2611 | pIter(p); |
---|
| 2612 | } |
---|
| 2613 | return d; |
---|
| 2614 | } |
---|
| 2615 | |
---|
[fbf8a6] | 2616 | int p_Size(poly p, const ring r) |
---|
| 2617 | { |
---|
| 2618 | int count = 0; |
---|
| 2619 | while ( p != NULL ) |
---|
| 2620 | { |
---|
| 2621 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
| 2622 | pIter( p ); |
---|
| 2623 | } |
---|
| 2624 | return count; |
---|
| 2625 | } |
---|
| 2626 | |
---|
[4e8ef90] | 2627 | /*2 |
---|
| 2628 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
| 2629 | *assume: deg(var(varnum))==1 |
---|
| 2630 | */ |
---|
| 2631 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
| 2632 | { |
---|
| 2633 | pFDegProc deg; |
---|
[5679049] | 2634 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2635 | deg=p_Totaldegree; |
---|
| 2636 | else |
---|
[9765f3] | 2637 | deg=r->pFDeg; |
---|
[4e8ef90] | 2638 | |
---|
| 2639 | poly q=NULL, qn; |
---|
| 2640 | int o,ii; |
---|
| 2641 | sBucket_pt bp; |
---|
| 2642 | |
---|
| 2643 | if (p!=NULL) |
---|
| 2644 | { |
---|
| 2645 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
| 2646 | { |
---|
| 2647 | return NULL; |
---|
| 2648 | } |
---|
| 2649 | o=deg(p,r); |
---|
| 2650 | q=pNext(p); |
---|
| 2651 | while (q != NULL) |
---|
| 2652 | { |
---|
| 2653 | ii=deg(q,r); |
---|
| 2654 | if (ii>o) o=ii; |
---|
| 2655 | pIter(q); |
---|
| 2656 | } |
---|
| 2657 | q = p_Copy(p,r); |
---|
| 2658 | bp = sBucketCreate(r); |
---|
| 2659 | while (q != NULL) |
---|
| 2660 | { |
---|
| 2661 | ii = o-deg(q,r); |
---|
| 2662 | if (ii!=0) |
---|
| 2663 | { |
---|
| 2664 | p_AddExp(q,varnum, (long)ii,r); |
---|
| 2665 | p_Setm(q,r); |
---|
| 2666 | } |
---|
| 2667 | qn = pNext(q); |
---|
| 2668 | pNext(q) = NULL; |
---|
| 2669 | sBucket_Add_p(bp, q, 1); |
---|
| 2670 | q = qn; |
---|
| 2671 | } |
---|
| 2672 | sBucketDestroyAdd(bp, &q, &ii); |
---|
| 2673 | } |
---|
| 2674 | return q; |
---|
| 2675 | } |
---|
| 2676 | |
---|
| 2677 | /*2 |
---|
| 2678 | *tests if p is homogeneous with respect to the actual weigths |
---|
| 2679 | */ |
---|
| 2680 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
| 2681 | { |
---|
| 2682 | poly qp=p; |
---|
| 2683 | int o; |
---|
| 2684 | |
---|
| 2685 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
| 2686 | pFDegProc d; |
---|
[5679049] | 2687 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2688 | d=p_Totaldegree; |
---|
[71ba5b8] | 2689 | else |
---|
[9765f3] | 2690 | d=r->pFDeg; |
---|
[8a8c9e] | 2691 | o = d(p,r); |
---|
[4e8ef90] | 2692 | do |
---|
| 2693 | { |
---|
| 2694 | if (d(qp,r) != o) return FALSE; |
---|
| 2695 | pIter(qp); |
---|
| 2696 | } |
---|
| 2697 | while (qp != NULL); |
---|
| 2698 | return TRUE; |
---|
| 2699 | } |
---|
| 2700 | |
---|
[cd246b] | 2701 | /*----------utilities for syzygies--------------*/ |
---|
| 2702 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
| 2703 | { |
---|
| 2704 | poly q=p,qq; |
---|
| 2705 | int i; |
---|
| 2706 | |
---|
| 2707 | while (q!=NULL) |
---|
| 2708 | { |
---|
| 2709 | if (p_LmIsConstantComp(q,r)) |
---|
| 2710 | { |
---|
| 2711 | i = p_GetComp(q,r); |
---|
| 2712 | qq = p; |
---|
| 2713 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2714 | if (qq == q) |
---|
| 2715 | { |
---|
| 2716 | *k = i; |
---|
| 2717 | return TRUE; |
---|
| 2718 | } |
---|
| 2719 | else |
---|
| 2720 | pIter(q); |
---|
| 2721 | } |
---|
| 2722 | else pIter(q); |
---|
| 2723 | } |
---|
| 2724 | return FALSE; |
---|
| 2725 | } |
---|
| 2726 | |
---|
| 2727 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
| 2728 | { |
---|
| 2729 | poly q=p,qq; |
---|
| 2730 | int i,j=0; |
---|
| 2731 | |
---|
| 2732 | *len = 0; |
---|
| 2733 | while (q!=NULL) |
---|
| 2734 | { |
---|
| 2735 | if (p_LmIsConstantComp(q,r)) |
---|
| 2736 | { |
---|
| 2737 | i = p_GetComp(q,r); |
---|
| 2738 | qq = p; |
---|
| 2739 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2740 | if (qq == q) |
---|
| 2741 | { |
---|
| 2742 | j = 0; |
---|
| 2743 | while (qq!=NULL) |
---|
| 2744 | { |
---|
| 2745 | if (p_GetComp(qq,r)==i) j++; |
---|
| 2746 | pIter(qq); |
---|
| 2747 | } |
---|
| 2748 | if ((*len == 0) || (j<*len)) |
---|
| 2749 | { |
---|
| 2750 | *len = j; |
---|
| 2751 | *k = i; |
---|
| 2752 | } |
---|
| 2753 | } |
---|
| 2754 | } |
---|
| 2755 | pIter(q); |
---|
| 2756 | } |
---|
| 2757 | } |
---|
| 2758 | |
---|
| 2759 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
| 2760 | { |
---|
| 2761 | poly q = *p; |
---|
| 2762 | |
---|
| 2763 | if (q==NULL) return NULL; |
---|
| 2764 | |
---|
| 2765 | poly qq=NULL,result = NULL; |
---|
| 2766 | |
---|
| 2767 | if (p_GetComp(q,r)==k) |
---|
| 2768 | { |
---|
| 2769 | result = q; /* *p */ |
---|
| 2770 | while ((q!=NULL) && (p_GetComp(q,r)==k)) |
---|
| 2771 | { |
---|
| 2772 | p_SetComp(q,0,r); |
---|
| 2773 | p_SetmComp(q,r); |
---|
| 2774 | qq = q; |
---|
| 2775 | pIter(q); |
---|
| 2776 | } |
---|
| 2777 | *p = q; |
---|
| 2778 | pNext(qq) = NULL; |
---|
| 2779 | } |
---|
| 2780 | if (q==NULL) return result; |
---|
| 2781 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2782 | while (pNext(q)!=NULL) |
---|
| 2783 | { |
---|
| 2784 | if (p_GetComp(pNext(q),r)==k) |
---|
| 2785 | { |
---|
| 2786 | if (result==NULL) |
---|
| 2787 | { |
---|
| 2788 | result = pNext(q); |
---|
| 2789 | qq = result; |
---|
| 2790 | } |
---|
| 2791 | else |
---|
| 2792 | { |
---|
| 2793 | pNext(qq) = pNext(q); |
---|
| 2794 | pIter(qq); |
---|
| 2795 | } |
---|
| 2796 | pNext(q) = pNext(pNext(q)); |
---|
| 2797 | pNext(qq) =NULL; |
---|
| 2798 | p_SetComp(qq,0,r); |
---|
| 2799 | p_SetmComp(qq,r); |
---|
| 2800 | } |
---|
| 2801 | else |
