[0e1846] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[416465] | 4 | /* $Id: ideals.cc,v 1.73 1999-11-15 17:20:06 obachman Exp $ */ |
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[0e1846] | 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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| 9 | /* includes */ |
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| 10 | #include "mod2.h" |
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| 11 | #include "tok.h" |
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| 12 | #include "mmemory.h" |
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| 13 | #include "febase.h" |
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| 14 | #include "numbers.h" |
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| 15 | #include "polys.h" |
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| 16 | #include "ipid.h" |
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| 17 | #include "ring.h" |
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| 18 | #include "kstd1.h" |
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| 19 | #include "matpol.h" |
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| 20 | #include "weight.h" |
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| 21 | #include "intvec.h" |
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| 22 | #include "syz.h" |
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| 23 | #include "ideals.h" |
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| 24 | #include "lists.h" |
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[416465] | 25 | #include "prCopy.h" |
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[0e1846] | 26 | |
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| 27 | |
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[ef72ff3] | 28 | /* #define WITH_OLD_MINOR */ |
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[416465] | 29 | #define pCopy_noCheck(p) pCopy(p) |
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[c616d1] | 30 | |
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[0e1846] | 31 | static poly * idpower; |
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| 32 | /*collects the monomials in makemonoms, must be allocated befor*/ |
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| 33 | static int idpowerpoint; |
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| 34 | /*index of the actual monomial in idpower*/ |
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| 35 | static poly * givenideal; |
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| 36 | /*the ideal from which a power is computed*/ |
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| 37 | |
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| 38 | /*0 implementation*/ |
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| 39 | |
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| 40 | /*2 |
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| 41 | * initialise an ideal |
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| 42 | */ |
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[c616d1] | 43 | #ifdef PDEBUG |
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[0e1846] | 44 | ideal idDBInit(int idsize, int rank, char *f, int l) |
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| 45 | #else |
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| 46 | ideal idInit(int idsize, int rank) |
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| 47 | #endif |
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| 48 | { |
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| 49 | /*- initialise an ideal -*/ |
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[c616d1] | 50 | #if defined(MDEBUG) && defined(PDEBUG) |
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[b7b08c] | 51 | ideal hh = (ideal )mmDBAllocBlock(sizeof(sip_sideal),f,l); |
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[0e1846] | 52 | #else |
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[b7b08c] | 53 | ideal hh = (ideal )AllocSizeOf(sip_sideal); |
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[0e1846] | 54 | #endif |
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| 55 | hh->nrows = 1; |
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| 56 | hh->rank = rank; |
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| 57 | IDELEMS(hh) = idsize; |
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| 58 | if (idsize>0) |
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| 59 | { |
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[c616d1] | 60 | #if defined(MDEBUG) && defined(PDEBUG) |
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[0e1846] | 61 | hh->m = (poly *)mmDBAllocBlock0(idsize*sizeof(poly),f,l); |
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| 62 | #else |
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| 63 | hh->m = (poly *)Alloc0(idsize*sizeof(poly)); |
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| 64 | #endif |
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| 65 | } |
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| 66 | else |
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| 67 | hh->m=NULL; |
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| 68 | return hh; |
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| 69 | } |
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| 70 | |
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[416465] | 71 | #ifndef __OPTIMIZE__ |
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| 72 | // this is mainly for outputting an ideal within the debugger |
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[b982ef] | 73 | void idPrint(ideal id) |
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| 74 | { |
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| 75 | Print("Module of rank %d,real rank %d and %d generators.\n", |
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| 76 | id->rank,idRankFreeModule(id),IDELEMS(id)); |
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| 77 | for (int i=0;i<IDELEMS(id);i++) |
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| 78 | { |
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| 79 | if (id->m[i]!=NULL) |
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| 80 | { |
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| 81 | Print("generator %d: ",i);pWrite(id->m[i]); |
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| 82 | } |
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| 83 | } |
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| 84 | } |
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[416465] | 85 | #endif |
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[b982ef] | 86 | |
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[0e1846] | 87 | /*2 |
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| 88 | * initialise the maximal ideal (at 0) |
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| 89 | */ |
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| 90 | ideal idMaxIdeal (void) |
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| 91 | { |
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| 92 | int l; |
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| 93 | ideal hh=NULL; |
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| 94 | |
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| 95 | hh=idInit(pVariables,1); |
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| 96 | for (l=0; l<pVariables; l++) |
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| 97 | { |
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| 98 | hh->m[l] = pOne(); |
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| 99 | pSetExp(hh->m[l],l+1,1); |
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| 100 | pSetm(hh->m[l]); |
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| 101 | } |
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| 102 | return hh; |
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| 103 | } |
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| 104 | |
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| 105 | /*2 |
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| 106 | * deletes an ideal/matrix |
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| 107 | */ |
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[c616d1] | 108 | #ifdef PDEBUG |
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[25f470] | 109 | void idDBDelete (ideal* h, char *f, int l) |
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| 110 | #else |
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[0e1846] | 111 | void idDelete (ideal * h) |
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[25f470] | 112 | #endif |
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[0e1846] | 113 | { |
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[25f470] | 114 | int j,elems; |
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| 115 | if (*h == NULL) |
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| 116 | return; |
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| 117 | elems=j=(*h)->nrows*(*h)->ncols; |
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[0e1846] | 118 | if (j>0) |
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| 119 | { |
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| 120 | do |
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| 121 | { |
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[055a19] | 122 | #if defined(MDEBUG) && defined(PDEBUG) |
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| 123 | pDBDelete(&((*h)->m[--j]),mm_specHeap, f,l); |
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[25f470] | 124 | #else |
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[0e1846] | 125 | pDelete(&((*h)->m[--j])); |
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[25f470] | 126 | #endif |
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[0e1846] | 127 | } |
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| 128 | while (j>0); |
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[c616d1] | 129 | #if defined(MDEBUG) && defined(PDEBUG) |
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[25f470] | 130 | mmDBFreeBlock((ADDRESS)((*h)->m),sizeof(poly)*elems,f,l); |
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| 131 | #else |
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| 132 | Free((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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| 133 | #endif |
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[0e1846] | 134 | } |
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[c616d1] | 135 | #if defined(MDEBUG) && defined(PDEBUG) |
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[b7b08c] | 136 | mmDBFreeBlock((ADDRESS)(*h),sizeof(sip_sideal),f,l); |
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[25f470] | 137 | #else |
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[b7b08c] | 138 | FreeSizeOf((ADDRESS)*h,sip_sideal); |
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[25f470] | 139 | #endif |
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[0e1846] | 140 | *h=NULL; |
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| 141 | } |
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| 142 | |
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| 143 | /*2 |
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| 144 | *gives an ideal the minimal possible size |
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| 145 | */ |
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| 146 | void idSkipZeroes (ideal ide) |
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| 147 | { |
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[25f470] | 148 | int k; |
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| 149 | int j = -1; |
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| 150 | BOOLEAN change=FALSE; |
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[0e1846] | 151 | for (k=0; k<IDELEMS(ide); k++) |
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| 152 | { |
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| 153 | if (ide->m[k] != NULL) |
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| 154 | { |
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| 155 | j++; |
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[25f470] | 156 | if (change) |
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| 157 | { |
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| 158 | ide->m[j] = ide->m[k]; |
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| 159 | } |
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| 160 | } |
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| 161 | else |
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| 162 | { |
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| 163 | change=TRUE; |
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[0e1846] | 164 | } |
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| 165 | } |
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[25f470] | 166 | if (change) |
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[0e1846] | 167 | { |
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[25f470] | 168 | if (j == -1) |
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| 169 | j = 0; |
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| 170 | else |
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[43580ac] | 171 | { |
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[25f470] | 172 | for (k=j+1; k<IDELEMS(ide); k++) |
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| 173 | ide->m[k] = NULL; |
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| 174 | } |
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| 175 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
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| 176 | IDELEMS(ide) = j+1; |
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[0e1846] | 177 | } |
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| 178 | } |
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| 179 | |
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| 180 | /*2 |
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| 181 | * ideal id = (id[i]) |
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| 182 | * result is leadcoeff(id[i]) = 1 |
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| 183 | */ |
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| 184 | void idNorm(ideal id) |
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| 185 | { |
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| 186 | for (int i=0; i<IDELEMS(id); i++) |
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| 187 | { |
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| 188 | if (id->m[i] != NULL) |
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| 189 | { |
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| 190 | pNorm(id->m[i]); |
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| 191 | } |
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| 192 | } |
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| 193 | } |
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| 194 | |
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| 195 | /*2 |
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| 196 | * ideal id = (id[i]), c any number |
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| 197 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
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| 198 | */ |
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| 199 | void idDelMultiples(ideal id) |
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| 200 | { |
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| 201 | int i, j, t; |
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| 202 | int k = IDELEMS(id), l = k; |
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| 203 | for (i=k-2; i>=0; i--) |
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| 204 | { |
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| 205 | if (id->m[i]!=NULL) |
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| 206 | { |
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| 207 | for (j=l-1; j>i; j--) |
