[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /*************************************************************** |
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| 5 | * File: p_polys.cc |
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[45d2332] | 6 | * Purpose: implementation of ring independent poly procedures? |
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[35aab3] | 7 | * Author: obachman (Olaf Bachmann) |
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| 8 | * Created: 8/00 |
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| 9 | *******************************************************************/ |
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| 10 | |
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[9982049] | 11 | |
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[22a09d] | 12 | #include "config.h" |
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| 13 | |
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| 14 | #include <ctype.h> |
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[f3094a] | 15 | |
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[22a09d] | 16 | #include <omalloc/omalloc.h> |
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[f3094a] | 17 | |
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| 18 | #include <misc/auxiliary.h> |
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| 19 | |
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[45d2332] | 20 | #include <misc/options.h> |
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| 21 | #include <misc/intvec.h> |
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| 22 | |
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| 23 | #include <coeffs/longrat.h> // ??? |
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[b38d70] | 24 | #include <coeffs/ffields.h> |
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| 25 | |
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[975db18] | 26 | #include <polys/PolyEnumerator.h> |
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| 27 | |
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[b38d70] | 28 | #define TRANSEXT_PRIVATES |
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| 29 | |
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[805d0b1] | 30 | #include <polys/ext_fields/transext.h> |
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| 31 | #include <polys/ext_fields/algext.h> |
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[45d2332] | 32 | |
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[805d0b1] | 33 | #include <polys/weight.h> |
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| 34 | #include <polys/simpleideals.h> |
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| 35 | |
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| 36 | #include "ring.h" |
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| 37 | #include "p_polys.h" |
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[9982049] | 38 | |
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[304ad9b] | 39 | #include <polys/templates/p_MemCmp.h> |
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| 40 | #include <polys/templates/p_MemAdd.h> |
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| 41 | #include <polys/templates/p_MemCopy.h> |
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| 42 | |
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[45d2332] | 43 | |
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[20b794] | 44 | // #include <???/ideals.h> |
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| 45 | // #include <???/int64vec.h> |
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[45d2332] | 46 | |
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[fc5095] | 47 | #ifndef NDEBUG |
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[20b794] | 48 | // #include <???/febase.h> |
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[fc5095] | 49 | #endif |
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[35aab3] | 50 | |
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[45d2332] | 51 | #ifdef HAVE_PLURAL |
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[af598e] | 52 | #include "nc/nc.h" |
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| 53 | #include "nc/sca.h" |
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[45d2332] | 54 | #endif |
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| 55 | |
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[af598e] | 56 | #include "coeffrings.h" |
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[0654122] | 57 | #ifdef HAVE_FACTORY |
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[af598e] | 58 | #include "clapsing.h" |
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[0654122] | 59 | #endif |
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[32d07a5] | 60 | |
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[0b0bc3] | 61 | /* |
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| 62 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
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| 63 | */ |
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| 64 | poly p_Farey(poly p, number N, const ring r) |
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| 65 | { |
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| 66 | poly h=p_Copy(p,r); |
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| 67 | poly hh=h; |
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| 68 | while(h!=NULL) |
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| 69 | { |
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| 70 | number c=pGetCoeff(h); |
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| 71 | pSetCoeff0(h,n_Farey(c,N,r->cf)); |
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| 72 | n_Delete(&c,r->cf); |
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| 73 | pIter(h); |
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| 74 | } |
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| 75 | while((hh!=NULL)&&(n_IsZero(pGetCoeff(hh),r->cf))) |
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| 76 | { |
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| 77 | p_LmDelete(&hh,r); |
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| 78 | } |
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| 79 | h=hh; |
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| 80 | while((h!=NULL) && (pNext(h)!=NULL)) |
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| 81 | { |
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| 82 | if(n_IsZero(pGetCoeff(pNext(h)),r->cf)) |
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| 83 | { |
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| 84 | p_LmDelete(&pNext(h),r); |
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| 85 | } |
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| 86 | else pIter(h); |
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| 87 | } |
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| 88 | return hh; |
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| 89 | } |
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| 90 | /*2 |
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| 91 | * xx,q: arrays of length 0..rl-1 |
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| 92 | * xx[i]: SB mod q[i] |
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| 93 | * assume: char=0 |
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| 94 | * assume: q[i]!=0 |
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| 95 | * destroys xx |
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| 96 | */ |
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| 97 | poly p_ChineseRemainder(poly *xx, number *x,number *q, int rl, const ring R) |
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| 98 | { |
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| 99 | poly r,h,hh; |
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| 100 | int j; |
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| 101 | poly res_p=NULL; |
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| 102 | loop |
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| 103 | { |
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| 104 | /* search the lead term */ |
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| 105 | r=NULL; |
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| 106 | for(j=rl-1;j>=0;j--) |
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| 107 | { |
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| 108 | h=xx[j]; |
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| 109 | if ((h!=NULL) |
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| 110 | &&((r==NULL)||(p_LmCmp(r,h,R)==-1))) |
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| 111 | r=h; |
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| 112 | } |
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| 113 | /* nothing found -> return */ |
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| 114 | if (r==NULL) break; |
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| 115 | /* create the monomial in h */ |
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| 116 | h=p_Head(r,R); |
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| 117 | /* collect the coeffs in x[..]*/ |
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| 118 | for(j=rl-1;j>=0;j--) |
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| 119 | { |
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| 120 | hh=xx[j]; |
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| 121 | if ((hh!=NULL) && (p_LmCmp(r,hh,R)==0)) |
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| 122 | { |
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| 123 | x[j]=pGetCoeff(hh); |
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| 124 | hh=p_LmFreeAndNext(hh,R); |
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| 125 | xx[j]=hh; |
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| 126 | } |
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| 127 | else |
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| 128 | x[j]=n_Init(0, R); |
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| 129 | } |
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[de27d8] | 130 | number n=n_ChineseRemainderSym(x,q,rl,TRUE,R->cf); |
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[0b0bc3] | 131 | for(j=rl-1;j>=0;j--) |
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| 132 | { |
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| 133 | x[j]=NULL; // nlInit(0...) takes no memory |
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| 134 | } |
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| 135 | if (n_IsZero(n,R)) p_Delete(&h,R); |
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| 136 | else |
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| 137 | { |
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| 138 | //Print("new mon:");pWrite(h); |
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[0366c4] | 139 | p_SetCoeff(h,n,R); |
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| 140 | pNext(h)=res_p; |
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| 141 | res_p=h; // building res_p in reverse order! |
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[0b0bc3] | 142 | } |
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| 143 | } |
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[0366c4] | 144 | res_p=pReverse(res_p); |
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[066b2f7] | 145 | p_Test(res_p, R); |
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[c462b60] | 146 | return res_p; |
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[0b0bc3] | 147 | } |
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[35aab3] | 148 | /*************************************************************** |
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| 149 | * |
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| 150 | * Completing what needs to be set for the monomial |
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| 151 | * |
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| 152 | ***************************************************************/ |
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| 153 | // this is special for the syz stuff |
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[eb72ba1] | 154 | static int* _components = NULL; |
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| 155 | static long* _componentsShifted = NULL; |
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| 156 | static int _componentsExternal = 0; |
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[35aab3] | 157 | |
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[fc5095] | 158 | BOOLEAN pSetm_error=0; |
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| 159 | |
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[324710] | 160 | #ifndef NDEBUG |
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| 161 | # define MYTEST 0 |
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| 162 | #else /* ifndef NDEBUG */ |
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| 163 | # define MYTEST 0 |
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| 164 | #endif /* ifndef NDEBUG */ |
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| 165 | |
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[33c36d] | 166 | void p_Setm_General(poly p, const ring r) |
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[35aab3] | 167 | { |
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| 168 | p_LmCheckPolyRing(p, r); |
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| 169 | int pos=0; |
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| 170 | if (r->typ!=NULL) |
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| 171 | { |
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| 172 | loop |
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| 173 | { |
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| 174 | long ord=0; |
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| 175 | sro_ord* o=&(r->typ[pos]); |
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| 176 | switch(o->ord_typ) |
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| 177 | { |
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| 178 | case ro_dp: |
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| 179 | { |
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| 180 | int a,e; |
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| 181 | a=o->data.dp.start; |
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| 182 | e=o->data.dp.end; |
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| 183 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
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| 184 | p->exp[o->data.dp.place]=ord; |
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| 185 | break; |
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| 186 | } |
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| 187 | case ro_wp_neg: |
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| 188 | ord=POLY_NEGWEIGHT_OFFSET; |
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| 189 | // no break; |
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| 190 | case ro_wp: |
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| 191 | { |
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| 192 | int a,e; |
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| 193 | a=o->data.wp.start; |
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| 194 | e=o->data.wp.end; |
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| 195 | int *w=o->data.wp.weights; |
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[fc5095] | 196 | #if 1 |
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[35aab3] | 197 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r)*w[i-a]; |
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[fc5095] | 198 | #else |
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| 199 | long ai; |
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| 200 | int ei,wi; |
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| 201 | for(int i=a;i<=e;i++) |
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| 202 | { |
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| 203 | ei=p_GetExp(p,i,r); |
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| 204 | wi=w[i-a]; |
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| 205 | ai=ei*wi; |
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| 206 | if (ai/ei!=wi) pSetm_error=TRUE; |
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| 207 | ord+=ai; |
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| 208 | if (ord<ai) pSetm_error=TRUE; |
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| 209 | } |
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[ab4778] | 210 | #endif |
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[35aab3] | 211 | p->exp[o->data.wp.place]=ord; |
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| 212 | break; |
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| 213 | } |
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[f93c5e9] | 214 | case ro_am: |
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| 215 | { |
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[3a8a0d9] | 216 | ord = POLY_NEGWEIGHT_OFFSET; |
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| 217 | const short a=o->data.am.start; |
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| 218 | const short e=o->data.am.end; |
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| 219 | const int * w=o->data.am.weights; |
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[f93c5e9] | 220 | #if 1 |
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[3a8a0d9] | 221 | for(short i=a; i<=e; i++, w++) |
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| 222 | ord += ((*w) * p_GetExp(p,i,r)); |
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[f93c5e9] | 223 | #else |
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| 224 | long ai; |
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| 225 | int ei,wi; |
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[3a8a0d9] | 226 | for(short i=a;i<=e;i++) |
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[f93c5e9] | 227 | { |
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| 228 | ei=p_GetExp(p,i,r); |
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| 229 | wi=w[i-a]; |
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| 230 | ai=ei*wi; |
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| 231 | if (ai/ei!=wi) pSetm_error=TRUE; |
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[3a8a0d9] | 232 | ord += ai; |
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[f93c5e9] | 233 | if (ord<ai) pSetm_error=TRUE; |
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| 234 | } |
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| 235 | #endif |
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[3a8a0d9] | 236 | const int c = p_GetComp(p,r); |
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| 237 | |
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| 238 | const short len_gen= o->data.am.len_gen; |
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[0366c4] | 239 | |
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[3a8a0d9] | 240 | if ((c > 0) && (c <= len_gen)) |
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[f93c5e9] | 241 | { |
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[599813] | 242 | assume( w == o->data.am.weights_m ); |
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| 243 | assume( w[0] == len_gen ); |
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| 244 | ord += w[c]; |
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[f93c5e9] | 245 | } |
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[0366c4] | 246 | |
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[3a8a0d9] | 247 | p->exp[o->data.am.place] = ord; |
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[f93c5e9] | 248 | break; |
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| 249 | } |
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[fc5095] | 250 | case ro_wp64: |
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| 251 | { |
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[ab4778] | 252 | int64 ord=0; |
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[fc5095] | 253 | int a,e; |
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| 254 | a=o->data.wp64.start; |
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| 255 | e=o->data.wp64.end; |
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| 256 | int64 *w=o->data.wp64.weights64; |
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| 257 | int64 ei,wi,ai; |
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[2132395] | 258 | for(int i=a;i<=e;i++) |
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[b5d4d1] | 259 | { |
