[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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| 23 | |
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[af598e] | 24 | #include "weight.h" |
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| 25 | #include "simpleideals.h" |
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[9982049] | 26 | |
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[af598e] | 27 | #include "monomials/ring.h" |
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| 28 | #include "monomials/p_polys.h" |
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[304ad9b] | 29 | #include <polys/templates/p_MemCmp.h> |
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| 30 | #include <polys/templates/p_MemAdd.h> |
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| 31 | #include <polys/templates/p_MemCopy.h> |
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| 32 | |
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[45d2332] | 33 | |
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[20b794] | 34 | // #include <???/ideals.h> |
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| 35 | // #include <???/int64vec.h> |
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[45d2332] | 36 | |
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[fc5095] | 37 | #ifndef NDEBUG |
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[20b794] | 38 | // #include <???/febase.h> |
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[fc5095] | 39 | #endif |
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[35aab3] | 40 | |
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[45d2332] | 41 | #ifdef HAVE_PLURAL |
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[af598e] | 42 | #include "nc/nc.h" |
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| 43 | #include "nc/sca.h" |
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[45d2332] | 44 | #endif |
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| 45 | |
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[af598e] | 46 | #include "coeffrings.h" |
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[0654122] | 47 | #ifdef HAVE_FACTORY |
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[af598e] | 48 | #include "clapsing.h" |
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[0654122] | 49 | #endif |
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[32d07a5] | 50 | |
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[35aab3] | 51 | /*************************************************************** |
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| 52 | * |
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| 53 | * Completing what needs to be set for the monomial |
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| 54 | * |
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| 55 | ***************************************************************/ |
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| 56 | // this is special for the syz stuff |
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[eb72ba1] | 57 | static int* _components = NULL; |
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| 58 | static long* _componentsShifted = NULL; |
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| 59 | static int _componentsExternal = 0; |
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[35aab3] | 60 | |
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[fc5095] | 61 | BOOLEAN pSetm_error=0; |
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| 62 | |
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[324710] | 63 | #ifndef NDEBUG |
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| 64 | # define MYTEST 0 |
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| 65 | #else /* ifndef NDEBUG */ |
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| 66 | # define MYTEST 0 |
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| 67 | #endif /* ifndef NDEBUG */ |
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| 68 | |
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[33c36d] | 69 | void p_Setm_General(poly p, const ring r) |
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[35aab3] | 70 | { |
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| 71 | p_LmCheckPolyRing(p, r); |
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| 72 | int pos=0; |
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| 73 | if (r->typ!=NULL) |
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| 74 | { |
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| 75 | loop |
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| 76 | { |
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| 77 | long ord=0; |
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| 78 | sro_ord* o=&(r->typ[pos]); |
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| 79 | switch(o->ord_typ) |
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| 80 | { |
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| 81 | case ro_dp: |
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| 82 | { |
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| 83 | int a,e; |
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| 84 | a=o->data.dp.start; |
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| 85 | e=o->data.dp.end; |
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| 86 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
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| 87 | p->exp[o->data.dp.place]=ord; |
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| 88 | break; |
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| 89 | } |
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| 90 | case ro_wp_neg: |
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| 91 | ord=POLY_NEGWEIGHT_OFFSET; |
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| 92 | // no break; |
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| 93 | case ro_wp: |
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| 94 | { |
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| 95 | int a,e; |
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| 96 | a=o->data.wp.start; |
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| 97 | e=o->data.wp.end; |
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| 98 | int *w=o->data.wp.weights; |
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[fc5095] | 99 | #if 1 |
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[35aab3] | 100 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r)*w[i-a]; |
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[fc5095] | 101 | #else |
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| 102 | long ai; |
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| 103 | int ei,wi; |
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| 104 | for(int i=a;i<=e;i++) |
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| 105 | { |
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| 106 | ei=p_GetExp(p,i,r); |
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| 107 | wi=w[i-a]; |
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| 108 | ai=ei*wi; |
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| 109 | if (ai/ei!=wi) pSetm_error=TRUE; |
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| 110 | ord+=ai; |
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| 111 | if (ord<ai) pSetm_error=TRUE; |
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| 112 | } |
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[ab4778] | 113 | #endif |
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[35aab3] | 114 | p->exp[o->data.wp.place]=ord; |
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| 115 | break; |
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| 116 | } |
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[fc5095] | 117 | case ro_wp64: |
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| 118 | { |
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[ab4778] | 119 | int64 ord=0; |
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[fc5095] | 120 | int a,e; |
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| 121 | a=o->data.wp64.start; |
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| 122 | e=o->data.wp64.end; |
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| 123 | int64 *w=o->data.wp64.weights64; |
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| 124 | int64 ei,wi,ai; |
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[2132395] | 125 | for(int i=a;i<=e;i++) |
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[b5d4d1] | 126 | { |
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[fc5095] | 127 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
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| 128 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
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| 129 | ei=(int64)p_GetExp(p,i,r); |
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| 130 | wi=w[i-a]; |
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| 131 | ai=ei*wi; |
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[2132395] | 132 | if(ei!=0 && ai/ei!=wi) |
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[b5d4d1] | 133 | { |
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[fc5095] | 134 | pSetm_error=TRUE; |
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[b5d4d1] | 135 | #if SIZEOF_LONG == 4 |
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[fc5095] | 136 | Print("ai %lld, wi %lld\n",ai,wi); |
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[b5d4d1] | 137 | #else |
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[2132395] | 138 | Print("ai %ld, wi %ld\n",ai,wi); |
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[b5d4d1] | 139 | #endif |
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[fc5095] | 140 | } |
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| 141 | ord+=ai; |
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[2132395] | 142 | if (ord<ai) |
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[b5d4d1] | 143 | { |
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[2132395] | 144 | pSetm_error=TRUE; |
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[b5d4d1] | 145 | #if SIZEOF_LONG == 4 |
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[2132395] | 146 | Print("ai %lld, ord %lld\n",ai,ord); |
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[b5d4d1] | 147 | #else |
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[2132395] | 148 | Print("ai %ld, ord %ld\n",ai,ord); |
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[b5d4d1] | 149 | #endif |
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[fc5095] | 150 | } |
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| 151 | } |
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| 152 | int64 mask=(int64)0x7fffffff; |
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| 153 | long a_0=(long)(ord&mask); //2^31 |
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| 154 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
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| 155 | |
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[ab4778] | 156 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
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| 157 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
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| 158 | //Print("mask: %d",mask); |
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[fc5095] | 159 | |
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| 160 | p->exp[o->data.wp64.place]=a_1; |
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[ab4778] | 161 | p->exp[o->data.wp64.place+1]=a_0; |
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[fc5095] | 162 | // if(p_Setm_error) Print("***************************\n |
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| 163 | // ***************************\n |
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| 164 | // **WARNING: overflow error**\n |
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| 165 | // ***************************\n |
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| 166 | // ***************************\n"); |
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| 167 | break; |
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| 168 | } |
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[35aab3] | 169 | case ro_cp: |
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| 170 | { |
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| 171 | int a,e; |
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| 172 | a=o->data.cp.start; |
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| 173 | e=o->data.cp.end; |
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| 174 | int pl=o->data.cp.place; |
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| 175 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
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| 176 | break; |
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| 177 | } |
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| 178 | case ro_syzcomp: |
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| 179 | { |
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| 180 | int c=p_GetComp(p,r); |
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| 181 | long sc = c; |
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[eb72ba1] | 182 | int* Components = (_componentsExternal ? _components : |
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[35aab3] | 183 | o->data.syzcomp.Components); |
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[eb72ba1] | 184 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
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[35aab3] | 185 | o->data.syzcomp.ShiftedComponents); |
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| 186 | if (ShiftedComponents != NULL) |
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| 187 | { |
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| 188 | assume(Components != NULL); |
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| 189 | assume(c == 0 || Components[c] != 0); |
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| 190 | sc = ShiftedComponents[Components[c]]; |
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| 191 | assume(c == 0 || sc != 0); |
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| 192 | } |
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| 193 | p->exp[o->data.syzcomp.place]=sc; |
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| 194 | break; |
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| 195 | } |
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| 196 | case ro_syz: |
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| 197 | { |
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[273fed] | 198 | const unsigned long c = p_GetComp(p, r); |
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| 199 | const short place = o->data.syz.place; |
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| 200 | const int limit = o->data.syz.limit; |
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| 201 | |
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| 202 | if (c > limit) |
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| 203 | p->exp[place] = o->data.syz.curr_index; |
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[35aab3] | 204 | else if (c > 0) |
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[273fed] | 205 | { |
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| 206 | assume( (1 <= c) && (c <= limit) ); |
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| 207 | p->exp[place]= o->data.syz.syz_index[c]; |
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| 208 | } |
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[35aab3] | 209 | else |
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| 210 | { |
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| 211 | assume(c == 0); |
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[273fed] | 212 | p->exp[place]= 0; |
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[35aab3] | 213 | } |
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| 214 | break; |
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| 215 | } |
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[645a19] | 216 | // Prefix for Induced Schreyer ordering |
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| 217 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
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| 218 | { |
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| 219 | assume(p != NULL); |
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| 220 | |
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| 221 | #ifndef NDEBUG |
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| 222 | #if MYTEST |
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[273fed] | 223 | Print("p_Setm_General: isTemp ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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[645a19] | 224 | #endif |
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| 225 | #endif |
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| 226 | int c = p_GetComp(p, r); |
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| 227 | |
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| 228 | assume( c >= 0 ); |
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| 229 | |
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| 230 | // Let's simulate case ro_syz above.... |
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| 231 | // Should accumulate (by Suffix) and be a level indicator |
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| 232 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
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| 233 | |
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| 234 | assume( pVarOffset != NULL ); |
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| 235 | |
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| 236 | // TODO: Can this be done in the suffix??? |
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| 237 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 238 | { |
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| 239 | const int vo = pVarOffset[i]; |
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| 240 | if( vo != -1) // TODO: optimize: can be done once! |
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| 241 | { |
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[5cb9ec] | 242 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
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| 243 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
