[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[341696] | 4 | /* $Id$ */ |
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[35aab3] | 5 | /* |
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| 6 | * ABSTRACT - all basic methods to manipulate ideals |
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| 7 | */ |
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| 8 | |
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[2ad10e9] | 9 | |
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[35aab3] | 10 | /* includes */ |
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[2ad10e9] | 11 | #include "config.h" |
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| 12 | #include <misc/auxiliary.h> |
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[f71e8c5] | 13 | #include <misc/options.h> |
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| 14 | #include <omalloc/omalloc.h> |
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| 15 | #include <polys/monomials/p_polys.h> |
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[f5c2d02] | 16 | #include <misc/intvec.h> |
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[2f5936] | 17 | #include <polys/simpleideals.h> |
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[35aab3] | 18 | |
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| 19 | /*2 |
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| 20 | * initialise an ideal |
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| 21 | */ |
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| 22 | ideal idInit(int idsize, int rank) |
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| 23 | { |
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| 24 | /*- initialise an ideal -*/ |
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| 25 | ideal hh = (ideal )omAllocBin(sip_sideal_bin); |
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| 26 | hh->nrows = 1; |
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| 27 | hh->rank = rank; |
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| 28 | IDELEMS(hh) = idsize; |
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| 29 | if (idsize>0) |
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| 30 | { |
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| 31 | hh->m = (poly *)omAlloc0(idsize*sizeof(poly)); |
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| 32 | } |
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| 33 | else |
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| 34 | hh->m=NULL; |
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| 35 | return hh; |
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| 36 | } |
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| 37 | |
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[e9c3b2] | 38 | #ifdef PDEBUG |
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[e070895] | 39 | // this is only for outputting an ideal within the debugger |
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[645a19] | 40 | void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint) |
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[35aab3] | 41 | { |
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[645a19] | 42 | assume( debugPrint >= 0 ); |
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[bead81] | 43 | |
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[52e2f6] | 44 | if( id == NULL ) |
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[f44fb9] | 45 | PrintS("(NULL)"); |
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[52e2f6] | 46 | else |
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[35aab3] | 47 | { |
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[6867f5] | 48 | Print("Module of rank %ld,real rank %ld and %d generators.\n", |
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[f71e8c5] | 49 | id->rank,id_RankFreeModule(id, lmRing, tailRing),IDELEMS(id)); |
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[645a19] | 50 | |
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| 51 | int j = (id->ncols*id->nrows) - 1; |
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| 52 | while ((j > 0) && (id->m[j]==NULL)) j--; |
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| 53 | for (int i = 0; i <= j; i++) |
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[35aab3] | 54 | { |
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[645a19] | 55 | Print("generator %d: ",i); p_DebugPrint(id->m[i], lmRing, tailRing, debugPrint); |
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[35aab3] | 56 | } |
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| 57 | } |
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| 58 | } |
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[e070895] | 59 | #endif |
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[35aab3] | 60 | |
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[dd5534] | 61 | /* index of generator with leading term in ground ring (if any); |
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| 62 | otherwise -1 */ |
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[f71e8c5] | 63 | int id_PosConstant(ideal id, const ring r) |
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[dd5534] | 64 | { |
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| 65 | int k; |
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| 66 | for (k = IDELEMS(id)-1; k>=0; k--) |
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| 67 | { |
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[f71e8c5] | 68 | if (p_LmIsConstantComp(id->m[k], r) == TRUE) |
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[dd5534] | 69 | return k; |
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| 70 | } |
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| 71 | return -1; |
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| 72 | } |
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| 73 | |
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[35aab3] | 74 | /*2 |
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| 75 | * initialise the maximal ideal (at 0) |
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| 76 | */ |
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[f71e8c5] | 77 | ideal id_MaxIdeal (const ring r) |
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[35aab3] | 78 | { |
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| 79 | int l; |
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| 80 | ideal hh=NULL; |
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| 81 | |
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[f71e8c5] | 82 | hh=idInit(rVar(r),1); |
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| 83 | for (l=0; l<rVar(r); l++) |
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[35aab3] | 84 | { |
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[f71e8c5] | 85 | hh->m[l] = p_One(r); |
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| 86 | p_SetExp(hh->m[l],l+1,1,r); |
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| 87 | p_Setm(hh->m[l],r); |
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[35aab3] | 88 | } |
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| 89 | return hh; |
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| 90 | } |
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| 91 | |
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| 92 | /*2 |
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| 93 | * deletes an ideal/matrix |
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| 94 | */ |
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| 95 | void id_Delete (ideal * h, ring r) |
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| 96 | { |
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| 97 | int j,elems; |
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| 98 | if (*h == NULL) |
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| 99 | return; |
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| 100 | elems=j=(*h)->nrows*(*h)->ncols; |
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| 101 | if (j>0) |
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| 102 | { |
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| 103 | do |
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| 104 | { |
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| 105 | p_Delete(&((*h)->m[--j]), r); |
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| 106 | } |
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| 107 | while (j>0); |
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| 108 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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| 109 | } |
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| 110 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
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| 111 | *h=NULL; |
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| 112 | } |
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| 113 | |
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| 114 | |
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| 115 | /*2 |
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| 116 | * Shallowdeletes an ideal/matrix |
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| 117 | */ |
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| 118 | void id_ShallowDelete (ideal *h, ring r) |
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| 119 | { |
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| 120 | int j,elems; |
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| 121 | if (*h == NULL) |
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| 122 | return; |
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| 123 | elems=j=(*h)->nrows*(*h)->ncols; |
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| 124 | if (j>0) |
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| 125 | { |
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| 126 | do |
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| 127 | { |
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| 128 | p_ShallowDelete(&((*h)->m[--j]), r); |
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| 129 | } |
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| 130 | while (j>0); |
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| 131 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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| 132 | } |
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| 133 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
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| 134 | *h=NULL; |
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| 135 | } |
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| 136 | |
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| 137 | /*2 |
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| 138 | *gives an ideal the minimal possible size |
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| 139 | */ |
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| 140 | void idSkipZeroes (ideal ide) |
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| 141 | { |
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| 142 | int k; |
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| 143 | int j = -1; |
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| 144 | BOOLEAN change=FALSE; |
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| 145 | for (k=0; k<IDELEMS(ide); k++) |
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| 146 | { |
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| 147 | if (ide->m[k] != NULL) |
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| 148 | { |
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| 149 | j++; |
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| 150 | if (change) |
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| 151 | { |
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| 152 | ide->m[j] = ide->m[k]; |
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| 153 | } |
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| 154 | } |
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| 155 | else |
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| 156 | { |
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| 157 | change=TRUE; |
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| 158 | } |
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| 159 | } |
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| 160 | if (change) |
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| 161 | { |
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| 162 | if (j == -1) |
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| 163 | j = 0; |
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| 164 | else |
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| 165 | { |
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| 166 | for (k=j+1; k<IDELEMS(ide); k++) |
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| 167 | ide->m[k] = NULL; |
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| 168 | } |
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| 169 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
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| 170 | IDELEMS(ide) = j+1; |
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| 171 | } |
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| 172 | } |
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| 173 | |
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[2b3caae] | 174 | /*2 |
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| 175 | * copies the first k (>= 1) entries of the given ideal |
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| 176 | * and returns these as a new ideal |
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| 177 | * (Note that the copied polynomials may be zero.) |
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| 178 | */ |
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[f71e8c5] | 179 | ideal id_CopyFirstK (const ideal ide, const int k,const ring r) |
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[2b3caae] | 180 | { |
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| 181 | ideal newI = idInit(k, 0); |