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[fc5095] | 260 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
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| 261 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
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| 262 | ei=(int64)p_GetExp(p,i,r); |
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| 263 | wi=w[i-a]; |
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| 264 | ai=ei*wi; |
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[2132395] | 265 | if(ei!=0 && ai/ei!=wi) |
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[b5d4d1] | 266 | { |
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[fc5095] | 267 | pSetm_error=TRUE; |
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[b5d4d1] | 268 | #if SIZEOF_LONG == 4 |
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[fc5095] | 269 | Print("ai %lld, wi %lld\n",ai,wi); |
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[b5d4d1] | 270 | #else |
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[2132395] | 271 | Print("ai %ld, wi %ld\n",ai,wi); |
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[b5d4d1] | 272 | #endif |
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[fc5095] | 273 | } |
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| 274 | ord+=ai; |
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[2132395] | 275 | if (ord<ai) |
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[b5d4d1] | 276 | { |
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[2132395] | 277 | pSetm_error=TRUE; |
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[b5d4d1] | 278 | #if SIZEOF_LONG == 4 |
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[2132395] | 279 | Print("ai %lld, ord %lld\n",ai,ord); |
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[b5d4d1] | 280 | #else |
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[2132395] | 281 | Print("ai %ld, ord %ld\n",ai,ord); |
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[b5d4d1] | 282 | #endif |
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[fc5095] | 283 | } |
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| 284 | } |
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| 285 | int64 mask=(int64)0x7fffffff; |
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| 286 | long a_0=(long)(ord&mask); //2^31 |
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| 287 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
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| 288 | |
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[ab4778] | 289 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
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| 290 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
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| 291 | //Print("mask: %d",mask); |
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[fc5095] | 292 | |
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| 293 | p->exp[o->data.wp64.place]=a_1; |
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[ab4778] | 294 | p->exp[o->data.wp64.place+1]=a_0; |
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[fc5095] | 295 | // if(p_Setm_error) Print("***************************\n |
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| 296 | // ***************************\n |
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| 297 | // **WARNING: overflow error**\n |
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| 298 | // ***************************\n |
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| 299 | // ***************************\n"); |
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| 300 | break; |
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| 301 | } |
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[35aab3] | 302 | case ro_cp: |
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| 303 | { |
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| 304 | int a,e; |
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| 305 | a=o->data.cp.start; |
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| 306 | e=o->data.cp.end; |
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| 307 | int pl=o->data.cp.place; |
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| 308 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
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| 309 | break; |
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| 310 | } |
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| 311 | case ro_syzcomp: |
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| 312 | { |
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| 313 | int c=p_GetComp(p,r); |
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| 314 | long sc = c; |
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[eb72ba1] | 315 | int* Components = (_componentsExternal ? _components : |
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[35aab3] | 316 | o->data.syzcomp.Components); |
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[eb72ba1] | 317 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
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[35aab3] | 318 | o->data.syzcomp.ShiftedComponents); |
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| 319 | if (ShiftedComponents != NULL) |
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| 320 | { |
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| 321 | assume(Components != NULL); |
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| 322 | assume(c == 0 || Components[c] != 0); |
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| 323 | sc = ShiftedComponents[Components[c]]; |
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| 324 | assume(c == 0 || sc != 0); |
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| 325 | } |
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| 326 | p->exp[o->data.syzcomp.place]=sc; |
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| 327 | break; |
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| 328 | } |
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| 329 | case ro_syz: |
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| 330 | { |
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[273fed] | 331 | const unsigned long c = p_GetComp(p, r); |
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| 332 | const short place = o->data.syz.place; |
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| 333 | const int limit = o->data.syz.limit; |
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[f93c5e9] | 334 | |
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[d30a399] | 335 | if (c > (unsigned long)limit) |
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[273fed] | 336 | p->exp[place] = o->data.syz.curr_index; |
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[35aab3] | 337 | else if (c > 0) |
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[273fed] | 338 | { |
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[d30a399] | 339 | assume( (1 <= c) && (c <= (unsigned long)limit) ); |
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[273fed] | 340 | p->exp[place]= o->data.syz.syz_index[c]; |
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| 341 | } |
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[35aab3] | 342 | else |
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| 343 | { |
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| 344 | assume(c == 0); |
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[273fed] | 345 | p->exp[place]= 0; |
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[35aab3] | 346 | } |
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| 347 | break; |
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| 348 | } |
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[645a19] | 349 | // Prefix for Induced Schreyer ordering |
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| 350 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
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| 351 | { |
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| 352 | assume(p != NULL); |
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| 353 | |
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| 354 | #ifndef NDEBUG |
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| 355 | #if MYTEST |
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[5c0183] | 356 | Print("p_Setm_General: ro_isTemp ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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[645a19] | 357 | #endif |
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| 358 | #endif |
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| 359 | int c = p_GetComp(p, r); |
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| 360 | |
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| 361 | assume( c >= 0 ); |
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| 362 | |
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| 363 | // Let's simulate case ro_syz above.... |
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| 364 | // Should accumulate (by Suffix) and be a level indicator |
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| 365 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
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| 366 | |
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| 367 | assume( pVarOffset != NULL ); |
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| 368 | |
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| 369 | // TODO: Can this be done in the suffix??? |
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| 370 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 371 | { |
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| 372 | const int vo = pVarOffset[i]; |
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| 373 | if( vo != -1) // TODO: optimize: can be done once! |
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| 374 | { |
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[5cb9ec] | 375 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
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| 376 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
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| 377 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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| 378 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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[645a19] | 379 | } |
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| 380 | } |
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| 381 | #ifndef NDEBUG |
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| 382 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
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| 383 | { |
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| 384 | const int vo = pVarOffset[i]; |
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| 385 | if( vo != -1) // TODO: optimize: can be done once! |
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| 386 | { |
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[5cb9ec] | 387 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
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| 388 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
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[645a19] | 389 | } |
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| 390 | } |
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| 391 | #if MYTEST |
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[1b816a3] | 392 | // if( p->exp[o->data.isTemp.start] > 0 ) |
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[5c0183] | 393 | PrintS("after Values: "); p_DebugPrint(p, r, r, 1); |
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[645a19] | 394 | #endif |
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| 395 | #endif |
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| 396 | break; |
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| 397 | } |
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| 398 | |
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| 399 | // Suffix for Induced Schreyer ordering |
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| 400 | case ro_is: |
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| 401 | { |
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[273fed] | 402 | #ifndef NDEBUG |
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| 403 | #if MYTEST |
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| 404 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
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| 405 | #endif |
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| 406 | #endif |
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| 407 | |
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[645a19] | 408 | assume(p != NULL); |
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| 409 | |
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| 410 | int c = p_GetComp(p, r); |
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| 411 | |
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| 412 | assume( c >= 0 ); |
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| 413 | const ideal F = o->data.is.F; |
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| 414 | const int limit = o->data.is.limit; |
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[e4f491] | 415 | assume( limit >= 0 ); |
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[5c0183] | 416 | const int start = o->data.is.start; |
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[645a19] | 417 | |
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| 418 | if( F != NULL && c > limit ) |
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| 419 | { |
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| 420 | #ifndef NDEBUG |
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| 421 | #if MYTEST |
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[6e66d2] | 422 | Print("p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit); // p_DebugPrint(p, r, r, 1); |
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[5c0183] | 423 | PrintS("preComputed Values: "); |
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| 424 | p_DebugPrint(p, r, r, 1); |
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[645a19] | 425 | #endif |
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| 426 | #endif |
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[e4f491] | 427 | // if( c > limit ) // BUG??? |
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| 428 | p->exp[start] = 1; |
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| 429 | // else |
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| 430 | // p->exp[start] = 0; |
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| 431 | |
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[645a19] | 432 | |
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| 433 | c -= limit; |
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| 434 | assume( c > 0 ); |
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| 435 | c--; |
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| 436 | |
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[e4f491] | 437 | if( c >= IDELEMS(F) ) |
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| 438 | break; |
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| 439 | |
---|
[de0a2a] | 440 | assume( c < IDELEMS(F) ); // What about others??? |
---|
[0366c4] | 441 | |
---|
[645a19] | 442 | const poly pp = F->m[c]; // get reference monomial!!! |
---|
| 443 | |
---|
[de0a2a] | 444 | if(pp == NULL) |
---|
| 445 | break; |
---|
[0366c4] | 446 | |
---|
[e4f491] | 447 | assume(pp != NULL); |
---|
| 448 | |
---|
[645a19] | 449 | #ifndef NDEBUG |
---|
| 450 | #if MYTEST |
---|
[f93c5e9] | 451 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
---|
[645a19] | 452 | p_DebugPrint(pp, r, r, 1); |
---|
| 453 | #endif |
---|
| 454 | #endif |
---|
| 455 | |
---|
| 456 | const int end = o->data.is.end; |
---|
| 457 | assume(start <= end); |
---|
[6e66d2] | 458 | |
---|
| 459 | |
---|
[f93c5e9] | 460 | // const int st = o->data.isTemp.start; |
---|
[5c0183] | 461 | |
---|
[6e66d2] | 462 | #ifndef NDEBUG |
---|
[5c0183] | 463 | Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]); |
---|
[e4f491] | 464 | #endif |
---|
[5c0183] | 465 | |
---|
| 466 | // p_ExpVectorAdd(p, pp, r); |
---|
[645a19] | 467 | |
---|
| 468 | for( int i = start; i <= end; i++) // v[0] may be here... |
---|
| 469 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
---|
| 470 | |
---|
[5c0183] | 471 | // p_MemAddAdjust(p, ri); |
---|
| 472 | if (r->NegWeightL_Offset != NULL) |
---|
| 473 | { |
---|
| 474 | for (int i=r->NegWeightL_Size-1; i>=0; i--) |
---|
| 475 | { |
---|
| 476 | const int _i = r->NegWeightL_Offset[i]; |
---|
| 477 | if( start <= _i && _i <= end ) |
---|
| 478 | p->exp[_i] -= POLY_NEGWEIGHT_OFFSET; |
---|
| 479 | } |
---|
| 480 | } |
---|
| 481 | |
---|
[6e66d2] | 482 | |
---|
[645a19] | 483 | #ifndef NDEBUG |
---|
| 484 | const int* const pVarOffset = o->data.is.pVarOffset; |
---|
| 485 | |
---|
| 486 | assume( pVarOffset != NULL ); |
---|
| 487 | |
---|
| 488 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
---|
| 489 | { |
---|
| 490 | const int vo = pVarOffset[i]; |
---|
| 491 | if( vo != -1) // TODO: optimize: can be done once! |
---|
[5cb9ec] | 492 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
---|
| 493 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
---|
[645a19] | 494 | } |
---|
| 495 | // TODO: how to check this for computed values??? |
---|
[5c0183] | 496 | #if MYTEST |
---|
| 497 | PrintS("Computed Values: "); p_DebugPrint(p, r, r, 1); |
---|
| 498 | #endif |
---|
[645a19] | 499 | #endif |
---|
| 500 | } else |
---|
| 501 | { |
---|
[5c0183] | 502 | p->exp[start] = 0; //!!!!????? where????? |
---|
[f93c5e9] | 503 | |
---|
[645a19] | 504 | const int* const pVarOffset = o->data.is.pVarOffset; |
---|
| 505 | |
---|
| 506 | // What about v[0] - component: it will be added later by |
---|
| 507 | // suffix!!! |
---|
| 508 | // TODO: Test it! |
---|
| 509 | const int vo = pVarOffset[0]; |
---|
| 510 | if( vo != -1 ) |
---|
| 511 | p->exp[vo] = c; // initial component v[0]! |
---|
[6e66d2] | 512 | |
---|
| 513 | #ifndef NDEBUG |
---|
| 514 | #if MYTEST |
---|
[5c0183] | 515 | Print("ELSE p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]); |
---|
[6e66d2] | 516 | p_DebugPrint(p, r, r, 1); |
---|
[5c0183] | 517 | #endif |
---|
| 518 | #endif |
---|
[645a19] | 519 | } |
---|
| 520 | |
---|
| 521 | break; |
---|
| 522 | } |
---|
[35aab3] | 523 | default: |
---|
| 524 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
---|
| 525 | return; |
---|
| 526 | } |
---|
| 527 | pos++; |
---|
| 528 | if (pos == r->OrdSize) return; |
---|
| 529 | } |
---|
| 530 | } |
---|
| 531 | } |
---|
| 532 | |
---|
| 533 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
---|
| 534 | { |
---|
[eb72ba1] | 535 | _components = Components; |
---|
| 536 | _componentsShifted = ShiftedComponents; |
---|
| 537 | _componentsExternal = 1; |
---|
[35aab3] | 538 | p_Setm_General(p, r); |
---|
[eb72ba1] | 539 | _componentsExternal = 0; |
---|
[35aab3] | 540 | } |
---|
| 541 | |
---|
| 542 | // dummy for lp, ls, etc |
---|
[33c36d] | 543 | void p_Setm_Dummy(poly p, const ring r) |
---|
[35aab3] | 544 | { |
---|
| 545 | p_LmCheckPolyRing(p, r); |
---|
| 546 | } |
---|
| 547 | |
---|
| 548 | // for dp, Dp, ds, etc |
---|
[33c36d] | 549 | void p_Setm_TotalDegree(poly p, const ring r) |
---|
[35aab3] | 550 | { |
---|
| 551 | p_LmCheckPolyRing(p, r); |
---|
[99bdcf] | 552 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
---|
[35aab3] | 553 | } |
---|
| 554 | |
---|
| 555 | // for wp, Wp, ws, etc |
---|
[33c36d] | 556 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
---|
[35aab3] | 557 | { |
---|
| 558 | p_LmCheckPolyRing(p, r); |
---|
[19ae652] | 559 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 560 | } |
---|
| 561 | |
---|
| 562 | p_SetmProc p_GetSetmProc(ring r) |
---|
| 563 | { |
---|
[ab4778] | 564 | // covers lp, rp, ls, |
---|
[35aab3] | 565 | if (r->typ == NULL) return p_Setm_Dummy; |
---|
| 566 | |
---|
| 567 | if (r->OrdSize == 1) |
---|
| 568 | { |
---|
[ab4778] | 569 | if (r->typ[0].ord_typ == ro_dp && |
---|
[35aab3] | 570 | r->typ[0].data.dp.start == 1 && |
---|
| 571 | r->typ[0].data.dp.end == r->N && |
---|
| 572 | r->typ[0].data.dp.place == r->pOrdIndex) |
---|
| 573 | return p_Setm_TotalDegree; |
---|
[ab4778] | 574 | if (r->typ[0].ord_typ == ro_wp && |
---|
[35aab3] | 575 | r->typ[0].data.wp.start == 1 && |
---|
| 576 | r->typ[0].data.wp.end == r->N && |
---|
| 577 | r->typ[0].data.wp.place == r->pOrdIndex && |
---|
| 578 | r->typ[0].data.wp.weights == r->firstwv) |
---|
| 579 | return p_Setm_WFirstTotalDegree; |
---|
| 580 | } |
---|
| 581 | return p_Setm_General; |
---|
| 582 | } |
---|
| 583 | |
---|
| 584 | |