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| 244 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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| 245 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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[645a19] | 246 | } |
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| 247 | } |
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| 248 | #ifndef NDEBUG |
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| 249 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 250 | { |
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| 251 | const int vo = pVarOffset[i]; |
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| 252 | if( vo != -1) // TODO: optimize: can be done once! |
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| 253 | { |
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[5cb9ec] | 254 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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| 255 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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[645a19] | 256 | } |
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| 257 | } |
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| 258 | #if MYTEST |
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[1b816a3] | 259 | // if( p->exp[o->data.isTemp.start] > 0 ) |
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| 260 | // { |
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| 261 | // PrintS("Initial Value: "); p_DebugPrint(p, r, r, 1); |
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| 262 | // } |
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[645a19] | 263 | #endif |
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| 264 | #endif |
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| 265 | break; |
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| 266 | } |
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| 267 | |
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| 268 | // Suffix for Induced Schreyer ordering |
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| 269 | case ro_is: |
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| 270 | { |
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[273fed] | 271 | #ifndef NDEBUG |
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| 272 | #if MYTEST |
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| 273 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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| 274 | #endif |
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| 275 | #endif |
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| 276 | |
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[645a19] | 277 | assume(p != NULL); |
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| 278 | |
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| 279 | int c = p_GetComp(p, r); |
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| 280 | |
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| 281 | assume( c >= 0 ); |
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| 282 | const ideal F = o->data.is.F; |
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| 283 | const int limit = o->data.is.limit; |
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| 284 | |
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| 285 | if( F != NULL && c > limit ) |
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| 286 | { |
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| 287 | #ifndef NDEBUG |
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| 288 | #if MYTEST |
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[6e66d2] | 289 | 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] | 290 | #endif |
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| 291 | #endif |
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| 292 | |
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| 293 | c -= limit; |
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| 294 | assume( c > 0 ); |
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| 295 | c--; |
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| 296 | |
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| 297 | assume( c < IDELEMS(F) ); // What about others??? |
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| 298 | |
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| 299 | const poly pp = F->m[c]; // get reference monomial!!! |
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| 300 | |
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| 301 | #ifndef NDEBUG |
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| 302 | #if MYTEST |
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| 303 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
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| 304 | p_DebugPrint(pp, r, r, 1); |
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| 305 | #endif |
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| 306 | #endif |
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| 307 | |
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| 308 | |
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[6e66d2] | 309 | assume(pp != NULL); |
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[645a19] | 310 | if(pp == NULL) break; |
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| 311 | |
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| 312 | const int start = o->data.is.start; |
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| 313 | const int end = o->data.is.end; |
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| 314 | |
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| 315 | assume(start <= end); |
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[6e66d2] | 316 | |
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| 317 | // const int limit = o->data.is.limit; |
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| 318 | assume( limit >= 0 ); |
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| 319 | |
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| 320 | // const int st = o->data.isTemp.start; |
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| 321 | |
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| 322 | if( c > limit ) |
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| 323 | p->exp[start] = 1; |
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| 324 | // else |
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| 325 | // p->exp[start] = 0; |
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| 326 | |
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| 327 | |
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| 328 | #ifndef NDEBUG |
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[a41623] | 329 | 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] | 330 | #endif |
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| 331 | |
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[645a19] | 332 | |
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| 333 | for( int i = start; i <= end; i++) // v[0] may be here... |
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| 334 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
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| 335 | |
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[6e66d2] | 336 | |
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| 337 | |
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| 338 | |
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[645a19] | 339 | #ifndef NDEBUG |
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| 340 | const int* const pVarOffset = o->data.is.pVarOffset; |
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| 341 | |
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| 342 | assume( pVarOffset != NULL ); |
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| 343 | |
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| 344 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 345 | { |
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| 346 | const int vo = pVarOffset[i]; |
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| 347 | if( vo != -1) // TODO: optimize: can be done once! |
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[5cb9ec] | 348 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
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| 349 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
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[645a19] | 350 | } |
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| 351 | // TODO: how to check this for computed values??? |
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| 352 | #endif |
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| 353 | } else |
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| 354 | { |
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| 355 | const int* const pVarOffset = o->data.is.pVarOffset; |
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| 356 | |
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| 357 | // What about v[0] - component: it will be added later by |
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| 358 | // suffix!!! |
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| 359 | // TODO: Test it! |
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| 360 | const int vo = pVarOffset[0]; |
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| 361 | if( vo != -1 ) |
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| 362 | p->exp[vo] = c; // initial component v[0]! |
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[6e66d2] | 363 | |
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| 364 | #ifndef NDEBUG |
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| 365 | #if MYTEST |
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| 366 | 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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| 367 | p_DebugPrint(p, r, r, 1); |
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| 368 | #endif |
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| 369 | #endif |
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[645a19] | 370 | } |
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[6e66d2] | 371 | |
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[645a19] | 372 | |
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| 373 | break; |
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| 374 | } |
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[35aab3] | 375 | default: |
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| 376 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
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| 377 | return; |
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| 378 | } |
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| 379 | pos++; |
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| 380 | if (pos == r->OrdSize) return; |
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| 381 | } |
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| 382 | } |
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| 383 | } |
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| 384 | |
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| 385 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
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| 386 | { |
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[eb72ba1] | 387 | _components = Components; |
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| 388 | _componentsShifted = ShiftedComponents; |
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| 389 | _componentsExternal = 1; |
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[35aab3] | 390 | p_Setm_General(p, r); |
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[eb72ba1] | 391 | _componentsExternal = 0; |
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[35aab3] | 392 | } |
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| 393 | |
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| 394 | // dummy for lp, ls, etc |
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[33c36d] | 395 | void p_Setm_Dummy(poly p, const ring r) |
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[35aab3] | 396 | { |
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| 397 | p_LmCheckPolyRing(p, r); |
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| 398 | } |
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| 399 | |
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| 400 | // for dp, Dp, ds, etc |
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[33c36d] | 401 | void p_Setm_TotalDegree(poly p, const ring r) |
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[35aab3] | 402 | { |
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| 403 | p_LmCheckPolyRing(p, r); |
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[99bdcf] | 404 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
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[35aab3] | 405 | } |
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| 406 | |
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| 407 | // for wp, Wp, ws, etc |
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[33c36d] | 408 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
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[35aab3] | 409 | { |
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| 410 | p_LmCheckPolyRing(p, r); |
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[19ae652] | 411 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
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[35aab3] | 412 | } |
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| 413 | |
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| 414 | p_SetmProc p_GetSetmProc(ring r) |
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| 415 | { |
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[ab4778] | 416 | // covers lp, rp, ls, |
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[35aab3] | 417 | if (r->typ == NULL) return p_Setm_Dummy; |
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| 418 | |
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| 419 | if (r->OrdSize == 1) |
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| 420 | { |
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[ab4778] | 421 | if (r->typ[0].ord_typ == ro_dp && |
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[35aab3] | 422 | r->typ[0].data.dp.start == 1 && |
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| 423 | r->typ[0].data.dp.end == r->N && |
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| 424 | r->typ[0].data.dp.place == r->pOrdIndex) |
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| 425 | return p_Setm_TotalDegree; |
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[ab4778] | 426 | if (r->typ[0].ord_typ == ro_wp && |
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[35aab3] | 427 | r->typ[0].data.wp.start == 1 && |
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| 428 | r->typ[0].data.wp.end == r->N && |
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| 429 | r->typ[0].data.wp.place == r->pOrdIndex && |
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| 430 | r->typ[0].data.wp.weights == r->firstwv) |
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| 431 | return p_Setm_WFirstTotalDegree; |
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| 432 | } |
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| 433 | return p_Setm_General; |
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| 434 | } |
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| 435 | |
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| 436 | |
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| 437 | /* -------------------------------------------------------------------*/ |
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| 438 | /* several possibilities for pFDeg: the degree of the head term */ |
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[b5d4d1] | 439 | |
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| 440 | /* comptible with ordering */ |
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[bf183f] | 441 | long p_Deg(poly a, const ring r) |
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[35aab3] | 442 | { |
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| 443 | p_LmCheckPolyRing(a, r); |
---|
[19ae652] | 444 | assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); |
---|
[35aab3] | 445 | return p_GetOrder(a, r); |
---|
| 446 | } |
---|
| 447 | |
---|
[19ae652] | 448 | // p_WTotalDegree for weighted orderings |
---|
[35aab3] | 449 | // whose first block covers all variables |
---|
[19ae652] | 450 | long p_WFirstTotalDegree(poly p, const ring r) |
---|
[35aab3] | 451 | { |
---|
| 452 | int i; |
---|
| 453 | long sum = 0; |
---|
[ab4778] | 454 | |
---|
[35aab3] | 455 | for (i=1; i<= r->firstBlockEnds; i++) |
---|
| 456 | { |
---|
| 457 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 458 | } |
---|
| 459 | return sum; |
---|
| 460 | } |
---|
| 461 | |
---|
| 462 | /*2 |
---|
| 463 | * compute the degree of the leading monomial of p |
---|
| 464 | * with respect to weigths from the ordering |
---|
| 465 | * the ordering is not compatible with degree so do not use p->Order |
---|
| 466 | */ |
---|
[19ae652] | 467 | long p_WTotaldegree(poly p, const ring r) |
---|
[35aab3] | 468 | { |
---|
| 469 | p_LmCheckPolyRing(p, r); |
---|
| 470 | int i, k; |
---|
| 471 | long j =0; |
---|
| 472 | |
---|
| 473 | // iterate through each block: |
---|
| 474 | for (i=0;r->order[i]!=0;i++) |
---|
| 475 | { |
---|
[ab4778] | 476 | int b0=r->block0[i]; |
---|
| 477 | int b1=r->block1[i]; |
---|
[35aab3] | 478 | switch(r->order[i]) |
---|
| 479 | { |
---|
[3e0a7b] | 480 | case ringorder_M: |
---|
[ab4778] | 481 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
| 482 | { // in jedem block: |
---|
| 483 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
---|
| 484 | } |
---|
| 485 | break; |
---|
[35aab3] | 486 | case ringorder_wp: |
---|
| 487 | case ringorder_ws: |
---|
| 488 | case ringorder_Wp: |
---|
| 489 | case ringorder_Ws: |
---|
[ab4778] | 490 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 491 | { // in jedem block: |
---|
[ab4778] | 492 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
---|
[35aab3] | 493 | } |
---|
| 494 | break; |
---|
| 495 | case ringorder_lp: |
---|
| 496 | case ringorder_ls: |
---|
[e519c5c] | 497 | case ringorder_rs: |
---|
[35aab3] | 498 | case ringorder_dp: |
---|
| 499 | case ringorder_ds: |
---|
| 500 | case ringorder_Dp: |
---|
| 501 | case ringorder_Ds: |
---|
| 502 | case ringorder_rp: |
---|