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| 182 | for (int i = 0; i < k; i++) |
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[f71e8c5] | 183 | newI->m[i] = p_Copy(ide->m[i],r); |
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[2b3caae] | 184 | return newI; |
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| 185 | } |
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| 186 | |
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[35aab3] | 187 | /*2 |
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| 188 | * ideal id = (id[i]) |
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| 189 | * result is leadcoeff(id[i]) = 1 |
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| 190 | */ |
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[9aa29b] | 191 | void id_Norm(ideal id, const ring r) |
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[35aab3] | 192 | { |
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[699567] | 193 | for (int i=IDELEMS(id)-1; i>=0; i--) |
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[35aab3] | 194 | { |
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| 195 | if (id->m[i] != NULL) |
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| 196 | { |
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[9aa29b] | 197 | p_Norm(id->m[i],r); |
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[35aab3] | 198 | } |
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| 199 | } |
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| 200 | } |
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| 201 | |
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| 202 | /*2 |
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[dd5534] | 203 | * ideal id = (id[i]), c any unit |
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[35aab3] | 204 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
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| 205 | */ |
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[f5c2d02] | 206 | void id_DelMultiples(ideal id, const ring r) |
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[35aab3] | 207 | { |
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[699567] | 208 | int i, j; |
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| 209 | int k = IDELEMS(id)-1; |
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| 210 | for (i=k; i>=0; i--) |
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[35aab3] | 211 | { |
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| 212 | if (id->m[i]!=NULL) |
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| 213 | { |
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[699567] | 214 | for (j=k; j>i; j--) |
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[35aab3] | 215 | { |
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[dd5534] | 216 | if (id->m[j]!=NULL) |
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[35aab3] | 217 | { |
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[dd5534] | 218 | #ifdef HAVE_RINGS |
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[f5c2d02] | 219 | if (rField_is_Ring(r)) |
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[dd5534] | 220 | { |
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| 221 | /* if id[j] = c*id[i] then delete id[j]. |
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| 222 | In the below cases of a ground field, we |
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| 223 | check whether id[i] = c*id[j] and, if so, |
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| 224 | delete id[j] for historical reasons (so |
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| 225 | that previous output does not change) */ |
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[f5c2d02] | 226 | if (p_ComparePolys(id->m[j], id->m[i],r)) p_Delete(&id->m[j],r); |
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[dd5534] | 227 | } |
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| 228 | else |
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| 229 | { |
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[f5c2d02] | 230 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
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[dd5534] | 231 | } |
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| 232 | #else |
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[f5c2d02] | 233 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
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[3d0808] | 234 | #endif |
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[35aab3] | 235 | } |
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| 236 | } |
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| 237 | } |
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| 238 | } |
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| 239 | } |
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| 240 | |
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| 241 | /*2 |
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| 242 | * ideal id = (id[i]) |
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| 243 | * if id[i] = id[j] then id[j] is deleted for j > i |
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| 244 | */ |
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[4a08e7] | 245 | void id_DelEquals(ideal id, const ring r) |
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[35aab3] | 246 | { |
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[7ac29f] | 247 | int i, j; |
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| 248 | int k = IDELEMS(id)-1; |
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| 249 | for (i=k; i>=0; i--) |
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[35aab3] | 250 | { |
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[7ac29f] | 251 | if (id->m[i]!=NULL) |
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[35aab3] | 252 | { |
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[7ac29f] | 253 | for (j=k; j>i; j--) |
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[35aab3] | 254 | { |
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[7ac29f] | 255 | if ((id->m[j]!=NULL) |
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[4a08e7] | 256 | && (p_EqualPolys(id->m[i], id->m[j],r))) |
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[7ac29f] | 257 | { |
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[4a08e7] | 258 | p_Delete(&id->m[j],r); |
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[7ac29f] | 259 | } |
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[35aab3] | 260 | } |
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| 261 | } |
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| 262 | } |
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| 263 | } |
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| 264 | |
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| 265 | // |
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[a8b44d] | 266 | // Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i |
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[35aab3] | 267 | // |
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[119853] | 268 | void id_DelLmEquals(ideal id, const ring r) |
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[35aab3] | 269 | { |
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[7ac29f] | 270 | int i, j; |
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| 271 | int k = IDELEMS(id)-1; |
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| 272 | for (i=k; i>=0; i--) |
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[35aab3] | 273 | { |
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[73df93] | 274 | if (id->m[i] != NULL) |
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[35aab3] | 275 | { |
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[7ac29f] | 276 | for (j=k; j>i; j--) |
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[35aab3] | 277 | { |
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[7ac29f] | 278 | if ((id->m[j] != NULL) |
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[119853] | 279 | && p_LmEqual(id->m[i], id->m[j],r) |
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[a8b44d] | 280 | #ifdef HAVE_RINGS |
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[c9c118] | 281 | && n_IsUnit(pGetCoeff(id->m[i]),r->cf) && n_IsUnit(pGetCoeff(id->m[j]),r->cf) |
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[a8b44d] | 282 | #endif |
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| 283 | ) |
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[35aab3] | 284 | { |
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[119853] | 285 | p_Delete(&id->m[j],r); |
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[35aab3] | 286 | } |
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| 287 | } |
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| 288 | } |
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| 289 | } |
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| 290 | } |
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| 291 | |
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[a8b44d] | 292 | // |
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| 293 | // delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., |
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| 294 | // delete id[i], if LT(i) == coeff*mon*LT(j) |
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| 295 | // |
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[3d0808] | 296 | void id_DelDiv(ideal id, const ring r) |
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[35aab3] | 297 | { |
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[7ac29f] | 298 | int i, j; |
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| 299 | int k = IDELEMS(id)-1; |
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| 300 | for (i=k; i>=0; i--) |
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[35aab3] | 301 | { |
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[73df93] | 302 | if (id->m[i] != NULL) |
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[35aab3] | 303 | { |
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[7ac29f] | 304 | for (j=k; j>i; j--) |
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[35aab3] | 305 | { |
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[7ac29f] | 306 | if (id->m[j]!=NULL) |
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[35aab3] | 307 | { |
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[a8b44d] | 308 | #ifdef HAVE_RINGS |
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[3d0808] | 309 | if (rField_is_Ring(r)) |
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[a8b44d] | 310 | { |
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[3d0808] | 311 | if (p_DivisibleByRingCase(id->m[i], id->m[j],r)) |
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[a8b44d] | 312 | { |
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[3d0808] | 313 | p_Delete(&id->m[j],r); |
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| 314 | } |
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| 315 | else if (p_DivisibleByRingCase(id->m[j], id->m[i],r)) |
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| 316 | { |
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| 317 | p_Delete(&id->m[i],r); |
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| 318 | break; |
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[a8b44d] | 319 | } |
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| 320 | } |
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| 321 | else |
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| 322 | { |
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| 323 | #endif |
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| 324 | /* the case of a ground field: */ |
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[3d0808] | 325 | if (p_DivisibleBy(id->m[i], id->m[j],r)) |
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[7ac29f] | 326 | { |
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[3d0808] | 327 | p_Delete(&id->m[j],r); |
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[7ac29f] | 328 | } |
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[3d0808] | 329 | else if (p_DivisibleBy(id->m[j], id->m[i],r)) |
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[7ac29f] | 330 | { |
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[3d0808] | 331 | p_Delete(&id->m[i],r); |
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[7ac29f] | 332 | break; |
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| 333 | } |
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[a8b44d] | 334 | #ifdef HAVE_RINGS |
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| 335 | } |
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[3d0808] | 336 | #endif |
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[35aab3] | 337 | } |
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| 338 | } |
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| 339 | } |
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| 340 | } |
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| 341 | } |
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| 342 | |
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| 343 | /*2 |
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| 344 | *test if the ideal has only constant polynomials |
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| 345 | */ |
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[2e7dee] | 346 | BOOLEAN id_IsConstant(ideal id, const ring r) |
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[35aab3] | 347 | { |
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| 348 | int k; |
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| 349 | for (k = IDELEMS(id)-1; k>=0; k--) |
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| 350 | { |
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[6f3273] | 351 | if (!p_IsConstantPoly(id->m[k],r)) |
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[35aab3] | 352 | return FALSE; |
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| 353 | } |
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| 354 | return TRUE; |