---|
| 585 | /* -------------------------------------------------------------------*/ |
---|
| 586 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
[b5d4d1] | 587 | |
---|
| 588 | /* comptible with ordering */ |
---|
[bf183f] | 589 | long p_Deg(poly a, const ring r) |
---|
[35aab3] | 590 | { |
---|
| 591 | p_LmCheckPolyRing(a, r); |
---|
[74f51f] | 592 | // assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); // WRONG assume! |
---|
[35aab3] | 593 | return p_GetOrder(a, r); |
---|
| 594 | } |
---|
| 595 | |
---|
[19ae652] | 596 | // p_WTotalDegree for weighted orderings |
---|
[35aab3] | 597 | // whose first block covers all variables |
---|
[19ae652] | 598 | long p_WFirstTotalDegree(poly p, const ring r) |
---|
[35aab3] | 599 | { |
---|
| 600 | int i; |
---|
| 601 | long sum = 0; |
---|
[ab4778] | 602 | |
---|
[35aab3] | 603 | for (i=1; i<= r->firstBlockEnds; i++) |
---|
| 604 | { |
---|
| 605 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 606 | } |
---|
| 607 | return sum; |
---|
| 608 | } |
---|
| 609 | |
---|
| 610 | /*2 |
---|
| 611 | * compute the degree of the leading monomial of p |
---|
| 612 | * with respect to weigths from the ordering |
---|
| 613 | * the ordering is not compatible with degree so do not use p->Order |
---|
| 614 | */ |
---|
[19ae652] | 615 | long p_WTotaldegree(poly p, const ring r) |
---|
[35aab3] | 616 | { |
---|
| 617 | p_LmCheckPolyRing(p, r); |
---|
| 618 | int i, k; |
---|
| 619 | long j =0; |
---|
| 620 | |
---|
| 621 | // iterate through each block: |
---|
| 622 | for (i=0;r->order[i]!=0;i++) |
---|
| 623 | { |
---|
[ab4778] | 624 | int b0=r->block0[i]; |
---|
| 625 | int b1=r->block1[i]; |
---|
[35aab3] | 626 | switch(r->order[i]) |
---|
| 627 | { |
---|
[3e0a7b] | 628 | case ringorder_M: |
---|
[ab4778] | 629 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
| 630 | { // in jedem block: |
---|
| 631 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
---|
| 632 | } |
---|
| 633 | break; |
---|
[35aab3] | 634 | case ringorder_wp: |
---|
| 635 | case ringorder_ws: |
---|
| 636 | case ringorder_Wp: |
---|
| 637 | case ringorder_Ws: |
---|
[ab4778] | 638 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 639 | { // in jedem block: |
---|
[ab4778] | 640 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
---|
[35aab3] | 641 | } |
---|
| 642 | break; |
---|
| 643 | case ringorder_lp: |
---|
| 644 | case ringorder_ls: |
---|
[e519c5c] | 645 | case ringorder_rs: |
---|
[35aab3] | 646 | case ringorder_dp: |
---|
| 647 | case ringorder_ds: |
---|
| 648 | case ringorder_Dp: |
---|
| 649 | case ringorder_Ds: |
---|
| 650 | case ringorder_rp: |
---|
[ab4778] | 651 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 652 | { |
---|
| 653 | j+= p_GetExp(p,k,r); |
---|
| 654 | } |
---|
| 655 | break; |
---|
[fc5095] | 656 | case ringorder_a64: |
---|
| 657 | { |
---|
| 658 | int64* w=(int64*)r->wvhdl[i]; |
---|
[ab4778] | 659 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
---|
| 660 | { |
---|
[fc5095] | 661 | //there should be added a line which checks if w[k]>2^31 |
---|
| 662 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
---|
| 663 | } |
---|
| 664 | //break; |
---|
| 665 | return j; |
---|
| 666 | } |
---|
[35aab3] | 667 | case ringorder_c: |
---|
| 668 | case ringorder_C: |
---|
| 669 | case ringorder_S: |
---|
| 670 | case ringorder_s: |
---|
| 671 | case ringorder_aa: |
---|
[74f51f] | 672 | case ringorder_IS: |
---|
| 673 | break; |
---|
[35aab3] | 674 | case ringorder_a: |
---|
[ab4778] | 675 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 676 | { // only one line |
---|
[ab4778] | 677 | j+= p_GetExp(p,k, r)*r->wvhdl[i][ k- b0 /*r->block0[i]*/]; |
---|
[35aab3] | 678 | } |
---|
[fc5095] | 679 | //break; |
---|
[35aab3] | 680 | return j; |
---|
[fc5095] | 681 | |
---|
[35aab3] | 682 | #ifndef NDEBUG |
---|
| 683 | default: |
---|
[19ae652] | 684 | Print("missing order %d in p_WTotaldegree\n",r->order[i]); |
---|
[35aab3] | 685 | break; |
---|
| 686 | #endif |
---|
| 687 | } |
---|
| 688 | } |
---|
| 689 | return j; |
---|
| 690 | } |
---|
| 691 | |
---|
[ba0fc3] | 692 | long p_DegW(poly p, const short *w, const ring R) |
---|
| 693 | { |
---|
| 694 | long r=~0L; |
---|
| 695 | |
---|
| 696 | while (p!=NULL) |
---|
| 697 | { |
---|
| 698 | long t=totaldegreeWecart_IV(p,R,w); |
---|
| 699 | if (t>r) r=t; |
---|
| 700 | pIter(p); |
---|
| 701 | } |
---|
| 702 | return r; |
---|
| 703 | } |
---|
| 704 | |
---|
[bf183f] | 705 | int p_Weight(int i, const ring r) |
---|
[35aab3] | 706 | { |
---|
| 707 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
| 708 | { |
---|
| 709 | return 1; |
---|
| 710 | } |
---|
| 711 | return r->firstwv[i-1]; |
---|
| 712 | } |
---|
| 713 | |
---|
[bf183f] | 714 | long p_WDegree(poly p, const ring r) |
---|
[35aab3] | 715 | { |
---|
[99bdcf] | 716 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
[35aab3] | 717 | p_LmCheckPolyRing(p, r); |
---|
[9f73e80] | 718 | int i; |
---|
[35aab3] | 719 | long j =0; |
---|
| 720 | |
---|
| 721 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
| 722 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 723 | |
---|
| 724 | for (;i<=r->N;i++) |
---|
[8a8c9e] | 725 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
[35aab3] | 726 | |
---|
| 727 | return j; |
---|
| 728 | } |
---|
| 729 | |
---|
| 730 | |
---|
| 731 | /* ---------------------------------------------------------------------*/ |
---|
| 732 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
| 733 | /* compute in l also the pLength of p */ |
---|
| 734 | |
---|
| 735 | /*2 |
---|
| 736 | * compute the length of a polynomial (in l) |
---|
| 737 | * and the degree of the monomial with maximal degree: the last one |
---|
| 738 | */ |
---|
[107986] | 739 | long pLDeg0(poly p,int *l, const ring r) |
---|
[35aab3] | 740 | { |
---|
| 741 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 742 | long k= p_GetComp(p, r); |
---|
[35aab3] | 743 | int ll=1; |
---|
| 744 | |
---|
| 745 | if (k > 0) |
---|
| 746 | { |
---|
| 747 | while ((pNext(p)!=NULL) && (p_GetComp(pNext(p), r)==k)) |
---|
| 748 | { |
---|
| 749 | pIter(p); |
---|
| 750 | ll++; |
---|
| 751 | } |
---|
| 752 | } |
---|
| 753 | else |
---|
| 754 | { |
---|
| 755 | while (pNext(p)!=NULL) |
---|
| 756 | { |
---|
| 757 | pIter(p); |
---|
| 758 | ll++; |
---|
| 759 | } |
---|
| 760 | } |
---|
| 761 | *l=ll; |
---|
| 762 | return r->pFDeg(p, r); |
---|
| 763 | } |
---|
| 764 | |
---|
| 765 | /*2 |
---|
| 766 | * compute the length of a polynomial (in l) |
---|
| 767 | * and the degree of the monomial with maximal degree: the last one |
---|
| 768 | * but search in all components before syzcomp |
---|
| 769 | */ |
---|
[107986] | 770 | long pLDeg0c(poly p,int *l, const ring r) |
---|
[35aab3] | 771 | { |
---|
| 772 | assume(p!=NULL); |
---|
| 773 | #ifdef PDEBUG |
---|
| 774 | _p_Test(p,r,PDEBUG); |
---|
| 775 | #endif |
---|
| 776 | p_CheckPolyRing(p, r); |
---|
| 777 | long o; |
---|
| 778 | int ll=1; |
---|
| 779 | |
---|
| 780 | if (! rIsSyzIndexRing(r)) |
---|
| 781 | { |
---|
[ab4778] | 782 | while (pNext(p) != NULL) |
---|
[35aab3] | 783 | { |
---|
| 784 | pIter(p); |
---|
| 785 | ll++; |
---|
| 786 | } |
---|
| 787 | o = r->pFDeg(p, r); |
---|
| 788 | } |
---|
| 789 | else |
---|
| 790 | { |
---|
| 791 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 792 | poly pp = p; |
---|
| 793 | while ((p=pNext(p))!=NULL) |
---|
| 794 | { |
---|
| 795 | if (p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
| 796 | ll++; |
---|
| 797 | else break; |
---|
| 798 | pp = p; |
---|
| 799 | } |
---|
| 800 | #ifdef PDEBUG |
---|
| 801 | _p_Test(pp,r,PDEBUG); |
---|
| 802 | #endif |
---|
| 803 | o = r->pFDeg(pp, r); |
---|
| 804 | } |
---|
| 805 | *l=ll; |
---|
| 806 | return o; |
---|
| 807 | } |
---|
| 808 | |
---|
| 809 | /*2 |
---|
| 810 | * compute the length of a polynomial (in l) |
---|
| 811 | * and the degree of the monomial with maximal degree: the first one |
---|
| 812 | * this works for the polynomial case with degree orderings |
---|
| 813 | * (both c,dp and dp,c) |
---|
| 814 | */ |
---|
[107986] | 815 | long pLDegb(poly p,int *l, const ring r) |
---|
[35aab3] | 816 | { |
---|
| 817 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 818 | long k= p_GetComp(p, r); |
---|
[35aab3] | 819 | long o = r->pFDeg(p, r); |
---|
| 820 | int ll=1; |
---|
| 821 | |
---|
| 822 | if (k != 0) |
---|
| 823 | { |
---|
| 824 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 825 | { |
---|
| 826 | ll++; |
---|
| 827 | } |
---|
| 828 | } |
---|
| 829 | else |
---|
| 830 | { |
---|
| 831 | while ((p=pNext(p)) !=NULL) |
---|
| 832 | { |
---|
| 833 | ll++; |
---|
| 834 | } |
---|
| 835 | } |
---|
| 836 | *l=ll; |
---|
| 837 | return o; |
---|
| 838 | } |
---|
| 839 | |
---|
| 840 | /*2 |
---|
| 841 | * compute the length of a polynomial (in l) |
---|
| 842 | * and the degree of the monomial with maximal degree: |
---|
| 843 | * this is NOT the last one, we have to look for it |
---|
| 844 | */ |
---|
[107986] | 845 | long pLDeg1(poly p,int *l, const ring r) |
---|
[35aab3] | 846 | { |
---|
| 847 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 848 | long k= p_GetComp(p, r); |
---|
[35aab3] | 849 | int ll=1; |
---|
| 850 | long t,max; |
---|
| 851 | |
---|
| 852 | max=r->pFDeg(p, r); |
---|
| 853 | if (k > 0) |
---|
| 854 | { |
---|
| 855 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 856 | { |
---|
| 857 | t=r->pFDeg(p, r); |
---|
| 858 | if (t>max) max=t; |
---|
| 859 | ll++; |
---|
| 860 | } |
---|
| 861 | } |
---|
| 862 | else |
---|
| 863 | { |
---|
| 864 | while ((p=pNext(p))!=NULL) |
---|
| 865 | { |
---|
| 866 | t=r->pFDeg(p, r); |
---|
| 867 | if (t>max) max=t; |
---|
| 868 | ll++; |
---|
| 869 | } |
---|
| 870 | } |
---|
| 871 | *l=ll; |
---|
| 872 | return max; |
---|
| 873 | } |
---|
| 874 | |
---|
| 875 | /*2 |
---|
| 876 | * compute the length of a polynomial (in l) |
---|
| 877 | * and the degree of the monomial with maximal degree: |
---|
| 878 | * this is NOT the last one, we have to look for it |
---|
| 879 | * in all components |
---|
| 880 | */ |
---|
[107986] | 881 | long pLDeg1c(poly p,int *l, const ring r) |
---|
[35aab3] | 882 | { |
---|
| 883 | p_CheckPolyRing(p, r); |
---|
| 884 | int ll=1; |
---|
| 885 | long t,max; |
---|
| 886 | |
---|
| 887 | max=r->pFDeg(p, r); |
---|
| 888 | if (rIsSyzIndexRing(r)) |
---|
| 889 | { |
---|
| 890 | long limit = rGetCurrSyzLimit(r); |
---|
| 891 | while ((p=pNext(p))!=NULL) |
---|
| 892 | { |
---|
| 893 | if (p_GetComp(p, r)<=limit) |
---|
| 894 | { |
---|
| 895 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 896 | ll++; |
---|
| 897 | } |
---|
| 898 | else break; |
---|
| 899 | } |
---|
| 900 | } |
---|
| 901 | else |
---|
| 902 | { |
---|
| 903 | while ((p=pNext(p))!=NULL) |
---|
| 904 | { |
---|
| 905 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 906 | ll++; |
---|
| 907 | } |
---|
| 908 | } |
---|
| 909 | *l=ll; |
---|
| 910 | return max; |
---|
| 911 | } |
---|
| 912 | |
---|
| 913 | // like pLDeg1, only pFDeg == pDeg |
---|
[107986] | 914 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 915 | { |
---|
[45d2332] | 916 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 917 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 918 | long k= p_GetComp(p, r); |
---|
[35aab3] | 919 | int ll=1; |
---|
| 920 | long t,max; |
---|
| 921 | |
---|
[b5d4d1] | 922 | max=p_GetOrder(p, r); |
---|
[35aab3] | 923 | if (k > 0) |
---|
| 924 | { |
---|
| 925 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 926 | { |
---|
[b5d4d1] | 927 | t=p_GetOrder(p, r); |
---|
[35aab3] | 928 | if (t>max) max=t; |
---|
| 929 | ll++; |
---|
| 930 | } |
---|
| 931 | } |
---|
| 932 | else |
---|
| 933 | { |
---|
| 934 | while ((p=pNext(p))!=NULL) |
---|
| 935 | { |
---|
[b5d4d1] | 936 | t=p_GetOrder(p, r); |
---|
[35aab3] | 937 | if (t>max) max=t; |
---|
| 938 | ll++; |
---|
| 939 | } |
---|
| 940 | } |
---|
| 941 | *l=ll; |
---|
| 942 | return max; |
---|
| 943 | } |
---|
| 944 | |
---|
[107986] | 945 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 946 | { |
---|
[45d2332] | 947 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 948 | p_CheckPolyRing(p, r); |
---|
| 949 | int ll=1; |
---|
| 950 | long t,max; |
---|
| 951 | |
---|
[b5d4d1] | 952 | max=p_GetOrder(p, r); |
---|
[35aab3] | 953 | if (rIsSyzIndexRing(r)) |
---|
| 954 | { |
---|
| 955 | long limit = rGetCurrSyzLimit(r); |
---|
| 956 | while ((p=pNext(p))!=NULL) |
---|
| 957 | { |
---|
| 958 | if (p_GetComp(p, r)<=limit) |
---|
| 959 | { |
---|
[b5d4d1] | 960 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 961 | ll++; |
---|
| 962 | } |
---|
| 963 | else break; |
---|
| 964 | } |
---|
| 965 | } |
---|
| 966 | else |
---|
| 967 | { |
---|
| 968 | while ((p=pNext(p))!=NULL) |
---|
| 969 | { |
---|
[b5d4d1] | 970 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 971 | ll++; |
---|
| 972 | } |
---|
| 973 | } |
---|
| 974 | *l=ll; |
---|
| 975 | return max; |
---|
| 976 | } |
---|
| 977 | |
---|
| 978 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
[107986] | 979 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 980 | { |
---|
| 981 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 982 | long k= p_GetComp(p, r); |
---|
[35aab3] | 983 | int ll=1; |
---|
| 984 | long t,max; |
---|
| 985 | |
---|
[99bdcf] | 986 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 987 | if (k > 0) |
---|
| 988 | { |
---|
| 989 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 990 | { |
---|
[99bdcf] | 991 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 992 | if (t>max) max=t; |
---|
| 993 | ll++; |
---|
| 994 | } |
---|
| 995 | } |
---|
| 996 | else |
---|
| 997 | { |
---|
| 998 | while ((p=pNext(p))!=NULL) |
---|
| 999 | { |
---|
[99bdcf] | 1000 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 1001 | if (t>max) max=t; |
---|
| 1002 | ll++; |
---|
| 1003 | } |
---|
| 1004 | } |
---|
| 1005 | *l=ll; |
---|
| 1006 | return max; |
---|
| 1007 | } |
---|
| 1008 | |
---|
[107986] | 1009 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 1010 | { |
---|
| 1011 | p_CheckPolyRing(p, r); |
---|
| 1012 | int ll=1; |
---|
| 1013 | long t,max; |
---|
| 1014 | |
---|
[99bdcf] | 1015 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 1016 | if (rIsSyzIndexRing(r)) |
---|
| 1017 | { |
---|
| 1018 | long limit = rGetCurrSyzLimit(r); |
---|
| 1019 | while ((p=pNext(p))!=NULL) |
---|
| 1020 | { |
---|
| 1021 | if (p_GetComp(p, r)<=limit) |
---|
| 1022 | { |
---|
[99bdcf] | 1023 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 1024 | ll++; |
---|
| 1025 | } |
---|
| 1026 | else break; |
---|
| 1027 | } |
---|
| 1028 | } |
---|
| 1029 | else |
---|
| 1030 | { |
---|
| 1031 | while ((p=pNext(p))!=NULL) |
---|
| 1032 | { |
---|
[99bdcf] | 1033 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 1034 | ll++; |
---|
| 1035 | } |
---|
| 1036 | } |
---|
| 1037 | *l=ll; |
---|
| 1038 | return max; |
---|
| 1039 | } |
---|
| 1040 | |
---|
[19ae652] | 1041 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
[107986] | 1042 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 1043 | { |
---|
| 1044 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 1045 | long k= p_GetComp(p, r); |
---|
[35aab3] | 1046 | int ll=1; |
---|
| 1047 | long t,max; |
---|
| 1048 | |
---|
[19ae652] | 1049 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 1050 | if (k > 0) |
---|
| 1051 | { |
---|
| 1052 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 1053 | { |
---|
[19ae652] | 1054 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 1055 | if (t>max) max=t; |
---|
| 1056 | ll++; |
---|
| 1057 | } |
---|
| 1058 | } |
---|
| 1059 | else |
---|
| 1060 | { |
---|
| 1061 | while ((p=pNext(p))!=NULL) |
---|
| 1062 | { |
---|
[19ae652] | 1063 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 1064 | if (t>max) max=t; |
---|
| 1065 | ll++; |
---|
| 1066 | } |
---|
| 1067 | } |
---|
| 1068 | *l=ll; |
---|
| 1069 | return max; |
---|
| 1070 | } |
---|
| 1071 | |
---|
[107986] | 1072 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 1073 | { |
---|
| 1074 | p_CheckPolyRing(p, r); |
---|
| 1075 | int ll=1; |
---|
| 1076 | long t,max; |
---|
| 1077 | |
---|
[19ae652] | 1078 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 1079 | if (rIsSyzIndexRing(r)) |
---|
| 1080 | { |
---|
| 1081 | long limit = rGetCurrSyzLimit(r); |
---|
| 1082 | while ((p=pNext(p))!=NULL) |
---|
| 1083 | { |
---|
| 1084 | if (p_GetComp(p, r)<=limit) |
---|
| 1085 | { |
---|
[99bdcf] | 1086 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 1087 | ll++; |
---|
| 1088 | } |
---|
| 1089 | else break; |
---|
| 1090 | } |
---|
| 1091 | } |
---|
| 1092 | else |
---|
| 1093 | { |
---|
| 1094 | while ((p=pNext(p))!=NULL) |
---|
| 1095 | { |
---|
[99bdcf] | 1096 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 1097 | ll++; |
---|
| 1098 | } |
---|
| 1099 | } |
---|
| 1100 | *l=ll; |
---|
| 1101 | return max; |
---|
| 1102 | } |
---|
| 1103 | |
---|
| 1104 | /*************************************************************** |
---|
| 1105 | * |
---|
| 1106 | * Maximal Exponent business |
---|
| 1107 | * |
---|
| 1108 | ***************************************************************/ |
---|
| 1109 | |
---|
[ab4778] | 1110 | static inline unsigned long |
---|
[107986] | 1111 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
[35aab3] | 1112 | unsigned long number_of_exp) |
---|
| 1113 | { |
---|
| 1114 | const unsigned long bitmask = r->bitmask; |
---|
| 1115 | unsigned long ml1 = l1 & bitmask; |
---|
| 1116 | unsigned long ml2 = l2 & bitmask; |
---|
| 1117 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
| 1118 | unsigned long j = number_of_exp - 1; |
---|
| 1119 | |
---|
| 1120 | if (j > 0) |
---|
| 1121 | { |
---|
| 1122 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
| 1123 | while (1) |
---|
| 1124 | { |
---|
| 1125 | ml1 = l1 & mask; |
---|
| 1126 | ml2 = l2 & mask; |
---|
| 1127 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
| 1128 | j--; |
---|
| 1129 | if (j == 0) break; |
---|
| 1130 | mask = mask << r->BitsPerExp; |
---|
| 1131 | } |
---|
| 1132 | } |
---|
| 1133 | return max; |
---|
| 1134 | } |
---|
| 1135 | |
---|
| 1136 | static inline unsigned long |
---|
[107986] | 1137 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
[35aab3] | 1138 | { |
---|
| 1139 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
| 1140 | } |
---|
| 1141 | |
---|
[107986] | 1142 | poly p_GetMaxExpP(poly p, const ring r) |
---|
[35aab3] | 1143 | { |
---|
| 1144 | p_CheckPolyRing(p, r); |
---|
| 1145 | if (p == NULL) return p_Init(r); |
---|
| 1146 | poly max = p_LmInit(p, r); |
---|
| 1147 | pIter(p); |
---|
| 1148 | if (p == NULL) return max; |
---|
| 1149 | int i, offset; |
---|
| 1150 | unsigned long l_p, l_max; |
---|
| 1151 | unsigned long divmask = r->divmask; |
---|
[ab4778] | 1152 | |
---|
[35aab3] | 1153 | do |
---|
| 1154 | { |
---|
| 1155 | offset = r->VarL_Offset[0]; |
---|
| 1156 | l_p = p->exp[offset]; |
---|
| 1157 | l_max = max->exp[offset]; |
---|
| 1158 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1159 | if (l_p > l_max || |
---|
[35aab3] | 1160 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1161 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1162 | |
---|
| 1163 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1164 | { |
---|
| 1165 | offset = r->VarL_Offset[i]; |
---|
| 1166 | l_p = p->exp[offset]; |
---|
| 1167 | l_max = max->exp[offset]; |
---|
| 1168 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1169 | if (l_p > l_max || |
---|
[35aab3] | 1170 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1171 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1172 | } |
---|
| 1173 | pIter(p); |
---|
| 1174 | } |
---|
| 1175 | while (p != NULL); |
---|
| 1176 | return max; |
---|
| 1177 | } |
---|
| 1178 | |
---|
[107986] | 1179 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
[35aab3] | 1180 | { |
---|
| 1181 | unsigned long l_p, divmask = r->divmask; |
---|
| 1182 | int i; |
---|
[ab4778] | 1183 | |
---|
[35aab3] | 1184 | while (p != NULL) |
---|
| 1185 | { |
---|
| 1186 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
| 1187 | if (l_p > l_max || |
---|
| 1188 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1189 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1190 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1191 | { |
---|
| 1192 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
| 1193 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1194 | if (l_p > l_max || |
---|
[35aab3] | 1195 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1196 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1197 | } |
---|
| 1198 | pIter(p); |
---|
| 1199 | } |
---|
| 1200 | return l_max; |
---|
| 1201 | } |
---|
| 1202 | |
---|
[fc5095] | 1203 | |
---|
| 1204 | |
---|
[ab4778] | 1205 | |
---|
[35aab3] | 1206 | /*************************************************************** |
---|
| 1207 | * |
---|
| 1208 | * Misc things |
---|
| 1209 | * |
---|
| 1210 | ***************************************************************/ |
---|