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| 208 | { |
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| 209 | if ((id->m[j]!=NULL) |
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| 210 | && (pComparePolys(id->m[i], id->m[j]))) |
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| 211 | { |
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| 212 | pDelete(&id->m[j]); |
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| 213 | l--; |
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| 214 | for(t=j; t<l; t++) |
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| 215 | { |
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| 216 | id->m[t] = id->m[t+1]; |
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| 217 | } |
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| 218 | } |
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| 219 | } |
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| 220 | } |
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| 221 | } |
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| 222 | if (l != k) |
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| 223 | { |
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| 224 | pEnlargeSet(&id->m, k, l-k); |
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| 225 | IDELEMS(id) = l; |
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| 226 | } |
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| 227 | } |
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| 228 | |
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| 229 | /*2 |
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| 230 | * ideal id = (id[i]) |
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| 231 | * if id[i] = id[j] then id[j] is deleted for j > i |
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| 232 | */ |
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| 233 | void idDelEquals(ideal id) |
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| 234 | { |
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| 235 | int i, j, t; |
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| 236 | int k = IDELEMS(id), l = k; |
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| 237 | for (i=k-2; i>=0; i--) |
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| 238 | { |
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| 239 | for (j=l-1; j>i; j--) |
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| 240 | { |
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| 241 | if (pEqualPolys(id->m[i], id->m[j])) |
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| 242 | { |
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| 243 | pDelete(&id->m[j]); |
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| 244 | l--; |
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| 245 | for(t=j; t<l; t++) |
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| 246 | { |
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| 247 | id->m[t] = id->m[t+1]; |
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| 248 | } |
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| 249 | } |
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| 250 | } |
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| 251 | } |
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| 252 | if (l != k) |
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| 253 | { |
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| 254 | pEnlargeSet(&id->m, k, l-k); |
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| 255 | IDELEMS(id) = l; |
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| 256 | } |
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| 257 | } |
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| 258 | |
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[26ae12] | 259 | // |
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| 260 | // Delete id[j], if Lm(j) == Lm(i) and j > i |
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| 261 | // |
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| 262 | void idDelLmEquals(ideal id) |
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| 263 | { |
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| 264 | int i, j, t; |
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| 265 | int k = IDELEMS(id), l = k; |
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| 266 | for (i=k-2; i>=0; i--) |
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| 267 | { |
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| 268 | for (j=l-1; j>i; j--) |
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| 269 | { |
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| 270 | if (pLmEqual(id->m[i], id->m[j])) |
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| 271 | { |
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| 272 | pDelete(&id->m[j]); |
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| 273 | l--; |
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| 274 | for(t=j; t<l; t++) |
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| 275 | { |
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| 276 | id->m[t] = id->m[t+1]; |
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| 277 | } |
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| 278 | } |
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| 279 | } |
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| 280 | } |
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| 281 | if (l != k) |
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| 282 | { |
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| 283 | pEnlargeSet(&id->m, k, l-k); |
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| 284 | IDELEMS(id) = l; |
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| 285 | } |
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| 286 | } |
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[eb816e] | 287 | |
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[26ae12] | 288 | void idDelDiv(ideal id) |
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| 289 | { |
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| 290 | int i, j, t; |
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| 291 | int k = IDELEMS(id), l = k; |
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| 292 | for (i=k-2; i>=0; i--) |
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| 293 | { |
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| 294 | for (j=l-1; j>i; j--) |
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| 295 | { |
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[eb816e] | 296 | |
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[26ae12] | 297 | if (((id->m[j] != NULL) && pDivisibleBy(id->m[i], id->m[j])) || |
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| 298 | (id->m[i] == NULL && id->m[j] == NULL)) |
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| 299 | { |
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| 300 | pDelete(&id->m[j]); |
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| 301 | l--; |
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| 302 | for(t=j; t<l; t++) |
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| 303 | { |
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| 304 | id->m[t] = id->m[t+1]; |
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| 305 | } |
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| 306 | } |
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| 307 | } |
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| 308 | } |
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| 309 | if (l != k) |
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| 310 | { |
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| 311 | pEnlargeSet(&id->m, k, l-k); |
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| 312 | IDELEMS(id) = l; |
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| 313 | } |
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| 314 | } |
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[eb816e] | 315 | |
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[26ae12] | 316 | |
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[0e1846] | 317 | /*2 |
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| 318 | * copy an ideal |
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| 319 | */ |
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[c616d1] | 320 | #ifdef PDEBUG |
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[0e1846] | 321 | ideal idDBCopy(ideal h1,char *f,int l) |
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| 322 | #else |
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| 323 | ideal idCopy (ideal h1) |
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| 324 | #endif |
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| 325 | { |
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| 326 | int i; |
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| 327 | ideal h2; |
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| 328 | |
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[9c7b9a] | 329 | #ifdef PDEBUG |
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| 330 | idDBTest(h1,f,l); |
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| 331 | #endif |
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[667247] | 332 | //#ifdef TEST |
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[0e1846] | 333 | if (h1 == NULL) |
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| 334 | { |
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[c616d1] | 335 | #ifdef PDEBUG |
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[0e1846] | 336 | h2=idDBInit(1,1,f,l); |
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| 337 | #else |
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| 338 | h2=idInit(1,1); |
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| 339 | #endif |
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| 340 | } |
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| 341 | else |
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[667247] | 342 | //#endif |
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[0e1846] | 343 | { |
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[c616d1] | 344 | #ifdef PDEBUG |
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[0e1846] | 345 | h2=idDBInit(IDELEMS(h1),h1->rank,f,l); |
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| 346 | #else |
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| 347 | h2=idInit(IDELEMS(h1),h1->rank); |
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| 348 | #endif |
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| 349 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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[055a19] | 350 | #if defined(PDEBUG) && defined(MDEBUG) |
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[0e1846] | 351 | h2->m[i] = pDBCopy(h1->m[i],f,l); |
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| 352 | #else |
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| 353 | h2->m[i] = pCopy(h1->m[i]); |
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| 354 | #endif |
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| 355 | } |
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| 356 | return h2; |
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| 357 | } |
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| 358 | |
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| 359 | #ifdef PDEBUG |
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| 360 | void idDBTest(ideal h1,char *f,int l) |
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| 361 | { |
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| 362 | int i; |
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| 363 | |
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| 364 | if (h1 != NULL) |
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| 365 | { |
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[25f470] | 366 | #ifdef MDEBUG |
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| 367 | mmDBTestBlock(h1,sizeof(*h1),f,l); |
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[055a19] | 368 | /* to be able to test matrices: */ |
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| 369 | mmDBTestBlock(h1->m,h1->ncols*h1->nrows*sizeof(poly),f,l); |
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[25f470] | 370 | #endif |
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[e974a2] | 371 | /* to be able to test matrices: */ |
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[055a19] | 372 | for (i=(h1->ncols*h1->nrows)-1; i>=0; i--) |
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[0e1846] | 373 | pDBTest(h1->m[i],f,l); |
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[9c7b9a] | 374 | int new_rk=idRankFreeModule(h1); |
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| 375 | if(new_rk > h1->rank) |
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| 376 | { |
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| 377 | Print("wrong rank %d (should be %d) in %s:%d\n", |
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| 378 | h1->rank, new_rk, f,l); |
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| 379 | h1->rank=new_rk; |
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| 380 | } |
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[0e1846] | 381 | } |
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| 382 | } |
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| 383 | #endif |
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| 384 | |
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| 385 | /*3 |
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| 386 | * for idSort: compare a and b revlex inclusive module comp. |
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| 387 | */ |
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| 388 | static int pComp_RevLex(poly a, poly b) |
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| 389 | { |
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| 390 | int l=pVariables; |
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[50619f7] | 391 | while ((l>0) && (pGetExp(a,l)==pGetExp(b,l))) l--; |
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| 392 | if (l==0) |
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| 393 | { |
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| 394 | if (pGetComp(a)==pGetComp(b)) return 0; |
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| 395 | if (pGetComp(a)>pGetComp(b)) return 1; |
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| 396 | } |
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[0e1846] | 397 | else if (pGetExp(a,l)>pGetExp(b,l)) |
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| 398 | return 1; |
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[50619f7] | 399 | return -1; |
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[0e1846] | 400 | } |
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| 401 | |
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| 402 | /*2 |
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| 403 | *sorts the ideal w.r.t. the actual ringordering |
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| 404 | *uses lex-ordering when nolex = FALSE |
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| 405 | */ |
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| 406 | intvec *idSort(ideal id,BOOLEAN nolex) |
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| 407 | { |
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| 408 | poly p,q; |
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[477993] | 409 | intvec * result = NewIntvec1(IDELEMS(id)); |
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[0e1846] | 410 | int i, j, actpos=0, newpos, l; |
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| 411 | int diff, olddiff, lastcomp, newcomp; |
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| 412 | BOOLEAN notFound; |
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| 413 | |
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| 414 | pCompProc oldComp=pComp0; |
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| 415 | |
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| 416 | if (!nolex) pComp0=pComp_RevLex; |