---|
| 2802 | { |
---|
| 2803 | pIter(q); |
---|
| 2804 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2805 | } |
---|
| 2806 | } |
---|
| 2807 | return result; |
---|
| 2808 | } |
---|
[74021a] | 2809 | |
---|
| 2810 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
| 2811 | { |
---|
| 2812 | poly q = *p,qq=NULL,result = NULL; |
---|
| 2813 | |
---|
| 2814 | if (q==NULL) return NULL; |
---|
| 2815 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
| 2816 | if (p_GetComp(q,r)==k) |
---|
| 2817 | { |
---|
| 2818 | result = q; |
---|
| 2819 | do |
---|
| 2820 | { |
---|
| 2821 | p_SetComp(q,0,r); |
---|
| 2822 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2823 | qq = q; |
---|
| 2824 | pIter(q); |
---|
| 2825 | } |
---|
| 2826 | while ((q!=NULL) && (p_GetComp(q,r)==k)); |
---|
| 2827 | *p = q; |
---|
| 2828 | pNext(qq) = NULL; |
---|
| 2829 | } |
---|
| 2830 | if (q==NULL) return result; |
---|
| 2831 | if (p_GetComp(q,r) > k) |
---|
| 2832 | { |
---|
| 2833 | p_SubComp(q,1,r); |
---|
| 2834 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2835 | } |
---|
| 2836 | poly pNext_q; |
---|
| 2837 | while ((pNext_q=pNext(q))!=NULL) |
---|
| 2838 | { |
---|
| 2839 | if (p_GetComp(pNext_q,r)==k) |
---|
| 2840 | { |
---|
| 2841 | if (result==NULL) |
---|
| 2842 | { |
---|
| 2843 | result = pNext_q; |
---|
| 2844 | qq = result; |
---|
| 2845 | } |
---|
| 2846 | else |
---|
| 2847 | { |
---|
| 2848 | pNext(qq) = pNext_q; |
---|
| 2849 | pIter(qq); |
---|
| 2850 | } |
---|
| 2851 | pNext(q) = pNext(pNext_q); |
---|
| 2852 | pNext(qq) =NULL; |
---|
| 2853 | p_SetComp(qq,0,r); |
---|
| 2854 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
| 2855 | } |
---|
| 2856 | else |
---|
| 2857 | { |
---|
| 2858 | /*pIter(q);*/ q=pNext_q; |
---|
| 2859 | if (p_GetComp(q,r) > k) |
---|
| 2860 | { |
---|
| 2861 | p_SubComp(q,1,r); |
---|
| 2862 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2863 | } |
---|
| 2864 | } |
---|
| 2865 | } |
---|
| 2866 | return result; |
---|
| 2867 | } |
---|
| 2868 | |
---|
| 2869 | // Splits *p into two polys: *q which consists of all monoms with |
---|
| 2870 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
| 2871 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
| 2872 | { |
---|
| 2873 | spolyrec pp, qq; |
---|
| 2874 | poly p, q, p_prev; |
---|
| 2875 | int l = 0; |
---|
| 2876 | |
---|
| 2877 | #ifdef HAVE_ASSUME |
---|
| 2878 | int lp = pLength(*r_p); |
---|
| 2879 | #endif |
---|
| 2880 | |
---|
| 2881 | pNext(&pp) = *r_p; |
---|
| 2882 | p = *r_p; |
---|
| 2883 | p_prev = &pp; |
---|
| 2884 | q = &qq; |
---|
| 2885 | |
---|
| 2886 | while(p != NULL) |
---|
| 2887 | { |
---|
| 2888 | while (p_GetComp(p,r) == comp) |
---|
| 2889 | { |
---|
| 2890 | pNext(q) = p; |
---|
| 2891 | pIter(q); |
---|
| 2892 | p_SetComp(p, 0,r); |
---|
| 2893 | p_SetmComp(p,r); |
---|
| 2894 | pIter(p); |
---|
| 2895 | l++; |
---|
| 2896 | if (p == NULL) |
---|
| 2897 | { |
---|
| 2898 | pNext(p_prev) = NULL; |
---|
| 2899 | goto Finish; |
---|
| 2900 | } |
---|
| 2901 | } |
---|
| 2902 | pNext(p_prev) = p; |
---|
| 2903 | p_prev = p; |
---|
| 2904 | pIter(p); |
---|
| 2905 | } |
---|
| 2906 | |
---|
| 2907 | Finish: |
---|
| 2908 | pNext(q) = NULL; |
---|
| 2909 | *r_p = pNext(&pp); |
---|
| 2910 | *r_q = pNext(&qq); |
---|
| 2911 | *lq = l; |
---|
| 2912 | #ifdef HAVE_ASSUME |
---|
| 2913 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
| 2914 | #endif |
---|
| 2915 | p_Test(*r_p,r); |
---|
| 2916 | p_Test(*r_q,r); |
---|
| 2917 | } |
---|
| 2918 | |
---|
| 2919 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
| 2920 | { |
---|
| 2921 | poly q; |
---|
| 2922 | |
---|
| 2923 | while ((*p!=NULL) && (p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
| 2924 | if (*p==NULL) return; |
---|
| 2925 | q = *p; |
---|
| 2926 | if (p_GetComp(q,r)>k) |
---|
| 2927 | { |
---|
| 2928 | p_SubComp(q,1,r); |
---|
| 2929 | p_SetmComp(q,r); |
---|
| 2930 | } |
---|
| 2931 | while (pNext(q)!=NULL) |
---|
| 2932 | { |
---|
| 2933 | if (p_GetComp(pNext(q),r)==k) |
---|
| 2934 | p_LmDelete(&(pNext(q)),r); |
---|
| 2935 | else |
---|
| 2936 | { |
---|
| 2937 | pIter(q); |
---|
| 2938 | if (p_GetComp(q,r)>k) |
---|
| 2939 | { |
---|
| 2940 | p_SubComp(q,1,r); |
---|
| 2941 | p_SetmComp(q,r); |
---|
| 2942 | } |
---|
| 2943 | } |
---|
| 2944 | } |
---|
| 2945 | } |
---|
[dd693a] | 2946 | |
---|
| 2947 | /*2 |
---|
| 2948 | * convert a vector to a set of polys, |
---|
| 2949 | * allocates the polyset, (entries 0..(*len)-1) |
---|
| 2950 | * the vector will not be changed |
---|
| 2951 | */ |
---|
| 2952 | void p_Vec2Polys(poly v, poly* *p, int *len, const ring r) |
---|
| 2953 | { |
---|
| 2954 | poly h; |
---|
| 2955 | int k; |
---|
| 2956 | |
---|
| 2957 | *len=p_MaxComp(v,r); |
---|
| 2958 | if (*len==0) *len=1; |
---|
| 2959 | *p=(poly*)omAlloc0((*len)*sizeof(poly)); |
---|
| 2960 | while (v!=NULL) |
---|
| 2961 | { |
---|
| 2962 | h=p_Head(v,r); |
---|
| 2963 | k=p_GetComp(h,r); |
---|
| 2964 | p_SetComp(h,0,r); |
---|
| 2965 | (*p)[k-1]=p_Add_q((*p)[k-1],h,r); |
---|
| 2966 | pIter(v); |
---|
| 2967 | } |
---|
| 2968 | } |
---|
| 2969 | |
---|
[949e57] | 2970 | // |
---|
| 2971 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
| 2972 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
[45d2332] | 2973 | // only uses pFDeg (and not p_Deg, or pTotalDegree, etc) |
---|
[949e57] | 2974 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
| 2975 | { |
---|
| 2976 | assume(new_FDeg != NULL); |
---|
| 2977 | r->pFDeg = new_FDeg; |
---|
| 2978 | |
---|
| 2979 | if (new_lDeg == NULL) |
---|
| 2980 | new_lDeg = r->pLDegOrig; |