| 1211 | // returns TRUE, if all monoms have the same component |
---|
[107986] | 1212 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
[35aab3] | 1213 | { |
---|
| 1214 | if(p!=NULL) |
---|
| 1215 | { |
---|
| 1216 | long i = p_GetComp(p, r); |
---|
| 1217 | while (pNext(p)!=NULL) |
---|
| 1218 | { |
---|
| 1219 | pIter(p); |
---|
| 1220 | if(i != p_GetComp(p, r)) return FALSE; |
---|
| 1221 | } |
---|
| 1222 | } |
---|
| 1223 | return TRUE; |
---|
| 1224 | } |
---|
| 1225 | |
---|
| 1226 | /*2 |
---|
| 1227 | *test if a monomial /head term is a pure power |
---|
| 1228 | */ |
---|
| 1229 | int p_IsPurePower(const poly p, const ring r) |
---|
| 1230 | { |
---|
| 1231 | int i,k=0; |
---|
| 1232 | |
---|
| 1233 | for (i=r->N;i;i--) |
---|
| 1234 | { |
---|
| 1235 | if (p_GetExp(p,i, r)!=0) |
---|
| 1236 | { |
---|
| 1237 | if(k!=0) return 0; |
---|
| 1238 | k=i; |
---|
| 1239 | } |
---|
| 1240 | } |
---|
| 1241 | return k; |
---|
| 1242 | } |
---|
| 1243 | |
---|
[2f0d83f] | 1244 | /*2 |
---|
| 1245 | *test if a polynomial is univariate |
---|
| 1246 | * return -1 for constant, |
---|
| 1247 | * 0 for not univariate,s |
---|
| 1248 | * i if dep. on var(i) |
---|
| 1249 | */ |
---|
| 1250 | int p_IsUnivariate(poly p, const ring r) |
---|
| 1251 | { |
---|
| 1252 | int i,k=-1; |
---|
| 1253 | |
---|
| 1254 | while (p!=NULL) |
---|
| 1255 | { |
---|
| 1256 | for (i=r->N;i;i--) |
---|
| 1257 | { |
---|
| 1258 | if (p_GetExp(p,i, r)!=0) |
---|
| 1259 | { |
---|
| 1260 | if((k!=-1)&&(k!=i)) return 0; |
---|
| 1261 | k=i; |
---|
| 1262 | } |
---|
| 1263 | } |
---|
| 1264 | pIter(p); |
---|
| 1265 | } |
---|
| 1266 | return k; |
---|
| 1267 | } |
---|
| 1268 | |
---|
[3931bf] | 1269 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
[f46646] | 1270 | int p_GetVariables(poly p, int * e, const ring r) |
---|
[3931bf] | 1271 | { |
---|
| 1272 | int i; |
---|
[f46646] | 1273 | int n=0; |
---|
[3931bf] | 1274 | while(p!=NULL) |
---|
| 1275 | { |
---|
[f46646] | 1276 | n=0; |
---|
[95450e] | 1277 | for(i=r->N; i>0; i--) |
---|
[3931bf] | 1278 | { |
---|
| 1279 | if(e[i]==0) |
---|
| 1280 | { |
---|
| 1281 | if (p_GetExp(p,i,r)>0) |
---|
[f46646] | 1282 | { |
---|
[3931bf] | 1283 | e[i]=1; |
---|
[f46646] | 1284 | n++; |
---|
| 1285 | } |
---|
[3931bf] | 1286 | } |
---|
[f46646] | 1287 | else |
---|
| 1288 | n++; |
---|
[3931bf] | 1289 | } |
---|
[f46646] | 1290 | if (n==r->N) break; |
---|
[3931bf] | 1291 | pIter(p); |
---|
| 1292 | } |
---|
[f46646] | 1293 | return n; |
---|
[3931bf] | 1294 | } |
---|
| 1295 | |
---|
| 1296 | |
---|
[35aab3] | 1297 | /*2 |
---|
| 1298 | * returns a polynomial representing the integer i |
---|
| 1299 | */ |
---|
[2f3764] | 1300 | poly p_ISet(long i, const ring r) |
---|
[35aab3] | 1301 | { |
---|
| 1302 | poly rc = NULL; |
---|
| 1303 | if (i!=0) |
---|
| 1304 | { |
---|
| 1305 | rc = p_Init(r); |
---|
[8a8c9e] | 1306 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
| 1307 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
[fb82895] | 1308 | p_LmDelete(&rc,r); |
---|
[35aab3] | 1309 | } |
---|
| 1310 | return rc; |
---|
| 1311 | } |
---|
| 1312 | |
---|
[1c33e0d] | 1313 | /*2 |
---|
| 1314 | * an optimized version of p_ISet for the special case 1 |
---|
| 1315 | */ |
---|
[5bc4103] | 1316 | poly p_One(const ring r) |
---|
[1c33e0d] | 1317 | { |
---|
| 1318 | poly rc = p_Init(r); |
---|
[8a8c9e] | 1319 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
[1c33e0d] | 1320 | return rc; |
---|
| 1321 | } |
---|
| 1322 | |
---|
[f34215] | 1323 | void p_Split(poly p, poly *h) |
---|
| 1324 | { |
---|
| 1325 | *h=pNext(p); |
---|
| 1326 | pNext(p)=NULL; |
---|
| 1327 | } |
---|
| 1328 | |
---|
| 1329 | /*2 |
---|
| 1330 | * pair has no common factor ? or is no polynomial |
---|
| 1331 | */ |
---|
| 1332 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
| 1333 | { |
---|
| 1334 | |
---|
| 1335 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
| 1336 | return FALSE; |
---|
| 1337 | int i = rVar(r); |
---|
| 1338 | loop |
---|
| 1339 | { |
---|
| 1340 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
| 1341 | return FALSE; |
---|
| 1342 | i--; |
---|
| 1343 | if (i == 0) |
---|
| 1344 | return TRUE; |
---|
| 1345 | } |
---|
| 1346 | } |
---|
| 1347 | |
---|
| 1348 | /*2 |
---|
| 1349 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
| 1350 | */ |
---|
| 1351 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
| 1352 | { |
---|
| 1353 | if (r==NULL) { rc=NULL;return st;} |
---|
| 1354 | int i,j; |
---|
| 1355 | rc = p_Init(r); |
---|
[8a8c9e] | 1356 | const char *s = r->cf->cfRead(st,&(rc->coef),r->cf); |
---|
[f34215] | 1357 | if (s==st) |
---|
| 1358 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
| 1359 | { |
---|
| 1360 | j = r_IsRingVar(s,r); |
---|
| 1361 | if (j >= 0) |
---|
| 1362 | { |
---|
| 1363 | p_IncrExp(rc,1+j,r); |
---|
| 1364 | while (*s!='\0') s++; |
---|
| 1365 | goto done; |
---|
| 1366 | } |
---|
| 1367 | } |
---|
| 1368 | while (*s!='\0') |
---|
| 1369 | { |
---|
| 1370 | char ss[2]; |
---|
| 1371 | ss[0] = *s++; |
---|
| 1372 | ss[1] = '\0'; |
---|
| 1373 | j = r_IsRingVar(ss,r); |
---|
| 1374 | if (j >= 0) |
---|
| 1375 | { |
---|
| 1376 | const char *s_save=s; |
---|
| 1377 | s = eati(s,&i); |
---|
| 1378 | if (((unsigned long)i) > r->bitmask) |
---|
| 1379 | { |
---|
| 1380 | // exponent to large: it is not a monomial |
---|
| 1381 | p_LmDelete(&rc,r); |
---|
| 1382 | return s_save; |
---|
| 1383 | } |
---|
| 1384 | p_AddExp(rc,1+j, (long)i, r); |
---|
| 1385 | } |
---|
| 1386 | else |
---|
| 1387 | { |
---|
| 1388 | // 1st char of is not a varname |
---|
[d0340f] | 1389 | // We return the parsed polynomial nevertheless. This is needed when |
---|
| 1390 | // we are parsing coefficients in a rational function field. |
---|
[f34215] | 1391 | s--; |
---|
| 1392 | return s; |
---|
| 1393 | } |
---|
| 1394 | } |
---|
| 1395 | done: |
---|
[8a8c9e] | 1396 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
[f34215] | 1397 | else |
---|
| 1398 | { |
---|
| 1399 | #ifdef HAVE_PLURAL |
---|
| 1400 | // in super-commutative ring |
---|
| 1401 | // squares of anti-commutative variables are zeroes! |
---|
| 1402 | if(rIsSCA(r)) |
---|
| 1403 | { |
---|
| 1404 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
| 1405 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
| 1406 | |
---|
| 1407 | assume(rc != NULL); |
---|
| 1408 | |
---|
| 1409 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
| 1410 | if( p_GetExp(rc, k, r) > 1 ) |
---|
| 1411 | { |
---|
| 1412 | p_LmDelete(&rc, r); |
---|
| 1413 | goto finish; |
---|
| 1414 | } |
---|
| 1415 | } |
---|
| 1416 | #endif |
---|
[71ba5b8] | 1417 | |
---|
[f34215] | 1418 | p_Setm(rc,r); |
---|
| 1419 | } |
---|
[71ba5b8] | 1420 | finish: |
---|
[f34215] | 1421 | return s; |
---|
| 1422 | } |
---|
| 1423 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
| 1424 | { |
---|
| 1425 | poly p; |
---|
| 1426 | const char *s=p_Read(st,p,r); |
---|
| 1427 | if (*s!='\0') |
---|
| 1428 | { |
---|
| 1429 | if ((s!=st)&&isdigit(st[0])) |
---|
| 1430 | { |
---|
| 1431 | errorreported=TRUE; |
---|
| 1432 | } |
---|
| 1433 | ok=FALSE; |
---|
| 1434 | p_Delete(&p,r); |
---|
| 1435 | return NULL; |
---|
| 1436 | } |
---|
| 1437 | #ifdef PDEBUG |
---|
| 1438 | _p_Test(p,r,PDEBUG); |
---|
| 1439 | #endif |
---|
| 1440 | ok=!errorreported; |
---|
| 1441 | return p; |
---|
| 1442 | } |
---|
| 1443 | |
---|
[35aab3] | 1444 | /*2 |
---|
| 1445 | * returns a polynomial representing the number n |
---|
| 1446 | * destroys n |
---|
| 1447 | */ |
---|
[107986] | 1448 | poly p_NSet(number n, const ring r) |
---|
[35aab3] | 1449 | { |
---|
[8a8c9e] | 1450 | if (n_IsZero(n,r->cf)) |
---|
[35aab3] | 1451 | { |
---|
[8a8c9e] | 1452 | n_Delete(&n, r->cf); |
---|
[35aab3] | 1453 | return NULL; |
---|
| 1454 | } |
---|
| 1455 | else |
---|
| 1456 | { |
---|
| 1457 | poly rc = p_Init(r); |
---|
| 1458 | pSetCoeff0(rc,n); |
---|
| 1459 | return rc; |
---|
| 1460 | } |
---|
| 1461 | } |
---|
[fb4075b] | 1462 | /*2 |
---|
[e5d267] | 1463 | * assumes that LM(a) = LM(b)*m, for some monomial m, |
---|
| 1464 | * returns the multiplicant m, |
---|
| 1465 | * leaves a and b unmodified |
---|
[fb4075b] | 1466 | */ |
---|
| 1467 | poly p_Divide(poly a, poly b, const ring r) |
---|
| 1468 | { |
---|
| 1469 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
| 1470 | int i; |
---|
[8a8c9e] | 1471 | poly result = p_Init(r); |
---|
[fb4075b] | 1472 | |
---|
| 1473 | for(i=(int)r->N; i; i--) |
---|
| 1474 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
| 1475 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
| 1476 | p_Setm(result,r); |
---|
| 1477 | return result; |
---|
| 1478 | } |
---|
| 1479 | |
---|
[8a8c9e] | 1480 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
| 1481 | { |
---|
[45d2332] | 1482 | pAssume(!n_IsZero(n,r->cf)); |
---|
[8a8c9e] | 1483 | p_Test(p, r); |
---|
| 1484 | |
---|
| 1485 | poly q = p; |
---|
| 1486 | while (p != NULL) |
---|
| 1487 | { |
---|
| 1488 | number nc = pGetCoeff(p); |
---|
| 1489 | pSetCoeff0(p, n_Div(nc, n, r->cf)); |
---|
| 1490 | n_Delete(&nc, r->cf); |
---|
| 1491 | pIter(p); |
---|
| 1492 | } |
---|
| 1493 | p_Test(q, r); |
---|
| 1494 | return q; |
---|
| 1495 | } |
---|
| 1496 | |
---|
[fb4075b] | 1497 | /*2 |
---|
| 1498 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
[e432a0] | 1499 | * assumes that b is not NULL, destroyes b |
---|
[fb4075b] | 1500 | */ |
---|
| 1501 | poly p_DivideM(poly a, poly b, const ring r) |
---|
| 1502 | { |
---|
[e432a0] | 1503 | if (a==NULL) { p_Delete(&b,r); return NULL; } |
---|
[fb4075b] | 1504 | poly result=a; |
---|
| 1505 | poly prev=NULL; |
---|
| 1506 | int i; |
---|
| 1507 | #ifdef HAVE_RINGS |
---|
| 1508 | number inv=pGetCoeff(b); |
---|
| 1509 | #else |
---|
| 1510 | number inv=n_Invers(pGetCoeff(b),r->cf); |
---|
| 1511 | #endif |
---|
| 1512 | |
---|
| 1513 | while (a!=NULL) |
---|
| 1514 | { |
---|
| 1515 | if (p_DivisibleBy(b,a,r)) |
---|
| 1516 | { |
---|
| 1517 | for(i=(int)r->N; i; i--) |
---|
| 1518 | p_SubExp(a,i, p_GetExp(b,i,r),r); |
---|
| 1519 | p_SubComp(a, p_GetComp(b,r),r); |
---|
| 1520 | p_Setm(a,r); |
---|
| 1521 | prev=a; |
---|
| 1522 | pIter(a); |
---|
| 1523 | } |
---|
| 1524 | else |
---|
| 1525 | { |
---|
| 1526 | if (prev==NULL) |
---|
| 1527 | { |
---|
[8a8c9e] | 1528 | p_LmDelete(&result,r); |
---|
[fb4075b] | 1529 | a=result; |
---|
| 1530 | } |
---|
| 1531 | else |
---|
| 1532 | { |
---|
[8a8c9e] | 1533 | p_LmDelete(&pNext(prev),r); |
---|
[fb4075b] | 1534 | a=pNext(prev); |
---|
| 1535 | } |
---|
| 1536 | } |
---|
| 1537 | } |
---|
| 1538 | #ifdef HAVE_RINGS |
---|
| 1539 | if (n_IsUnit(inv,r->cf)) |
---|
| 1540 | { |
---|
| 1541 | inv = n_Invers(inv,r->cf); |
---|
| 1542 | p_Mult_nn(result,inv,r); |
---|
| 1543 | n_Delete(&inv, r->cf); |
---|
| 1544 | } |
---|
| 1545 | else |
---|
| 1546 | { |
---|
| 1547 | p_Div_nn(result,inv,r); |
---|
| 1548 | } |
---|
| 1549 | #else |
---|
| 1550 | p_Mult_nn(result,inv,r); |
---|
| 1551 | n_Delete(&inv, r->cf); |
---|
| 1552 | #endif |
---|
| 1553 | p_Delete(&b, r); |
---|
| 1554 | return result; |
---|
| 1555 | } |
---|
[35aab3] | 1556 | |
---|
[3d0808] | 1557 | #ifdef HAVE_RINGS |
---|
| 1558 | /* TRUE iff LT(f) | LT(g) */ |
---|
| 1559 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
| 1560 | { |
---|
| 1561 | int exponent; |
---|
| 1562 | for(int i = (int)rVar(r); i>0; i--) |
---|
| 1563 | { |
---|
| 1564 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
| 1565 | if (exponent < 0) return FALSE; |
---|
| 1566 | } |
---|
| 1567 | return n_DivBy(pGetCoeff(g), pGetCoeff(f), r->cf); |
---|
| 1568 | } |
---|
| 1569 | #endif |
---|
| 1570 | |
---|
[f7a3f2] | 1571 | // returns the LCM of the head terms of a and b in *m |
---|
| 1572 | void p_Lcm(const poly a, const poly b, poly m, const ring r) |
---|
[a7ee69] | 1573 | { |
---|
[f7a3f2] | 1574 | for (int i=rVar(r); i; --i) |
---|
[a7ee69] | 1575 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
[0366c4] | 1576 | |
---|
[a7ee69] | 1577 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
| 1578 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
| 1579 | } |
---|
| 1580 | |
---|
[f0b01f] | 1581 | /* assumes that p and divisor are univariate polynomials in r, |
---|
[ba2359] | 1582 | mentioning the same variable; |
---|
| 1583 | assumes divisor != NULL; |
---|
[f0b01f] | 1584 | p may be NULL; |
---|
[ba2359] | 1585 | assumes a global monomial ordering in r; |
---|
[f0b01f] | 1586 | performs polynomial division of p by divisor: |
---|
| 1587 | - afterwards p contains the remainder of the division, i.e., |
---|
| 1588 | p_before = result * divisor + p_afterwards; |
---|
[ba2359] | 1589 | - if needResult == TRUE, then the method computes and returns 'result', |
---|
| 1590 | otherwise NULL is returned (This parametrization can be used when |
---|
| 1591 | one is only interested in the remainder of the division. In this |
---|
[f0b01f] | 1592 | case, the method will be slightly faster.) |
---|
| 1593 | leaves divisor unmodified */ |
---|
[20c540] | 1594 | poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r) |
---|
[ba2359] | 1595 | { |
---|
| 1596 | assume(divisor != NULL); |
---|
[f0b01f] | 1597 | if (p == NULL) return NULL; |
---|
[f93c5e9] | 1598 | |
---|
[69fb9d0] | 1599 | poly result = NULL; |
---|
[f0b01f] | 1600 | number divisorLC = p_GetCoeff(divisor, r); |
---|
| 1601 | int divisorLE = p_GetExp(divisor, 1, r); |
---|
[c28ecf] | 1602 | while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r))) |
---|
[69fb9d0] | 1603 | { |
---|
[f0b01f] | 1604 | /* determine t = LT(p) / LT(divisor) */ |
---|
[69fb9d0] | 1605 | poly t = p_ISet(1, r); |
---|
[f0b01f] | 1606 | number c = n_Div(p_GetCoeff(p, r), divisorLC, r->cf); |
---|
[07ff96] | 1607 | n_Normalize(c,r->cf); |
---|
[69fb9d0] | 1608 | p_SetCoeff(t, c, r); |
---|
[f0b01f] | 1609 | int e = p_GetExp(p, 1, r) - divisorLE; |
---|
[69fb9d0] | 1610 | p_SetExp(t, 1, e, r); |
---|
| 1611 | p_Setm(t, r); |
---|
[f0b01f] | 1612 | if (needResult) result = p_Add_q(result, p_Copy(t, r), r); |
---|
| 1613 | p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r); |
---|
[69fb9d0] | 1614 | } |
---|
| 1615 | return result; |
---|
| 1616 | } |
---|
| 1617 | |
---|
[ac0bd6] | 1618 | /*2 |
---|
| 1619 | * returns the partial differentiate of a by the k-th variable |
---|
| 1620 | * does not destroy the input |
---|
| 1621 | */ |
---|
| 1622 | poly p_Diff(poly a, int k, const ring r) |
---|
| 1623 | { |
---|
| 1624 | poly res, f, last; |
---|
| 1625 | number t; |
---|
| 1626 | |
---|
| 1627 | last = res = NULL; |
---|
| 1628 | while (a!=NULL) |
---|
| 1629 | { |
---|
| 1630 | if (p_GetExp(a,k,r)!=0) |
---|
| 1631 | { |
---|
| 1632 | f = p_LmInit(a,r); |
---|
| 1633 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
| 1634 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
| 1635 | n_Delete(&t,r->cf); |
---|
| 1636 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
| 1637 | p_LmDelete(&f,r); |
---|
| 1638 | else |
---|
| 1639 | { |
---|
| 1640 | p_DecrExp(f,k,r); |
---|
| 1641 | p_Setm(f,r); |
---|
| 1642 | if (res==NULL) |
---|
| 1643 | { |
---|
| 1644 | res=last=f; |
---|
| 1645 | } |
---|
| 1646 | else |
---|
| 1647 | { |
---|
| 1648 | pNext(last)=f; |
---|
| 1649 | last=f; |
---|
| 1650 | } |
---|
| 1651 | } |
---|
| 1652 | } |
---|
| 1653 | pIter(a); |
---|
| 1654 | } |
---|
| 1655 | return res; |
---|
| 1656 | } |
---|
[5162db] | 1657 | |
---|
[8a8c9e] | 1658 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
[5162db] | 1659 | { |
---|
| 1660 | int i,j,s; |
---|
| 1661 | number n,h,hh; |
---|
| 1662 | poly p=p_One(r); |
---|
| 1663 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
| 1664 | for(i=rVar(r);i>0;i--) |
---|
| 1665 | { |
---|
| 1666 | s=p_GetExp(b,i,r); |
---|
| 1667 | if (s<p_GetExp(a,i,r)) |
---|
| 1668 | { |
---|
| 1669 | n_Delete(&n,r->cf); |
---|
| 1670 | p_LmDelete(&p,r); |
---|
| 1671 | return NULL; |
---|
| 1672 | } |
---|
| 1673 | if (multiply) |
---|
| 1674 | { |
---|
| 1675 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
| 1676 | { |
---|
| 1677 | h = n_Init(s,r->cf); |
---|
| 1678 | hh=n_Mult(n,h,r->cf); |
---|
| 1679 | n_Delete(&h,r->cf); |
---|
| 1680 | n_Delete(&n,r->cf); |
---|
| 1681 | n=hh; |
---|
| 1682 | s--; |
---|
| 1683 | } |
---|
| 1684 | p_SetExp(p,i,s,r); |
---|
| 1685 | } |
---|
| 1686 | else |
---|
| 1687 | { |
---|
| 1688 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
| 1689 | } |
---|
| 1690 | } |
---|
| 1691 | p_Setm(p,r); |
---|
| 1692 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
| 1693 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
| 1694 | return p; |
---|
| 1695 | } |
---|
| 1696 | |
---|
| 1697 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
| 1698 | { |
---|
| 1699 | poly result=NULL; |
---|
| 1700 | poly h; |
---|
| 1701 | for(;a!=NULL;pIter(a)) |
---|
| 1702 | { |
---|
| 1703 | for(h=b;h!=NULL;pIter(h)) |
---|
| 1704 | { |
---|
| 1705 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
| 1706 | } |
---|
| 1707 | } |
---|
| 1708 | return result; |
---|
| 1709 | } |
---|
[bf183f] | 1710 | /*2 |
---|
| 1711 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
| 1712 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
| 1713 | */ |
---|
| 1714 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
| 1715 | { |
---|
| 1716 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
| 1717 | } |
---|
| 1718 | |
---|
| 1719 | /*3 |
---|
| 1720 | * compute for a monomial m |
---|
| 1721 | * the power m^exp, exp > 1 |
---|
| 1722 | * destroys p |
---|
| 1723 | */ |
---|
| 1724 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
| 1725 | { |
---|
| 1726 | int i; |
---|
| 1727 | |
---|
[8a8c9e] | 1728 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
[bf183f] | 1729 | { |
---|
| 1730 | number x, y; |
---|
| 1731 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1732 | n_Power(y,exp,&x,r->cf); |
---|
| 1733 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1734 | pSetCoeff0(p,x); |
---|
| 1735 | } |
---|
| 1736 | for (i=rVar(r); i!=0; i--) |
---|
| 1737 | { |
---|
| 1738 | p_MultExp(p,i, exp,r); |
---|
| 1739 | } |
---|
| 1740 | p_Setm(p,r); |
---|
| 1741 | return p; |
---|
| 1742 | } |
---|
| 1743 | |
---|
| 1744 | /*3 |
---|
| 1745 | * compute for monomials p*q |
---|
| 1746 | * destroys p, keeps q |
---|
| 1747 | */ |
---|
| 1748 | static void p_MonMult(poly p, poly q, const ring r) |
---|
| 1749 | { |
---|
| 1750 | number x, y; |
---|
| 1751 | |
---|
| 1752 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1753 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
| 1754 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1755 | pSetCoeff0(p,x); |
---|
[abb4787] | 1756 | //for (int i=pVariables; i!=0; i--) |
---|
[bf183f] | 1757 | //{ |
---|
| 1758 | // pAddExp(p,i, pGetExp(q,i)); |
---|
| 1759 | //} |
---|
| 1760 | //p->Order += q->Order; |
---|
| 1761 | p_ExpVectorAdd(p,q,r); |
---|
| 1762 | } |
---|
| 1763 | |
---|
| 1764 | /*3 |
---|
| 1765 | * compute for monomials p*q |
---|
| 1766 | * keeps p, q |
---|
| 1767 | */ |
---|
| 1768 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
| 1769 | { |
---|
| 1770 | number x; |
---|
| 1771 | poly r = p_Init(rr); |
---|
| 1772 | |
---|
[8a8c9e] | 1773 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
[bf183f] | 1774 | pSetCoeff0(r,x); |
---|
| 1775 | p_ExpVectorSum(r,p, q, rr); |
---|
| 1776 | return r; |
---|
| 1777 | } |
---|
| 1778 | |
---|
[5679049] | 1779 | /*3 |
---|
| 1780 | * create binomial coef. |
---|
| 1781 | */ |
---|
| 1782 | static number* pnBin(int exp, const ring r) |
---|
| 1783 | { |
---|
| 1784 | int e, i, h; |
---|
| 1785 | number x, y, *bin=NULL; |
---|
| 1786 | |
---|
| 1787 | x = n_Init(exp,r->cf); |
---|
| 1788 | if (n_IsZero(x,r->cf)) |
---|
| 1789 | { |
---|
| 1790 | n_Delete(&x,r->cf); |
---|
| 1791 | return bin; |
---|
| 1792 | } |
---|
| 1793 | h = (exp >> 1) + 1; |
---|
| 1794 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
| 1795 | bin[1] = x; |
---|
| 1796 | if (exp < 4) |
---|
| 1797 | return bin; |
---|
| 1798 | i = exp - 1; |
---|
| 1799 | for (e=2; e<h; e++) |
---|
| 1800 | { |
---|
| 1801 | x = n_Init(i,r->cf); |
---|
| 1802 | i--; |
---|
| 1803 | y = n_Mult(x,bin[e-1],r->cf); |
---|
| 1804 | n_Delete(&x,r->cf); |
---|
| 1805 | x = n_Init(e,r->cf); |
---|
| 1806 | bin[e] = n_IntDiv(y,x,r->cf); |
---|
| 1807 | n_Delete(&x,r->cf); |
---|
| 1808 | n_Delete(&y,r->cf); |
---|
| 1809 | } |
---|
| 1810 | return bin; |
---|
| 1811 | } |
---|
| 1812 | |
---|
[1389a4] | 1813 | static void pnFreeBin(number *bin, int exp,const coeffs r) |
---|
| 1814 | { |
---|
| 1815 | int e, h = (exp >> 1) + 1; |
---|
| 1816 | |
---|
| 1817 | if (bin[1] != NULL) |
---|
| 1818 | { |
---|
| 1819 | for (e=1; e<h; e++) |
---|
| 1820 | n_Delete(&(bin[e]),r); |
---|
| 1821 | } |
---|
| 1822 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
---|
| 1823 | } |
---|
| 1824 | |
---|
[bf183f] | 1825 | /* |
---|
| 1826 | * compute for a poly p = head+tail, tail is monomial |
---|
| 1827 | * (head + tail)^exp, exp > 1 |
---|
| 1828 | * with binomial coef. |
---|
| 1829 | */ |
---|