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| 417 | |
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| 418 | for (i=0;i<IDELEMS(id);i++) |
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| 419 | { |
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| 420 | if (id->m[i]!=NULL) |
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| 421 | { |
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| 422 | notFound = TRUE; |
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| 423 | newpos = actpos / 2; |
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| 424 | diff = (actpos+1) / 2; |
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| 425 | diff = (diff+1) / 2; |
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| 426 | lastcomp = pComp0(id->m[i],id->m[(*result)[newpos]]); |
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| 427 | if (lastcomp<0) |
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| 428 | { |
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| 429 | newpos -= diff; |
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| 430 | } |
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| 431 | else if (lastcomp>0) |
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| 432 | { |
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| 433 | newpos += diff; |
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| 434 | } |
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| 435 | else |
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| 436 | { |
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| 437 | notFound = FALSE; |
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| 438 | } |
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| 439 | while ((newpos>=0) && (newpos<actpos) && (notFound)) |
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| 440 | { |
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| 441 | newcomp = pComp0(id->m[i],id->m[(*result)[newpos]]); |
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| 442 | olddiff = diff; |
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| 443 | if (diff>1) |
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| 444 | { |
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| 445 | diff = (diff+1) / 2; |
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| 446 | if ((newcomp==1) |
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| 447 | && (actpos-newpos>1) |
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| 448 | && (diff>1) |
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| 449 | && (newpos+diff>=actpos)) |
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| 450 | { |
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| 451 | diff = actpos-newpos-1; |
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| 452 | } |
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| 453 | else if ((newcomp==-1) |
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| 454 | && (diff>1) |
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| 455 | && (newpos<diff)) |
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| 456 | { |
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| 457 | diff = newpos; |
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| 458 | } |
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| 459 | } |
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| 460 | if (newcomp<0) |
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| 461 | { |
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| 462 | if ((olddiff==1) && (lastcomp>0)) |
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| 463 | notFound = FALSE; |
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| 464 | else |
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| 465 | newpos -= diff; |
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| 466 | } |
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| 467 | else if (newcomp>0) |
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| 468 | { |
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| 469 | if ((olddiff==1) && (lastcomp<0)) |
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| 470 | { |
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| 471 | notFound = FALSE; |
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| 472 | newpos++; |
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| 473 | } |
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| 474 | else |
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| 475 | { |
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| 476 | newpos += diff; |
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| 477 | } |
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| 478 | } |
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| 479 | else |
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| 480 | { |
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| 481 | notFound = FALSE; |
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| 482 | } |
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| 483 | lastcomp = newcomp; |
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| 484 | if (diff==0) notFound=FALSE; /*hs*/ |
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| 485 | } |
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| 486 | if (newpos<0) newpos = 0; |
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[0e1284] | 487 | if (newpos>actpos) newpos = actpos; |
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| 488 | while ((newpos<actpos) && (pComp0(id->m[i],id->m[(*result)[newpos]])==0)) |
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| 489 | newpos++; |
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| 490 | for (j=actpos;j>newpos;j--) |
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[0e1846] | 491 | { |
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[0e1284] | 492 | (*result)[j] = (*result)[j-1]; |
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[0e1846] | 493 | } |
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[0e1284] | 494 | (*result)[newpos] = i; |
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[0e1846] | 495 | actpos++; |
---|
| 496 | } |
---|
| 497 | } |
---|
| 498 | for (j=0;j<actpos;j++) (*result)[j]++; |
---|
| 499 | pComp0=oldComp; |
---|
| 500 | return result; |
---|
| 501 | } |
---|
| 502 | |
---|
| 503 | /*2 |
---|
| 504 | * concat the lists h1 and h2 without zeros |
---|
| 505 | */ |
---|
| 506 | ideal idSimpleAdd (ideal h1,ideal h2) |
---|
| 507 | { |
---|
| 508 | int i,j,r,l; |
---|
| 509 | ideal result; |
---|
| 510 | |
---|
| 511 | if (h1==NULL) return idCopy(h2); |
---|
| 512 | if (h2==NULL) return idCopy(h1); |
---|
[4b5c87] | 513 | j = IDELEMS(h1)-1; |
---|
| 514 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
| 515 | i = IDELEMS(h2)-1; |
---|
| 516 | while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
| 517 | r = max(h1->rank,h2->rank); |
---|
| 518 | if (i+j==(-2)) |
---|
| 519 | return idInit(1,r); |
---|
[0e1846] | 520 | else |
---|
[4b5c87] | 521 | result=idInit(i+j+2,r); |
---|
| 522 | for (l=j; l>=0; l--) |
---|
[0e1846] | 523 | { |
---|
[4b5c87] | 524 | result->m[l] = pCopy(h1->m[l]); |
---|
[0e1846] | 525 | } |
---|
[4b5c87] | 526 | r = i+j+1; |
---|
| 527 | for (l=i; l>=0; l--, r--) |
---|
[0e1846] | 528 | { |
---|
| 529 | result->m[r] = pCopy(h2->m[l]); |
---|
| 530 | } |
---|
| 531 | return result; |
---|
| 532 | } |
---|
| 533 | |
---|
| 534 | /*2 |
---|
| 535 | * h1 + h2 |
---|
| 536 | */ |
---|
| 537 | ideal idAdd (ideal h1,ideal h2) |
---|
| 538 | { |
---|
| 539 | ideal result = idSimpleAdd(h1,h2); |
---|
| 540 | ideal tmp = idCompactify(result); |
---|
| 541 | |
---|
| 542 | idDelete(&result); |
---|
| 543 | return tmp; |
---|
| 544 | } |
---|
| 545 | |
---|
| 546 | /*2 |
---|
| 547 | * h1 * h2 |
---|
| 548 | */ |
---|
| 549 | ideal idMult (ideal h1,ideal h2) |
---|
| 550 | { |
---|
| 551 | int i,j,k; |
---|
| 552 | ideal hh; |
---|
| 553 | |
---|
| 554 | j = IDELEMS(h1); |
---|
| 555 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
| 556 | i = IDELEMS(h2); |
---|
| 557 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
| 558 | j = j * i; |
---|
| 559 | if (j == 0) |
---|
| 560 | hh = idInit(1,1); |
---|
| 561 | else |
---|
| 562 | hh=idInit(j,1); |
---|
| 563 | if (h1->rank<h2->rank) |
---|
| 564 | hh->rank = h2->rank; |
---|
| 565 | else |
---|
| 566 | hh->rank = h1->rank; |
---|
| 567 | if (j==0) return hh; |
---|
| 568 | k = 0; |
---|
| 569 | for (i=0; i<IDELEMS(h1); i++) |
---|
| 570 | { |
---|
| 571 | if (h1->m[i] != NULL) |
---|
| 572 | { |
---|
| 573 | for (j=0; j<IDELEMS(h2); j++) |
---|
| 574 | { |
---|
| 575 | if (h2->m[j] != NULL) |
---|
| 576 | { |
---|
| 577 | hh->m[k] = pMult(pCopy(h1->m[i]),pCopy(h2->m[j])); |
---|
| 578 | k++; |
---|
| 579 | } |
---|
| 580 | } |
---|
| 581 | } |
---|
| 582 | } |
---|
| 583 | { |
---|
| 584 | ideal tmp = idCompactify(hh); |
---|
| 585 | idDelete(&hh); |
---|
| 586 | return tmp; |
---|
[5990ae] | 587 | //return hh; |
---|
[0e1846] | 588 | } |
---|
| 589 | } |
---|
| 590 | |
---|
| 591 | /*2 |
---|
| 592 | *returns true if h is the zero ideal |
---|
| 593 | */ |
---|
| 594 | BOOLEAN idIs0 (ideal h) |
---|
| 595 | { |
---|
| 596 | int i; |
---|
| 597 | |
---|
| 598 | if (h == NULL) return TRUE; |
---|
| 599 | i = IDELEMS(h); |
---|
| 600 | while ((i > 0) && (h->m[i-1] == NULL)) |
---|
| 601 | { |
---|
| 602 | i--; |
---|
| 603 | } |
---|
| 604 | if (i == 0) |
---|
| 605 | return TRUE; |
---|
| 606 | else |
---|
| 607 | return FALSE; |
---|
| 608 | } |
---|
| 609 | |
---|
| 610 | /*2 |
---|
| 611 | * return the maximal component number found in any polynomial in s |
---|
| 612 | */ |
---|
| 613 | int idRankFreeModule (ideal s) |
---|
| 614 | { |
---|
| 615 | if (s!=NULL) |
---|
| 616 | { |
---|
| 617 | int j=0; |
---|
| 618 | int l=IDELEMS(s); |
---|
| 619 | poly *p=s->m; |
---|
| 620 | int k; |
---|
| 621 | |
---|
| 622 | for (; l != 0; l--) |
---|
| 623 | { |
---|
| 624 | if (*p!=NULL) |
---|
| 625 | { |
---|
| 626 | k = pMaxComp(*p); |
---|
| 627 | if (k>j) j = k; |
---|
| 628 | } |
---|
| 629 | p++; |
---|
| 630 | } |
---|
| 631 | return j; |
---|
| 632 | } |
---|
| 633 | return -1; |
---|
| 634 | } |
---|
| 635 | |
---|
| 636 | /*2 |
---|
| 637 | *returns true if id is homogenous with respect to the aktual weights |
---|
| 638 | */ |
---|
| 639 | BOOLEAN idHomIdeal (ideal id, ideal Q) |
---|
| 640 | { |
---|
| 641 | int i; |
---|
| 642 | BOOLEAN b; |
---|
| 643 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
---|
| 644 | i = 0; |
---|
| 645 | b = TRUE; |
---|
| 646 | while ((i < IDELEMS(id)) && b) |
---|
| 647 | { |
---|
| 648 | b = pIsHomogeneous(id->m[i]); |
---|
| 649 | i++; |
---|
| 650 | } |
---|
| 651 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
| 652 | { |
---|
| 653 | i=0; |
---|
| 654 | while ((i < IDELEMS(Q)) && b) |
---|
| 655 | { |
---|
| 656 | b = pIsHomogeneous(Q->m[i]); |
---|
| 657 | i++; |
---|
| 658 | } |
---|
| 659 | } |
---|
| 660 | return b; |
---|
| 661 | } |
---|
| 662 | |
---|
| 663 | /*2 |
---|
| 664 | *returns a minimized set of generators of h1 |
---|
| 665 | */ |
---|
| 666 | ideal idMinBase (ideal h1) |
---|
| 667 | { |
---|
| 668 | ideal h2, h3,h4,e; |
---|
| 669 | int j,k; |
---|
| 670 | int i,l,ll; |
---|
| 671 | intvec * wth; |
---|
| 672 | BOOLEAN homog; |
---|
| 673 | |
---|
| 674 | homog = idHomModule(h1,currQuotient,&wth); |
---|
| 675 | if ((currRing->OrdSgn == 1) && (!homog)) |
---|
| 676 | { |
---|
| 677 | Warn("minbase applies only to the local or homogeneous case"); |
---|
| 678 | e=idCopy(h1); |
---|
| 679 | return e; |
---|
| 680 | } |
---|
| 681 | if ((currRing->OrdSgn == 1) && (homog)) |
---|
| 682 | { |
---|
[7ae776] | 683 | lists re=min_std(h1,currQuotient,(tHomog)homog,&wth,NULL,0,3); |
---|
[0e1846] | 684 | h2 = (ideal)re->m[1].data; |
---|
| 685 | re->m[1].data = NULL; |
---|
| 686 | re->m[1].rtyp = NONE; |
---|
| 687 | re->Clean(); |
---|
| 688 | return h2; |
---|
| 689 | } |
---|
| 690 | e=idInit(1,h1->rank); |
---|
| 691 | if (idIs0(h1)) |
---|
| 692 | { |
---|
| 693 | return e; |
---|
| 694 | } |
---|
| 695 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
---|
| 696 | IDELEMS(e) = 16; |
---|
[a1c44e] | 697 | h2 = kStd(h1,currQuotient,isNotHomog,NULL); |
---|
[0e1846] | 698 | h3 = idMaxIdeal(); |
---|
| 699 | h4=idMult(h2,h3); |
---|
| 700 | idDelete(&h3); |
---|
[a1c44e] | 701 | h3=kStd(h4,currQuotient,isNotHomog,NULL); |
---|
[0e1846] | 702 | k = IDELEMS(h3); |
---|
| 703 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
---|
| 704 | j = -1; |
---|
| 705 | l = IDELEMS(h2); |
---|
| 706 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
---|
| 707 | for (i=l-1; i>=0; i--) |
---|
| 708 | { |
---|
| 709 | if (h2->m[i] != NULL) |
---|
| 710 | { |
---|
| 711 | ll = 0; |
---|
| 712 | while ((ll < k) && ((h3->m[ll] == NULL) |
---|
| 713 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
---|
| 714 | ll++; |
---|
| 715 | if (ll >= k) |
---|
| 716 | { |
---|
| 717 | j++; |
---|
| 718 | if (j > IDELEMS(e)-1) |
---|
| 719 | { |
---|
| 720 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
| 721 | IDELEMS(e) += 16; |
---|
| 722 | } |
---|
| 723 | e->m[j] = pCopy(h2->m[i]); |
---|
| 724 | } |
---|
| 725 | } |
---|
| 726 | } |
---|
| 727 | idDelete(&h2); |
---|
| 728 | idDelete(&h3); |
---|
| 729 | idDelete(&h4); |
---|
[58bbda] | 730 | if (currQuotient!=NULL) |
---|
[0e1846] | 731 | { |
---|
[58bbda] | 732 | h3=idInit(1,e->rank); |
---|
| 733 | h2=kNF(h3,currQuotient,e); |
---|
| 734 | idDelete(&h3); |
---|
[0e1846] | 735 | idDelete(&e); |
---|
| 736 | e=h2; |
---|
| 737 | } |
---|
| 738 | idSkipZeroes(e); |
---|
| 739 | return e; |
---|
| 740 | } |
---|
| 741 | |
---|
| 742 | /*2 |
---|
| 743 | *the minimal index of used variables - 1 |
---|
| 744 | */ |
---|
| 745 | int pLowVar (poly p) |
---|
| 746 | { |
---|
| 747 | int k,l,lex; |
---|
| 748 | |
---|
| 749 | if (p == NULL) return -1; |
---|
| 750 | |
---|
| 751 | k = 32000;/*a very large dummy value*/ |
---|
| 752 | while (p != NULL) |
---|
| 753 | { |
---|
| 754 | l = 1; |
---|
| 755 | lex = pGetExp(p,l); |
---|
[7b4121] | 756 | while ((l < pVariables) && (lex == 0)) |
---|
[0e1846] | 757 | { |
---|
| 758 | l++; |
---|
| 759 | lex = pGetExp(p,l); |
---|
| 760 | } |
---|
| 761 | l--; |
---|
| 762 | if (l < k) k = l; |
---|
| 763 | pIter(p); |
---|
| 764 | } |
---|
| 765 | return k; |
---|
| 766 | } |
---|
| 767 | |
---|
| 768 | /*3 |
---|
| 769 | *multiplies p with t (!cas) or (t-1) |
---|
| 770 | *the index of t is:1, so we have to shift all variables |
---|
| 771 | *p is NOT in the actual ring, it has no t |
---|
| 772 | */ |
---|
| 773 | static poly pMultWithT (poly p,BOOLEAN cas) |
---|
| 774 | { |
---|
| 775 | /*qp is the working pointer in p*/ |
---|
| 776 | /*result is the result, qresult is the working pointer*/ |
---|
| 777 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
---|
| 778 | poly result,qp,pp; |
---|
| 779 | poly qresult=NULL; |
---|
| 780 | poly qpp=NULL; |
---|
| 781 | int i,j,lex; |
---|
| 782 | number n; |
---|
| 783 | |
---|
| 784 | pp = NULL; |
---|
| 785 | result = NULL; |
---|
| 786 | qp = p; |
---|
| 787 | while (qp != NULL) |
---|
| 788 | { |
---|
| 789 | i = 0; |
---|
| 790 | if (result == NULL) |
---|
| 791 | {/*first monomial*/ |
---|
[e78cce] | 792 | result = pInit(); |
---|
[0e1846] | 793 | qresult = result; |
---|
| 794 | } |
---|
| 795 | else |
---|
| 796 | { |
---|
[e78cce] | 797 | qresult->next = pInit(); |
---|
[0e1846] | 798 | pIter(qresult); |
---|
| 799 | } |
---|
| 800 | for (j=pVariables-1; j>0; j--) |
---|
| 801 | { |
---|
| 802 | lex = pGetExp(qp,j); |
---|
| 803 | pSetExp(qresult,j+1,lex);/*copy all variables*/ |
---|
| 804 | } |
---|
| 805 | lex = pGetComp(qp); |
---|
| 806 | pSetComp(qresult,lex); |
---|
| 807 | n=nCopy(pGetCoeff(qp)); |
---|
| 808 | pSetCoeff0(qresult,n); |
---|
| 809 | qresult->next = NULL; |
---|
| 810 | pSetm(qresult); |
---|
| 811 | /*qresult is now qp brought into the actual ring*/ |
---|
| 812 | if (cas) |
---|
| 813 | { /*case: mult with t-1*/ |
---|
| 814 | pSetExp(qresult,1,0); |
---|
| 815 | pSetm(qresult); |
---|
| 816 | if (pp == NULL) |
---|
| 817 | { /*first monomial*/ |
---|
| 818 | pp = pCopy(qresult); |
---|
| 819 | qpp = pp; |
---|
| 820 | } |
---|
| 821 | else |
---|
| 822 | { |
---|
| 823 | qpp->next = pCopy(qresult); |