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| 355 | } |
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| 356 | |
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| 357 | /*2 |
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| 358 | * copy an ideal |
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| 359 | */ |
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[2e7dee] | 360 | #ifdef PDEBUG |
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| 361 | ideal id_DBCopy(ideal h1,const char *f,int l, const ring r) |
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| 362 | { |
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| 363 | int i; |
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| 364 | ideal h2; |
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[d523f3] | 365 | |
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[2e7dee] | 366 | id_DBTest(h1,PDEBUG,f,l,r); |
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| 367 | //#ifdef TEST |
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| 368 | if (h1 == NULL) |
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| 369 | { |
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| 370 | h2=idDBInit(1,1,f,l); |
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| 371 | } |
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| 372 | else |
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| 373 | //#endif |
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| 374 | { |
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| 375 | h2=idDBInit(IDELEMS(h1),h1->rank,f,l); |
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| 376 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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| 377 | h2->m[i] = p_Copy(h1->m[i],r); |
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| 378 | } |
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| 379 | return h2; |
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| 380 | } |
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| 381 | #else |
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| 382 | ideal id_Copy(ideal h1, const ring r) |
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[d523f3] | 383 | { |
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| 384 | int i; |
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| 385 | ideal h2; |
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| 386 | |
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| 387 | //#ifdef TEST |
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| 388 | if (h1 == NULL) |
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| 389 | { |
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| 390 | h2=idInit(1,1); |
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| 391 | } |
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| 392 | else |
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| 393 | //#endif |
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| 394 | { |
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| 395 | h2=idInit(IDELEMS(h1),h1->rank); |
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| 396 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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| 397 | h2->m[i] = p_Copy(h1->m[i],r); |
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| 398 | } |
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| 399 | return h2; |
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| 400 | } |
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[2e7dee] | 401 | #endif |
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[35aab3] | 402 | |
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| 403 | #ifdef PDEBUG |
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[91a72f] | 404 | void id_DBTest(ideal h1, int level, const char *f,const int l, const ring r) |
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[35aab3] | 405 | { |
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| 406 | int i; |
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| 407 | |
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| 408 | if (h1 != NULL) |
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| 409 | { |
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| 410 | // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix |
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| 411 | omCheckAddrSize(h1,sizeof(*h1)); |
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| 412 | omdebugAddrSize(h1->m,h1->ncols*h1->nrows*sizeof(poly)); |
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| 413 | /* to be able to test matrices: */ |
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| 414 | for (i=(h1->ncols*h1->nrows)-1; i>=0; i--) |
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[91a72f] | 415 | _p_Test(h1->m[i], r, level); |
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| 416 | int new_rk=id_RankFreeModule(h1,r); |
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[35aab3] | 417 | if(new_rk > h1->rank) |
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| 418 | { |
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| 419 | dReportError("wrong rank %d (should be %d) in %s:%d\n", |
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| 420 | h1->rank, new_rk, f,l); |
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| 421 | omPrintAddrInfo(stderr, h1, " for ideal"); |
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| 422 | h1->rank=new_rk; |
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| 423 | } |
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| 424 | } |
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| 425 | } |
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| 426 | #endif |
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| 427 | |
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| 428 | /*3 |
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| 429 | * for idSort: compare a and b revlex inclusive module comp. |
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| 430 | */ |
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[2e4757c] | 431 | static int p_Comp_RevLex(poly a, poly b,BOOLEAN nolex, const ring R) |
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[35aab3] | 432 | { |
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| 433 | if (b==NULL) return 1; |
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| 434 | if (a==NULL) return -1; |
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| 435 | |
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[3d0808] | 436 | if (nolex) |
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[2c872b] | 437 | { |
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[2e4757c] | 438 | int r=p_LmCmp(a,b,R); |
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[2c872b] | 439 | if (r!=0) return r; |
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[2e4757c] | 440 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
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| 441 | r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
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| 442 | n_Delete(&h, R->cf); |
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[2c872b] | 443 | return r; |
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| 444 | } |
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[2e4757c] | 445 | int l=rVar(R); |
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| 446 | while ((l>0) && (p_GetExp(a,l,R)==p_GetExp(b,l,R))) l--; |
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[35aab3] | 447 | if (l==0) |
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| 448 | { |
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[2e4757c] | 449 | if (p_GetComp(a,R)==p_GetComp(b,R)) |
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[2c872b] | 450 | { |
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[2e4757c] | 451 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
---|
| 452 | int r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
---|
| 453 | n_Delete(&h,R->cf); |
---|
[2c872b] | 454 | return r; |
---|
| 455 | } |
---|
[2e4757c] | 456 | if (p_GetComp(a,R)>p_GetComp(b,R)) return 1; |
---|
[35aab3] | 457 | } |
---|
[2e4757c] | 458 | else if (p_GetExp(a,l,R)>p_GetExp(b,l,R)) |
---|
[35aab3] | 459 | return 1; |
---|
| 460 | return -1; |
---|
| 461 | } |
---|
| 462 | |
---|
| 463 | /*2 |
---|
| 464 | *sorts the ideal w.r.t. the actual ringordering |
---|
| 465 | *uses lex-ordering when nolex = FALSE |
---|
| 466 | */ |
---|
[91a72f] | 467 | intvec *id_Sort(ideal id,BOOLEAN nolex, const ring r) |
---|
[35aab3] | 468 | { |
---|
| 469 | poly p,q; |
---|
| 470 | intvec * result = new intvec(IDELEMS(id)); |
---|
| 471 | int i, j, actpos=0, newpos, l; |
---|
| 472 | int diff, olddiff, lastcomp, newcomp; |
---|
| 473 | BOOLEAN notFound; |
---|
| 474 | |
---|
| 475 | for (i=0;i<IDELEMS(id);i++) |
---|
| 476 | { |
---|
| 477 | if (id->m[i]!=NULL) |
---|
| 478 | { |
---|
| 479 | notFound = TRUE; |
---|
| 480 | newpos = actpos / 2; |
---|
| 481 | diff = (actpos+1) / 2; |
---|
| 482 | diff = (diff+1) / 2; |
---|
[91a72f] | 483 | lastcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
---|
[35aab3] | 484 | if (lastcomp<0) |
---|
| 485 | { |
---|
| 486 | newpos -= diff; |
---|
| 487 | } |
---|
| 488 | else if (lastcomp>0) |
---|
| 489 | { |
---|
| 490 | newpos += diff; |
---|
| 491 | } |
---|
| 492 | else |
---|
| 493 | { |
---|
| 494 | notFound = FALSE; |
---|
| 495 | } |
---|
| 496 | //while ((newpos>=0) && (newpos<actpos) && (notFound)) |
---|
| 497 | while (notFound && (newpos>=0) && (newpos<actpos)) |
---|
| 498 | { |
---|
[91a72f] | 499 | newcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
---|
[35aab3] | 500 | olddiff = diff; |
---|
| 501 | if (diff>1) |
---|
| 502 | { |
---|
| 503 | diff = (diff+1) / 2; |
---|
| 504 | if ((newcomp==1) |
---|
| 505 | && (actpos-newpos>1) |
---|
| 506 | && (diff>1) |
---|
| 507 | && (newpos+diff>=actpos)) |
---|
| 508 | { |
---|
| 509 | diff = actpos-newpos-1; |
---|
| 510 | } |
---|
| 511 | else if ((newcomp==-1) |
---|
| 512 | && (diff>1) |
---|
| 513 | && (newpos<diff)) |
---|
| 514 | { |
---|
| 515 | diff = newpos; |
---|
| 516 | } |
---|
| 517 | } |
---|
| 518 | if (newcomp<0) |
---|
| 519 | { |
---|
| 520 | if ((olddiff==1) && (lastcomp>0)) |
---|
| 521 | notFound = FALSE; |
---|
| 522 | else |
---|
| 523 | newpos -= diff; |
---|
| 524 | } |
---|
| 525 | else if (newcomp>0) |
---|
| 526 | { |
---|
| 527 | if ((olddiff==1) && (lastcomp<0)) |
---|
| 528 | { |
---|
| 529 | notFound = FALSE; |
---|
| 530 | newpos++; |
---|
| 531 | } |
---|
| 532 | else |
---|
| 533 | { |
---|
| 534 | newpos += diff; |
---|
| 535 | } |
---|
| 536 | } |
---|
| 537 | else |
---|
| 538 | { |
---|
| 539 | notFound = FALSE; |
---|
| 540 | } |
---|
| 541 | lastcomp = newcomp; |
---|
| 542 | if (diff==0) notFound=FALSE; /*hs*/ |
---|
| 543 | } |
---|
| 544 | if (newpos<0) newpos = 0; |
---|
| 545 | if (newpos>actpos) newpos = actpos; |
---|
[91a72f] | 546 | while ((newpos<actpos) && (p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r)==0)) |
---|
[35aab3] | 547 | newpos++; |
---|
| 548 | for (j=actpos;j>newpos;j--) |
---|
| 549 | { |
---|
| 550 | (*result)[j] = (*result)[j-1]; |
---|
| 551 | } |
---|
| 552 | (*result)[newpos] = i; |
---|
| 553 | actpos++; |
---|
| 554 | } |
---|
| 555 | } |
---|
| 556 | for (j=0;j<actpos;j++) (*result)[j]++; |
---|
| 557 | return result; |
---|
| 558 | } |
---|
| 559 | |
---|
| 560 | /*2 |
---|
| 561 | * concat the lists h1 and h2 without zeros |
---|
| 562 | */ |
---|
[2f5936] | 563 | ideal id_SimpleAdd (ideal h1,ideal h2, const ring R) |
---|
[35aab3] | 564 | { |
---|
| 565 | int i,j,r,l; |
---|
| 566 | ideal result; |
---|
| 567 | |
---|
[2f5936] | 568 | if (h1==NULL) return id_Copy(h2,R); |
---|
| 569 | if (h2==NULL) return id_Copy(h1,R); |
---|
[35aab3] | 570 | j = IDELEMS(h1)-1; |
---|
| 571 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
| 572 | i = IDELEMS(h2)-1; |
---|
| 573 | while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
| 574 | r = si_max(h1->rank,h2->rank); |
---|
| 575 | if (i+j==(-2)) |
---|
| 576 | return idInit(1,r); |
---|
| 577 | else |
---|
| 578 | result=idInit(i+j+2,r); |
---|
| 579 | for (l=j; l>=0; l--) |
---|
| 580 | { |
---|
[2f5936] | 581 | result->m[l] = p_Copy(h1->m[l],R); |
---|
[35aab3] | 582 | } |
---|
| 583 | r = i+j+1; |
---|
| 584 | for (l=i; l>=0; l--, r--) |
---|
| 585 | { |
---|
[2f5936] | 586 | result->m[r] = p_Copy(h2->m[l],R); |
---|
[35aab3] | 587 | } |
---|
| 588 | return result; |
---|
| 589 | } |
---|
| 590 | |
---|
[e070895] | 591 | /*2 |
---|
[ded085] | 592 | * insert h2 into h1 (if h2 is not the zero polynomial) |
---|
| 593 | * return TRUE iff h2 was indeed inserted |
---|
[e070895] | 594 | */ |
---|
[ded085] | 595 | BOOLEAN idInsertPoly (ideal h1, poly h2) |
---|
[e070895] | 596 | { |
---|
[ded085] | 597 | if (h2==NULL) return FALSE; |
---|
[e070895] | 598 | int j = IDELEMS(h1)-1; |
---|
| 599 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
| 600 | j++; |
---|
| 601 | if (j==IDELEMS(h1)) |
---|
| 602 | { |
---|
| 603 | pEnlargeSet(&(h1->m),IDELEMS(h1),16); |
---|
| 604 | IDELEMS(h1)+=16; |
---|
| 605 | } |
---|
| 606 | h1->m[j]=h2; |
---|
[ded085] | 607 | return TRUE; |
---|
[e070895] | 608 | } |
---|
| 609 | |
---|
[1a68d1d] | 610 | /*2 |
---|
[2b3caae] | 611 | * insert h2 into h1 depending on the two boolean parameters: |
---|
| 612 | * - if zeroOk is true, then h2 will also be inserted when it is zero |
---|
| 613 | * - if duplicateOk is true, then h2 will also be inserted when it is |
---|
| 614 | * already present in h1 |
---|
[ded085] | 615 | * return TRUE iff h2 was indeed inserted |
---|
[1a68d1d] | 616 | */ |
---|
[2f5936] | 617 | BOOLEAN id_InsertPolyWithTests (ideal h1, const int validEntries, |
---|
| 618 | const poly h2, const bool zeroOk, const bool duplicateOk, const ring r) |
---|
[1a68d1d] | 619 | { |
---|
[2b3caae] | 620 | if ((!zeroOk) && (h2 == NULL)) return FALSE; |
---|
| 621 | if (!duplicateOk) |
---|
[1a68d1d] | 622 | { |
---|
[2b3caae] | 623 | bool h2FoundInH1 = false; |
---|
| 624 | int i = 0; |
---|
| 625 | while ((i < validEntries) && (!h2FoundInH1)) |
---|
| 626 | { |
---|