| 1830 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
| 1831 | { |
---|
| 1832 | int eh, e; |
---|
| 1833 | long al; |
---|
| 1834 | poly *a; |
---|
| 1835 | poly tail, b, res, h; |
---|
| 1836 | number x; |
---|
[7eb7b5] | 1837 | number *bin = pnBin(exp,r); |
---|
[bf183f] | 1838 | |
---|
| 1839 | tail = pNext(p); |
---|
| 1840 | if (bin == NULL) |
---|
| 1841 | { |
---|
| 1842 | p_MonPower(p,exp,r); |
---|
| 1843 | p_MonPower(tail,exp,r); |
---|
| 1844 | #ifdef PDEBUG |
---|
| 1845 | p_Test(p,r); |
---|
| 1846 | #endif |
---|
| 1847 | return p; |
---|
| 1848 | } |
---|
| 1849 | eh = exp >> 1; |
---|
| 1850 | al = (exp + 1) * sizeof(poly); |
---|
| 1851 | a = (poly *)omAlloc(al); |
---|
| 1852 | a[1] = p; |
---|
| 1853 | for (e=1; e<exp; e++) |
---|
| 1854 | { |
---|
| 1855 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
| 1856 | } |
---|
| 1857 | res = a[exp]; |
---|
| 1858 | b = p_Head(tail,r); |
---|
| 1859 | for (e=exp-1; e>eh; e--) |
---|
| 1860 | { |
---|
| 1861 | h = a[e]; |
---|
[8a8c9e] | 1862 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1863 | p_SetCoeff(h,x,r); |
---|
| 1864 | p_MonMult(h,b,r); |
---|
| 1865 | res = pNext(res) = h; |
---|
| 1866 | p_MonMult(b,tail,r); |
---|
| 1867 | } |
---|
| 1868 | for (e=eh; e!=0; e--) |
---|
| 1869 | { |
---|
| 1870 | h = a[e]; |
---|
[8a8c9e] | 1871 | x = n_Mult(bin[e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1872 | p_SetCoeff(h,x,r); |
---|
| 1873 | p_MonMult(h,b,r); |
---|
| 1874 | res = pNext(res) = h; |
---|
| 1875 | p_MonMult(b,tail,r); |
---|
| 1876 | } |
---|
| 1877 | p_LmDelete(&tail,r); |
---|
| 1878 | pNext(res) = b; |
---|
| 1879 | pNext(b) = NULL; |
---|
| 1880 | res = a[exp]; |
---|
| 1881 | omFreeSize((ADDRESS)a, al); |
---|
[1389a4] | 1882 | pnFreeBin(bin, exp, r->cf); |
---|
[bf183f] | 1883 | // tail=res; |
---|
| 1884 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
| 1885 | // { |
---|
| 1886 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
| 1887 | // { |
---|
| 1888 | // pLmDelete(&pNext(tail)); |
---|
| 1889 | // } |
---|
| 1890 | // else |
---|
| 1891 | // pIter(tail); |
---|
| 1892 | // } |
---|
| 1893 | #ifdef PDEBUG |
---|
| 1894 | p_Test(res,r); |
---|
| 1895 | #endif |
---|
| 1896 | return res; |
---|
| 1897 | } |
---|
| 1898 | |
---|
| 1899 | static poly p_Pow(poly p, int i, const ring r) |
---|
| 1900 | { |
---|
| 1901 | poly rc = p_Copy(p,r); |
---|
| 1902 | i -= 2; |
---|
| 1903 | do |
---|
| 1904 | { |
---|
| 1905 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
| 1906 | p_Normalize(rc,r); |
---|
| 1907 | i--; |
---|
| 1908 | } |
---|
| 1909 | while (i != 0); |
---|
| 1910 | return p_Mult_q(rc,p,r); |
---|
| 1911 | } |
---|
| 1912 | |
---|
| 1913 | /*2 |
---|
| 1914 | * returns the i-th power of p |
---|
| 1915 | * p will be destroyed |
---|
| 1916 | */ |
---|
| 1917 | poly p_Power(poly p, int i, const ring r) |
---|
| 1918 | { |
---|
| 1919 | poly rc=NULL; |
---|
| 1920 | |
---|
| 1921 | if (i==0) |
---|
| 1922 | { |
---|
| 1923 | p_Delete(&p,r); |
---|
| 1924 | return p_One(r); |
---|
| 1925 | } |
---|
| 1926 | |
---|
| 1927 | if(p!=NULL) |
---|
| 1928 | { |
---|
| 1929 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask))) |
---|
| 1930 | { |
---|
| 1931 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
| 1932 | return NULL; |
---|
| 1933 | } |
---|
| 1934 | switch (i) |
---|
| 1935 | { |
---|
| 1936 | // cannot happen, see above |
---|
| 1937 | // case 0: |
---|
| 1938 | // { |
---|
| 1939 | // rc=pOne(); |
---|
| 1940 | // pDelete(&p); |
---|
| 1941 | // break; |
---|
| 1942 | // } |
---|
| 1943 | case 1: |
---|
| 1944 | rc=p; |
---|
| 1945 | break; |
---|
| 1946 | case 2: |
---|
| 1947 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
| 1948 | break; |
---|
| 1949 | default: |
---|
| 1950 | if (i < 0) |
---|
| 1951 | { |
---|
| 1952 | p_Delete(&p,r); |
---|
| 1953 | return NULL; |
---|
| 1954 | } |
---|
| 1955 | else |
---|
| 1956 | { |
---|
| 1957 | #ifdef HAVE_PLURAL |
---|
| 1958 | if (rIsPluralRing(r)) /* in the NC case nothing helps :-( */ |
---|
| 1959 | { |
---|
| 1960 | int j=i; |
---|
| 1961 | rc = p_Copy(p,r); |
---|
| 1962 | while (j>1) |
---|
| 1963 | { |
---|
| 1964 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
| 1965 | j--; |
---|
| 1966 | } |
---|
| 1967 | p_Delete(&p,r); |
---|
| 1968 | return rc; |
---|
| 1969 | } |
---|
| 1970 | #endif |
---|
| 1971 | rc = pNext(p); |
---|
| 1972 | if (rc == NULL) |
---|
| 1973 | return p_MonPower(p,i,r); |
---|
| 1974 | /* else: binom ?*/ |
---|
| 1975 | int char_p=rChar(r); |
---|
| 1976 | if ((pNext(rc) != NULL) |
---|
| 1977 | #ifdef HAVE_RINGS |
---|
| 1978 | || rField_is_Ring(r) |
---|
| 1979 | #endif |
---|
| 1980 | ) |
---|
| 1981 | return p_Pow(p,i,r); |
---|
| 1982 | if ((char_p==0) || (i<=char_p)) |
---|
| 1983 | return p_TwoMonPower(p,i,r); |
---|
[131ab78] | 1984 | return p_Pow(p,i,r); |
---|
[bf183f] | 1985 | } |
---|
| 1986 | /*end default:*/ |
---|
| 1987 | } |
---|
| 1988 | } |
---|
| 1989 | return rc; |
---|
| 1990 | } |
---|
[8d1d30c] | 1991 | |
---|
| 1992 | /* --------------------------------------------------------------------------------*/ |
---|
| 1993 | /* content suff */ |
---|
| 1994 | |
---|
| 1995 | static number p_InitContent(poly ph, const ring r); |
---|
| 1996 | |
---|
[e56eb1a] | 1997 | #define CLEARENUMERATORS 1 |
---|
[8d341e] | 1998 | |
---|
[8d1d30c] | 1999 | void p_Content(poly ph, const ring r) |
---|
| 2000 | { |
---|
[dc79bd] | 2001 | assume( ph != NULL ); |
---|
| 2002 | |
---|
[0366c4] | 2003 | assume( r != NULL ); assume( r->cf != NULL ); |
---|
[dc79bd] | 2004 | |
---|
| 2005 | |
---|
[8d341e] | 2006 | #if CLEARENUMERATORS |
---|
[dc79bd] | 2007 | if( 0 ) |
---|
[975db18] | 2008 | { |
---|
[d30a399] | 2009 | const coeffs C = r->cf; |
---|
[dc79bd] | 2010 | // experimentall (recursive enumerator treatment) of alg. Ext! |
---|
[975db18] | 2011 | CPolyCoeffsEnumerator itr(ph); |
---|
| 2012 | n_ClearContent(itr, r->cf); |
---|
[8d341e] | 2013 | |
---|
[dc79bd] | 2014 | p_Test(ph, r); n_Test(pGetCoeff(ph), C); |
---|
| 2015 | assume(n_GreaterZero(pGetCoeff(ph), C)); // ?? |
---|
| 2016 | |
---|
| 2017 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8d341e] | 2018 | return; |
---|
[975db18] | 2019 | } |
---|
| 2020 | #endif |
---|
[0366c4] | 2021 | |
---|
| 2022 | |
---|
[8d1d30c] | 2023 | #ifdef HAVE_RINGS |
---|
| 2024 | if (rField_is_Ring(r)) |
---|
| 2025 | { |
---|
[dc79bd] | 2026 | if (rField_has_Units(r)) |
---|
[8d1d30c] | 2027 | { |
---|
[8a8c9e] | 2028 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
[8d1d30c] | 2029 | if (!n_IsOne(k,r->cf)) |
---|
| 2030 | { |
---|
| 2031 | number tmpGMP = k; |
---|
| 2032 | k = n_Invers(k,r->cf); |
---|
| 2033 | n_Delete(&tmpGMP,r->cf); |
---|
| 2034 | poly h = pNext(ph); |
---|
| 2035 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
| 2036 | while (h != NULL) |
---|
| 2037 | { |
---|
| 2038 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
| 2039 | pIter(h); |
---|
| 2040 | } |
---|
[dc79bd] | 2041 | // assume( n_GreaterZero(pGetCoeff(ph),r->cf) ); |
---|
| 2042 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8d1d30c] | 2043 | } |
---|
| 2044 | n_Delete(&k,r->cf); |
---|
| 2045 | } |
---|
| 2046 | return; |
---|
| 2047 | } |
---|
| 2048 | #endif |
---|
| 2049 | number h,d; |
---|
| 2050 | poly p; |
---|
| 2051 | |
---|
| 2052 | if(TEST_OPT_CONTENTSB) return; |
---|
| 2053 | if(pNext(ph)==NULL) |
---|
| 2054 | { |
---|
[8a8c9e] | 2055 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
[8d1d30c] | 2056 | } |
---|
| 2057 | else |
---|
| 2058 | { |
---|
[dc79bd] | 2059 | assume( pNext(ph) != NULL ); |
---|
[8d341e] | 2060 | #if CLEARENUMERATORS |
---|
[dc79bd] | 2061 | if( nCoeff_is_Q(r->cf) || nCoeff_is_Q_a(r->cf) ) |
---|
[8d341e] | 2062 | { |
---|
[dc79bd] | 2063 | // experimentall (recursive enumerator treatment) of alg. Ext! |
---|
[8d341e] | 2064 | CPolyCoeffsEnumerator itr(ph); |
---|
| 2065 | n_ClearContent(itr, r->cf); |
---|
[dc79bd] | 2066 | |
---|
[d30a399] | 2067 | p_Test(ph, r); n_Test(pGetCoeff(ph), r->cf); |
---|
| 2068 | assume(n_GreaterZero(pGetCoeff(ph), r->cf)); // ?? |
---|
[0366c4] | 2069 | |
---|
[dc79bd] | 2070 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8d341e] | 2071 | return; |
---|
| 2072 | } |
---|
| 2073 | #endif |
---|
[0366c4] | 2074 | |
---|
[8d1d30c] | 2075 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 2076 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[dc79bd] | 2077 | if (rField_is_Q(r)) // should not be used anymore if CLEARENUMERATORS is 1 |
---|
[8d1d30c] | 2078 | { |
---|
| 2079 | h=p_InitContent(ph,r); |
---|
| 2080 | p=ph; |
---|
| 2081 | } |
---|
| 2082 | else |
---|
| 2083 | { |
---|
| 2084 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2085 | p = pNext(ph); |
---|
| 2086 | } |
---|
| 2087 | while (p!=NULL) |
---|
| 2088 | { |
---|
| 2089 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2090 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2091 | n_Delete(&h,r->cf); |
---|
| 2092 | h = d; |
---|
| 2093 | if(n_IsOne(h,r->cf)) |
---|
| 2094 | { |
---|
| 2095 | break; |
---|
| 2096 | } |
---|
| 2097 | pIter(p); |
---|
| 2098 | } |
---|
| 2099 | p = ph; |
---|
| 2100 | //number tmp; |
---|
| 2101 | if(!n_IsOne(h,r->cf)) |
---|
| 2102 | { |
---|
| 2103 | while (p!=NULL) |
---|
| 2104 | { |
---|
| 2105 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2106 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2107 | //if (!nEqual(d,tmp)) |
---|
| 2108 | //{ |
---|
| 2109 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2110 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
[00d2a4] | 2111 | // nWrite(tmp);Print(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s); |
---|
[8d1d30c] | 2112 | //} |
---|
| 2113 | //nDelete(&tmp); |
---|
| 2114 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2115 | p_SetCoeff(p,d,r); |
---|
| 2116 | pIter(p); |
---|
| 2117 | } |
---|
| 2118 | } |
---|
| 2119 | n_Delete(&h,r->cf); |
---|
| 2120 | #ifdef HAVE_FACTORY |
---|
[aa98be] | 2121 | // if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2122 | // { |
---|
| 2123 | // singclap_divide_content(ph, r); |
---|
| 2124 | // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2125 | // } |
---|
[8d1d30c] | 2126 | #endif |
---|
[0366c4] | 2127 | if (rField_is_Q_a(r)) |
---|
[8d1d30c] | 2128 | { |
---|
[aa98be] | 2129 | // we only need special handling for alg. ext. |
---|
| 2130 | if (getCoeffType(r->cf)==n_algExt) |
---|
[8d1d30c] | 2131 | { |
---|
[aa98be] | 2132 | number hzz = n_Init(1, r->cf->extRing->cf); |
---|
[8d1d30c] | 2133 | p=ph; |
---|
| 2134 | while (p!=NULL) |
---|
| 2135 | { // each monom: coeff in Q_a |
---|
[aa98be] | 2136 | poly c_n_n=(poly)pGetCoeff(p); |
---|
| 2137 | poly c_n=c_n_n; |
---|
[8d1d30c] | 2138 | while (c_n!=NULL) |
---|
| 2139 | { // each monom: coeff in Q |
---|
[aa98be] | 2140 | d=n_Lcm(hzz,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2141 | n_Delete(&hzz,r->cf->extRing->cf); |
---|
| 2142 | hzz=d; |
---|
[8d1d30c] | 2143 | pIter(c_n); |
---|
| 2144 | } |
---|
[90aec7] | 2145 | pIter(p); |
---|
[aa98be] | 2146 | } |
---|
| 2147 | /* hzz contains the 1/lcm of all denominators in c_n_n*/ |
---|
| 2148 | h=n_Invers(hzz,r->cf->extRing->cf); |
---|
| 2149 | n_Delete(&hzz,r->cf->extRing->cf); |
---|
| 2150 | n_Normalize(h,r->cf->extRing->cf); |
---|
| 2151 | if(!n_IsOne(h,r->cf->extRing->cf)) |
---|
| 2152 | { |
---|
| 2153 | p=ph; |
---|
| 2154 | while (p!=NULL) |
---|
| 2155 | { // each monom: coeff in Q_a |
---|
| 2156 | poly c_n=(poly)pGetCoeff(p); |
---|
| 2157 | while (c_n!=NULL) |
---|
| 2158 | { // each monom: coeff in Q |
---|
| 2159 | d=n_Mult(h,pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2160 | n_Normalize(d,r->cf->extRing->cf); |
---|
| 2161 | n_Delete(&pGetCoeff(c_n),r->cf->extRing->cf); |
---|
| 2162 | pGetCoeff(c_n)=d; |
---|
| 2163 | pIter(c_n); |
---|
| 2164 | } |
---|
| 2165 | pIter(p); |
---|
[8d1d30c] | 2166 | } |
---|
| 2167 | } |
---|
[aa98be] | 2168 | n_Delete(&h,r->cf->extRing->cf); |
---|
[8d1d30c] | 2169 | } |
---|
| 2170 | } |
---|
| 2171 | } |
---|
[f9a64e] | 2172 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8d1d30c] | 2173 | } |
---|
[e48172] | 2174 | |
---|
| 2175 | // Not yet? |
---|
| 2176 | #if 1 // currently only used by Singular/janet |
---|
| 2177 | void p_SimpleContent(poly ph, int smax, const ring r) |
---|
[8d1d30c] | 2178 | { |
---|
| 2179 | if(TEST_OPT_CONTENTSB) return; |
---|
| 2180 | if (ph==NULL) return; |
---|
| 2181 | if (pNext(ph)==NULL) |
---|
| 2182 | { |
---|
[e48172] | 2183 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
[8d1d30c] | 2184 | return; |
---|
| 2185 | } |
---|
| 2186 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
| 2187 | { |
---|
| 2188 | return; |
---|
| 2189 | } |
---|
| 2190 | number d=p_InitContent(ph,r); |
---|
[e48172] | 2191 | if (n_Size(d,r->cf)<=smax) |
---|
[8d1d30c] | 2192 | { |
---|
| 2193 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
| 2194 | return; |
---|
| 2195 | } |
---|
[e48172] | 2196 | |
---|
[f93c5e9] | 2197 | |
---|
[8d1d30c] | 2198 | poly p=ph; |
---|
| 2199 | number h=d; |
---|
| 2200 | if (smax==1) smax=2; |
---|
| 2201 | while (p!=NULL) |
---|
| 2202 | { |
---|
| 2203 | #if 0 |
---|
| 2204 | d=nlGcd(h,pGetCoeff(p),r->cf); |
---|
| 2205 | nlDelete(&h,r->cf); |
---|
| 2206 | h = d; |
---|
| 2207 | #else |
---|
| 2208 | nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
| 2209 | #endif |
---|
| 2210 | if(nlSize(h,r->cf)<smax) |
---|
| 2211 | { |
---|
| 2212 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
| 2213 | return; |
---|
| 2214 | } |
---|
| 2215 | pIter(p); |
---|
| 2216 | } |
---|
| 2217 | p = ph; |
---|
| 2218 | if (!nlGreaterZero(pGetCoeff(p),r->cf)) h=nlNeg(h,r->cf); |
---|
| 2219 | if(nlIsOne(h,r->cf)) return; |
---|
| 2220 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
| 2221 | while (p!=NULL) |
---|
| 2222 | { |
---|
| 2223 | #if 1 |
---|
| 2224 | d = nlIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2225 | p_SetCoeff(p,d,r); |
---|
| 2226 | #else |
---|
| 2227 | nlInpIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2228 | #endif |
---|
| 2229 | pIter(p); |
---|
| 2230 | } |
---|
| 2231 | nlDelete(&h,r->cf); |
---|
| 2232 | } |
---|
[5698bb] | 2233 | #endif |
---|
[8d1d30c] | 2234 | |
---|
| 2235 | static number p_InitContent(poly ph, const ring r) |
---|
| 2236 | // only for coefficients in Q |
---|
| 2237 | #if 0 |
---|
| 2238 | { |
---|
| 2239 | assume(!TEST_OPT_CONTENTSB); |
---|
| 2240 | assume(ph!=NULL); |
---|
| 2241 | assume(pNext(ph)!=NULL); |
---|
| 2242 | assume(rField_is_Q(r)); |
---|
| 2243 | if (pNext(pNext(ph))==NULL) |
---|
| 2244 | { |
---|
| 2245 | return nlGetNom(pGetCoeff(pNext(ph)),r->cf); |
---|
| 2246 | } |
---|
| 2247 | poly p=ph; |
---|
| 2248 | number n1=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2249 | pIter(p); |
---|
| 2250 | number n2=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2251 | pIter(p); |
---|
| 2252 | number d; |
---|
| 2253 | number t; |
---|
| 2254 | loop |
---|
| 2255 | { |
---|
| 2256 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2257 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2258 | if (nlGreaterZero(t,r->cf)) |
---|
| 2259 | d=nlAdd(n1,t,r->cf); |
---|
| 2260 | else |
---|
| 2261 | d=nlSub(n1,t,r->cf); |
---|
| 2262 | nlDelete(&t,r->cf); |
---|
| 2263 | nlDelete(&n1,r->cf); |
---|
| 2264 | n1=d; |
---|
| 2265 | pIter(p); |
---|
| 2266 | if (p==NULL) break; |
---|
| 2267 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2268 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2269 | if (nlGreaterZero(t,r->cf)) |
---|
| 2270 | d=nlAdd(n2,t,r->cf); |
---|
| 2271 | else |
---|
| 2272 | d=nlSub(n2,t,r->cf); |
---|
| 2273 | nlDelete(&t,r->cf); |
---|
| 2274 | nlDelete(&n2,r->cf); |
---|
| 2275 | n2=d; |
---|
| 2276 | pIter(p); |
---|
| 2277 | if (p==NULL) break; |
---|
| 2278 | } |
---|
| 2279 | d=nlGcd(n1,n2,r->cf); |
---|
| 2280 | nlDelete(&n1,r->cf); |
---|
| 2281 | nlDelete(&n2,r->cf); |
---|
| 2282 | return d; |
---|
| 2283 | } |
---|
| 2284 | #else |
---|
| 2285 | { |
---|
| 2286 | number d=pGetCoeff(ph); |
---|
| 2287 | if(SR_HDL(d)&SR_INT) return d; |
---|
| 2288 | int s=mpz_size1(d->z); |
---|
| 2289 | int s2=-1; |
---|
| 2290 | number d2; |
---|
| 2291 | loop |
---|
| 2292 | { |
---|
| 2293 | pIter(ph); |
---|
| 2294 | if(ph==NULL) |
---|
| 2295 | { |
---|
| 2296 | if (s2==-1) return nlCopy(d,r->cf); |
---|
| 2297 | break; |
---|
| 2298 | } |
---|
| 2299 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
| 2300 | { |
---|
| 2301 | s2=s; |
---|
| 2302 | d2=d; |
---|
| 2303 | s=0; |
---|
| 2304 | d=pGetCoeff(ph); |
---|
| 2305 | if (s2==0) break; |
---|
| 2306 | } |
---|
| 2307 | else |
---|
| 2308 | if (mpz_size1((pGetCoeff(ph)->z))<=s) |
---|
| 2309 | { |
---|
| 2310 | s2=s; |
---|
| 2311 | d2=d; |
---|
| 2312 | d=pGetCoeff(ph); |
---|
| 2313 | s=mpz_size1(d->z); |
---|
| 2314 | } |
---|
| 2315 | } |
---|
| 2316 | return nlGcd(d,d2,r->cf); |
---|
| 2317 | } |
---|
| 2318 | #endif |
---|
| 2319 | |
---|
| 2320 | //void pContent(poly ph) |
---|
| 2321 | //{ |
---|
| 2322 | // number h,d; |
---|
| 2323 | // poly p; |
---|
| 2324 | // |
---|
| 2325 | // p = ph; |
---|
| 2326 | // if(pNext(p)==NULL) |
---|
| 2327 | // { |
---|
| 2328 | // pSetCoeff(p,nInit(1)); |
---|
| 2329 | // } |
---|
| 2330 | // else |
---|
| 2331 | // { |
---|
| 2332 | //#ifdef PDEBUG |
---|
| 2333 | // if (!pTest(p)) return; |
---|
| 2334 | //#endif |
---|
| 2335 | // nNormalize(pGetCoeff(p)); |
---|
| 2336 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
| 2337 | // { |
---|
| 2338 | // ph = pNeg(ph); |
---|
| 2339 | // nNormalize(pGetCoeff(p)); |
---|
| 2340 | // } |
---|
| 2341 | // h=pGetCoeff(p); |
---|
| 2342 | // pIter(p); |
---|
| 2343 | // while (p!=NULL) |
---|
| 2344 | // { |
---|
| 2345 | // nNormalize(pGetCoeff(p)); |
---|
| 2346 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
| 2347 | // pIter(p); |
---|
| 2348 | // } |
---|
| 2349 | // h=nCopy(h); |
---|
| 2350 | // p=ph; |
---|
| 2351 | // while (p!=NULL) |
---|
| 2352 | // { |
---|
[32d07a5] | 2353 | // d=n_Gcd(h,pGetCoeff(p)); |
---|
[8d1d30c] | 2354 | // nDelete(&h); |
---|
| 2355 | // h = d; |
---|
| 2356 | // if(nIsOne(h)) |
---|
| 2357 | // { |
---|
| 2358 | // break; |
---|
| 2359 | // } |
---|
| 2360 | // pIter(p); |
---|
| 2361 | // } |
---|
| 2362 | // p = ph; |
---|
| 2363 | // //number tmp; |
---|
| 2364 | // if(!nIsOne(h)) |
---|
| 2365 | // { |
---|
| 2366 | // while (p!=NULL) |
---|
| 2367 | // { |
---|
| 2368 | // d = nIntDiv(pGetCoeff(p),h); |
---|
| 2369 | // pSetCoeff(p,d); |
---|
| 2370 | // pIter(p); |
---|
| 2371 | // } |
---|
| 2372 | // } |
---|
| 2373 | // nDelete(&h); |
---|
| 2374 | //#ifdef HAVE_FACTORY |
---|
| 2375 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2376 | // { |
---|
| 2377 | // pTest(ph); |
---|
| 2378 | // singclap_divide_content(ph); |
---|
| 2379 | // pTest(ph); |
---|
| 2380 | // } |
---|
| 2381 | //#endif |
---|
| 2382 | // } |
---|
| 2383 | //} |
---|
| 2384 | #if 0 |
---|
| 2385 | void p_Content(poly ph, const ring r) |
---|
| 2386 | { |
---|
| 2387 | number h,d; |
---|
| 2388 | poly p; |
---|
| 2389 | |
---|
| 2390 | if(pNext(ph)==NULL) |
---|
| 2391 | { |
---|
| 2392 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
| 2393 | } |
---|
| 2394 | else |
---|
| 2395 | { |
---|
| 2396 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 2397 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2398 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2399 | p = pNext(ph); |
---|
| 2400 | while (p!=NULL) |
---|
| 2401 | { |
---|
| 2402 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2403 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2404 | n_Delete(&h,r->cf); |
---|
| 2405 | h = d; |
---|
| 2406 | if(n_IsOne(h,r->cf)) |
---|
| 2407 | { |
---|
| 2408 | break; |
---|
| 2409 | } |
---|
| 2410 | pIter(p); |
---|
| 2411 | } |
---|
| 2412 | p = ph; |
---|
| 2413 | //number tmp; |
---|
| 2414 | if(!n_IsOne(h,r->cf)) |
---|
| 2415 | { |
---|
| 2416 | while (p!=NULL) |
---|
| 2417 | { |
---|
| 2418 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2419 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2420 | //if (!nEqual(d,tmp)) |
---|
| 2421 | //{ |
---|
| 2422 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2423 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
[00d2a4] | 2424 | // nWrite(tmp);Print(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s); |
---|
[8d1d30c] | 2425 | //} |
---|
| 2426 | //nDelete(&tmp); |
---|
| 2427 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2428 | p_SetCoeff(p,d,r->cf); |
---|
| 2429 | pIter(p); |
---|
| 2430 | } |
---|
| 2431 | } |
---|
| 2432 | n_Delete(&h,r->cf); |
---|
| 2433 | #ifdef HAVE_FACTORY |
---|
| 2434 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2435 | //{ |
---|
| 2436 | // singclap_divide_content(ph); |
---|
| 2437 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
| 2438 | //} |
---|
| 2439 | #endif |
---|
| 2440 | } |
---|
| 2441 | } |
---|
| 2442 | #endif |
---|
[fbf8a6] | 2443 | /* ---------------------------------------------------------------------------*/ |