---|
| 824 | pIter(qpp); |
---|
| 825 | } |
---|
| 826 | pGetCoeff(qpp)=nNeg(pGetCoeff(qpp)); |
---|
| 827 | /*now qpp contains -1*qp*/ |
---|
| 828 | } |
---|
| 829 | pSetExp(qresult,1,1);/*this is mult. by t*/ |
---|
| 830 | pSetm(qresult); |
---|
| 831 | pIter(qp); |
---|
| 832 | } |
---|
| 833 | /* |
---|
| 834 | *now p is processed: |
---|
| 835 | *result contains t*p |
---|
| 836 | * if cas: pp contains -1*p (in the new ring) |
---|
| 837 | */ |
---|
| 838 | if (cas) qresult->next = pp; |
---|
| 839 | /* else qresult->next = NULL;*/ |
---|
| 840 | return result; |
---|
| 841 | } |
---|
| 842 | |
---|
| 843 | /*3 |
---|
| 844 | *deletes the place of t in p (t: variable with index 1) |
---|
| 845 | *p is NOT in the actual ring: it has pVariables+1 variables |
---|
| 846 | */ |
---|
| 847 | static poly pDivByT (poly * p,int size) |
---|
| 848 | { |
---|
| 849 | |
---|
| 850 | poly result=NULL, |
---|
| 851 | resultp=NULL , /** working pointer in result **/ |
---|
| 852 | pp; |
---|
| 853 | int i,j; |
---|
| 854 | |
---|
| 855 | while (*p != NULL) |
---|
| 856 | { |
---|
| 857 | i = 0; |
---|
| 858 | if (result == NULL) |
---|
| 859 | {/*the first monomial*/ |
---|
[e78cce] | 860 | result = pInit(); |
---|
[0e1846] | 861 | resultp = result; |
---|
| 862 | resultp->next = NULL; |
---|
| 863 | } |
---|
| 864 | else |
---|
| 865 | { |
---|
[e78cce] | 866 | resultp->next = pInit(); |
---|
[0e1846] | 867 | pIter(resultp); |
---|
| 868 | resultp->next = NULL; |
---|
| 869 | } |
---|
| 870 | for (j=1; j<=pVariables; j++) |
---|
| 871 | { |
---|
| 872 | pSetExp(resultp,j,pGetExp(*p,j+1)); |
---|
| 873 | } |
---|
| 874 | pSetComp(resultp,pGetComp(*p)); |
---|
| 875 | pSetCoeff0(resultp,pGetCoeff(*p)); |
---|
| 876 | pSetm(resultp); |
---|
| 877 | pp = (*p)->next; |
---|
| 878 | Free((ADDRESS)*p,size); |
---|
| 879 | *p = pp; |
---|
| 880 | } |
---|
| 881 | return result; |
---|
| 882 | } |
---|
| 883 | |
---|
| 884 | /*2 |
---|
| 885 | *dehomogenized the generators of the ideal id1 with the leading |
---|
| 886 | *monomial of p replaced by n |
---|
| 887 | */ |
---|
| 888 | ideal idDehomogen (ideal id1,poly p,number n) |
---|
| 889 | { |
---|
| 890 | int i; |
---|
| 891 | ideal result; |
---|
| 892 | |
---|
| 893 | if (idIs0(id1)) |
---|
| 894 | { |
---|
| 895 | return idInit(1,id1->rank); |
---|
| 896 | } |
---|
| 897 | result=idInit(IDELEMS(id1),id1->rank); |
---|
| 898 | for (i=0; i<IDELEMS(id1); i++) |
---|
| 899 | { |
---|
| 900 | result->m[i] = pDehomogen(id1->m[i],p,n); |
---|
| 901 | } |
---|
| 902 | return result; |
---|
| 903 | } |
---|
| 904 | |
---|
| 905 | /*2 |
---|
| 906 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
| 907 | */ |
---|
| 908 | void pShift (poly * p,int i) |
---|
| 909 | { |
---|
| 910 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
| 911 | int j = pMaxComp(*p),k = pMinComp(*p); |
---|
| 912 | |
---|
| 913 | if (j+i < 0) return ; |
---|
| 914 | while (qp1 != NULL) |
---|
| 915 | { |
---|
| 916 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
---|
| 917 | { |
---|
| 918 | pSetComp(qp1,pGetComp(qp1)+i); |
---|
[b9a806] | 919 | pSetmComp(qp1); |
---|
[0e1846] | 920 | qp2 = qp1; |
---|
| 921 | pIter(qp1); |
---|
| 922 | } |
---|
| 923 | else |
---|
| 924 | { |
---|
| 925 | if (qp2 == *p) |
---|
| 926 | { |
---|
| 927 | pIter(*p); |
---|
| 928 | qp2->next = NULL; |
---|
| 929 | pDelete(&qp2); |
---|
| 930 | qp2 = *p; |
---|
| 931 | qp1 = *p; |
---|
| 932 | } |
---|
| 933 | else |
---|
| 934 | { |
---|
| 935 | qp2->next = qp1->next; |
---|
| 936 | qp1->next = NULL; |
---|
| 937 | pDelete(&qp1); |
---|
| 938 | qp1 = qp2->next; |
---|
| 939 | } |
---|
| 940 | } |
---|
| 941 | } |
---|
| 942 | } |
---|
| 943 | |
---|
| 944 | /*2 |
---|
| 945 | *initialized a field with r numbers between beg and end for the |
---|
| 946 | *procedure idNextChoise |
---|
| 947 | */ |
---|
| 948 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
| 949 | { |
---|
| 950 | /*returns the first choise of r numbers between beg and end*/ |
---|
| 951 | int i; |
---|
| 952 | for (i=0; i<r; i++) |
---|
| 953 | { |
---|
| 954 | choise[i] = 0; |
---|
| 955 | } |
---|
| 956 | if (r <= end-beg+1) |
---|
| 957 | for (i=0; i<r; i++) |
---|
| 958 | { |
---|
| 959 | choise[i] = beg+i; |
---|
| 960 | } |
---|
| 961 | if (r > end-beg+1) |
---|
| 962 | *endch = TRUE; |
---|
| 963 | else |
---|
| 964 | *endch = FALSE; |
---|
| 965 | } |
---|
| 966 | |
---|
| 967 | /*2 |
---|
| 968 | *returns the next choise of r numbers between beg and end |
---|
| 969 | */ |
---|
| 970 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
| 971 | { |
---|
| 972 | int i = r-1,j; |
---|
| 973 | while ((i >= 0) && (choise[i] == end)) |
---|
| 974 | { |
---|
| 975 | i--; |
---|
| 976 | end--; |
---|
| 977 | } |
---|
| 978 | if (i == -1) |
---|
| 979 | *endch = TRUE; |
---|
| 980 | else |
---|
| 981 | { |
---|
| 982 | choise[i]++; |
---|
| 983 | for (j=i+1; j<r; j++) |
---|
| 984 | { |
---|
| 985 | choise[j] = choise[i]+j-i; |
---|
| 986 | } |
---|
| 987 | *endch = FALSE; |
---|
| 988 | } |
---|
| 989 | } |
---|
| 990 | |
---|
| 991 | /*2 |
---|
| 992 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
| 993 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
| 994 | * w.r.t. the algorithm of construction |
---|
| 995 | */ |
---|
| 996 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
| 997 | { |
---|
| 998 | int * localchoise,i,result=0; |
---|
| 999 | BOOLEAN b=FALSE; |
---|
| 1000 | |
---|
| 1001 | if (d<=1) return 1; |
---|
| 1002 | localchoise=(int*)Alloc((d-1)*sizeof(int)); |
---|
| 1003 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
| 1004 | while (!b) |
---|
| 1005 | { |
---|
| 1006 | result++; |
---|
| 1007 | i = 0; |
---|
| 1008 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
| 1009 | if (i>=t) |
---|
| 1010 | { |
---|
| 1011 | i = t+1; |
---|
| 1012 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
| 1013 | if (i>=d) |
---|
| 1014 | { |
---|
| 1015 | Free((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
| 1016 | return result; |
---|
| 1017 | } |
---|
| 1018 | } |
---|
| 1019 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
| 1020 | } |
---|
| 1021 | Free((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
| 1022 | return 0; |
---|
| 1023 | } |
---|
| 1024 | |
---|
| 1025 | /*2 |
---|
| 1026 | *computes the binomial coefficient |
---|
| 1027 | */ |
---|
| 1028 | int binom (int n,int r) |
---|
| 1029 | { |
---|
| 1030 | int i,result; |
---|
| 1031 | |
---|
| 1032 | if (r==0) return 1; |
---|
| 1033 | if (n-r<r) return binom(n,n-r); |
---|
| 1034 | result = n-r+1; |
---|
| 1035 | for (i=2;i<=r;i++) |
---|
| 1036 | { |
---|
| 1037 | result *= n-r+i; |
---|
| 1038 | result /= i; |
---|
| 1039 | } |
---|
| 1040 | return result; |
---|
| 1041 | } |
---|
| 1042 | |
---|
| 1043 | /*2 |
---|
| 1044 | *the free module of rank i |
---|
| 1045 | */ |
---|
| 1046 | ideal idFreeModule (int i) |
---|
| 1047 | { |
---|
| 1048 | int j; |
---|
| 1049 | ideal h; |
---|
| 1050 | |
---|
| 1051 | h=idInit(i,i); |
---|
| 1052 | for (j=0; j<i; j++) |
---|
| 1053 | { |
---|
| 1054 | h->m[j] = pOne(); |
---|
| 1055 | pSetComp(h->m[j],j+1); |
---|
[66a672] | 1056 | pSetmComp(h->m[j]); |
---|
[0e1846] | 1057 | } |
---|
| 1058 | return h; |
---|
| 1059 | } |
---|
| 1060 | |
---|
| 1061 | /*2 |
---|
| 1062 | * h3 := h1 intersect h2 |
---|
| 1063 | */ |
---|
| 1064 | ideal idSect (ideal h1,ideal h2) |
---|
| 1065 | { |
---|
| 1066 | ideal first=h2,second=h1,temp,temp1,result; |
---|
| 1067 | int i,j,k,flength,slength,length,rank=min(h1->rank,h2->rank); |
---|
[4c001a] | 1068 | intvec *w; |
---|
[0e1846] | 1069 | poly p,q; |
---|
| 1070 | |
---|
| 1071 | if ((idIs0(h1)) && (idIs0(h2))) return idInit(1,rank); |
---|
| 1072 | if (IDELEMS(h1)<IDELEMS(h2)) |
---|
| 1073 | { |
---|
| 1074 | first = h1; |
---|
| 1075 | second = h2; |
---|
| 1076 | } |
---|
| 1077 | flength = idRankFreeModule(first); |
---|
| 1078 | slength = idRankFreeModule(second); |
---|
| 1079 | length = max(flength,slength); |
---|
| 1080 | if (length==0) |
---|
| 1081 | { |
---|
| 1082 | length = 1; |
---|
| 1083 | } |
---|
[e960943] | 1084 | j = IDELEMS(first); |
---|
[7bab5d] | 1085 | temp = idInit(j /*IDELEMS(first)*/,length+j); |
---|
[e960943] | 1086 | |
---|
| 1087 | ring orig_ring=currRing; |
---|
[9d06971] | 1088 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
[416465] | 1089 | rSetSyzComp(length); |
---|
[e960943] | 1090 | |
---|
[0e1846] | 1091 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
---|
| 1092 | k = 0; |
---|
| 1093 | for (i=0;i<j;i++) |
---|
| 1094 | { |
---|
| 1095 | if (first->m[i]!=NULL) |
---|
| 1096 | { |
---|
[e960943] | 1097 | if (syz_ring==orig_ring) |
---|
| 1098 | temp->m[k] = pCopy(first->m[i]); |
---|
| 1099 | else |
---|
[416465] | 1100 | temp->m[k] = prCopyR(first->m[i], orig_ring); |
---|
[0e1846] | 1101 | q = pOne(); |
---|
| 1102 | pSetComp(q,i+1+length); |
---|
[66a672] | 1103 | pSetmComp(q); |
---|
[0e1846] | 1104 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
| 1105 | p = temp->m[k]; |
---|
[66a672] | 1106 | while (pNext(p)!=NULL) pIter(p); |
---|
[0e1846] | 1107 | pNext(p) = q; |
---|
| 1108 | k++; |
---|
| 1109 | } |
---|
| 1110 | } |
---|
| 1111 | pEnlargeSet(&(temp->m),IDELEMS(temp),j+IDELEMS(second)-IDELEMS(temp)); |
---|
| 1112 | IDELEMS(temp) = j+IDELEMS(second); |
---|
| 1113 | for (i=0;i<IDELEMS(second);i++) |
---|
| 1114 | { |
---|
| 1115 | if (second->m[i]!=NULL) |
---|
| 1116 | { |
---|
[e960943] | 1117 | if (syz_ring==orig_ring) |
---|
| 1118 | temp->m[k] = pCopy(second->m[i]); |
---|
| 1119 | else |
---|
[416465] | 1120 | temp->m[k] = prCopyR(second->m[i], orig_ring); |
---|
[0e1846] | 1121 | if (slength==0) pShift(&(temp->m[k]),1); |
---|
| 1122 | k++; |
---|
| 1123 | } |
---|
| 1124 | } |
---|
[a1c44e] | 1125 | temp1 = kStd(temp,currQuotient,testHomog,&w,NULL,length); |
---|
[4c001a] | 1126 | if (w!=NULL) delete w; |
---|
[0e1846] | 1127 | idDelete(&temp); |
---|
[e960943] | 1128 | |
---|
| 1129 | if(syz_ring!=orig_ring) |
---|
| 1130 | rChangeCurrRing(orig_ring,TRUE); |
---|
| 1131 | |
---|
[0e1846] | 1132 | result = idInit(IDELEMS(temp1),rank); |
---|
| 1133 | j = 0; |
---|
| 1134 | for (i=0;i<IDELEMS(temp1);i++) |
---|
| 1135 | { |
---|
| 1136 | if ((temp1->m[i]!=NULL) |
---|
[e960943] | 1137 | && (pRingGetComp(syz_ring,temp1->m[i])>length)) |
---|
[0e1846] | 1138 | { |
---|
[e960943] | 1139 | if(syz_ring==orig_ring) |
---|
| 1140 | p = pCopy(temp1->m[i]); |
---|
| 1141 | else |
---|
[416465] | 1142 | p = prCopyR(temp1->m[i], syz_ring); |
---|
[0e1846] | 1143 | while (p!=NULL) |
---|
| 1144 | { |
---|
| 1145 | q = pNext(p); |
---|
| 1146 | pNext(p) = NULL; |
---|
| 1147 | k = pGetComp(p)-1-length; |
---|
| 1148 | pSetComp(p,0); |
---|
[66a672] | 1149 | pSetmComp(p); |
---|
[0e1846] | 1150 | result->m[j] = pAdd(result->m[j],pMult(pCopy(first->m[k]),p)); |
---|
| 1151 | p = q; |
---|
| 1152 | } |
---|
| 1153 | j++; |
---|
| 1154 | } |
---|
| 1155 | } |
---|
[e960943] | 1156 | if(syz_ring!=orig_ring) |
---|
[87bef42] | 1157 | { |
---|
[b9a806] | 1158 | rChangeCurrRing(syz_ring,FALSE); |
---|
| 1159 | idDelete(&temp1); |
---|
[e960943] | 1160 | rChangeCurrRing(orig_ring,TRUE); |
---|
| 1161 | rKill(syz_ring); |
---|
[87bef42] | 1162 | } |
---|
[b9a806] | 1163 | else |
---|
| 1164 | { |
---|
| 1165 | idDelete(&temp1); |
---|
| 1166 | } |
---|
[e960943] | 1167 | |
---|
[0e1846] | 1168 | idSkipZeroes(result); |
---|
| 1169 | return result; |
---|
| 1170 | } |
---|
| 1171 | |
---|
| 1172 | /*2 |
---|
| 1173 | * ideal/module intersection for a list of objects |
---|
| 1174 | * given as 'resolvente' |
---|
| 1175 | */ |
---|
| 1176 | ideal idMultSect(resolvente arg, int length) |
---|
| 1177 | { |
---|
| 1178 | int i,j=0,k=0,syzComp,l,maxrk=-1,realrki; |
---|
| 1179 | ideal bigmat,tempstd,result; |
---|
| 1180 | poly p; |
---|
| 1181 | int isIdeal=0; |
---|
| 1182 | intvec * w=NULL; |
---|
| 1183 | |
---|
| 1184 | /* find 0-ideals and max rank -----------------------------------*/ |
---|
| 1185 | for (i=0;i<length;i++) |
---|
| 1186 | { |
---|
| 1187 | if (!idIs0(arg[i])) |
---|
| 1188 | { |
---|
| 1189 | realrki=idRankFreeModule(arg[i]); |
---|
| 1190 | k++; |
---|
| 1191 | j += IDELEMS(arg[i]); |
---|
| 1192 | if (realrki>maxrk) maxrk = realrki; |
---|
| 1193 | } |
---|
| 1194 | else |
---|
| 1195 | { |
---|
| 1196 | if (arg[i]!=NULL) |
---|
| 1197 | { |
---|
| 1198 | return idInit(1,arg[i]->rank); |
---|
| 1199 | } |
---|
| 1200 | } |
---|
| 1201 | } |
---|
| 1202 | if (maxrk == 0) |
---|
| 1203 | { |
---|
| 1204 | isIdeal = 1; |
---|
| 1205 | maxrk = 1; |
---|
| 1206 | } |
---|
| 1207 | /* init -----------------------------------------------------------*/ |
---|
| 1208 | j += maxrk; |
---|
| 1209 | syzComp = k*maxrk; |
---|
[b9a806] | 1210 | |
---|
[e960943] | 1211 | ring orig_ring=currRing; |
---|
[9d06971] | 1212 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
[416465] | 1213 | rSetSyzComp(syzComp); |
---|
[e960943] | 1214 | |
---|
| 1215 | bigmat = idInit(j,(k+1)*maxrk); |
---|
[0e1846] | 1216 | /* create unit matrices ------------------------------------------*/ |
---|
| 1217 | for (i=0;i<maxrk;i++) |
---|
| 1218 | { |
---|
| 1219 | for (j=0;j<=k;j++) |
---|
| 1220 | { |
---|
| 1221 | p = pOne(); |
---|
| 1222 | pSetComp(p,i+1+j*maxrk); |
---|
[b9a806] | 1223 | pSetmComp(p); |
---|
[0e1846] | 1224 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
---|
| 1225 | } |
---|
| 1226 | } |
---|
| 1227 | /* enter given ideals ------------------------------------------*/ |
---|
| 1228 | i = maxrk; |
---|
| 1229 | k = 0; |
---|
| 1230 | for (j=0;j<length;j++) |
---|
| 1231 | { |
---|
| 1232 | if (arg[j]!=NULL) |
---|
| 1233 | { |
---|
| 1234 | for (l=0;l<IDELEMS(arg[j]);l++) |
---|
| 1235 | { |
---|
| 1236 | if (arg[j]->m[l]!=NULL) |
---|
| 1237 | { |
---|
[e960943] | 1238 | if (syz_ring==orig_ring) |
---|
| 1239 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
---|
| 1240 | else |
---|
[416465] | 1241 | bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring); |
---|
[0e1846] | 1242 | pShift(&(bigmat->m[i]),k*maxrk+isIdeal); |
---|
| 1243 | i++; |
---|
| 1244 | } |
---|
| 1245 | } |
---|
| 1246 | k++; |
---|
| 1247 | } |
---|
| 1248 | } |
---|
| 1249 | /* std computation --------------------------------------------*/ |
---|
[a1c44e] | 1250 | tempstd = kStd(bigmat,currQuotient,testHomog,&w,NULL,syzComp); |
---|
[0e1846] | 1251 | if (w!=NULL) delete w; |
---|
| 1252 | idDelete(&bigmat); |
---|
[e960943] | 1253 | |
---|
| 1254 | if(syz_ring!=orig_ring) |
---|
| 1255 | rChangeCurrRing(orig_ring,TRUE); |
---|
| 1256 | |
---|
[0e1846] | 1257 | /* interprete result ----------------------------------------*/ |
---|
| 1258 | result = idInit(8,maxrk); |
---|
| 1259 | k = 0; |
---|
| 1260 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
| 1261 | { |
---|
[e960943] | 1262 | if ((tempstd->m[j]!=NULL) && (pRingGetComp(syz_ring,tempstd->m[j])>syzComp)) |
---|
[0e1846] | 1263 | { |
---|
| 1264 | if (k>=IDELEMS(result)) |
---|
| 1265 | { |
---|
| 1266 | pEnlargeSet(&(result->m),IDELEMS(result),8); |
---|
| 1267 | IDELEMS(result) += 8; |
---|
| 1268 | } |
---|
[e960943] | 1269 | if (syz_ring==orig_ring) |
---|
| 1270 | p = pCopy(tempstd->m[j]); |
---|
| 1271 | else |
---|
[416465] | 1272 | p = prCopyR(tempstd->m[j], syz_ring); |
---|
[0e1846] | 1273 | pShift(&p,-syzComp-isIdeal); |
---|
| 1274 | result->m[k] = p; |
---|
| 1275 | k++; |
---|
| 1276 | } |
---|
| 1277 | } |
---|
| 1278 | /* clean up ----------------------------------------------------*/ |
---|
[e960943] | 1279 | if(syz_ring!=orig_ring) |
---|
| 1280 | rChangeCurrRing(syz_ring,FALSE); |
---|
[0e1846] | 1281 | idDelete(&tempstd); |
---|
[e960943] | 1282 | if(syz_ring!=orig_ring) |
---|
| 1283 | { |
---|
| 1284 | rChangeCurrRing(orig_ring,TRUE); |
---|
| 1285 | rKill(syz_ring); |
---|
| 1286 | } |
---|
[0e1846] | 1287 | idSkipZeroes(result); |
---|
| 1288 | return result; |
---|
| 1289 | } |
---|
| 1290 | |
---|
| 1291 | /*2 |
---|
| 1292 | *computes syzygies of h1, |
---|
| 1293 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
[e960943] | 1294 | *works always in a ring with ringorder_s |
---|
[0e1846] | 1295 | */ |
---|
[416465] | 1296 | static ideal idPrepare (ideal h1, tHomog h, int syzcomp, intvec **w) |
---|
[0e1846] | 1297 | { |
---|
| 1298 | ideal h2, h3; |
---|
| 1299 | int i; |
---|
[27f5f1e] | 1300 | int j,jj=0,k; |