[ab4778] | 503 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 504 | { |
---|
| 505 | j+= p_GetExp(p,k,r); |
---|
| 506 | } |
---|
| 507 | break; |
---|
[fc5095] | 508 | case ringorder_a64: |
---|
| 509 | { |
---|
| 510 | int64* w=(int64*)r->wvhdl[i]; |
---|
[ab4778] | 511 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
---|
| 512 | { |
---|
[fc5095] | 513 | //there should be added a line which checks if w[k]>2^31 |
---|
| 514 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
---|
| 515 | } |
---|
| 516 | //break; |
---|
| 517 | return j; |
---|
| 518 | } |
---|
[35aab3] | 519 | case ringorder_c: |
---|
| 520 | case ringorder_C: |
---|
| 521 | case ringorder_S: |
---|
| 522 | case ringorder_s: |
---|
[645a19] | 523 | case ringorder_IS: |
---|
[35aab3] | 524 | case ringorder_aa: |
---|
| 525 | break; |
---|
| 526 | case ringorder_a: |
---|
[ab4778] | 527 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 528 | { // only one line |
---|
[ab4778] | 529 | j+= p_GetExp(p,k, r)*r->wvhdl[i][ k- b0 /*r->block0[i]*/]; |
---|
[35aab3] | 530 | } |
---|
[fc5095] | 531 | //break; |
---|
[35aab3] | 532 | return j; |
---|
[fc5095] | 533 | |
---|
[35aab3] | 534 | #ifndef NDEBUG |
---|
| 535 | default: |
---|
[19ae652] | 536 | Print("missing order %d in p_WTotaldegree\n",r->order[i]); |
---|
[35aab3] | 537 | break; |
---|
| 538 | #endif |
---|
| 539 | } |
---|
| 540 | } |
---|
| 541 | return j; |
---|
| 542 | } |
---|
| 543 | |
---|
[ba0fc3] | 544 | long p_DegW(poly p, const short *w, const ring R) |
---|
| 545 | { |
---|
| 546 | long r=~0L; |
---|
| 547 | |
---|
| 548 | while (p!=NULL) |
---|
| 549 | { |
---|
| 550 | long t=totaldegreeWecart_IV(p,R,w); |
---|
| 551 | if (t>r) r=t; |
---|
| 552 | pIter(p); |
---|
| 553 | } |
---|
| 554 | return r; |
---|
| 555 | } |
---|
| 556 | |
---|
[bf183f] | 557 | int p_Weight(int i, const ring r) |
---|
[35aab3] | 558 | { |
---|
| 559 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
| 560 | { |
---|
| 561 | return 1; |
---|
| 562 | } |
---|
| 563 | return r->firstwv[i-1]; |
---|
| 564 | } |
---|
| 565 | |
---|
[bf183f] | 566 | long p_WDegree(poly p, const ring r) |
---|
[35aab3] | 567 | { |
---|
[99bdcf] | 568 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
[35aab3] | 569 | p_LmCheckPolyRing(p, r); |
---|
[9f73e80] | 570 | int i; |
---|
[35aab3] | 571 | long j =0; |
---|
| 572 | |
---|
| 573 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
| 574 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 575 | |
---|
| 576 | for (;i<=r->N;i++) |
---|
[8a8c9e] | 577 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
[35aab3] | 578 | |
---|
| 579 | return j; |
---|
| 580 | } |
---|
| 581 | |
---|
| 582 | |
---|
| 583 | /* ---------------------------------------------------------------------*/ |
---|
| 584 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
| 585 | /* compute in l also the pLength of p */ |
---|
| 586 | |
---|
| 587 | /*2 |
---|
| 588 | * compute the length of a polynomial (in l) |
---|
| 589 | * and the degree of the monomial with maximal degree: the last one |
---|
| 590 | */ |
---|
[107986] | 591 | long pLDeg0(poly p,int *l, const ring r) |
---|
[35aab3] | 592 | { |
---|
| 593 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 594 | long k= p_GetComp(p, r); |
---|
[35aab3] | 595 | int ll=1; |
---|
| 596 | |
---|
| 597 | if (k > 0) |
---|
| 598 | { |
---|
| 599 | while ((pNext(p)!=NULL) && (p_GetComp(pNext(p), r)==k)) |
---|
| 600 | { |
---|
| 601 | pIter(p); |
---|
| 602 | ll++; |
---|
| 603 | } |
---|
| 604 | } |
---|
| 605 | else |
---|
| 606 | { |
---|
| 607 | while (pNext(p)!=NULL) |
---|
| 608 | { |
---|
| 609 | pIter(p); |
---|
| 610 | ll++; |
---|
| 611 | } |
---|
| 612 | } |
---|
| 613 | *l=ll; |
---|
| 614 | return r->pFDeg(p, r); |
---|
| 615 | } |
---|
| 616 | |
---|
| 617 | /*2 |
---|
| 618 | * compute the length of a polynomial (in l) |
---|
| 619 | * and the degree of the monomial with maximal degree: the last one |
---|
| 620 | * but search in all components before syzcomp |
---|
| 621 | */ |
---|
[107986] | 622 | long pLDeg0c(poly p,int *l, const ring r) |
---|
[35aab3] | 623 | { |
---|
| 624 | assume(p!=NULL); |
---|
| 625 | #ifdef PDEBUG |
---|
| 626 | _p_Test(p,r,PDEBUG); |
---|
| 627 | #endif |
---|
| 628 | p_CheckPolyRing(p, r); |
---|
| 629 | long o; |
---|
| 630 | int ll=1; |
---|
| 631 | |
---|
| 632 | if (! rIsSyzIndexRing(r)) |
---|
| 633 | { |
---|
[ab4778] | 634 | while (pNext(p) != NULL) |
---|
[35aab3] | 635 | { |
---|
| 636 | pIter(p); |
---|
| 637 | ll++; |
---|
| 638 | } |
---|
| 639 | o = r->pFDeg(p, r); |
---|
| 640 | } |
---|
| 641 | else |
---|
| 642 | { |
---|
| 643 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 644 | poly pp = p; |
---|
| 645 | while ((p=pNext(p))!=NULL) |
---|
| 646 | { |
---|
| 647 | if (p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
| 648 | ll++; |
---|
| 649 | else break; |
---|
| 650 | pp = p; |
---|
| 651 | } |
---|
| 652 | #ifdef PDEBUG |
---|
| 653 | _p_Test(pp,r,PDEBUG); |
---|
| 654 | #endif |
---|
| 655 | o = r->pFDeg(pp, r); |
---|
| 656 | } |
---|
| 657 | *l=ll; |
---|
| 658 | return o; |
---|
| 659 | } |
---|
| 660 | |
---|
| 661 | /*2 |
---|
| 662 | * compute the length of a polynomial (in l) |
---|
| 663 | * and the degree of the monomial with maximal degree: the first one |
---|
| 664 | * this works for the polynomial case with degree orderings |
---|
| 665 | * (both c,dp and dp,c) |
---|
| 666 | */ |
---|
[107986] | 667 | long pLDegb(poly p,int *l, const ring r) |
---|
[35aab3] | 668 | { |
---|
| 669 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 670 | long k= p_GetComp(p, r); |
---|
[35aab3] | 671 | long o = r->pFDeg(p, r); |
---|
| 672 | int ll=1; |
---|
| 673 | |
---|
| 674 | if (k != 0) |
---|
| 675 | { |
---|
| 676 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 677 | { |
---|
| 678 | ll++; |
---|
| 679 | } |
---|
| 680 | } |
---|
| 681 | else |
---|
| 682 | { |
---|
| 683 | while ((p=pNext(p)) !=NULL) |
---|
| 684 | { |
---|
| 685 | ll++; |
---|
| 686 | } |
---|
| 687 | } |
---|
| 688 | *l=ll; |
---|
| 689 | return o; |
---|
| 690 | } |
---|
| 691 | |
---|
| 692 | /*2 |
---|
| 693 | * compute the length of a polynomial (in l) |
---|
| 694 | * and the degree of the monomial with maximal degree: |
---|
| 695 | * this is NOT the last one, we have to look for it |
---|
| 696 | */ |
---|
[107986] | 697 | long pLDeg1(poly p,int *l, const ring r) |
---|
[35aab3] | 698 | { |
---|
| 699 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 700 | long k= p_GetComp(p, r); |
---|
[35aab3] | 701 | int ll=1; |
---|
| 702 | long t,max; |
---|
| 703 | |
---|
| 704 | max=r->pFDeg(p, r); |
---|
| 705 | if (k > 0) |
---|
| 706 | { |
---|
| 707 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 708 | { |
---|
| 709 | t=r->pFDeg(p, r); |
---|
| 710 | if (t>max) max=t; |
---|
| 711 | ll++; |
---|
| 712 | } |
---|
| 713 | } |
---|
| 714 | else |
---|
| 715 | { |
---|
| 716 | while ((p=pNext(p))!=NULL) |
---|
| 717 | { |
---|
| 718 | t=r->pFDeg(p, r); |
---|
| 719 | if (t>max) max=t; |
---|
| 720 | ll++; |
---|
| 721 | } |
---|
| 722 | } |
---|
| 723 | *l=ll; |
---|
| 724 | return max; |
---|
| 725 | } |
---|
| 726 | |
---|
| 727 | /*2 |
---|
| 728 | * compute the length of a polynomial (in l) |
---|
| 729 | * and the degree of the monomial with maximal degree: |
---|
| 730 | * this is NOT the last one, we have to look for it |
---|
| 731 | * in all components |
---|
| 732 | */ |
---|
[107986] | 733 | long pLDeg1c(poly p,int *l, const ring r) |
---|
[35aab3] | 734 | { |
---|
| 735 | p_CheckPolyRing(p, r); |
---|
| 736 | int ll=1; |
---|
| 737 | long t,max; |
---|
| 738 | |
---|
| 739 | max=r->pFDeg(p, r); |
---|
| 740 | if (rIsSyzIndexRing(r)) |
---|
| 741 | { |
---|
| 742 | long limit = rGetCurrSyzLimit(r); |
---|
| 743 | while ((p=pNext(p))!=NULL) |
---|
| 744 | { |
---|
| 745 | if (p_GetComp(p, r)<=limit) |
---|
| 746 | { |
---|
| 747 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 748 | ll++; |
---|
| 749 | } |
---|
| 750 | else break; |
---|
| 751 | } |
---|
| 752 | } |
---|
| 753 | else |
---|
| 754 | { |
---|
| 755 | while ((p=pNext(p))!=NULL) |
---|
| 756 | { |
---|
| 757 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 758 | ll++; |
---|
| 759 | } |
---|
| 760 | } |
---|
| 761 | *l=ll; |
---|
| 762 | return max; |
---|
| 763 | } |
---|
| 764 | |
---|
| 765 | // like pLDeg1, only pFDeg == pDeg |
---|
[107986] | 766 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 767 | { |
---|
[45d2332] | 768 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 769 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 770 | long k= p_GetComp(p, r); |
---|
[35aab3] | 771 | int ll=1; |
---|
| 772 | long t,max; |
---|
| 773 | |
---|
[b5d4d1] | 774 | max=p_GetOrder(p, r); |
---|
[35aab3] | 775 | if (k > 0) |
---|
| 776 | { |
---|
| 777 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 778 | { |
---|
[b5d4d1] | 779 | t=p_GetOrder(p, r); |
---|
[35aab3] | 780 | if (t>max) max=t; |
---|
| 781 | ll++; |
---|
| 782 | } |
---|
| 783 | } |
---|
| 784 | else |
---|
| 785 | { |
---|
| 786 | while ((p=pNext(p))!=NULL) |
---|
| 787 | { |
---|
[b5d4d1] | 788 | t=p_GetOrder(p, r); |
---|
[35aab3] | 789 | if (t>max) max=t; |
---|
| 790 | ll++; |
---|
| 791 | } |
---|
| 792 | } |
---|
| 793 | *l=ll; |
---|
| 794 | return max; |
---|
| 795 | } |
---|
| 796 | |
---|
[107986] | 797 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 798 | { |
---|
[45d2332] | 799 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 800 | p_CheckPolyRing(p, r); |
---|
| 801 | int ll=1; |
---|
| 802 | long t,max; |
---|
| 803 | |
---|
[b5d4d1] | 804 | max=p_GetOrder(p, r); |
---|
[35aab3] | 805 | if (rIsSyzIndexRing(r)) |
---|
| 806 | { |
---|
| 807 | long limit = rGetCurrSyzLimit(r); |
---|
| 808 | while ((p=pNext(p))!=NULL) |
---|
| 809 | { |
---|
| 810 | if (p_GetComp(p, r)<=limit) |
---|
| 811 | { |
---|
[b5d4d1] | 812 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 813 | ll++; |
---|
| 814 | } |
---|
| 815 | else break; |
---|
| 816 | } |
---|
| 817 | } |
---|
| 818 | else |
---|
| 819 | { |
---|
| 820 | while ((p=pNext(p))!=NULL) |
---|
| 821 | { |
---|
[b5d4d1] | 822 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 823 | ll++; |
---|
| 824 | } |
---|
| 825 | } |
---|
| 826 | *l=ll; |
---|
| 827 | return max; |
---|
| 828 | } |
---|
| 829 | |
---|
| 830 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
[107986] | 831 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 832 | { |
---|
| 833 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 834 | long k= p_GetComp(p, r); |
---|
[35aab3] | 835 | int ll=1; |
---|
| 836 | long t,max; |
---|
| 837 | |
---|
[99bdcf] | 838 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 839 | if (k > 0) |
---|
| 840 | { |
---|
| 841 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 842 | { |
---|
[99bdcf] | 843 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 844 | if (t>max) max=t; |
---|
| 845 | ll++; |
---|
| 846 | } |
---|
| 847 | } |
---|
| 848 | else |
---|
| 849 | { |
---|
| 850 | while ((p=pNext(p))!=NULL) |
---|
| 851 | { |
---|
[99bdcf] | 852 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 853 | if (t>max) max=t; |
---|
| 854 | ll++; |
---|
| 855 | } |
---|
| 856 | } |
---|
| 857 | *l=ll; |
---|
| 858 | return max; |
---|
| 859 | } |
---|
| 860 | |
---|
[107986] | 861 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 862 | { |
---|
| 863 | p_CheckPolyRing(p, r); |
---|
| 864 | int ll=1; |
---|
| 865 | long t,max; |
---|
| 866 | |
---|
[99bdcf] | 867 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 868 | if (rIsSyzIndexRing(r)) |
---|
| 869 | { |
---|
| 870 | long limit = rGetCurrSyzLimit(r); |
---|
| 871 | while ((p=pNext(p))!=NULL) |
---|
| 872 | { |
---|
| 873 | if (p_GetComp(p, r)<=limit) |
---|
| 874 | { |
---|
[99bdcf] | 875 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 876 | ll++; |
---|
| 877 | } |
---|
| 878 | else break; |
---|
| 879 | } |
---|
| 880 | } |
---|
| 881 | else |
---|
| 882 | { |
---|
| 883 | while ((p=pNext(p))!=NULL) |
---|
| 884 | { |
---|
[99bdcf] | 885 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 886 | ll++; |
---|
| 887 | } |
---|
| 888 | } |
---|
| 889 | *l=ll; |
---|
| 890 | return max; |
---|
| 891 | } |
---|
| 892 | |
---|
[19ae652] | 893 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
[107986] | 894 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 895 | { |
---|
| 896 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 897 | long k= p_GetComp(p, r); |
---|
[35aab3] | 898 | int ll=1; |
---|
| 899 | long t,max; |
---|
| 900 | |
---|
[19ae652] | 901 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 902 | if (k > 0) |
---|
| 903 | { |
---|
| 904 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 905 | { |
---|
[19ae652] | 906 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 907 | if (t>max) max=t; |
---|
| 908 | ll++; |
---|
| 909 | } |
---|
| 910 | } |
---|
| 911 | else |
---|
| 912 | { |
---|
| 913 | while ((p=pNext(p))!=NULL) |
---|
| 914 | { |
---|
[19ae652] | 915 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 916 | if (t>max) max=t; |
---|
| 917 | ll++; |
---|
| 918 | } |
---|
| 919 | } |
---|
| 920 | *l=ll; |
---|
| 921 | return max; |
---|
| 922 | } |
---|
| 923 | |
---|
[107986] | 924 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 925 | { |
---|
| 926 | p_CheckPolyRing(p, r); |
---|
| 927 | int ll=1; |
---|
| 928 | long t,max; |
---|
| 929 | |
---|
[19ae652] | 930 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 931 | if (rIsSyzIndexRing(r)) |
---|
| 932 | { |
---|
| 933 | long limit = rGetCurrSyzLimit(r); |
---|
| 934 | while ((p=pNext(p))!=NULL) |
---|
| 935 | { |
---|
| 936 | if (p_GetComp(p, r)<=limit) |
---|
| 937 | { |
---|
[99bdcf] | 938 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 939 | ll++; |
---|
| 940 | } |
---|
| 941 | else break; |
---|
| 942 | } |
---|
| 943 | } |
---|
| 944 | else |
---|
| 945 | { |
---|
| 946 | while ((p=pNext(p))!=NULL) |
---|
| 947 | { |
---|
[99bdcf] | 948 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 949 | ll++; |
---|
| 950 | } |
---|
| 951 | } |
---|
| 952 | *l=ll; |
---|
| 953 | return max; |
---|
| 954 | } |
---|
| 955 | |
---|
| 956 | /*************************************************************** |
---|
| 957 | * |
---|
| 958 | * Maximal Exponent business |
---|
| 959 | * |
---|
| 960 | ***************************************************************/ |
---|
| 961 | |
---|
[ab4778] | 962 | static inline unsigned long |
---|
[107986] | 963 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
[35aab3] | 964 | unsigned long number_of_exp) |
---|
| 965 | { |
---|
| 966 | const unsigned long bitmask = r->bitmask; |
---|
| 967 | unsigned long ml1 = l1 & bitmask; |
---|
| 968 | unsigned long ml2 = l2 & bitmask; |
---|
| 969 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
| 970 | unsigned long j = number_of_exp - 1; |
---|
| 971 | |
---|
| 972 | if (j > 0) |
---|
| 973 | { |
---|
| 974 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
| 975 | while (1) |
---|
| 976 | { |
---|
| 977 | ml1 = l1 & mask; |
---|
| 978 | ml2 = l2 & mask; |
---|
| 979 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
| 980 | j--; |
---|
| 981 | if (j == 0) break; |
---|
| 982 | mask = mask << r->BitsPerExp; |
---|
| 983 | } |
---|
| 984 | } |
---|
| 985 | return max; |
---|
| 986 | } |
---|
| 987 | |
---|
| 988 | static inline unsigned long |
---|
[107986] | 989 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
[35aab3] | 990 | { |
---|
| 991 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
| 992 | } |
---|
| 993 | |
---|
[107986] | 994 | poly p_GetMaxExpP(poly p, const ring r) |
---|
[35aab3] | 995 | { |
---|
| 996 | p_CheckPolyRing(p, r); |
---|
| 997 | if (p == NULL) return p_Init(r); |
---|
| 998 | poly max = p_LmInit(p, r); |
---|
| 999 | pIter(p); |
---|
| 1000 | if (p == NULL) return max; |
---|
| 1001 | int i, offset; |
---|
| 1002 | unsigned long l_p, l_max; |
---|
| 1003 | unsigned long divmask = r->divmask; |
---|
[ab4778] | 1004 | |
---|
[35aab3] | 1005 | do |
---|
| 1006 | { |
---|
| 1007 | offset = r->VarL_Offset[0]; |
---|
| 1008 | l_p = p->exp[offset]; |
---|
| 1009 | l_max = max->exp[offset]; |
---|
| 1010 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1011 | if (l_p > l_max || |
---|
[35aab3] | 1012 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1013 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1014 | |
---|
| 1015 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1016 | { |
---|
| 1017 | offset = r->VarL_Offset[i]; |
---|
| 1018 | l_p = p->exp[offset]; |
---|
| 1019 | l_max = max->exp[offset]; |
---|
| 1020 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1021 | if (l_p > l_max || |
---|
[35aab3] | 1022 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1023 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1024 | } |
---|
| 1025 | pIter(p); |
---|
| 1026 | } |
---|
| 1027 | while (p != NULL); |
---|
| 1028 | return max; |
---|
| 1029 | } |
---|
| 1030 | |
---|
[107986] | 1031 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
[35aab3] | 1032 | { |
---|
| 1033 | unsigned long l_p, divmask = r->divmask; |
---|
| 1034 | int i; |
---|
[ab4778] | 1035 | |
---|
[35aab3] | 1036 | while (p != NULL) |
---|
| 1037 | { |
---|
| 1038 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
| 1039 | if (l_p > l_max || |
---|
| 1040 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1041 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1042 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1043 | { |
---|
| 1044 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
| 1045 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1046 | if (l_p > l_max || |
---|
[35aab3] | 1047 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1048 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1049 | } |
---|
| 1050 | pIter(p); |
---|
| 1051 | } |
---|
| 1052 | return l_max; |
---|
| 1053 | } |
---|
| 1054 | |
---|
[fc5095] | 1055 | |
---|
| 1056 | |
---|
[ab4778] | 1057 | |
---|
[35aab3] | 1058 | /*************************************************************** |
---|
| 1059 | * |
---|
| 1060 | * Misc things |
---|
| 1061 | * |
---|
| 1062 | ***************************************************************/ |
---|
| 1063 | // returns TRUE, if all monoms have the same component |
---|
[107986] | 1064 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
[35aab3] | 1065 | { |
---|
| 1066 | if(p!=NULL) |
---|
| 1067 | { |
---|
| 1068 | long i = p_GetComp(p, r); |
---|
| 1069 | while (pNext(p)!=NULL) |
---|
| 1070 | { |
---|
| 1071 | pIter(p); |
---|
| 1072 | if(i != p_GetComp(p, r)) return FALSE; |
---|
| 1073 | } |
---|
| 1074 | } |
---|
| 1075 | return TRUE; |
---|
| 1076 | } |
---|
| 1077 | |
---|
| 1078 | /*2 |
---|
| 1079 | *test if a monomial /head term is a pure power |