---|
| 2444 | /* cleardenom suff */ |
---|
[8d1d30c] | 2445 | poly p_Cleardenom(poly ph, const ring r) |
---|
| 2446 | { |
---|
[dc79bd] | 2447 | if( ph == NULL ) |
---|
| 2448 | return NULL; |
---|
[975db18] | 2449 | |
---|
[dc79bd] | 2450 | assume( r != NULL ); assume( r->cf != NULL ); const coeffs C = r->cf; |
---|
[0366c4] | 2451 | |
---|
[8d341e] | 2452 | #if CLEARENUMERATORS |
---|
[dc79bd] | 2453 | if( 0 ) |
---|
[975db18] | 2454 | { |
---|
| 2455 | CPolyCoeffsEnumerator itr(ph); |
---|
[dc79bd] | 2456 | |
---|
[8d341e] | 2457 | n_ClearDenominators(itr, C); |
---|
[dc79bd] | 2458 | |
---|
[8d341e] | 2459 | n_ClearContent(itr, C); // divide out the content |
---|
| 2460 | |
---|
[dc79bd] | 2461 | p_Test(ph, r); n_Test(pGetCoeff(ph), C); |
---|
| 2462 | assume(n_GreaterZero(pGetCoeff(ph), C)); // ?? |
---|
| 2463 | // if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r); |
---|
| 2464 | |
---|
| 2465 | return ph; |
---|
[975db18] | 2466 | } |
---|
| 2467 | #endif |
---|
[dc79bd] | 2468 | |
---|
| 2469 | poly start=ph; |
---|
| 2470 | |
---|
[8d1d30c] | 2471 | number d, h; |
---|
| 2472 | poly p; |
---|
| 2473 | |
---|
| 2474 | #ifdef HAVE_RINGS |
---|
| 2475 | if (rField_is_Ring(r)) |
---|
| 2476 | { |
---|
| 2477 | p_Content(ph,r); |
---|
[8d341e] | 2478 | assume( n_GreaterZero(pGetCoeff(ph),C) ); |
---|
[dc79bd] | 2479 | if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r); |
---|
[8d1d30c] | 2480 | return start; |
---|
| 2481 | } |
---|
| 2482 | #endif |
---|
[8d341e] | 2483 | |
---|
| 2484 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) |
---|
| 2485 | { |
---|
[dc79bd] | 2486 | if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r); |
---|
[8d341e] | 2487 | return start; |
---|
| 2488 | } |
---|
[8d1d30c] | 2489 | p = ph; |
---|
[8d341e] | 2490 | |
---|
| 2491 | assume(p != NULL); |
---|
[0366c4] | 2492 | |
---|
[8d1d30c] | 2493 | if(pNext(p)==NULL) |
---|
| 2494 | { |
---|
| 2495 | if (TEST_OPT_CONTENTSB) |
---|
| 2496 | { |
---|
| 2497 | number n=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2498 | if (!n_IsOne(n,r->cf)) |
---|
| 2499 | { |
---|
| 2500 | number nn=n_Mult(pGetCoeff(p),n,r->cf); |
---|
| 2501 | n_Normalize(nn,r->cf); |
---|
| 2502 | p_SetCoeff(p,nn,r); |
---|
| 2503 | } |
---|
| 2504 | n_Delete(&n,r->cf); |
---|
| 2505 | } |
---|
| 2506 | else |
---|
| 2507 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
[8d341e] | 2508 | |
---|
| 2509 | assume( n_GreaterZero(pGetCoeff(ph),C) ); |
---|
[dc79bd] | 2510 | if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r); |
---|
[0366c4] | 2511 | |
---|
[8d341e] | 2512 | return start; |
---|
[8d1d30c] | 2513 | } |
---|
[8d341e] | 2514 | |
---|
[dc79bd] | 2515 | assume(pNext(p)!=NULL); |
---|
| 2516 | |
---|
[8d341e] | 2517 | #if CLEARENUMERATORS |
---|
[dc79bd] | 2518 | if( nCoeff_is_Q(C) || nCoeff_is_Q_a(C) ) |
---|
[8d341e] | 2519 | { |
---|
| 2520 | CPolyCoeffsEnumerator itr(ph); |
---|
[dc79bd] | 2521 | |
---|
[8d341e] | 2522 | n_ClearDenominators(itr, C); |
---|
[dc79bd] | 2523 | |
---|
[8d341e] | 2524 | n_ClearContent(itr, C); // divide out the content |
---|
| 2525 | |
---|
[dc79bd] | 2526 | p_Test(ph, r); n_Test(pGetCoeff(ph), C); |
---|
| 2527 | assume(n_GreaterZero(pGetCoeff(ph), C)); // ?? |
---|
| 2528 | // if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r); |
---|
[0366c4] | 2529 | |
---|
[8d341e] | 2530 | return start; |
---|
| 2531 | } |
---|
| 2532 | #endif |
---|
| 2533 | |
---|
| 2534 | if(1) |
---|
[8d1d30c] | 2535 | { |
---|
| 2536 | h = n_Init(1,r->cf); |
---|
| 2537 | while (p!=NULL) |
---|
| 2538 | { |
---|
[8a8c9e] | 2539 | n_Normalize(pGetCoeff(p),r->cf); |
---|
[8d1d30c] | 2540 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2541 | n_Delete(&h,r->cf); |
---|
| 2542 | h=d; |
---|
| 2543 | pIter(p); |
---|
| 2544 | } |
---|
| 2545 | /* contains the 1/lcm of all denominators */ |
---|
| 2546 | if(!n_IsOne(h,r->cf)) |
---|
| 2547 | { |
---|
| 2548 | p = ph; |
---|
| 2549 | while (p!=NULL) |
---|
| 2550 | { |
---|
| 2551 | /* should be: |
---|
| 2552 | * number hh; |
---|
| 2553 | * nGetDenom(p->coef,&hh); |
---|
| 2554 | * nMult(&h,&hh,&d); |
---|
| 2555 | * nNormalize(d); |
---|
| 2556 | * nDelete(&hh); |
---|
| 2557 | * nMult(d,p->coef,&hh); |
---|
| 2558 | * nDelete(&d); |
---|
| 2559 | * nDelete(&(p->coef)); |
---|
| 2560 | * p->coef =hh; |
---|
| 2561 | */ |
---|
| 2562 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2563 | n_Normalize(d,r->cf); |
---|
| 2564 | p_SetCoeff(p,d,r); |
---|
| 2565 | pIter(p); |
---|
| 2566 | } |
---|
| 2567 | n_Delete(&h,r->cf); |
---|
[5679049] | 2568 | if (n_GetChar(r->cf)==1) |
---|
[8d1d30c] | 2569 | { |
---|
| 2570 | loop |
---|
| 2571 | { |
---|
| 2572 | h = n_Init(1,r->cf); |
---|
| 2573 | p=ph; |
---|
| 2574 | while (p!=NULL) |
---|
| 2575 | { |
---|
| 2576 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2577 | n_Delete(&h,r->cf); |
---|
| 2578 | h=d; |
---|
| 2579 | pIter(p); |
---|
| 2580 | } |
---|
| 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 | n_Delete(&h,r->cf); |
---|
| 2604 | } |
---|
| 2605 | else |
---|
| 2606 | { |
---|
| 2607 | n_Delete(&h,r->cf); |
---|
| 2608 | break; |
---|
| 2609 | } |
---|
| 2610 | } |
---|
| 2611 | } |
---|
| 2612 | } |
---|
| 2613 | if (h!=NULL) n_Delete(&h,r->cf); |
---|
[71ba5b8] | 2614 | |
---|
[8d1d30c] | 2615 | p_Content(ph,r); |
---|
| 2616 | #ifdef HAVE_RATGRING |
---|
| 2617 | if (rIsRatGRing(r)) |
---|
| 2618 | { |
---|
| 2619 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
| 2620 | pContentRat(ph); |
---|
| 2621 | start=ph; |
---|
| 2622 | } |
---|
| 2623 | #endif |
---|
| 2624 | } |
---|
[8d341e] | 2625 | |
---|
| 2626 | assume( n_GreaterZero(pGetCoeff(ph),C) ); |
---|
[dc79bd] | 2627 | if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r); |
---|
[0366c4] | 2628 | |
---|
[8d1d30c] | 2629 | return start; |
---|
| 2630 | } |
---|
| 2631 | |
---|
| 2632 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
| 2633 | { |
---|
[8d341e] | 2634 | const coeffs C = r->cf; |
---|
| 2635 | number d, h; |
---|
| 2636 | |
---|
[dc79bd] | 2637 | assume( ph != NULL ); |
---|
[8d341e] | 2638 | |
---|
[dc79bd] | 2639 | poly p = ph; |
---|
[8d341e] | 2640 | |
---|
| 2641 | #if CLEARENUMERATORS |
---|
[dc79bd] | 2642 | if( 0 ) |
---|
[975db18] | 2643 | { |
---|
| 2644 | CPolyCoeffsEnumerator itr(ph); |
---|
[dc79bd] | 2645 | |
---|
[8d341e] | 2646 | n_ClearDenominators(itr, d, C); // multiply with common denom. d |
---|
[0366c4] | 2647 | n_ClearContent(itr, h, C); // divide by the content h |
---|
[8d341e] | 2648 | |
---|
[0366c4] | 2649 | c = n_Div(d, h, C); // d/h |
---|
[8d341e] | 2650 | |
---|
| 2651 | n_Delete(&d, C); |
---|
| 2652 | n_Delete(&h, C); |
---|
| 2653 | |
---|
[dc79bd] | 2654 | n_Test(c, C); |
---|
| 2655 | |
---|
| 2656 | p_Test(ph, r); n_Test(pGetCoeff(ph), C); |
---|
| 2657 | assume(n_GreaterZero(pGetCoeff(ph), C)); // ?? |
---|
| 2658 | /* |
---|
| 2659 | if(!n_GreaterZero(pGetCoeff(ph),C)) |
---|
| 2660 | { |
---|
| 2661 | ph = p_Neg(ph,r); |
---|
| 2662 | c = n_Neg(c, C); |
---|
| 2663 | } |
---|
| 2664 | */ |
---|
[8d341e] | 2665 | return; |
---|
[975db18] | 2666 | } |
---|
| 2667 | #endif |
---|
[0366c4] | 2668 | |
---|
| 2669 | |
---|
[dc79bd] | 2670 | if( pNext(p) == NULL ) |
---|
[8d1d30c] | 2671 | { |
---|
[8d341e] | 2672 | c=n_Invers(pGetCoeff(p), C); |
---|
| 2673 | p_SetCoeff(p, n_Init(1, C), r); |
---|
| 2674 | |
---|
| 2675 | assume( n_GreaterZero(pGetCoeff(ph),C) ); |
---|
[dc79bd] | 2676 | if(!n_GreaterZero(pGetCoeff(ph),C)) |
---|
| 2677 | { |
---|
| 2678 | ph = p_Neg(ph,r); |
---|
| 2679 | c = n_Neg(c, C); |
---|
| 2680 | } |
---|
[0366c4] | 2681 | |
---|
[8d341e] | 2682 | return; |
---|
[8d1d30c] | 2683 | } |
---|
[8d341e] | 2684 | |
---|
[dc79bd] | 2685 | assume( pNext(p) != NULL ); |
---|
[0366c4] | 2686 | |
---|
[8d341e] | 2687 | #if CLEARENUMERATORS |
---|
[dc79bd] | 2688 | if( nCoeff_is_Q(C) || nCoeff_is_Q_a(C) ) |
---|
[8d341e] | 2689 | { |
---|
| 2690 | CPolyCoeffsEnumerator itr(ph); |
---|
[0366c4] | 2691 | |
---|
[8d341e] | 2692 | n_ClearDenominators(itr, d, C); // multiply with common denom. d |
---|
[0366c4] | 2693 | n_ClearContent(itr, h, C); // divide by the content h |
---|
[8d341e] | 2694 | |
---|
[0366c4] | 2695 | c = n_Div(d, h, C); // d/h |
---|
[8d341e] | 2696 | |
---|
| 2697 | n_Delete(&d, C); |
---|
| 2698 | n_Delete(&h, C); |
---|
| 2699 | |
---|
[dc79bd] | 2700 | n_Test(c, C); |
---|
| 2701 | |
---|
| 2702 | p_Test(ph, r); n_Test(pGetCoeff(ph), C); |
---|
| 2703 | assume(n_GreaterZero(pGetCoeff(ph), C)); // ?? |
---|
| 2704 | /* |
---|
| 2705 | if(!n_GreaterZero(pGetCoeff(ph),C)) |
---|
| 2706 | { |
---|
| 2707 | ph = p_Neg(ph,r); |
---|
| 2708 | c = n_Neg(c, C); |
---|
| 2709 | } |
---|
| 2710 | */ |
---|
[8d341e] | 2711 | return; |
---|
| 2712 | } |
---|
| 2713 | #endif |
---|
| 2714 | |
---|
[0366c4] | 2715 | |
---|
| 2716 | |
---|
[8d341e] | 2717 | |
---|
| 2718 | if(1) |
---|
[8d1d30c] | 2719 | { |
---|
| 2720 | h = n_Init(1,r->cf); |
---|
| 2721 | while (p!=NULL) |
---|
| 2722 | { |
---|
| 2723 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2724 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2725 | n_Delete(&h,r->cf); |
---|
| 2726 | h=d; |
---|
| 2727 | pIter(p); |
---|
| 2728 | } |
---|
| 2729 | c=h; |
---|
| 2730 | /* contains the 1/lcm of all denominators */ |
---|
| 2731 | if(!n_IsOne(h,r->cf)) |
---|
| 2732 | { |
---|
| 2733 | p = ph; |
---|
| 2734 | while (p!=NULL) |
---|
| 2735 | { |
---|
| 2736 | /* should be: |
---|
| 2737 | * number hh; |
---|
| 2738 | * nGetDenom(p->coef,&hh); |
---|
| 2739 | * nMult(&h,&hh,&d); |
---|
| 2740 | * nNormalize(d); |
---|
| 2741 | * nDelete(&hh); |
---|
| 2742 | * nMult(d,p->coef,&hh); |
---|
| 2743 | * nDelete(&d); |
---|
| 2744 | * nDelete(&(p->coef)); |
---|
| 2745 | * p->coef =hh; |
---|
| 2746 | */ |
---|
| 2747 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2748 | n_Normalize(d,r->cf); |
---|
| 2749 | p_SetCoeff(p,d,r); |
---|
| 2750 | pIter(p); |
---|
| 2751 | } |
---|
| 2752 | if (rField_is_Q_a(r)) |
---|
| 2753 | { |
---|
| 2754 | loop |
---|
| 2755 | { |
---|
| 2756 | h = n_Init(1,r->cf); |
---|
| 2757 | p=ph; |
---|
| 2758 | while (p!=NULL) |
---|
| 2759 | { |
---|
| 2760 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2761 | n_Delete(&h,r->cf); |
---|
| 2762 | h=d; |
---|
| 2763 | pIter(p); |
---|
| 2764 | } |
---|
| 2765 | /* contains the 1/lcm of all denominators */ |
---|
| 2766 | if(!n_IsOne(h,r->cf)) |
---|
| 2767 | { |
---|
| 2768 | p = ph; |
---|
| 2769 | while (p!=NULL) |
---|
| 2770 | { |
---|
| 2771 | /* should be: |
---|
| 2772 | * number hh; |
---|
| 2773 | * nGetDenom(p->coef,&hh); |
---|
| 2774 | * nMult(&h,&hh,&d); |
---|
| 2775 | * nNormalize(d); |
---|
| 2776 | * nDelete(&hh); |
---|
| 2777 | * nMult(d,p->coef,&hh); |
---|
| 2778 | * nDelete(&d); |
---|
| 2779 | * nDelete(&(p->coef)); |
---|
| 2780 | * p->coef =hh; |
---|
| 2781 | */ |
---|
| 2782 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2783 | n_Normalize(d,r->cf); |
---|
| 2784 | p_SetCoeff(p,d,r); |
---|
| 2785 | pIter(p); |
---|
| 2786 | } |
---|
| 2787 | number t=n_Mult(c,h,r->cf); |
---|
| 2788 | n_Delete(&c,r->cf); |
---|
| 2789 | c=t; |
---|
| 2790 | } |
---|
| 2791 | else |
---|
| 2792 | { |
---|
| 2793 | break; |
---|
| 2794 | } |
---|
| 2795 | n_Delete(&h,r->cf); |
---|
| 2796 | } |
---|
| 2797 | } |
---|
| 2798 | } |
---|
| 2799 | } |
---|
[8d341e] | 2800 | |
---|
[dc79bd] | 2801 | if(!n_GreaterZero(pGetCoeff(ph),C)) |
---|
| 2802 | { |
---|
| 2803 | ph = p_Neg(ph,r); |
---|
| 2804 | c = n_Neg(c, C); |
---|
| 2805 | } |
---|
[0366c4] | 2806 | |
---|
[8d1d30c] | 2807 | } |
---|
| 2808 | |
---|
| 2809 | number p_GetAllDenom(poly ph, const ring r) |
---|
| 2810 | { |
---|
| 2811 | number d=n_Init(1,r->cf); |
---|
| 2812 | poly p = ph; |
---|
| 2813 | |
---|
| 2814 | while (p!=NULL) |
---|
| 2815 | { |
---|
| 2816 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2817 | if (!n_IsOne(h,r->cf)) |
---|
| 2818 | { |
---|
| 2819 | number dd=n_Mult(d,h,r->cf); |
---|
| 2820 | n_Delete(&d,r->cf); |
---|
| 2821 | d=dd; |
---|
| 2822 | } |
---|
| 2823 | n_Delete(&h,r->cf); |
---|
| 2824 | pIter(p); |
---|
| 2825 | } |
---|
| 2826 | return d; |
---|
| 2827 | } |
---|
| 2828 | |
---|
[fbf8a6] | 2829 | int p_Size(poly p, const ring r) |
---|
| 2830 | { |
---|
| 2831 | int count = 0; |
---|
| 2832 | while ( p != NULL ) |
---|
| 2833 | { |
---|
| 2834 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
| 2835 | pIter( p ); |
---|
| 2836 | } |
---|
| 2837 | return count; |
---|
| 2838 | } |
---|
| 2839 | |
---|
[4e8ef90] | 2840 | /*2 |
---|
| 2841 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
| 2842 | *assume: deg(var(varnum))==1 |
---|
| 2843 | */ |
---|
| 2844 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
| 2845 | { |
---|
| 2846 | pFDegProc deg; |
---|
[5679049] | 2847 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2848 | deg=p_Totaldegree; |
---|
| 2849 | else |
---|
[9765f3] | 2850 | deg=r->pFDeg; |
---|
[4e8ef90] | 2851 | |
---|
| 2852 | poly q=NULL, qn; |
---|
| 2853 | int o,ii; |
---|
| 2854 | sBucket_pt bp; |
---|
| 2855 | |
---|
| 2856 | if (p!=NULL) |
---|
| 2857 | { |
---|
| 2858 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
| 2859 | { |
---|
| 2860 | return NULL; |
---|
| 2861 | } |
---|
| 2862 | o=deg(p,r); |
---|
| 2863 | q=pNext(p); |
---|
| 2864 | while (q != NULL) |
---|
| 2865 | { |
---|
| 2866 | ii=deg(q,r); |
---|
| 2867 | if (ii>o) o=ii; |
---|
| 2868 | pIter(q); |
---|
| 2869 | } |
---|
| 2870 | q = p_Copy(p,r); |
---|
| 2871 | bp = sBucketCreate(r); |
---|
| 2872 | while (q != NULL) |
---|
| 2873 | { |
---|
| 2874 | ii = o-deg(q,r); |
---|
| 2875 | if (ii!=0) |
---|
| 2876 | { |
---|
| 2877 | p_AddExp(q,varnum, (long)ii,r); |
---|
| 2878 | p_Setm(q,r); |
---|
| 2879 | } |
---|
| 2880 | qn = pNext(q); |
---|
| 2881 | pNext(q) = NULL; |
---|
| 2882 | sBucket_Add_p(bp, q, 1); |
---|
| 2883 | q = qn; |
---|
| 2884 | } |
---|
| 2885 | sBucketDestroyAdd(bp, &q, &ii); |
---|
| 2886 | } |
---|
| 2887 | return q; |
---|
| 2888 | } |
---|
| 2889 | |
---|
| 2890 | /*2 |
---|
| 2891 | *tests if p is homogeneous with respect to the actual weigths |
---|
| 2892 | */ |
---|
| 2893 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
| 2894 | { |
---|
| 2895 | poly qp=p; |
---|
| 2896 | int o; |
---|
| 2897 | |
---|
| 2898 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
| 2899 | pFDegProc d; |
---|
[5679049] | 2900 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2901 | d=p_Totaldegree; |
---|
[71ba5b8] | 2902 | else |
---|
[9765f3] | 2903 | d=r->pFDeg; |
---|
[8a8c9e] | 2904 | o = d(p,r); |
---|
[4e8ef90] | 2905 | do |
---|
| 2906 | { |
---|
| 2907 | if (d(qp,r) != o) return FALSE; |
---|
| 2908 | pIter(qp); |
---|
| 2909 | } |
---|
| 2910 | while (qp != NULL); |
---|
| 2911 | return TRUE; |
---|
| 2912 | } |
---|
| 2913 | |
---|
[cd246b] | 2914 | /*----------utilities for syzygies--------------*/ |
---|
| 2915 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
| 2916 | { |
---|
| 2917 | poly q=p,qq; |
---|
| 2918 | int i; |
---|
| 2919 | |
---|
| 2920 | while (q!=NULL) |
---|
| 2921 | { |
---|
| 2922 | if (p_LmIsConstantComp(q,r)) |
---|
| 2923 | { |
---|
| 2924 | i = p_GetComp(q,r); |
---|
| 2925 | qq = p; |
---|
| 2926 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2927 | if (qq == q) |
---|
| 2928 | { |
---|
| 2929 | *k = i; |
---|
| 2930 | return TRUE; |
---|
| 2931 | } |
---|
| 2932 | else |
---|
| 2933 | pIter(q); |
---|
| 2934 | } |
---|
| 2935 | else pIter(q); |
---|
| 2936 | } |
---|
| 2937 | return FALSE; |
---|
| 2938 | } |
---|
| 2939 | |
---|
| 2940 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
| 2941 | { |
---|
| 2942 | poly q=p,qq; |
---|
| 2943 | int i,j=0; |
---|
| 2944 | |
---|
| 2945 | *len = 0; |
---|
| 2946 | while (q!=NULL) |
---|
| 2947 | { |
---|
| 2948 | if (p_LmIsConstantComp(q,r)) |
---|
| 2949 | { |
---|
| 2950 | i = p_GetComp(q,r); |
---|
| 2951 | qq = p; |
---|
| 2952 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2953 | if (qq == q) |
---|
| 2954 | { |
---|
| 2955 | j = 0; |
---|
| 2956 | while (qq!=NULL) |
---|
| 2957 | { |
---|
| 2958 | if (p_GetComp(qq,r)==i) j++; |
---|
| 2959 | pIter(qq); |
---|
| 2960 | } |
---|
| 2961 | if ((*len == 0) || (j<*len)) |
---|
| 2962 | { |
---|
| 2963 | *len = j; |
---|
| 2964 | *k = i; |
---|
| 2965 | } |
---|
| 2966 | } |
---|
| 2967 | } |
---|
| 2968 | pIter(q); |
---|
| 2969 | } |
---|
| 2970 | } |
---|
| 2971 | |
---|
| 2972 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
| 2973 | { |
---|
| 2974 | poly q = *p; |
---|
| 2975 | |
---|
| 2976 | if (q==NULL) return NULL; |
---|
| 2977 | |
---|
| 2978 | poly qq=NULL,result = NULL; |
---|
| 2979 | |
---|
| 2980 | if (p_GetComp(q,r)==k) |
---|
| 2981 | { |
---|
| 2982 | result = q; /* *p */ |
---|
| 2983 | while ((q!=NULL) && (p_GetComp(q,r)==k)) |
---|
| 2984 | { |
---|
| 2985 | p_SetComp(q,0,r); |
---|
| 2986 | p_SetmComp(q,r); |
---|
| 2987 | qq = q; |
---|
| 2988 | pIter(q); |
---|
| 2989 | } |
---|
| 2990 | *p = q; |
---|
| 2991 | pNext(qq) = NULL; |
---|
| 2992 | } |
---|
| 2993 | if (q==NULL) return result; |
---|
| 2994 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2995 | while (pNext(q)!=NULL) |
---|
| 2996 | { |
---|
| 2997 | if (p_GetComp(pNext(q),r)==k) |
---|
| 2998 | { |
---|
| 2999 | if (result==NULL) |
---|
| 3000 | { |
---|
| 3001 | result = pNext(q); |
---|
| 3002 | qq = result; |
---|
| 3003 | } |
---|
| 3004 | else |
---|
| 3005 | { |
---|
| 3006 | pNext(qq) = pNext(q); |
---|
| 3007 | pIter(qq); |
---|
| 3008 | } |
---|
| 3009 | pNext(q) = pNext(pNext(q)); |
---|
| 3010 | pNext(qq) =NULL; |
---|
| 3011 | p_SetComp(qq,0,r); |
---|
| 3012 | p_SetmComp(qq,r); |
---|
| 3013 | } |
---|
| 3014 | else |
---|
| 3015 | { |
---|
| 3016 | pIter(q); |
---|
| 3017 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 3018 | } |
---|
| 3019 | } |
---|
| 3020 | return result; |
---|
| 3021 | } |
---|
[74021a] | 3022 | |
---|
| 3023 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
| 3024 | { |
---|
| 3025 | poly q = *p,qq=NULL,result = NULL; |
---|
| 3026 | |
---|
| 3027 | if (q==NULL) return NULL; |
---|
| 3028 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
| 3029 | if (p_GetComp(q,r)==k) |
---|
| 3030 | { |
---|
| 3031 | result = q; |
---|
| 3032 | do |
---|
| 3033 | { |
---|
| 3034 | p_SetComp(q,0,r); |
---|
| 3035 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 3036 | qq = q; |
---|
| 3037 | pIter(q); |
---|
| 3038 | } |
---|
| 3039 | while ((q!=NULL) && (p_GetComp(q,r)==k)); |
---|
| 3040 | *p = q; |
---|
| 3041 | pNext(qq) = NULL; |
---|
| 3042 | } |
---|
| 3043 | if (q==NULL) return result; |
---|
| 3044 | if (p_GetComp(q,r) > k) |
---|
| 3045 | { |
---|
| 3046 | p_SubComp(q,1,r); |
---|
| 3047 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 3048 | } |
---|
| 3049 | poly pNext_q; |
---|
| 3050 | while ((pNext_q=pNext(q))!=NULL) |
---|
| 3051 | { |
---|
| 3052 | if (p_GetComp(pNext_q,r)==k) |
---|
| 3053 | { |
---|
| 3054 | if (result==NULL) |
---|
| 3055 | { |
---|
| 3056 | result = pNext_q; |
---|
| 3057 | qq = result; |
---|
| 3058 | } |
---|
| 3059 | else |
---|
| 3060 | { |
---|
| 3061 | pNext(qq) = pNext_q; |
---|
| 3062 | pIter(qq); |
---|
| 3063 | } |
---|
| 3064 | pNext(q) = pNext(pNext_q); |
---|
| 3065 | pNext(qq) =NULL; |
---|
| 3066 | p_SetComp(qq,0,r); |
---|
| 3067 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
| 3068 | } |
---|
| 3069 | else |
---|
| 3070 | { |
---|
| 3071 | /*pIter(q);*/ q=pNext_q; |
---|
| 3072 | if (p_GetComp(q,r) > k) |
---|
| 3073 | { |
---|
| 3074 | p_SubComp(q,1,r); |
---|
| 3075 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 3076 | } |
---|
| 3077 | } |
---|
| 3078 | } |
---|
| 3079 | return result; |
---|
| 3080 | } |
---|
| 3081 | |
---|
| 3082 | // Splits *p into two polys: *q which consists of all monoms with |
---|
| 3083 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
| 3084 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
| 3085 | { |
---|
| 3086 | spolyrec pp, qq; |
---|
| 3087 | poly p, q, p_prev; |
---|
| 3088 | int l = 0; |
---|
| 3089 | |
---|
| 3090 | #ifdef HAVE_ASSUME |
---|
| 3091 | int lp = pLength(*r_p); |
---|
| 3092 | #endif |
---|
| 3093 | |
---|
| 3094 | pNext(&pp) = *r_p; |
---|
| 3095 | p = *r_p; |
---|
| 3096 | p_prev = &pp; |
---|
| 3097 | q = &qq; |
---|
| 3098 | |
---|
| 3099 | while(p != NULL) |
---|
| 3100 | { |
---|
| 3101 | while (p_GetComp(p,r) == comp) |
---|
| 3102 | { |
---|
| 3103 | pNext(q) = p; |
---|
| 3104 | pIter(q); |
---|
| 3105 | p_SetComp(p, 0,r); |
---|
| 3106 | p_SetmComp(p,r); |
---|
| 3107 | pIter(p); |
---|
| 3108 | l++; |
---|
| 3109 | if (p == NULL) |
---|
| 3110 | { |
---|
| 3111 | pNext(p_prev) = NULL; |
---|
| 3112 | goto Finish; |
---|
| 3113 | } |
---|
| 3114 | } |
---|
| 3115 | pNext(p_prev) = p; |
---|
| 3116 | p_prev = p; |
---|
| 3117 | pIter(p); |
---|
| 3118 | } |
---|
| 3119 | |
---|
| 3120 | Finish: |
---|
| 3121 | pNext(q) = NULL; |
---|
| 3122 | *r_p = pNext(&pp); |
---|
| 3123 | *r_q = pNext(&qq); |
---|
| 3124 | *lq = l; |
---|