---|
| 2981 | |
---|
| 2982 | r->pLDeg = new_lDeg; |
---|
| 2983 | } |
---|
| 2984 | |
---|
| 2985 | // restores pFDeg and pLDeg: |
---|
| 2986 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
| 2987 | { |
---|
| 2988 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
| 2989 | r->pFDeg = old_FDeg; |
---|
| 2990 | r->pLDeg = old_lDeg; |
---|
| 2991 | } |
---|
| 2992 | |
---|
[5bc2461] | 2993 | /*-------- several access procedures to monomials -------------------- */ |
---|
| 2994 | /* |
---|
| 2995 | * the module weights for std |
---|
| 2996 | */ |
---|
| 2997 | static pFDegProc pOldFDeg; |
---|
| 2998 | static pLDegProc pOldLDeg; |
---|
| 2999 | static BOOLEAN pOldLexOrder; |
---|
| 3000 | |
---|
[8a8c9e] | 3001 | static long pModDeg(poly p, ring r) |
---|
[5bc2461] | 3002 | { |
---|
| 3003 | long d=pOldFDeg(p, r); |
---|
| 3004 | int c=p_GetComp(p, r); |
---|
| 3005 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
| 3006 | return d; |
---|
| 3007 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
| 3008 | } |
---|
| 3009 | |
---|
| 3010 | void p_SetModDeg(intvec *w, ring r) |
---|
| 3011 | { |
---|
| 3012 | if (w!=NULL) |
---|
| 3013 | { |
---|
| 3014 | r->pModW = w; |
---|
| 3015 | pOldFDeg = r->pFDeg; |
---|
| 3016 | pOldLDeg = r->pLDeg; |
---|
| 3017 | pOldLexOrder = r->pLexOrder; |
---|
| 3018 | pSetDegProcs(r,pModDeg); |
---|
| 3019 | r->pLexOrder = TRUE; |
---|
| 3020 | } |
---|
| 3021 | else |
---|
| 3022 | { |
---|
| 3023 | r->pModW = NULL; |
---|
[5679049] | 3024 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
[5bc2461] | 3025 | r->pLexOrder = pOldLexOrder; |
---|
| 3026 | } |
---|
| 3027 | } |
---|
| 3028 | |
---|
[c6a3eb2] | 3029 | /*2 |
---|
| 3030 | * handle memory request for sets of polynomials (ideals) |
---|
| 3031 | * l is the length of *p, increment is the difference (may be negative) |
---|
| 3032 | */ |
---|
| 3033 | void pEnlargeSet(poly* *p, int l, int increment) |
---|
| 3034 | { |
---|
| 3035 | poly* h; |
---|
| 3036 | |
---|
| 3037 | h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
| 3038 | if (increment>0) |
---|
| 3039 | { |
---|
| 3040 | //for (i=l; i<l+increment; i++) |
---|
| 3041 | // h[i]=NULL; |
---|
| 3042 | memset(&(h[l]),0,increment*sizeof(poly)); |
---|
| 3043 | } |
---|
| 3044 | *p=h; |
---|
| 3045 | } |
---|
| 3046 | |
---|
[71ba5b8] | 3047 | /*2 |
---|
| 3048 | *divides p1 by its leading coefficient |
---|
| 3049 | */ |
---|
| 3050 | void p_Norm(poly p1, const ring r) |
---|
| 3051 | { |
---|
| 3052 | #ifdef HAVE_RINGS |
---|
| 3053 | if (rField_is_Ring(r)) |
---|
| 3054 | { |
---|
[45d2332] | 3055 | if (!n_IsUnit(pGetCoeff(p1), r->cf)) return; |
---|
[71ba5b8] | 3056 | // Werror("p_Norm not possible in the case of coefficient rings."); |
---|
| 3057 | } |
---|
| 3058 | else |
---|
| 3059 | #endif |
---|
| 3060 | if (p1!=NULL) |
---|
| 3061 | { |
---|
| 3062 | if (pNext(p1)==NULL) |
---|
| 3063 | { |
---|
| 3064 | p_SetCoeff(p1,n_Init(1,r->cf),r); |
---|
| 3065 | return; |
---|
| 3066 | } |
---|
| 3067 | poly h; |
---|
| 3068 | if (!n_IsOne(pGetCoeff(p1),r->cf)) |
---|
| 3069 | { |
---|
| 3070 | number k, c; |
---|
| 3071 | n_Normalize(pGetCoeff(p1),r->cf); |
---|
| 3072 | k = pGetCoeff(p1); |
---|
| 3073 | c = n_Init(1,r->cf); |
---|
| 3074 | pSetCoeff0(p1,c); |
---|
| 3075 | h = pNext(p1); |
---|
| 3076 | while (h!=NULL) |
---|
| 3077 | { |
---|
| 3078 | c=n_Div(pGetCoeff(h),k,r->cf); |
---|
| 3079 | // no need to normalize: Z/p, R |
---|
| 3080 | // normalize already in nDiv: Q_a, Z/p_a |
---|
| 3081 | // remains: Q |
---|
| 3082 | if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) n_Normalize(c,r->cf); |
---|
| 3083 | p_SetCoeff(h,c,r); |
---|
| 3084 | pIter(h); |
---|
| 3085 | } |
---|
| 3086 | n_Delete(&k,r->cf); |
---|
| 3087 | } |
---|
| 3088 | else |
---|
| 3089 | { |
---|
| 3090 | //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE |
---|
| 3091 | { |
---|
| 3092 | h = pNext(p1); |
---|
| 3093 | while (h!=NULL) |
---|
| 3094 | { |
---|
| 3095 | n_Normalize(pGetCoeff(h),r->cf); |
---|
| 3096 | pIter(h); |
---|
| 3097 | } |
---|
| 3098 | } |
---|
| 3099 | } |
---|
| 3100 | } |
---|
| 3101 | } |
---|
| 3102 | |
---|
| 3103 | /*2 |
---|
| 3104 | *normalize all coefficients |
---|
| 3105 | */ |
---|
| 3106 | void p_Normalize(poly p,const ring r) |
---|
| 3107 | { |
---|
| 3108 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
| 3109 | while (p!=NULL) |
---|
| 3110 | { |
---|
| 3111 | #ifdef LDEBUG |
---|
[45d2332] | 3112 | n_Test(pGetCoeff(p), r->cf); |
---|
[71ba5b8] | 3113 | #endif |
---|
| 3114 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 3115 | pIter(p); |
---|
| 3116 | } |
---|
| 3117 | } |
---|
| 3118 | |
---|
| 3119 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
| 3120 | // Poly with Exp(n) != 0 is reversed |
---|
| 3121 | static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r) |
---|
| 3122 | { |
---|
| 3123 | if (p == NULL) |
---|
| 3124 | { |
---|
| 3125 | *non_zero = NULL; |
---|
| 3126 | *zero = NULL; |
---|
| 3127 | return; |
---|
| 3128 | } |
---|
| 3129 | spolyrec sz; |
---|
| 3130 | poly z, n_z, next; |
---|
| 3131 | z = &sz; |
---|
| 3132 | n_z = NULL; |
---|
| 3133 | |
---|
| 3134 | while(p != NULL) |
---|
| 3135 | { |
---|
| 3136 | next = pNext(p); |
---|
| 3137 | if (p_GetExp(p, n,r) == 0) |
---|
| 3138 | { |
---|
| 3139 | pNext(z) = p; |
---|
| 3140 | pIter(z); |
---|
| 3141 | } |
---|
| 3142 | else |
---|
| 3143 | { |
---|
| 3144 | pNext(p) = n_z; |
---|
| 3145 | n_z = p; |
---|
| 3146 | } |
---|
| 3147 | p = next; |
---|
| 3148 | } |
---|
| 3149 | pNext(z) = NULL; |
---|