---|
| 1080 | */ |
---|
| 1081 | int p_IsPurePower(const poly p, const ring r) |
---|
| 1082 | { |
---|
| 1083 | int i,k=0; |
---|
| 1084 | |
---|
| 1085 | for (i=r->N;i;i--) |
---|
| 1086 | { |
---|
| 1087 | if (p_GetExp(p,i, r)!=0) |
---|
| 1088 | { |
---|
| 1089 | if(k!=0) return 0; |
---|
| 1090 | k=i; |
---|
| 1091 | } |
---|
| 1092 | } |
---|
| 1093 | return k; |
---|
| 1094 | } |
---|
| 1095 | |
---|
[2f0d83f] | 1096 | /*2 |
---|
| 1097 | *test if a polynomial is univariate |
---|
| 1098 | * return -1 for constant, |
---|
| 1099 | * 0 for not univariate,s |
---|
| 1100 | * i if dep. on var(i) |
---|
| 1101 | */ |
---|
| 1102 | int p_IsUnivariate(poly p, const ring r) |
---|
| 1103 | { |
---|
| 1104 | int i,k=-1; |
---|
| 1105 | |
---|
| 1106 | while (p!=NULL) |
---|
| 1107 | { |
---|
| 1108 | for (i=r->N;i;i--) |
---|
| 1109 | { |
---|
| 1110 | if (p_GetExp(p,i, r)!=0) |
---|
| 1111 | { |
---|
| 1112 | if((k!=-1)&&(k!=i)) return 0; |
---|
| 1113 | k=i; |
---|
| 1114 | } |
---|
| 1115 | } |
---|
| 1116 | pIter(p); |
---|
| 1117 | } |
---|
| 1118 | return k; |
---|
| 1119 | } |
---|
| 1120 | |
---|
[3931bf] | 1121 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
[f46646] | 1122 | int p_GetVariables(poly p, int * e, const ring r) |
---|
[3931bf] | 1123 | { |
---|
| 1124 | int i; |
---|
[f46646] | 1125 | int n=0; |
---|
[3931bf] | 1126 | while(p!=NULL) |
---|
| 1127 | { |
---|
[f46646] | 1128 | n=0; |
---|
[95450e] | 1129 | for(i=r->N; i>0; i--) |
---|
[3931bf] | 1130 | { |
---|
| 1131 | if(e[i]==0) |
---|
| 1132 | { |
---|
| 1133 | if (p_GetExp(p,i,r)>0) |
---|
[f46646] | 1134 | { |
---|
[3931bf] | 1135 | e[i]=1; |
---|
[f46646] | 1136 | n++; |
---|
| 1137 | } |
---|
[3931bf] | 1138 | } |
---|
[f46646] | 1139 | else |
---|
| 1140 | n++; |
---|
[3931bf] | 1141 | } |
---|
[f46646] | 1142 | if (n==r->N) break; |
---|
[3931bf] | 1143 | pIter(p); |
---|
| 1144 | } |
---|
[f46646] | 1145 | return n; |
---|
[3931bf] | 1146 | } |
---|
| 1147 | |
---|
| 1148 | |
---|
[35aab3] | 1149 | /*2 |
---|
| 1150 | * returns a polynomial representing the integer i |
---|
| 1151 | */ |
---|
[107986] | 1152 | poly p_ISet(int i, const ring r) |
---|
[35aab3] | 1153 | { |
---|
| 1154 | poly rc = NULL; |
---|
| 1155 | if (i!=0) |
---|
| 1156 | { |
---|
| 1157 | rc = p_Init(r); |
---|
[8a8c9e] | 1158 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
| 1159 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
[fb82895] | 1160 | p_LmDelete(&rc,r); |
---|
[35aab3] | 1161 | } |
---|
| 1162 | return rc; |
---|
| 1163 | } |
---|
| 1164 | |
---|
[1c33e0d] | 1165 | /*2 |
---|
| 1166 | * an optimized version of p_ISet for the special case 1 |
---|
| 1167 | */ |
---|
[5bc4103] | 1168 | poly p_One(const ring r) |
---|
[1c33e0d] | 1169 | { |
---|
| 1170 | poly rc = p_Init(r); |
---|
[8a8c9e] | 1171 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
[1c33e0d] | 1172 | return rc; |
---|
| 1173 | } |
---|
| 1174 | |
---|
[f34215] | 1175 | void p_Split(poly p, poly *h) |
---|
| 1176 | { |
---|
| 1177 | *h=pNext(p); |
---|
| 1178 | pNext(p)=NULL; |
---|
| 1179 | } |
---|
| 1180 | |
---|
| 1181 | /*2 |
---|
| 1182 | * pair has no common factor ? or is no polynomial |
---|
| 1183 | */ |
---|
| 1184 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
| 1185 | { |
---|
| 1186 | |
---|
| 1187 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
| 1188 | return FALSE; |
---|
| 1189 | int i = rVar(r); |
---|
| 1190 | loop |
---|
| 1191 | { |
---|
| 1192 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
| 1193 | return FALSE; |
---|
| 1194 | i--; |
---|
| 1195 | if (i == 0) |
---|
| 1196 | return TRUE; |
---|
| 1197 | } |
---|
| 1198 | } |
---|
| 1199 | |
---|
| 1200 | /*2 |
---|
| 1201 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
| 1202 | */ |
---|
| 1203 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
| 1204 | { |
---|
| 1205 | if (r==NULL) { rc=NULL;return st;} |
---|
| 1206 | int i,j; |
---|
| 1207 | rc = p_Init(r); |
---|
[8a8c9e] | 1208 | const char *s = r->cf->cfRead(st,&(rc->coef),r->cf); |
---|
[f34215] | 1209 | if (s==st) |
---|
| 1210 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
| 1211 | { |
---|
| 1212 | j = r_IsRingVar(s,r); |
---|
| 1213 | if (j >= 0) |
---|
| 1214 | { |
---|
| 1215 | p_IncrExp(rc,1+j,r); |
---|
| 1216 | while (*s!='\0') s++; |
---|
| 1217 | goto done; |
---|
| 1218 | } |
---|
| 1219 | } |
---|
| 1220 | while (*s!='\0') |
---|
| 1221 | { |
---|
| 1222 | char ss[2]; |
---|
| 1223 | ss[0] = *s++; |
---|
| 1224 | ss[1] = '\0'; |
---|
| 1225 | j = r_IsRingVar(ss,r); |
---|
| 1226 | if (j >= 0) |
---|
| 1227 | { |
---|
| 1228 | const char *s_save=s; |
---|
| 1229 | s = eati(s,&i); |
---|
| 1230 | if (((unsigned long)i) > r->bitmask) |
---|
| 1231 | { |
---|
| 1232 | // exponent to large: it is not a monomial |
---|
| 1233 | p_LmDelete(&rc,r); |
---|
| 1234 | return s_save; |
---|
| 1235 | } |
---|
| 1236 | p_AddExp(rc,1+j, (long)i, r); |
---|
| 1237 | } |
---|
| 1238 | else |
---|
| 1239 | { |
---|
| 1240 | // 1st char of is not a varname |
---|
| 1241 | p_LmDelete(&rc,r); |
---|
| 1242 | s--; |
---|
| 1243 | return s; |
---|
| 1244 | } |
---|
| 1245 | } |
---|
| 1246 | done: |
---|
[8a8c9e] | 1247 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
[f34215] | 1248 | else |
---|
| 1249 | { |
---|
| 1250 | #ifdef HAVE_PLURAL |
---|
| 1251 | // in super-commutative ring |
---|
| 1252 | // squares of anti-commutative variables are zeroes! |
---|
| 1253 | if(rIsSCA(r)) |
---|
| 1254 | { |
---|
| 1255 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
| 1256 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
| 1257 | |
---|
| 1258 | assume(rc != NULL); |
---|
| 1259 | |
---|
| 1260 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
| 1261 | if( p_GetExp(rc, k, r) > 1 ) |
---|
| 1262 | { |
---|
| 1263 | p_LmDelete(&rc, r); |
---|
| 1264 | goto finish; |
---|
| 1265 | } |
---|
| 1266 | } |
---|
| 1267 | #endif |
---|
[71ba5b8] | 1268 | |
---|
[f34215] | 1269 | p_Setm(rc,r); |
---|
| 1270 | } |
---|
[71ba5b8] | 1271 | finish: |
---|
[f34215] | 1272 | return s; |
---|
| 1273 | } |
---|
| 1274 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
| 1275 | { |
---|
| 1276 | poly p; |
---|
| 1277 | const char *s=p_Read(st,p,r); |
---|
| 1278 | if (*s!='\0') |
---|
| 1279 | { |
---|
| 1280 | if ((s!=st)&&isdigit(st[0])) |
---|
| 1281 | { |
---|
| 1282 | errorreported=TRUE; |
---|
| 1283 | } |
---|
| 1284 | ok=FALSE; |
---|
| 1285 | p_Delete(&p,r); |
---|
| 1286 | return NULL; |
---|
| 1287 | } |
---|
| 1288 | #ifdef PDEBUG |
---|
| 1289 | _p_Test(p,r,PDEBUG); |
---|
| 1290 | #endif |
---|
| 1291 | ok=!errorreported; |
---|
| 1292 | return p; |
---|
| 1293 | } |
---|
| 1294 | |
---|
[35aab3] | 1295 | /*2 |
---|
| 1296 | * returns a polynomial representing the number n |
---|
| 1297 | * destroys n |
---|
| 1298 | */ |
---|
[107986] | 1299 | poly p_NSet(number n, const ring r) |
---|
[35aab3] | 1300 | { |
---|
[8a8c9e] | 1301 | if (n_IsZero(n,r->cf)) |
---|
[35aab3] | 1302 | { |
---|
[8a8c9e] | 1303 | n_Delete(&n, r->cf); |
---|
[35aab3] | 1304 | return NULL; |
---|
| 1305 | } |
---|
| 1306 | else |
---|
| 1307 | { |
---|
| 1308 | poly rc = p_Init(r); |
---|
| 1309 | pSetCoeff0(rc,n); |
---|
| 1310 | return rc; |
---|
| 1311 | } |
---|
| 1312 | } |
---|
[fb4075b] | 1313 | /*2 |
---|
[e5d267] | 1314 | * assumes that LM(a) = LM(b)*m, for some monomial m, |
---|
| 1315 | * returns the multiplicant m, |
---|
| 1316 | * leaves a and b unmodified |
---|
[fb4075b] | 1317 | */ |
---|
| 1318 | poly p_Divide(poly a, poly b, const ring r) |
---|
| 1319 | { |
---|
| 1320 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
| 1321 | int i; |
---|
[8a8c9e] | 1322 | poly result = p_Init(r); |
---|
[fb4075b] | 1323 | |
---|
| 1324 | for(i=(int)r->N; i; i--) |
---|
| 1325 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
| 1326 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
| 1327 | p_Setm(result,r); |
---|
| 1328 | return result; |
---|
| 1329 | } |
---|
| 1330 | |
---|
[8a8c9e] | 1331 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
| 1332 | { |
---|
[45d2332] | 1333 | pAssume(!n_IsZero(n,r->cf)); |
---|
[8a8c9e] | 1334 | p_Test(p, r); |
---|
| 1335 | |
---|
| 1336 | poly q = p; |
---|
| 1337 | while (p != NULL) |
---|
| 1338 | { |
---|
| 1339 | number nc = pGetCoeff(p); |
---|
| 1340 | pSetCoeff0(p, n_Div(nc, n, r->cf)); |
---|
| 1341 | n_Delete(&nc, r->cf); |
---|
| 1342 | pIter(p); |
---|
| 1343 | } |
---|
| 1344 | p_Test(q, r); |
---|
| 1345 | return q; |
---|
| 1346 | } |
---|
| 1347 | |
---|
[fb4075b] | 1348 | /*2 |
---|
| 1349 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
[e432a0] | 1350 | * assumes that b is not NULL, destroyes b |
---|
[fb4075b] | 1351 | */ |
---|
| 1352 | poly p_DivideM(poly a, poly b, const ring r) |
---|
| 1353 | { |
---|
[e432a0] | 1354 | if (a==NULL) { p_Delete(&b,r); return NULL; } |
---|
[fb4075b] | 1355 | poly result=a; |
---|
| 1356 | poly prev=NULL; |
---|
| 1357 | int i; |
---|
| 1358 | #ifdef HAVE_RINGS |
---|
| 1359 | number inv=pGetCoeff(b); |
---|
| 1360 | #else |
---|
| 1361 | number inv=n_Invers(pGetCoeff(b),r->cf); |
---|
| 1362 | #endif |
---|
| 1363 | |
---|
| 1364 | while (a!=NULL) |
---|
| 1365 | { |
---|
| 1366 | if (p_DivisibleBy(b,a,r)) |
---|
| 1367 | { |
---|
| 1368 | for(i=(int)r->N; i; i--) |
---|
| 1369 | p_SubExp(a,i, p_GetExp(b,i,r),r); |
---|
| 1370 | p_SubComp(a, p_GetComp(b,r),r); |
---|
| 1371 | p_Setm(a,r); |
---|
| 1372 | prev=a; |
---|
| 1373 | pIter(a); |
---|
| 1374 | } |
---|
| 1375 | else |
---|
| 1376 | { |
---|
| 1377 | if (prev==NULL) |
---|
| 1378 | { |
---|
[8a8c9e] | 1379 | p_LmDelete(&result,r); |
---|
[fb4075b] | 1380 | a=result; |
---|
| 1381 | } |
---|
| 1382 | else |
---|
| 1383 | { |
---|
[8a8c9e] | 1384 | p_LmDelete(&pNext(prev),r); |
---|
[fb4075b] | 1385 | a=pNext(prev); |
---|
| 1386 | } |
---|
| 1387 | } |
---|
| 1388 | } |
---|
| 1389 | #ifdef HAVE_RINGS |
---|
| 1390 | if (n_IsUnit(inv,r->cf)) |
---|
| 1391 | { |
---|
| 1392 | inv = n_Invers(inv,r->cf); |
---|
| 1393 | p_Mult_nn(result,inv,r); |
---|
| 1394 | n_Delete(&inv, r->cf); |
---|
| 1395 | } |
---|
| 1396 | else |
---|
| 1397 | { |
---|
| 1398 | p_Div_nn(result,inv,r); |
---|
| 1399 | } |
---|
| 1400 | #else |
---|
| 1401 | p_Mult_nn(result,inv,r); |
---|
| 1402 | n_Delete(&inv, r->cf); |
---|
| 1403 | #endif |
---|
| 1404 | p_Delete(&b, r); |
---|
| 1405 | return result; |
---|
| 1406 | } |
---|
[35aab3] | 1407 | |
---|
[3d0808] | 1408 | #ifdef HAVE_RINGS |
---|
| 1409 | /* TRUE iff LT(f) | LT(g) */ |
---|
| 1410 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
| 1411 | { |
---|
| 1412 | int exponent; |
---|
| 1413 | for(int i = (int)rVar(r); i>0; i--) |
---|
| 1414 | { |
---|
| 1415 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
| 1416 | if (exponent < 0) return FALSE; |
---|
| 1417 | } |
---|
| 1418 | return n_DivBy(pGetCoeff(g), pGetCoeff(f), r->cf); |
---|
| 1419 | } |
---|
| 1420 | #endif |
---|
| 1421 | |
---|
[a7ee69] | 1422 | /*2 |
---|
| 1423 | * returns the LCM of the head terms of a and b in *m |
---|
| 1424 | */ |
---|
| 1425 | void p_Lcm(poly a, poly b, poly m, const ring r) |
---|
| 1426 | { |
---|
| 1427 | int i; |
---|
| 1428 | for (i=rVar(r); i; i--) |
---|
| 1429 | { |
---|
| 1430 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
| 1431 | } |
---|
| 1432 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
| 1433 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
| 1434 | } |
---|
| 1435 | |
---|
[f0b01f] | 1436 | /* assumes that p and divisor are univariate polynomials in r, |
---|
[ba2359] | 1437 | mentioning the same variable; |
---|
| 1438 | assumes divisor != NULL; |
---|
[f0b01f] | 1439 | p may be NULL; |
---|
[ba2359] | 1440 | assumes a global monomial ordering in r; |
---|
[f0b01f] | 1441 | performs polynomial division of p by divisor: |
---|
| 1442 | - afterwards p contains the remainder of the division, i.e., |
---|
| 1443 | p_before = result * divisor + p_afterwards; |
---|
[ba2359] | 1444 | - if needResult == TRUE, then the method computes and returns 'result', |
---|
| 1445 | otherwise NULL is returned (This parametrization can be used when |
---|
| 1446 | one is only interested in the remainder of the division. In this |
---|
[f0b01f] | 1447 | case, the method will be slightly faster.) |
---|
| 1448 | leaves divisor unmodified */ |
---|
| 1449 | poly p_PolyDiv(poly &p, poly divisor, BOOLEAN needResult, ring r) |
---|
[ba2359] | 1450 | { |
---|
| 1451 | assume(divisor != NULL); |
---|
[f0b01f] | 1452 | if (p == NULL) return NULL; |
---|
[ba2359] | 1453 | |
---|
[69fb9d0] | 1454 | poly result = NULL; |
---|
[f0b01f] | 1455 | number divisorLC = p_GetCoeff(divisor, r); |
---|
| 1456 | int divisorLE = p_GetExp(divisor, 1, r); |
---|
[c28ecf] | 1457 | while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r))) |
---|
[69fb9d0] | 1458 | { |
---|
[f0b01f] | 1459 | /* determine t = LT(p) / LT(divisor) */ |
---|
[69fb9d0] | 1460 | poly t = p_ISet(1, r); |
---|
[f0b01f] | 1461 | number c = n_Div(p_GetCoeff(p, r), divisorLC, r->cf); |
---|
[69fb9d0] | 1462 | p_SetCoeff(t, c, r); |
---|
[f0b01f] | 1463 | int e = p_GetExp(p, 1, r) - divisorLE; |
---|
[69fb9d0] | 1464 | p_SetExp(t, 1, e, r); |
---|
| 1465 | p_Setm(t, r); |
---|
[f0b01f] | 1466 | if (needResult) result = p_Add_q(result, p_Copy(t, r), r); |
---|
| 1467 | p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r); |
---|
[69fb9d0] | 1468 | } |
---|
| 1469 | return result; |
---|
| 1470 | } |
---|
| 1471 | |
---|
[c28ecf] | 1472 | /* returns NULL if p == NULL, otherwise makes p monic by dividing |
---|
| 1473 | by its leading coefficient (only done if this is not already 1); |
---|
| 1474 | this assumes that we are over a ground field so that division |
---|
| 1475 | is well-defined; |
---|
| 1476 | modifies p */ |
---|
| 1477 | void p_Monic(poly &p, ring r) |
---|
| 1478 | { |
---|
| 1479 | if (p == NULL) return; |
---|
| 1480 | poly pp = p; |
---|
| 1481 | number lc = p_GetCoeff(p, r); |
---|
| 1482 | if (n_IsOne(lc, r->cf)) return; |
---|
[cfb500] | 1483 | number lcInverse = n_Invers(lc, r->cf); |
---|
| 1484 | number n = n_Init(1, r->cf); |
---|
| 1485 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
[c28ecf] | 1486 | p = pIter(p); |
---|
| 1487 | while (p != NULL) |
---|
| 1488 | { |
---|
[cfb500] | 1489 | number n = n_Mult(p_GetCoeff(p, r), lcInverse, r->cf); |
---|
| 1490 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
[c28ecf] | 1491 | p = pIter(p); |
---|
| 1492 | } |
---|
[cfb500] | 1493 | n_Delete(&lcInverse, r->cf); |
---|
[c28ecf] | 1494 | p = pp; |
---|
| 1495 | } |
---|
| 1496 | |
---|
[69fb9d0] | 1497 | /* see p_Gcd; |
---|
[f0b01f] | 1498 | additional assumption: deg(p) >= deg(q); |
---|
| 1499 | must destroy p and q (unless one of them is returned) */ |
---|
| 1500 | poly p_GcdHelper(poly &p, poly &q, ring r) |
---|
[69fb9d0] | 1501 | { |
---|
[c28ecf] | 1502 | if (q == NULL) |
---|
| 1503 | { |
---|
| 1504 | /* We have to make p monic before we return it, so that if the |
---|
| 1505 | gcd is a unit in the ground field, we will actually return 1. */ |
---|
| 1506 | p_Monic(p, r); |
---|
| 1507 | return p; |
---|
| 1508 | } |
---|
[69fb9d0] | 1509 | else |
---|
| 1510 | { |
---|
[f0b01f] | 1511 | p_PolyDiv(p, q, FALSE, r); |
---|
[69fb9d0] | 1512 | return p_GcdHelper(q, p, r); |
---|
| 1513 | } |
---|
[ba2359] | 1514 | } |
---|
| 1515 | |
---|
| 1516 | /* assumes that p and q are univariate polynomials in r, |
---|
| 1517 | mentioning the same variable; |
---|
| 1518 | assumes a global monomial ordering in r; |
---|
| 1519 | assumes that not both p and q are NULL; |
---|
[69fb9d0] | 1520 | returns the gcd of p and q; |
---|
| 1521 | leaves p and q unmodified */ |
---|
[ba2359] | 1522 | poly p_Gcd(poly p, poly q, ring r) |
---|
| 1523 | { |
---|
| 1524 | assume((p != NULL) || (q != NULL)); |
---|
| 1525 | |
---|
[69fb9d0] | 1526 | poly a = p; poly b = q; |
---|
| 1527 | if (p_Deg(a, r) < p_Deg(b, r)) { a = q; b = p; } |
---|
| 1528 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
[f0b01f] | 1529 | return p_GcdHelper(a, b, r); |
---|
[69fb9d0] | 1530 | } |
---|
| 1531 | |
---|
| 1532 | /* see p_ExtGcd; |
---|
[f0b01f] | 1533 | additional assumption: deg(p) >= deg(q); |
---|
| 1534 | must destroy p and q (unless one of them is returned) */ |
---|
| 1535 | poly p_ExtGcdHelper(poly &p, poly &pFactor, poly &q, poly &qFactor, |
---|
[69fb9d0] | 1536 | ring r) |
---|
| 1537 | { |
---|
| 1538 | if (q == NULL) |
---|
| 1539 | { |
---|
[c28ecf] | 1540 | qFactor = NULL; |
---|
| 1541 | pFactor = p_ISet(1, r); |
---|
| 1542 | p_SetCoeff(pFactor, n_Invers(p_GetCoeff(p, r), r->cf), r); |
---|
| 1543 | p_Monic(p, r); |
---|
| 1544 | return p; |
---|
[69fb9d0] | 1545 | } |
---|
| 1546 | else |
---|
| 1547 | { |
---|
[f0b01f] | 1548 | poly pDivQ = p_PolyDiv(p, q, TRUE, r); |
---|
[c28ecf] | 1549 | poly ppFactor = NULL; poly qqFactor = NULL; |
---|
| 1550 | poly theGcd = p_ExtGcdHelper(q, qqFactor, p, ppFactor, r); |
---|
| 1551 | pFactor = ppFactor; |
---|
| 1552 | qFactor = p_Add_q(qqFactor, |
---|
| 1553 | p_Neg(p_Mult_q(pDivQ, p_Copy(ppFactor, r), r), r), |
---|
[f0b01f] | 1554 | r); |
---|
[69fb9d0] | 1555 | return theGcd; |
---|
| 1556 | } |
---|
[ba2359] | 1557 | } |
---|
| 1558 | |
---|
| 1559 | /* assumes that p and q are univariate polynomials in r, |
---|
| 1560 | mentioning the same variable; |
---|
| 1561 | assumes a global monomial ordering in r; |
---|
| 1562 | assumes that not both p and q are NULL; |
---|
| 1563 | returns the gcd of p and q; |
---|
[f0b01f] | 1564 | moreover, afterwards pFactor and qFactor contain appropriate |
---|
| 1565 | factors such that gcd(p, q) = p * pFactor + q * qFactor; |
---|
[69fb9d0] | 1566 | leaves p and q unmodified */ |
---|
[f0b01f] | 1567 | poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r) |
---|
[ba2359] | 1568 | { |
---|
[f0b01f] | 1569 | assume((p != NULL) || (q != NULL)); |
---|
[c28ecf] | 1570 | poly a = p; poly b = q; BOOLEAN aCorrespondsToP = TRUE; |
---|
[69fb9d0] | 1571 | if (p_Deg(a, r) < p_Deg(b, r)) |
---|
[c28ecf] | 1572 | { a = q; b = p; aCorrespondsToP = FALSE; } |
---|
[69fb9d0] | 1573 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
[c28ecf] | 1574 | poly aFactor = NULL; poly bFactor = NULL; |
---|
| 1575 | poly theGcd = p_ExtGcdHelper(a, aFactor, b, bFactor, r); |
---|
| 1576 | if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; } |
---|
| 1577 | else { pFactor = bFactor; qFactor = aFactor; } |
---|
| 1578 | return theGcd; |
---|
[ba2359] | 1579 | } |
---|
| 1580 | |
---|
[ac0bd6] | 1581 | /*2 |
---|
| 1582 | * returns the partial differentiate of a by the k-th variable |
---|
| 1583 | * does not destroy the input |
---|
| 1584 | */ |
---|
| 1585 | poly p_Diff(poly a, int k, const ring r) |
---|
| 1586 | { |
---|
| 1587 | poly res, f, last; |
---|
| 1588 | number t; |
---|
| 1589 | |
---|