| 3125 | #ifdef HAVE_ASSUME |
---|
| 3126 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
| 3127 | #endif |
---|
| 3128 | p_Test(*r_p,r); |
---|
| 3129 | p_Test(*r_q,r); |
---|
| 3130 | } |
---|
| 3131 | |
---|
| 3132 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
| 3133 | { |
---|
| 3134 | poly q; |
---|
| 3135 | |
---|
| 3136 | while ((*p!=NULL) && (p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
| 3137 | if (*p==NULL) return; |
---|
| 3138 | q = *p; |
---|
| 3139 | if (p_GetComp(q,r)>k) |
---|
| 3140 | { |
---|
| 3141 | p_SubComp(q,1,r); |
---|
| 3142 | p_SetmComp(q,r); |
---|
| 3143 | } |
---|
| 3144 | while (pNext(q)!=NULL) |
---|
| 3145 | { |
---|
| 3146 | if (p_GetComp(pNext(q),r)==k) |
---|
| 3147 | p_LmDelete(&(pNext(q)),r); |
---|
| 3148 | else |
---|
| 3149 | { |
---|
| 3150 | pIter(q); |
---|
| 3151 | if (p_GetComp(q,r)>k) |
---|
| 3152 | { |
---|
| 3153 | p_SubComp(q,1,r); |
---|
| 3154 | p_SetmComp(q,r); |
---|
| 3155 | } |
---|
| 3156 | } |
---|
| 3157 | } |
---|
| 3158 | } |
---|
[dd693a] | 3159 | |
---|
| 3160 | /*2 |
---|
| 3161 | * convert a vector to a set of polys, |
---|
| 3162 | * allocates the polyset, (entries 0..(*len)-1) |
---|
| 3163 | * the vector will not be changed |
---|
| 3164 | */ |
---|
| 3165 | void p_Vec2Polys(poly v, poly* *p, int *len, const ring r) |
---|
| 3166 | { |
---|
| 3167 | poly h; |
---|
| 3168 | int k; |
---|
| 3169 | |
---|
| 3170 | *len=p_MaxComp(v,r); |
---|
| 3171 | if (*len==0) *len=1; |
---|
| 3172 | *p=(poly*)omAlloc0((*len)*sizeof(poly)); |
---|
| 3173 | while (v!=NULL) |
---|
| 3174 | { |
---|
| 3175 | h=p_Head(v,r); |
---|
| 3176 | k=p_GetComp(h,r); |
---|
| 3177 | p_SetComp(h,0,r); |
---|
| 3178 | (*p)[k-1]=p_Add_q((*p)[k-1],h,r); |
---|
| 3179 | pIter(v); |
---|
| 3180 | } |
---|
| 3181 | } |
---|
| 3182 | |
---|
[949e57] | 3183 | // |
---|
| 3184 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
| 3185 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
[45d2332] | 3186 | // only uses pFDeg (and not p_Deg, or pTotalDegree, etc) |
---|
[949e57] | 3187 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
| 3188 | { |
---|
| 3189 | assume(new_FDeg != NULL); |
---|
| 3190 | r->pFDeg = new_FDeg; |
---|
| 3191 | |
---|
| 3192 | if (new_lDeg == NULL) |
---|
| 3193 | new_lDeg = r->pLDegOrig; |
---|
| 3194 | |
---|
| 3195 | r->pLDeg = new_lDeg; |
---|
| 3196 | } |
---|
| 3197 | |
---|
| 3198 | // restores pFDeg and pLDeg: |
---|
| 3199 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
| 3200 | { |
---|
| 3201 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
| 3202 | r->pFDeg = old_FDeg; |
---|
| 3203 | r->pLDeg = old_lDeg; |
---|
| 3204 | } |
---|
| 3205 | |
---|
[5bc2461] | 3206 | /*-------- several access procedures to monomials -------------------- */ |
---|
| 3207 | /* |
---|
| 3208 | * the module weights for std |
---|
| 3209 | */ |
---|
| 3210 | static pFDegProc pOldFDeg; |
---|
| 3211 | static pLDegProc pOldLDeg; |
---|
| 3212 | static BOOLEAN pOldLexOrder; |
---|
| 3213 | |
---|
[8a8c9e] | 3214 | static long pModDeg(poly p, ring r) |
---|
[5bc2461] | 3215 | { |
---|
| 3216 | long d=pOldFDeg(p, r); |
---|
| 3217 | int c=p_GetComp(p, r); |
---|
| 3218 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
| 3219 | return d; |
---|
| 3220 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
| 3221 | } |
---|
| 3222 | |
---|
| 3223 | void p_SetModDeg(intvec *w, ring r) |
---|
| 3224 | { |
---|
| 3225 | if (w!=NULL) |
---|
| 3226 | { |
---|
| 3227 | r->pModW = w; |
---|
| 3228 | pOldFDeg = r->pFDeg; |
---|
| 3229 | pOldLDeg = r->pLDeg; |
---|
| 3230 | pOldLexOrder = r->pLexOrder; |
---|
| 3231 | pSetDegProcs(r,pModDeg); |
---|
| 3232 | r->pLexOrder = TRUE; |
---|
| 3233 | } |
---|
| 3234 | else |
---|
| 3235 | { |
---|
| 3236 | r->pModW = NULL; |
---|
[5679049] | 3237 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
[5bc2461] | 3238 | r->pLexOrder = pOldLexOrder; |
---|
| 3239 | } |
---|
| 3240 | } |
---|
| 3241 | |
---|
[c6a3eb2] | 3242 | /*2 |
---|
| 3243 | * handle memory request for sets of polynomials (ideals) |
---|
| 3244 | * l is the length of *p, increment is the difference (may be negative) |
---|
| 3245 | */ |
---|
| 3246 | void pEnlargeSet(poly* *p, int l, int increment) |
---|
| 3247 | { |
---|
| 3248 | poly* h; |
---|
| 3249 | |
---|
| 3250 | h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
| 3251 | if (increment>0) |
---|
| 3252 | { |
---|
| 3253 | //for (i=l; i<l+increment; i++) |
---|
| 3254 | // h[i]=NULL; |
---|
| 3255 | memset(&(h[l]),0,increment*sizeof(poly)); |
---|
| 3256 | } |
---|
| 3257 | *p=h; |
---|
| 3258 | } |
---|
| 3259 | |
---|
[71ba5b8] | 3260 | /*2 |
---|
| 3261 | *divides p1 by its leading coefficient |
---|
| 3262 | */ |
---|
| 3263 | void p_Norm(poly p1, const ring r) |
---|
| 3264 | { |
---|
| 3265 | #ifdef HAVE_RINGS |
---|
| 3266 | if (rField_is_Ring(r)) |
---|
| 3267 | { |
---|
[45d2332] | 3268 | if (!n_IsUnit(pGetCoeff(p1), r->cf)) return; |
---|
[71ba5b8] | 3269 | // Werror("p_Norm not possible in the case of coefficient rings."); |
---|
| 3270 | } |
---|
| 3271 | else |
---|
| 3272 | #endif |
---|
| 3273 | if (p1!=NULL) |
---|
| 3274 | { |
---|
| 3275 | if (pNext(p1)==NULL) |
---|
| 3276 | { |
---|
| 3277 | p_SetCoeff(p1,n_Init(1,r->cf),r); |
---|
| 3278 | return; |
---|
| 3279 | } |
---|
| 3280 | poly h; |
---|
| 3281 | if (!n_IsOne(pGetCoeff(p1),r->cf)) |
---|
| 3282 | { |
---|
| 3283 | number k, c; |
---|
| 3284 | n_Normalize(pGetCoeff(p1),r->cf); |
---|
| 3285 | k = pGetCoeff(p1); |
---|
| 3286 | c = n_Init(1,r->cf); |
---|
| 3287 | pSetCoeff0(p1,c); |
---|
| 3288 | h = pNext(p1); |
---|
| 3289 | while (h!=NULL) |
---|
| 3290 | { |
---|
| 3291 | c=n_Div(pGetCoeff(h),k,r->cf); |
---|
| 3292 | // no need to normalize: Z/p, R |
---|
| 3293 | // normalize already in nDiv: Q_a, Z/p_a |
---|
| 3294 | // remains: Q |
---|
| 3295 | if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) n_Normalize(c,r->cf); |
---|
| 3296 | p_SetCoeff(h,c,r); |
---|
| 3297 | pIter(h); |
---|
| 3298 | } |
---|
| 3299 | n_Delete(&k,r->cf); |
---|
| 3300 | } |
---|
| 3301 | else |
---|
| 3302 | { |
---|
| 3303 | //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE |
---|
| 3304 | { |
---|
| 3305 | h = pNext(p1); |
---|
| 3306 | while (h!=NULL) |
---|
| 3307 | { |
---|
| 3308 | n_Normalize(pGetCoeff(h),r->cf); |
---|
| 3309 | pIter(h); |
---|
| 3310 | } |
---|
| 3311 | } |
---|
| 3312 | } |
---|
| 3313 | } |
---|
| 3314 | } |
---|
| 3315 | |
---|
| 3316 | /*2 |
---|
| 3317 | *normalize all coefficients |
---|
| 3318 | */ |
---|
| 3319 | void p_Normalize(poly p,const ring r) |
---|
| 3320 | { |
---|
| 3321 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
| 3322 | while (p!=NULL) |
---|
| 3323 | { |
---|
| 3324 | #ifdef LDEBUG |
---|
[45d2332] | 3325 | n_Test(pGetCoeff(p), r->cf); |
---|
[71ba5b8] | 3326 | #endif |
---|
| 3327 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 3328 | pIter(p); |
---|
| 3329 | } |
---|
| 3330 | } |
---|
| 3331 | |
---|
| 3332 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
| 3333 | // Poly with Exp(n) != 0 is reversed |
---|
| 3334 | static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r) |
---|
| 3335 | { |
---|
| 3336 | if (p == NULL) |
---|
| 3337 | { |
---|
| 3338 | *non_zero = NULL; |
---|
| 3339 | *zero = NULL; |
---|
| 3340 | return; |
---|
| 3341 | } |
---|
| 3342 | spolyrec sz; |
---|
| 3343 | poly z, n_z, next; |
---|
| 3344 | z = &sz; |
---|
| 3345 | n_z = NULL; |
---|
| 3346 | |
---|
| 3347 | while(p != NULL) |
---|
| 3348 | { |
---|
| 3349 | next = pNext(p); |
---|
| 3350 | if (p_GetExp(p, n,r) == 0) |
---|
| 3351 | { |
---|
| 3352 | pNext(z) = p; |
---|
| 3353 | pIter(z); |
---|
| 3354 | } |
---|
| 3355 | else |
---|
| 3356 | { |
---|
| 3357 | pNext(p) = n_z; |
---|
| 3358 | n_z = p; |
---|
| 3359 | } |
---|
| 3360 | p = next; |
---|
| 3361 | } |
---|
| 3362 | pNext(z) = NULL; |
---|
| 3363 | *zero = pNext(&sz); |
---|
| 3364 | *non_zero = n_z; |
---|
| 3365 | } |
---|
| 3366 | /*3 |
---|
| 3367 | * substitute the n-th variable by 1 in p |
---|
| 3368 | * destroy p |
---|
| 3369 | */ |
---|
| 3370 | static poly p_Subst1 (poly p,int n, const ring r) |
---|
| 3371 | { |
---|
| 3372 | poly qq=NULL, result = NULL; |
---|
| 3373 | poly zero=NULL, non_zero=NULL; |
---|
| 3374 | |
---|
| 3375 | // reverse, so that add is likely to be linear |
---|
| 3376 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3377 | |
---|
| 3378 | while (non_zero != NULL) |
---|
| 3379 | { |
---|
| 3380 | assume(p_GetExp(non_zero, n,r) != 0); |
---|
| 3381 | qq = non_zero; |
---|
| 3382 | pIter(non_zero); |
---|
| 3383 | qq->next = NULL; |
---|
| 3384 | p_SetExp(qq,n,0,r); |
---|
| 3385 | p_Setm(qq,r); |
---|
| 3386 | result = p_Add_q(result,qq,r); |
---|
| 3387 | } |
---|
| 3388 | p = p_Add_q(result, zero,r); |
---|
| 3389 | p_Test(p,r); |
---|
| 3390 | return p; |
---|
| 3391 | } |
---|
| 3392 | |
---|
| 3393 | /*3 |
---|
| 3394 | * substitute the n-th variable by number e in p |
---|
| 3395 | * destroy p |
---|
| 3396 | */ |
---|
| 3397 | static poly p_Subst2 (poly p,int n, number e, const ring r) |
---|
| 3398 | { |
---|
| 3399 | assume( ! n_IsZero(e,r->cf) ); |
---|
| 3400 | poly qq,result = NULL; |
---|
| 3401 | number nn, nm; |
---|
| 3402 | poly zero, non_zero; |
---|
| 3403 | |
---|
| 3404 | // reverse, so that add is likely to be linear |
---|
| 3405 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3406 | |
---|
| 3407 | while (non_zero != NULL) |
---|
| 3408 | { |
---|
[45d2332] | 3409 | assume(p_GetExp(non_zero, n, r) != 0); |
---|
[71ba5b8] | 3410 | qq = non_zero; |
---|
| 3411 | pIter(non_zero); |
---|
| 3412 | qq->next = NULL; |
---|
| 3413 | n_Power(e, p_GetExp(qq, n, r), &nn,r->cf); |
---|
| 3414 | nm = n_Mult(nn, pGetCoeff(qq),r->cf); |
---|
| 3415 | #ifdef HAVE_RINGS |
---|
| 3416 | if (n_IsZero(nm,r->cf)) |
---|
| 3417 | { |
---|
| 3418 | p_LmFree(&qq,r); |
---|
| 3419 | n_Delete(&nm,r->cf); |
---|
| 3420 | } |
---|
| 3421 | else |
---|
| 3422 | #endif |
---|
| 3423 | { |
---|
| 3424 | p_SetCoeff(qq, nm,r); |
---|
| 3425 | p_SetExp(qq, n, 0,r); |
---|
| 3426 | p_Setm(qq,r); |
---|
| 3427 | result = p_Add_q(result,qq,r); |
---|
| 3428 | } |
---|
| 3429 | n_Delete(&nn,r->cf); |
---|
| 3430 | } |
---|
| 3431 | p = p_Add_q(result, zero,r); |
---|
| 3432 | p_Test(p,r); |
---|
| 3433 | return p; |
---|
| 3434 | } |
---|
| 3435 | |
---|
| 3436 | |
---|
| 3437 | /* delete monoms whose n-th exponent is different from zero */ |
---|
| 3438 | static poly p_Subst0(poly p, int n, const ring r) |
---|
| 3439 | { |
---|
| 3440 | spolyrec res; |
---|
| 3441 | poly h = &res; |
---|
| 3442 | pNext(h) = p; |
---|
| 3443 | |
---|
| 3444 | while (pNext(h)!=NULL) |
---|
| 3445 | { |
---|
| 3446 | if (p_GetExp(pNext(h),n,r)!=0) |
---|
| 3447 | { |
---|
| 3448 | p_LmDelete(&pNext(h),r); |
---|
| 3449 | } |
---|
| 3450 | else |
---|
| 3451 | { |
---|
| 3452 | pIter(h); |
---|
| 3453 | } |
---|
| 3454 | } |
---|
| 3455 | p_Test(pNext(&res),r); |
---|
| 3456 | return pNext(&res); |
---|
| 3457 | } |
---|
| 3458 | |
---|
| 3459 | /*2 |
---|
| 3460 | * substitute the n-th variable by e in p |
---|
| 3461 | * destroy p |
---|
| 3462 | */ |
---|
| 3463 | poly p_Subst(poly p, int n, poly e, const ring r) |
---|
| 3464 | { |
---|
| 3465 | if (e == NULL) return p_Subst0(p, n,r); |
---|
| 3466 | |
---|
| 3467 | if (p_IsConstant(e,r)) |
---|
| 3468 | { |
---|
| 3469 | if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r); |
---|
| 3470 | else return p_Subst2(p, n, pGetCoeff(e),r); |
---|
| 3471 | } |
---|
| 3472 | |
---|
| 3473 | #ifdef HAVE_PLURAL |
---|
| 3474 | if (rIsPluralRing(r)) |
---|
| 3475 | { |
---|
| 3476 | return nc_pSubst(p,n,e,r); |
---|
| 3477 | } |
---|
| 3478 | #endif |
---|
| 3479 | |
---|
| 3480 | int exponent,i; |
---|
| 3481 | poly h, res, m; |
---|
| 3482 | int *me,*ee; |
---|
| 3483 | number nu,nu1; |
---|
| 3484 | |
---|
| 3485 | me=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3486 | ee=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3487 | if (e!=NULL) p_GetExpV(e,ee,r); |
---|
| 3488 | res=NULL; |
---|
| 3489 | h=p; |
---|
| 3490 | while (h!=NULL) |
---|
| 3491 | { |
---|
| 3492 | if ((e!=NULL) || (p_GetExp(h,n,r)==0)) |
---|
| 3493 | { |
---|
| 3494 | m=p_Head(h,r); |
---|
| 3495 | p_GetExpV(m,me,r); |
---|
| 3496 | exponent=me[n]; |
---|
| 3497 | me[n]=0; |
---|
| 3498 | for(i=rVar(r);i>0;i--) |
---|
| 3499 | me[i]+=exponent*ee[i]; |
---|
| 3500 | p_SetExpV(m,me,r); |
---|
| 3501 | if (e!=NULL) |
---|
| 3502 | { |
---|
| 3503 | n_Power(pGetCoeff(e),exponent,&nu,r->cf); |
---|
| 3504 | nu1=n_Mult(pGetCoeff(m),nu,r->cf); |
---|
| 3505 | n_Delete(&nu,r->cf); |
---|
| 3506 | p_SetCoeff(m,nu1,r); |
---|
| 3507 | } |
---|
| 3508 | res=p_Add_q(res,m,r); |
---|
| 3509 | } |
---|
| 3510 | p_LmDelete(&h,r); |
---|
| 3511 | } |
---|
| 3512 | omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int)); |
---|
| 3513 | omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int)); |
---|
| 3514 | return res; |
---|
| 3515 | } |
---|
[83a1714] | 3516 | |
---|
| 3517 | /*2 |
---|
[f93c5e9] | 3518 | * returns a re-ordered convertion of a number as a polynomial, |
---|
[83a1714] | 3519 | * with permutation of parameters |
---|
| 3520 | * NOTE: this only works for Frank's alg. & trans. fields |
---|
| 3521 | */ |
---|
[2d2e40] | 3522 | poly n_PermNumber(const number z, const int *par_perm, const int , const ring src, const ring dst) |
---|
[83a1714] | 3523 | { |
---|
| 3524 | #if 0 |
---|
| 3525 | PrintS("\nSource Ring: \n"); |
---|
| 3526 | rWrite(src); |
---|
| 3527 | |
---|
| 3528 | if(0) |
---|
| 3529 | { |
---|
| 3530 | number zz = n_Copy(z, src->cf); |
---|
[ce1f78] | 3531 | PrintS("z: "); n_Write(zz, src); |
---|
[83a1714] | 3532 | n_Delete(&zz, src->cf); |
---|
| 3533 | } |
---|
[f93c5e9] | 3534 | |
---|
[83a1714] | 3535 | PrintS("\nDestination Ring: \n"); |
---|
| 3536 | rWrite(dst); |
---|
[f93c5e9] | 3537 | |
---|
[83a1714] | 3538 | Print("\nOldPar: %d\n", OldPar); |
---|
| 3539 | for( int i = 1; i <= OldPar; i++ ) |
---|
| 3540 | { |
---|
| 3541 | Print("par(%d) -> par/var (%d)\n", i, par_perm[i-1]); |
---|
| 3542 | } |
---|
| 3543 | #endif |
---|
| 3544 | if( z == NULL ) |
---|
| 3545 | return NULL; |
---|
[f93c5e9] | 3546 | |
---|
[83a1714] | 3547 | const coeffs srcCf = src->cf; |
---|
| 3548 | assume( srcCf != NULL ); |
---|
| 3549 | |
---|
| 3550 | assume( !nCoeff_is_GF(srcCf) ); |
---|
| 3551 | assume( rField_is_Extension(src) ); |
---|
[f93c5e9] | 3552 | |
---|
[83a1714] | 3553 | poly zz = NULL; |
---|
[f93c5e9] | 3554 | |
---|
[83a1714] | 3555 | const ring srcExtRing = srcCf->extRing; |
---|
| 3556 | assume( srcExtRing != NULL ); |
---|
[f93c5e9] | 3557 | |
---|
[83a1714] | 3558 | const coeffs dstCf = dst->cf; |
---|
| 3559 | assume( dstCf != NULL ); |
---|
| 3560 | |
---|
| 3561 | if( nCoeff_is_algExt(srcCf) ) // nCoeff_is_GF(srcCf)? |
---|
| 3562 | { |
---|
| 3563 | zz = (poly) z; |
---|
| 3564 | |
---|
| 3565 | if( zz == NULL ) |
---|
| 3566 | return NULL; |
---|
[f93c5e9] | 3567 | |
---|
| 3568 | } else if (nCoeff_is_transExt(srcCf)) |
---|
| 3569 | { |
---|
[83a1714] | 3570 | assume( !IS0(z) ); |
---|
[f93c5e9] | 3571 | |
---|
[83a1714] | 3572 | zz = NUM(z); |
---|
| 3573 | p_Test (zz, srcExtRing); |
---|
[f93c5e9] | 3574 | |
---|
[83a1714] | 3575 | if( zz == NULL ) |
---|
| 3576 | return NULL; |
---|
[f93c5e9] | 3577 | |
---|
[90f57e] | 3578 | //if( !DENIS1(z) ) |
---|
| 3579 | //WarnS("Not implemented yet: Cannot permute a rational fraction and make a polynomial out of it! Ignorring the denumerator."); |
---|
[83a1714] | 3580 | } else |
---|
| 3581 | { |
---|
[f93c5e9] | 3582 | assume (FALSE); |
---|
| 3583 | Werror("Number permutation is not implemented for this data yet!"); |
---|
| 3584 | return NULL; |
---|
[83a1714] | 3585 | } |
---|
[f93c5e9] | 3586 | |
---|
[83a1714] | 3587 | assume( zz != NULL ); |
---|
| 3588 | p_Test (zz, srcExtRing); |
---|
| 3589 | |
---|
[f93c5e9] | 3590 | |
---|
[83a1714] | 3591 | nMapFunc nMap = n_SetMap(srcExtRing->cf, dstCf); |
---|
[f93c5e9] | 3592 | |
---|
[83a1714] | 3593 | assume( nMap != NULL ); |
---|
[f93c5e9] | 3594 | |
---|
[83a1714] | 3595 | poly qq = p_PermPoly(zz, par_perm - 1, srcExtRing, dst, nMap, NULL, rVar(srcExtRing) ); |
---|
| 3596 | // poly p_PermPoly (poly p, int * perm, const ring oldRing, const ring dst, nMapFunc nMap, int *par_perm, int OldPar) |
---|
[f93c5e9] | 3597 | |
---|
[83a1714] | 3598 | // assume( FALSE ); WarnS("longalg missing 2"); |
---|
[f93c5e9] | 3599 | |
---|
[83a1714] | 3600 | return qq; |
---|
| 3601 | } |
---|
| 3602 | |
---|
| 3603 | |
---|
[deca086] | 3604 | /*2 |
---|
| 3605 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
| 3606 | */ |
---|
[83a1714] | 3607 | poly p_PermPoly (poly p, const int * perm, const ring oldRing, const ring dst, |
---|
| 3608 | nMapFunc nMap, const int *par_perm, int OldPar) |
---|
[deca086] | 3609 | { |
---|
[83a1714] | 3610 | #if 0 |
---|
| 3611 | p_Test(p, oldRing); |
---|
| 3612 | PrintS("\np_PermPoly::p: "); p_Write(p, oldRing, oldRing); PrintLn(); |
---|
| 3613 | #endif |
---|
[f93c5e9] | 3614 | |
---|
[b38d70] | 3615 | const int OldpVariables = rVar(oldRing); |
---|
[deca086] | 3616 | poly result = NULL; |
---|
| 3617 | poly result_last = NULL; |
---|
[83a1714] | 3618 | poly aq = NULL; /* the map coefficient */ |
---|
[deca086] | 3619 | poly qq; /* the mapped monomial */ |
---|
| 3620 | |
---|
[bcfd11a] | 3621 | assume(dst != NULL); |
---|
| 3622 | assume(dst->cf != NULL); |
---|
[0366c4] | 3623 | |
---|
[deca086] | 3624 | while (p != NULL) |
---|
| 3625 | { |
---|
[b38d70] | 3626 | // map the coefficient |
---|
[83a1714] | 3627 | if ( ((OldPar == 0) || (par_perm == NULL) || rField_is_GF(oldRing)) && (nMap != NULL) ) |
---|
[deca086] | 3628 | { |
---|
| 3629 | qq = p_Init(dst); |
---|
[83a1714] | 3630 | assume( nMap != NULL ); |
---|
[b38d70] | 3631 | number n = nMap(p_GetCoeff(p, oldRing), oldRing->cf, dst->cf); |
---|
[f93c5e9] | 3632 | |
---|
[bcfd11a] | 3633 | if ( nCoeff_is_algExt(dst->cf) ) |
---|
[b38d70] | 3634 | n_Normalize(n, dst->cf); |
---|
[f93c5e9] | 3635 | |
---|
[9e26458] | 3636 | p_GetCoeff(qq, dst) = n;// Note: n can be a ZERO!!! |
---|
[0366c4] | 3637 | // coef may be zero: |
---|
[9e26458] | 3638 | // p_Test(qq, dst); |
---|
[deca086] | 3639 | } |
---|
| 3640 | else |
---|
| 3641 | { |
---|
[f93c5e9] | 3642 | qq = p_One(dst); |
---|
[83a1714] | 3643 | |
---|
| 3644 | // aq = naPermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing); // no dst??? |
---|
| 3645 | // poly n_PermNumber(const number z, const int *par_perm, const int P, const ring src, const ring dst) |
---|
| 3646 | aq = n_PermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing, dst); |
---|
| 3647 | |
---|
| 3648 | p_Test(aq, dst); |
---|
[f93c5e9] | 3649 | |
---|
[bcfd11a] | 3650 | if ( nCoeff_is_algExt(dst->cf) ) |
---|
[1f414c8] | 3651 | p_Normalize(aq,dst); |
---|
[0366c4] | 3652 | |
---|
[83a1714] | 3653 | if (aq == NULL) |
---|
[f93c5e9] | 3654 | p_SetCoeff(qq, n_Init(0, dst->cf),dst); // Very dirty trick!!! |
---|
| 3655 | |
---|
[b38d70] | 3656 | p_Test(aq, dst); |
---|
[deca086] | 3657 | } |
---|
[f93c5e9] | 3658 | |
---|
| 3659 | if (rRing_has_Comp(dst)) |
---|
[b38d70] | 3660 | p_SetComp(qq, p_GetComp(p, oldRing), dst); |
---|
| 3661 | |
---|
| 3662 | if ( n_IsZero(pGetCoeff(qq), dst->cf) ) |
---|
[deca086] | 3663 | { |
---|
| 3664 | p_LmDelete(&qq,dst); |
---|
[b38d70] | 3665 | qq = NULL; |
---|
[f93c5e9] | 3666 | } |
---|
[deca086] | 3667 | else |
---|
| 3668 | { |
---|
[b38d70] | 3669 | // map pars: |
---|
| 3670 | int mapped_to_par = 0; |
---|
| 3671 | for(int i = 1; i <= OldpVariables; i++) |
---|
[deca086] | 3672 | { |
---|
[b38d70] | 3673 | int e = p_GetExp(p, i, oldRing); |
---|
| 3674 | if (e != 0) |
---|
[deca086] | 3675 | { |
---|
| 3676 | if (perm==NULL) |
---|
[b38d70] | 3677 | p_SetExp(qq, i, e, dst); |
---|
[deca086] | 3678 | else if (perm[i]>0) |
---|
| 3679 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
| 3680 | else if (perm[i]<0) |
---|
| 3681 | { |
---|
[b38d70] | 3682 | number c = p_GetCoeff(qq, dst); |
---|
[deca086] | 3683 | if (rField_is_GF(dst)) |
---|
| 3684 | { |
---|
[7fee876] | 3685 | assume( dst->cf->extRing == NULL ); |
---|
| 3686 | number ee = n_Param(1, dst); |
---|
[b38d70] | 3687 | |
---|
[f93c5e9] | 3688 | number eee; |
---|
| 3689 | n_Power(ee, e, &eee, dst->cf); //nfDelete(ee,dst); |
---|
| 3690 | |
---|
[b38d70] | 3691 | ee = n_Mult(c, eee, dst->cf); |
---|
[8a8c9e] | 3692 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
[deca086] | 3693 | pSetCoeff0(qq,ee); |
---|
| 3694 | } |
---|
[b38d70] | 3695 | else if (nCoeff_is_Extension(dst->cf)) |
---|
[deca086] | 3696 | { |
---|
[f93c5e9] | 3697 | const int par = -perm[i]; |
---|
| 3698 | assume( par > 0 ); |
---|
[83a1714] | 3699 | |
---|
[b38d70] | 3700 | // WarnS("longalg missing 3"); |
---|
| 3701 | #if 1 |
---|
[f93c5e9] | 3702 | const coeffs C = dst->cf; |
---|
| 3703 | assume( C != NULL ); |
---|
| 3704 | |
---|
| 3705 | const ring R = C->extRing; |
---|
| 3706 | assume( R != NULL ); |
---|
| 3707 | |
---|
| 3708 | assume( par <= rVar(R) ); |
---|
| 3709 | |