[2f5936] | 627 | h2FoundInH1 = p_EqualPolys(h1->m[i], h2,r); |
---|
[2b3caae] | 628 | i++; |
---|
| 629 | } |
---|
| 630 | if (h2FoundInH1) return FALSE; |
---|
[1a68d1d] | 631 | } |
---|
[2b3caae] | 632 | if (validEntries == IDELEMS(h1)) |
---|
| 633 | { |
---|
| 634 | pEnlargeSet(&(h1->m), IDELEMS(h1), 16); |
---|
| 635 | IDELEMS(h1) += 16; |
---|
| 636 | } |
---|
| 637 | h1->m[validEntries] = h2; |
---|
| 638 | return TRUE; |
---|
[1a68d1d] | 639 | } |
---|
| 640 | |
---|
[35aab3] | 641 | /*2 |
---|
| 642 | * h1 + h2 |
---|
| 643 | */ |
---|
[2f5936] | 644 | ideal id_Add (ideal h1,ideal h2, const ring r) |
---|
[35aab3] | 645 | { |
---|
[2f5936] | 646 | ideal result = id_SimpleAdd(h1,h2,r); |
---|
| 647 | id_Compactify(result,r); |
---|
[35c62a9] | 648 | return result; |
---|
[35aab3] | 649 | } |
---|
| 650 | |
---|
| 651 | /*2 |
---|
| 652 | * h1 * h2 |
---|
| 653 | */ |
---|
[a665eb] | 654 | ideal id_Mult (ideal h1,ideal h2, const ring r) |
---|
[35aab3] | 655 | { |
---|
| 656 | int i,j,k; |
---|
| 657 | ideal hh; |
---|
| 658 | |
---|
| 659 | j = IDELEMS(h1); |
---|
| 660 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
| 661 | i = IDELEMS(h2); |
---|
| 662 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
| 663 | j = j * i; |
---|
| 664 | if (j == 0) |
---|
| 665 | hh = idInit(1,1); |
---|
| 666 | else |
---|
| 667 | hh=idInit(j,1); |
---|
| 668 | if (h1->rank<h2->rank) |
---|
| 669 | hh->rank = h2->rank; |
---|
| 670 | else |
---|
| 671 | hh->rank = h1->rank; |
---|
| 672 | if (j==0) return hh; |
---|
| 673 | k = 0; |
---|
| 674 | for (i=0; i<IDELEMS(h1); i++) |
---|
| 675 | { |
---|
| 676 | if (h1->m[i] != NULL) |
---|
| 677 | { |
---|
| 678 | for (j=0; j<IDELEMS(h2); j++) |
---|
| 679 | { |
---|
| 680 | if (h2->m[j] != NULL) |
---|
| 681 | { |
---|
[a665eb] | 682 | hh->m[k] = pp_Mult_qq(h1->m[i],h2->m[j],r); |
---|
[35aab3] | 683 | k++; |
---|
| 684 | } |
---|
| 685 | } |
---|
| 686 | } |
---|
| 687 | } |
---|
| 688 | { |
---|
[a665eb] | 689 | id_Compactify(hh,r); |
---|
[10ea45f] | 690 | return hh; |
---|
[35aab3] | 691 | } |
---|
| 692 | } |
---|
| 693 | |
---|
| 694 | /*2 |
---|
| 695 | *returns true if h is the zero ideal |
---|
| 696 | */ |
---|
| 697 | BOOLEAN idIs0 (ideal h) |
---|
| 698 | { |
---|
| 699 | int i; |
---|
| 700 | |
---|
| 701 | if (h == NULL) return TRUE; |
---|
[9dd6270] | 702 | i = IDELEMS(h)-1; |
---|
| 703 | while ((i >= 0) && (h->m[i] == NULL)) |
---|
[35aab3] | 704 | { |
---|
| 705 | i--; |
---|
| 706 | } |
---|
[9dd6270] | 707 | if (i < 0) |
---|
[35aab3] | 708 | return TRUE; |
---|
| 709 | else |
---|
| 710 | return FALSE; |
---|
| 711 | } |
---|
| 712 | |
---|
| 713 | /*2 |
---|
| 714 | * return the maximal component number found in any polynomial in s |
---|
| 715 | */ |
---|
| 716 | long idRankFreeModule (ideal s, ring lmRing, ring tailRing) |
---|
| 717 | { |
---|
| 718 | if (s!=NULL) |
---|
| 719 | { |
---|
| 720 | int j=0; |
---|
| 721 | |
---|
| 722 | if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing)) |
---|
| 723 | { |
---|
| 724 | int l=IDELEMS(s); |
---|
| 725 | poly *p=s->m; |
---|
| 726 | int k; |
---|
| 727 | for (; l != 0; l--) |
---|
| 728 | { |
---|
| 729 | if (*p!=NULL) |
---|
| 730 | { |
---|
| 731 | pp_Test(*p, lmRing, tailRing); |
---|
| 732 | k = p_MaxComp(*p, lmRing, tailRing); |
---|
| 733 | if (k>j) j = k; |
---|
| 734 | } |
---|
| 735 | p++; |
---|
| 736 | } |
---|
| 737 | } |
---|
| 738 | return j; |
---|
| 739 | } |
---|
| 740 | return -1; |
---|
| 741 | } |
---|
| 742 | |
---|
| 743 | BOOLEAN idIsModule(ideal id, ring r) |
---|
| 744 | { |
---|
| 745 | if (id != NULL && rRing_has_Comp(r)) |
---|
| 746 | { |
---|
| 747 | int j, l = IDELEMS(id); |
---|
| 748 | for (j=0; j<l; j++) |
---|
| 749 | { |
---|
| 750 | if (id->m[j] != NULL && p_GetComp(id->m[j], r) > 0) return TRUE; |
---|
| 751 | } |
---|
| 752 | } |
---|
| 753 | return FALSE; |
---|
| 754 | } |
---|
| 755 | |
---|
| 756 | |
---|
| 757 | /*2 |
---|
| 758 | *returns true if id is homogenous with respect to the aktual weights |
---|
| 759 | */ |
---|
[a665eb] | 760 | BOOLEAN id_HomIdeal (ideal id, ideal Q, const ring r) |
---|
[35aab3] | 761 | { |
---|
| 762 | int i; |
---|
| 763 | BOOLEAN b; |
---|
| 764 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
---|
| 765 | i = 0; |
---|
| 766 | b = TRUE; |
---|
| 767 | while ((i < IDELEMS(id)) && b) |
---|
| 768 | { |
---|
[a665eb] | 769 | b = p_IsHomogeneous(id->m[i],r); |
---|
[35aab3] | 770 | i++; |
---|
| 771 | } |
---|
| 772 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
| 773 | { |
---|
| 774 | i=0; |
---|
| 775 | while ((i < IDELEMS(Q)) && b) |
---|
| 776 | { |
---|
[a665eb] | 777 | b = p_IsHomogeneous(Q->m[i],r); |
---|
[35aab3] | 778 | i++; |
---|
| 779 | } |
---|
| 780 | } |
---|
| 781 | return b; |
---|
| 782 | } |
---|
| 783 | |
---|
| 784 | /*2 |
---|
| 785 | *the minimal index of used variables - 1 |
---|
| 786 | */ |
---|
[a665eb] | 787 | int p_LowVar (poly p, const ring r) |
---|
[35aab3] | 788 | { |
---|
| 789 | int k,l,lex; |
---|
| 790 | |
---|
| 791 | if (p == NULL) return -1; |
---|
| 792 | |
---|
| 793 | k = 32000;/*a very large dummy value*/ |
---|
| 794 | while (p != NULL) |
---|
| 795 | { |
---|
| 796 | l = 1; |
---|
[a665eb] | 797 | lex = p_GetExp(p,l,r); |
---|
| 798 | while ((l < rVar(r)) && (lex == 0)) |
---|
[35aab3] | 799 | { |
---|
| 800 | l++; |
---|
[a665eb] | 801 | lex = p_GetExp(p,l,r); |
---|
[35aab3] | 802 | } |
---|
| 803 | l--; |
---|
| 804 | if (l < k) k = l; |
---|
| 805 | pIter(p); |
---|
| 806 | } |
---|
| 807 | return k; |
---|
| 808 | } |
---|
| 809 | |
---|
| 810 | /*3 |
---|
| 811 | *multiplies p with t (!cas) or (t-1) |
---|
| 812 | *the index of t is:1, so we have to shift all variables |
---|
| 813 | *p is NOT in the actual ring, it has no t |
---|
| 814 | */ |
---|
[a665eb] | 815 | static poly p_MultWithT (poly p,BOOLEAN cas, const ring r) |
---|
[35aab3] | 816 | { |
---|
| 817 | /*qp is the working pointer in p*/ |
---|
| 818 | /*result is the result, qresult is the working pointer*/ |
---|
| 819 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
---|
| 820 | poly result,qp,pp; |
---|
| 821 | poly qresult=NULL; |
---|
| 822 | poly qpp=NULL; |
---|
| 823 | int i,j,lex; |
---|
| 824 | number n; |
---|
| 825 | |
---|
| 826 | pp = NULL; |
---|
| 827 | result = NULL; |
---|
| 828 | qp = p; |
---|
| 829 | while (qp != NULL) |
---|
| 830 | { |
---|
| 831 | i = 0; |
---|
| 832 | if (result == NULL) |
---|
| 833 | {/*first monomial*/ |
---|
[a665eb] | 834 | result = p_Init(r); |
---|
[35aab3] | 835 | qresult = result; |
---|
| 836 | } |
---|
| 837 | else |
---|
| 838 | { |
---|
[a665eb] | 839 | qresult->next = p_Init(r); |
---|
[35aab3] | 840 | pIter(qresult); |
---|
| 841 | } |
---|
[a665eb] | 842 | for (j=rVar(r)-1; j>0; j--) |
---|
[35aab3] | 843 | { |
---|
[a665eb] | 844 | lex = p_GetExp(qp,j,r); |
---|
| 845 | p_SetExp(qresult,j+1,lex,r);/*copy all variables*/ |
---|
[35aab3] | 846 | } |
---|
[a665eb] | 847 | lex = p_GetComp(qp,r); |
---|
| 848 | p_SetComp(qresult,lex,r); |
---|
| 849 | n=n_Copy(pGetCoeff(qp),r->cf); |
---|
[35aab3] | 850 | pSetCoeff0(qresult,n); |
---|
| 851 | qresult->next = NULL; |
---|
[a665eb] | 852 | p_Setm(qresult,r); |
---|
[35aab3] | 853 | /*qresult is now qp brought into the actual ring*/ |
---|
| 854 | if (cas) |
---|
| 855 | { /*case: mult with t-1*/ |
---|
[a665eb] | 856 | p_SetExp(qresult,1,0,r); |
---|
| 857 | p_Setm(qresult,r); |
---|
[35aab3] | 858 | if (pp == NULL) |
---|
| 859 | { /*first monomial*/ |
---|
[a665eb] | 860 | pp = p_Copy(qresult,r); |
---|
[35aab3] | 861 | qpp = pp; |
---|
| 862 | } |
---|
| 863 | else |
---|
| 864 | { |
---|
[a665eb] | 865 | qpp->next = p_Copy(qresult,r); |
---|
[35aab3] | 866 | pIter(qpp); |
---|
| 867 | } |
---|
[a665eb] | 868 | pGetCoeff(qpp)=n_Neg(pGetCoeff(qpp),r->cf); |
---|
[35aab3] | 869 | /*now qpp contains -1*qp*/ |
---|
| 870 | } |
---|
[a665eb] | 871 | p_SetExp(qresult,1,1,r);/*this is mult. by t*/ |
---|
| 872 | p_Setm(qresult,r); |
---|
[35aab3] | 873 | pIter(qp); |
---|
| 874 | } |
---|
| 875 | /* |
---|
| 876 | *now p is processed: |
---|
| 877 | *result contains t*p |
---|
| 878 | * if cas: pp contains -1*p (in the new ring) |
---|
| 879 | */ |
---|
| 880 | if (cas) qresult->next = pp; |
---|
| 881 | /* else qresult->next = NULL;*/ |
---|
| 882 | return result; |
---|
| 883 | } |
---|
| 884 | |
---|
| 885 | /*2 |
---|
| 886 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
| 887 | */ |
---|
| 888 | void pShift (poly * p,int i) |
---|
| 889 | { |
---|
| 890 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
| 891 | int j = pMaxComp(*p),k = pMinComp(*p); |
---|
| 892 | |
---|
| 893 | if (j+i < 0) return ; |
---|
| 894 | while (qp1 != NULL) |
---|
| 895 | { |
---|
| 896 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
---|
| 897 | { |
---|
[959263] | 898 | pAddComp(qp1,i); |
---|
[35aab3] | 899 | pSetmComp(qp1); |
---|
| 900 | qp2 = qp1; |
---|
| 901 | pIter(qp1); |
---|
| 902 | } |
---|
| 903 | else |
---|
| 904 | { |
---|
| 905 | if (qp2 == *p) |
---|
| 906 | { |
---|
| 907 | pIter(*p); |
---|
[fb82895] | 908 | pLmDelete(&qp2); |
---|
[35aab3] | 909 | qp2 = *p; |
---|
| 910 | qp1 = *p; |
---|
| 911 | } |
---|
| 912 | else |
---|
| 913 | { |
---|
| 914 | qp2->next = qp1->next; |
---|
[fb82895] | 915 | if (qp1!=NULL) pLmDelete(&qp1); |
---|
[35aab3] | 916 | qp1 = qp2->next; |
---|
| 917 | } |
---|
| 918 | } |
---|
| 919 | } |
---|
| 920 | } |
---|
| 921 | |
---|
| 922 | /*2 |
---|
| 923 | *initialized a field with r numbers between beg and end for the |
---|
| 924 | *procedure idNextChoise |
---|
| 925 | */ |
---|
| 926 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
| 927 | { |
---|
| 928 | /*returns the first choise of r numbers between beg and end*/ |
---|
| 929 | int i; |
---|
| 930 | for (i=0; i<r; i++) |
---|
| 931 | { |
---|
| 932 | choise[i] = 0; |
---|
| 933 | } |
---|
| 934 | if (r <= end-beg+1) |
---|
| 935 | for (i=0; i<r; i++) |
---|
| 936 | { |
---|
| 937 | choise[i] = beg+i; |
---|
| 938 | } |
---|
| 939 | if (r > end-beg+1) |
---|
| 940 | *endch = TRUE; |
---|
| 941 | else |
---|
| 942 | *endch = FALSE; |
---|
| 943 | } |
---|
| 944 | |
---|
| 945 | /*2 |
---|
| 946 | *returns the next choise of r numbers between beg and end |
---|
| 947 | */ |
---|
| 948 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
| 949 | { |
---|
| 950 | int i = r-1,j; |
---|
| 951 | while ((i >= 0) && (choise[i] == end)) |
---|
| 952 | { |
---|
| 953 | i--; |
---|
| 954 | end--; |
---|
| 955 | } |
---|
| 956 | if (i == -1) |
---|
| 957 | *endch = TRUE; |
---|
| 958 | else |
---|
| 959 | { |
---|
| 960 | choise[i]++; |
---|
| 961 | for (j=i+1; j<r; j++) |
---|
| 962 | { |
---|
| 963 | choise[j] = choise[i]+j-i; |
---|
| 964 | } |
---|
| 965 | *endch = FALSE; |
---|
| 966 | } |
---|
| 967 | } |
---|
| 968 | |
---|
| 969 | /*2 |
---|
| 970 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
| 971 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
| 972 | * w.r.t. the algorithm of construction |
---|
| 973 | */ |
---|
| 974 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
| 975 | { |
---|
| 976 | int * localchoise,i,result=0; |
---|
| 977 | BOOLEAN b=FALSE; |
---|
| 978 | |
---|
| 979 | if (d<=1) return 1; |
---|
| 980 | localchoise=(int*)omAlloc((d-1)*sizeof(int)); |
---|
| 981 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
| 982 | while (!b) |
---|
| 983 | { |
---|
| 984 | result++; |
---|
| 985 | i = 0; |
---|
| 986 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
| 987 | if (i>=t) |
---|
| 988 | { |
---|
| 989 | i = t+1; |
---|
| 990 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
| 991 | if (i>=d) |
---|
[f71e8c5] | 992 | { |
---|
| 993 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
| 994 | return result; |
---|
[35aab3] | 995 | } |
---|
| 996 | } |
---|
[f71e8c5] | 997 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
[35aab3] | 998 | } |
---|
[f71e8c5] | 999 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
| 1000 | return 0; |
---|
[35aab3] | 1001 | } |
---|
| 1002 | |
---|
| 1003 | /*2 |
---|
[f71e8c5] | 1004 | *computes the binomial coefficient |
---|
[35aab3] | 1005 | */ |
---|
[f71e8c5] | 1006 | int binom (int n,int r) |
---|
| 1007 | { |
---|
| 1008 | int i,result; |
---|
[35aab3] | 1009 | |
---|
[f71e8c5] | 1010 | if (r==0) return 1; |
---|
| 1011 | if (n-r<r) return binom(n,n-r); |
---|
| 1012 | result = n-r+1; |
---|
| 1013 | for (i=2;i<=r;i++) |
---|
[35aab3] | 1014 | { |
---|
[f71e8c5] | 1015 | result *= n-r+i; |
---|
| 1016 | if (result<0) |
---|
[35aab3] | 1017 | { |
---|
[f71e8c5] | 1018 | WarnS("overflow in binomials"); |
---|
| 1019 | return 0; |
---|
[35aab3] | 1020 | } |
---|
[f71e8c5] | 1021 | result /= i; |
---|
[35aab3] | 1022 | } |
---|
[f71e8c5] | 1023 | return result; |
---|
[35aab3] | 1024 | } |
---|
[f71e8c5] | 1025 | |
---|
[35aab3] | 1026 | /*2 |
---|
[f71e8c5] | 1027 | *the free module of rank i |
---|
[35aab3] | 1028 | */ |
---|
[f71e8c5] | 1029 | ideal idFreeModule (int i) |
---|
[35aab3] | 1030 | { |
---|
[f71e8c5] | 1031 | int j; |
---|
| 1032 | ideal h; |
---|
| 1033 | |
---|
| 1034 | h=idInit(i,i); |
---|
| 1035 | for (j=0; j<i; j++) |
---|
[35aab3] | 1036 | { |
---|
[2f5936] | 1037 | h->m[j] = p_One(r); |
---|
[f71e8c5] | 1038 | pSetComp(h->m[j],j+1); |
---|
| 1039 | pSetmComp(h->m[j]); |
---|
[35aab3] | 1040 | } |
---|
[f71e8c5] | 1041 | return h; |
---|
| 1042 | } |
---|
[35aab3] | 1043 | |
---|
[f71e8c5] | 1044 | ideal idSectWithElim (ideal h1,ideal h2) |
---|
| 1045 | // does not destroy h1,h2 |
---|
| 1046 | { |
---|
| 1047 | if (TEST_OPT_PROT) PrintS("intersect by elimination method\n"); |
---|
| 1048 | assume(!idIs0(h1)); |
---|
| 1049 | assume(!idIs0(h2)); |
---|
| 1050 | assume(IDELEMS(h1)<=IDELEMS(h2)); |
---|
| 1051 | assume(idRankFreeModule(h1)==0); |
---|
| 1052 | assume(idRankFreeModule(h2)==0); |
---|
| 1053 | // add a new variable: |
---|
| 1054 | int j; |
---|
| 1055 | ring origRing=currRing; |
---|
| 1056 | ring r=rCopy0(origRing); |
---|
| 1057 | r->N++; |
---|
| 1058 | r->block0[0]=1; |
---|
| 1059 | r->block1[0]= r->N; |
---|
| 1060 | omFree(r->order); |
---|
| 1061 | r->order=(int*)omAlloc0(3*sizeof(int*)); |
---|
| 1062 | r->order[0]=ringorder_dp; |
---|
| 1063 | r->order[1]=ringorder_C; |
---|
| 1064 | char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr)); |
---|