| 1590 | last = res = NULL; |
---|
| 1591 | while (a!=NULL) |
---|
| 1592 | { |
---|
| 1593 | if (p_GetExp(a,k,r)!=0) |
---|
| 1594 | { |
---|
| 1595 | f = p_LmInit(a,r); |
---|
| 1596 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
| 1597 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
| 1598 | n_Delete(&t,r->cf); |
---|
| 1599 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
| 1600 | p_LmDelete(&f,r); |
---|
| 1601 | else |
---|
| 1602 | { |
---|
| 1603 | p_DecrExp(f,k,r); |
---|
| 1604 | p_Setm(f,r); |
---|
| 1605 | if (res==NULL) |
---|
| 1606 | { |
---|
| 1607 | res=last=f; |
---|
| 1608 | } |
---|
| 1609 | else |
---|
| 1610 | { |
---|
| 1611 | pNext(last)=f; |
---|
| 1612 | last=f; |
---|
| 1613 | } |
---|
| 1614 | } |
---|
| 1615 | } |
---|
| 1616 | pIter(a); |
---|
| 1617 | } |
---|
| 1618 | return res; |
---|
| 1619 | } |
---|
[5162db] | 1620 | |
---|
[8a8c9e] | 1621 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
[5162db] | 1622 | { |
---|
| 1623 | int i,j,s; |
---|
| 1624 | number n,h,hh; |
---|
| 1625 | poly p=p_One(r); |
---|
| 1626 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
| 1627 | for(i=rVar(r);i>0;i--) |
---|
| 1628 | { |
---|
| 1629 | s=p_GetExp(b,i,r); |
---|
| 1630 | if (s<p_GetExp(a,i,r)) |
---|
| 1631 | { |
---|
| 1632 | n_Delete(&n,r->cf); |
---|
| 1633 | p_LmDelete(&p,r); |
---|
| 1634 | return NULL; |
---|
| 1635 | } |
---|
| 1636 | if (multiply) |
---|
| 1637 | { |
---|
| 1638 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
| 1639 | { |
---|
| 1640 | h = n_Init(s,r->cf); |
---|
| 1641 | hh=n_Mult(n,h,r->cf); |
---|
| 1642 | n_Delete(&h,r->cf); |
---|
| 1643 | n_Delete(&n,r->cf); |
---|
| 1644 | n=hh; |
---|
| 1645 | s--; |
---|
| 1646 | } |
---|
| 1647 | p_SetExp(p,i,s,r); |
---|
| 1648 | } |
---|
| 1649 | else |
---|
| 1650 | { |
---|
| 1651 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
| 1652 | } |
---|
| 1653 | } |
---|
| 1654 | p_Setm(p,r); |
---|
| 1655 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
| 1656 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
| 1657 | return p; |
---|
| 1658 | } |
---|
| 1659 | |
---|
| 1660 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
| 1661 | { |
---|
| 1662 | poly result=NULL; |
---|
| 1663 | poly h; |
---|
| 1664 | for(;a!=NULL;pIter(a)) |
---|
| 1665 | { |
---|
| 1666 | for(h=b;h!=NULL;pIter(h)) |
---|
| 1667 | { |
---|
| 1668 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
| 1669 | } |
---|
| 1670 | } |
---|
| 1671 | return result; |
---|
| 1672 | } |
---|
[bf183f] | 1673 | /*2 |
---|
| 1674 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
| 1675 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
| 1676 | */ |
---|
| 1677 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
| 1678 | { |
---|
| 1679 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
| 1680 | } |
---|
| 1681 | |
---|
| 1682 | /*3 |
---|
| 1683 | * compute for a monomial m |
---|
| 1684 | * the power m^exp, exp > 1 |
---|
| 1685 | * destroys p |
---|
| 1686 | */ |
---|
| 1687 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
| 1688 | { |
---|
| 1689 | int i; |
---|
| 1690 | |
---|
[8a8c9e] | 1691 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
[bf183f] | 1692 | { |
---|
| 1693 | number x, y; |
---|
| 1694 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1695 | n_Power(y,exp,&x,r->cf); |
---|
| 1696 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1697 | pSetCoeff0(p,x); |
---|
| 1698 | } |
---|
| 1699 | for (i=rVar(r); i!=0; i--) |
---|
| 1700 | { |
---|
| 1701 | p_MultExp(p,i, exp,r); |
---|
| 1702 | } |
---|
| 1703 | p_Setm(p,r); |
---|
| 1704 | return p; |
---|
| 1705 | } |
---|
| 1706 | |
---|
| 1707 | /*3 |
---|
| 1708 | * compute for monomials p*q |
---|
| 1709 | * destroys p, keeps q |
---|
| 1710 | */ |
---|
| 1711 | static void p_MonMult(poly p, poly q, const ring r) |
---|
| 1712 | { |
---|
| 1713 | number x, y; |
---|
| 1714 | |
---|
| 1715 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1716 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
| 1717 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1718 | pSetCoeff0(p,x); |
---|
[abb4787] | 1719 | //for (int i=pVariables; i!=0; i--) |
---|
[bf183f] | 1720 | //{ |
---|
| 1721 | // pAddExp(p,i, pGetExp(q,i)); |
---|
| 1722 | //} |
---|
| 1723 | //p->Order += q->Order; |
---|
| 1724 | p_ExpVectorAdd(p,q,r); |
---|
| 1725 | } |
---|
| 1726 | |
---|
| 1727 | /*3 |
---|
| 1728 | * compute for monomials p*q |
---|
| 1729 | * keeps p, q |
---|
| 1730 | */ |
---|
| 1731 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
| 1732 | { |
---|
| 1733 | number x; |
---|
| 1734 | poly r = p_Init(rr); |
---|
| 1735 | |
---|
[8a8c9e] | 1736 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
[bf183f] | 1737 | pSetCoeff0(r,x); |
---|
| 1738 | p_ExpVectorSum(r,p, q, rr); |
---|
| 1739 | return r; |
---|
| 1740 | } |
---|
| 1741 | |
---|
[5679049] | 1742 | /*3 |
---|
| 1743 | * create binomial coef. |
---|
| 1744 | */ |
---|
| 1745 | static number* pnBin(int exp, const ring r) |
---|
| 1746 | { |
---|
| 1747 | int e, i, h; |
---|
| 1748 | number x, y, *bin=NULL; |
---|
| 1749 | |
---|
| 1750 | x = n_Init(exp,r->cf); |
---|
| 1751 | if (n_IsZero(x,r->cf)) |
---|
| 1752 | { |
---|
| 1753 | n_Delete(&x,r->cf); |
---|
| 1754 | return bin; |
---|
| 1755 | } |
---|
| 1756 | h = (exp >> 1) + 1; |
---|
| 1757 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
| 1758 | bin[1] = x; |
---|
| 1759 | if (exp < 4) |
---|
| 1760 | return bin; |
---|
| 1761 | i = exp - 1; |
---|
| 1762 | for (e=2; e<h; e++) |
---|
| 1763 | { |
---|
| 1764 | x = n_Init(i,r->cf); |
---|
| 1765 | i--; |
---|
| 1766 | y = n_Mult(x,bin[e-1],r->cf); |
---|
| 1767 | n_Delete(&x,r->cf); |
---|
| 1768 | x = n_Init(e,r->cf); |
---|
| 1769 | bin[e] = n_IntDiv(y,x,r->cf); |
---|
| 1770 | n_Delete(&x,r->cf); |
---|
| 1771 | n_Delete(&y,r->cf); |
---|
| 1772 | } |
---|
| 1773 | return bin; |
---|
| 1774 | } |
---|
| 1775 | |
---|
[1389a4] | 1776 | static void pnFreeBin(number *bin, int exp,const coeffs r) |
---|
| 1777 | { |
---|
| 1778 | int e, h = (exp >> 1) + 1; |
---|
| 1779 | |
---|
| 1780 | if (bin[1] != NULL) |
---|
| 1781 | { |
---|
| 1782 | for (e=1; e<h; e++) |
---|
| 1783 | n_Delete(&(bin[e]),r); |
---|
| 1784 | } |
---|
| 1785 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
---|
| 1786 | } |
---|
| 1787 | |
---|
[bf183f] | 1788 | /* |
---|
| 1789 | * compute for a poly p = head+tail, tail is monomial |
---|
| 1790 | * (head + tail)^exp, exp > 1 |
---|
| 1791 | * with binomial coef. |
---|
| 1792 | */ |
---|
| 1793 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
| 1794 | { |
---|
| 1795 | int eh, e; |
---|
| 1796 | long al; |
---|
| 1797 | poly *a; |
---|
| 1798 | poly tail, b, res, h; |
---|
| 1799 | number x; |
---|
[7eb7b5] | 1800 | number *bin = pnBin(exp,r); |
---|
[bf183f] | 1801 | |
---|
| 1802 | tail = pNext(p); |
---|
| 1803 | if (bin == NULL) |
---|
| 1804 | { |
---|
| 1805 | p_MonPower(p,exp,r); |
---|
| 1806 | p_MonPower(tail,exp,r); |
---|
| 1807 | #ifdef PDEBUG |
---|
| 1808 | p_Test(p,r); |
---|
| 1809 | #endif |
---|
| 1810 | return p; |
---|
| 1811 | } |
---|
| 1812 | eh = exp >> 1; |
---|
| 1813 | al = (exp + 1) * sizeof(poly); |
---|
| 1814 | a = (poly *)omAlloc(al); |
---|
| 1815 | a[1] = p; |
---|
| 1816 | for (e=1; e<exp; e++) |
---|
| 1817 | { |
---|
| 1818 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
| 1819 | } |
---|
| 1820 | res = a[exp]; |
---|
| 1821 | b = p_Head(tail,r); |
---|
| 1822 | for (e=exp-1; e>eh; e--) |
---|
| 1823 | { |
---|
| 1824 | h = a[e]; |
---|
[8a8c9e] | 1825 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1826 | p_SetCoeff(h,x,r); |
---|
| 1827 | p_MonMult(h,b,r); |
---|
| 1828 | res = pNext(res) = h; |
---|
| 1829 | p_MonMult(b,tail,r); |
---|
| 1830 | } |
---|
| 1831 | for (e=eh; e!=0; e--) |
---|
| 1832 | { |
---|
| 1833 | h = a[e]; |
---|
[8a8c9e] | 1834 | x = n_Mult(bin[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 | p_LmDelete(&tail,r); |
---|
| 1841 | pNext(res) = b; |
---|
| 1842 | pNext(b) = NULL; |
---|
| 1843 | res = a[exp]; |
---|
| 1844 | omFreeSize((ADDRESS)a, al); |
---|
[1389a4] | 1845 | pnFreeBin(bin, exp, r->cf); |
---|
[bf183f] | 1846 | // tail=res; |
---|
| 1847 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
| 1848 | // { |
---|
| 1849 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
| 1850 | // { |
---|
| 1851 | // pLmDelete(&pNext(tail)); |
---|
| 1852 | // } |
---|
| 1853 | // else |
---|
| 1854 | // pIter(tail); |
---|
| 1855 | // } |
---|
| 1856 | #ifdef PDEBUG |
---|
| 1857 | p_Test(res,r); |
---|
| 1858 | #endif |
---|
| 1859 | return res; |
---|
| 1860 | } |
---|
| 1861 | |
---|
| 1862 | static poly p_Pow(poly p, int i, const ring r) |
---|
| 1863 | { |
---|
| 1864 | poly rc = p_Copy(p,r); |
---|
| 1865 | i -= 2; |
---|
| 1866 | do |
---|
| 1867 | { |
---|
| 1868 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
| 1869 | p_Normalize(rc,r); |
---|
| 1870 | i--; |
---|
| 1871 | } |
---|
| 1872 | while (i != 0); |
---|
| 1873 | return p_Mult_q(rc,p,r); |
---|
| 1874 | } |
---|
| 1875 | |
---|
| 1876 | /*2 |
---|
| 1877 | * returns the i-th power of p |
---|
| 1878 | * p will be destroyed |
---|
| 1879 | */ |
---|
| 1880 | poly p_Power(poly p, int i, const ring r) |
---|
| 1881 | { |
---|
| 1882 | poly rc=NULL; |
---|
| 1883 | |
---|
| 1884 | if (i==0) |
---|
| 1885 | { |
---|
| 1886 | p_Delete(&p,r); |
---|
| 1887 | return p_One(r); |
---|
| 1888 | } |
---|
| 1889 | |
---|
| 1890 | if(p!=NULL) |
---|
| 1891 | { |
---|
| 1892 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask))) |
---|
| 1893 | { |
---|
| 1894 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
| 1895 | return NULL; |
---|
| 1896 | } |
---|
| 1897 | switch (i) |
---|
| 1898 | { |
---|
| 1899 | // cannot happen, see above |
---|
| 1900 | // case 0: |
---|
| 1901 | // { |
---|
| 1902 | // rc=pOne(); |
---|
| 1903 | // pDelete(&p); |
---|
| 1904 | // break; |
---|
| 1905 | // } |
---|
| 1906 | case 1: |
---|
| 1907 | rc=p; |
---|
| 1908 | break; |
---|
| 1909 | case 2: |
---|
| 1910 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
| 1911 | break; |
---|
| 1912 | default: |
---|
| 1913 | if (i < 0) |
---|
| 1914 | { |
---|
| 1915 | p_Delete(&p,r); |
---|
| 1916 | return NULL; |
---|
| 1917 | } |
---|
| 1918 | else |
---|
| 1919 | { |
---|
| 1920 | #ifdef HAVE_PLURAL |
---|
| 1921 | if (rIsPluralRing(r)) /* in the NC case nothing helps :-( */ |
---|
| 1922 | { |
---|
| 1923 | int j=i; |
---|
| 1924 | rc = p_Copy(p,r); |
---|
| 1925 | while (j>1) |
---|
| 1926 | { |
---|
| 1927 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
| 1928 | j--; |
---|
| 1929 | } |
---|
| 1930 | p_Delete(&p,r); |
---|
| 1931 | return rc; |
---|
| 1932 | } |
---|
| 1933 | #endif |
---|
| 1934 | rc = pNext(p); |
---|
| 1935 | if (rc == NULL) |
---|
| 1936 | return p_MonPower(p,i,r); |
---|
| 1937 | /* else: binom ?*/ |
---|
| 1938 | int char_p=rChar(r); |
---|
| 1939 | if ((pNext(rc) != NULL) |
---|
| 1940 | #ifdef HAVE_RINGS |
---|
| 1941 | || rField_is_Ring(r) |
---|
| 1942 | #endif |
---|
| 1943 | ) |
---|
| 1944 | return p_Pow(p,i,r); |
---|
| 1945 | if ((char_p==0) || (i<=char_p)) |
---|
| 1946 | return p_TwoMonPower(p,i,r); |
---|
| 1947 | poly p_p=p_TwoMonPower(p_Copy(p,r),char_p,r); |
---|
| 1948 | return p_Mult_q(p_Power(p,i-char_p,r),p_p,r); |
---|
| 1949 | } |
---|
| 1950 | /*end default:*/ |
---|
| 1951 | } |
---|
| 1952 | } |
---|
| 1953 | return rc; |
---|
| 1954 | } |
---|
[8d1d30c] | 1955 | |
---|
| 1956 | /* --------------------------------------------------------------------------------*/ |
---|
| 1957 | /* content suff */ |
---|
| 1958 | |
---|
| 1959 | static number p_InitContent(poly ph, const ring r); |
---|
| 1960 | static number p_InitContent_a(poly ph, const ring r); |
---|
| 1961 | |
---|
| 1962 | void p_Content(poly ph, const ring r) |
---|
| 1963 | { |
---|
| 1964 | #ifdef HAVE_RINGS |
---|
| 1965 | if (rField_is_Ring(r)) |
---|
| 1966 | { |
---|
| 1967 | if ((ph!=NULL) && rField_has_Units(r)) |
---|
| 1968 | { |
---|
[8a8c9e] | 1969 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
[8d1d30c] | 1970 | if (!n_IsOne(k,r->cf)) |
---|
| 1971 | { |
---|
| 1972 | number tmpGMP = k; |
---|
| 1973 | k = n_Invers(k,r->cf); |
---|
| 1974 | n_Delete(&tmpGMP,r->cf); |
---|
| 1975 | poly h = pNext(ph); |
---|
| 1976 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
| 1977 | while (h != NULL) |
---|
| 1978 | { |
---|
| 1979 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
| 1980 | pIter(h); |
---|
| 1981 | } |
---|
| 1982 | } |
---|
| 1983 | n_Delete(&k,r->cf); |
---|
| 1984 | } |
---|
| 1985 | return; |
---|
| 1986 | } |
---|
| 1987 | #endif |
---|
| 1988 | number h,d; |
---|
| 1989 | poly p; |
---|
| 1990 | |
---|
| 1991 | if(TEST_OPT_CONTENTSB) return; |
---|
| 1992 | if(pNext(ph)==NULL) |
---|
| 1993 | { |
---|
[8a8c9e] | 1994 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
[8d1d30c] | 1995 | } |
---|
| 1996 | else |
---|
| 1997 | { |
---|
| 1998 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 1999 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8a8c9e] | 2000 | if (rField_is_Q(r)) |
---|
[8d1d30c] | 2001 | { |
---|
| 2002 | h=p_InitContent(ph,r); |
---|
| 2003 | p=ph; |
---|
| 2004 | } |
---|
[4c6e420] | 2005 | else if (rField_is_Extension(r) |
---|
| 2006 | && |
---|
| 2007 | ( |
---|
| 2008 | (rPar(r)>1) || rMinpolyIsNULL(r) |
---|
| 2009 | ) |
---|
| 2010 | ) |
---|
[8d1d30c] | 2011 | { |
---|
| 2012 | h=p_InitContent_a(ph,r); |
---|
| 2013 | p=ph; |
---|
| 2014 | } |
---|
| 2015 | else |
---|
| 2016 | { |
---|
| 2017 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2018 | p = pNext(ph); |
---|
| 2019 | } |
---|
| 2020 | while (p!=NULL) |
---|
| 2021 | { |
---|
| 2022 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2023 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2024 | n_Delete(&h,r->cf); |
---|
| 2025 | h = d; |
---|
| 2026 | if(n_IsOne(h,r->cf)) |
---|
| 2027 | { |
---|
| 2028 | break; |
---|
| 2029 | } |
---|
| 2030 | pIter(p); |
---|
| 2031 | } |
---|
| 2032 | p = ph; |
---|
| 2033 | //number tmp; |
---|
| 2034 | if(!n_IsOne(h,r->cf)) |
---|
| 2035 | { |
---|
| 2036 | while (p!=NULL) |
---|
| 2037 | { |
---|
| 2038 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2039 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2040 | //if (!nEqual(d,tmp)) |
---|
| 2041 | //{ |
---|
| 2042 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2043 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
| 2044 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
| 2045 | //} |
---|
| 2046 | //nDelete(&tmp); |
---|
| 2047 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2048 | p_SetCoeff(p,d,r); |
---|
| 2049 | pIter(p); |
---|
| 2050 | } |
---|
| 2051 | } |
---|
| 2052 | n_Delete(&h,r->cf); |
---|
| 2053 | #ifdef HAVE_FACTORY |
---|
[02c42d] | 2054 | if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
[8d1d30c] | 2055 | { |
---|
[ce3f53c] | 2056 | singclap_divide_content(ph, r); |
---|
[8d1d30c] | 2057 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2058 | } |
---|
| 2059 | #endif |
---|
| 2060 | if (rField_is_Q_a(r)) |
---|
| 2061 | { |
---|
[abb4787] | 2062 | //number hzz = nlInit(1, r->cf); |
---|
[8d1d30c] | 2063 | h = nlInit(1, r->cf); |
---|
| 2064 | p=ph; |
---|
[fd01a8] | 2065 | Werror("longalg missing 1"); |
---|
[9c83f2] | 2066 | #if 0 |
---|
[8d1d30c] | 2067 | while (p!=NULL) |
---|
| 2068 | { // each monom: coeff in Q_a |
---|
| 2069 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
[8a8c9e] | 2070 | poly c_n=c_n_n->z; |
---|
[8d1d30c] | 2071 | while (c_n!=NULL) |
---|
| 2072 | { // each monom: coeff in Q |
---|
[6ccdd3a] | 2073 | d=nlLcm(hzz,pGetCoeff(c_n),r->extRing->cf); |
---|
| 2074 | n_Delete(&hzz,r->extRing->cf); |
---|
[8d1d30c] | 2075 | hzz=d; |
---|
| 2076 | pIter(c_n); |
---|
| 2077 | } |
---|
| 2078 | c_n=c_n_n->n; |
---|
| 2079 | while (c_n!=NULL) |
---|
| 2080 | { // each monom: coeff in Q |
---|
[6ccdd3a] | 2081 | d=nlLcm(h,pGetCoeff(c_n),r->extRing->cf); |
---|
| 2082 | n_Delete(&h,r->extRing->cf); |
---|
[8d1d30c] | 2083 | h=d; |
---|
| 2084 | pIter(c_n); |
---|
| 2085 | } |
---|
| 2086 | pIter(p); |
---|
| 2087 | } |
---|
| 2088 | /* hzz contains the 1/lcm of all denominators in c_n_n->z*/ |
---|
| 2089 | /* h contains the 1/lcm of all denominators in c_n_n->n*/ |
---|
[6ccdd3a] | 2090 | number htmp=nlInvers(h,r->extRing->cf); |
---|
| 2091 | number hzztmp=nlInvers(hzz,r->extRing->cf); |
---|
| 2092 | number hh=nlMult(hzz,h,r->extRing->cf); |
---|
| 2093 | nlDelete(&hzz,r->extRing->cf); |
---|
| 2094 | nlDelete(&h,r->extRing->cf); |
---|
| 2095 | number hg=nlGcd(hzztmp,htmp,r->extRing->cf); |
---|
| 2096 | nlDelete(&hzztmp,r->extRing->cf); |
---|
| 2097 | nlDelete(&htmp,r->extRing->cf); |
---|
| 2098 | h=nlMult(hh,hg,r->extRing->cf); |
---|
| 2099 | nlDelete(&hg,r->extRing->cf); |
---|
| 2100 | nlDelete(&hh,r->extRing->cf); |
---|
| 2101 | nlNormalize(h,r->extRing->cf); |
---|
| 2102 | if(!nlIsOne(h,r->extRing->cf)) |
---|
[8d1d30c] | 2103 | { |
---|
| 2104 | p=ph; |
---|
| 2105 | while (p!=NULL) |
---|
| 2106 | { // each monom: coeff in Q_a |
---|
| 2107 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
[8a8c9e] | 2108 | poly c_n=c_n_n->z; |
---|
[8d1d30c] | 2109 | while (c_n!=NULL) |
---|
| 2110 | { // each monom: coeff in Q |
---|
[6ccdd3a] | 2111 | d=nlMult(h,pGetCoeff(c_n),r->extRing->cf); |
---|
| 2112 | nlNormalize(d,r->extRing->cf); |
---|
| 2113 | nlDelete(&pGetCoeff(c_n),r->extRing->cf); |
---|
[8d1d30c] | 2114 | pGetCoeff(c_n)=d; |
---|
| 2115 | pIter(c_n); |
---|
| 2116 | } |
---|
| 2117 | c_n=c_n_n->n; |
---|
| 2118 | while (c_n!=NULL) |
---|
| 2119 | { // each monom: coeff in Q |
---|
[6ccdd3a] | 2120 | d=nlMult(h,pGetCoeff(c_n),r->extRing->cf); |
---|
| 2121 | nlNormalize(d,r->extRing->cf); |
---|
| 2122 | nlDelete(&pGetCoeff(c_n),r->extRing->cf); |
---|
[8d1d30c] | 2123 | pGetCoeff(c_n)=d; |
---|
| 2124 | pIter(c_n); |
---|
| 2125 | } |
---|
| 2126 | pIter(p); |
---|
| 2127 | } |
---|
| 2128 | } |
---|
[6ccdd3a] | 2129 | nlDelete(&h,r->extRing->cf); |
---|
[9c83f2] | 2130 | #endif |
---|
[8d1d30c] | 2131 | } |
---|
| 2132 | } |
---|
| 2133 | } |
---|
[5698bb] | 2134 | #if 0 // currently not used |
---|
[8d1d30c] | 2135 | void p_SimpleContent(poly ph,int smax, const ring r) |
---|
| 2136 | { |
---|
| 2137 | if(TEST_OPT_CONTENTSB) return; |
---|
| 2138 | if (ph==NULL) return; |
---|
| 2139 | if (pNext(ph)==NULL) |
---|
| 2140 | { |
---|
| 2141 | p_SetCoeff(ph,n_Init(1,r_cf),r); |
---|
| 2142 | return; |
---|
| 2143 | } |
---|
| 2144 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
| 2145 | { |
---|
| 2146 | return; |
---|
| 2147 | } |
---|
| 2148 | number d=p_InitContent(ph,r); |
---|
| 2149 | if (nlSize(d,r->cf)<=smax) |
---|
| 2150 | { |
---|
| 2151 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