---|
[0e1846] | 1301 | poly p,q; |
---|
| 1302 | |
---|
| 1303 | if (idIs0(h1)) return NULL; |
---|
[b9a806] | 1304 | k = idRankFreeModule(h1); |
---|
[0e1846] | 1305 | h2=idCopy(h1); |
---|
| 1306 | i = IDELEMS(h2)-1; |
---|
| 1307 | if (k == 0) |
---|
| 1308 | { |
---|
| 1309 | for (j=0; j<=i; j++) pShift(&(h2->m[j]),1); |
---|
[e960943] | 1310 | k = 1; |
---|
| 1311 | } |
---|
| 1312 | if (syzcomp<k) |
---|
| 1313 | { |
---|
| 1314 | Warn("syzcomp too low, should be %d instead of %d",k,syzcomp); |
---|
| 1315 | syzcomp = k; |
---|
[416465] | 1316 | rSetSyzComp(k); |
---|
[0e1846] | 1317 | } |
---|
[e960943] | 1318 | h2->rank = syzcomp+i+1; |
---|
[0e1846] | 1319 | for (j=0; j<=i; j++) |
---|
| 1320 | { |
---|
| 1321 | p = h2->m[j]; |
---|
| 1322 | q = pOne(); |
---|
[e960943] | 1323 | pSetComp(q,syzcomp+1+j); |
---|
[b9a806] | 1324 | pSetmComp(q); |
---|
[0e1846] | 1325 | if (p!=NULL) |
---|
| 1326 | { |
---|
| 1327 | while (pNext(p)) pIter(p); |
---|
| 1328 | p->next = q; |
---|
| 1329 | } |
---|
| 1330 | else |
---|
| 1331 | h2->m[j]=q; |
---|
| 1332 | } |
---|
[27f5f1e] | 1333 | |
---|
[0e1846] | 1334 | #ifdef PDEBUG |
---|
| 1335 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
| 1336 | #endif |
---|
[416465] | 1337 | h3=kStd(h2,currQuotient,h,w,NULL,syzcomp); |
---|
[0e1846] | 1338 | idDelete(&h2); |
---|
| 1339 | return h3; |
---|
| 1340 | } |
---|
| 1341 | |
---|
[87bef42] | 1342 | /*2 |
---|
[b9a806] | 1343 | * compute the syzygies of h1 in R/quot, |
---|
[87bef42] | 1344 | * weights of components are in w |
---|
| 1345 | * if setRegularity, return the regularity in deg |
---|
[416465] | 1346 | * do not change h1, w |
---|
[87bef42] | 1347 | */ |
---|
[416465] | 1348 | ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp, |
---|
[0e1846] | 1349 | BOOLEAN setRegularity, int °) |
---|
| 1350 | { |
---|
[416465] | 1351 | ideal s_h1; |
---|
[0e1846] | 1352 | poly p; |
---|
[416465] | 1353 | int i, j, k, length=0,reg; |
---|
[0e1846] | 1354 | BOOLEAN isMonomial=TRUE; |
---|
| 1355 | |
---|
| 1356 | #ifdef PDEBUG |
---|
| 1357 | int ii; |
---|
| 1358 | for(ii=0;ii<IDELEMS(h1);ii++) pTest(h1->m[ii]); |
---|
| 1359 | #endif |
---|
| 1360 | if (idIs0(h1)) |
---|
| 1361 | return idFreeModule(IDELEMS(h1)); |
---|
[87bef42] | 1362 | k=max(1,idRankFreeModule(h1)); |
---|
[e960943] | 1363 | |
---|
[c54075] | 1364 | assume(currRing != NULL); |
---|
[e960943] | 1365 | ring orig_ring=currRing; |
---|
[9d06971] | 1366 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
[7bab5d] | 1367 | |
---|
[416465] | 1368 | if (setSyzComp) |
---|
| 1369 | rSetSyzComp(k); |
---|
[87bef42] | 1370 | |
---|
[416465] | 1371 | if (orig_ring != syz_ring) |
---|
| 1372 | { |
---|
| 1373 | s_h1=idrCopyR_NoSort(h1,orig_ring); |
---|
| 1374 | } |
---|
| 1375 | else |
---|
| 1376 | { |
---|
| 1377 | s_h1 = h1; |
---|
| 1378 | } |
---|
[e960943] | 1379 | |
---|
[416465] | 1380 | ideal s_h3=idPrepare(s_h1,h,k,w); |
---|
[e960943] | 1381 | |
---|
| 1382 | if (s_h3==NULL) |
---|
| 1383 | { |
---|
[0e1846] | 1384 | return idFreeModule(IDELEMS(h1)); |
---|
[e960943] | 1385 | } |
---|
[416465] | 1386 | |
---|
| 1387 | if (orig_ring != syz_ring) |
---|
[0e1846] | 1388 | { |
---|
[416465] | 1389 | idDelete(&s_h1); |
---|
| 1390 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
[0e1846] | 1391 | { |
---|
[416465] | 1392 | if (s_h3->m[j] != NULL) |
---|
[0e1846] | 1393 | { |
---|
[416465] | 1394 | if (pMinComp(s_h3->m[j],syz_ring) > k) |
---|
| 1395 | pShift(&s_h3->m[j], -k); |
---|
[e960943] | 1396 | else |
---|
[416465] | 1397 | pDelete(&s_h3->m[j]); |
---|
[0e1846] | 1398 | } |
---|
[416465] | 1399 | } |
---|
| 1400 | idSkipZeroes(s_h3); |
---|
| 1401 | s_h3->rank -= k; |
---|
| 1402 | rChangeCurrRing(orig_ring, TRUE); |
---|
| 1403 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
| 1404 | rKill(syz_ring); |
---|
| 1405 | idTest(s_h3); |
---|
| 1406 | return s_h3; |
---|
| 1407 | } |
---|
| 1408 | |
---|
| 1409 | ideal e = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
| 1410 | |
---|
| 1411 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
| 1412 | { |
---|
| 1413 | if (s_h3->m[j] != NULL) |
---|
| 1414 | { |
---|
| 1415 | if (pMinComp(s_h3->m[j],syz_ring) <= k) |
---|
[0e1846] | 1416 | { |
---|
[416465] | 1417 | e->m[j] = s_h3->m[j]; |
---|
[e960943] | 1418 | isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL); |
---|
[416465] | 1419 | pDelete(&pNext(s_h3->m[j])); |
---|
| 1420 | s_h3->m[j] = NULL; |
---|
[0e1846] | 1421 | } |
---|
| 1422 | } |
---|
| 1423 | } |
---|
[416465] | 1424 | |
---|
| 1425 | idSkipZeroes(s_h3); |
---|
| 1426 | idSkipZeroes(e); |
---|
| 1427 | |
---|
[e960943] | 1428 | if ((!isMonomial) |
---|
| 1429 | && (!TEST_OPT_NOTREGULARITY) |
---|
| 1430 | && (setRegularity) |
---|
| 1431 | && (h==isHomog)) |
---|
[0e1846] | 1432 | { |
---|
[416465] | 1433 | ring dp_C_ring = rCurrRingAssure_dp_C(); |
---|
| 1434 | if (dp_C_ring != syz_ring) |
---|
| 1435 | e = idrMoveR_NoSort(e, syz_ring); |
---|
| 1436 | resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE); |
---|
[0e1846] | 1437 | intvec * dummy = syBetti(res,length,®, *w); |
---|
| 1438 | deg = reg+2; |
---|
| 1439 | delete dummy; |
---|
| 1440 | for (j=0;j<length;j++) |
---|
| 1441 | { |
---|
| 1442 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
| 1443 | } |
---|
| 1444 | Free((ADDRESS)res,length*sizeof(ideal)); |
---|
[416465] | 1445 | idDelete(&e); |
---|
| 1446 | if (dp_C_ring != syz_ring) |
---|
| 1447 | { |
---|
| 1448 | rChangeCurrRing(syz_ring, TRUE); |
---|
| 1449 | rKill(dp_C_ring); |
---|
| 1450 | } |
---|
[0e1846] | 1451 | } |
---|
[416465] | 1452 | else |
---|
[e960943] | 1453 | { |
---|
[416465] | 1454 | idDelete(&e); |
---|
[e960943] | 1455 | } |
---|
[416465] | 1456 | idTest(s_h3); |
---|
| 1457 | return s_h3; |
---|
[0e1846] | 1458 | } |
---|
| 1459 | |
---|
| 1460 | /* |
---|
| 1461 | *computes a standard basis for h1 and stores the transformation matrix |
---|
| 1462 | * in ma |
---|
| 1463 | */ |
---|
[416465] | 1464 | ideal idLiftStd (ideal h1, matrix* ma, tHomog h) |
---|
[0e1846] | 1465 | { |
---|
[416465] | 1466 | int i, j, k, t, inputIsIdeal=idRankFreeModule(h1); |
---|
[0e1846] | 1467 | poly p=NULL, q, qq; |
---|
| 1468 | intvec *w=NULL; |
---|
| 1469 | |
---|
| 1470 | idDelete((ideal*)ma); |
---|
| 1471 | *ma=mpNew(1,0); |
---|
| 1472 | if (idIs0(h1)) |
---|
| 1473 | return idInit(1,h1->rank); |
---|
[87bef42] | 1474 | k=max(1,idRankFreeModule(h1)); |
---|
[b9a806] | 1475 | |
---|
| 1476 | ring orig_ring=currRing; |
---|
[9d06971] | 1477 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
[416465] | 1478 | rSetSyzComp(k); |
---|
| 1479 | |
---|
| 1480 | ideal s_h1=h1; |
---|
[b9a806] | 1481 | |
---|
[416465] | 1482 | if (orig_ring != syz_ring) |
---|
| 1483 | s_h1 = idrCopyR_NoSort(h1,orig_ring); |
---|
| 1484 | else |
---|
| 1485 | s_h1 = h1; |
---|
[b9a806] | 1486 | |
---|
[416465] | 1487 | ideal s_h3=idPrepare(s_h1,h,k,&w); |
---|
[e1b9f91] | 1488 | ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
[b9a806] | 1489 | |
---|
[0e1846] | 1490 | if (w!=NULL) delete w; |
---|
| 1491 | i = 0; |
---|
[b9a806] | 1492 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
[0e1846] | 1493 | { |
---|
[b9a806] | 1494 | if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j],syz_ring) <= k)) |
---|
[0e1846] | 1495 | { |
---|
[e1b9f91] | 1496 | i++; |
---|
| 1497 | q = s_h3->m[j]; |
---|
[0e1846] | 1498 | while (pNext(q) != NULL) |
---|
| 1499 | { |
---|
| 1500 | if (pGetComp(pNext(q)) > k) |
---|
| 1501 | { |
---|
[e1b9f91] | 1502 | s_h2->m[j] = pNext(q); |
---|
| 1503 | pNext(q) = NULL; |
---|
[0e1846] | 1504 | } |
---|
| 1505 | else |
---|
| 1506 | { |
---|
| 1507 | pIter(q); |
---|
| 1508 | } |
---|
| 1509 | } |
---|
[e1b9f91] | 1510 | if (!inputIsIdeal) pShift(&(s_h3->m[j]), -1); |
---|
| 1511 | } |
---|
| 1512 | else |
---|
| 1513 | { |
---|
| 1514 | pDelete(&(s_h3->m[j])); |
---|
| 1515 | } |
---|
| 1516 | } |
---|
| 1517 | |
---|
| 1518 | idSkipZeroes(s_h3); |
---|
| 1519 | j = IDELEMS(s_h1); |
---|
[7bab5d] | 1520 | |
---|
[e1b9f91] | 1521 | if (syz_ring!=orig_ring) |
---|
[416465] | 1522 | { |
---|
| 1523 | idDelete(&s_h1); |
---|
[e1b9f91] | 1524 | rChangeCurrRing(orig_ring,TRUE); |
---|
[416465] | 1525 | } |
---|
| 1526 | |
---|
[e1b9f91] | 1527 | idDelete((ideal*)ma); |
---|
| 1528 | *ma = mpNew(j,i); |
---|
| 1529 | |
---|
| 1530 | i = 1; |
---|
| 1531 | for (j=0; j<IDELEMS(s_h2); j++) |
---|
| 1532 | { |
---|
| 1533 | if (s_h2->m[j] != NULL) |
---|
| 1534 | { |
---|
[416465] | 1535 | q = prMoveR( s_h2->m[j], syz_ring); |
---|
[e1b9f91] | 1536 | s_h2->m[j] = NULL; |
---|
[7bab5d] | 1537 | |
---|
[e1b9f91] | 1538 | while (q != NULL) |
---|
[0e1846] | 1539 | { |
---|
[e1b9f91] | 1540 | p = q; |
---|
| 1541 | pIter(q); |
---|
| 1542 | pNext(p) = NULL; |
---|
| 1543 | t=pGetComp(p); |
---|
| 1544 | pSetComp(p,0); |
---|
| 1545 | pSetmComp(p); |
---|
| 1546 | MATELEM(*ma,t-k,i) = pAdd(MATELEM(*ma,t-k,i),p); |
---|
[0e1846] | 1547 | } |
---|
[e1b9f91] | 1548 | i++; |
---|
[0e1846] | 1549 | } |
---|
| 1550 | } |
---|
[e1b9f91] | 1551 | idDelete(&s_h2); |
---|
| 1552 | |
---|
| 1553 | for (i=0; i<IDELEMS(s_h3); i++) |
---|
[b9a806] | 1554 | { |
---|
[416465] | 1555 | s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], syz_ring); |
---|
[b9a806] | 1556 | } |
---|
[e1b9f91] | 1557 | |
---|
| 1558 | if (syz_ring!=orig_ring) rKill(syz_ring); |
---|
| 1559 | return s_h3; |
---|
[0e1846] | 1560 | } |
---|
| 1561 | |
---|
| 1562 | /*2 |
---|
| 1563 | *computes a representation of the generators of submod with respect to those |
---|
| 1564 | * of mod |
---|
| 1565 | */ |
---|
[b982ef] | 1566 | ideal idLiftNonStB (ideal mod, ideal submod,BOOLEAN goodShape) |
---|
[0e1846] | 1567 | { |
---|
[416465] | 1568 | int lsmod =idRankFreeModule(submod), i, j, k; |
---|
[0e1846] | 1569 | |
---|
| 1570 | if (idIs0(mod)) |
---|
| 1571 | return idInit(1,mod->rank); |
---|
| 1572 | |
---|
[b9a806] | 1573 | k=idRankFreeModule(mod); |
---|
| 1574 | if ((k!=0) && (lsmod==0)) lsmod=1; |
---|
| 1575 | k=max(k,1); |
---|
| 1576 | |
---|
| 1577 | ring orig_ring=currRing; |
---|
[9d06971] | 1578 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
[416465] | 1579 | rSetSyzComp(k); |
---|
[b9a806] | 1580 | |
---|
[416465] | 1581 | ideal s_mod, s_temp; |
---|
| 1582 | if (orig_ring != syz_ring) |
---|
| 1583 | { |
---|
| 1584 | s_mod = idrCopyR_NoSort(mod,orig_ring); |
---|
| 1585 | s_temp = idrCopyR_NoSort(submod,orig_ring); |
---|
| 1586 | } |
---|
| 1587 | else |
---|
| 1588 | { |
---|
| 1589 | s_mod = mod; |
---|
| 1590 | s_temp = idCopy(submod); |
---|
| 1591 | } |
---|
[b9a806] | 1592 | |
---|
[416465] | 1593 | ideal s_h3=idPrepare(s_mod,(tHomog)FALSE,k,NULL); |
---|
[b9a806] | 1594 | |
---|
[b982ef] | 1595 | if (!goodShape) |
---|
[0e1846] | 1596 | { |
---|
[b9a806] | 1597 | for (j=0;j<IDELEMS(s_h3);j++) |
---|
[b982ef] | 1598 | { |
---|
[b9a806] | 1599 | if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k)) |
---|
| 1600 | pDelete(&(s_h3->m[j])); |
---|
[b982ef] | 1601 | } |
---|
[0e1846] | 1602 | } |
---|
[b9a806] | 1603 | idSkipZeroes(s_h3); |
---|
[0e1846] | 1604 | if (lsmod==0) |
---|
| 1605 | { |
---|
[b9a806] | 1606 | for (j=IDELEMS(s_temp);j>0;j--) |
---|
[0e1846] | 1607 | { |
---|
[b9a806] | 1608 | if (s_temp->m[j-1]!=NULL) |
---|
| 1609 | pShift(&(s_temp->m[j-1]),1); |
---|
[0e1846] | 1610 | } |
---|
| 1611 | } |
---|
[b9a806] | 1612 | ideal s_result = kNF(s_h3,currQuotient,s_temp,k); |
---|
| 1613 | s_result->rank = s_h3->rank; |
---|
| 1614 | idDelete(&s_h3); |
---|
| 1615 | idDelete(&s_temp); |
---|
| 1616 | |
---|
| 1617 | for (j=0;j<IDELEMS(s_result);j++) |
---|
[0e1846] | 1618 | { |
---|
[b9a806] | 1619 | if (s_result->m[j]!=NULL) |
---|
[0e1846] | 1620 | { |
---|
[b9a806] | 1621 | if (pGetComp(s_result->m[j])<=k) |
---|
[0e1846] | 1622 | { |
---|
[da97958] | 1623 | WerrorS("2nd module lies not in the first"); |
---|
[b9a806] | 1624 | idDelete(&s_result); |
---|
| 1625 | s_result=idInit(1,1); |
---|
| 1626 | break; |
---|
[0e1846] | 1627 | } |
---|
| 1628 | else |
---|
| 1629 | { |
---|
[b9a806] | 1630 | pShift(&(s_result->m[j]),-k); |
---|
| 1631 | pNeg(s_result->m[j]); |
---|
[0e1846] | 1632 | } |
---|
| 1633 | } |
---|
| 1634 | } |
---|
[b9a806] | 1635 | |
---|
| 1636 | if(syz_ring!=orig_ring) |
---|
| 1637 | { |
---|
[416465] | 1638 | idDelete(&s_mod); |
---|
[b9a806] | 1639 | rChangeCurrRing(orig_ring,TRUE); |
---|
[416465] | 1640 | s_result = idrMoveR_NoSort(s_result, syz_ring); |
---|
[b9a806] | 1641 | rKill(syz_ring); |
---|
| 1642 | } |
---|
[416465] | 1643 | return s_result; |
---|
[0e1846] | 1644 | } |
---|
| 1645 | |
---|
| 1646 | /*2 |
---|
| 1647 | *computes a representation of the generators of submod with respect to those |
---|
| 1648 | * of mod which is given as standardbasis, |
---|
| 1649 | * uses currQuotient as the quotient ideal (if not NULL) |
---|
| 1650 | */ |
---|
| 1651 | ideal idLift (ideal mod,ideal submod) |
---|
| 1652 | { |
---|
| 1653 | int j,k; |
---|
| 1654 | poly p,q; |
---|
| 1655 | BOOLEAN reported=FALSE; |
---|
| 1656 | |
---|
| 1657 | if (idIs0(mod)) return idInit(1,mod->rank); |
---|
[b9a806] | 1658 | |
---|
| 1659 | k = idRankFreeModule(mod); |
---|
| 1660 | |
---|
| 1661 | |
---|
| 1662 | ring orig_ring=currRing; |
---|
[9d06971] | 1663 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
[416465] | 1664 | rSetSyzComp(max(k,1)); |
---|
[b9a806] | 1665 | |
---|
| 1666 | ideal s_result=idInit(IDELEMS(submod),submod->rank); |
---|
[416465] | 1667 | ideal s_temp; |
---|
| 1668 | |
---|
| 1669 | if (syz_ring != orig_ring) |
---|
| 1670 | { |
---|
| 1671 | s_temp = idrCopyR_NoSort(mod,orig_ring); |
---|
| 1672 | } |
---|
| 1673 | else |
---|
| 1674 | { |
---|
| 1675 | s_temp = idCopy(mod); |
---|
| 1676 | } |
---|
| 1677 | |
---|
[0e1846] | 1678 | if (k == 0) |
---|
| 1679 | { |
---|
[b9a806] | 1680 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
[0e1846] | 1681 | { |
---|
[b9a806] | 1682 | if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1); |
---|
[0e1846] | 1683 | } |
---|
| 1684 | k = 1; |
---|
| 1685 | } |
---|
[b9a806] | 1686 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
[0e1846] | 1687 | { |
---|
[b9a806] | 1688 | if (s_temp->m[j]!=NULL) |
---|
[0e1846] | 1689 | { |
---|
[b9a806] | 1690 | p = s_temp->m[j]; |
---|
[0e1846] | 1691 | q = pOne(); |
---|
| 1692 | pGetCoeff(q)=nNeg(pGetCoeff(q)); //set q to -1 |
---|
| 1693 | pSetComp(q,k+1+j); |
---|
[b9a806] | 1694 | pSetmComp(q); |
---|
[0e1846] | 1695 | while (pNext(p)) pIter(p); |
---|
| 1696 | pNext(p) = q; |
---|
| 1697 | } |
---|
| 1698 | } |
---|
[b9a806] | 1699 | |
---|
[0e1846] | 1700 | for (j=0; j<IDELEMS(submod); j++) |
---|
| 1701 | { |
---|
| 1702 | if (submod->m[j]!=NULL) |
---|
| 1703 | { |
---|
[b9a806] | 1704 | if (syz_ring==orig_ring) |
---|
| 1705 | p = pCopy(submod->m[j]); |
---|
| 1706 | else |
---|
[416465] | 1707 | p=prCopyR(submod->m[j], orig_ring); |
---|
[0e1846] | 1708 | if (pGetComp(p)==0) pSetCompP(p,1); |
---|
[b9a806] | 1709 | q = kNF(s_temp,currQuotient,p,k); |
---|
[0e1846] | 1710 | pDelete(&p); |
---|
| 1711 | if (q!=NULL) |
---|
| 1712 | { |
---|
| 1713 | if (pMinComp(q)<=k) |
---|
| 1714 | { |
---|
| 1715 | if (!reported) |
---|
| 1716 | { |
---|
[a1c9c02] | 1717 | WarnS("first module not a standardbasis\n" |
---|
[9c7b9a] | 1718 | "// ** or second not a proper submodule"); |
---|
[0e1846] | 1719 | reported=TRUE; |
---|
| 1720 | } |
---|
| 1721 | pDelete(&q); |
---|
| 1722 | } |
---|
| 1723 | else |
---|
| 1724 | { |
---|
| 1725 | pShift(&q,-k); |
---|
[b9a806] | 1726 | s_result->m[j] = q; |
---|
[0e1846] | 1727 | } |
---|
| 1728 | } |
---|
| 1729 | } |
---|
| 1730 | } |
---|
[b9a806] | 1731 | idDelete(&s_temp); |
---|
| 1732 | |
---|
| 1733 | if(syz_ring!=orig_ring) |
---|
| 1734 | { |
---|
| 1735 | rChangeCurrRing(orig_ring,TRUE); |
---|
[416465] | 1736 | s_result = idrMoveR_NoSort(s_result, syz_ring); |
---|
[b9a806] | 1737 | rKill(syz_ring); |
---|
| 1738 | } |
---|
| 1739 | |
---|
| 1740 | return s_result; |
---|
[0e1846] | 1741 | } |
---|
| 1742 | |
---|
[416465] | 1743 | |
---|
[0e1846] | 1744 | /*2 |
---|
| 1745 | *computes the quotient of h1,h2 |
---|
| 1746 | */ |
---|
[416465] | 1747 | static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, |
---|
| 1748 | BOOLEAN *addOnlyOne, int *kkmax) |
---|
[0e1846] | 1749 | { |
---|
[416465] | 1750 | ideal temph1; |
---|