| 3150 | *zero = pNext(&sz); |
---|
| 3151 | *non_zero = n_z; |
---|
| 3152 | } |
---|
| 3153 | /*3 |
---|
| 3154 | * substitute the n-th variable by 1 in p |
---|
| 3155 | * destroy p |
---|
| 3156 | */ |
---|
| 3157 | static poly p_Subst1 (poly p,int n, const ring r) |
---|
| 3158 | { |
---|
| 3159 | poly qq=NULL, result = NULL; |
---|
| 3160 | poly zero=NULL, non_zero=NULL; |
---|
| 3161 | |
---|
| 3162 | // reverse, so that add is likely to be linear |
---|
| 3163 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3164 | |
---|
| 3165 | while (non_zero != NULL) |
---|
| 3166 | { |
---|
| 3167 | assume(p_GetExp(non_zero, n,r) != 0); |
---|
| 3168 | qq = non_zero; |
---|
| 3169 | pIter(non_zero); |
---|
| 3170 | qq->next = NULL; |
---|
| 3171 | p_SetExp(qq,n,0,r); |
---|
| 3172 | p_Setm(qq,r); |
---|
| 3173 | result = p_Add_q(result,qq,r); |
---|
| 3174 | } |
---|
| 3175 | p = p_Add_q(result, zero,r); |
---|
| 3176 | p_Test(p,r); |
---|
| 3177 | return p; |
---|
| 3178 | } |
---|
| 3179 | |
---|
| 3180 | /*3 |
---|
| 3181 | * substitute the n-th variable by number e in p |
---|
| 3182 | * destroy p |
---|
| 3183 | */ |
---|
| 3184 | static poly p_Subst2 (poly p,int n, number e, const ring r) |
---|
| 3185 | { |
---|
| 3186 | assume( ! n_IsZero(e,r->cf) ); |
---|
| 3187 | poly qq,result = NULL; |
---|
| 3188 | number nn, nm; |
---|
| 3189 | poly zero, non_zero; |
---|
| 3190 | |
---|
| 3191 | // reverse, so that add is likely to be linear |
---|
| 3192 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3193 | |
---|
| 3194 | while (non_zero != NULL) |
---|
| 3195 | { |
---|
[45d2332] | 3196 | assume(p_GetExp(non_zero, n, r) != 0); |
---|
[71ba5b8] | 3197 | qq = non_zero; |
---|
| 3198 | pIter(non_zero); |
---|
| 3199 | qq->next = NULL; |
---|
| 3200 | n_Power(e, p_GetExp(qq, n, r), &nn,r->cf); |
---|
| 3201 | nm = n_Mult(nn, pGetCoeff(qq),r->cf); |
---|
| 3202 | #ifdef HAVE_RINGS |
---|
| 3203 | if (n_IsZero(nm,r->cf)) |
---|
| 3204 | { |
---|
| 3205 | p_LmFree(&qq,r); |
---|
| 3206 | n_Delete(&nm,r->cf); |
---|
| 3207 | } |
---|
| 3208 | else |
---|
| 3209 | #endif |
---|
| 3210 | { |
---|
| 3211 | p_SetCoeff(qq, nm,r); |
---|
| 3212 | p_SetExp(qq, n, 0,r); |
---|
| 3213 | p_Setm(qq,r); |
---|
| 3214 | result = p_Add_q(result,qq,r); |
---|
| 3215 | } |
---|
| 3216 | n_Delete(&nn,r->cf); |
---|
| 3217 | } |
---|
| 3218 | p = p_Add_q(result, zero,r); |
---|
| 3219 | p_Test(p,r); |
---|
| 3220 | return p; |
---|
| 3221 | } |
---|
| 3222 | |
---|
| 3223 | |
---|
| 3224 | /* delete monoms whose n-th exponent is different from zero */ |
---|
| 3225 | static poly p_Subst0(poly p, int n, const ring r) |
---|
| 3226 | { |
---|
| 3227 | spolyrec res; |
---|
| 3228 | poly h = &res; |
---|
| 3229 | pNext(h) = p; |
---|
| 3230 | |
---|
| 3231 | while (pNext(h)!=NULL) |
---|
| 3232 | { |
---|
| 3233 | if (p_GetExp(pNext(h),n,r)!=0) |
---|
| 3234 | { |
---|
| 3235 | p_LmDelete(&pNext(h),r); |
---|
| 3236 | } |
---|
| 3237 | else |
---|
| 3238 | { |
---|
| 3239 | pIter(h); |
---|
| 3240 | } |
---|
| 3241 | } |
---|
| 3242 | p_Test(pNext(&res),r); |
---|
| 3243 | return pNext(&res); |
---|
| 3244 | } |
---|
| 3245 | |
---|
| 3246 | /*2 |
---|
| 3247 | * substitute the n-th variable by e in p |
---|
| 3248 | * destroy p |
---|
| 3249 | */ |
---|
| 3250 | poly p_Subst(poly p, int n, poly e, const ring r) |
---|
| 3251 | { |
---|
| 3252 | if (e == NULL) return p_Subst0(p, n,r); |
---|
| 3253 | |
---|
| 3254 | if (p_IsConstant(e,r)) |
---|
| 3255 | { |
---|
| 3256 | if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r); |
---|
| 3257 | else return p_Subst2(p, n, pGetCoeff(e),r); |
---|
| 3258 | } |
---|
| 3259 | |
---|
| 3260 | #ifdef HAVE_PLURAL |
---|
| 3261 | if (rIsPluralRing(r)) |
---|
| 3262 | { |
---|
| 3263 | return nc_pSubst(p,n,e,r); |
---|
| 3264 | } |
---|
| 3265 | #endif |
---|
| 3266 | |
---|
| 3267 | int exponent,i; |
---|
| 3268 | poly h, res, m; |
---|
| 3269 | int *me,*ee; |
---|
| 3270 | number nu,nu1; |
---|
| 3271 | |
---|
| 3272 | me=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3273 | ee=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3274 | if (e!=NULL) p_GetExpV(e,ee,r); |
---|
| 3275 | res=NULL; |
---|
| 3276 | h=p; |
---|
| 3277 | while (h!=NULL) |
---|
| 3278 | { |
---|
| 3279 | if ((e!=NULL) || (p_GetExp(h,n,r)==0)) |
---|
| 3280 | { |
---|
| 3281 | m=p_Head(h,r); |
---|
| 3282 | p_GetExpV(m,me,r); |
---|
| 3283 | exponent=me[n]; |
---|
| 3284 | me[n]=0; |
---|
| 3285 | for(i=rVar(r);i>0;i--) |
---|
| 3286 | me[i]+=exponent*ee[i]; |
---|
| 3287 | p_SetExpV(m,me,r); |
---|
| 3288 | if (e!=NULL) |
---|
| 3289 | { |
---|
| 3290 | n_Power(pGetCoeff(e),exponent,&nu,r->cf); |
---|
| 3291 | nu1=n_Mult(pGetCoeff(m),nu,r->cf); |
---|
| 3292 | n_Delete(&nu,r->cf); |
---|
| 3293 | p_SetCoeff(m,nu1,r); |
---|
| 3294 | } |
---|
| 3295 | res=p_Add_q(res,m,r); |
---|
| 3296 | } |
---|
| 3297 | p_LmDelete(&h,r); |
---|
| 3298 | } |
---|
| 3299 | omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int)); |
---|
| 3300 | omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int)); |
---|
| 3301 | return res; |
---|
| 3302 | } |
---|
[83a1714] | 3303 | |
---|
| 3304 | /*2 |
---|
| 3305 | * returns a re-ordered convertion of a number as a polynomial, |
---|
| 3306 | * with permutation of parameters |
---|
| 3307 | * NOTE: this only works for Frank's alg. & trans. fields |
---|
| 3308 | */ |
---|
| 3309 | poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst) |
---|
| 3310 | { |
---|
| 3311 | #if 0 |
---|
| 3312 | PrintS("\nSource Ring: \n"); |
---|
| 3313 | rWrite(src); |
---|
| 3314 | |
---|
| 3315 | if(0) |
---|
| 3316 | { |
---|