---|
| 3710 | poly pcn; // = (number)c |
---|
| 3711 | |
---|
| 3712 | assume( !n_IsZero(c, C) ); |
---|
| 3713 | |
---|
| 3714 | if( nCoeff_is_algExt(C) ) |
---|
| 3715 | pcn = (poly) c; |
---|
| 3716 | else // nCoeff_is_transExt(C) |
---|
| 3717 | pcn = NUM(c); |
---|
| 3718 | |
---|
[b38d70] | 3719 | if (pNext(pcn) == NULL) // c->z |
---|
| 3720 | p_AddExp(pcn, -perm[i], e, R); |
---|
[deca086] | 3721 | else /* more difficult: we have really to multiply: */ |
---|
| 3722 | { |
---|
[b38d70] | 3723 | poly mmc = p_ISet(1, R); |
---|
| 3724 | p_SetExp(mmc, -perm[i], e, R); |
---|
| 3725 | p_Setm(mmc, R); |
---|
[f93c5e9] | 3726 | |
---|
| 3727 | number nnc; |
---|
| 3728 | // convert back to a number: number nnc = mmc; |
---|
| 3729 | if( nCoeff_is_algExt(C) ) |
---|
| 3730 | nnc = (number) mmc; |
---|
| 3731 | else // nCoeff_is_transExt(C) |
---|
| 3732 | nnc = ntInit(mmc, C); |
---|
| 3733 | |
---|
[b38d70] | 3734 | p_GetCoeff(qq, dst) = n_Mult((number)c, nnc, C); |
---|
| 3735 | n_Delete((number *)&c, C); |
---|
| 3736 | n_Delete((number *)&nnc, C); |
---|
[deca086] | 3737 | } |
---|
[f93c5e9] | 3738 | |
---|
[deca086] | 3739 | mapped_to_par=1; |
---|
[1f414c8] | 3740 | #endif |
---|
[deca086] | 3741 | } |
---|
| 3742 | } |
---|
| 3743 | else |
---|
| 3744 | { |
---|
| 3745 | /* this variable maps to 0 !*/ |
---|
[b38d70] | 3746 | p_LmDelete(&qq, dst); |
---|
[deca086] | 3747 | break; |
---|
| 3748 | } |
---|
| 3749 | } |
---|
| 3750 | } |
---|
[bcfd11a] | 3751 | if ( mapped_to_par && nCoeff_is_algExt(dst->cf) ) |
---|
[deca086] | 3752 | { |
---|
[b38d70] | 3753 | number n = p_GetCoeff(qq, dst); |
---|
[bcfd11a] | 3754 | n_Normalize(n, dst->cf); |
---|
[b38d70] | 3755 | p_GetCoeff(qq, dst) = n; |
---|
[deca086] | 3756 | } |
---|
| 3757 | } |
---|
| 3758 | pIter(p); |
---|
[f93c5e9] | 3759 | |
---|
[83a1714] | 3760 | #if 0 |
---|
| 3761 | p_Test(aq,dst); |
---|
| 3762 | PrintS("\naq: "); p_Write(aq, dst, dst); PrintLn(); |
---|
| 3763 | #endif |
---|
[f93c5e9] | 3764 | |
---|
[b38d70] | 3765 | |
---|
[deca086] | 3766 | #if 1 |
---|
| 3767 | if (qq!=NULL) |
---|
| 3768 | { |
---|
| 3769 | p_Setm(qq,dst); |
---|
[f93c5e9] | 3770 | |
---|
[deca086] | 3771 | p_Test(aq,dst); |
---|
| 3772 | p_Test(qq,dst); |
---|
[f93c5e9] | 3773 | |
---|
[83a1714] | 3774 | #if 0 |
---|
| 3775 | p_Test(qq,dst); |
---|
| 3776 | PrintS("\nqq: "); p_Write(qq, dst, dst); PrintLn(); |
---|
| 3777 | #endif |
---|
[f93c5e9] | 3778 | |
---|
| 3779 | if (aq!=NULL) |
---|
| 3780 | qq=p_Mult_q(aq,qq,dst); |
---|
| 3781 | |
---|
[deca086] | 3782 | aq = qq; |
---|
[f93c5e9] | 3783 | |
---|
[deca086] | 3784 | while (pNext(aq) != NULL) pIter(aq); |
---|
[f93c5e9] | 3785 | |
---|
[deca086] | 3786 | if (result_last==NULL) |
---|
| 3787 | { |
---|
| 3788 | result=qq; |
---|
| 3789 | } |
---|
| 3790 | else |
---|
| 3791 | { |
---|
| 3792 | pNext(result_last)=qq; |
---|
| 3793 | } |
---|
| 3794 | result_last=aq; |
---|
| 3795 | aq = NULL; |
---|
| 3796 | } |
---|
| 3797 | else if (aq!=NULL) |
---|
| 3798 | { |
---|
| 3799 | p_Delete(&aq,dst); |
---|
| 3800 | } |
---|
| 3801 | } |
---|
[f93c5e9] | 3802 | |
---|
[deca086] | 3803 | result=p_SortAdd(result,dst); |
---|
| 3804 | #else |
---|
| 3805 | // if (qq!=NULL) |
---|
| 3806 | // { |
---|
| 3807 | // pSetm(qq); |
---|
| 3808 | // pTest(qq); |
---|
| 3809 | // pTest(aq); |
---|
| 3810 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
| 3811 | // aq = qq; |
---|
| 3812 | // while (pNext(aq) != NULL) pIter(aq); |
---|
| 3813 | // pNext(aq) = result; |
---|
| 3814 | // aq = NULL; |
---|
| 3815 | // result = qq; |
---|
| 3816 | // } |
---|
| 3817 | // else if (aq!=NULL) |
---|
| 3818 | // { |
---|
| 3819 | // pDelete(&aq); |
---|
| 3820 | // } |
---|
| 3821 | //} |
---|
| 3822 | //p = result; |
---|
| 3823 | //result = NULL; |
---|
| 3824 | //while (p != NULL) |
---|
| 3825 | //{ |
---|
| 3826 | // qq = p; |
---|
| 3827 | // pIter(p); |
---|
| 3828 | // qq->next = NULL; |
---|
| 3829 | // result = pAdd(result, qq); |
---|
| 3830 | //} |
---|
| 3831 | #endif |
---|
| 3832 | p_Test(result,dst); |
---|
[f93c5e9] | 3833 | |
---|
[83a1714] | 3834 | #if 0 |
---|
| 3835 | p_Test(result,dst); |
---|
| 3836 | PrintS("\nresult: "); p_Write(result,dst,dst); PrintLn(); |
---|
| 3837 | #endif |
---|
[deca086] | 3838 | return result; |
---|
| 3839 | } |
---|
[f550e86] | 3840 | /************************************************************** |
---|
| 3841 | * |
---|
| 3842 | * Jet |
---|
| 3843 | * |
---|
| 3844 | **************************************************************/ |
---|
| 3845 | |
---|
| 3846 | poly pp_Jet(poly p, int m, const ring R) |
---|
| 3847 | { |
---|
| 3848 | poly r=NULL; |
---|
| 3849 | poly t=NULL; |
---|
| 3850 | |
---|
| 3851 | while (p!=NULL) |
---|
| 3852 | { |
---|
| 3853 | if (p_Totaldegree(p,R)<=m) |
---|
| 3854 | { |
---|
| 3855 | if (r==NULL) |
---|
| 3856 | r=p_Head(p,R); |
---|
| 3857 | else |
---|
| 3858 | if (t==NULL) |
---|
| 3859 | { |
---|
| 3860 | pNext(r)=p_Head(p,R); |
---|
| 3861 | t=pNext(r); |
---|
| 3862 | } |
---|
| 3863 | else |
---|
| 3864 | { |
---|
| 3865 | pNext(t)=p_Head(p,R); |
---|
| 3866 | pIter(t); |
---|
| 3867 | } |
---|
| 3868 | } |
---|
| 3869 | pIter(p); |
---|
| 3870 | } |
---|
| 3871 | return r; |
---|
| 3872 | } |
---|
| 3873 | |
---|
| 3874 | poly p_Jet(poly p, int m,const ring R) |
---|
| 3875 | { |
---|
| 3876 | while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R); |
---|
| 3877 | if (p==NULL) return NULL; |
---|
| 3878 | poly r=p; |
---|
| 3879 | while (pNext(p)!=NULL) |
---|
| 3880 | { |
---|
| 3881 | if (p_Totaldegree(pNext(p),R)>m) |
---|
| 3882 | { |
---|
| 3883 | p_LmDelete(&pNext(p),R); |
---|
| 3884 | } |
---|
| 3885 | else |
---|
| 3886 | pIter(p); |
---|
| 3887 | } |
---|
| 3888 | return r; |
---|
| 3889 | } |
---|
| 3890 | |
---|
| 3891 | poly pp_JetW(poly p, int m, short *w, const ring R) |
---|
| 3892 | { |
---|
| 3893 | poly r=NULL; |
---|
| 3894 | poly t=NULL; |
---|
| 3895 | while (p!=NULL) |
---|
| 3896 | { |
---|
| 3897 | if (totaldegreeWecart_IV(p,R,w)<=m) |
---|
| 3898 | { |
---|
| 3899 | if (r==NULL) |
---|
| 3900 | r=p_Head(p,R); |
---|
| 3901 | else |
---|
| 3902 | if (t==NULL) |
---|
| 3903 | { |
---|
| 3904 | pNext(r)=p_Head(p,R); |
---|
| 3905 | t=pNext(r); |
---|
| 3906 | } |
---|
| 3907 | else |
---|
| 3908 | { |
---|
| 3909 | pNext(t)=p_Head(p,R); |
---|
| 3910 | pIter(t); |
---|
| 3911 | } |
---|
| 3912 | } |
---|
| 3913 | pIter(p); |
---|
| 3914 | } |
---|
| 3915 | return r; |
---|
| 3916 | } |
---|
| 3917 | |
---|
| 3918 | poly p_JetW(poly p, int m, short *w, const ring R) |
---|
| 3919 | { |
---|
| 3920 | while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R); |
---|
| 3921 | if (p==NULL) return NULL; |
---|
| 3922 | poly r=p; |
---|
| 3923 | while (pNext(p)!=NULL) |
---|
| 3924 | { |
---|
| 3925 | if (totaldegreeWecart_IV(pNext(p),R,w)>m) |
---|
| 3926 | { |
---|
| 3927 | p_LmDelete(&pNext(p),R); |
---|
| 3928 | } |
---|
| 3929 | else |
---|
| 3930 | pIter(p); |
---|
| 3931 | } |
---|
| 3932 | return r; |
---|
| 3933 | } |
---|
[5c39a9] | 3934 | |
---|
[ba0fc3] | 3935 | /*************************************************************/ |
---|
| 3936 | int p_MinDeg(poly p,intvec *w, const ring R) |
---|
| 3937 | { |
---|
| 3938 | if(p==NULL) |
---|
| 3939 | return -1; |
---|
| 3940 | int d=-1; |
---|
| 3941 | while(p!=NULL) |
---|
| 3942 | { |
---|
| 3943 | int d0=0; |
---|
| 3944 | for(int j=0;j<rVar(R);j++) |
---|
| 3945 | if(w==NULL||j>=w->length()) |
---|
| 3946 | d0+=p_GetExp(p,j+1,R); |
---|
| 3947 | else |
---|
| 3948 | d0+=(*w)[j]*p_GetExp(p,j+1,R); |
---|
| 3949 | if(d0<d||d==-1) |
---|
| 3950 | d=d0; |
---|
| 3951 | pIter(p); |
---|
| 3952 | } |
---|
| 3953 | return d; |
---|
| 3954 | } |
---|
| 3955 | |
---|
[a4081e5] | 3956 | /***************************************************************/ |
---|
| 3957 | |
---|
| 3958 | poly p_Series(int n,poly p,poly u, intvec *w, const ring R) |
---|
| 3959 | { |
---|
| 3960 | short *ww=iv2array(w,R); |
---|
| 3961 | if(p!=NULL) |
---|
| 3962 | { |
---|
| 3963 | if(u==NULL) |
---|
| 3964 | p=p_JetW(p,n,ww,R); |
---|
| 3965 | else |
---|
| 3966 | p=p_JetW(p_Mult_q(p,p_Invers(n-p_MinDeg(p,w,R),u,w,R),R),n,ww,R); |
---|
| 3967 | } |
---|
| 3968 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3969 | return p; |
---|
| 3970 | } |
---|
| 3971 | |
---|
| 3972 | poly p_Invers(int n,poly u,intvec *w, const ring R) |
---|
| 3973 | { |
---|
| 3974 | if(n<0) |
---|
| 3975 | return NULL; |
---|
| 3976 | number u0=n_Invers(pGetCoeff(u),R->cf); |
---|
| 3977 | poly v=p_NSet(u0,R); |
---|
| 3978 | if(n==0) |
---|
| 3979 | return v; |
---|
| 3980 | short *ww=iv2array(w,R); |
---|
| 3981 | poly u1=p_JetW(p_Sub(p_One(R),p_Mult_nn(u,u0,R),R),n,ww,R); |
---|
| 3982 | if(u1==NULL) |
---|
| 3983 | { |
---|
| 3984 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3985 | return v; |
---|
| 3986 | } |
---|
| 3987 | poly v1=p_Mult_nn(p_Copy(u1,R),u0,R); |
---|
| 3988 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3989 | for(int i=n/p_MinDeg(u1,w,R);i>1;i--) |
---|
| 3990 | { |
---|
| 3991 | v1=p_JetW(p_Mult_q(v1,p_Copy(u1,R),R),n,ww,R); |
---|
| 3992 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3993 | } |
---|
| 3994 | p_Delete(&u1,R); |
---|
| 3995 | p_Delete(&v1,R); |
---|
| 3996 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3997 | return v; |
---|
| 3998 | } |
---|
| 3999 | |
---|
[7dce2d7] | 4000 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r) |
---|
| 4001 | { |
---|
| 4002 | while ((p1 != NULL) && (p2 != NULL)) |
---|
| 4003 | { |
---|
| 4004 | if (! p_LmEqual(p1, p2,r)) |
---|
| 4005 | return FALSE; |
---|
[07ff96] | 4006 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r->cf )) |
---|
[7dce2d7] | 4007 | return FALSE; |
---|
| 4008 | pIter(p1); |
---|
| 4009 | pIter(p2); |
---|
| 4010 | } |
---|
| 4011 | return (p1==p2); |
---|
| 4012 | } |
---|
[32d07a5] | 4013 | |
---|
[55e2df0] | 4014 | static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r1, const ring r2) |
---|
| 4015 | { |
---|
| 4016 | assume( r1 == r2 || rSamePolyRep(r1, r2) ); |
---|
| 4017 | |
---|
| 4018 | p_LmCheckPolyRing1(p1, r1); |
---|
| 4019 | p_LmCheckPolyRing1(p2, r2); |
---|
| 4020 | |
---|
| 4021 | int i = r1->ExpL_Size; |
---|
| 4022 | |
---|
| 4023 | assume( r1->ExpL_Size == r2->ExpL_Size ); |
---|
| 4024 | |
---|
| 4025 | unsigned long *ep = p1->exp; |
---|
| 4026 | unsigned long *eq = p2->exp; |
---|
| 4027 | |
---|
| 4028 | do |
---|
| 4029 | { |
---|
| 4030 | i--; |
---|
| 4031 | if (ep[i] != eq[i]) return FALSE; |
---|
| 4032 | } |
---|
| 4033 | while (i); |
---|
| 4034 | |
---|
| 4035 | return TRUE; |
---|
| 4036 | } |
---|
| 4037 | |
---|
| 4038 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r1, const ring r2) |
---|
| 4039 | { |
---|
| 4040 | assume( r1 == r2 || rSamePolyRep(r1, r2) ); // will be used in rEqual! |
---|
| 4041 | assume( r1->cf == r2->cf ); |
---|
[0366c4] | 4042 | |
---|
[55e2df0] | 4043 | while ((p1 != NULL) && (p2 != NULL)) |
---|
| 4044 | { |
---|
| 4045 | // returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !! |
---|
| 4046 | // #define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r) |
---|
| 4047 | |
---|
| 4048 | if (! p_ExpVectorEqual(p1, p2, r1, r2)) |
---|
| 4049 | return FALSE; |
---|
[0366c4] | 4050 | |
---|
[55e2df0] | 4051 | if (! n_Equal(p_GetCoeff(p1,r1), p_GetCoeff(p2,r2), r1->cf )) |
---|
| 4052 | return FALSE; |
---|
[0366c4] | 4053 | |
---|
[55e2df0] | 4054 | pIter(p1); |
---|
| 4055 | pIter(p2); |
---|
| 4056 | } |
---|
| 4057 | return (p1==p2); |
---|
| 4058 | } |
---|
| 4059 | |
---|
[32d07a5] | 4060 | /*2 |
---|
| 4061 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
| 4062 | *assume p1 != NULL and p2 != NULL |
---|
| 4063 | */ |
---|
| 4064 | BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r) |
---|
| 4065 | { |
---|
| 4066 | number n,nn; |
---|
| 4067 | pAssume(p1 != NULL && p2 != NULL); |
---|
| 4068 | |
---|
| 4069 | if (!p_LmEqual(p1,p2,r)) //compare leading mons |
---|
| 4070 | return FALSE; |
---|
| 4071 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
---|
| 4072 | return FALSE; |
---|
| 4073 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
---|
| 4074 | return FALSE; |
---|
| 4075 | if (pLength(p1) != pLength(p2)) |
---|
| 4076 | return FALSE; |
---|
| 4077 | #ifdef HAVE_RINGS |
---|
| 4078 | if (rField_is_Ring(r)) |
---|
| 4079 | { |
---|
| 4080 | if (!n_DivBy(p_GetCoeff(p1, r), p_GetCoeff(p2, r), r)) return FALSE; |
---|
| 4081 | } |
---|
| 4082 | #endif |
---|
| 4083 | n=n_Div(p_GetCoeff(p1,r),p_GetCoeff(p2,r),r); |
---|
| 4084 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
| 4085 | { |
---|
| 4086 | if ( ! p_LmEqual(p1, p2,r)) |
---|
| 4087 | { |
---|
| 4088 | n_Delete(&n, r); |
---|
| 4089 | return FALSE; |
---|
| 4090 | } |
---|
[07ff96] | 4091 | if (!n_Equal(p_GetCoeff(p1, r), nn = n_Mult(p_GetCoeff(p2, r),n, r->cf), r->cf)) |
---|
[32d07a5] | 4092 | { |
---|
| 4093 | n_Delete(&n, r); |
---|
| 4094 | n_Delete(&nn, r); |
---|
| 4095 | return FALSE; |
---|
| 4096 | } |
---|
| 4097 | n_Delete(&nn, r); |
---|
| 4098 | pIter(p1); |
---|
| 4099 | pIter(p2); |
---|
| 4100 | } |
---|
| 4101 | n_Delete(&n, r); |
---|
| 4102 | return TRUE; |
---|
| 4103 | } |
---|
| 4104 | |
---|
[1fdb6e] | 4105 | /*2 |
---|
| 4106 | * returns the length of a (numbers of monomials) |
---|
| 4107 | * respect syzComp |
---|
| 4108 | */ |
---|
[a497a1] | 4109 | poly p_Last(const poly p, int &l, const ring r) |
---|
[1fdb6e] | 4110 | { |
---|
[a497a1] | 4111 | if (p == NULL) |
---|
[1fdb6e] | 4112 | { |
---|
| 4113 | l = 0; |
---|
| 4114 | return NULL; |
---|
| 4115 | } |
---|
| 4116 | l = 1; |
---|
[a497a1] | 4117 | poly a = p; |
---|
[1fdb6e] | 4118 | if (! rIsSyzIndexRing(r)) |
---|
| 4119 | { |
---|
[a497a1] | 4120 | poly next = pNext(a); |
---|
| 4121 | while (next!=NULL) |
---|
[1fdb6e] | 4122 | { |
---|
[a497a1] | 4123 | a = next; |
---|
[0366c4] | 4124 | next = pNext(a); |
---|
[1fdb6e] | 4125 | l++; |
---|
| 4126 | } |
---|
| 4127 | } |
---|
| 4128 | else |
---|
| 4129 | { |
---|
| 4130 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 4131 | poly pp = a; |
---|
| 4132 | while ((a=pNext(a))!=NULL) |
---|
| 4133 | { |
---|
| 4134 | if (p_GetComp(a,r)<=curr_limit/*syzComp*/) |
---|
| 4135 | l++; |
---|
| 4136 | else break; |
---|
| 4137 | pp = a; |
---|
| 4138 | } |
---|
| 4139 | a=pp; |
---|
| 4140 | } |
---|
| 4141 | return a; |
---|
| 4142 | } |
---|
[32d07a5] | 4143 | |
---|
[73ad0c] | 4144 | int p_Var(poly m,const ring r) |
---|
| 4145 | { |
---|
| 4146 | if (m==NULL) return 0; |
---|
| 4147 | if (pNext(m)!=NULL) return 0; |
---|
| 4148 | int i,e=0; |
---|
| 4149 | for (i=rVar(r); i>0; i--) |
---|
| 4150 | { |
---|
| 4151 | int exp=p_GetExp(m,i,r); |
---|
| 4152 | if (exp==1) |
---|
| 4153 | { |
---|
| 4154 | if (e==0) e=i; |
---|
| 4155 | else return 0; |
---|
| 4156 | } |
---|
| 4157 | else if (exp!=0) |
---|
| 4158 | { |
---|
| 4159 | return 0; |
---|
| 4160 | } |
---|
| 4161 | } |
---|
| 4162 | return e; |
---|
| 4163 | } |
---|
| 4164 | |
---|
| 4165 | /*2 |
---|
| 4166 | *the minimal index of used variables - 1 |
---|
| 4167 | */ |
---|
| 4168 | int p_LowVar (poly p, const ring r) |
---|
| 4169 | { |
---|
| 4170 | int k,l,lex; |
---|
| 4171 | |
---|
| 4172 | if (p == NULL) return -1; |
---|
| 4173 | |
---|
| 4174 | k = 32000;/*a very large dummy value*/ |
---|
| 4175 | while (p != NULL) |
---|
| 4176 | { |
---|
| 4177 | l = 1; |
---|
| 4178 | lex = p_GetExp(p,l,r); |
---|
| 4179 | while ((l < (rVar(r))) && (lex == 0)) |
---|
| 4180 | { |
---|
| 4181 | l++; |
---|
| 4182 | lex = p_GetExp(p,l,r); |
---|
| 4183 | } |
---|
| 4184 | l--; |
---|
| 4185 | if (l < k) k = l; |
---|
| 4186 | pIter(p); |
---|
| 4187 | } |
---|
| 4188 | return k; |
---|
| 4189 | } |
---|
| 4190 | |
---|
[b7cfaf] | 4191 | /*2 |
---|
| 4192 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
| 4193 | */ |
---|
| 4194 | void p_Shift (poly * p,int i, const ring r) |
---|
| 4195 | { |
---|
| 4196 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
| 4197 | int j = p_MaxComp(*p,r),k = p_MinComp(*p,r); |
---|
| 4198 | |
---|
| 4199 | if (j+i < 0) return ; |
---|
| 4200 | while (qp1 != NULL) |
---|
| 4201 | { |
---|
| 4202 | if ((p_GetComp(qp1,r)+i > 0) || ((j == -i) && (j == k))) |
---|
| 4203 | { |
---|
| 4204 | p_AddComp(qp1,i,r); |
---|
| 4205 | p_SetmComp(qp1,r); |
---|
| 4206 | qp2 = qp1; |
---|
| 4207 | pIter(qp1); |
---|
| 4208 | } |
---|
| 4209 | else |
---|
| 4210 | { |
---|
| 4211 | if (qp2 == *p) |
---|
| 4212 | { |
---|
| 4213 | pIter(*p); |
---|
| 4214 | p_LmDelete(&qp2,r); |
---|
| 4215 | qp2 = *p; |
---|
| 4216 | qp1 = *p; |
---|
| 4217 | } |
---|
| 4218 | else |
---|
| 4219 | { |
---|
| 4220 | qp2->next = qp1->next; |
---|
| 4221 | if (qp1!=NULL) p_LmDelete(&qp1,r); |
---|
| 4222 | qp1 = qp2->next; |
---|
| 4223 | } |
---|
| 4224 | } |
---|
| 4225 | } |
---|
| 4226 | } |
---|
[f3094a] | 4227 | |
---|
| 4228 | /*************************************************************** |
---|
| 4229 | * |
---|
| 4230 | * Storage Managament Routines |
---|
| 4231 | * |
---|
| 4232 | ***************************************************************/ |
---|
| 4233 | |
---|
| 4234 | |
---|
| 4235 | static inline unsigned long GetBitFields(long e, |
---|
| 4236 | unsigned int s, unsigned int n) |
---|
| 4237 | { |
---|
| 4238 | #define Sy_bit_L(x) (((unsigned long)1L)<<(x)) |
---|
| 4239 | unsigned int i = 0; |
---|
| 4240 | unsigned long ev = 0L; |
---|
| 4241 | assume(n > 0 && s < BIT_SIZEOF_LONG); |
---|
| 4242 | do |
---|
| 4243 | { |
---|
| 4244 | assume(s+i < BIT_SIZEOF_LONG); |
---|
| 4245 | if (e > (long) i) ev |= Sy_bit_L(s+i); |
---|
| 4246 | else break; |
---|
| 4247 | i++; |
---|
| 4248 | } |
---|
| 4249 | while (i < n); |
---|
| 4250 | return ev; |
---|
| 4251 | } |
---|
| 4252 | |
---|
| 4253 | // Short Exponent Vectors are used for fast divisibility tests |
---|
| 4254 | // ShortExpVectors "squeeze" an exponent vector into one word as follows: |
---|
| 4255 | // Let n = BIT_SIZEOF_LONG / pVariables. |
---|
| 4256 | // If n == 0 (i.e. pVariables > BIT_SIZE_OF_LONG), let m == the number |
---|
| 4257 | // of non-zero exponents. If (m>BIT_SIZEOF_LONG), then sev = ~0, else |
---|
| 4258 | // first m bits of sev are set to 1. |
---|
| 4259 | // Otherwise (i.e. pVariables <= BIT_SIZE_OF_LONG) |
---|
| 4260 | // represented by a bit-field of length n (resp. n+1 for some |
---|
| 4261 | // exponents). If the value of an exponent is greater or equal to n, then |
---|
| 4262 | // all of its respective n bits are set to 1. If the value of an exponent |
---|
| 4263 | // is smaller than n, say m, then only the first m bits of the respective |
---|
| 4264 | // n bits are set to 1, the others are set to 0. |
---|
| 4265 | // This way, we have: |
---|
| 4266 | // exp1 / exp2 ==> (ev1 & ~ev2) == 0, i.e., |
---|
| 4267 | // if (ev1 & ~ev2) then exp1 does not divide exp2 |
---|
| 4268 | unsigned long p_GetShortExpVector(poly p, const ring r) |
---|
| 4269 | { |
---|
| 4270 | assume(p != NULL); |
---|
| 4271 | if (p == NULL) return 0; |
---|
| 4272 | unsigned long ev = 0; // short exponent vector |
---|
| 4273 | unsigned int n = BIT_SIZEOF_LONG / r->N; // number of bits per exp |
---|
| 4274 | unsigned int m1; // highest bit which is filled with (n+1) |
---|
| 4275 | unsigned int i = 0, j=1; |
---|
| 4276 | |
---|
| 4277 | if (n == 0) |
---|
| 4278 | { |
---|
| 4279 | if (r->N <2*BIT_SIZEOF_LONG) |
---|
| 4280 | { |
---|
| 4281 | n=1; |
---|
| 4282 | m1=0; |
---|
| 4283 | } |
---|
| 4284 | else |
---|
| 4285 | { |
---|
| 4286 | for (; j<=(unsigned long) r->N; j++) |
---|
| 4287 | { |
---|
| 4288 | if (p_GetExp(p,j,r) > 0) i++; |
---|
| 4289 | if (i == BIT_SIZEOF_LONG) break; |
---|
| 4290 | } |
---|
| 4291 | if (i>0) |
---|
| 4292 | ev = ~((unsigned long)0) >> ((unsigned long) (BIT_SIZEOF_LONG - i)); |
---|
| 4293 | return ev; |
---|
| 4294 | } |
---|
| 4295 | } |
---|
| 4296 | else |
---|
| 4297 | { |
---|
| 4298 | m1 = (n+1)*(BIT_SIZEOF_LONG - n*r->N); |
---|
| 4299 | } |
---|
| 4300 | |
---|
| 4301 | n++; |
---|
| 4302 | while (i<m1) |
---|
| 4303 | { |
---|
| 4304 | ev |= GetBitFields(p_GetExp(p, j,r), i, n); |
---|
| 4305 | i += n; |
---|
| 4306 | j++; |
---|
| 4307 | } |
---|
| 4308 | |
---|
| 4309 | n--; |
---|
| 4310 | while (i<BIT_SIZEOF_LONG) |
---|
| 4311 | { |
---|
| 4312 | ev |= GetBitFields(p_GetExp(p, j,r), i, n); |
---|
| 4313 | i += n; |
---|
| 4314 | j++; |
---|
| 4315 | } |
---|
| 4316 | return ev; |
---|
| 4317 | } |
---|
| 4318 | |
---|
[50c414] | 4319 | /*************************************************************** |
---|
| 4320 | * |
---|
| 4321 | * p_ShallowDelete |
---|
| 4322 | * |
---|
| 4323 | ***************************************************************/ |
---|
| 4324 | #undef LINKAGE |
---|
| 4325 | #define LINKAGE |
---|
[38500a] | 4326 | #undef p_Delete__T |
---|
| 4327 | #define p_Delete__T p_ShallowDelete |
---|
[35eaf8] | 4328 | #undef n_Delete__T |
---|
[d101b1] | 4329 | #define n_Delete__T(n, r) do {} while (0) |
---|
[50c414] | 4330 | |
---|
[20b794] | 4331 | #include <polys/templates/p_Delete__T.cc> |
---|
[50c414] | 4332 | |
---|