[0e1846] | 1751 | poly p,q = NULL; |
---|
[416465] | 1752 | int i,l,ll,k,kkk,kmax; |
---|
| 1753 | int j = 0; |
---|
| 1754 | int k1 = idRankFreeModule(h1); |
---|
| 1755 | int k2 = idRankFreeModule(h2); |
---|
| 1756 | tHomog hom=isNotHomog; |
---|
[0e1846] | 1757 | |
---|
| 1758 | k=max(k1,k2); |
---|
[416465] | 1759 | if (k==0) |
---|
| 1760 | k = 1; |
---|
| 1761 | if ((k2==0) && (k>1)) *addOnlyOne = FALSE; |
---|
| 1762 | |
---|
| 1763 | intvec * weights; |
---|
| 1764 | hom = (tHomog)idHomModule(h1,currQuotient,&weights); |
---|
| 1765 | if (addOnlyOne && (!h1IsStb)) |
---|
| 1766 | temph1 = kStd(h1,currQuotient,hom,&weights,NULL); |
---|
| 1767 | else |
---|
| 1768 | temph1 = idCopy(h1); |
---|
| 1769 | if (weights!=NULL) delete weights; |
---|
| 1770 | idTest(temph1); |
---|
| 1771 | /*--- making a single vector from h2 ---------------------*/ |
---|
[0e1846] | 1772 | for (i=0; i<IDELEMS(h2); i++) |
---|
| 1773 | { |
---|
| 1774 | if (h2->m[i] != NULL) |
---|
| 1775 | { |
---|
| 1776 | p = pCopy(h2->m[i]); |
---|
| 1777 | if (k2 == 0) |
---|
| 1778 | pShift(&p,j*k+1); |
---|
| 1779 | else |
---|
| 1780 | pShift(&p,j*k); |
---|
| 1781 | q = pAdd(q,p); |
---|
| 1782 | j++; |
---|
| 1783 | } |
---|
| 1784 | } |
---|
[416465] | 1785 | *kkmax = kmax = j*k+1; |
---|
| 1786 | /*--- adding a monomial for the result (syzygy) ----------*/ |
---|
| 1787 | p = q; |
---|
| 1788 | while (pNext(p)!=NULL) pIter(p); |
---|
| 1789 | pNext(p) = pOne(); |
---|
| 1790 | pIter(p); |
---|
[0e1846] | 1791 | pSetComp(p,kmax); |
---|
[66a672] | 1792 | pSetmComp(p); |
---|
[416465] | 1793 | /*--- constructing the big matrix ------------------------*/ |
---|
| 1794 | ideal h4 = idInit(16,kmax); |
---|
[0e1846] | 1795 | h4->m[0] = q; |
---|
| 1796 | if (k2 == 0) |
---|
| 1797 | { |
---|
| 1798 | if (k > IDELEMS(h4)) |
---|
| 1799 | { |
---|
| 1800 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
| 1801 | IDELEMS(h4) = k; |
---|
| 1802 | } |
---|
| 1803 | for (i=1; i<k; i++) |
---|
| 1804 | { |
---|
[416465] | 1805 | p = pCopy_noCheck(h4->m[i-1]); |
---|
[0e1846] | 1806 | pShift(&p,1); |
---|
| 1807 | h4->m[i] = p; |
---|
| 1808 | } |
---|
| 1809 | } |
---|
[416465] | 1810 | |
---|
[0e1846] | 1811 | kkk = IDELEMS(h4); |
---|
[416465] | 1812 | i = IDELEMS(temph1); |
---|
| 1813 | while ((i>0) && (temph1->m[i-1]==NULL)) i--; |
---|
[0e1846] | 1814 | for (l=0; l<i; l++) |
---|
| 1815 | { |
---|
[416465] | 1816 | if(temph1->m[l]!=NULL) |
---|
[0e1846] | 1817 | { |
---|
| 1818 | for (ll=0; ll<j; ll++) |
---|
| 1819 | { |
---|
[416465] | 1820 | p = pCopy(temph1->m[l]); |
---|
[0e1846] | 1821 | if (k1 == 0) |
---|
| 1822 | pShift(&p,ll*k+1); |
---|
| 1823 | else |
---|
| 1824 | pShift(&p,ll*k); |
---|
| 1825 | if (kkk >= IDELEMS(h4)) |
---|
| 1826 | { |
---|
| 1827 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
| 1828 | IDELEMS(h4) += 16; |
---|
| 1829 | } |
---|
| 1830 | h4->m[kkk] = p; |
---|
| 1831 | kkk++; |
---|
| 1832 | } |
---|
| 1833 | } |
---|
| 1834 | } |
---|
[416465] | 1835 | /*--- if h2 goes in as single vector - the h1-part is just SB ---*/ |
---|
| 1836 | if (*addOnlyOne) |
---|
[0e1846] | 1837 | { |
---|
[416465] | 1838 | p = h4->m[0]; |
---|
| 1839 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
[0e1846] | 1840 | { |
---|
[416465] | 1841 | h4->m[i] = h4->m[i+1]; |
---|
[0e1846] | 1842 | } |
---|
[416465] | 1843 | h4->m[IDELEMS(h4)-1] = p; |
---|
| 1844 | idSkipZeroes(h4); |
---|
| 1845 | test |= Sy_bit(OPT_SB_1); |
---|
[0e1846] | 1846 | } |
---|
[416465] | 1847 | idDelete(&temph1); |
---|
| 1848 | idTest(h4); |
---|
[0e1846] | 1849 | return h4; |
---|
| 1850 | } |
---|
[416465] | 1851 | /*2 |
---|
| 1852 | *computes the quotient of h1,h2 |
---|
| 1853 | */ |
---|
[761e9a5] | 1854 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal) |
---|
[0e1846] | 1855 | { |
---|
[761e9a5] | 1856 | // first check for special case h1:(0) |
---|
[0e1846] | 1857 | if (idIs0(h2)) |
---|
| 1858 | { |
---|
[b9a806] | 1859 | ideal res; |
---|
[761e9a5] | 1860 | if (resultIsIdeal) |
---|
[0e1846] | 1861 | { |
---|
[b9a806] | 1862 | res = idInit(1,1); |
---|
| 1863 | res->m[0] = pOne(); |
---|
[0e1846] | 1864 | } |
---|
| 1865 | else |
---|
[b9a806] | 1866 | res = idFreeModule(h1->rank); |
---|
| 1867 | return res; |
---|
[0e1846] | 1868 | } |
---|
[761e9a5] | 1869 | BITSET old_test=test; |
---|
| 1870 | poly p,q = NULL; |
---|
| 1871 | int i,l,ll,k,kkk,kmax; |
---|
| 1872 | BOOLEAN addOnlyOne=TRUE; |
---|
| 1873 | tHomog hom=isNotHomog; |
---|
[416465] | 1874 | intvec * weights1; |
---|
[761e9a5] | 1875 | |
---|
[416465] | 1876 | ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax); |
---|
| 1877 | hom = (tHomog)idHomModule(s_h4,currQuotient,&weights1); |
---|
[b9a806] | 1878 | ring orig_ring=currRing; |
---|
[9d06971] | 1879 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
[416465] | 1880 | rSetSyzComp(kmax-1); |
---|
| 1881 | if (orig_ring!=syz_ring) |
---|
| 1882 | s_h4 = idrMoveR_NoSort(s_h4,syz_ring); |
---|
[b9a806] | 1883 | |
---|
| 1884 | ideal s_h3; |
---|
[0e1846] | 1885 | if (addOnlyOne) |
---|
| 1886 | { |
---|
[b9a806] | 1887 | s_h3 = kStd(s_h4,currQuotient,hom,&weights1,NULL,kmax-1,IDELEMS(s_h4)-1); |
---|
[0e1846] | 1888 | } |
---|
| 1889 | else |
---|
| 1890 | { |
---|
[b9a806] | 1891 | s_h3 = kStd(s_h4,currQuotient,hom,&weights1,NULL,kmax-1); |
---|
[0e1846] | 1892 | } |
---|
[b9a806] | 1893 | idTest(s_h3); |
---|
| 1894 | if (weights1!=NULL) delete weights1; |
---|
| 1895 | idDelete(&s_h4); |
---|
| 1896 | |
---|
| 1897 | |
---|
[416465] | 1898 | for (i=0;i<IDELEMS(s_h3);i++) |
---|
[0e1846] | 1899 | { |
---|
[416465] | 1900 | if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax)) |
---|
[0e1846] | 1901 | { |
---|
| 1902 | if (resultIsIdeal) |
---|
[416465] | 1903 | pShift(&s_h3->m[i],-kmax); |
---|
[0e1846] | 1904 | else |
---|
[416465] | 1905 | pShift(&s_h3->m[i],-kmax+1); |
---|
[0e1846] | 1906 | } |
---|
| 1907 | else |
---|
[416465] | 1908 | pDelete(&s_h3->m[i]); |
---|
[0e1846] | 1909 | } |
---|
[7bab5d] | 1910 | if (resultIsIdeal) |
---|
[416465] | 1911 | s_h3->rank = 1; |
---|
[7bab5d] | 1912 | else |
---|
[416465] | 1913 | s_h3->rank = h1->rank; |
---|
[b9a806] | 1914 | if(syz_ring!=orig_ring) |
---|
| 1915 | { |
---|
[416465] | 1916 | // pDelete(&q); |
---|
[b9a806] | 1917 | rChangeCurrRing(orig_ring,TRUE); |
---|
[416465] | 1918 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
[b9a806] | 1919 | rKill(syz_ring); |
---|
| 1920 | } |
---|
[416465] | 1921 | idSkipZeroes(s_h3); |
---|
[0e1846] | 1922 | test = old_test; |
---|
[416465] | 1923 | idTest(s_h3); |
---|
| 1924 | return s_h3; |
---|
[0e1846] | 1925 | } |
---|
| 1926 | |
---|
| 1927 | /*2 |
---|
| 1928 | *computes recursively all monomials of a certain degree |
---|
| 1929 | *in every step the actvar-th entry in the exponential |
---|
| 1930 | *vector is incremented and the other variables are |
---|
| 1931 | *computed by recursive calls of makemonoms |
---|
| 1932 | *if the last variable is reached, the difference to the |
---|
| 1933 | *degree is computed directly |
---|
| 1934 | *vars is the number variables |
---|
| 1935 | *actvar is the actual variable to handle |
---|
| 1936 | *deg is the degree of the monomials to compute |
---|
| 1937 | *monomdeg is the actual degree of the monomial in consideration |
---|
| 1938 | */ |
---|
| 1939 | static void makemonoms(int vars,int actvar,int deg,int monomdeg) |
---|
| 1940 | { |
---|
| 1941 | poly p; |
---|
| 1942 | int i=0; |
---|
| 1943 | |
---|
| 1944 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
| 1945 | { |
---|
| 1946 | idpower[idpowerpoint] = pOne(); |
---|
| 1947 | monomdeg = 0; |
---|
| 1948 | } |
---|
| 1949 | while (i<=deg) |
---|
| 1950 | { |
---|
| 1951 | if (deg == monomdeg) |
---|
| 1952 | { |
---|
| 1953 | pSetm(idpower[idpowerpoint]); |
---|
| 1954 | idpowerpoint++; |
---|
| 1955 | return; |
---|
| 1956 | } |
---|
| 1957 | if (actvar == vars) |
---|
| 1958 | { |
---|
| 1959 | pSetExp(idpower[idpowerpoint],actvar,deg-monomdeg); |
---|
| 1960 | pSetm(idpower[idpowerpoint]); |
---|
[055a19] | 1961 | pTest(idpower[idpowerpoint]); |
---|
[0e1846] | 1962 | idpowerpoint++; |
---|
| 1963 | return; |
---|
| 1964 | } |
---|
| 1965 | else |
---|
| 1966 | { |
---|
| 1967 | p = pCopy(idpower[idpowerpoint]); |
---|
| 1968 | makemonoms(vars,actvar+1,deg,monomdeg); |
---|
| 1969 | idpower[idpowerpoint] = p; |
---|
| 1970 | } |
---|
| 1971 | monomdeg++; |
---|
| 1972 | pSetExp(idpower[idpowerpoint],actvar,pGetExp(idpower[idpowerpoint],actvar)+1); |
---|
| 1973 | pSetm(idpower[idpowerpoint]); |
---|
[055a19] | 1974 | pTest(idpower[idpowerpoint]); |
---|
[0e1846] | 1975 | i++; |
---|
| 1976 | } |
---|
| 1977 | } |
---|
| 1978 | |
---|
| 1979 | /*2 |
---|
| 1980 | *returns the deg-th power of the maximal ideal of 0 |
---|
| 1981 | */ |
---|
| 1982 | ideal idMaxIdeal(int deg) |
---|
| 1983 | { |
---|
[163cb1] | 1984 | if (deg < 0) |
---|
| 1985 | { |
---|
| 1986 | WarnS("maxideal: power must be non-negative"); |
---|
| 1987 | } |
---|
| 1988 | if (deg < 1) |
---|
| 1989 | { |
---|
| 1990 | ideal I=idInit(1,1); |
---|
| 1991 | I->m[0]=pOne(); |
---|
[cf29809] | 1992 | return I; |
---|
[163cb1] | 1993 | } |
---|
| 1994 | if (deg == 1) |
---|
[0e1846] | 1995 | { |
---|
| 1996 | return idMaxIdeal(); |
---|
| 1997 | } |
---|
[163cb1] | 1998 | |
---|
| 1999 | int vars = currRing->N; |
---|
| 2000 | int i = binom(vars+deg-1,deg); |
---|
| 2001 | ideal id=idInit(i,1); |
---|
[0e1846] | 2002 | idpower = id->m; |
---|
| 2003 | idpowerpoint = 0; |
---|
| 2004 | makemonoms(vars,1,deg,0); |
---|
| 2005 | idpower = NULL; |
---|
| 2006 | idpowerpoint = 0; |
---|
| 2007 | return id; |
---|
| 2008 | } |
---|
| 2009 | |
---|
| 2010 | /*2 |
---|
| 2011 | *computes recursively all generators of a certain degree |
---|
| 2012 | *of the ideal "givenideal" |
---|
| 2013 | *elms is the number elements in the given ideal |
---|
| 2014 | *actelm is the actual element to handle |
---|
| 2015 | *deg is the degree of the power to compute |
---|
| 2016 | *gendeg is the actual degree of the generator in consideration |
---|
| 2017 | */ |
---|
| 2018 | static void makepotence(int elms,int actelm,int deg,int gendeg) |
---|
| 2019 | { |
---|
| 2020 | poly p; |
---|
| 2021 | int i=0; |
---|
| 2022 | |
---|
| 2023 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
| 2024 | { |
---|
| 2025 | idpower[idpowerpoint] = pOne(); |
---|
| 2026 | gendeg = 0; |
---|
| 2027 | } |
---|
| 2028 | while (i<=deg) |
---|
| 2029 | { |
---|
| 2030 | if (deg == gendeg) |
---|
| 2031 | { |
---|
| 2032 | idpowerpoint++; |
---|
| 2033 | return; |
---|
| 2034 | } |
---|
| 2035 | if (actelm == elms) |
---|
| 2036 | { |
---|
| 2037 | p=pPower(pCopy(givenideal[actelm-1]),deg-gendeg); |
---|
| 2038 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],p); |
---|
| 2039 | idpowerpoint++; |
---|
| 2040 | return; |
---|
| 2041 | } |
---|
| 2042 | else |
---|
| 2043 | { |
---|
| 2044 | p = pCopy(idpower[idpowerpoint]); |
---|
| 2045 | makepotence(elms,actelm+1,deg,gendeg); |
---|
| 2046 | idpower[idpowerpoint] = p; |
---|
| 2047 | } |
---|
| 2048 | gendeg++; |
---|
| 2049 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],pCopy(givenideal[actelm-1])); |
---|
| 2050 | i++; |
---|
| 2051 | } |
---|
| 2052 | } |
---|
| 2053 | |
---|
| 2054 | /*2 |
---|
| 2055 | *returns the deg-th power of the ideal gid |
---|
| 2056 | */ |
---|
| 2057 | //ideal idPower(ideal gid,int deg) |
---|
| 2058 | //{ |
---|
| 2059 | // int i; |
---|
| 2060 | // ideal id; |
---|
| 2061 | // |
---|
| 2062 | // if (deg < 1) deg = 1; |
---|
| 2063 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
| 2064 | // id=idInit(i,1); |
---|
| 2065 | // idpower = id->m; |
---|
| 2066 | // givenideal = gid->m; |
---|
| 2067 | // idpowerpoint = 0; |
---|
| 2068 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
| 2069 | // idpower = NULL; |
---|
| 2070 | // givenideal = NULL; |
---|
| 2071 | // idpowerpoint = 0; |
---|
| 2072 | // return id; |
---|
| 2073 | //} |
---|
| 2074 | static void idNextPotence(ideal given, ideal result, |
---|
| 2075 | int begin, int end, int deg, int restdeg, poly ap) |
---|
| 2076 | { |
---|
| 2077 | poly p; |
---|
| 2078 | int i; |
---|
| 2079 | |
---|
| 2080 | p = pPower(pCopy(given->m[begin]),restdeg); |
---|
| 2081 | i = result->nrows; |
---|
| 2082 | result->m[i] = pMult(pCopy(ap),p); |
---|
| 2083 | //PrintS("."); |
---|
| 2084 | (result->nrows)++; |
---|
| 2085 | if (result->nrows >= IDELEMS(result)) |
---|
| 2086 | { |
---|
| 2087 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
| 2088 | IDELEMS(result) += 16; |
---|
| 2089 | } |
---|
| 2090 | if (begin == end) return; |
---|
[0d5b99] | 2091 | for (i=restdeg-1;i>0;i--) |
---|
[0e1846] | 2092 | { |
---|
| 2093 | p = pPower(pCopy(given->m[begin]),i); |
---|
| 2094 | p = pMult(pCopy(ap),p); |
---|
| 2095 | idNextPotence(given, result, begin+1, end, deg, restdeg-i, p); |
---|
| 2096 | pDelete(&p); |
---|
| 2097 | } |
---|
[0d5b99] | 2098 | idNextPotence(given, result, begin+1, end, deg, restdeg, ap); |
---|
[0e1846] | 2099 | } |
---|
| 2100 | |
---|
| 2101 | ideal idPower(ideal given,int exp) |
---|
| 2102 | { |
---|
| 2103 | ideal result,temp; |
---|
| 2104 | poly p1; |
---|
| 2105 | int i; |
---|
| 2106 | |
---|
| 2107 | if (idIs0(given)) return idInit(1,1); |
---|
| 2108 | temp = idCopy(given); |
---|
| 2109 | idSkipZeroes(temp); |
---|
| 2110 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
| 2111 | result = idInit(i,1); |
---|
| 2112 | result->nrows = 0; |
---|
| 2113 | //Print("ideal contains %d elements\n",i); |
---|
| 2114 | p1=pOne(); |
---|
| 2115 | idNextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1); |
---|
| 2116 | pDelete(&p1); |
---|
| 2117 | idDelete(&temp); |
---|
| 2118 | result->nrows = 1; |
---|
[5990ae] | 2119 | idSkipZeroes(result); |
---|
| 2120 | idDelEquals(result); |
---|
[0e1846] | 2121 | return result; |
---|
| 2122 | } |
---|
| 2123 | |
---|
| 2124 | /*2 |
---|
| 2125 | * eliminate delVar (product of vars) in h1 |
---|
| 2126 | */ |
---|
| 2127 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
| 2128 | { |
---|
| 2129 | int i,j=0,k,l; |
---|
| 2130 | ideal h,hh, h3; |
---|
| 2131 | int *ord,*block0,*block1; |
---|
| 2132 | int ordersize=2; |
---|
[055a19] | 2133 | int **wv; |
---|
[0e1846] | 2134 | tHomog hom; |
---|
| 2135 | intvec * w; |
---|
[e78cce] | 2136 | sip_sring tmpR; |
---|
[47faf56] | 2137 | ring origR = currRing; |
---|
[0e1846] | 2138 | |
---|
| 2139 | if (delVar==NULL) |
---|
| 2140 | { |
---|
| 2141 | return idCopy(h1); |
---|
| 2142 | } |
---|
| 2143 | if (currQuotient!=NULL) |
---|
| 2144 | { |
---|
[da97958] | 2145 | WerrorS("cannot eliminate in a qring"); |
---|
[0e1846] | 2146 | return idCopy(h1); |
---|
| 2147 | } |
---|
| 2148 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
| 2149 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
| 2150 | h3=idInit(16,h1->rank); |
---|
| 2151 | for (k=0;; k++) |
---|
| 2152 | { |
---|
| 2153 | if (currRing->order[k]!=0) ordersize++; |
---|
| 2154 | else break; |
---|
| 2155 | } |
---|
| 2156 | ord=(int*)Alloc0(ordersize*sizeof(int)); |
---|
| 2157 | block0=(int*)Alloc(ordersize*sizeof(int)); |
---|
| 2158 | block1=(int*)Alloc(ordersize*sizeof(int)); |
---|
| 2159 | for (k=0;; k++) |
---|
| 2160 | { |
---|
| 2161 | if (currRing->order[k]!=0) |
---|
| 2162 | { |
---|
| 2163 | block0[k+1] = currRing->block0[k]; |
---|
| 2164 | block1[k+1] = currRing->block1[k]; |
---|
| 2165 | ord[k+1] = currRing->order[k]; |
---|
| 2166 | } |
---|
| 2167 | else |
---|
| 2168 | break; |
---|
| 2169 | } |
---|
| 2170 | block0[0] = 1; |
---|
| 2171 | block1[0] = pVariables; |
---|
[055a19] | 2172 | wv=(int**) Alloc0(ordersize*sizeof(int**)); |
---|
| 2173 | memcpy4(wv+1,currRing->wvhdl,(ordersize-1)*sizeof(int**)); |
---|
| 2174 | wv[0]=(int*)AllocL((pVariables+1)*sizeof(int)); |
---|
| 2175 | memset(wv[0],0,(pVariables+1)*sizeof(int)); |
---|
[e78cce] | 2176 | for (j=0;j<pVariables;j++) |
---|
[0e1846] | 2177 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
| 2178 | ord[0] = ringorder_a; |
---|
[e78cce] | 2179 | |
---|
| 2180 | // fill in tmp ring to get back the data later on |
---|
[47faf56] | 2181 | tmpR = *origR; |
---|
[e78cce] | 2182 | tmpR.order = ord; |
---|
| 2183 | tmpR.block0 = block0; |
---|
| 2184 | tmpR.block1 = block1; |
---|
| 2185 | tmpR.wvhdl = wv; |
---|
[055a19] | 2186 | rComplete(&tmpR, 1); |