| 3317 | number zz = n_Copy(z, src->cf); |
---|
| 3318 | PrintS("z: "); n_Write(zz, src->cf); |
---|
| 3319 | n_Delete(&zz, src->cf); |
---|
| 3320 | } |
---|
| 3321 | |
---|
| 3322 | PrintS("\nDestination Ring: \n"); |
---|
| 3323 | rWrite(dst); |
---|
| 3324 | |
---|
| 3325 | Print("\nOldPar: %d\n", OldPar); |
---|
| 3326 | for( int i = 1; i <= OldPar; i++ ) |
---|
| 3327 | { |
---|
| 3328 | Print("par(%d) -> par/var (%d)\n", i, par_perm[i-1]); |
---|
| 3329 | } |
---|
| 3330 | #endif |
---|
| 3331 | if( z == NULL ) |
---|
| 3332 | return NULL; |
---|
| 3333 | |
---|
| 3334 | const coeffs srcCf = src->cf; |
---|
| 3335 | assume( srcCf != NULL ); |
---|
| 3336 | |
---|
| 3337 | assume( !nCoeff_is_GF(srcCf) ); |
---|
| 3338 | assume( rField_is_Extension(src) ); |
---|
| 3339 | |
---|
| 3340 | poly zz = NULL; |
---|
| 3341 | |
---|
| 3342 | const ring srcExtRing = srcCf->extRing; |
---|
| 3343 | assume( srcExtRing != NULL ); |
---|
| 3344 | |
---|
| 3345 | const coeffs dstCf = dst->cf; |
---|
| 3346 | assume( dstCf != NULL ); |
---|
| 3347 | |
---|
| 3348 | if( nCoeff_is_algExt(srcCf) ) // nCoeff_is_GF(srcCf)? |
---|
| 3349 | { |
---|
| 3350 | zz = (poly) z; |
---|
| 3351 | |
---|
| 3352 | if( zz == NULL ) |
---|
| 3353 | return NULL; |
---|
| 3354 | |
---|
| 3355 | } else if (nCoeff_is_transExt(srcCf)) |
---|
| 3356 | { |
---|
| 3357 | assume( !IS0(z) ); |
---|
| 3358 | |
---|
| 3359 | zz = NUM(z); |
---|
| 3360 | p_Test (zz, srcExtRing); |
---|
| 3361 | |
---|
| 3362 | if( zz == NULL ) |
---|
| 3363 | return NULL; |
---|
| 3364 | |
---|
| 3365 | if( !DENIS1(z) ) |
---|
| 3366 | WarnS("Not implemented yet: Cannot permute a rational fraction and make a polynomial out of it! Ignorring the denumerator."); |
---|
| 3367 | } else |
---|
| 3368 | { |
---|
| 3369 | assume (FALSE); |
---|
| 3370 | Werror("Number permutation is not implemented for this data yet!"); |
---|
| 3371 | return NULL; |
---|
| 3372 | } |
---|
| 3373 | |
---|
| 3374 | assume( zz != NULL ); |
---|
| 3375 | p_Test (zz, srcExtRing); |
---|
| 3376 | |
---|
| 3377 | |
---|
| 3378 | nMapFunc nMap = n_SetMap(srcExtRing->cf, dstCf); |
---|
| 3379 | |
---|
| 3380 | assume( nMap != NULL ); |
---|
| 3381 | |
---|
| 3382 | poly qq = p_PermPoly(zz, par_perm - 1, srcExtRing, dst, nMap, NULL, rVar(srcExtRing) ); |
---|
| 3383 | // poly p_PermPoly (poly p, int * perm, const ring oldRing, const ring dst, nMapFunc nMap, int *par_perm, int OldPar) |
---|
| 3384 | |
---|
| 3385 | // assume( FALSE ); WarnS("longalg missing 2"); |
---|
| 3386 | |
---|
| 3387 | return qq; |
---|
| 3388 | } |
---|
| 3389 | |
---|
| 3390 | |
---|
[deca086] | 3391 | /*2 |
---|
| 3392 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
| 3393 | */ |
---|
[83a1714] | 3394 | poly p_PermPoly (poly p, const int * perm, const ring oldRing, const ring dst, |
---|
| 3395 | nMapFunc nMap, const int *par_perm, int OldPar) |
---|
[deca086] | 3396 | { |
---|
[83a1714] | 3397 | #if 0 |
---|
| 3398 | p_Test(p, oldRing); |
---|
| 3399 | PrintS("\np_PermPoly::p: "); p_Write(p, oldRing, oldRing); PrintLn(); |
---|
| 3400 | #endif |
---|
| 3401 | |
---|
[b38d70] | 3402 | const int OldpVariables = rVar(oldRing); |
---|
[deca086] | 3403 | poly result = NULL; |
---|
| 3404 | poly result_last = NULL; |
---|
[83a1714] | 3405 | poly aq = NULL; /* the map coefficient */ |
---|
[deca086] | 3406 | poly qq; /* the mapped monomial */ |
---|
| 3407 | |
---|
| 3408 | while (p != NULL) |
---|
| 3409 | { |
---|
[b38d70] | 3410 | // map the coefficient |
---|
[83a1714] | 3411 | if ( ((OldPar == 0) || (par_perm == NULL) || rField_is_GF(oldRing)) && (nMap != NULL) ) |
---|
[deca086] | 3412 | { |
---|
| 3413 | qq = p_Init(dst); |
---|
[83a1714] | 3414 | assume( nMap != NULL ); |
---|
[b38d70] | 3415 | number n = nMap(p_GetCoeff(p, oldRing), oldRing->cf, dst->cf); |
---|
| 3416 | |
---|
| 3417 | if ( (!rMinpolyIsNULL(dst)) && (rField_is_Zp_a(dst) || rField_is_Q_a(dst)) ) |
---|
| 3418 | n_Normalize(n, dst->cf); |
---|
| 3419 | |
---|
| 3420 | p_GetCoeff(qq, dst) = n; |
---|
| 3421 | // coef may be zero: |
---|
| 3422 | p_Test(qq, dst); |
---|
[deca086] | 3423 | } |
---|
| 3424 | else |
---|
| 3425 | { |
---|
[83a1714] | 3426 | qq = p_One(dst); |
---|
| 3427 | |
---|
| 3428 | // aq = naPermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing); // no dst??? |
---|
| 3429 | // poly n_PermNumber(const number z, const int *par_perm, const int P, const ring src, const ring dst) |
---|
| 3430 | aq = n_PermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing, dst); |
---|
| 3431 | |
---|
| 3432 | p_Test(aq, dst); |
---|
[b38d70] | 3433 | |
---|
| 3434 | if ( (!rMinpolyIsNULL(dst)) && (rField_is_Zp_a(dst) || rField_is_Q_a(dst)) ) |
---|
[deca086] | 3435 | { |
---|
[1f414c8] | 3436 | p_Normalize(aq,dst); |
---|
[b38d70] | 3437 | |
---|
[deca086] | 3438 | } |
---|
[83a1714] | 3439 | if (aq == NULL) |
---|
| 3440 | p_SetCoeff(qq, n_Init(0, dst->cf),dst); // Very dirty trick!!! |
---|
| 3441 | |
---|
[b38d70] | 3442 | p_Test(aq, dst); |
---|
[deca086] | 3443 | } |
---|
[b38d70] | 3444 | |
---|
| 3445 | if (rRing_has_Comp(dst)) |
---|
| 3446 | p_SetComp(qq, p_GetComp(p, oldRing), dst); |
---|
| 3447 | |
---|
| 3448 | if ( n_IsZero(pGetCoeff(qq), dst->cf) ) |
---|
[deca086] | 3449 | { |
---|
| 3450 | p_LmDelete(&qq,dst); |
---|
[b38d70] | 3451 | qq = NULL; |
---|
| 3452 | } |
---|
[deca086] | 3453 | else |
---|
| 3454 | { |
---|
[b38d70] | 3455 | // map pars: |
---|
| 3456 | int mapped_to_par = 0; |
---|
| 3457 | for(int i = 1; i <= OldpVariables; i++) |
---|
[deca086] | 3458 | { |
---|
[b38d70] | 3459 | int e = p_GetExp(p, i, oldRing); |
---|