| 1065 | for (j=0;j<r->N-1;j++) names[j]=r->names[j]; |
---|
| 1066 | names[r->N-1]=omStrDup("@"); |
---|
| 1067 | omFree(r->names); |
---|
| 1068 | r->names=names; |
---|
| 1069 | rComplete(r,TRUE); |
---|
| 1070 | // fetch h1, h2 |
---|
| 1071 | ideal h; |
---|
| 1072 | h1=idrCopyR(h1,origRing,r); |
---|
| 1073 | h2=idrCopyR(h2,origRing,r); |
---|
| 1074 | // switch to temp. ring r |
---|
| 1075 | rChangeCurrRing(r); |
---|
| 1076 | // create 1-t, t |
---|
[2f5936] | 1077 | poly omt=p_One(r); |
---|
[f71e8c5] | 1078 | pSetExp(omt,r->N,1); |
---|
| 1079 | poly t=pCopy(omt); |
---|
| 1080 | pSetm(omt); |
---|
| 1081 | omt=pNeg(omt); |
---|
[2f5936] | 1082 | omt=pAdd(omt,p_One(r)); |
---|
[f71e8c5] | 1083 | // compute (1-t)*h1 |
---|
| 1084 | h1=(ideal)mpMultP((matrix)h1,omt); |
---|
| 1085 | // compute t*h2 |
---|
| 1086 | h2=(ideal)mpMultP((matrix)h2,pCopy(t)); |
---|
| 1087 | // (1-t)h1 + t*h2 |
---|
| 1088 | h=idInit(IDELEMS(h1)+IDELEMS(h2),1); |
---|
| 1089 | int l; |
---|
| 1090 | for (l=IDELEMS(h1)-1; l>=0; l--) |
---|
[35aab3] | 1091 | { |
---|
[f71e8c5] | 1092 | h->m[l] = h1->m[l]; h1->m[l]=NULL; |
---|
[35aab3] | 1093 | } |
---|
[f71e8c5] | 1094 | j=IDELEMS(h1); |
---|
| 1095 | for (l=IDELEMS(h2)-1; l>=0; l--) |
---|
[35aab3] | 1096 | { |
---|
[f71e8c5] | 1097 | h->m[l+j] = h2->m[l]; h2->m[l]=NULL; |
---|
[35aab3] | 1098 | } |
---|
[f71e8c5] | 1099 | idDelete(&h1); |
---|
| 1100 | idDelete(&h2); |
---|
| 1101 | // eliminate t: |
---|
| 1102 | |
---|
| 1103 | ideal res=idElimination(h,t); |
---|
[3d0808] | 1104 | // cleanup |
---|
[f71e8c5] | 1105 | idDelete(&h); |
---|
| 1106 | res=idrMoveR(res,r,origRing); |
---|
| 1107 | rChangeCurrRing(origRing); |
---|
| 1108 | rKill(r); |
---|
| 1109 | return res; |
---|
[35aab3] | 1110 | } |
---|
| 1111 | |
---|
| 1112 | /*2 |
---|
| 1113 | *computes recursively all monomials of a certain degree |
---|
| 1114 | *in every step the actvar-th entry in the exponential |
---|
| 1115 | *vector is incremented and the other variables are |
---|
| 1116 | *computed by recursive calls of makemonoms |
---|
| 1117 | *if the last variable is reached, the difference to the |
---|
| 1118 | *degree is computed directly |
---|
| 1119 | *vars is the number variables |
---|
| 1120 | *actvar is the actual variable to handle |
---|
| 1121 | *deg is the degree of the monomials to compute |
---|
| 1122 | *monomdeg is the actual degree of the monomial in consideration |
---|
| 1123 | */ |
---|
| 1124 | static void makemonoms(int vars,int actvar,int deg,int monomdeg) |
---|
| 1125 | { |
---|
| 1126 | poly p; |
---|
| 1127 | int i=0; |
---|
| 1128 | |
---|
| 1129 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
| 1130 | { |
---|
[2f5936] | 1131 | idpower[idpowerpoint] = p_One(r); |
---|
[35aab3] | 1132 | monomdeg = 0; |
---|
| 1133 | } |
---|
| 1134 | while (i<=deg) |
---|
| 1135 | { |
---|
| 1136 | if (deg == monomdeg) |
---|
| 1137 | { |
---|
| 1138 | pSetm(idpower[idpowerpoint]); |
---|
| 1139 | idpowerpoint++; |
---|
| 1140 | return; |
---|
| 1141 | } |
---|
| 1142 | if (actvar == vars) |
---|
| 1143 | { |
---|
| 1144 | pSetExp(idpower[idpowerpoint],actvar,deg-monomdeg); |
---|
| 1145 | pSetm(idpower[idpowerpoint]); |
---|
| 1146 | pTest(idpower[idpowerpoint]); |
---|
| 1147 | idpowerpoint++; |
---|
| 1148 | return; |
---|
| 1149 | } |
---|
| 1150 | else |
---|
| 1151 | { |
---|
| 1152 | p = pCopy(idpower[idpowerpoint]); |
---|
| 1153 | makemonoms(vars,actvar+1,deg,monomdeg); |
---|
| 1154 | idpower[idpowerpoint] = p; |
---|
| 1155 | } |
---|
| 1156 | monomdeg++; |
---|
| 1157 | pSetExp(idpower[idpowerpoint],actvar,pGetExp(idpower[idpowerpoint],actvar)+1); |
---|
| 1158 | pSetm(idpower[idpowerpoint]); |
---|
| 1159 | pTest(idpower[idpowerpoint]); |
---|
| 1160 | i++; |
---|
| 1161 | } |
---|
| 1162 | } |
---|
| 1163 | |
---|
| 1164 | /*2 |
---|
| 1165 | *returns the deg-th power of the maximal ideal of 0 |
---|
| 1166 | */ |
---|
[a665eb] | 1167 | ideal id_MaxIdeal(int deg, const ring r) |
---|
[35aab3] | 1168 | { |
---|
| 1169 | if (deg < 0) |
---|
| 1170 | { |
---|
| 1171 | WarnS("maxideal: power must be non-negative"); |
---|
| 1172 | } |
---|
| 1173 | if (deg < 1) |
---|
| 1174 | { |
---|
| 1175 | ideal I=idInit(1,1); |
---|
[2f5936] | 1176 | I->m[0]=p_One(r); |
---|
[35aab3] | 1177 | return I; |
---|
| 1178 | } |
---|
| 1179 | if (deg == 1) |
---|
| 1180 | { |
---|
[a665eb] | 1181 | return idMaxIdeal(r); |
---|
[35aab3] | 1182 | } |
---|
| 1183 | |
---|
[a665eb] | 1184 | int vars = rVar(r); |
---|
[35aab3] | 1185 | int i = binom(vars+deg-1,deg); |
---|
| 1186 | if (i<=0) return idInit(1,1); |
---|
| 1187 | ideal id=idInit(i,1); |
---|
| 1188 | idpower = id->m; |
---|
| 1189 | idpowerpoint = 0; |
---|
| 1190 | makemonoms(vars,1,deg,0); |
---|
| 1191 | idpower = NULL; |
---|
| 1192 | idpowerpoint = 0; |
---|
| 1193 | return id; |
---|
| 1194 | } |
---|
| 1195 | |
---|
| 1196 | /*2 |
---|
| 1197 | *computes recursively all generators of a certain degree |
---|
| 1198 | *of the ideal "givenideal" |
---|
| 1199 | *elms is the number elements in the given ideal |
---|
| 1200 | *actelm is the actual element to handle |
---|
| 1201 | *deg is the degree of the power to compute |
---|
| 1202 | *gendeg is the actual degree of the generator in consideration |
---|
| 1203 | */ |
---|
| 1204 | static void makepotence(int elms,int actelm,int deg,int gendeg) |
---|
| 1205 | { |
---|
| 1206 | poly p; |
---|
| 1207 | int i=0; |
---|
| 1208 | |
---|
| 1209 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
| 1210 | { |
---|
[2f5936] | 1211 | idpower[idpowerpoint] = p_One(r); |
---|
[35aab3] | 1212 | gendeg = 0; |
---|
| 1213 | } |
---|
| 1214 | while (i<=deg) |
---|
| 1215 | { |
---|
| 1216 | if (deg == gendeg) |
---|
| 1217 | { |
---|
| 1218 | idpowerpoint++; |
---|
| 1219 | return; |
---|
| 1220 | } |
---|
| 1221 | if (actelm == elms) |
---|
| 1222 | { |
---|
| 1223 | p=pPower(pCopy(givenideal[actelm-1]),deg-gendeg); |
---|
| 1224 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],p); |
---|
| 1225 | idpowerpoint++; |
---|
| 1226 | return; |
---|
| 1227 | } |
---|
| 1228 | else |
---|
| 1229 | { |
---|
| 1230 | p = pCopy(idpower[idpowerpoint]); |
---|
| 1231 | makepotence(elms,actelm+1,deg,gendeg); |
---|
| 1232 | idpower[idpowerpoint] = p; |
---|
| 1233 | } |
---|
| 1234 | gendeg++; |
---|
| 1235 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],pCopy(givenideal[actelm-1])); |
---|
| 1236 | i++; |
---|
| 1237 | } |
---|
| 1238 | } |
---|
| 1239 | |
---|
| 1240 | /*2 |
---|
| 1241 | *returns the deg-th power of the ideal gid |
---|
| 1242 | */ |
---|
| 1243 | //ideal idPower(ideal gid,int deg) |
---|
| 1244 | //{ |
---|
| 1245 | // int i; |
---|
| 1246 | // ideal id; |
---|
| 1247 | // |
---|
| 1248 | // if (deg < 1) deg = 1; |
---|
| 1249 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
| 1250 | // id=idInit(i,1); |
---|
| 1251 | // idpower = id->m; |
---|
| 1252 | // givenideal = gid->m; |
---|
| 1253 | // idpowerpoint = 0; |
---|
| 1254 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
| 1255 | // idpower = NULL; |
---|
| 1256 | // givenideal = NULL; |
---|
| 1257 | // idpowerpoint = 0; |
---|
| 1258 | // return id; |
---|
| 1259 | //} |
---|
| 1260 | static void idNextPotence(ideal given, ideal result, |
---|
| 1261 | int begin, int end, int deg, int restdeg, poly ap) |
---|
| 1262 | { |
---|
| 1263 | poly p; |
---|
| 1264 | int i; |
---|
| 1265 | |
---|
| 1266 | p = pPower(pCopy(given->m[begin]),restdeg); |
---|
| 1267 | i = result->nrows; |
---|
| 1268 | result->m[i] = pMult(pCopy(ap),p); |
---|
| 1269 | //PrintS("."); |
---|
| 1270 | (result->nrows)++; |
---|
| 1271 | if (result->nrows >= IDELEMS(result)) |
---|
| 1272 | { |
---|
| 1273 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
| 1274 | IDELEMS(result) += 16; |
---|
| 1275 | } |
---|
| 1276 | if (begin == end) return; |
---|
| 1277 | for (i=restdeg-1;i>0;i--) |
---|
| 1278 | { |
---|
| 1279 | p = pPower(pCopy(given->m[begin]),i); |
---|
| 1280 | p = pMult(pCopy(ap),p); |
---|
| 1281 | idNextPotence(given, result, begin+1, end, deg, restdeg-i, p); |
---|
| 1282 | pDelete(&p); |
---|
| 1283 | } |
---|
| 1284 | idNextPotence(given, result, begin+1, end, deg, restdeg, ap); |
---|
| 1285 | } |
---|
| 1286 | |
---|
[2f5936] | 1287 | ideal id_Power(ideal given,int exp, const ring r) |
---|
[35aab3] | 1288 | { |
---|
| 1289 | ideal result,temp; |
---|
| 1290 | poly p1; |
---|
| 1291 | int i; |
---|
| 1292 | |
---|
| 1293 | if (idIs0(given)) return idInit(1,1); |
---|
[2f5936] | 1294 | temp = id_Copy(given,r); |
---|
[35aab3] | 1295 | idSkipZeroes(temp); |
---|
| 1296 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
| 1297 | result = idInit(i,1); |
---|
| 1298 | result->nrows = 0; |
---|
| 1299 | //Print("ideal contains %d elements\n",i); |
---|
[2f5936] | 1300 | p1=p_One(r); |
---|
[35aab3] | 1301 | idNextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1); |
---|
[2f5936] | 1302 | p_Delete(&p1,r); |
---|
| 1303 | id_Delete(&temp,r); |
---|
[35aab3] | 1304 | result->nrows = 1; |
---|
[2f5936] | 1305 | id_DelEquals(result,r); |
---|
[ff2fd1] | 1306 | idSkipZeroes(result); |
---|
[35aab3] | 1307 | return result; |
---|
| 1308 | } |
---|
| 1309 | |
---|
[0a64b14] | 1310 | /*2 |
---|
| 1311 | * compute the which-th ar-minor of the matrix a |
---|
| 1312 | */ |
---|
| 1313 | poly idMinor(matrix a, int ar, unsigned long which, ideal R) |
---|
| 1314 | { |
---|
| 1315 | int i,j,k,size; |
---|
| 1316 | unsigned long curr; |
---|
| 1317 | int *rowchoise,*colchoise; |
---|
| 1318 | BOOLEAN rowch,colch; |
---|
| 1319 | ideal result; |
---|
| 1320 | matrix tmp; |
---|
| 1321 | poly p,q; |
---|
| 1322 | |
---|
| 1323 | i = binom(a->rows(),ar); |
---|
| 1324 | j = binom(a->cols(),ar); |
---|
| 1325 | |
---|
| 1326 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1327 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1328 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
| 1329 | else size=i*j; |
---|
| 1330 | result=idInit(size,1); |
---|
| 1331 | tmp=mpNew(ar,ar); |
---|
| 1332 | k = 0; /* the index in result*/ |
---|
| 1333 | curr = 0; /* index of current minor */ |
---|
| 1334 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
| 1335 | while (!rowch) |
---|
| 1336 | { |
---|
| 1337 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
| 1338 | while (!colch) |
---|
| 1339 | { |
---|
| 1340 | if (curr == which) |
---|
| 1341 | { |
---|
| 1342 | for (i=1; i<=ar; i++) |
---|
| 1343 | { |
---|
| 1344 | for (j=1; j<=ar; j++) |
---|
| 1345 | { |
---|
| 1346 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
| 1347 | } |
---|
| 1348 | } |
---|
| 1349 | p = mpDetBareiss(tmp); |
---|
| 1350 | if (p!=NULL) |
---|
| 1351 | { |
---|
| 1352 | if (R!=NULL) |
---|
| 1353 | { |
---|
| 1354 | q = p; |
---|
| 1355 | p = kNF(R,currQuotient,q); |
---|
| 1356 | pDelete(&q); |
---|
| 1357 | } |
---|
| 1358 | /*delete the matrix tmp*/ |
---|
| 1359 | for (i=1; i<=ar; i++) |
---|
| 1360 | { |
---|
| 1361 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
| 1362 | } |
---|
| 1363 | idDelete((ideal*)&tmp); |
---|
| 1364 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
| 1365 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
| 1366 | return (p); |
---|
| 1367 | } |
---|
| 1368 | } |
---|
| 1369 | curr++; |
---|
| 1370 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
| 1371 | } |
---|
| 1372 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
| 1373 | } |
---|
| 1374 | return (poly) 1; |
---|
| 1375 | } |
---|
| 1376 | |
---|
[35aab3] | 1377 | #ifdef WITH_OLD_MINOR |
---|
| 1378 | /*2 |
---|
| 1379 | * compute all ar-minors of the matrix a |
---|
| 1380 | */ |
---|
| 1381 | ideal idMinors(matrix a, int ar, ideal R) |
---|
| 1382 | { |
---|
| 1383 | int i,j,k,size; |
---|
| 1384 | int *rowchoise,*colchoise; |
---|
| 1385 | BOOLEAN rowch,colch; |
---|
| 1386 | ideal result; |
---|
| 1387 | matrix tmp; |
---|
| 1388 | poly p,q; |
---|
| 1389 | |
---|
| 1390 | i = binom(a->rows(),ar); |
---|
| 1391 | j = binom(a->cols(),ar); |
---|
| 1392 | |
---|
| 1393 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1394 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1395 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
| 1396 | else size=i*j; |
---|
| 1397 | result=idInit(size,1); |
---|
| 1398 | tmp=mpNew(ar,ar); |
---|
| 1399 | k = 0; /* the index in result*/ |
---|
| 1400 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
| 1401 | while (!rowch) |
---|
| 1402 | { |
---|
| 1403 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
| 1404 | while (!colch) |
---|
| 1405 | { |
---|
| 1406 | for (i=1; i<=ar; i++) |
---|
| 1407 | { |
---|
| 1408 | for (j=1; j<=ar; j++) |
---|
| 1409 | { |
---|
| 1410 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
| 1411 | } |
---|
| 1412 | } |
---|
| 1413 | p = mpDetBareiss(tmp); |
---|
| 1414 | if (p!=NULL) |
---|
| 1415 | { |
---|
| 1416 | if (R!=NULL) |
---|
| 1417 | { |
---|
| 1418 | q = p; |
---|
| 1419 | p = kNF(R,currQuotient,q); |
---|
| 1420 | pDelete(&q); |
---|
| 1421 | } |
---|
| 1422 | if (p!=NULL) |
---|
| 1423 | { |
---|
| 1424 | if (k>=size) |
---|
| 1425 | { |
---|
| 1426 | pEnlargeSet(&result->m,size,32); |
---|
| 1427 | size += 32; |
---|
| 1428 | } |
---|
| 1429 | result->m[k] = p; |
---|
| 1430 | k++; |
---|
| 1431 | } |
---|
| 1432 | } |
---|
| 1433 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
| 1434 | } |
---|
| 1435 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
| 1436 | } |
---|
| 1437 | /*delete the matrix tmp*/ |
---|
| 1438 | for (i=1; i<=ar; i++) |
---|
| 1439 | { |
---|
| 1440 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
| 1441 | } |
---|
| 1442 | idDelete((ideal*)&tmp); |
---|
| 1443 | if (k==0) |
---|
| 1444 | { |
---|
| 1445 | k=1; |
---|
| 1446 | result->m[0]=NULL; |
---|
| 1447 | } |
---|
| 1448 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
| 1449 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
| 1450 | pEnlargeSet(&result->m,size,k-size); |
---|
| 1451 | IDELEMS(result) = k; |
---|
| 1452 | return (result); |
---|
| 1453 | } |
---|
| 1454 | #else |
---|
| 1455 | /*2 |
---|
| 1456 | * compute all ar-minors of the matrix a |
---|
| 1457 | * the caller of mpRecMin |
---|
| 1458 | * the elements of the result are not in R (if R!=NULL) |
---|
| 1459 | */ |
---|
| 1460 | ideal idMinors(matrix a, int ar, ideal R) |