| 2152 | return; |
---|
| 2153 | } |
---|
| 2154 | poly p=ph; |
---|
| 2155 | number h=d; |
---|
| 2156 | if (smax==1) smax=2; |
---|
| 2157 | while (p!=NULL) |
---|
| 2158 | { |
---|
| 2159 | #if 0 |
---|
| 2160 | d=nlGcd(h,pGetCoeff(p),r->cf); |
---|
| 2161 | nlDelete(&h,r->cf); |
---|
| 2162 | h = d; |
---|
| 2163 | #else |
---|
| 2164 | nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
| 2165 | #endif |
---|
| 2166 | if(nlSize(h,r->cf)<smax) |
---|
| 2167 | { |
---|
| 2168 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
| 2169 | return; |
---|
| 2170 | } |
---|
| 2171 | pIter(p); |
---|
| 2172 | } |
---|
| 2173 | p = ph; |
---|
| 2174 | if (!nlGreaterZero(pGetCoeff(p),r->cf)) h=nlNeg(h,r->cf); |
---|
| 2175 | if(nlIsOne(h,r->cf)) return; |
---|
| 2176 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
| 2177 | while (p!=NULL) |
---|
| 2178 | { |
---|
| 2179 | #if 1 |
---|
| 2180 | d = nlIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2181 | p_SetCoeff(p,d,r); |
---|
| 2182 | #else |
---|
| 2183 | nlInpIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2184 | #endif |
---|
| 2185 | pIter(p); |
---|
| 2186 | } |
---|
| 2187 | nlDelete(&h,r->cf); |
---|
| 2188 | } |
---|
[5698bb] | 2189 | #endif |
---|
[8d1d30c] | 2190 | |
---|
| 2191 | static number p_InitContent(poly ph, const ring r) |
---|
| 2192 | // only for coefficients in Q |
---|
| 2193 | #if 0 |
---|
| 2194 | { |
---|
| 2195 | assume(!TEST_OPT_CONTENTSB); |
---|
| 2196 | assume(ph!=NULL); |
---|
| 2197 | assume(pNext(ph)!=NULL); |
---|
| 2198 | assume(rField_is_Q(r)); |
---|
| 2199 | if (pNext(pNext(ph))==NULL) |
---|
| 2200 | { |
---|
| 2201 | return nlGetNom(pGetCoeff(pNext(ph)),r->cf); |
---|
| 2202 | } |
---|
| 2203 | poly p=ph; |
---|
| 2204 | number n1=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2205 | pIter(p); |
---|
| 2206 | number n2=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2207 | pIter(p); |
---|
| 2208 | number d; |
---|
| 2209 | number t; |
---|
| 2210 | loop |
---|
| 2211 | { |
---|
| 2212 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2213 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2214 | if (nlGreaterZero(t,r->cf)) |
---|
| 2215 | d=nlAdd(n1,t,r->cf); |
---|
| 2216 | else |
---|
| 2217 | d=nlSub(n1,t,r->cf); |
---|
| 2218 | nlDelete(&t,r->cf); |
---|
| 2219 | nlDelete(&n1,r->cf); |
---|
| 2220 | n1=d; |
---|
| 2221 | pIter(p); |
---|
| 2222 | if (p==NULL) break; |
---|
| 2223 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2224 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2225 | if (nlGreaterZero(t,r->cf)) |
---|
| 2226 | d=nlAdd(n2,t,r->cf); |
---|
| 2227 | else |
---|
| 2228 | d=nlSub(n2,t,r->cf); |
---|
| 2229 | nlDelete(&t,r->cf); |
---|
| 2230 | nlDelete(&n2,r->cf); |
---|
| 2231 | n2=d; |
---|
| 2232 | pIter(p); |
---|
| 2233 | if (p==NULL) break; |
---|
| 2234 | } |
---|
| 2235 | d=nlGcd(n1,n2,r->cf); |
---|
| 2236 | nlDelete(&n1,r->cf); |
---|
| 2237 | nlDelete(&n2,r->cf); |
---|
| 2238 | return d; |
---|
| 2239 | } |
---|
| 2240 | #else |
---|
| 2241 | { |
---|
| 2242 | number d=pGetCoeff(ph); |
---|
| 2243 | if(SR_HDL(d)&SR_INT) return d; |
---|
| 2244 | int s=mpz_size1(d->z); |
---|
| 2245 | int s2=-1; |
---|
| 2246 | number d2; |
---|
| 2247 | loop |
---|
| 2248 | { |
---|
| 2249 | pIter(ph); |
---|
| 2250 | if(ph==NULL) |
---|
| 2251 | { |
---|
| 2252 | if (s2==-1) return nlCopy(d,r->cf); |
---|
| 2253 | break; |
---|
| 2254 | } |
---|
| 2255 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
| 2256 | { |
---|
| 2257 | s2=s; |
---|
| 2258 | d2=d; |
---|
| 2259 | s=0; |
---|
| 2260 | d=pGetCoeff(ph); |
---|
| 2261 | if (s2==0) break; |
---|
| 2262 | } |
---|
| 2263 | else |
---|
| 2264 | if (mpz_size1((pGetCoeff(ph)->z))<=s) |
---|
| 2265 | { |
---|
| 2266 | s2=s; |
---|
| 2267 | d2=d; |
---|
| 2268 | d=pGetCoeff(ph); |
---|
| 2269 | s=mpz_size1(d->z); |
---|
| 2270 | } |
---|
| 2271 | } |
---|
| 2272 | return nlGcd(d,d2,r->cf); |
---|
| 2273 | } |
---|
| 2274 | #endif |
---|
| 2275 | |
---|
| 2276 | number p_InitContent_a(poly ph, const ring r) |
---|
[0afa07] | 2277 | // only for coefficients in K(a)/<minpoly(a)> and K(t_1, t_2, ..., t_n) |
---|
[8d1d30c] | 2278 | { |
---|
| 2279 | number d=pGetCoeff(ph); |
---|
[0afa07] | 2280 | /* old: int s=n_ParDeg(d,r->cf); new: */ |
---|
| 2281 | int s = p_Totaldegree((poly)d, r->cf->extRing); |
---|
| 2282 | if (s <=1) return n_Copy(d,r->cf); |
---|
[8d1d30c] | 2283 | int s2=-1; |
---|
| 2284 | number d2; |
---|
| 2285 | int ss; |
---|
| 2286 | loop |
---|
| 2287 | { |
---|
| 2288 | pIter(ph); |
---|
| 2289 | if(ph==NULL) |
---|
| 2290 | { |
---|
[1389a4] | 2291 | if (s2==-1) return n_Copy(d,r->cf); |
---|
[8d1d30c] | 2292 | break; |
---|
| 2293 | } |
---|
[0afa07] | 2294 | /* old: if ((ss=n_ParDeg(pGetCoeff(ph),r->cf))<s) new: */ |
---|
| 2295 | if ((ss = p_Totaldegree((poly)pGetCoeff(ph), r->cf->extRing)) < s) |
---|
[8d1d30c] | 2296 | { |
---|
| 2297 | s2=s; |
---|
| 2298 | d2=d; |
---|
| 2299 | s=ss; |
---|
| 2300 | d=pGetCoeff(ph); |
---|
| 2301 | if (s2<=1) break; |
---|
| 2302 | } |
---|
| 2303 | } |
---|
[1389a4] | 2304 | return n_Gcd(d,d2,r->cf); |
---|
[8d1d30c] | 2305 | } |
---|
| 2306 | |
---|
| 2307 | |
---|
| 2308 | //void pContent(poly ph) |
---|
| 2309 | //{ |
---|
| 2310 | // number h,d; |
---|
| 2311 | // poly p; |
---|
| 2312 | // |
---|
| 2313 | // p = ph; |
---|
| 2314 | // if(pNext(p)==NULL) |
---|
| 2315 | // { |
---|
| 2316 | // pSetCoeff(p,nInit(1)); |
---|
| 2317 | // } |
---|
| 2318 | // else |
---|
| 2319 | // { |
---|
| 2320 | //#ifdef PDEBUG |
---|
| 2321 | // if (!pTest(p)) return; |
---|
| 2322 | //#endif |
---|
| 2323 | // nNormalize(pGetCoeff(p)); |
---|
| 2324 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
| 2325 | // { |
---|
| 2326 | // ph = pNeg(ph); |
---|
| 2327 | // nNormalize(pGetCoeff(p)); |
---|
| 2328 | // } |
---|
| 2329 | // h=pGetCoeff(p); |
---|
| 2330 | // pIter(p); |
---|
| 2331 | // while (p!=NULL) |
---|
| 2332 | // { |
---|
| 2333 | // nNormalize(pGetCoeff(p)); |
---|
| 2334 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
| 2335 | // pIter(p); |
---|
| 2336 | // } |
---|
| 2337 | // h=nCopy(h); |
---|
| 2338 | // p=ph; |
---|
| 2339 | // while (p!=NULL) |
---|
| 2340 | // { |
---|
[32d07a5] | 2341 | // d=n_Gcd(h,pGetCoeff(p)); |
---|
[8d1d30c] | 2342 | // nDelete(&h); |
---|
| 2343 | // h = d; |
---|
| 2344 | // if(nIsOne(h)) |
---|
| 2345 | // { |
---|
| 2346 | // break; |
---|
| 2347 | // } |
---|
| 2348 | // pIter(p); |
---|
| 2349 | // } |
---|
| 2350 | // p = ph; |
---|
| 2351 | // //number tmp; |
---|
| 2352 | // if(!nIsOne(h)) |
---|
| 2353 | // { |
---|
| 2354 | // while (p!=NULL) |
---|
| 2355 | // { |
---|
| 2356 | // d = nIntDiv(pGetCoeff(p),h); |
---|
| 2357 | // pSetCoeff(p,d); |
---|
| 2358 | // pIter(p); |
---|
| 2359 | // } |
---|
| 2360 | // } |
---|
| 2361 | // nDelete(&h); |
---|
| 2362 | //#ifdef HAVE_FACTORY |
---|
| 2363 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2364 | // { |
---|
| 2365 | // pTest(ph); |
---|
| 2366 | // singclap_divide_content(ph); |
---|
| 2367 | // pTest(ph); |
---|
| 2368 | // } |
---|
| 2369 | //#endif |
---|
| 2370 | // } |
---|
| 2371 | //} |
---|
| 2372 | #if 0 |
---|
| 2373 | void p_Content(poly ph, const ring r) |
---|
| 2374 | { |
---|
| 2375 | number h,d; |
---|
| 2376 | poly p; |
---|
| 2377 | |
---|
| 2378 | if(pNext(ph)==NULL) |
---|
| 2379 | { |
---|
| 2380 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
| 2381 | } |
---|
| 2382 | else |
---|
| 2383 | { |
---|
| 2384 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 2385 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2386 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2387 | p = pNext(ph); |
---|
| 2388 | while (p!=NULL) |
---|
| 2389 | { |
---|
| 2390 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2391 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2392 | n_Delete(&h,r->cf); |
---|
| 2393 | h = d; |
---|
| 2394 | if(n_IsOne(h,r->cf)) |
---|
| 2395 | { |
---|
| 2396 | break; |
---|
| 2397 | } |
---|
| 2398 | pIter(p); |
---|
| 2399 | } |
---|
| 2400 | p = ph; |
---|
| 2401 | //number tmp; |
---|
| 2402 | if(!n_IsOne(h,r->cf)) |
---|
| 2403 | { |
---|
| 2404 | while (p!=NULL) |
---|
| 2405 | { |
---|
| 2406 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2407 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2408 | //if (!nEqual(d,tmp)) |
---|
| 2409 | //{ |
---|
| 2410 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2411 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
| 2412 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
| 2413 | //} |
---|
| 2414 | //nDelete(&tmp); |
---|
| 2415 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2416 | p_SetCoeff(p,d,r->cf); |
---|
| 2417 | pIter(p); |
---|
| 2418 | } |
---|
| 2419 | } |
---|
| 2420 | n_Delete(&h,r->cf); |
---|
| 2421 | #ifdef HAVE_FACTORY |
---|
| 2422 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2423 | //{ |
---|
| 2424 | // singclap_divide_content(ph); |
---|
| 2425 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
| 2426 | //} |
---|
| 2427 | #endif |
---|
| 2428 | } |
---|
| 2429 | } |
---|
| 2430 | #endif |
---|
[fbf8a6] | 2431 | /* ---------------------------------------------------------------------------*/ |
---|
| 2432 | /* cleardenom suff */ |
---|
[8d1d30c] | 2433 | poly p_Cleardenom(poly ph, const ring r) |
---|
| 2434 | { |
---|
| 2435 | poly start=ph; |
---|
| 2436 | number d, h; |
---|
| 2437 | poly p; |
---|
| 2438 | |
---|
| 2439 | #ifdef HAVE_RINGS |
---|
| 2440 | if (rField_is_Ring(r)) |
---|
| 2441 | { |
---|
| 2442 | p_Content(ph,r); |
---|
| 2443 | return start; |
---|
| 2444 | } |
---|
| 2445 | #endif |
---|
| 2446 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) return start; |
---|
| 2447 | p = ph; |
---|
| 2448 | if(pNext(p)==NULL) |
---|
| 2449 | { |
---|
| 2450 | if (TEST_OPT_CONTENTSB) |
---|
| 2451 | { |
---|
| 2452 | number n=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2453 | if (!n_IsOne(n,r->cf)) |
---|
| 2454 | { |
---|
| 2455 | number nn=n_Mult(pGetCoeff(p),n,r->cf); |
---|
| 2456 | n_Normalize(nn,r->cf); |
---|
| 2457 | p_SetCoeff(p,nn,r); |
---|
| 2458 | } |
---|
| 2459 | n_Delete(&n,r->cf); |
---|
| 2460 | } |
---|
| 2461 | else |
---|
| 2462 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
| 2463 | } |
---|
| 2464 | else |
---|
| 2465 | { |
---|
| 2466 | h = n_Init(1,r->cf); |
---|
| 2467 | while (p!=NULL) |
---|
| 2468 | { |
---|
[8a8c9e] | 2469 | n_Normalize(pGetCoeff(p),r->cf); |
---|
[8d1d30c] | 2470 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2471 | n_Delete(&h,r->cf); |
---|
| 2472 | h=d; |
---|
| 2473 | pIter(p); |
---|
| 2474 | } |
---|
| 2475 | /* contains the 1/lcm of all denominators */ |
---|
| 2476 | if(!n_IsOne(h,r->cf)) |
---|
| 2477 | { |
---|
| 2478 | p = ph; |
---|
| 2479 | while (p!=NULL) |
---|
| 2480 | { |
---|
| 2481 | /* should be: |
---|
| 2482 | * number hh; |
---|
| 2483 | * nGetDenom(p->coef,&hh); |
---|
| 2484 | * nMult(&h,&hh,&d); |
---|
| 2485 | * nNormalize(d); |
---|
| 2486 | * nDelete(&hh); |
---|
| 2487 | * nMult(d,p->coef,&hh); |
---|
| 2488 | * nDelete(&d); |
---|
| 2489 | * nDelete(&(p->coef)); |
---|
| 2490 | * p->coef =hh; |
---|
| 2491 | */ |
---|
| 2492 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2493 | n_Normalize(d,r->cf); |
---|
| 2494 | p_SetCoeff(p,d,r); |
---|
| 2495 | pIter(p); |
---|
| 2496 | } |
---|
| 2497 | n_Delete(&h,r->cf); |
---|
[5679049] | 2498 | if (n_GetChar(r->cf)==1) |
---|
[8d1d30c] | 2499 | { |
---|
| 2500 | loop |
---|
| 2501 | { |
---|
| 2502 | h = n_Init(1,r->cf); |
---|
| 2503 | p=ph; |
---|
| 2504 | while (p!=NULL) |
---|
| 2505 | { |
---|
| 2506 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2507 | n_Delete(&h,r->cf); |
---|
| 2508 | h=d; |
---|
| 2509 | pIter(p); |
---|
| 2510 | } |
---|
| 2511 | /* contains the 1/lcm of all denominators */ |
---|
| 2512 | if(!n_IsOne(h,r->cf)) |
---|
| 2513 | { |
---|
| 2514 | p = ph; |
---|
| 2515 | while (p!=NULL) |
---|
| 2516 | { |
---|
| 2517 | /* should be: |
---|
| 2518 | * number hh; |
---|
| 2519 | * nGetDenom(p->coef,&hh); |
---|
| 2520 | * nMult(&h,&hh,&d); |
---|
| 2521 | * nNormalize(d); |
---|
| 2522 | * nDelete(&hh); |
---|
| 2523 | * nMult(d,p->coef,&hh); |
---|
| 2524 | * nDelete(&d); |
---|
| 2525 | * nDelete(&(p->coef)); |
---|
| 2526 | * p->coef =hh; |
---|
| 2527 | */ |
---|
| 2528 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2529 | n_Normalize(d,r->cf); |
---|
| 2530 | p_SetCoeff(p,d,r); |
---|
| 2531 | pIter(p); |
---|
| 2532 | } |
---|
| 2533 | n_Delete(&h,r->cf); |
---|
| 2534 | } |
---|
| 2535 | else |
---|
| 2536 | { |
---|
| 2537 | n_Delete(&h,r->cf); |
---|
| 2538 | break; |
---|
| 2539 | } |
---|
| 2540 | } |
---|
| 2541 | } |
---|
| 2542 | } |
---|
| 2543 | if (h!=NULL) n_Delete(&h,r->cf); |
---|
[71ba5b8] | 2544 | |
---|
[8d1d30c] | 2545 | p_Content(ph,r); |
---|
| 2546 | #ifdef HAVE_RATGRING |
---|
| 2547 | if (rIsRatGRing(r)) |
---|
| 2548 | { |
---|
| 2549 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
| 2550 | pContentRat(ph); |
---|
| 2551 | start=ph; |
---|
| 2552 | } |
---|
| 2553 | #endif |
---|
| 2554 | } |
---|
| 2555 | return start; |
---|
| 2556 | } |
---|
| 2557 | |
---|
| 2558 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
| 2559 | { |
---|
| 2560 | number d, h; |
---|
| 2561 | poly p; |
---|
| 2562 | |
---|
| 2563 | p = ph; |
---|
| 2564 | if(pNext(p)==NULL) |
---|
| 2565 | { |
---|
| 2566 | c=n_Invers(pGetCoeff(p),r->cf); |
---|
| 2567 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
| 2568 | } |
---|
| 2569 | else |
---|
| 2570 | { |
---|
| 2571 | h = n_Init(1,r->cf); |
---|
| 2572 | while (p!=NULL) |
---|
| 2573 | { |
---|
| 2574 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2575 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2576 | n_Delete(&h,r->cf); |
---|
| 2577 | h=d; |
---|
| 2578 | pIter(p); |
---|
| 2579 | } |
---|
| 2580 | c=h; |
---|
| 2581 | /* contains the 1/lcm of all denominators */ |
---|
| 2582 | if(!n_IsOne(h,r->cf)) |
---|
| 2583 | { |
---|
| 2584 | p = ph; |
---|
| 2585 | while (p!=NULL) |
---|
| 2586 | { |
---|
| 2587 | /* should be: |
---|
| 2588 | * number hh; |
---|
| 2589 | * nGetDenom(p->coef,&hh); |
---|
| 2590 | * nMult(&h,&hh,&d); |
---|
| 2591 | * nNormalize(d); |
---|
| 2592 | * nDelete(&hh); |
---|
| 2593 | * nMult(d,p->coef,&hh); |
---|
| 2594 | * nDelete(&d); |
---|
| 2595 | * nDelete(&(p->coef)); |
---|
| 2596 | * p->coef =hh; |
---|
| 2597 | */ |
---|
| 2598 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2599 | n_Normalize(d,r->cf); |
---|
| 2600 | p_SetCoeff(p,d,r); |
---|
| 2601 | pIter(p); |
---|
| 2602 | } |
---|
| 2603 | if (rField_is_Q_a(r)) |
---|
| 2604 | { |
---|
| 2605 | loop |
---|
| 2606 | { |
---|
| 2607 | h = n_Init(1,r->cf); |
---|
| 2608 | p=ph; |
---|
| 2609 | while (p!=NULL) |
---|
| 2610 | { |
---|
| 2611 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2612 | n_Delete(&h,r->cf); |
---|
| 2613 | h=d; |
---|
| 2614 | pIter(p); |
---|
| 2615 | } |
---|
| 2616 | /* contains the 1/lcm of all denominators */ |
---|
| 2617 | if(!n_IsOne(h,r->cf)) |
---|
| 2618 | { |
---|
| 2619 | p = ph; |
---|
| 2620 | while (p!=NULL) |
---|
| 2621 | { |
---|
| 2622 | /* should be: |
---|
| 2623 | * number hh; |
---|
| 2624 | * nGetDenom(p->coef,&hh); |
---|
| 2625 | * nMult(&h,&hh,&d); |
---|
| 2626 | * nNormalize(d); |
---|
| 2627 | * nDelete(&hh); |
---|
| 2628 | * nMult(d,p->coef,&hh); |
---|
| 2629 | * nDelete(&d); |
---|
| 2630 | * nDelete(&(p->coef)); |
---|
| 2631 | * p->coef =hh; |
---|
| 2632 | */ |
---|
| 2633 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2634 | n_Normalize(d,r->cf); |
---|
| 2635 | p_SetCoeff(p,d,r); |
---|
| 2636 | pIter(p); |
---|
| 2637 | } |
---|
| 2638 | number t=n_Mult(c,h,r->cf); |
---|
| 2639 | n_Delete(&c,r->cf); |
---|
| 2640 | c=t; |
---|
| 2641 | } |
---|
| 2642 | else |
---|
| 2643 | { |
---|
| 2644 | break; |
---|
| 2645 | } |
---|
| 2646 | n_Delete(&h,r->cf); |
---|
| 2647 | } |
---|
| 2648 | } |
---|
| 2649 | } |
---|
| 2650 | } |
---|
| 2651 | } |
---|
| 2652 | |
---|
| 2653 | number p_GetAllDenom(poly ph, const ring r) |
---|
| 2654 | { |
---|
| 2655 | number d=n_Init(1,r->cf); |
---|
| 2656 | poly p = ph; |
---|
| 2657 | |
---|
| 2658 | while (p!=NULL) |
---|
| 2659 | { |
---|
| 2660 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2661 | if (!n_IsOne(h,r->cf)) |
---|
| 2662 | { |
---|
| 2663 | number dd=n_Mult(d,h,r->cf); |
---|
| 2664 | n_Delete(&d,r->cf); |
---|
| 2665 | d=dd; |
---|
| 2666 | } |
---|
| 2667 | n_Delete(&h,r->cf); |
---|
| 2668 | pIter(p); |
---|
| 2669 | } |
---|
| 2670 | return d; |
---|
| 2671 | } |
---|
| 2672 | |
---|
[fbf8a6] | 2673 | int p_Size(poly p, const ring r) |
---|
| 2674 | { |
---|
| 2675 | int count = 0; |
---|
| 2676 | while ( p != NULL ) |
---|
| 2677 | { |
---|
| 2678 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
| 2679 | pIter( p ); |
---|
| 2680 | } |
---|
| 2681 | return count; |
---|
| 2682 | } |
---|
| 2683 | |
---|
[4e8ef90] | 2684 | /*2 |
---|
| 2685 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
| 2686 | *assume: deg(var(varnum))==1 |
---|
| 2687 | */ |
---|
| 2688 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
| 2689 | { |
---|
| 2690 | pFDegProc deg; |
---|
[5679049] | 2691 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2692 | deg=p_Totaldegree; |
---|
| 2693 | else |
---|
[9765f3] | 2694 | deg=r->pFDeg; |
---|
[4e8ef90] | 2695 | |
---|
| 2696 | poly q=NULL, qn; |
---|
| 2697 | int o,ii; |
---|
| 2698 | sBucket_pt bp; |
---|
| 2699 | |
---|
| 2700 | if (p!=NULL) |
---|
| 2701 | { |
---|
| 2702 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
| 2703 | { |
---|
| 2704 | return NULL; |
---|
| 2705 | } |
---|
| 2706 | o=deg(p,r); |
---|
| 2707 | q=pNext(p); |
---|
| 2708 | while (q != NULL) |
---|
| 2709 | { |
---|
| 2710 | ii=deg(q,r); |
---|
| 2711 | if (ii>o) o=ii; |
---|
| 2712 | pIter(q); |
---|
| 2713 | } |
---|
| 2714 | q = p_Copy(p,r); |
---|
| 2715 | bp = sBucketCreate(r); |
---|
| 2716 | while (q != NULL) |
---|
| 2717 | { |
---|
| 2718 | ii = o-deg(q,r); |
---|
| 2719 | if (ii!=0) |
---|
| 2720 | { |
---|
| 2721 | p_AddExp(q,varnum, (long)ii,r); |
---|
| 2722 | p_Setm(q,r); |
---|
| 2723 | } |
---|
| 2724 | qn = pNext(q); |
---|
| 2725 | pNext(q) = NULL; |
---|
| 2726 | sBucket_Add_p(bp, q, 1); |
---|
| 2727 | q = qn; |
---|
| 2728 | } |
---|
| 2729 | sBucketDestroyAdd(bp, &q, &ii); |
---|
| 2730 | } |
---|
| 2731 | return q; |
---|
| 2732 | } |
---|
| 2733 | |
---|
| 2734 | /*2 |
---|
| 2735 | *tests if p is homogeneous with respect to the actual weigths |
---|
| 2736 | */ |
---|
| 2737 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
| 2738 | { |
---|
| 2739 | poly qp=p; |
---|
| 2740 | int o; |
---|
| 2741 | |
---|
| 2742 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
| 2743 | pFDegProc d; |