---|
[43580ac] | 2187 | |
---|
[e78cce] | 2188 | // change into the new ring |
---|
[25003c] | 2189 | //pChangeRing(pVariables,currRing->OrdSgn,ord,block0,block1,wv); |
---|
| 2190 | rChangeCurrRing(&tmpR, TRUE); |
---|
[47faf56] | 2191 | currRing = &tmpR; |
---|
[0e1846] | 2192 | h = idInit(IDELEMS(h1),1); |
---|
[e78cce] | 2193 | // fetch data from the old ring |
---|
[416465] | 2194 | for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR); |
---|
[a1c44e] | 2195 | // compute kStd |
---|
| 2196 | hh = kStd(h,NULL,hom,&w,hilb); |
---|
[0e1846] | 2197 | idDelete(&h); |
---|
[e78cce] | 2198 | |
---|
| 2199 | // go back to the original ring |
---|
[25003c] | 2200 | rChangeCurrRing(origR,TRUE); |
---|
[0e1846] | 2201 | i = IDELEMS(hh)-1; |
---|
| 2202 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
| 2203 | j = -1; |
---|
[e78cce] | 2204 | // fetch data from temp ring |
---|
[0e1846] | 2205 | for (k=0; k<=i; k++) |
---|
| 2206 | { |
---|
| 2207 | l=pVariables; |
---|
[e78cce] | 2208 | while ((l>0) && (pRingGetExp(&tmpR, hh->m[k],l)*pGetExp(delVar,l)==0)) l--; |
---|
[0e1846] | 2209 | if (l==0) |
---|
| 2210 | { |
---|
| 2211 | j++; |
---|
| 2212 | if (j >= IDELEMS(h3)) |
---|
| 2213 | { |
---|
| 2214 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
| 2215 | IDELEMS(h3) += 16; |
---|
| 2216 | } |
---|
[416465] | 2217 | h3->m[j] = prCopyR( hh->m[k], &tmpR); |
---|
[0e1846] | 2218 | } |
---|
| 2219 | } |
---|
[055a19] | 2220 | rChangeCurrRing(&tmpR, FALSE); |
---|
[0e1846] | 2221 | idDelete(&hh); |
---|
[055a19] | 2222 | rChangeCurrRing(origR, TRUE); |
---|
[0e1846] | 2223 | idSkipZeroes(h3); |
---|
[055a19] | 2224 | FreeL((ADDRESS)wv[0]); |
---|
| 2225 | Free((ADDRESS)wv,ordersize*sizeof(int**)); |
---|
[0e1846] | 2226 | Free((ADDRESS)ord,ordersize*sizeof(int)); |
---|
| 2227 | Free((ADDRESS)block0,ordersize*sizeof(int)); |
---|
| 2228 | Free((ADDRESS)block1,ordersize*sizeof(int)); |
---|
[055a19] | 2229 | rUnComplete(&tmpR); |
---|
[0e1846] | 2230 | if (w!=NULL) |
---|
| 2231 | delete w; |
---|
| 2232 | return h3; |
---|
| 2233 | } |
---|
| 2234 | |
---|
[c616d1] | 2235 | //void idEnterSet (poly p,ideal r, int * next) |
---|
| 2236 | //{ |
---|
| 2237 | // |
---|
| 2238 | // if ((*next) == IDELEMS(r)-1) |
---|
| 2239 | // { |
---|
| 2240 | // pEnlargeSet(&(r->m),IDELEMS(r),16); |
---|
| 2241 | // IDELEMS(r)+=16; |
---|
| 2242 | // } |
---|
| 2243 | // int at; |
---|
| 2244 | // int i; |
---|
| 2245 | // if (*next==0) at=0; |
---|
| 2246 | // else |
---|
| 2247 | // { |
---|
| 2248 | // int an = 0; |
---|
| 2249 | // int en= *next-1; |
---|
| 2250 | // int c; |
---|
| 2251 | // if (pComp0(r->m[(*next)-1],p)!= 1) |
---|
| 2252 | // at=*next; |
---|
| 2253 | // else |
---|
| 2254 | // { |
---|
| 2255 | // loop |
---|
| 2256 | // { |
---|
| 2257 | // if (an >= en-1) |
---|
| 2258 | // { |
---|
| 2259 | // if (pComp0(r->m[an],p) == 1) |
---|
| 2260 | // { |
---|
| 2261 | // at=an; break; |
---|
| 2262 | // } |
---|
| 2263 | // else |
---|
| 2264 | // { |
---|
| 2265 | // at=en; break; |
---|
| 2266 | // } |
---|
| 2267 | // } |
---|
| 2268 | // i=(an+en) / 2; |
---|
| 2269 | // if (pComp0(r->m[i],p) == 1) en=i; |
---|
| 2270 | // else an=i; |
---|
| 2271 | // } |
---|
| 2272 | // } |
---|
| 2273 | // } |
---|
| 2274 | // if (pComp(r->m[at],p)==0) |
---|
| 2275 | // { |
---|
| 2276 | // pDelete(&p); |
---|
| 2277 | // } |
---|
| 2278 | // else |
---|
| 2279 | // { |
---|
| 2280 | // (*next)++; |
---|
| 2281 | // for (i=(*next); i>=at+1; i--) |
---|
| 2282 | // { |
---|
| 2283 | // r->m[i] = r->m[i-1]; |
---|
| 2284 | // } |
---|
| 2285 | // /*- save result -*/ |
---|
| 2286 | // r->m[at] = p; |
---|
| 2287 | // } |
---|
| 2288 | //} |
---|
[d353551] | 2289 | |
---|
[c616d1] | 2290 | #ifdef WITH_OLD_MINOR |
---|
| 2291 | /*2 |
---|
| 2292 | * compute all ar-minors of the matrix a |
---|
| 2293 | */ |
---|
| 2294 | ideal idMinors(matrix a, int ar) |
---|
| 2295 | { |
---|
| 2296 | int i,j,k,size; |
---|
| 2297 | int *rowchoise,*colchoise; |
---|
| 2298 | BOOLEAN rowch,colch; |
---|
| 2299 | ideal result; |
---|
| 2300 | matrix tmp; |
---|
| 2301 | poly p; |
---|
| 2302 | |
---|
| 2303 | i = binom(a->rows(),ar); |
---|
| 2304 | j = binom(a->cols(),ar); |
---|
| 2305 | |
---|
| 2306 | rowchoise=(int *)Alloc(ar*sizeof(int)); |
---|
| 2307 | colchoise=(int *)Alloc(ar*sizeof(int)); |
---|
| 2308 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
| 2309 | else size=i*j; |
---|
| 2310 | result=idInit(size,1); |
---|
| 2311 | tmp=mpNew(ar,ar); |
---|
| 2312 | k = 0; /* the index in result*/ |
---|
| 2313 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
| 2314 | while (!rowch) |
---|
| 2315 | { |
---|
| 2316 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
| 2317 | while (!colch) |
---|
| 2318 | { |
---|
| 2319 | for (i=1; i<=ar; i++) |
---|
| 2320 | { |
---|
| 2321 | for (j=1; j<=ar; j++) |
---|
| 2322 | { |
---|
| 2323 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
| 2324 | } |
---|
| 2325 | } |
---|
| 2326 | p = mpDetBareiss(tmp); |
---|
| 2327 | if (p!=NULL) |
---|
| 2328 | { |
---|
| 2329 | if (k>=size) |
---|
| 2330 | { |
---|
| 2331 | pEnlargeSet(&result->m,size,32); |
---|
| 2332 | size += 32; |
---|
| 2333 | } |
---|
| 2334 | result->m[k] = p; |
---|
| 2335 | k++; |
---|
| 2336 | } |
---|
| 2337 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
| 2338 | } |
---|
| 2339 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
| 2340 | } |
---|
| 2341 | /*delete the matrix tmp*/ |
---|
| 2342 | for (i=1; i<=ar; i++) |
---|
| 2343 | { |
---|
| 2344 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
| 2345 | } |
---|
| 2346 | idDelete((ideal*)&tmp); |
---|
| 2347 | if (k==0) |
---|
| 2348 | { |
---|
| 2349 | k=1; |
---|
| 2350 | result->m[0]=NULL; |
---|
| 2351 | } |
---|
| 2352 | Free((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
| 2353 | Free((ADDRESS)colchoise,ar*sizeof(int)); |
---|
| 2354 | pEnlargeSet(&result->m,size,k-size); |
---|
| 2355 | IDELEMS(result) = k; |
---|
| 2356 | return (result); |
---|
| 2357 | } |
---|
| 2358 | #else |
---|
[d353551] | 2359 | /*2 |
---|
| 2360 | * compute all ar-minors of the matrix a |
---|
[ef72ff3] | 2361 | * the caller of mpRecMin |
---|
[d353551] | 2362 | */ |
---|
[43580ac] | 2363 | ideal idMinors(matrix a, int ar) |
---|
[d353551] | 2364 | { |
---|
[ef72ff3] | 2365 | ideal result; |
---|
| 2366 | int elems=0; |
---|
| 2367 | |
---|
[d353551] | 2368 | if((ar<=0) || (ar>min(a->ncols,a->nrows))) |
---|
| 2369 | { |
---|
[74ec24c] | 2370 | Werror("%d-th minor, matrix is %dx%d",ar,a->ncols,a->nrows); |
---|
[d353551] | 2371 | return NULL; |
---|
| 2372 | } |
---|
[ef72ff3] | 2373 | a = mpCopy(a); |
---|
[87ff23] | 2374 | result=idInit(32,1); |
---|
[ef72ff3] | 2375 | if(ar>1) mpRecMin(ar-1,result,elems,a,a->nrows,a->ncols,NULL); |
---|
| 2376 | else mpMinorToResult(result,elems,a,a->nrows,a->ncols); |
---|
| 2377 | idDelete((ideal *)&a); |
---|
[d353551] | 2378 | idSkipZeroes(result); |
---|
[ef72ff3] | 2379 | idTest(result); |
---|
[d353551] | 2380 | return result; |
---|
| 2381 | } |
---|
[c616d1] | 2382 | #endif |
---|
| 2383 | |
---|
[0e1846] | 2384 | /*2 |
---|
| 2385 | *returns TRUE if p is a unit element in the current ring |
---|
| 2386 | */ |
---|
| 2387 | BOOLEAN pIsUnit(poly p) |
---|
| 2388 | { |
---|
[e78cce] | 2389 | int i; |
---|
[0e1846] | 2390 | |
---|
| 2391 | if (p == NULL) return FALSE; |
---|
[e78cce] | 2392 | i = 1; |
---|
| 2393 | while (i<=pVariables && pGetExp(p,i) == 0) i++; |
---|
| 2394 | if (i > pVariables && (pGetComp(p) == 0)) |
---|
[0e1846] | 2395 | { |
---|
[e78cce] | 2396 | if (currRing->OrdSgn == 1 && pNext(p) !=NULL) return FALSE; |
---|
| 2397 | return TRUE; |
---|
[0e1846] | 2398 | } |
---|
[e78cce] | 2399 | return FALSE; |
---|
[0e1846] | 2400 | } |
---|
| 2401 | |
---|
| 2402 | /*2 |
---|
| 2403 | *skips all zeroes and double elements, searches also for units |
---|
| 2404 | */ |
---|
| 2405 | ideal idCompactify(ideal id) |
---|
| 2406 | { |
---|
| 2407 | int i,j; |
---|
| 2408 | BOOLEAN b=FALSE; |
---|
| 2409 | |
---|
[b711e1] | 2410 | i = IDELEMS(id)-1; |
---|
[4b5c87] | 2411 | while ((! b) && (i>=0)) |
---|
[0e1846] | 2412 | { |
---|
[b711e1] | 2413 | b=pIsUnit(id->m[i]); |
---|
[4b5c87] | 2414 | i--; |
---|
[0e1846] | 2415 | } |
---|
| 2416 | if (b) |
---|
| 2417 | { |
---|
[b711e1] | 2418 | ideal result=idInit(1,id->rank); |
---|
[0e1846] | 2419 | result->m[0]=pOne(); |
---|
[b711e1] | 2420 | return result; |
---|
[0e1846] | 2421 | } |
---|
| 2422 | else |
---|
| 2423 | { |
---|
[b711e1] | 2424 | ideal result=idCopy(id); |
---|
[0e1846] | 2425 | for (i=1;i<IDELEMS(result);i++) |
---|
| 2426 | { |
---|
| 2427 | if (result->m[i]!=NULL) |
---|
| 2428 | { |
---|
| 2429 | for (j=0;j<i;j++) |
---|
| 2430 | { |
---|
| 2431 | if ((result->m[j]!=NULL) |
---|
| 2432 | && (pComparePolys(result->m[i],result->m[j]))) |
---|
| 2433 | { |
---|
| 2434 | pDelete(&(result->m[j])); |
---|
| 2435 | } |
---|
| 2436 | } |
---|
| 2437 | } |
---|
| 2438 | } |
---|
[b711e1] | 2439 | idSkipZeroes(result); |
---|
| 2440 | return result; |
---|
[0e1846] | 2441 | } |
---|
| 2442 | } |
---|
| 2443 | |
---|
| 2444 | /*2 |
---|
| 2445 | *returns TRUE if id1 is a submodule of id2 |
---|
| 2446 | */ |
---|
| 2447 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
| 2448 | { |
---|
| 2449 | int i; |
---|
| 2450 | poly p; |
---|
| 2451 | |
---|
| 2452 | if (idIs0(id1)) return TRUE; |
---|
| 2453 | for (i=0;i<IDELEMS(id1);i++) |
---|
| 2454 | { |
---|
| 2455 | if (id1->m[i] != NULL) |
---|
| 2456 | { |
---|
| 2457 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
| 2458 | if (p != NULL) |
---|
| 2459 | { |
---|
| 2460 | pDelete(&p); |
---|
| 2461 | return FALSE; |
---|
| 2462 | } |
---|
| 2463 | } |
---|
| 2464 | } |
---|
| 2465 | return TRUE; |
---|
| 2466 | } |
---|
| 2467 | |
---|
| 2468 | /*2 |
---|
| 2469 | * returns the ideals of initial terms |
---|
| 2470 | */ |
---|
| 2471 | ideal idHead(ideal h) |
---|
| 2472 | { |
---|
| 2473 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
| 2474 | int i; |
---|
| 2475 | |
---|
[4b5c87] | 2476 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
[0e1846] | 2477 | { |
---|
[4b5c87] | 2478 | if (h->m[i]!=NULL) m->m[i]=pHead(h->m[i]); |
---|
[0e1846] | 2479 | } |
---|
| 2480 | return m; |
---|
| 2481 | } |
---|
| 2482 | |
---|
| 2483 | ideal idHomogen(ideal h, int varnum) |
---|
| 2484 | { |
---|
| 2485 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
| 2486 | int i; |
---|
| 2487 | |
---|
[4b5c87] | 2488 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
[0e1846] | 2489 | { |
---|
| 2490 | m->m[i]=pHomogen(h->m[i],varnum); |
---|
| 2491 | } |
---|
| 2492 | return m; |
---|
| 2493 | } |
---|
| 2494 | |
---|
| 2495 | /*------------------type conversions----------------*/ |
---|
| 2496 | ideal idVec2Ideal(poly vec) |
---|
| 2497 | { |
---|
| 2498 | ideal result=idInit(1,1); |
---|
[b7b08c] | 2499 | FreeSizeOf((ADDRESS)result->m,poly); |
---|
[0e1846] | 2500 | result->m=NULL; // remove later |
---|
| 2501 | pVec2Polys(vec, &(result->m), &(IDELEMS(result))); |
---|
| 2502 | return result; |
---|
| 2503 | } |
---|
| 2504 | |
---|
[87bef42] | 2505 | // converts mat to module, destroys mat |
---|
[0e1846] | 2506 | ideal idMatrix2Module(matrix mat) |
---|
| 2507 | { |
---|
| 2508 | ideal result = idInit(MATCOLS(mat),MATROWS(mat)); |
---|
| 2509 | int i,j; |
---|
| 2510 | poly h; |
---|
| 2511 | #ifdef DRING |
---|
| 2512 | poly p; |
---|
| 2513 | #endif |
---|
| 2514 | |
---|
| 2515 | for(j=0;j<MATCOLS(mat);j++) /* j is also index in result->m */ |
---|
| 2516 | { |
---|
| 2517 | for (i=1;i<=MATROWS(mat);i++) |
---|
| 2518 | { |
---|
| 2519 | h = MATELEM(mat,i,j+1); |
---|
| 2520 | if (h!=NULL) |
---|
| 2521 | { |
---|
| 2522 | MATELEM(mat,i,j+1)=NULL; |
---|
| 2523 | pSetCompP(h,i); |
---|
| 2524 | #ifdef DRING |
---|
[311499] | 2525 | pdSetDFlagP(h,0); |
---|
[0e1846] | 2526 | #endif |
---|
| 2527 | result->m[j] = pAdd(result->m[j],h); |
---|
| 2528 | } |
---|
| 2529 | } |
---|
| 2530 | } |
---|
[b7b08c] | 2531 | // obachman: need to clean this up |
---|
| 2532 | idDelete((ideal*) &mat); |
---|
[0e1846] | 2533 | return result; |
---|
| 2534 | } |
---|
| 2535 | |
---|
| 2536 | /*2 |
---|
| 2537 | * converts a module into a matrix, destroyes the input |
---|
| 2538 | */ |
---|
| 2539 | matrix idModule2Matrix(ideal mod) |
---|
| 2540 | { |
---|
| 2541 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
| 2542 | int i,cp; |
---|
| 2543 | poly p,h; |
---|
| 2544 | |
---|
| 2545 | for(i=0;i<IDELEMS(mod);i++) |
---|
| 2546 | { |
---|
| 2547 | p=mod->m[i]; |
---|
| 2548 | mod->m[i]=NULL; |
---|
| 2549 | while (p!=NULL) |
---|
| 2550 | { |
---|
| 2551 | h=p; |
---|
| 2552 | pIter(p); |
---|
| 2553 | pNext(h)=NULL; |
---|
| 2554 | // cp = max(1,pGetComp(h)); // if used for ideals too |
---|
| 2555 | cp = pGetComp(h); |
---|
| 2556 | pSetComp(h,0); |
---|
[66a672] | 2557 | pSetmComp(h); |
---|
[0e1846] | 2558 | #ifdef TEST |
---|
| 2559 | if (cp>mod->rank) |
---|
| 2560 | { |
---|
| 2561 | Print("## inv. rank %d -> %d\n",mod->rank,cp); |
---|
| 2562 | int k,l,o=mod->rank; |
---|
| 2563 | mod->rank=cp; |
---|
| 2564 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
| 2565 | for (l=1; l<=o; l++) |
---|
| 2566 | { |
---|
| 2567 | for (k=1; k<=IDELEMS(mod); k++) |
---|
| 2568 | { |
---|
| 2569 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
| 2570 | MATELEM(result,l,k)=NULL; |
---|
| 2571 | } |
---|
| 2572 | } |
---|
| 2573 | idDelete((ideal *)&result); |
---|
| 2574 | result=d; |
---|
| 2575 | } |
---|
| 2576 | #endif |
---|
| 2577 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
| 2578 | } |
---|
| 2579 | } |
---|
[87bef42] | 2580 | // obachman 10/99: added the following line, otherwise memory lack! |
---|
[b7b08c] | 2581 | idDelete(&mod); |
---|
[0e1846] | 2582 | return result; |
---|
| 2583 | } |
---|
| 2584 | |
---|
| 2585 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols) |
---|
| 2586 | { |
---|
| 2587 | matrix result = mpNew(rows,cols); |
---|
| 2588 | int i,cp,r=idRankFreeModule(mod),c=IDELEMS(mod); |
---|
| 2589 | poly p,h; |
---|
| 2590 | |
---|
| 2591 | if (r>rows) r = rows; |
---|
| 2592 | if (c>cols) c = cols; |
---|
| 2593 | for(i=0;i<c;i++) |
---|
| 2594 | { |
---|
| 2595 | p=mod->m[i]; |
---|
| 2596 | mod->m[i]=NULL; |
---|
| 2597 | while (p!=NULL) |
---|
| 2598 | { |
---|
| 2599 | h=p; |
---|
| 2600 | pIter(p); |
---|
| 2601 | pNext(h)=NULL; |
---|
| 2602 | cp = pGetComp(h); |
---|
| 2603 | if (cp<=r) |
---|
| 2604 | { |
---|
| 2605 | pSetComp(h,0); |
---|
[66a672] | 2606 | pSetmComp(h); |
---|
[0e1846] | 2607 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
| 2608 | } |
---|
| 2609 | else |
---|
| 2610 | pDelete(&h); |
---|
| 2611 | } |
---|
| 2612 | } |
---|
| 2613 | idDelete(&mod); |
---|
| 2614 | return result; |
---|
| 2615 | } |
---|
| 2616 | |
---|
| 2617 | /*2 |
---|
| 2618 | * substitute the n-th variable by the monomial e in id |
---|
| 2619 | * destroy id |
---|
| 2620 | */ |
---|
| 2621 | ideal idSubst(ideal id, int n, poly e) |
---|
| 2622 | { |
---|
| 2623 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
| 2624 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
| 2625 | |
---|
| 2626 | res->rank = id->rank; |
---|
| 2627 | for(k--;k>=0;k--) |
---|
| 2628 | { |
---|
| 2629 | res->m[k]=pSubst(id->m[k],n,e); |
---|
| 2630 | id->m[k]=NULL; |
---|
| 2631 | } |
---|
| 2632 | idDelete(&id); |
---|
| 2633 | return res; |
---|
| 2634 | } |
---|
| 2635 | |
---|
| 2636 | BOOLEAN idHomModule(ideal m, ideal Q, intvec **w) |
---|
| 2637 | { |
---|
[9734571] | 2638 | if (w!=NULL) *w=NULL; |
---|
| 2639 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) return FALSE; |
---|
| 2640 | if (idIs0(m)) return TRUE; |
---|
| 2641 | |
---|
[0e1846] | 2642 | int i,j,cmax=2,order=0,ord,* diff,* iscom,diffmin=32000; |
---|
| 2643 | poly p=NULL; |
---|
| 2644 | int length=IDELEMS(m); |
---|
| 2645 | polyset P=m->m; |
---|
[9734571] | 2646 | polyset F=(polyset)Alloc(length*sizeof(poly)); |
---|
[0e1846] | 2647 | for (i=length-1;i>=0;i--) |
---|
| 2648 | { |
---|
| 2649 | p=F[i]=P[i]; |
---|
| 2650 | cmax=max(cmax,pMaxComp(p)+1); |
---|
| 2651 | } |
---|
| 2652 | diff = (int *)Alloc0(cmax*sizeof(int)); |
---|
[477993] | 2653 | if (w!=NULL) *w=NewIntvec1(cmax-1); |
---|
[0e1846] | 2654 | iscom = (int *)Alloc0(cmax*sizeof(int)); |
---|
| 2655 | i=0; |
---|