| 3460 | if (e != 0) |
---|
[deca086] | 3461 | { |
---|
| 3462 | if (perm==NULL) |
---|
[b38d70] | 3463 | p_SetExp(qq, i, e, dst); |
---|
[deca086] | 3464 | else if (perm[i]>0) |
---|
| 3465 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
| 3466 | else if (perm[i]<0) |
---|
| 3467 | { |
---|
[b38d70] | 3468 | number c = p_GetCoeff(qq, dst); |
---|
[deca086] | 3469 | if (rField_is_GF(dst)) |
---|
| 3470 | { |
---|
[b38d70] | 3471 | assume( dst->cf->extRing == NULL ); |
---|
| 3472 | number ee = nfPar(1, dst->cf); // NOTE: using nfPar is a BAD thing to do... |
---|
| 3473 | |
---|
| 3474 | number eee; |
---|
| 3475 | n_Power(ee, e, &eee, dst->cf); //nfDelete(ee,dst); |
---|
| 3476 | |
---|
| 3477 | ee = n_Mult(c, eee, dst->cf); |
---|
[8a8c9e] | 3478 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
[deca086] | 3479 | pSetCoeff0(qq,ee); |
---|
| 3480 | } |
---|
[b38d70] | 3481 | else if (nCoeff_is_Extension(dst->cf)) |
---|
[deca086] | 3482 | { |
---|
[b38d70] | 3483 | const int par = -perm[i]; |
---|
| 3484 | assume( par > 0 ); |
---|
[83a1714] | 3485 | |
---|
[b38d70] | 3486 | // WarnS("longalg missing 3"); |
---|
| 3487 | #if 1 |
---|
| 3488 | const coeffs C = dst->cf; |
---|
| 3489 | assume( C != NULL ); |
---|
| 3490 | |
---|
| 3491 | const ring R = C->extRing; |
---|
| 3492 | assume( R != NULL ); |
---|
| 3493 | |
---|
| 3494 | assume( par <= rVar(R) ); |
---|
| 3495 | |
---|
| 3496 | poly pcn; // = (number)c |
---|
| 3497 | |
---|
| 3498 | assume( !n_IsZero(c, C) ); |
---|
| 3499 | |
---|
| 3500 | if( nCoeff_is_algExt(C) ) |
---|
| 3501 | pcn = (poly) c; |
---|
| 3502 | else // nCoeff_is_transExt(C) |
---|
| 3503 | pcn = NUM(c); |
---|
| 3504 | |
---|
| 3505 | if (pNext(pcn) == NULL) // c->z |
---|
| 3506 | p_AddExp(pcn, -perm[i], e, R); |
---|
[deca086] | 3507 | else /* more difficult: we have really to multiply: */ |
---|
| 3508 | { |
---|
[b38d70] | 3509 | poly mmc = p_ISet(1, R); |
---|
| 3510 | p_SetExp(mmc, -perm[i], e, R); |
---|
| 3511 | p_Setm(mmc, R); |
---|
| 3512 | |
---|
| 3513 | number nnc; |
---|
| 3514 | // convert back to a number: number nnc = mmc; |
---|
| 3515 | if( nCoeff_is_algExt(C) ) |
---|
| 3516 | nnc = (number) mmc; |
---|
| 3517 | else // nCoeff_is_transExt(C) |
---|
| 3518 | nnc = ntInit(mmc, C); |
---|
| 3519 | |
---|
| 3520 | p_GetCoeff(qq, dst) = n_Mult((number)c, nnc, C); |
---|
| 3521 | n_Delete((number *)&c, C); |
---|
| 3522 | n_Delete((number *)&nnc, C); |
---|
[deca086] | 3523 | } |
---|
[b38d70] | 3524 | |
---|
[deca086] | 3525 | mapped_to_par=1; |
---|
[1f414c8] | 3526 | #endif |
---|
[deca086] | 3527 | } |
---|
| 3528 | } |
---|
| 3529 | else |
---|
| 3530 | { |
---|
| 3531 | /* this variable maps to 0 !*/ |
---|
[b38d70] | 3532 | p_LmDelete(&qq, dst); |
---|
[deca086] | 3533 | break; |
---|
| 3534 | } |
---|
| 3535 | } |
---|
| 3536 | } |
---|
[b38d70] | 3537 | if ( mapped_to_par && (!rMinpolyIsNULL(dst)) ) |
---|
[deca086] | 3538 | { |
---|
[b38d70] | 3539 | number n = p_GetCoeff(qq, dst); |
---|
[deca086] | 3540 | n_Normalize(n,dst->cf); |
---|
[b38d70] | 3541 | p_GetCoeff(qq, dst) = n; |
---|
[deca086] | 3542 | } |
---|
| 3543 | } |
---|
| 3544 | pIter(p); |
---|
[83a1714] | 3545 | |
---|
| 3546 | #if 0 |
---|
| 3547 | p_Test(aq,dst); |
---|
| 3548 | PrintS("\naq: "); p_Write(aq, dst, dst); PrintLn(); |
---|
| 3549 | #endif |
---|
| 3550 | |
---|
[b38d70] | 3551 | |
---|
[deca086] | 3552 | #if 1 |
---|
| 3553 | if (qq!=NULL) |
---|
| 3554 | { |
---|
| 3555 | p_Setm(qq,dst); |
---|
[83a1714] | 3556 | |
---|
[deca086] | 3557 | p_Test(aq,dst); |
---|
| 3558 | p_Test(qq,dst); |
---|
[83a1714] | 3559 | |
---|
| 3560 | #if 0 |
---|
| 3561 | p_Test(qq,dst); |
---|
| 3562 | PrintS("\nqq: "); p_Write(qq, dst, dst); PrintLn(); |
---|
| 3563 | #endif |
---|
| 3564 | |
---|
| 3565 | if (aq!=NULL) |
---|
| 3566 | qq=p_Mult_q(aq,qq,dst); |
---|
| 3567 | |
---|
[deca086] | 3568 | aq = qq; |
---|
[83a1714] | 3569 | |
---|
[deca086] | 3570 | while (pNext(aq) != NULL) pIter(aq); |
---|
[83a1714] | 3571 | |
---|
[deca086] | 3572 | if (result_last==NULL) |
---|
| 3573 | { |
---|
| 3574 | result=qq; |
---|
| 3575 | } |
---|
| 3576 | else |
---|
| 3577 | { |
---|
| 3578 | pNext(result_last)=qq; |
---|
| 3579 | } |
---|
| 3580 | result_last=aq; |
---|
| 3581 | aq = NULL; |
---|
| 3582 | } |
---|
| 3583 | else if (aq!=NULL) |
---|
| 3584 | { |
---|
| 3585 | p_Delete(&aq,dst); |
---|
| 3586 | } |
---|
| 3587 | } |
---|
[83a1714] | 3588 | |
---|
[deca086] | 3589 | result=p_SortAdd(result,dst); |
---|
| 3590 | #else |
---|
| 3591 | // if (qq!=NULL) |
---|
| 3592 | // { |
---|
| 3593 | // pSetm(qq); |
---|
| 3594 | // pTest(qq); |
---|
| 3595 | // pTest(aq); |
---|
| 3596 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
| 3597 | // aq = qq; |
---|
| 3598 | // while (pNext(aq) != NULL) pIter(aq); |
---|
| 3599 | // pNext(aq) = result; |
---|
| 3600 | // aq = NULL; |
---|
| 3601 | // result = qq; |
---|
| 3602 | // } |
---|
| 3603 | // else if (aq!=NULL) |
---|
| 3604 | // { |
---|
| 3605 | // pDelete(&aq); |
---|
| 3606 | // } |
---|
| 3607 | //} |
---|
| 3608 | //p = result; |
---|
| 3609 | //result = NULL; |
---|
| 3610 | //while (p != NULL) |
---|
| 3611 | //{ |
---|
| 3612 | // qq = p; |
---|
| 3613 | // pIter(p); |
---|
| 3614 | // qq->next = NULL; |
---|
| 3615 | // result = pAdd(result, qq); |
---|
| 3616 | //} |
---|
| 3617 | #endif |
---|
| 3618 | p_Test(result,dst); |
---|
[83a1714] | 3619 | |
---|
| 3620 | #if 0 |
---|
| 3621 | p_Test(result,dst); |
---|
| 3622 | PrintS("\nresult: "); p_Write(result,dst,dst); PrintLn(); |
---|
| 3623 | #endif |
---|
[deca086] | 3624 | return result; |
---|
| 3625 | } |