---|
| 1461 | { |
---|
| 1462 | int elems=0; |
---|
| 1463 | int r=a->nrows,c=a->ncols; |
---|
| 1464 | int i; |
---|
| 1465 | matrix b; |
---|
| 1466 | ideal result,h; |
---|
| 1467 | ring origR; |
---|
[ab453da] | 1468 | ring tmpR; |
---|
[0b5e3d] | 1469 | long bound; |
---|
[35aab3] | 1470 | |
---|
| 1471 | if((ar<=0) || (ar>r) || (ar>c)) |
---|
| 1472 | { |
---|
| 1473 | Werror("%d-th minor, matrix is %dx%d",ar,r,c); |
---|
| 1474 | return NULL; |
---|
| 1475 | } |
---|
| 1476 | h = idMatrix2Module(mpCopy(a)); |
---|
| 1477 | bound = smExpBound(h,c,r,ar); |
---|
| 1478 | idDelete(&h); |
---|
[ab453da] | 1479 | tmpR=smRingChange(&origR,bound); |
---|
[35aab3] | 1480 | b = mpNew(r,c); |
---|
| 1481 | for (i=r*c-1;i>=0;i--) |
---|
| 1482 | { |
---|
| 1483 | if (a->m[i]) |
---|
| 1484 | b->m[i] = prCopyR(a->m[i],origR); |
---|
| 1485 | } |
---|
[7012d0] | 1486 | if (R!=NULL) |
---|
| 1487 | { |
---|
| 1488 | R = idrCopyR(R,origR); |
---|
[3060a7] | 1489 | //if (ar>1) // otherwise done in mpMinorToResult |
---|
| 1490 | //{ |
---|
| 1491 | // matrix bb=(matrix)kNF(R,currQuotient,(ideal)b); |
---|
| 1492 | // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols; |
---|
| 1493 | // idDelete((ideal*)&b); b=bb; |
---|
| 1494 | //} |
---|
[7012d0] | 1495 | } |
---|
[35aab3] | 1496 | result=idInit(32,1); |
---|
| 1497 | if(ar>1) mpRecMin(ar-1,result,elems,b,r,c,NULL,R); |
---|
| 1498 | else mpMinorToResult(result,elems,b,r,c,R); |
---|
| 1499 | idDelete((ideal *)&b); |
---|
[7012d0] | 1500 | if (R!=NULL) idDelete(&R); |
---|
[35aab3] | 1501 | idSkipZeroes(result); |
---|
| 1502 | rChangeCurrRing(origR); |
---|
[ab453da] | 1503 | result = idrMoveR(result,tmpR); |
---|
| 1504 | smKillModifiedRing(tmpR); |
---|
[35aab3] | 1505 | idTest(result); |
---|
| 1506 | return result; |
---|
| 1507 | } |
---|
| 1508 | #endif |
---|
| 1509 | |
---|
| 1510 | /*2 |
---|
| 1511 | *skips all zeroes and double elements, searches also for units |
---|
| 1512 | */ |
---|
[2f5936] | 1513 | void id_Compactify(ideal id, const ring r) |
---|
[35aab3] | 1514 | { |
---|
| 1515 | int i,j; |
---|
| 1516 | BOOLEAN b=FALSE; |
---|
| 1517 | |
---|
| 1518 | i = IDELEMS(id)-1; |
---|
| 1519 | while ((! b) && (i>=0)) |
---|
| 1520 | { |
---|
[2f5936] | 1521 | b=p_IsUnit(id->m[i],r); |
---|
[35aab3] | 1522 | i--; |
---|
| 1523 | } |
---|
| 1524 | if (b) |
---|
| 1525 | { |
---|
[2f5936] | 1526 | for(i=IDELEMS(id)-1;i>=0;i--) p_Delete(&id->m[i],r); |
---|
| 1527 | id->m[0]=p_One(r); |
---|
[35aab3] | 1528 | } |
---|
| 1529 | else |
---|
| 1530 | { |
---|
[2f5936] | 1531 | id_DelMultiples(id,r); |
---|
[35aab3] | 1532 | } |
---|
[962de7] | 1533 | idSkipZeroes(id); |
---|
[35aab3] | 1534 | } |
---|
| 1535 | |
---|
| 1536 | /*2 |
---|
| 1537 | *returns TRUE if id1 is a submodule of id2 |
---|
| 1538 | */ |
---|
| 1539 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
| 1540 | { |
---|
| 1541 | int i; |
---|
| 1542 | poly p; |
---|
| 1543 | |
---|
| 1544 | if (idIs0(id1)) return TRUE; |
---|
| 1545 | for (i=0;i<IDELEMS(id1);i++) |
---|
| 1546 | { |
---|
| 1547 | if (id1->m[i] != NULL) |
---|
| 1548 | { |
---|
| 1549 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
| 1550 | if (p != NULL) |
---|
| 1551 | { |
---|
| 1552 | pDelete(&p); |
---|
| 1553 | return FALSE; |
---|
| 1554 | } |
---|
| 1555 | } |
---|
| 1556 | } |
---|
| 1557 | return TRUE; |
---|
| 1558 | } |
---|
| 1559 | |
---|
| 1560 | /*2 |
---|
| 1561 | * returns the ideals of initial terms |
---|
| 1562 | */ |
---|
| 1563 | ideal idHead(ideal h) |
---|
| 1564 | { |
---|
| 1565 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
| 1566 | int i; |
---|
| 1567 | |
---|
| 1568 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
| 1569 | { |
---|
| 1570 | if (h->m[i]!=NULL) m->m[i]=pHead(h->m[i]); |
---|
| 1571 | } |
---|
| 1572 | return m; |
---|
| 1573 | } |
---|
| 1574 | |
---|
| 1575 | ideal idHomogen(ideal h, int varnum) |
---|
| 1576 | { |
---|
| 1577 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
| 1578 | int i; |
---|
| 1579 | |
---|
| 1580 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
| 1581 | { |
---|
| 1582 | m->m[i]=pHomogen(h->m[i],varnum); |
---|
| 1583 | } |
---|
| 1584 | return m; |
---|
| 1585 | } |
---|
| 1586 | |
---|
| 1587 | /*------------------type conversions----------------*/ |
---|
| 1588 | ideal idVec2Ideal(poly vec) |
---|
| 1589 | { |
---|
| 1590 | ideal result=idInit(1,1); |
---|
| 1591 | omFree((ADDRESS)result->m); |
---|
| 1592 | result->m=NULL; // remove later |
---|
| 1593 | pVec2Polys(vec, &(result->m), &(IDELEMS(result))); |
---|
| 1594 | return result; |
---|
| 1595 | } |
---|
| 1596 | |
---|
[ca3e7b] | 1597 | #define NEW_STUFF |
---|
[35aab3] | 1598 | #ifndef NEW_STUFF |
---|
| 1599 | // converts mat to module, destroys mat |
---|
| 1600 | ideal idMatrix2Module(matrix mat) |
---|
| 1601 | { |
---|
| 1602 | int mc=MATCOLS(mat); |
---|
| 1603 | int mr=MATROWS(mat); |
---|
| 1604 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
| 1605 | int i,j; |
---|
| 1606 | poly h; |
---|
| 1607 | |
---|
| 1608 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
| 1609 | { |
---|
| 1610 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
| 1611 | { |
---|
| 1612 | h = MATELEM(mat,i,j+1); |
---|
| 1613 | if (h!=NULL) |
---|
| 1614 | { |
---|
| 1615 | MATELEM(mat,i,j+1)=NULL; |
---|
| 1616 | pSetCompP(h,i); |
---|
| 1617 | result->m[j] = pAdd(result->m[j],h); |
---|
| 1618 | } |
---|
| 1619 | } |
---|
| 1620 | } |
---|
| 1621 | // obachman: need to clean this up |
---|
| 1622 | idDelete((ideal*) &mat); |
---|
| 1623 | return result; |
---|
| 1624 | } |
---|
| 1625 | #else |
---|
| 1626 | |
---|
[2ad10e9] | 1627 | #include "sbuckets.h" |
---|
[35aab3] | 1628 | |
---|
| 1629 | // converts mat to module, destroys mat |
---|
| 1630 | ideal idMatrix2Module(matrix mat) |
---|
| 1631 | { |
---|
| 1632 | int mc=MATCOLS(mat); |
---|
| 1633 | int mr=MATROWS(mat); |
---|
| 1634 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
| 1635 | int i,j, l; |
---|
| 1636 | poly h; |
---|
| 1637 | poly p; |
---|
[cbeafc2] | 1638 | sBucket_pt bucket = sBucketCreate(currRing); |
---|
[35aab3] | 1639 | |
---|
| 1640 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
| 1641 | { |
---|
| 1642 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
| 1643 | { |
---|
| 1644 | h = MATELEM(mat,i,j+1); |
---|
| 1645 | if (h!=NULL) |
---|
| 1646 | { |
---|
[ca3e7b] | 1647 | l=pLength(h); |
---|
[35aab3] | 1648 | MATELEM(mat,i,j+1)=NULL; |
---|
[cbeafc2] | 1649 | p_SetCompP(h,i, currRing); |
---|
[35aab3] | 1650 | sBucket_Merge_p(bucket, h, l); |
---|
| 1651 | } |
---|
| 1652 | } |
---|
| 1653 | sBucketClearMerge(bucket, &(result->m[j]), &l); |
---|
| 1654 | } |
---|
[cbeafc2] | 1655 | sBucketDestroy(&bucket); |
---|
[35aab3] | 1656 | |
---|
| 1657 | // obachman: need to clean this up |
---|
| 1658 | idDelete((ideal*) &mat); |
---|
| 1659 | return result; |
---|
| 1660 | } |
---|
| 1661 | #endif |
---|
| 1662 | |
---|
| 1663 | /*2 |
---|
| 1664 | * converts a module into a matrix, destroyes the input |
---|
| 1665 | */ |
---|
| 1666 | matrix idModule2Matrix(ideal mod) |
---|
| 1667 | { |
---|
| 1668 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
| 1669 | int i,cp; |
---|
| 1670 | poly p,h; |
---|
| 1671 | |
---|
| 1672 | for(i=0;i<IDELEMS(mod);i++) |
---|
| 1673 | { |
---|
[d0164d9] | 1674 | p=pReverse(mod->m[i]); |
---|
[35aab3] | 1675 | mod->m[i]=NULL; |
---|
| 1676 | while (p!=NULL) |
---|
| 1677 | { |
---|
| 1678 | h=p; |
---|
| 1679 | pIter(p); |
---|
| 1680 | pNext(h)=NULL; |
---|
| 1681 | // cp = si_max(1,pGetComp(h)); // if used for ideals too |
---|
| 1682 | cp = pGetComp(h); |
---|
| 1683 | pSetComp(h,0); |
---|
| 1684 | pSetmComp(h); |
---|
| 1685 | #ifdef TEST |
---|
| 1686 | if (cp>mod->rank) |
---|
| 1687 | { |
---|
[6867f5] | 1688 | Print("## inv. rank %ld -> %d\n",mod->rank,cp); |
---|
[35aab3] | 1689 | int k,l,o=mod->rank; |
---|
| 1690 | mod->rank=cp; |
---|
| 1691 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
| 1692 | for (l=1; l<=o; l++) |
---|
| 1693 | { |
---|
| 1694 | for (k=1; k<=IDELEMS(mod); k++) |
---|
| 1695 | { |
---|
| 1696 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
| 1697 | MATELEM(result,l,k)=NULL; |
---|
| 1698 | } |
---|
| 1699 | } |
---|
| 1700 | idDelete((ideal *)&result); |
---|
| 1701 | result=d; |
---|
| 1702 | } |
---|
| 1703 | #endif |
---|
| 1704 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
| 1705 | } |
---|
| 1706 | } |
---|
| 1707 | // obachman 10/99: added the following line, otherwise memory leack! |
---|
| 1708 | idDelete(&mod); |
---|
| 1709 | return result; |
---|
| 1710 | } |
---|
| 1711 | |
---|
| 1712 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols) |
---|
| 1713 | { |
---|
| 1714 | matrix result = mpNew(rows,cols); |
---|
| 1715 | int i,cp,r=idRankFreeModule(mod),c=IDELEMS(mod); |
---|
| 1716 | poly p,h; |
---|
| 1717 | |
---|
| 1718 | if (r>rows) r = rows; |
---|
| 1719 | if (c>cols) c = cols; |
---|
| 1720 | for(i=0;i<c;i++) |
---|
| 1721 | { |
---|
[bafaec0] | 1722 | p=pReverse(mod->m[i]); |
---|
[35aab3] | 1723 | mod->m[i]=NULL; |
---|
| 1724 | while (p!=NULL) |
---|
| 1725 | { |
---|
| 1726 | h=p; |
---|
| 1727 | pIter(p); |
---|
| 1728 | pNext(h)=NULL; |
---|
| 1729 | cp = pGetComp(h); |
---|
| 1730 | if (cp<=r) |
---|
| 1731 | { |
---|
| 1732 | pSetComp(h,0); |
---|
| 1733 | pSetmComp(h); |
---|
| 1734 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
| 1735 | } |
---|
| 1736 | else |
---|
| 1737 | pDelete(&h); |
---|
| 1738 | } |
---|
| 1739 | } |
---|
| 1740 | idDelete(&mod); |
---|
| 1741 | return result; |
---|
| 1742 | } |
---|
| 1743 | |
---|
| 1744 | /*2 |
---|
| 1745 | * substitute the n-th variable by the monomial e in id |
---|
| 1746 | * destroy id |
---|
| 1747 | */ |
---|
| 1748 | ideal idSubst(ideal id, int n, poly e) |
---|
| 1749 | { |
---|
| 1750 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
| 1751 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
| 1752 | |
---|
| 1753 | res->rank = id->rank; |
---|
| 1754 | for(k--;k>=0;k--) |
---|
| 1755 | { |
---|
| 1756 | res->m[k]=pSubst(id->m[k],n,e); |
---|
| 1757 | id->m[k]=NULL; |
---|
| 1758 | } |
---|
| 1759 | idDelete(&id); |
---|
| 1760 | return res; |
---|
| 1761 | } |
---|
| 1762 | |
---|
| 1763 | BOOLEAN idHomModule(ideal m, ideal Q, intvec **w) |
---|
| 1764 | { |
---|
| 1765 | if (w!=NULL) *w=NULL; |
---|
| 1766 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) return FALSE; |
---|
[43ebb1] | 1767 | if (idIs0(m)) |
---|
| 1768 | { |
---|
[a12776] | 1769 | if (w!=NULL) (*w)=new intvec(m->rank); |
---|
[43ebb1] | 1770 | return TRUE; |
---|
| 1771 | } |
---|
[35aab3] | 1772 | |
---|
[4e63600] | 1773 | long cmax=1,order=0,ord,* diff,diffmin=32000; |
---|
| 1774 | int *iscom; |
---|
| 1775 | int i,j; |
---|
[35aab3] | 1776 | poly p=NULL; |
---|
[1f5db38] | 1777 | pFDegProc d; |
---|
| 1778 | if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
[99bdcf] | 1779 | d=p_Totaldegree; |
---|
[bead81] | 1780 | else |
---|
[1f5db38] | 1781 | d=pFDeg; |
---|
[35aab3] | 1782 | int length=IDELEMS(m); |
---|
| 1783 | polyset P=m->m; |
---|
| 1784 | polyset F=(polyset)omAlloc(length*sizeof(poly)); |
---|
| 1785 | for (i=length-1;i>=0;i--) |
---|
| 1786 | { |
---|
| 1787 | p=F[i]=P[i]; |
---|
[4e63600] | 1788 | cmax=si_max(cmax,(long)pMaxComp(p)); |
---|
[35aab3] | 1789 | } |
---|
[4e63600] | 1790 | cmax++; |
---|
| 1791 | diff = (long *)omAlloc0(cmax*sizeof(long)); |
---|
[35aab3] | 1792 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
| 1793 | iscom = (int *)omAlloc0(cmax*sizeof(int)); |
---|
| 1794 | i=0; |
---|
| 1795 | while (i<=length) |
---|
| 1796 | { |
---|
| 1797 | if (i<length) |
---|
| 1798 | { |
---|
| 1799 | p=F[i]; |
---|
[4e63600] | 1800 | while ((p!=NULL) && (iscom[pGetComp(p)]==0)) pIter(p); |
---|
[35aab3] | 1801 | } |
---|
| 1802 | if ((p==NULL) && (i<length)) |
---|
| 1803 | { |
---|
| 1804 | i++; |
---|
| 1805 | } |
---|
| 1806 | else |
---|
| 1807 | { |
---|
[4e63600] | 1808 | if (p==NULL) /* && (i==length) */ |
---|
[35aab3] | 1809 | { |
---|
| 1810 | i=0; |
---|
| 1811 | while ((i<length) && (F[i]==NULL)) i++; |
---|
| 1812 | if (i>=length) break; |
---|
| 1813 | p = F[i]; |
---|
| 1814 | } |
---|
[1f5db38] | 1815 | //if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
| 1816 | // order=pTotaldegree(p); |
---|
| 1817 | //else |
---|
[35aab3] | 1818 | // order = p->order; |
---|
[1f5db38] | 1819 | // order = pFDeg(p,currRing); |
---|
| 1820 | order = d(p,currRing) +diff[pGetComp(p)]; |
---|
| 1821 | //order += diff[pGetComp(p)]; |
---|
[35aab3] | 1822 | p = F[i]; |
---|
| 1823 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
| 1824 | F[i] = NULL; |
---|
| 1825 | i=0; |
---|
| 1826 | } |
---|
| 1827 | while (p!=NULL) |
---|
| 1828 | { |
---|
[4e63600] | 1829 | if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
| 1830 | ord=pTotaldegree(p); |
---|
| 1831 | else |
---|
[35aab3] | 1832 | // ord = p->order; |
---|
[4e63600] | 1833 | ord = pFDeg(p,currRing); |
---|
| 1834 | if (iscom[pGetComp(p)]==0) |
---|
[35aab3] | 1835 | { |
---|
| 1836 | diff[pGetComp(p)] = order-ord; |
---|
| 1837 | iscom[pGetComp(p)] = 1; |
---|
| 1838 | /* |
---|
| 1839 | *PrintS("new diff: "); |
---|
| 1840 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
| 1841 | *PrintLn(); |
---|
| 1842 | *PrintS("new iscom: "); |
---|
| 1843 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
| 1844 | *PrintLn(); |
---|
| 1845 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
| 1846 | */ |
---|
| 1847 | } |
---|
| 1848 | else |
---|
| 1849 | { |
---|
| 1850 | /* |
---|
| 1851 | *PrintS("new diff: "); |
---|
| 1852 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
| 1853 | *PrintLn(); |
---|
| 1854 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
| 1855 | */ |
---|
[4e63600] | 1856 | if (order != (ord+diff[pGetComp(p)])) |
---|
[35aab3] | 1857 | { |
---|
| 1858 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
[4e63600] | 1859 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
[35aab3] | 1860 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
| 1861 | delete *w;*w=NULL; |
---|
| 1862 | return FALSE; |
---|
| 1863 | } |
---|
| 1864 | } |
---|
| 1865 | pIter(p); |
---|
| 1866 | } |
---|
| 1867 | } |
---|
| 1868 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