---|
[5679049] | 2744 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2745 | d=p_Totaldegree; |
---|
[71ba5b8] | 2746 | else |
---|
[9765f3] | 2747 | d=r->pFDeg; |
---|
[8a8c9e] | 2748 | o = d(p,r); |
---|
[4e8ef90] | 2749 | do |
---|
| 2750 | { |
---|
| 2751 | if (d(qp,r) != o) return FALSE; |
---|
| 2752 | pIter(qp); |
---|
| 2753 | } |
---|
| 2754 | while (qp != NULL); |
---|
| 2755 | return TRUE; |
---|
| 2756 | } |
---|
| 2757 | |
---|
[cd246b] | 2758 | /*----------utilities for syzygies--------------*/ |
---|
| 2759 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
| 2760 | { |
---|
| 2761 | poly q=p,qq; |
---|
| 2762 | int i; |
---|
| 2763 | |
---|
| 2764 | while (q!=NULL) |
---|
| 2765 | { |
---|
| 2766 | if (p_LmIsConstantComp(q,r)) |
---|
| 2767 | { |
---|
| 2768 | i = p_GetComp(q,r); |
---|
| 2769 | qq = p; |
---|
| 2770 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2771 | if (qq == q) |
---|
| 2772 | { |
---|
| 2773 | *k = i; |
---|
| 2774 | return TRUE; |
---|
| 2775 | } |
---|
| 2776 | else |
---|
| 2777 | pIter(q); |
---|
| 2778 | } |
---|
| 2779 | else pIter(q); |
---|
| 2780 | } |
---|
| 2781 | return FALSE; |
---|
| 2782 | } |
---|
| 2783 | |
---|
| 2784 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
| 2785 | { |
---|
| 2786 | poly q=p,qq; |
---|
| 2787 | int i,j=0; |
---|
| 2788 | |
---|
| 2789 | *len = 0; |
---|
| 2790 | while (q!=NULL) |
---|
| 2791 | { |
---|
| 2792 | if (p_LmIsConstantComp(q,r)) |
---|
| 2793 | { |
---|
| 2794 | i = p_GetComp(q,r); |
---|
| 2795 | qq = p; |
---|
| 2796 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2797 | if (qq == q) |
---|
| 2798 | { |
---|
| 2799 | j = 0; |
---|
| 2800 | while (qq!=NULL) |
---|
| 2801 | { |
---|
| 2802 | if (p_GetComp(qq,r)==i) j++; |
---|
| 2803 | pIter(qq); |
---|
| 2804 | } |
---|
| 2805 | if ((*len == 0) || (j<*len)) |
---|
| 2806 | { |
---|
| 2807 | *len = j; |
---|
| 2808 | *k = i; |
---|
| 2809 | } |
---|
| 2810 | } |
---|
| 2811 | } |
---|
| 2812 | pIter(q); |
---|
| 2813 | } |
---|
| 2814 | } |
---|
| 2815 | |
---|
| 2816 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
| 2817 | { |
---|
| 2818 | poly q = *p; |
---|
| 2819 | |
---|
| 2820 | if (q==NULL) return NULL; |
---|
| 2821 | |
---|
| 2822 | poly qq=NULL,result = NULL; |
---|
| 2823 | |
---|
| 2824 | if (p_GetComp(q,r)==k) |
---|
| 2825 | { |
---|
| 2826 | result = q; /* *p */ |
---|
| 2827 | while ((q!=NULL) && (p_GetComp(q,r)==k)) |
---|
| 2828 | { |
---|
| 2829 | p_SetComp(q,0,r); |
---|
| 2830 | p_SetmComp(q,r); |
---|
| 2831 | qq = q; |
---|
| 2832 | pIter(q); |
---|
| 2833 | } |
---|
| 2834 | *p = q; |
---|
| 2835 | pNext(qq) = NULL; |
---|
| 2836 | } |
---|
| 2837 | if (q==NULL) return result; |
---|
| 2838 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2839 | while (pNext(q)!=NULL) |
---|
| 2840 | { |
---|
| 2841 | if (p_GetComp(pNext(q),r)==k) |
---|
| 2842 | { |
---|
| 2843 | if (result==NULL) |
---|
| 2844 | { |
---|
| 2845 | result = pNext(q); |
---|
| 2846 | qq = result; |
---|
| 2847 | } |
---|
| 2848 | else |
---|
| 2849 | { |
---|
| 2850 | pNext(qq) = pNext(q); |
---|
| 2851 | pIter(qq); |
---|
| 2852 | } |
---|
| 2853 | pNext(q) = pNext(pNext(q)); |
---|
| 2854 | pNext(qq) =NULL; |
---|
| 2855 | p_SetComp(qq,0,r); |
---|
| 2856 | p_SetmComp(qq,r); |
---|
| 2857 | } |
---|
| 2858 | else |
---|
| 2859 | { |
---|
| 2860 | pIter(q); |
---|
| 2861 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2862 | } |
---|
| 2863 | } |
---|
| 2864 | return result; |
---|
| 2865 | } |
---|
[74021a] | 2866 | |
---|
| 2867 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
| 2868 | { |
---|
| 2869 | poly q = *p,qq=NULL,result = NULL; |
---|
| 2870 | |
---|
| 2871 | if (q==NULL) return NULL; |
---|
| 2872 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
| 2873 | if (p_GetComp(q,r)==k) |
---|
| 2874 | { |
---|
| 2875 | result = q; |
---|
| 2876 | do |
---|
| 2877 | { |
---|
| 2878 | p_SetComp(q,0,r); |
---|
| 2879 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2880 | qq = q; |
---|
| 2881 | pIter(q); |
---|
| 2882 | } |
---|
| 2883 | while ((q!=NULL) && (p_GetComp(q,r)==k)); |
---|
| 2884 | *p = q; |
---|
| 2885 | pNext(qq) = NULL; |
---|
| 2886 | } |
---|
| 2887 | if (q==NULL) return result; |
---|
| 2888 | if (p_GetComp(q,r) > k) |
---|
| 2889 | { |
---|
| 2890 | p_SubComp(q,1,r); |
---|
| 2891 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2892 | } |
---|
| 2893 | poly pNext_q; |
---|
| 2894 | while ((pNext_q=pNext(q))!=NULL) |
---|
| 2895 | { |
---|
| 2896 | if (p_GetComp(pNext_q,r)==k) |
---|
| 2897 | { |
---|
| 2898 | if (result==NULL) |
---|
| 2899 | { |
---|
| 2900 | result = pNext_q; |
---|
| 2901 | qq = result; |
---|
| 2902 | } |
---|
| 2903 | else |
---|
| 2904 | { |
---|
| 2905 | pNext(qq) = pNext_q; |
---|
| 2906 | pIter(qq); |
---|
| 2907 | } |
---|
| 2908 | pNext(q) = pNext(pNext_q); |
---|
| 2909 | pNext(qq) =NULL; |
---|
| 2910 | p_SetComp(qq,0,r); |
---|
| 2911 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
| 2912 | } |
---|
| 2913 | else |
---|
| 2914 | { |
---|
| 2915 | /*pIter(q);*/ q=pNext_q; |
---|
| 2916 | if (p_GetComp(q,r) > k) |
---|
| 2917 | { |
---|
| 2918 | p_SubComp(q,1,r); |
---|
| 2919 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2920 | } |
---|
| 2921 | } |
---|
| 2922 | } |
---|
| 2923 | return result; |
---|
| 2924 | } |
---|
| 2925 | |
---|
| 2926 | // Splits *p into two polys: *q which consists of all monoms with |
---|
| 2927 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
| 2928 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
| 2929 | { |
---|
| 2930 | spolyrec pp, qq; |
---|
| 2931 | poly p, q, p_prev; |
---|
| 2932 | int l = 0; |
---|
| 2933 | |
---|
| 2934 | #ifdef HAVE_ASSUME |
---|
| 2935 | int lp = pLength(*r_p); |
---|
| 2936 | #endif |
---|
| 2937 | |
---|
| 2938 | pNext(&pp) = *r_p; |
---|
| 2939 | p = *r_p; |
---|
| 2940 | p_prev = &pp; |
---|
| 2941 | q = &qq; |
---|
| 2942 | |
---|
| 2943 | while(p != NULL) |
---|
| 2944 | { |
---|
| 2945 | while (p_GetComp(p,r) == comp) |
---|
| 2946 | { |
---|
| 2947 | pNext(q) = p; |
---|
| 2948 | pIter(q); |
---|
| 2949 | p_SetComp(p, 0,r); |
---|
| 2950 | p_SetmComp(p,r); |
---|
| 2951 | pIter(p); |
---|
| 2952 | l++; |
---|
| 2953 | if (p == NULL) |
---|
| 2954 | { |
---|
| 2955 | pNext(p_prev) = NULL; |
---|
| 2956 | goto Finish; |
---|
| 2957 | } |
---|
| 2958 | } |
---|
| 2959 | pNext(p_prev) = p; |
---|
| 2960 | p_prev = p; |
---|
| 2961 | pIter(p); |
---|
| 2962 | } |
---|
| 2963 | |
---|
| 2964 | Finish: |
---|
| 2965 | pNext(q) = NULL; |
---|
| 2966 | *r_p = pNext(&pp); |
---|
| 2967 | *r_q = pNext(&qq); |
---|
| 2968 | *lq = l; |
---|
| 2969 | #ifdef HAVE_ASSUME |
---|
| 2970 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
| 2971 | #endif |
---|
| 2972 | p_Test(*r_p,r); |
---|
| 2973 | p_Test(*r_q,r); |
---|
| 2974 | } |
---|
| 2975 | |
---|
| 2976 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
| 2977 | { |
---|
| 2978 | poly q; |
---|
| 2979 | |
---|
| 2980 | while ((*p!=NULL) && (p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
| 2981 | if (*p==NULL) return; |
---|
| 2982 | q = *p; |
---|
| 2983 | if (p_GetComp(q,r)>k) |
---|
| 2984 | { |
---|
| 2985 | p_SubComp(q,1,r); |
---|
| 2986 | p_SetmComp(q,r); |
---|
| 2987 | } |
---|
| 2988 | while (pNext(q)!=NULL) |
---|
| 2989 | { |
---|
| 2990 | if (p_GetComp(pNext(q),r)==k) |
---|
| 2991 | p_LmDelete(&(pNext(q)),r); |
---|
| 2992 | else |
---|
| 2993 | { |
---|
| 2994 | pIter(q); |
---|
| 2995 | if (p_GetComp(q,r)>k) |
---|
| 2996 | { |
---|
| 2997 | p_SubComp(q,1,r); |
---|
| 2998 | p_SetmComp(q,r); |
---|
| 2999 | } |
---|
| 3000 | } |
---|
| 3001 | } |
---|
| 3002 | } |
---|
[dd693a] | 3003 | |
---|
| 3004 | /*2 |
---|
| 3005 | * convert a vector to a set of polys, |
---|
| 3006 | * allocates the polyset, (entries 0..(*len)-1) |
---|
| 3007 | * the vector will not be changed |
---|
| 3008 | */ |
---|
| 3009 | void p_Vec2Polys(poly v, poly* *p, int *len, const ring r) |
---|
| 3010 | { |
---|
| 3011 | poly h; |
---|
| 3012 | int k; |
---|
| 3013 | |
---|
| 3014 | *len=p_MaxComp(v,r); |
---|
| 3015 | if (*len==0) *len=1; |
---|
| 3016 | *p=(poly*)omAlloc0((*len)*sizeof(poly)); |
---|
| 3017 | while (v!=NULL) |
---|
| 3018 | { |
---|
| 3019 | h=p_Head(v,r); |
---|
| 3020 | k=p_GetComp(h,r); |
---|
| 3021 | p_SetComp(h,0,r); |
---|
| 3022 | (*p)[k-1]=p_Add_q((*p)[k-1],h,r); |
---|
| 3023 | pIter(v); |
---|
| 3024 | } |
---|
| 3025 | } |
---|
| 3026 | |
---|
[5c39a9] | 3027 | /* -------------------------------------------------------- */ |
---|
| 3028 | /*2 |
---|
| 3029 | * change all global variables to fit the description of the new ring |
---|
| 3030 | */ |
---|
| 3031 | |
---|
| 3032 | void p_SetGlobals(const ring r, BOOLEAN complete) |
---|
| 3033 | { |
---|
[5679049] | 3034 | if (r->ppNoether!=NULL) p_Delete(&r->ppNoether,r); |
---|
[5c39a9] | 3035 | |
---|
| 3036 | if (complete) |
---|
| 3037 | { |
---|
| 3038 | test &= ~ TEST_RINGDEP_OPTS; |
---|
| 3039 | test |= r->options; |
---|
| 3040 | } |
---|
| 3041 | } |
---|
[949e57] | 3042 | // |
---|
| 3043 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
| 3044 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
[45d2332] | 3045 | // only uses pFDeg (and not p_Deg, or pTotalDegree, etc) |
---|
[949e57] | 3046 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
| 3047 | { |
---|
| 3048 | assume(new_FDeg != NULL); |
---|
| 3049 | r->pFDeg = new_FDeg; |
---|
| 3050 | |
---|
| 3051 | if (new_lDeg == NULL) |
---|
| 3052 | new_lDeg = r->pLDegOrig; |
---|
| 3053 | |
---|
| 3054 | r->pLDeg = new_lDeg; |
---|
| 3055 | } |
---|
| 3056 | |
---|
| 3057 | // restores pFDeg and pLDeg: |
---|
| 3058 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
| 3059 | { |
---|
| 3060 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
| 3061 | r->pFDeg = old_FDeg; |
---|
| 3062 | r->pLDeg = old_lDeg; |
---|
| 3063 | } |
---|
| 3064 | |
---|
[5bc2461] | 3065 | /*-------- several access procedures to monomials -------------------- */ |
---|
| 3066 | /* |
---|
| 3067 | * the module weights for std |
---|
| 3068 | */ |
---|
| 3069 | static pFDegProc pOldFDeg; |
---|
| 3070 | static pLDegProc pOldLDeg; |
---|
| 3071 | static intvec * pModW; |
---|
| 3072 | static BOOLEAN pOldLexOrder; |
---|
| 3073 | |
---|
[8a8c9e] | 3074 | static long pModDeg(poly p, ring r) |
---|
[5bc2461] | 3075 | { |
---|
| 3076 | long d=pOldFDeg(p, r); |
---|
| 3077 | int c=p_GetComp(p, r); |
---|
| 3078 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
| 3079 | return d; |
---|
| 3080 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
| 3081 | } |
---|
| 3082 | |
---|
| 3083 | void p_SetModDeg(intvec *w, ring r) |
---|
| 3084 | { |
---|
| 3085 | if (w!=NULL) |
---|
| 3086 | { |
---|
| 3087 | r->pModW = w; |
---|
| 3088 | pOldFDeg = r->pFDeg; |
---|
| 3089 | pOldLDeg = r->pLDeg; |
---|
| 3090 | pOldLexOrder = r->pLexOrder; |
---|
| 3091 | pSetDegProcs(r,pModDeg); |
---|
| 3092 | r->pLexOrder = TRUE; |
---|
| 3093 | } |
---|
| 3094 | else |
---|
| 3095 | { |
---|
| 3096 | r->pModW = NULL; |
---|
[5679049] | 3097 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
[5bc2461] | 3098 | r->pLexOrder = pOldLexOrder; |
---|
| 3099 | } |
---|
| 3100 | } |
---|
| 3101 | |
---|
[c6a3eb2] | 3102 | /*2 |
---|
| 3103 | * handle memory request for sets of polynomials (ideals) |
---|
| 3104 | * l is the length of *p, increment is the difference (may be negative) |
---|
| 3105 | */ |
---|
| 3106 | void pEnlargeSet(poly* *p, int l, int increment) |
---|
| 3107 | { |
---|
| 3108 | poly* h; |
---|
| 3109 | |
---|
| 3110 | h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
| 3111 | if (increment>0) |
---|
| 3112 | { |
---|
| 3113 | //for (i=l; i<l+increment; i++) |
---|
| 3114 | // h[i]=NULL; |
---|
| 3115 | memset(&(h[l]),0,increment*sizeof(poly)); |
---|
| 3116 | } |
---|
| 3117 | *p=h; |
---|
| 3118 | } |
---|
| 3119 | |
---|
[71ba5b8] | 3120 | /*2 |
---|
| 3121 | *divides p1 by its leading coefficient |
---|
| 3122 | */ |
---|
| 3123 | void p_Norm(poly p1, const ring r) |
---|
| 3124 | { |
---|
| 3125 | #ifdef HAVE_RINGS |
---|
| 3126 | if (rField_is_Ring(r)) |
---|
| 3127 | { |
---|
[45d2332] | 3128 | if (!n_IsUnit(pGetCoeff(p1), r->cf)) return; |
---|
[71ba5b8] | 3129 | // Werror("p_Norm not possible in the case of coefficient rings."); |
---|
| 3130 | } |
---|
| 3131 | else |
---|
| 3132 | #endif |
---|
| 3133 | if (p1!=NULL) |
---|
| 3134 | { |
---|
| 3135 | if (pNext(p1)==NULL) |
---|
| 3136 | { |
---|
| 3137 | p_SetCoeff(p1,n_Init(1,r->cf),r); |
---|
| 3138 | return; |
---|
| 3139 | } |
---|
| 3140 | poly h; |
---|
| 3141 | if (!n_IsOne(pGetCoeff(p1),r->cf)) |
---|
| 3142 | { |
---|
| 3143 | number k, c; |
---|
| 3144 | n_Normalize(pGetCoeff(p1),r->cf); |
---|
| 3145 | k = pGetCoeff(p1); |
---|
| 3146 | c = n_Init(1,r->cf); |
---|
| 3147 | pSetCoeff0(p1,c); |
---|
| 3148 | h = pNext(p1); |
---|
| 3149 | while (h!=NULL) |
---|
| 3150 | { |
---|
| 3151 | c=n_Div(pGetCoeff(h),k,r->cf); |
---|
| 3152 | // no need to normalize: Z/p, R |
---|
| 3153 | // normalize already in nDiv: Q_a, Z/p_a |
---|
| 3154 | // remains: Q |
---|
| 3155 | if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) n_Normalize(c,r->cf); |
---|
| 3156 | p_SetCoeff(h,c,r); |
---|
| 3157 | pIter(h); |
---|
| 3158 | } |
---|
| 3159 | n_Delete(&k,r->cf); |
---|
| 3160 | } |
---|
| 3161 | else |
---|
| 3162 | { |
---|
| 3163 | //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE |
---|
| 3164 | { |
---|
| 3165 | h = pNext(p1); |
---|
| 3166 | while (h!=NULL) |
---|
| 3167 | { |
---|
| 3168 | n_Normalize(pGetCoeff(h),r->cf); |
---|
| 3169 | pIter(h); |
---|
| 3170 | } |
---|
| 3171 | } |
---|
| 3172 | } |
---|
| 3173 | } |
---|
| 3174 | } |
---|
| 3175 | |
---|
| 3176 | /*2 |
---|
| 3177 | *normalize all coefficients |
---|
| 3178 | */ |
---|
| 3179 | void p_Normalize(poly p,const ring r) |
---|
| 3180 | { |
---|
| 3181 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
| 3182 | while (p!=NULL) |
---|
| 3183 | { |
---|
| 3184 | #ifdef LDEBUG |
---|
[45d2332] | 3185 | n_Test(pGetCoeff(p), r->cf); |
---|
[71ba5b8] | 3186 | #endif |
---|
| 3187 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 3188 | pIter(p); |
---|
| 3189 | } |
---|
| 3190 | } |
---|
| 3191 | |
---|
| 3192 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
| 3193 | // Poly with Exp(n) != 0 is reversed |
---|
| 3194 | static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r) |
---|
| 3195 | { |
---|
| 3196 | if (p == NULL) |
---|
| 3197 | { |
---|
| 3198 | *non_zero = NULL; |
---|
| 3199 | *zero = NULL; |
---|
| 3200 | return; |
---|
| 3201 | } |
---|
| 3202 | spolyrec sz; |
---|
| 3203 | poly z, n_z, next; |
---|
| 3204 | z = &sz; |
---|
| 3205 | n_z = NULL; |
---|
| 3206 | |
---|
| 3207 | while(p != NULL) |
---|
| 3208 | { |
---|
| 3209 | next = pNext(p); |
---|
| 3210 | if (p_GetExp(p, n,r) == 0) |
---|
| 3211 | { |
---|
| 3212 | pNext(z) = p; |
---|
| 3213 | pIter(z); |
---|
| 3214 | } |
---|
| 3215 | else |
---|
| 3216 | { |
---|
| 3217 | pNext(p) = n_z; |
---|
| 3218 | n_z = p; |
---|
| 3219 | } |
---|
| 3220 | p = next; |
---|
| 3221 | } |
---|
| 3222 | pNext(z) = NULL; |
---|
| 3223 | *zero = pNext(&sz); |
---|
| 3224 | *non_zero = n_z; |
---|
| 3225 | } |
---|
| 3226 | /*3 |
---|
| 3227 | * substitute the n-th variable by 1 in p |
---|
| 3228 | * destroy p |
---|
| 3229 | */ |
---|
| 3230 | static poly p_Subst1 (poly p,int n, const ring r) |
---|
| 3231 | { |
---|
| 3232 | poly qq=NULL, result = NULL; |
---|
| 3233 | poly zero=NULL, non_zero=NULL; |
---|
| 3234 | |
---|
| 3235 | // reverse, so that add is likely to be linear |
---|
| 3236 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3237 | |
---|
| 3238 | while (non_zero != NULL) |
---|
| 3239 | { |
---|
| 3240 | assume(p_GetExp(non_zero, n,r) != 0); |
---|
| 3241 | qq = non_zero; |
---|
| 3242 | pIter(non_zero); |
---|
| 3243 | qq->next = NULL; |
---|
| 3244 | p_SetExp(qq,n,0,r); |
---|
| 3245 | p_Setm(qq,r); |
---|
| 3246 | result = p_Add_q(result,qq,r); |
---|
| 3247 | } |
---|
| 3248 | p = p_Add_q(result, zero,r); |
---|
| 3249 | p_Test(p,r); |
---|
| 3250 | return p; |
---|
| 3251 | } |
---|
| 3252 | |
---|
| 3253 | /*3 |
---|
| 3254 | * substitute the n-th variable by number e in p |
---|
| 3255 | * destroy p |
---|
| 3256 | */ |
---|
| 3257 | static poly p_Subst2 (poly p,int n, number e, const ring r) |
---|
| 3258 | { |
---|
| 3259 | assume( ! n_IsZero(e,r->cf) ); |
---|
| 3260 | poly qq,result = NULL; |
---|
| 3261 | number nn, nm; |
---|
| 3262 | poly zero, non_zero; |
---|
| 3263 | |
---|
| 3264 | // reverse, so that add is likely to be linear |
---|
| 3265 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3266 | |
---|
| 3267 | while (non_zero != NULL) |
---|
| 3268 | { |
---|
[45d2332] | 3269 | assume(p_GetExp(non_zero, n, r) != 0); |
---|
[71ba5b8] | 3270 | qq = non_zero; |
---|
| 3271 | pIter(non_zero); |
---|
| 3272 | qq->next = NULL; |
---|
| 3273 | n_Power(e, p_GetExp(qq, n, r), &nn,r->cf); |
---|
| 3274 | nm = n_Mult(nn, pGetCoeff(qq),r->cf); |
---|
| 3275 | #ifdef HAVE_RINGS |
---|
| 3276 | if (n_IsZero(nm,r->cf)) |
---|
| 3277 | { |
---|
| 3278 | p_LmFree(&qq,r); |
---|
| 3279 | n_Delete(&nm,r->cf); |
---|
| 3280 | } |
---|
| 3281 | else |
---|
| 3282 | #endif |
---|
| 3283 | { |
---|
| 3284 | p_SetCoeff(qq, nm,r); |
---|
| 3285 | p_SetExp(qq, n, 0,r); |
---|
| 3286 | p_Setm(qq,r); |
---|
| 3287 | result = p_Add_q(result,qq,r); |
---|
| 3288 | } |
---|
| 3289 | n_Delete(&nn,r->cf); |
---|
| 3290 | } |
---|
| 3291 | p = p_Add_q(result, zero,r); |
---|
| 3292 | p_Test(p,r); |
---|
| 3293 | return p; |
---|
| 3294 | } |
---|
| 3295 | |
---|
| 3296 | |
---|
| 3297 | /* delete monoms whose n-th exponent is different from zero */ |
---|
| 3298 | static poly p_Subst0(poly p, int n, const ring r) |
---|
| 3299 | { |
---|
| 3300 | spolyrec res; |
---|
| 3301 | poly h = &res; |
---|
| 3302 | pNext(h) = p; |
---|
| 3303 | |
---|
| 3304 | while (pNext(h)!=NULL) |
---|
| 3305 | { |
---|
| 3306 | if (p_GetExp(pNext(h),n,r)!=0) |
---|
| 3307 | { |
---|
| 3308 | p_LmDelete(&pNext(h),r); |
---|
| 3309 | } |
---|
| 3310 | else |
---|
| 3311 | { |
---|
| 3312 | pIter(h); |
---|
| 3313 | } |
---|
| 3314 | } |
---|
| 3315 | p_Test(pNext(&res),r); |
---|
| 3316 | return pNext(&res); |
---|
| 3317 | } |
---|
| 3318 | |
---|
| 3319 | /*2 |
---|
| 3320 | * substitute the n-th variable by e in p |
---|
| 3321 | * destroy p |
---|
| 3322 | */ |
---|
| 3323 | poly p_Subst(poly p, int n, poly e, const ring r) |
---|
| 3324 | { |
---|
| 3325 | if (e == NULL) return p_Subst0(p, n,r); |
---|
| 3326 | |
---|
| 3327 | if (p_IsConstant(e,r)) |
---|
| 3328 | { |
---|
| 3329 | if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r); |
---|
| 3330 | else return p_Subst2(p, n, pGetCoeff(e),r); |
---|
| 3331 | } |
---|
| 3332 | |
---|
| 3333 | #ifdef HAVE_PLURAL |