---|
[f550e86] | 3626 | /************************************************************** |
---|
| 3627 | * |
---|
| 3628 | * Jet |
---|
| 3629 | * |
---|
| 3630 | **************************************************************/ |
---|
| 3631 | |
---|
| 3632 | poly pp_Jet(poly p, int m, const ring R) |
---|
| 3633 | { |
---|
| 3634 | poly r=NULL; |
---|
| 3635 | poly t=NULL; |
---|
| 3636 | |
---|
| 3637 | while (p!=NULL) |
---|
| 3638 | { |
---|
| 3639 | if (p_Totaldegree(p,R)<=m) |
---|
| 3640 | { |
---|
| 3641 | if (r==NULL) |
---|
| 3642 | r=p_Head(p,R); |
---|
| 3643 | else |
---|
| 3644 | if (t==NULL) |
---|
| 3645 | { |
---|
| 3646 | pNext(r)=p_Head(p,R); |
---|
| 3647 | t=pNext(r); |
---|
| 3648 | } |
---|
| 3649 | else |
---|
| 3650 | { |
---|
| 3651 | pNext(t)=p_Head(p,R); |
---|
| 3652 | pIter(t); |
---|
| 3653 | } |
---|
| 3654 | } |
---|
| 3655 | pIter(p); |
---|
| 3656 | } |
---|
| 3657 | return r; |
---|
| 3658 | } |
---|
| 3659 | |
---|
| 3660 | poly p_Jet(poly p, int m,const ring R) |
---|
| 3661 | { |
---|
| 3662 | while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R); |
---|
| 3663 | if (p==NULL) return NULL; |
---|
| 3664 | poly r=p; |
---|
| 3665 | while (pNext(p)!=NULL) |
---|
| 3666 | { |
---|
| 3667 | if (p_Totaldegree(pNext(p),R)>m) |
---|
| 3668 | { |
---|
| 3669 | p_LmDelete(&pNext(p),R); |
---|
| 3670 | } |
---|
| 3671 | else |
---|
| 3672 | pIter(p); |
---|
| 3673 | } |
---|
| 3674 | return r; |
---|
| 3675 | } |
---|
| 3676 | |
---|
| 3677 | poly pp_JetW(poly p, int m, short *w, const ring R) |
---|
| 3678 | { |
---|
| 3679 | poly r=NULL; |
---|
| 3680 | poly t=NULL; |
---|
| 3681 | while (p!=NULL) |
---|
| 3682 | { |
---|
| 3683 | if (totaldegreeWecart_IV(p,R,w)<=m) |
---|
| 3684 | { |
---|
| 3685 | if (r==NULL) |
---|
| 3686 | r=p_Head(p,R); |
---|
| 3687 | else |
---|
| 3688 | if (t==NULL) |
---|
| 3689 | { |
---|
| 3690 | pNext(r)=p_Head(p,R); |
---|
| 3691 | t=pNext(r); |
---|
| 3692 | } |
---|
| 3693 | else |
---|
| 3694 | { |
---|
| 3695 | pNext(t)=p_Head(p,R); |
---|
| 3696 | pIter(t); |
---|
| 3697 | } |
---|
| 3698 | } |
---|
| 3699 | pIter(p); |
---|
| 3700 | } |
---|
| 3701 | return r; |
---|
| 3702 | } |
---|
| 3703 | |
---|
| 3704 | poly p_JetW(poly p, int m, short *w, const ring R) |
---|
| 3705 | { |
---|
| 3706 | while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R); |
---|
| 3707 | if (p==NULL) return NULL; |
---|
| 3708 | poly r=p; |
---|
| 3709 | while (pNext(p)!=NULL) |
---|
| 3710 | { |
---|
| 3711 | if (totaldegreeWecart_IV(pNext(p),R,w)>m) |
---|
| 3712 | { |
---|
| 3713 | p_LmDelete(&pNext(p),R); |
---|
| 3714 | } |
---|
| 3715 | else |
---|
| 3716 | pIter(p); |
---|
| 3717 | } |
---|
| 3718 | return r; |
---|
| 3719 | } |
---|
[5c39a9] | 3720 | |
---|
[ba0fc3] | 3721 | /*************************************************************/ |
---|
| 3722 | int p_MinDeg(poly p,intvec *w, const ring R) |
---|
| 3723 | { |
---|
| 3724 | if(p==NULL) |
---|
| 3725 | return -1; |
---|
| 3726 | int d=-1; |
---|
| 3727 | while(p!=NULL) |
---|
| 3728 | { |
---|
| 3729 | int d0=0; |
---|
| 3730 | for(int j=0;j<rVar(R);j++) |
---|
| 3731 | if(w==NULL||j>=w->length()) |
---|
| 3732 | d0+=p_GetExp(p,j+1,R); |
---|
| 3733 | else |
---|
| 3734 | d0+=(*w)[j]*p_GetExp(p,j+1,R); |
---|
| 3735 | if(d0<d||d==-1) |
---|
| 3736 | d=d0; |
---|
| 3737 | pIter(p); |
---|
| 3738 | } |
---|
| 3739 | return d; |
---|
| 3740 | } |
---|
| 3741 | |
---|
[a4081e5] | 3742 | /***************************************************************/ |
---|
| 3743 | |
---|
| 3744 | poly p_Series(int n,poly p,poly u, intvec *w, const ring R) |
---|
| 3745 | { |
---|
| 3746 | short *ww=iv2array(w,R); |
---|
| 3747 | if(p!=NULL) |
---|
| 3748 | { |
---|
| 3749 | if(u==NULL) |
---|
| 3750 | p=p_JetW(p,n,ww,R); |
---|
| 3751 | else |
---|
| 3752 | p=p_JetW(p_Mult_q(p,p_Invers(n-p_MinDeg(p,w,R),u,w,R),R),n,ww,R); |
---|
| 3753 | } |
---|
| 3754 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3755 | return p; |
---|
| 3756 | } |
---|
| 3757 | |
---|
| 3758 | poly p_Invers(int n,poly u,intvec *w, const ring R) |
---|
| 3759 | { |
---|
| 3760 | if(n<0) |
---|
| 3761 | return NULL; |
---|
| 3762 | number u0=n_Invers(pGetCoeff(u),R->cf); |
---|
| 3763 | poly v=p_NSet(u0,R); |
---|
| 3764 | if(n==0) |
---|
| 3765 | return v; |
---|
| 3766 | short *ww=iv2array(w,R); |
---|
| 3767 | poly u1=p_JetW(p_Sub(p_One(R),p_Mult_nn(u,u0,R),R),n,ww,R); |
---|
| 3768 | if(u1==NULL) |
---|
| 3769 | { |
---|
| 3770 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3771 | return v; |
---|
| 3772 | } |
---|
| 3773 | poly v1=p_Mult_nn(p_Copy(u1,R),u0,R); |
---|
| 3774 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3775 | for(int i=n/p_MinDeg(u1,w,R);i>1;i--) |
---|
| 3776 | { |
---|
| 3777 | v1=p_JetW(p_Mult_q(v1,p_Copy(u1,R),R),n,ww,R); |
---|
| 3778 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3779 | } |
---|
| 3780 | p_Delete(&u1,R); |
---|
| 3781 | p_Delete(&v1,R); |
---|
| 3782 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3783 | return v; |
---|
| 3784 | } |
---|
| 3785 | |
---|
[7dce2d7] | 3786 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r) |
---|
| 3787 | { |
---|
| 3788 | while ((p1 != NULL) && (p2 != NULL)) |
---|
| 3789 | { |
---|
| 3790 | if (! p_LmEqual(p1, p2,r)) |
---|
| 3791 | return FALSE; |
---|
| 3792 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r )) |
---|
| 3793 | return FALSE; |
---|
| 3794 | pIter(p1); |
---|
| 3795 | pIter(p2); |
---|
| 3796 | } |
---|
| 3797 | return (p1==p2); |
---|
| 3798 | } |
---|
[32d07a5] | 3799 | |
---|
| 3800 | /*2 |
---|