| 1869 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
[4e63600] | 1870 | for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]); |
---|
[35aab3] | 1871 | for (i=1;i<cmax;i++) |
---|
| 1872 | { |
---|
| 1873 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
| 1874 | } |
---|
| 1875 | if (w!=NULL) |
---|
| 1876 | { |
---|
| 1877 | for (i=1;i<cmax;i++) |
---|
| 1878 | { |
---|
[4e63600] | 1879 | (**w)[i-1]=(int)(diff[i]-diffmin); |
---|
[35aab3] | 1880 | } |
---|
| 1881 | } |
---|
[4e63600] | 1882 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
[35aab3] | 1883 | return TRUE; |
---|
| 1884 | } |
---|
| 1885 | |
---|
[30b8381] | 1886 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
| 1887 | { |
---|
| 1888 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
| 1889 | if (idIs0(m)) return TRUE; |
---|
| 1890 | |
---|
| 1891 | int cmax=-1; |
---|
| 1892 | int i; |
---|
| 1893 | poly p=NULL; |
---|
| 1894 | int length=IDELEMS(m); |
---|
| 1895 | polyset P=m->m; |
---|
| 1896 | for (i=length-1;i>=0;i--) |
---|
| 1897 | { |
---|
| 1898 | p=P[i]; |
---|
| 1899 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
| 1900 | } |
---|
[8324cc] | 1901 | if (w != NULL) |
---|
[30b8381] | 1902 | if (w->length()+1 < cmax) |
---|
[4d13e7] | 1903 | { |
---|
[30b8381] | 1904 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
| 1905 | return FALSE; |
---|
| 1906 | } |
---|
[8324cc] | 1907 | |
---|
| 1908 | if(w!=NULL) |
---|
| 1909 | pSetModDeg(w); |
---|
| 1910 | |
---|
[30b8381] | 1911 | for (i=length-1;i>=0;i--) |
---|
| 1912 | { |
---|
| 1913 | p=P[i]; |
---|
| 1914 | poly q=p; |
---|
| 1915 | if (p!=NULL) |
---|
| 1916 | { |
---|
[b130fb] | 1917 | int d=pFDeg(p,currRing); |
---|
[30b8381] | 1918 | loop |
---|
| 1919 | { |
---|
| 1920 | pIter(p); |
---|
| 1921 | if (p==NULL) break; |
---|
[4d13e7] | 1922 | if (d!=pFDeg(p,currRing)) |
---|
[30b8381] | 1923 | { |
---|
[4d13e7] | 1924 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
[8324cc] | 1925 | if(w!=NULL) |
---|
| 1926 | pSetModDeg(NULL); |
---|
[4d13e7] | 1927 | return FALSE; |
---|
[30b8381] | 1928 | } |
---|
| 1929 | } |
---|
| 1930 | } |
---|
| 1931 | } |
---|
[cbc7e3] | 1932 | |
---|
[8324cc] | 1933 | if(w!=NULL) |
---|
| 1934 | pSetModDeg(NULL); |
---|
[cbc7e3] | 1935 | |
---|
[30b8381] | 1936 | return TRUE; |
---|
| 1937 | } |
---|
| 1938 | |
---|
[35aab3] | 1939 | ideal idJet(ideal i,int d) |
---|
| 1940 | { |
---|
| 1941 | ideal r=idInit((i->nrows)*(i->ncols),i->rank); |
---|
| 1942 | r->nrows = i-> nrows; |
---|
| 1943 | r->ncols = i-> ncols; |
---|
| 1944 | //r->rank = i-> rank; |
---|
| 1945 | int k; |
---|
| 1946 | for(k=(i->nrows)*(i->ncols)-1;k>=0; k--) |
---|
| 1947 | { |
---|
| 1948 | r->m[k]=ppJet(i->m[k],d); |
---|
| 1949 | } |
---|
| 1950 | return r; |
---|
| 1951 | } |
---|
| 1952 | |
---|
| 1953 | ideal idJetW(ideal i,int d, intvec * iv) |
---|
| 1954 | { |
---|
| 1955 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
| 1956 | if (ecartWeights!=NULL) |
---|
| 1957 | { |
---|
| 1958 | WerrorS("cannot compute weighted jets now"); |
---|
| 1959 | } |
---|
| 1960 | else |
---|
| 1961 | { |
---|
| 1962 | short *w=iv2array(iv); |
---|
| 1963 | int k; |
---|
| 1964 | for(k=0; k<IDELEMS(i); k++) |
---|
| 1965 | { |
---|
| 1966 | r->m[k]=ppJetW(i->m[k],d,w); |
---|
| 1967 | } |
---|
[a665eb] | 1968 | omFreeSize((ADDRESS)w,(rVar(r)+1)*sizeof(short)); |
---|
[35aab3] | 1969 | } |
---|
| 1970 | return r; |
---|
| 1971 | } |
---|
| 1972 | |
---|
| 1973 | int idMinDegW(ideal M,intvec *w) |
---|
| 1974 | { |
---|
| 1975 | int d=-1; |
---|
| 1976 | for(int i=0;i<IDELEMS(M);i++) |
---|
| 1977 | { |
---|
| 1978 | int d0=pMinDeg(M->m[i],w); |
---|
| 1979 | if(-1<d0&&(d0<d||d==-1)) |
---|
| 1980 | d=d0; |
---|
| 1981 | } |
---|
| 1982 | return d; |
---|
| 1983 | } |
---|
| 1984 | |
---|
| 1985 | ideal idSeries(int n,ideal M,matrix U,intvec *w) |
---|
| 1986 | { |
---|
| 1987 | for(int i=IDELEMS(M)-1;i>=0;i--) |
---|
| 1988 | { |
---|
| 1989 | if(U==NULL) |
---|
| 1990 | M->m[i]=pSeries(n,M->m[i],NULL,w); |
---|
| 1991 | else |
---|
| 1992 | { |
---|
| 1993 | M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w); |
---|
| 1994 | MATELEM(U,i+1,i+1)=NULL; |
---|
| 1995 | } |
---|
| 1996 | } |
---|
| 1997 | if(U!=NULL) |
---|
| 1998 | idDelete((ideal*)&U); |
---|
| 1999 | return M; |
---|
| 2000 | } |
---|
| 2001 | |
---|
| 2002 | matrix idDiff(matrix i, int k) |
---|
| 2003 | { |
---|
| 2004 | int e=MATCOLS(i)*MATROWS(i); |
---|
| 2005 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
[360507] | 2006 | r->rank=i->rank; |
---|
[35aab3] | 2007 | int j; |
---|
| 2008 | for(j=0; j<e; j++) |
---|
| 2009 | { |
---|
| 2010 | r->m[j]=pDiff(i->m[j],k); |
---|
| 2011 | } |
---|
| 2012 | return r; |
---|
| 2013 | } |
---|
| 2014 | |
---|
| 2015 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
| 2016 | { |
---|
| 2017 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
| 2018 | int i,j; |
---|
| 2019 | for(i=0; i<IDELEMS(I); i++) |
---|
| 2020 | { |
---|
| 2021 | for(j=0; j<IDELEMS(J); j++) |
---|
| 2022 | { |
---|
| 2023 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
| 2024 | } |
---|
| 2025 | } |
---|
| 2026 | return r; |
---|
| 2027 | } |
---|
| 2028 | |
---|
[b3930d] | 2029 | int idElem(const ideal F) |
---|
[35aab3] | 2030 | { |
---|
[b3930d] | 2031 | int i=0,j=IDELEMS(F)-1; |
---|
[35aab3] | 2032 | |
---|
[b3930d] | 2033 | while(j>=0) |
---|
[35aab3] | 2034 | { |
---|
[b3930d] | 2035 | if ((F->m)[j]!=NULL) i++; |
---|
| 2036 | j--; |
---|
[35aab3] | 2037 | } |
---|
| 2038 | return i; |
---|
| 2039 | } |
---|
| 2040 | |
---|
| 2041 | /* |
---|
| 2042 | *computes module-weights for liftings of homogeneous modules |
---|
| 2043 | */ |
---|
| 2044 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
| 2045 | { |
---|
| 2046 | if (idIs0(mod)) return new intvec(2); |
---|
| 2047 | int i=IDELEMS(mod); |
---|
| 2048 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
| 2049 | intvec *result = new intvec(i+1); |
---|
| 2050 | while (i>0) |
---|
| 2051 | { |
---|
[b130fb] | 2052 | (*result)[i]=pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])]; |
---|
[35aab3] | 2053 | } |
---|
| 2054 | return result; |
---|
| 2055 | } |
---|
| 2056 | |
---|
| 2057 | /*2 |
---|
| 2058 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
| 2059 | *with x_max,...,x_1) |
---|
| 2060 | */ |
---|
| 2061 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
| 2062 | { |
---|
| 2063 | int i; |
---|
| 2064 | ideal result; |
---|
| 2065 | |
---|
| 2066 | if (idIs0(kBase)) return NULL; |
---|
| 2067 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
| 2068 | *convert = idSort(kBase,FALSE); |
---|
| 2069 | for (i=0;i<(*convert)->length();i++) |
---|
| 2070 | { |
---|
| 2071 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
| 2072 | } |
---|
| 2073 | return result; |
---|
| 2074 | } |
---|
| 2075 | |
---|
| 2076 | /*2 |
---|
| 2077 | *returns the index of a given monom in the list of the special kbase |
---|
| 2078 | */ |
---|
| 2079 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
| 2080 | { |
---|
| 2081 | int j=IDELEMS(kbase); |
---|
| 2082 | |
---|
| 2083 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
| 2084 | if (j==0) return -1; |
---|
[a665eb] | 2085 | int i=rVar(r); |
---|
[35aab3] | 2086 | while (i>0) |
---|
| 2087 | { |
---|
| 2088 | loop |
---|
| 2089 | { |
---|
| 2090 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
| 2091 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
| 2092 | j--; |
---|
| 2093 | if (j==0) return -1; |
---|
| 2094 | } |
---|
| 2095 | if (i==1) |
---|
| 2096 | { |
---|
| 2097 | while(j>0) |
---|
| 2098 | { |
---|
| 2099 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
| 2100 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
| 2101 | j--; |
---|
| 2102 | } |
---|
| 2103 | } |
---|
| 2104 | i--; |
---|
| 2105 | } |
---|
| 2106 | return -1; |
---|
| 2107 | } |
---|
| 2108 | |
---|
| 2109 | /*2 |
---|
| 2110 | *decomposes the monom in a part of coefficients described by the |
---|
| 2111 | *complement of how and a monom in variables occuring in how, the |
---|
| 2112 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
| 2113 | *exists) |
---|
| 2114 | */ |
---|
| 2115 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
| 2116 | { |
---|
| 2117 | int i; |
---|
[2f5936] | 2118 | poly coeff=p_One(r), base=p_One(r); |
---|
[35aab3] | 2119 | |
---|
[a665eb] | 2120 | for (i=1;i<=rVar(r);i++) |
---|
[35aab3] | 2121 | { |
---|
| 2122 | if (pGetExp(how,i)>0) |
---|
| 2123 | { |
---|
| 2124 | pSetExp(base,i,pGetExp(monom,i)); |
---|
| 2125 | } |
---|
| 2126 | else |
---|
| 2127 | { |
---|
| 2128 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
| 2129 | } |
---|
| 2130 | } |
---|
| 2131 | pSetComp(base,pGetComp(monom)); |
---|
| 2132 | pSetm(base); |
---|
| 2133 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
| 2134 | pSetm(coeff); |
---|
| 2135 | *pos = idIndexOfKBase(base,kbase); |
---|
| 2136 | if (*pos<0) |
---|
| 2137 | pDelete(&coeff); |
---|
| 2138 | pDelete(&base); |
---|
| 2139 | return coeff; |
---|
| 2140 | } |
---|
| 2141 | |
---|
| 2142 | /*2 |
---|
| 2143 | *returns a matrix A of coefficients with kbase*A=arg |
---|
| 2144 | *if all monomials in variables of how occur in kbase |
---|
| 2145 | *the other are deleted |
---|
| 2146 | */ |
---|
| 2147 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
| 2148 | { |
---|
| 2149 | matrix result; |
---|
| 2150 | ideal tempKbase; |
---|
| 2151 | poly p,q; |
---|
| 2152 | intvec * convert; |
---|
| 2153 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
| 2154 | #if 0 |
---|
| 2155 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
| 2156 | if (idIs0(arg)) |
---|
| 2157 | return mpNew(i,1); |
---|
| 2158 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
| 2159 | result = mpNew(i,j); |
---|
| 2160 | #else |
---|
| 2161 | result = mpNew(i, j); |
---|
| 2162 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
| 2163 | #endif |
---|
| 2164 | |
---|
| 2165 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
| 2166 | for (k=0;k<j;k++) |
---|
| 2167 | { |
---|
| 2168 | p = arg->m[k]; |
---|
| 2169 | while (p!=NULL) |
---|
| 2170 | { |
---|
| 2171 | q = idDecompose(p,how,tempKbase,&pos); |
---|
| 2172 | if (pos>=0) |
---|
| 2173 | { |
---|
| 2174 | MATELEM(result,(*convert)[pos],k+1) = |
---|
| 2175 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
| 2176 | } |
---|
| 2177 | else |
---|
| 2178 | pDelete(&q); |
---|
| 2179 | pIter(p); |
---|
| 2180 | } |
---|
| 2181 | } |
---|
| 2182 | idDelete(&tempKbase); |
---|
| 2183 | return result; |
---|
| 2184 | } |
---|
| 2185 | |
---|
| 2186 | /*3 |
---|
[b8f199] | 2187 | * searches for the next unit in the components of the module arg and |
---|
| 2188 | * returns the first one; |
---|
[35aab3] | 2189 | */ |
---|
[2f5936] | 2190 | static int id_ReadOutPivot(ideal arg,int* comp, const ring r) |
---|
[35aab3] | 2191 | { |
---|
[1d138c] | 2192 | if (idIs0(arg)) return -1; |
---|
[8421b8] | 2193 | int i=0,j, generator=-1; |
---|
| 2194 | int rk_arg=arg->rank; //idRankFreeModule(arg); |
---|
| 2195 | int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int)); |
---|
[fc7902] | 2196 | poly p; |
---|
[35aab3] | 2197 | |
---|
[8421b8] | 2198 | while ((generator<0) && (i<IDELEMS(arg))) |
---|
[35aab3] | 2199 | { |
---|
[8421b8] | 2200 | memset(componentIsUsed,0,(rk_arg+1)*sizeof(int)); |
---|
[35aab3] | 2201 | p = arg->m[i]; |
---|
| 2202 | while (p!=NULL) |
---|
| 2203 | { |
---|
[2f5936] | 2204 | j = p_GetComp(p,r); |
---|
[8421b8] | 2205 | if (componentIsUsed[j]==0) |
---|
[35aab3] | 2206 | { |
---|
[b8f199] | 2207 | #ifdef HAVE_RINGS |
---|
[2f5936] | 2208 | if (p_LmIsConstantComp(p,r) && |
---|
| 2209 | (!rField_is_Ring(r) || n_IsUnit(pGetCoeff(p),r->cf))) |
---|
[b8f199] | 2210 | { |
---|
| 2211 | #else |
---|
[2f5936] | 2212 | if (p_LmIsConstantComp(p,r)) |
---|
[35aab3] | 2213 | { |
---|
[b8f199] | 2214 | #endif |
---|
[35aab3] | 2215 | generator = i; |
---|
[8421b8] | 2216 | componentIsUsed[j] = 1; |
---|
[35aab3] | 2217 | } |
---|
| 2218 | else |
---|
| 2219 | { |
---|
[8421b8] | 2220 | componentIsUsed[j] = -1; |
---|
[35aab3] | 2221 | } |
---|
| 2222 | } |
---|
[8421b8] | 2223 | else if (componentIsUsed[j]>0) |
---|
[35aab3] | 2224 | { |
---|
[8421b8] | 2225 | (componentIsUsed[j])++; |
---|
[35aab3] | 2226 | } |
---|
| 2227 | pIter(p); |
---|
| 2228 | } |
---|
| 2229 | i++; |
---|
| 2230 | } |
---|
| 2231 | i = 0; |
---|
| 2232 | *comp = -1; |
---|
| 2233 | for (j=0;j<=rk_arg;j++) |
---|
| 2234 | { |
---|
[8421b8] | 2235 | if (componentIsUsed[j]>0) |
---|
[35aab3] | 2236 | { |
---|
[8421b8] | 2237 | if ((*comp==-1) || (componentIsUsed[j]<i)) |
---|
[35aab3] | 2238 | { |
---|
| 2239 | *comp = j; |
---|
[8421b8] | 2240 | i= componentIsUsed[j]; |
---|
[35aab3] | 2241 | } |
---|
| 2242 | } |
---|
| 2243 | } |
---|
[8421b8] | 2244 | omFree(componentIsUsed); |
---|
[35aab3] | 2245 | return generator; |
---|
| 2246 | } |
---|
| 2247 | |
---|
[955025] | 2248 | #if 0 |
---|
[35aab3] | 2249 | static void idDeleteComp(ideal arg,int red_comp) |
---|
| 2250 | { |
---|
| 2251 | int i,j; |
---|
| 2252 | poly p; |
---|
| 2253 | |
---|
| 2254 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
| 2255 | { |
---|
| 2256 | p = arg->m[i]; |
---|
| 2257 | while (p!=NULL) |
---|
| 2258 | { |
---|
| 2259 | j = pGetComp(p); |
---|
| 2260 | if (j>red_comp) |
---|
| 2261 | { |
---|
| 2262 | pSetComp(p,j-1); |
---|
| 2263 | pSetm(p); |
---|
| 2264 | } |
---|
| 2265 | pIter(p); |
---|
| 2266 | } |
---|
| 2267 | } |
---|
| 2268 | (arg->rank)--; |
---|
| 2269 | } |
---|
[955025] | 2270 | #endif |
---|
| 2271 | |
---|
| 2272 | static void idDeleteComps(ideal arg,int* red_comp,int del) |
---|
| 2273 | // red_comp is an array [0..args->rank] |
---|
| 2274 | { |
---|
| 2275 | int i,j; |
---|
| 2276 | poly p; |
---|
| 2277 | |
---|
| 2278 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
| 2279 | { |
---|
| 2280 | p = arg->m[i]; |
---|
| 2281 | while (p!=NULL) |
---|
| 2282 | { |
---|
| 2283 | j = pGetComp(p); |
---|
| 2284 | if (red_comp[j]!=j) |
---|
| 2285 | { |
---|
| 2286 | pSetComp(p,red_comp[j]); |
---|
| 2287 | pSetmComp(p); |
---|
| 2288 | } |
---|
| 2289 | pIter(p); |
---|
| 2290 | } |
---|
| 2291 | } |
---|
| 2292 | (arg->rank) -= del; |
---|
| 2293 | } |
---|
[35aab3] | 2294 | |
---|
| 2295 | /*2 |