---|
| 3334 | if (rIsPluralRing(r)) |
---|
| 3335 | { |
---|
| 3336 | return nc_pSubst(p,n,e,r); |
---|
| 3337 | } |
---|
| 3338 | #endif |
---|
| 3339 | |
---|
| 3340 | int exponent,i; |
---|
| 3341 | poly h, res, m; |
---|
| 3342 | int *me,*ee; |
---|
| 3343 | number nu,nu1; |
---|
| 3344 | |
---|
| 3345 | me=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3346 | ee=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3347 | if (e!=NULL) p_GetExpV(e,ee,r); |
---|
| 3348 | res=NULL; |
---|
| 3349 | h=p; |
---|
| 3350 | while (h!=NULL) |
---|
| 3351 | { |
---|
| 3352 | if ((e!=NULL) || (p_GetExp(h,n,r)==0)) |
---|
| 3353 | { |
---|
| 3354 | m=p_Head(h,r); |
---|
| 3355 | p_GetExpV(m,me,r); |
---|
| 3356 | exponent=me[n]; |
---|
| 3357 | me[n]=0; |
---|
| 3358 | for(i=rVar(r);i>0;i--) |
---|
| 3359 | me[i]+=exponent*ee[i]; |
---|
| 3360 | p_SetExpV(m,me,r); |
---|
| 3361 | if (e!=NULL) |
---|
| 3362 | { |
---|
| 3363 | n_Power(pGetCoeff(e),exponent,&nu,r->cf); |
---|
| 3364 | nu1=n_Mult(pGetCoeff(m),nu,r->cf); |
---|
| 3365 | n_Delete(&nu,r->cf); |
---|
| 3366 | p_SetCoeff(m,nu1,r); |
---|
| 3367 | } |
---|
| 3368 | res=p_Add_q(res,m,r); |
---|
| 3369 | } |
---|
| 3370 | p_LmDelete(&h,r); |
---|
| 3371 | } |
---|
| 3372 | omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int)); |
---|
| 3373 | omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int)); |
---|
| 3374 | return res; |
---|
| 3375 | } |
---|
[deca086] | 3376 | /*2 |
---|
| 3377 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
| 3378 | */ |
---|
| 3379 | poly p_PermPoly (poly p, int * perm, const ring oldRing, const ring dst, |
---|
| 3380 | nMapFunc nMap, int *par_perm, int OldPar) |
---|
| 3381 | { |
---|
| 3382 | int OldpVariables = oldRing->N; |
---|
| 3383 | poly result = NULL; |
---|
| 3384 | poly result_last = NULL; |
---|
| 3385 | poly aq=NULL; /* the map coefficient */ |
---|
| 3386 | poly qq; /* the mapped monomial */ |
---|
| 3387 | |
---|
| 3388 | while (p != NULL) |
---|
| 3389 | { |
---|
| 3390 | if ((OldPar==0)||(rField_is_GF(oldRing))) |
---|
| 3391 | { |
---|
| 3392 | qq = p_Init(dst); |
---|
[4581a96] | 3393 | number n=nMap(pGetCoeff(p),oldRing->cf,dst->cf); |
---|
[4c6e420] | 3394 | if ((!rMinpolyIsNULL(dst)) |
---|
[deca086] | 3395 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
| 3396 | { |
---|
| 3397 | n_Normalize(n,dst->cf); |
---|
| 3398 | } |
---|
| 3399 | pGetCoeff(qq)=n; |
---|
| 3400 | // coef may be zero: pTest(qq); |
---|
| 3401 | } |
---|
| 3402 | else |
---|
| 3403 | { |
---|
| 3404 | qq=p_One(dst); |
---|
[fd01a8] | 3405 | WerrorS("longalg missing 2"); |
---|
[4581a96] | 3406 | #if 0 |
---|
[deca086] | 3407 | aq=naPermNumber(pGetCoeff(p),par_perm,OldPar, oldRing); |
---|
[4c6e420] | 3408 | if ((!rMinpolyIsNULL(dst)) |
---|
[deca086] | 3409 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
| 3410 | { |
---|
[df43d9] | 3411 | p_Normalize(aq,dst); |
---|
| 3412 | if (aq==NULL) |
---|
| 3413 | p_SetCoeff(qq,n_Init(0,dst->cf),dst); |
---|
[deca086] | 3414 | } |
---|
[7eb7b5] | 3415 | p_Test(aq,dst); |
---|
[4581a96] | 3416 | #endif |
---|
[deca086] | 3417 | } |
---|
| 3418 | if (rRing_has_Comp(dst)) p_SetComp(qq, p_GetComp(p,oldRing),dst); |
---|
| 3419 | if (n_IsZero(pGetCoeff(qq),dst->cf)) |
---|
| 3420 | { |
---|
| 3421 | p_LmDelete(&qq,dst); |
---|
| 3422 | } |
---|
| 3423 | else |
---|
| 3424 | { |
---|
| 3425 | int i; |
---|
| 3426 | int mapped_to_par=0; |
---|
| 3427 | for(i=1; i<=OldpVariables; i++) |
---|
| 3428 | { |
---|
| 3429 | int e=p_GetExp(p,i,oldRing); |
---|
| 3430 | if (e!=0) |
---|
| 3431 | { |
---|
| 3432 | if (perm==NULL) |
---|
| 3433 | { |
---|
| 3434 | p_SetExp(qq,i, e, dst); |
---|
| 3435 | } |
---|
| 3436 | else if (perm[i]>0) |
---|
| 3437 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
| 3438 | else if (perm[i]<0) |
---|
| 3439 | { |
---|
| 3440 | if (rField_is_GF(dst)) |
---|
| 3441 | { |
---|
| 3442 | number c=pGetCoeff(qq); |
---|
[0afa07] | 3443 | number ee=(number)rGetVar(1, dst->cf->extRing); |
---|
[1389a4] | 3444 | number eee;n_Power(ee,e,&eee,dst->cf); //nfDelete(ee,dst); |
---|
| 3445 | ee=n_Mult(c,eee,dst->cf); |
---|
[8a8c9e] | 3446 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
[deca086] | 3447 | pSetCoeff0(qq,ee); |
---|
| 3448 | } |
---|
| 3449 | else |
---|
| 3450 | { |
---|
[fd01a8] | 3451 | WerrorS("longalg missing 3"); |
---|
[71ba5b8] | 3452 | #if 0 |
---|
[deca086] | 3453 | lnumber c=(lnumber)pGetCoeff(qq); |
---|
| 3454 | if (c->z->next==NULL) |
---|
[6ccdd3a] | 3455 | p_AddExp(c->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->extRing); |
---|
[deca086] | 3456 | else /* more difficult: we have really to multiply: */ |
---|
| 3457 | { |
---|
[8a8c9e] | 3458 | lnumber mmc=(lnumber)naInit(1,dst); |
---|
[6ccdd3a] | 3459 | p_SetExp(mmc->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->extRing); |
---|
| 3460 | p_Setm(mmc->z,dst->extRing->cf); |
---|
[1389a4] | 3461 | pGetCoeff(qq)=n_Mult((number)c,(number)mmc,dst->cf); |
---|
[deca086] | 3462 | n_Delete((number *)&c,dst->cf); |
---|
[71ba5b8] | 3463 | n_Delete((number *)&mmc,dst->cf); |
---|
[deca086] | 3464 | } |
---|
| 3465 | mapped_to_par=1; |
---|
[71ba5b8] | 3466 | #endif |
---|
[deca086] | 3467 | } |
---|
| 3468 | } |
---|
| 3469 | else |
---|
| 3470 | { |
---|
| 3471 | /* this variable maps to 0 !*/ |
---|
| 3472 | p_LmDelete(&qq,dst); |
---|
| 3473 | break; |
---|
| 3474 | } |
---|
| 3475 | } |
---|
| 3476 | } |
---|
| 3477 | if (mapped_to_par |
---|
[4c6e420] | 3478 | && (!rMinpolyIsNULL(dst))) |
---|
[deca086] | 3479 | { |
---|
| 3480 | number n=pGetCoeff(qq); |
---|
| 3481 | n_Normalize(n,dst->cf); |
---|
| 3482 | pGetCoeff(qq)=n; |
---|
| 3483 | } |
---|
| 3484 | } |
---|
| 3485 | pIter(p); |
---|
| 3486 | #if 1 |
---|
| 3487 | if (qq!=NULL) |
---|
| 3488 | { |
---|
| 3489 | p_Setm(qq,dst); |
---|
| 3490 | p_Test(aq,dst); |
---|
| 3491 | p_Test(qq,dst); |
---|
[5679049] | 3492 | if (aq!=NULL) qq=p_Mult_q(aq,qq,dst); |
---|
[deca086] | 3493 | aq = qq; |
---|
| 3494 | while (pNext(aq) != NULL) pIter(aq); |
---|
| 3495 | if (result_last==NULL) |
---|
| 3496 | { |
---|
| 3497 | result=qq; |
---|
| 3498 | } |
---|
| 3499 | else |
---|
| 3500 | { |
---|
| 3501 | pNext(result_last)=qq; |
---|
| 3502 | } |
---|
| 3503 | result_last=aq; |
---|
| 3504 | aq = NULL; |
---|
| 3505 | } |
---|
| 3506 | else if (aq!=NULL) |
---|
| 3507 | { |
---|
| 3508 | p_Delete(&aq,dst); |
---|
| 3509 | } |
---|
| 3510 | } |
---|
| 3511 | result=p_SortAdd(result,dst); |
---|
| 3512 | #else |
---|
| 3513 | // if (qq!=NULL) |
---|
| 3514 | // { |
---|
| 3515 | // pSetm(qq); |
---|
| 3516 | // pTest(qq); |
---|
| 3517 | // pTest(aq); |
---|
| 3518 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
| 3519 | // aq = qq; |
---|
| 3520 | // while (pNext(aq) != NULL) pIter(aq); |
---|
| 3521 | // pNext(aq) = result; |
---|
| 3522 | // aq = NULL; |
---|
| 3523 | // result = qq; |
---|
| 3524 | // } |
---|
| 3525 | // else if (aq!=NULL) |
---|
| 3526 | // { |
---|
| 3527 | // pDelete(&aq); |
---|
| 3528 | // } |
---|
| 3529 | //} |
---|
| 3530 | //p = result; |
---|
| 3531 | //result = NULL; |
---|
| 3532 | //while (p != NULL) |
---|
| 3533 | //{ |
---|
| 3534 | // qq = p; |
---|
| 3535 | // pIter(p); |
---|
| 3536 | // qq->next = NULL; |
---|
| 3537 | // result = pAdd(result, qq); |
---|
| 3538 | //} |
---|
| 3539 | #endif |
---|
| 3540 | p_Test(result,dst); |
---|
| 3541 | return result; |
---|
| 3542 | } |
---|
[f550e86] | 3543 | /************************************************************** |
---|
| 3544 | * |
---|
| 3545 | * Jet |
---|
| 3546 | * |
---|
| 3547 | **************************************************************/ |
---|
| 3548 | |
---|
| 3549 | poly pp_Jet(poly p, int m, const ring R) |
---|
| 3550 | { |
---|
| 3551 | poly r=NULL; |
---|
| 3552 | poly t=NULL; |
---|
| 3553 | |
---|
| 3554 | while (p!=NULL) |
---|
| 3555 | { |
---|
| 3556 | if (p_Totaldegree(p,R)<=m) |
---|
| 3557 | { |
---|
| 3558 | if (r==NULL) |
---|
| 3559 | r=p_Head(p,R); |
---|
| 3560 | else |
---|
| 3561 | if (t==NULL) |
---|
| 3562 | { |
---|
| 3563 | pNext(r)=p_Head(p,R); |
---|
| 3564 | t=pNext(r); |
---|
| 3565 | } |
---|
| 3566 | else |
---|
| 3567 | { |
---|
| 3568 | pNext(t)=p_Head(p,R); |
---|
| 3569 | pIter(t); |
---|
| 3570 | } |
---|
| 3571 | } |
---|
| 3572 | pIter(p); |
---|
| 3573 | } |
---|
| 3574 | return r; |
---|
| 3575 | } |
---|
| 3576 | |
---|
| 3577 | poly p_Jet(poly p, int m,const ring R) |
---|
| 3578 | { |
---|
| 3579 | poly t=NULL; |
---|
| 3580 | |
---|
| 3581 | while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R); |
---|
| 3582 | if (p==NULL) return NULL; |
---|
| 3583 | poly r=p; |
---|
| 3584 | while (pNext(p)!=NULL) |
---|
| 3585 | { |
---|
| 3586 | if (p_Totaldegree(pNext(p),R)>m) |
---|
| 3587 | { |
---|
| 3588 | p_LmDelete(&pNext(p),R); |
---|
| 3589 | } |
---|
| 3590 | else |
---|
| 3591 | pIter(p); |
---|
| 3592 | } |
---|
| 3593 | return r; |
---|
| 3594 | } |
---|
| 3595 | |
---|
| 3596 | poly pp_JetW(poly p, int m, short *w, const ring R) |
---|
| 3597 | { |
---|
| 3598 | poly r=NULL; |
---|
| 3599 | poly t=NULL; |
---|
| 3600 | while (p!=NULL) |
---|
| 3601 | { |
---|
| 3602 | if (totaldegreeWecart_IV(p,R,w)<=m) |
---|
| 3603 | { |
---|
| 3604 | if (r==NULL) |
---|
| 3605 | r=p_Head(p,R); |
---|
| 3606 | else |
---|
| 3607 | if (t==NULL) |
---|
| 3608 | { |
---|
| 3609 | pNext(r)=p_Head(p,R); |
---|
| 3610 | t=pNext(r); |
---|
| 3611 | } |
---|
| 3612 | else |
---|
| 3613 | { |
---|
| 3614 | pNext(t)=p_Head(p,R); |
---|
| 3615 | pIter(t); |
---|
| 3616 | } |
---|
| 3617 | } |
---|
| 3618 | pIter(p); |
---|
| 3619 | } |
---|
| 3620 | return r; |
---|
| 3621 | } |
---|
| 3622 | |
---|
| 3623 | poly p_JetW(poly p, int m, short *w, const ring R) |
---|
| 3624 | { |
---|
| 3625 | while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R); |
---|
| 3626 | if (p==NULL) return NULL; |
---|
| 3627 | poly r=p; |
---|
| 3628 | while (pNext(p)!=NULL) |
---|
| 3629 | { |
---|
| 3630 | if (totaldegreeWecart_IV(pNext(p),R,w)>m) |
---|
| 3631 | { |
---|
| 3632 | p_LmDelete(&pNext(p),R); |
---|
| 3633 | } |
---|
| 3634 | else |
---|
| 3635 | pIter(p); |
---|
| 3636 | } |
---|
| 3637 | return r; |
---|
| 3638 | } |
---|
[5c39a9] | 3639 | |
---|
[ba0fc3] | 3640 | /*************************************************************/ |
---|
| 3641 | int p_MinDeg(poly p,intvec *w, const ring R) |
---|
| 3642 | { |
---|
| 3643 | if(p==NULL) |
---|
| 3644 | return -1; |
---|
| 3645 | int d=-1; |
---|
| 3646 | while(p!=NULL) |
---|
| 3647 | { |
---|
| 3648 | int d0=0; |
---|
| 3649 | for(int j=0;j<rVar(R);j++) |
---|
| 3650 | if(w==NULL||j>=w->length()) |
---|
| 3651 | d0+=p_GetExp(p,j+1,R); |
---|
| 3652 | else |
---|
| 3653 | d0+=(*w)[j]*p_GetExp(p,j+1,R); |
---|
| 3654 | if(d0<d||d==-1) |
---|
| 3655 | d=d0; |
---|
| 3656 | pIter(p); |
---|
| 3657 | } |
---|
| 3658 | return d; |
---|
| 3659 | } |
---|
| 3660 | |
---|
[a4081e5] | 3661 | /***************************************************************/ |
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| 3662 | |
---|
| 3663 | poly p_Series(int n,poly p,poly u, intvec *w, const ring R) |
---|
| 3664 | { |
---|
| 3665 | short *ww=iv2array(w,R); |
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| 3666 | if(p!=NULL) |
---|
| 3667 | { |
---|
| 3668 | if(u==NULL) |
---|
| 3669 | p=p_JetW(p,n,ww,R); |
---|
| 3670 | else |
---|
| 3671 | p=p_JetW(p_Mult_q(p,p_Invers(n-p_MinDeg(p,w,R),u,w,R),R),n,ww,R); |
---|
| 3672 | } |
---|
| 3673 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
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| 3674 | return p; |
---|
| 3675 | } |
---|
| 3676 | |
---|
| 3677 | poly p_Invers(int n,poly u,intvec *w, const ring R) |
---|
| 3678 | { |
---|
| 3679 | if(n<0) |
---|
| 3680 | return NULL; |
---|
| 3681 | number u0=n_Invers(pGetCoeff(u),R->cf); |
---|
| 3682 | poly v=p_NSet(u0,R); |
---|
| 3683 | if(n==0) |
---|
| 3684 | return v; |
---|
| 3685 | short *ww=iv2array(w,R); |
---|
| 3686 | poly u1=p_JetW(p_Sub(p_One(R),p_Mult_nn(u,u0,R),R),n,ww,R); |
---|
| 3687 | if(u1==NULL) |
---|
| 3688 | { |
---|
| 3689 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3690 | return v; |
---|
| 3691 | } |
---|
| 3692 | poly v1=p_Mult_nn(p_Copy(u1,R),u0,R); |
---|
| 3693 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3694 | for(int i=n/p_MinDeg(u1,w,R);i>1;i--) |
---|
| 3695 | { |
---|
| 3696 | v1=p_JetW(p_Mult_q(v1,p_Copy(u1,R),R),n,ww,R); |
---|
| 3697 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3698 | } |
---|
| 3699 | p_Delete(&u1,R); |
---|
| 3700 | p_Delete(&v1,R); |
---|
| 3701 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3702 | return v; |
---|
| 3703 | } |
---|
| 3704 | |
---|
[7dce2d7] | 3705 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r) |
---|
| 3706 | { |
---|
| 3707 | while ((p1 != NULL) && (p2 != NULL)) |
---|
| 3708 | { |
---|
| 3709 | if (! p_LmEqual(p1, p2,r)) |
---|
| 3710 | return FALSE; |
---|
| 3711 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r )) |
---|
| 3712 | return FALSE; |
---|
| 3713 | pIter(p1); |
---|
| 3714 | pIter(p2); |
---|
| 3715 | } |
---|
| 3716 | return (p1==p2); |
---|
| 3717 | } |
---|
[32d07a5] | 3718 | |
---|
| 3719 | /*2 |
---|
| 3720 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
| 3721 | *assume p1 != NULL and p2 != NULL |
---|
| 3722 | */ |
---|
| 3723 | BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r) |
---|
| 3724 | { |
---|
| 3725 | number n,nn; |
---|
| 3726 | pAssume(p1 != NULL && p2 != NULL); |
---|
| 3727 | |
---|
| 3728 | if (!p_LmEqual(p1,p2,r)) //compare leading mons |
---|
| 3729 | return FALSE; |
---|
| 3730 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
---|
| 3731 | return FALSE; |
---|
| 3732 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
---|
| 3733 | return FALSE; |
---|
| 3734 | if (pLength(p1) != pLength(p2)) |
---|
| 3735 | return FALSE; |
---|
| 3736 | #ifdef HAVE_RINGS |
---|
| 3737 | if (rField_is_Ring(r)) |
---|
| 3738 | { |
---|
| 3739 | if (!n_DivBy(p_GetCoeff(p1, r), p_GetCoeff(p2, r), r)) return FALSE; |
---|
| 3740 | } |
---|
| 3741 | #endif |
---|
| 3742 | n=n_Div(p_GetCoeff(p1,r),p_GetCoeff(p2,r),r); |
---|
| 3743 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
| 3744 | { |
---|
| 3745 | if ( ! p_LmEqual(p1, p2,r)) |
---|
| 3746 | { |
---|
| 3747 | n_Delete(&n, r); |
---|
| 3748 | return FALSE; |
---|
| 3749 | } |
---|
| 3750 | if (!n_Equal(p_GetCoeff(p1, r), nn = n_Mult(p_GetCoeff(p2, r),n, r), r)) |
---|
| 3751 | { |
---|
| 3752 | n_Delete(&n, r); |
---|
| 3753 | n_Delete(&nn, r); |
---|
| 3754 | return FALSE; |
---|
| 3755 | } |
---|
| 3756 | n_Delete(&nn, r); |
---|
| 3757 | pIter(p1); |
---|
| 3758 | pIter(p2); |
---|
| 3759 | } |
---|
| 3760 | n_Delete(&n, r); |
---|
| 3761 | return TRUE; |
---|
| 3762 | } |
---|
| 3763 | |
---|
[1fdb6e] | 3764 | /*2 |
---|
| 3765 | * returns the length of a (numbers of monomials) |
---|
| 3766 | * respect syzComp |
---|
| 3767 | */ |
---|
| 3768 | poly p_Last(poly a, int &l, const ring r) |
---|
| 3769 | { |
---|
| 3770 | if (a == NULL) |
---|
| 3771 | { |
---|
| 3772 | l = 0; |
---|
| 3773 | return NULL; |
---|
| 3774 | } |
---|
| 3775 | l = 1; |
---|
| 3776 | if (! rIsSyzIndexRing(r)) |
---|
| 3777 | { |
---|
| 3778 | while (pNext(a)!=NULL) |
---|
| 3779 | { |
---|
| 3780 | pIter(a); |
---|
| 3781 | l++; |
---|
| 3782 | } |
---|
| 3783 | } |
---|
| 3784 | else |
---|
| 3785 | { |
---|
| 3786 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 3787 | poly pp = a; |
---|
| 3788 | while ((a=pNext(a))!=NULL) |
---|
| 3789 | { |
---|
| 3790 | if (p_GetComp(a,r)<=curr_limit/*syzComp*/) |
---|
| 3791 | l++; |
---|
| 3792 | else break; |
---|
| 3793 | pp = a; |
---|
| 3794 | } |
---|
| 3795 | a=pp; |
---|
| 3796 | } |
---|
| 3797 | return a; |
---|
| 3798 | } |
---|
[32d07a5] | 3799 | |
---|
[73ad0c] | 3800 | int p_Var(poly m,const ring r) |
---|
| 3801 | { |
---|
| 3802 | if (m==NULL) return 0; |
---|
| 3803 | if (pNext(m)!=NULL) return 0; |
---|
| 3804 | int i,e=0; |
---|
| 3805 | for (i=rVar(r); i>0; i--) |
---|
| 3806 | { |
---|
| 3807 | int exp=p_GetExp(m,i,r); |
---|
| 3808 | if (exp==1) |
---|
| 3809 | { |
---|
| 3810 | if (e==0) e=i; |
---|
| 3811 | else return 0; |
---|
| 3812 | } |
---|
| 3813 | else if (exp!=0) |
---|
| 3814 | { |
---|
| 3815 | return 0; |
---|
| 3816 | } |
---|
| 3817 | } |
---|
| 3818 | return e; |
---|
| 3819 | } |
---|
| 3820 | |
---|
| 3821 | /*2 |
---|
| 3822 | *the minimal index of used variables - 1 |
---|
| 3823 | */ |
---|
| 3824 | int p_LowVar (poly p, const ring r) |
---|
| 3825 | { |
---|
| 3826 | int k,l,lex; |
---|
| 3827 | |
---|
| 3828 | if (p == NULL) return -1; |
---|
| 3829 | |
---|
| 3830 | k = 32000;/*a very large dummy value*/ |
---|
| 3831 | while (p != NULL) |
---|
| 3832 | { |
---|
| 3833 | l = 1; |
---|
| 3834 | lex = p_GetExp(p,l,r); |
---|
| 3835 | while ((l < (rVar(r))) && (lex == 0)) |
---|
| 3836 | { |
---|
| 3837 | l++; |
---|
| 3838 | lex = p_GetExp(p,l,r); |
---|
| 3839 | } |
---|
| 3840 | l--; |
---|
| 3841 | if (l < k) k = l; |
---|
| 3842 | pIter(p); |
---|
| 3843 | } |
---|
| 3844 | return k; |
---|
| 3845 | } |
---|
| 3846 | |
---|
[b7cfaf] | 3847 | /*2 |
---|
| 3848 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
| 3849 | */ |
---|
| 3850 | void p_Shift (poly * p,int i, const ring r) |
---|
| 3851 | { |
---|
| 3852 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
| 3853 | int j = p_MaxComp(*p,r),k = p_MinComp(*p,r); |
---|
| 3854 | |
---|
| 3855 | if (j+i < 0) return ; |
---|
| 3856 | while (qp1 != NULL) |
---|
| 3857 | { |
---|
| 3858 | if ((p_GetComp(qp1,r)+i > 0) || ((j == -i) && (j == k))) |
---|
| 3859 | { |
---|
| 3860 | p_AddComp(qp1,i,r); |
---|
| 3861 | p_SetmComp(qp1,r); |
---|
| 3862 | qp2 = qp1; |
---|
| 3863 | pIter(qp1); |
---|
| 3864 | } |
---|
| 3865 | else |
---|
| 3866 | { |
---|
| 3867 | if (qp2 == *p) |
---|
| 3868 | { |
---|
| 3869 | pIter(*p); |
---|
| 3870 | p_LmDelete(&qp2,r); |
---|
| 3871 | qp2 = *p; |
---|
| 3872 | qp1 = *p; |
---|
| 3873 | } |
---|
| 3874 | else |
---|
| 3875 | { |
---|
| 3876 | qp2->next = qp1->next; |
---|
| 3877 | if (qp1!=NULL) p_LmDelete(&qp1,r); |
---|
| 3878 | qp1 = qp2->next; |
---|
| 3879 | } |
---|
| 3880 | } |
---|
| 3881 | } |
---|
| 3882 | } |
---|
[50c414] | 3883 | /*************************************************************** |
---|
| 3884 | * |
---|
| 3885 | * p_ShallowDelete |
---|
| 3886 | * |
---|
| 3887 | ***************************************************************/ |
---|
| 3888 | #undef LINKAGE |
---|
| 3889 | #define LINKAGE |
---|
[38500a] | 3890 | #undef p_Delete__T |
---|
| 3891 | #define p_Delete__T p_ShallowDelete |
---|
[35eaf8] | 3892 | #undef n_Delete__T |
---|
| 3893 | #define n_Delete__T(n, r) ((void)0) |
---|
[50c414] | 3894 | |
---|
[20b794] | 3895 | #include <polys/templates/p_Delete__T.cc> |
---|
[50c414] | 3896 | |
---|