| 3801 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
| 3802 | *assume p1 != NULL and p2 != NULL |
---|
| 3803 | */ |
---|
| 3804 | BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r) |
---|
| 3805 | { |
---|
| 3806 | number n,nn; |
---|
| 3807 | pAssume(p1 != NULL && p2 != NULL); |
---|
| 3808 | |
---|
| 3809 | if (!p_LmEqual(p1,p2,r)) //compare leading mons |
---|
| 3810 | return FALSE; |
---|
| 3811 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
---|
| 3812 | return FALSE; |
---|
| 3813 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
---|
| 3814 | return FALSE; |
---|
| 3815 | if (pLength(p1) != pLength(p2)) |
---|
| 3816 | return FALSE; |
---|
| 3817 | #ifdef HAVE_RINGS |
---|
| 3818 | if (rField_is_Ring(r)) |
---|
| 3819 | { |
---|
| 3820 | if (!n_DivBy(p_GetCoeff(p1, r), p_GetCoeff(p2, r), r)) return FALSE; |
---|
| 3821 | } |
---|
| 3822 | #endif |
---|
| 3823 | n=n_Div(p_GetCoeff(p1,r),p_GetCoeff(p2,r),r); |
---|
| 3824 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
| 3825 | { |
---|
| 3826 | if ( ! p_LmEqual(p1, p2,r)) |
---|
| 3827 | { |
---|
| 3828 | n_Delete(&n, r); |
---|
| 3829 | return FALSE; |
---|
| 3830 | } |
---|
| 3831 | if (!n_Equal(p_GetCoeff(p1, r), nn = n_Mult(p_GetCoeff(p2, r),n, r), r)) |
---|
| 3832 | { |
---|
| 3833 | n_Delete(&n, r); |
---|
| 3834 | n_Delete(&nn, r); |
---|
| 3835 | return FALSE; |
---|
| 3836 | } |
---|
| 3837 | n_Delete(&nn, r); |
---|
| 3838 | pIter(p1); |
---|
| 3839 | pIter(p2); |
---|
| 3840 | } |
---|
| 3841 | n_Delete(&n, r); |
---|
| 3842 | return TRUE; |
---|
| 3843 | } |
---|
| 3844 | |
---|
[1fdb6e] | 3845 | /*2 |
---|
| 3846 | * returns the length of a (numbers of monomials) |
---|
| 3847 | * respect syzComp |
---|
| 3848 | */ |
---|
| 3849 | poly p_Last(poly a, int &l, const ring r) |
---|
| 3850 | { |
---|
| 3851 | if (a == NULL) |
---|
| 3852 | { |
---|
| 3853 | l = 0; |
---|
| 3854 | return NULL; |
---|
| 3855 | } |
---|
| 3856 | l = 1; |
---|
| 3857 | if (! rIsSyzIndexRing(r)) |
---|
| 3858 | { |
---|
| 3859 | while (pNext(a)!=NULL) |
---|
| 3860 | { |
---|
| 3861 | pIter(a); |
---|
| 3862 | l++; |
---|
| 3863 | } |
---|
| 3864 | } |
---|
| 3865 | else |
---|
| 3866 | { |
---|
| 3867 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 3868 | poly pp = a; |
---|
| 3869 | while ((a=pNext(a))!=NULL) |
---|
| 3870 | { |
---|
| 3871 | if (p_GetComp(a,r)<=curr_limit/*syzComp*/) |
---|
| 3872 | l++; |
---|
| 3873 | else break; |
---|
| 3874 | pp = a; |
---|
| 3875 | } |
---|
| 3876 | a=pp; |
---|
| 3877 | } |
---|
| 3878 | return a; |
---|
| 3879 | } |
---|
[32d07a5] | 3880 | |
---|
[73ad0c] | 3881 | int p_Var(poly m,const ring r) |
---|
| 3882 | { |
---|
| 3883 | if (m==NULL) return 0; |
---|
| 3884 | if (pNext(m)!=NULL) return 0; |
---|
| 3885 | int i,e=0; |
---|
| 3886 | for (i=rVar(r); i>0; i--) |
---|
| 3887 | { |
---|
| 3888 | int exp=p_GetExp(m,i,r); |
---|
| 3889 | if (exp==1) |
---|
| 3890 | { |
---|
| 3891 | if (e==0) e=i; |
---|
| 3892 | else return 0; |
---|
| 3893 | } |
---|
| 3894 | else if (exp!=0) |
---|
| 3895 | { |
---|
| 3896 | return 0; |
---|
| 3897 | } |
---|
| 3898 | } |
---|
| 3899 | return e; |
---|
| 3900 | } |
---|
| 3901 | |
---|
| 3902 | /*2 |
---|
| 3903 | *the minimal index of used variables - 1 |
---|
| 3904 | */ |
---|
| 3905 | int p_LowVar (poly p, const ring r) |
---|
| 3906 | { |
---|
| 3907 | int k,l,lex; |
---|
| 3908 | |
---|
| 3909 | if (p == NULL) return -1; |
---|
| 3910 | |
---|
| 3911 | k = 32000;/*a very large dummy value*/ |
---|
| 3912 | while (p != NULL) |
---|
| 3913 | { |
---|
| 3914 | l = 1; |
---|
| 3915 | lex = p_GetExp(p,l,r); |
---|
| 3916 | while ((l < (rVar(r))) && (lex == 0)) |
---|
| 3917 | { |
---|
| 3918 | l++; |
---|
| 3919 | lex = p_GetExp(p,l,r); |
---|
| 3920 | } |
---|
| 3921 | l--; |
---|
| 3922 | if (l < k) k = l; |
---|
| 3923 | pIter(p); |
---|
| 3924 | } |
---|
| 3925 | return k; |
---|
| 3926 | } |
---|
| 3927 | |
---|
[b7cfaf] | 3928 | /*2 |
---|
| 3929 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
| 3930 | */ |
---|
| 3931 | void p_Shift (poly * p,int i, const ring r) |
---|
| 3932 | { |
---|
| 3933 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
| 3934 | int j = p_MaxComp(*p,r),k = p_MinComp(*p,r); |
---|
| 3935 | |
---|
| 3936 | if (j+i < 0) return ; |
---|
| 3937 | while (qp1 != NULL) |
---|
| 3938 | { |
---|
| 3939 | if ((p_GetComp(qp1,r)+i > 0) || ((j == -i) && (j == k))) |
---|
| 3940 | { |
---|
| 3941 | p_AddComp(qp1,i,r); |
---|
| 3942 | p_SetmComp(qp1,r); |
---|
| 3943 | qp2 = qp1; |
---|
| 3944 | pIter(qp1); |
---|
| 3945 | } |
---|
| 3946 | else |
---|
| 3947 | { |
---|
| 3948 | if (qp2 == *p) |
---|
| 3949 | { |
---|
| 3950 | pIter(*p); |
---|
| 3951 | p_LmDelete(&qp2,r); |
---|
| 3952 | qp2 = *p; |
---|
| 3953 | qp1 = *p; |
---|
| 3954 | } |
---|
| 3955 | else |
---|
| 3956 | { |
---|
| 3957 | qp2->next = qp1->next; |
---|
| 3958 | if (qp1!=NULL) p_LmDelete(&qp1,r); |
---|
| 3959 | qp1 = qp2->next; |
---|
| 3960 | } |
---|
| 3961 | } |
---|
| 3962 | } |
---|
| 3963 | } |
---|
[50c414] | 3964 | /*************************************************************** |
---|
| 3965 | * |
---|
| 3966 | * p_ShallowDelete |
---|
| 3967 | * |
---|
| 3968 | ***************************************************************/ |
---|
| 3969 | #undef LINKAGE |
---|
| 3970 | #define LINKAGE |
---|
[38500a] | 3971 | #undef p_Delete__T |
---|
| 3972 | #define p_Delete__T p_ShallowDelete |
---|
[35eaf8] | 3973 | #undef n_Delete__T |
---|
| 3974 | #define n_Delete__T(n, r) ((void)0) |
---|
[50c414] | 3975 | |
---|
[20b794] | 3976 | #include <polys/templates/p_Delete__T.cc> |
---|
[50c414] | 3977 | |
---|