---|
| 2296 | * returns the presentation of an isomorphic, minimally |
---|
| 2297 | * embedded module (arg represents the quotient!) |
---|
| 2298 | */ |
---|
[2f5936] | 2299 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w, const ring r) |
---|
[35aab3] | 2300 | { |
---|
| 2301 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
[3504d7] | 2302 | int i,next_gen,next_comp; |
---|
[35aab3] | 2303 | ideal res=arg; |
---|
[2f5936] | 2304 | if (!inPlace) res = id_Copy(arg,r); |
---|
| 2305 | res->rank=si_max(res->rank,id_RankFreeModule(res,r)); |
---|
[955025] | 2306 | int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int)); |
---|
| 2307 | for (i=res->rank;i>=0;i--) red_comp[i]=i; |
---|
[8421b8] | 2308 | |
---|
[07b3e1] | 2309 | int del=0; |
---|
[35aab3] | 2310 | loop |
---|
| 2311 | { |
---|
[b8f199] | 2312 | next_gen = idReadOutPivot(res,&next_comp); |
---|
[35aab3] | 2313 | if (next_gen<0) break; |
---|
[07b3e1] | 2314 | del++; |
---|
[35aab3] | 2315 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
---|
[955025] | 2316 | for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--; |
---|
[cf108d] | 2317 | if ((w !=NULL)&&(*w!=NULL)) |
---|
| 2318 | { |
---|
[07b3e1] | 2319 | for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i]; |
---|
[3504d7] | 2320 | } |
---|
| 2321 | } |
---|
[955025] | 2322 | |
---|
| 2323 | idDeleteComps(res,red_comp,del); |
---|
| 2324 | idSkipZeroes(res); |
---|
| 2325 | omFree(red_comp); |
---|
| 2326 | |
---|
[07b3e1] | 2327 | if ((w !=NULL)&&(*w!=NULL) &&(del>0)) |
---|
[3504d7] | 2328 | { |
---|
[07b3e1] | 2329 | intvec *wtmp=new intvec((*w)->length()-del); |
---|
| 2330 | for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i]; |
---|
[3504d7] | 2331 | delete *w; |
---|
| 2332 | *w=wtmp; |
---|
[35aab3] | 2333 | } |
---|
| 2334 | return res; |
---|
| 2335 | } |
---|
| 2336 | |
---|
| 2337 | intvec * idQHomWeight(ideal id) |
---|
| 2338 | { |
---|
| 2339 | poly head, tail; |
---|
| 2340 | int k; |
---|
| 2341 | int in=IDELEMS(id)-1, ready=0, all=0, |
---|
[a665eb] | 2342 | coldim=rVar(r), rowmax=2*coldim; |
---|
[35aab3] | 2343 | if (in<0) return NULL; |
---|
| 2344 | intvec *imat=new intvec(rowmax+1,coldim,0); |
---|
| 2345 | |
---|
| 2346 | do |
---|
| 2347 | { |
---|
| 2348 | head = id->m[in--]; |
---|
| 2349 | if (head!=NULL) |
---|
| 2350 | { |
---|
| 2351 | tail = pNext(head); |
---|
| 2352 | while (tail!=NULL) |
---|
| 2353 | { |
---|
| 2354 | all++; |
---|
| 2355 | for (k=1;k<=coldim;k++) |
---|
| 2356 | IMATELEM(*imat,all,k) = pGetExpDiff(head,tail,k); |
---|
| 2357 | if (all==rowmax) |
---|
| 2358 | { |
---|
| 2359 | ivTriangIntern(imat, ready, all); |
---|
| 2360 | if (ready==coldim) |
---|
| 2361 | { |
---|
| 2362 | delete imat; |
---|
| 2363 | return NULL; |
---|
| 2364 | } |
---|
| 2365 | } |
---|
| 2366 | pIter(tail); |
---|
| 2367 | } |
---|
| 2368 | } |
---|
| 2369 | } while (in>=0); |
---|
| 2370 | if (all>ready) |
---|
| 2371 | { |
---|
| 2372 | ivTriangIntern(imat, ready, all); |
---|
| 2373 | if (ready==coldim) |
---|
| 2374 | { |
---|
| 2375 | delete imat; |
---|
| 2376 | return NULL; |
---|
| 2377 | } |
---|
| 2378 | } |
---|
| 2379 | intvec *result = ivSolveKern(imat, ready); |
---|
| 2380 | delete imat; |
---|
| 2381 | return result; |
---|
| 2382 | } |
---|
| 2383 | |
---|
| 2384 | BOOLEAN idIsZeroDim(ideal I) |
---|
| 2385 | { |
---|
[a665eb] | 2386 | BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(rVar(r)*sizeof(BOOLEAN)); |
---|
[35aab3] | 2387 | int i,n; |
---|
| 2388 | poly po; |
---|
| 2389 | BOOLEAN res=TRUE; |
---|
| 2390 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
| 2391 | { |
---|
| 2392 | po=I->m[i]; |
---|
| 2393 | if ((po!=NULL) &&((n=pIsPurePower(po))!=0)) UsedAxis[n-1]=TRUE; |
---|
| 2394 | } |
---|
[a665eb] | 2395 | for(i=rVar(r)-1;i>=0;i--) |
---|
[35aab3] | 2396 | { |
---|
| 2397 | if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim. |
---|
| 2398 | } |
---|
[a665eb] | 2399 | omFreeSize(UsedAxis,rVar(r)*sizeof(BOOLEAN)); |
---|
[35aab3] | 2400 | return res; |
---|
| 2401 | } |
---|
| 2402 | |
---|
[2f5936] | 2403 | void id_Normalize(ideal I,const ring r) |
---|
[35aab3] | 2404 | { |
---|
[2f5936] | 2405 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
[35aab3] | 2406 | int i; |
---|
| 2407 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
| 2408 | { |
---|
[2f5936] | 2409 | p_Normalize(I->m[i],r); |
---|
[35aab3] | 2410 | } |
---|
| 2411 | } |
---|
[225d94] | 2412 | |
---|
[2ad10e9] | 2413 | // #include <kernel/clapsing.h> |
---|
[225d94] | 2414 | |
---|
[2f6fc61] | 2415 | #ifdef HAVE_FACTORY |
---|
[225d94] | 2416 | poly id_GCD(poly f, poly g, const ring r) |
---|
| 2417 | { |
---|
[a665eb] | 2418 | ring save_r=r; |
---|
[225d94] | 2419 | rChangeCurrRing(r); |
---|
| 2420 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
| 2421 | intvec *w = NULL; |
---|
| 2422 | ideal S=idSyzygies(I,testHomog,&w); |
---|
| 2423 | if (w!=NULL) delete w; |
---|
| 2424 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
| 2425 | idDelete(&S); |
---|
| 2426 | poly gcd_p=singclap_pdivide(f,gg); |
---|
| 2427 | pDelete(&gg); |
---|
| 2428 | rChangeCurrRing(save_r); |
---|
| 2429 | return gcd_p; |
---|
| 2430 | } |
---|
[2f6fc61] | 2431 | #endif |
---|
[bba835] | 2432 | |
---|
| 2433 | /*2 |
---|
| 2434 | * xx,q: arrays of length 0..rl-1 |
---|
| 2435 | * xx[i]: SB mod q[i] |
---|
| 2436 | * assume: char=0 |
---|
| 2437 | * assume: q[i]!=0 |
---|
| 2438 | * destroys xx |
---|
| 2439 | */ |
---|
[2f6fc61] | 2440 | #ifdef HAVE_FACTORY |
---|
[a665eb] | 2441 | ideal idChineseRemainder(ideal *xx, number *q, int rl, const ring r) |
---|
[bba835] | 2442 | { |
---|
[07969d] | 2443 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
| 2444 | ideal result=idInit(cnt,xx[0]->rank); |
---|
| 2445 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
| 2446 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
[bba835] | 2447 | int i,j; |
---|
[cbc7e3] | 2448 | poly r,h,hh,res_p; |
---|
[bba835] | 2449 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
[07969d] | 2450 | for(i=cnt-1;i>=0;i--) |
---|
[bba835] | 2451 | { |
---|
| 2452 | res_p=NULL; |
---|
| 2453 | loop |
---|
| 2454 | { |
---|
| 2455 | r=NULL; |
---|
| 2456 | for(j=rl-1;j>=0;j--) |
---|
| 2457 | { |
---|
| 2458 | h=xx[j]->m[i]; |
---|
[4d8843] | 2459 | if ((h!=NULL) |
---|
| 2460 | &&((r==NULL)||(pLmCmp(r,h)==-1))) |
---|
| 2461 | r=h; |
---|
[bba835] | 2462 | } |
---|
| 2463 | if (r==NULL) break; |
---|
[cbc7e3] | 2464 | h=pHead(r); |
---|
[bba835] | 2465 | for(j=rl-1;j>=0;j--) |
---|
| 2466 | { |
---|
[cbc7e3] | 2467 | hh=xx[j]->m[i]; |
---|
| 2468 | if ((hh!=NULL) && (pLmCmp(r,hh)==0)) |
---|
| 2469 | { |
---|
[38f763] | 2470 | x[j]=pGetCoeff(hh); |
---|
[cbc7e3] | 2471 | hh=pLmFreeAndNext(hh); |
---|
| 2472 | xx[j]->m[i]=hh; |
---|
[bba835] | 2473 | } |
---|
| 2474 | else |
---|
[a665eb] | 2475 | x[j]=nlInit(0, r); |
---|
[bba835] | 2476 | } |
---|
| 2477 | number n=nlChineseRemainder(x,q,rl); |
---|
| 2478 | for(j=rl-1;j>=0;j--) |
---|
| 2479 | { |
---|
[38f763] | 2480 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
[bba835] | 2481 | } |
---|
[a8ef67] | 2482 | if (nlIsZero(n)) pDelete(&h); |
---|
| 2483 | else |
---|
| 2484 | { |
---|
| 2485 | pSetCoeff(h,n); |
---|
| 2486 | //Print("new mon:");pWrite(h); |
---|
| 2487 | res_p=pAdd(res_p,h); |
---|
| 2488 | } |
---|
[bba835] | 2489 | } |
---|
| 2490 | result->m[i]=res_p; |
---|
| 2491 | } |
---|
| 2492 | omFree(x); |
---|
| 2493 | for(i=rl-1;i>=0;i--) idDelete(&(xx[i])); |
---|
| 2494 | omFree(xx); |
---|
| 2495 | return result; |
---|
| 2496 | } |
---|
[2f6fc61] | 2497 | #endif |
---|
[3580b7] | 2498 | /* currently unsed: |
---|
[94eaef] | 2499 | ideal idChineseRemainder(ideal *xx, intvec *iv) |
---|
| 2500 | { |
---|
| 2501 | int rl=iv->length(); |
---|
| 2502 | number *q=(number *)omAlloc(rl*sizeof(number)); |
---|
| 2503 | int i; |
---|
| 2504 | for(i=0; i<rl; i++) |
---|
| 2505 | { |
---|
| 2506 | q[i]=nInit((*iv)[i]); |
---|
| 2507 | } |
---|
| 2508 | return idChineseRemainder(xx,q,rl); |
---|
[cbc7e3] | 2509 | } |
---|
[3580b7] | 2510 | */ |
---|
[3149a5] | 2511 | /* |
---|
| 2512 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
---|
| 2513 | */ |
---|
[2f5936] | 2514 | ideal id_Farey(ideal x, number N, const ring r) |
---|
[3149a5] | 2515 | { |
---|
[b86768] | 2516 | int cnt=IDELEMS(x)*x->nrows; |
---|
| 2517 | ideal result=idInit(cnt,x->rank); |
---|
| 2518 | result->nrows=x->nrows; // for lifting matrices |
---|
| 2519 | result->ncols=x->ncols; // for lifting matrices |
---|
| 2520 | |
---|
[3149a5] | 2521 | int i; |
---|
[b86768] | 2522 | for(i=cnt-1;i>=0;i--) |
---|
[3149a5] | 2523 | { |
---|
[2f5936] | 2524 | poly h=p_Copy(x->m[i],r); |
---|
[3149a5] | 2525 | result->m[i]=h; |
---|
| 2526 | while(h!=NULL) |
---|
| 2527 | { |
---|
| 2528 | number c=pGetCoeff(h); |
---|
| 2529 | pSetCoeff0(h,nlFarey(c,N)); |
---|
[2f5936] | 2530 | n_Delete(&c,r->cf); |
---|
[3149a5] | 2531 | pIter(h); |
---|
| 2532 | } |
---|
[2f5936] | 2533 | while((result->m[i]!=NULL)&&(n_IsZero(pGetCoeff(result->m[i]),r->cf))) |
---|
[b86768] | 2534 | { |
---|
[2f5936] | 2535 | p_LmDelete(&(result->m[i]),r); |
---|
[b86768] | 2536 | } |
---|
| 2537 | h=result->m[i]; |
---|
| 2538 | while((h!=NULL) && (pNext(h)!=NULL)) |
---|
| 2539 | { |
---|
[2f5936] | 2540 | if(n_IsZero(pGetCoeff(pNext(h)),r->cf)) |
---|
[b86768] | 2541 | { |
---|
[2f5936] | 2542 | p_LmDelete(&pNext(h),r); |
---|
[b86768] | 2543 | } |
---|
| 2544 | else pIter(h); |
---|
| 2545 | } |
---|
[3149a5] | 2546 | } |
---|
| 2547 | return result; |
---|
| 2548 | } |
---|
[90a60f] | 2549 | |
---|
| 2550 | /*2 |
---|
| 2551 | * transpose a module |
---|
| 2552 | */ |
---|
| 2553 | ideal id_Transp(ideal a, const ring rRing) |
---|
| 2554 | { |
---|
| 2555 | int r = a->rank, c = IDELEMS(a); |
---|
| 2556 | ideal b = idInit(r,c); |
---|
| 2557 | |
---|
| 2558 | for (int i=c; i>0; i--) |
---|
| 2559 | { |
---|
| 2560 | poly p=a->m[i-1]; |
---|
| 2561 | while(p!=NULL) |
---|
| 2562 | { |
---|
| 2563 | poly h=p_Head(p, rRing); |
---|
| 2564 | int co=p_GetComp(h, rRing)-1; |
---|
| 2565 | p_SetComp(h, i, rRing); |
---|
| 2566 | p_Setm(h, rRing); |
---|
| 2567 | b->m[co] = p_Add_q(b->m[co], h, rRing); |
---|
| 2568 | pIter(p); |
---|
| 2569 | } |
---|
| 2570 | } |
---|
| 2571 | return b; |
---|
| 2572 | } |
---|
| 2573 | |
---|
| 2574 | |
---|
| 2575 | |
---|
| 2576 | /*2 |
---|
| 2577 | * The following is needed to compute the image of certain map used in |
---|
| 2578 | * the computation of cohomologies via BGG |
---|
| 2579 | * let M = { w_1, ..., w_k }, k = size(M) == ncols(M), n = nvars(currRing). |
---|
| 2580 | * assuming that nrows(M) <= m*n; the procedure computes: |
---|
| 2581 | * transpose(M) * transpose( var(1) I_m | ... | var(n) I_m ) :== transpose(module{f_1, ... f_k}), |
---|
| 2582 | * where f_i = \sum_{j=1}^{m} (w_i, v_j) gen(j), (w_i, v_j) is a `scalar` multiplication. |
---|
| 2583 | * that is, if w_i = (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) then |
---|
| 2584 | |
---|
| 2585 | (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) |
---|
| 2586 | * var_1 ... var_1 | var_2 ... var_2 | ... | var_n ... var(n) |
---|
| 2587 | * gen_1 ... gen_m | gen_1 ... gen_m | ... | gen_1 ... gen_m |
---|
| 2588 | + => |
---|
| 2589 | f_i = |
---|
| 2590 | |
---|
| 2591 | a^1_1 * var(1) * gen(1) + ... + a^1_m * var(1) * gen(m) + |
---|
| 2592 | a^2_1 * var(2) * gen(1) + ... + a^2_m * var(2) * gen(m) + |
---|
| 2593 | ... |
---|
| 2594 | a^n_1 * var(n) * gen(1) + ... + a^n_m * var(n) * gen(m); |
---|
| 2595 | |
---|
| 2596 | NOTE: for every f_i we run only ONCE along w_i saving partial sums into a temporary array of polys of size m |
---|
| 2597 | */ |
---|
[9c1b63] | 2598 | ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing) |
---|
[90a60f] | 2599 | { |
---|
| 2600 | // #ifdef DEBU |
---|
| 2601 | // WarnS("tensorModuleMult!!!!"); |
---|
| 2602 | |
---|
| 2603 | assume(m > 0); |
---|
| 2604 | assume(M != NULL); |
---|
| 2605 | |
---|
| 2606 | const int n = rRing->N; |
---|
| 2607 | |
---|
| 2608 | assume(M->rank <= m * n); |
---|
| 2609 | |
---|
| 2610 | const int k = IDELEMS(M); |
---|
| 2611 | |
---|
| 2612 | ideal idTemp = idInit(k,m); // = {f_1, ..., f_k } |
---|
| 2613 | |
---|
| 2614 | for( int i = 0; i < k; i++ ) // for every w \in M |
---|
| 2615 | { |
---|
| 2616 | poly pTempSum = NULL; |
---|
| 2617 | |
---|
| 2618 | poly w = M->m[i]; |
---|
| 2619 | |
---|
| 2620 | while(w != NULL) // for each term of w... |
---|
| 2621 | { |
---|
| 2622 | poly h = p_Head(w, rRing); |
---|
| 2623 | |
---|
| 2624 | const int gen = p_GetComp(h, rRing); // 1 ... |
---|
| 2625 | |
---|
| 2626 | assume(gen > 0); |
---|
| 2627 | assume(gen <= n*m); |
---|
| 2628 | |
---|
| 2629 | // TODO: write a formula with %, / instead of while! |
---|
| 2630 | /* |
---|
| 2631 | int c = gen; |
---|
| 2632 | int v = 1; |
---|
| 2633 | while(c > m) |
---|
| 2634 | { |
---|
| 2635 | c -= m; |
---|
| 2636 | v++; |
---|
| 2637 | } |
---|
| 2638 | */ |
---|
| 2639 | |
---|
[592906] | 2640 | int cc = gen % m; |
---|
[90a60f] | 2641 | if( cc == 0) cc = m; |
---|
| 2642 | int vv = 1 + (gen - cc) / m; |
---|
| 2643 | |
---|
| 2644 | // assume( cc == c ); |
---|
| 2645 | // assume( vv == v ); |
---|
| 2646 | |
---|
| 2647 | // 1<= c <= m |
---|
| 2648 | assume( cc > 0 ); |
---|
| 2649 | assume( cc <= m ); |
---|
| 2650 | |
---|
| 2651 | assume( vv > 0 ); |
---|
| 2652 | assume( vv <= n ); |
---|
| 2653 | |
---|
| 2654 | assume( (cc + (vv-1)*m) == gen ); |
---|
| 2655 | |
---|
[9c1b63] | 2656 | p_IncrExp(h, vv, rRing); // h *= var(j) && // p_AddExp(h, vv, 1, rRing); |
---|
[592906] | 2657 | p_SetComp(h, cc, rRing); |
---|
[90a60f] | 2658 | |
---|
| 2659 | p_Setm(h, rRing); // addjust degree after the previous steps! |
---|
| 2660 | |
---|
| 2661 | pTempSum = p_Add_q(pTempSum, h, rRing); // it is slow since h will be usually put to the back of pTempSum!!! |
---|
| 2662 | |
---|
| 2663 | pIter(w); |
---|
| 2664 | } |
---|
| 2665 | |
---|
| 2666 | idTemp->m[i] = pTempSum; |
---|
| 2667 | } |
---|
| 2668 | |
---|
| 2669 | // simplify idTemp??? |
---|
| 2670 | |
---|
| 2671 | ideal idResult = id_Transp(idTemp, rRing); |
---|
| 2672 | |
---|
| 2673 | id_Delete(&idTemp, rRing); |
---|
| 2674 | |
---|
| 2675 | return(idResult); |
---|
| 2676 | } |
---|