| 2656 | while (i<=length) |
---|
| 2657 | { |
---|
| 2658 | if (i<length) |
---|
| 2659 | { |
---|
| 2660 | p=F[i]; |
---|
| 2661 | while ((p!=NULL) && (!iscom[pGetComp(p)])) pIter(p); |
---|
| 2662 | } |
---|
| 2663 | if ((p==NULL) && (i<length)) |
---|
| 2664 | { |
---|
| 2665 | i++; |
---|
| 2666 | } |
---|
| 2667 | else |
---|
| 2668 | { |
---|
| 2669 | if (p==NULL) |
---|
| 2670 | { |
---|
| 2671 | i=0; |
---|
| 2672 | while ((i<length) && (F[i]==NULL)) i++; |
---|
| 2673 | if (i>=length) break; |
---|
| 2674 | p = F[i]; |
---|
| 2675 | } |
---|
[9734571] | 2676 | if (pLexOrder) |
---|
| 2677 | order=pTotaldegree(p); |
---|
| 2678 | else |
---|
[0e1846] | 2679 | // order = p->order; |
---|
[9734571] | 2680 | order = pFDeg(p); |
---|
[0e1846] | 2681 | order += diff[pGetComp(p)]; |
---|
| 2682 | p = F[i]; |
---|
| 2683 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
| 2684 | F[i] = NULL; |
---|
| 2685 | i=0; |
---|
| 2686 | } |
---|
| 2687 | while (p!=NULL) |
---|
| 2688 | { |
---|
| 2689 | //if (pLexOrder) |
---|
| 2690 | // ord=pTotaldegree(p); |
---|
| 2691 | //else |
---|
| 2692 | // ord = p->order; |
---|
| 2693 | ord = pFDeg(p); |
---|
| 2694 | if (!iscom[pGetComp(p)]) |
---|
| 2695 | { |
---|
| 2696 | diff[pGetComp(p)] = order-ord; |
---|
| 2697 | iscom[pGetComp(p)] = 1; |
---|
| 2698 | /* |
---|
| 2699 | *PrintS("new diff: "); |
---|
| 2700 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
| 2701 | *PrintLn(); |
---|
| 2702 | *PrintS("new iscom: "); |
---|
| 2703 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
| 2704 | *PrintLn(); |
---|
| 2705 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
| 2706 | */ |
---|
| 2707 | } |
---|
| 2708 | else |
---|
| 2709 | { |
---|
| 2710 | /* |
---|
| 2711 | *PrintS("new diff: "); |
---|
| 2712 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
| 2713 | *PrintLn(); |
---|
| 2714 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
| 2715 | */ |
---|
| 2716 | if (order != ord+diff[pGetComp(p)]) |
---|
| 2717 | { |
---|
| 2718 | Free((ADDRESS) iscom,cmax*sizeof(int)); |
---|
| 2719 | Free((ADDRESS) diff,cmax*sizeof(int)); |
---|
| 2720 | Free((ADDRESS) F,length*sizeof(poly)); |
---|
| 2721 | delete *w;*w=NULL; |
---|
| 2722 | return FALSE; |
---|
| 2723 | } |
---|
| 2724 | } |
---|
| 2725 | pIter(p); |
---|
| 2726 | } |
---|
| 2727 | } |
---|
| 2728 | Free((ADDRESS) iscom,cmax*sizeof(int)); |
---|
| 2729 | Free((ADDRESS) F,length*sizeof(poly)); |
---|
| 2730 | for (i=1;i<cmax;i++) (**w)[i-1]=diff[i]; |
---|
| 2731 | for (i=1;i<cmax;i++) |
---|
| 2732 | { |
---|
| 2733 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
| 2734 | } |
---|
[dc87300] | 2735 | if (w!=NULL) |
---|
[0e1846] | 2736 | { |
---|
[dc87300] | 2737 | for (i=1;i<cmax;i++) |
---|
| 2738 | { |
---|
| 2739 | (**w)[i-1]=diff[i]-diffmin; |
---|
| 2740 | } |
---|
[0e1846] | 2741 | } |
---|
| 2742 | Free((ADDRESS) diff,cmax*sizeof(int)); |
---|
| 2743 | return TRUE; |
---|
| 2744 | } |
---|
| 2745 | |
---|
| 2746 | ideal idJet(ideal i,int d) |
---|
| 2747 | { |
---|
[f70c18] | 2748 | ideal r=idInit((i->nrows)*(i->ncols),i->rank); |
---|
[473707b] | 2749 | r->nrows = i-> nrows; |
---|
[f70c18] | 2750 | r->ncols = i-> ncols; |
---|
[473707b] | 2751 | //r->rank = i-> rank; |
---|
[0e1846] | 2752 | int k; |
---|
[473707b] | 2753 | for(k=(i->nrows)*(i->ncols)-1;k>=0; k--) |
---|
[0e1846] | 2754 | { |
---|
| 2755 | r->m[k]=pJet(i->m[k],d); |
---|
| 2756 | } |
---|
| 2757 | return r; |
---|
| 2758 | } |
---|
| 2759 | |
---|
| 2760 | ideal idJetW(ideal i,int d, intvec * iv) |
---|
| 2761 | { |
---|
| 2762 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
| 2763 | if (ecartWeights!=NULL) |
---|
| 2764 | { |
---|
[da97958] | 2765 | WerrorS("cannot compute weighted jets now"); |
---|
[0e1846] | 2766 | } |
---|
| 2767 | else |
---|
| 2768 | { |
---|
| 2769 | short *w=iv2array(iv); |
---|
| 2770 | int k; |
---|
| 2771 | for(k=0; k<IDELEMS(i); k++) |
---|
| 2772 | { |
---|
| 2773 | r->m[k]=pJetW(i->m[k],d,w); |
---|
| 2774 | } |
---|
| 2775 | Free((ADDRESS)w,(pVariables+1)*sizeof(short)); |
---|
| 2776 | } |
---|
| 2777 | return r; |
---|
| 2778 | } |
---|
| 2779 | |
---|
| 2780 | matrix idDiff(matrix i, int k) |
---|
| 2781 | { |
---|
| 2782 | int e=MATCOLS(i)*MATROWS(i); |
---|
| 2783 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
| 2784 | int j; |
---|
| 2785 | for(j=0; j<e; j++) |
---|
| 2786 | { |
---|
| 2787 | r->m[j]=pDiff(i->m[j],k); |
---|
| 2788 | } |
---|
| 2789 | return r; |
---|
| 2790 | } |
---|
| 2791 | |
---|
| 2792 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
| 2793 | { |
---|
| 2794 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
| 2795 | int i,j; |
---|
| 2796 | for(i=0; i<IDELEMS(I); i++) |
---|
| 2797 | { |
---|
| 2798 | for(j=0; j<IDELEMS(J); j++) |
---|
| 2799 | { |
---|
| 2800 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
| 2801 | } |
---|
| 2802 | } |
---|
| 2803 | return r; |
---|
| 2804 | } |
---|
| 2805 | |
---|
[416465] | 2806 | /*3 |
---|
| 2807 | *handles for some ideal operations the ring/syzcomp managment |
---|
| 2808 | *returns all syzygies (componentwise-)shifted by -syzcomp |
---|
| 2809 | *or -syzcomp-1 (in case of ideals as input) |
---|
| 2810 | static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE) |
---|
| 2811 | { |
---|
| 2812 | ring orig_ring=currRing; |
---|
| 2813 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
| 2814 | rSetSyzComp(length); |
---|
| 2815 | |
---|
| 2816 | ideal s_temp; |
---|
| 2817 | if (orig_ring!=syz_ring) |
---|
| 2818 | s_temp=idrMoveR_NoSort(arg,orig_ring); |
---|
| 2819 | else |
---|
| 2820 | s_temp=arg; |
---|
| 2821 | |
---|
| 2822 | ideal s_temp1 = kStd(s_temp,currQuotient,testHomog,&w,NULL,length); |
---|
| 2823 | if (w!=NULL) delete w; |
---|
| 2824 | |
---|
| 2825 | if (syz_ring!=orig_ring) |
---|
| 2826 | { |
---|
| 2827 | idDelete(&s_temp); |
---|
| 2828 | rChangeCurrRing(orig_ring,TRUE); |
---|
| 2829 | } |
---|
| 2830 | |
---|
| 2831 | idDelete(&temp); |
---|
| 2832 | ideal temp1=idRingCopy(s_temp1,syz_ring); |
---|
| 2833 | |
---|
| 2834 | if (syz_ring!=orig_ring) |
---|
| 2835 | { |
---|
| 2836 | rChangeCurrRing(syz_ring,FALSE); |
---|
| 2837 | idDelete(&s_temp1); |
---|
| 2838 | rChangeCurrRing(orig_ring,TRUE); |
---|
| 2839 | rKill(syz_ring); |
---|
| 2840 | } |
---|
| 2841 | |
---|
| 2842 | for (i=0;i<IDELEMS(temp1);i++) |
---|
| 2843 | { |
---|
| 2844 | if ((temp1->m[i]!=NULL) |
---|
| 2845 | && (pGetComp(temp1->m[i])<=length)) |
---|
| 2846 | { |
---|
| 2847 | pDelete(&(temp1->m[i])); |
---|
| 2848 | } |
---|
| 2849 | else |
---|
| 2850 | { |
---|
| 2851 | pShift(&(temp1->m[i]),-length); |
---|
| 2852 | } |
---|
| 2853 | } |
---|
| 2854 | temp1->rank = rk; |
---|
| 2855 | idSkipZeroes(temp1); |
---|
| 2856 | |
---|
| 2857 | return temp1; |
---|
| 2858 | } |
---|
| 2859 | */ |
---|
[0e1846] | 2860 | /*2 |
---|
| 2861 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
| 2862 | */ |
---|
| 2863 | ideal idModulo (ideal h2,ideal h1) |
---|
| 2864 | { |
---|
| 2865 | int i,j,k,rk,flength=0,slength,length; |
---|
[4c001a] | 2866 | intvec * w; |
---|
[0e1846] | 2867 | poly p,q; |
---|
| 2868 | |
---|
| 2869 | if (idIs0(h2)) |
---|
| 2870 | return idFreeModule(max(1,h2->ncols)); |
---|
| 2871 | if (!idIs0(h1)) |
---|
| 2872 | flength = idRankFreeModule(h1); |
---|
| 2873 | slength = idRankFreeModule(h2); |
---|
| 2874 | length = max(flength,slength); |
---|
| 2875 | if (length==0) |
---|
| 2876 | { |
---|
| 2877 | length = 1; |
---|
| 2878 | } |
---|
[7bab5d] | 2879 | ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2)); |
---|
[0e1846] | 2880 | for (i=0;i<IDELEMS(h2);i++) |
---|
| 2881 | { |
---|
| 2882 | temp->m[i] = pCopy(h2->m[i]); |
---|
| 2883 | q = pOne(); |
---|
| 2884 | pSetComp(q,i+1+length); |
---|
[66a672] | 2885 | pSetmComp(q); |
---|
[0e1846] | 2886 | if(temp->m[i]!=NULL) |
---|
| 2887 | { |
---|
| 2888 | if (slength==0) pShift(&(temp->m[i]),1); |
---|
| 2889 | p = temp->m[i]; |
---|
| 2890 | while (pNext(p)!=NULL) pIter(p); |
---|
| 2891 | pNext(p) = q; |
---|
| 2892 | } |
---|
| 2893 | else |
---|
| 2894 | temp->m[i]=q; |
---|
| 2895 | } |
---|
| 2896 | rk = k = IDELEMS(h2); |
---|
| 2897 | if (!idIs0(h1)) |
---|
| 2898 | { |
---|
| 2899 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
| 2900 | IDELEMS(temp) += IDELEMS(h1); |
---|
| 2901 | for (i=0;i<IDELEMS(h1);i++) |
---|
| 2902 | { |
---|
| 2903 | if (h1->m[i]!=NULL) |
---|
| 2904 | { |
---|
| 2905 | temp->m[k] = pCopy(h1->m[i]); |
---|
| 2906 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
| 2907 | k++; |
---|
| 2908 | } |
---|
| 2909 | } |
---|
| 2910 | } |
---|
[b9a806] | 2911 | |
---|
| 2912 | ring orig_ring=currRing; |
---|
[9d06971] | 2913 | ring syz_ring=rCurrRingAssureSyzComp(); |
---|
[416465] | 2914 | rSetSyzComp(length); |
---|
| 2915 | ideal s_temp; |
---|
| 2916 | |
---|
| 2917 | if (syz_ring != orig_ring) |
---|
[b9a806] | 2918 | { |
---|
[416465] | 2919 | s_temp = idrCopyR_NoSort(temp, orig_ring); |
---|
[b9a806] | 2920 | } |
---|
[416465] | 2921 | else |
---|
[b9a806] | 2922 | { |
---|
[416465] | 2923 | s_temp = temp; |
---|
[b9a806] | 2924 | } |
---|
[416465] | 2925 | |
---|
| 2926 | ideal s_temp1 = kStd(s_temp,currQuotient,testHomog,&w,NULL,length); |
---|
| 2927 | if (w!=NULL) delete w; |
---|
[b9a806] | 2928 | |
---|
[416465] | 2929 | for (i=0;i<IDELEMS(s_temp1);i++) |
---|
[0e1846] | 2930 | { |
---|
[416465] | 2931 | if ((s_temp1->m[i]!=NULL) |
---|
| 2932 | && (pGetComp(s_temp1->m[i])<=length)) |
---|
[0e1846] | 2933 | { |
---|
[416465] | 2934 | pDelete(&(s_temp1->m[i])); |
---|
[0e1846] | 2935 | } |
---|
| 2936 | else |
---|
| 2937 | { |
---|
[416465] | 2938 | pShift(&(s_temp1->m[i]),-length); |
---|
[0e1846] | 2939 | } |
---|
| 2940 | } |
---|
[416465] | 2941 | s_temp1->rank = rk; |
---|
| 2942 | idSkipZeroes(s_temp1); |
---|
[b9a806] | 2943 | |
---|
[416465] | 2944 | if (syz_ring!=orig_ring) |
---|
| 2945 | { |
---|
| 2946 | rChangeCurrRing(orig_ring,TRUE); |
---|
| 2947 | s_temp = idrMoveR_NoSort(s_temp, syz_ring); |
---|
| 2948 | idDelete(&temp); |
---|
| 2949 | rKill(syz_ring); |
---|
| 2950 | } |
---|
| 2951 | return s_temp1; |
---|
[0e1846] | 2952 | } |
---|
| 2953 | |
---|
| 2954 | int idElem(ideal F) |
---|
| 2955 | { |
---|
| 2956 | int i=0,j=0; |
---|
| 2957 | |
---|
| 2958 | while(j<IDELEMS(F)) |
---|
| 2959 | { |
---|
| 2960 | if ((F->m)[j]!=NULL) i++; |
---|
| 2961 | j++; |
---|
| 2962 | } |
---|
| 2963 | return i; |
---|
| 2964 | } |
---|
| 2965 | |
---|
| 2966 | /* |
---|
| 2967 | *computes module-weights for liftings of homogeneous modules |
---|
| 2968 | */ |
---|
| 2969 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
| 2970 | { |
---|
[477993] | 2971 | if (idIs0(mod)) return NewIntvec1(2); |
---|
[0e1846] | 2972 | int i=IDELEMS(mod); |
---|
| 2973 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
[477993] | 2974 | intvec *result = NewIntvec1(i+1); |
---|
[0e1846] | 2975 | while (i>0) |
---|
| 2976 | { |
---|
| 2977 | (*result)[i]=pFDeg(mod->m[i])+(*weights)[pGetComp(mod->m[i])]; |
---|
| 2978 | } |
---|
| 2979 | return result; |
---|
| 2980 | } |
---|
| 2981 | |
---|
| 2982 | /*2 |
---|
| 2983 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
| 2984 | *with x_max,...,x_1) |
---|
| 2985 | */ |
---|
| 2986 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
| 2987 | { |
---|
| 2988 | int i; |
---|
| 2989 | ideal result; |
---|
| 2990 | |
---|
| 2991 | if (idIs0(kBase)) return NULL; |
---|
| 2992 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
| 2993 | *convert = idSort(kBase,FALSE); |
---|
| 2994 | for (i=0;i<(*convert)->length();i++) |
---|
| 2995 | { |
---|
| 2996 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
| 2997 | } |
---|
| 2998 | return result; |
---|
| 2999 | } |
---|
| 3000 | |
---|
| 3001 | /*2 |
---|
| 3002 | *returns the index of a given monom in the list of the special kbase |
---|
| 3003 | */ |
---|
| 3004 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
| 3005 | { |
---|
| 3006 | int j=IDELEMS(kbase); |
---|
| 3007 | |
---|
| 3008 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
| 3009 | if (j==0) return -1; |
---|
| 3010 | int i=pVariables; |
---|
[50619f7] | 3011 | while (i>0) |
---|
[0e1846] | 3012 | { |
---|
[50619f7] | 3013 | loop |
---|
| 3014 | { |
---|
| 3015 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
| 3016 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
| 3017 | j--; |
---|
| 3018 | if (j==0) return -1; |
---|
| 3019 | } |
---|
| 3020 | if (i==1) |
---|
| 3021 | { |
---|
| 3022 | while(j>0) |
---|
| 3023 | { |
---|
| 3024 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
| 3025 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
| 3026 | j--; |
---|
| 3027 | } |
---|
| 3028 | } |
---|
| 3029 | i--; |
---|
[0e1846] | 3030 | } |
---|
| 3031 | return -1; |
---|
| 3032 | } |
---|
| 3033 | |
---|
| 3034 | /*2 |
---|
| 3035 | *decomposes the monom in a part of coefficients described by the |
---|
| 3036 | *complement of how and a monom in variables occuring in how, the |
---|
| 3037 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
| 3038 | *exists) |
---|
| 3039 | */ |
---|
| 3040 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
| 3041 | { |
---|
| 3042 | int i; |
---|
| 3043 | poly coeff=pOne(), base=pOne(); |
---|
| 3044 | |
---|
| 3045 | for (i=1;i<=pVariables;i++) |
---|
| 3046 | { |
---|
| 3047 | if (pGetExp(how,i)>0) |
---|
| 3048 | { |
---|
| 3049 | pSetExp(base,i,pGetExp(monom,i)); |
---|
| 3050 | } |
---|
| 3051 | else |
---|
| 3052 | { |
---|
| 3053 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
| 3054 | } |
---|
| 3055 | } |
---|
| 3056 | pSetComp(base,pGetComp(monom)); |
---|
| 3057 | pSetm(base); |
---|
| 3058 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
| 3059 | pSetm(coeff); |
---|
| 3060 | *pos = idIndexOfKBase(base,kbase); |
---|
| 3061 | if (*pos<0) |
---|
| 3062 | pDelete(&coeff); |
---|
| 3063 | pDelete(&base); |
---|
| 3064 | return coeff; |
---|
| 3065 | } |
---|
| 3066 | |
---|
| 3067 | /*2 |
---|
| 3068 | *returns a matrix A of coefficients with kbase*A=arg |
---|
| 3069 | *if all monomials in variables of how occur in kbase |
---|
| 3070 | *the other are deleted |
---|
| 3071 | */ |
---|
| 3072 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
| 3073 | { |
---|
| 3074 | matrix result; |
---|
| 3075 | ideal tempKbase; |
---|
| 3076 | poly p,q; |
---|
| 3077 | intvec * convert; |
---|
| 3078 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
[16262b7] | 3079 | #if 0 |
---|
[0e1846] | 3080 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
| 3081 | if (idIs0(arg)) |
---|
| 3082 | return mpNew(i,1); |
---|
| 3083 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
| 3084 | result = mpNew(i,j); |
---|
[16262b7] | 3085 | #else |
---|
| 3086 | result = mpNew(i, j); |
---|
| 3087 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
| 3088 | #endif |
---|
| 3089 | |
---|
[0e1846] | 3090 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
| 3091 | for (k=0;k<j;k++) |
---|
| 3092 | { |
---|
| 3093 | p = arg->m[k]; |
---|
| 3094 | while (p!=NULL) |
---|
| 3095 | { |
---|
| 3096 | q = idDecompose(p,how,tempKbase,&pos); |
---|
| 3097 | if (pos>=0) |
---|
| 3098 | { |
---|
| 3099 | MATELEM(result,(*convert)[pos],k+1) = |
---|
| 3100 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
| 3101 | } |
---|
| 3102 | else |
---|
| 3103 | pDelete(&q); |
---|
[50619f7] | 3104 | pIter(p); |
---|
[0e1846] | 3105 | } |
---|
| 3106 | } |
---|
| 3107 | idDelete(&tempKbase); |
---|
| 3108 | return result; |
---|
| 3109 | } |
---|
| 3110 | |
---|
| 3111 | intvec * idQHomWeights(ideal id) |
---|
| 3112 | { |
---|
[477993] | 3113 | intvec * imat=NewIntvec3(2*pVariables,pVariables,0); |
---|
[0e1846] | 3114 | poly actHead=NULL,wPoint=NULL; |
---|
| 3115 | int actIndex,i=-1,j=1,k; |
---|
| 3116 | BOOLEAN notReady=TRUE; |
---|
| 3117 | |
---|
| 3118 | while (notReady) |
---|
| 3119 | { |
---|
| 3120 | if (wPoint==NULL) |
---|
| 3121 | { |
---|
| 3122 | i++; |
---|
| 3123 | while ((i<IDELEMS(id)) |
---|
| 3124 | && ((id->m[i]==NULL) || (pNext(id->m[i])==NULL))) |
---|
| 3125 | i++; |
---|
| 3126 | if (i<IDELEMS(id)) |
---|
| 3127 | { |
---|
| 3128 | actHead = id->m[i]; |
---|
| 3129 | wPoint = pNext(actHead); |
---|
| 3130 | } |
---|
| 3131 | } |
---|
| 3132 | while ((wPoint!=NULL) && (j<=2*pVariables)) |
---|
| 3133 | { |
---|
| 3134 | for (k=1;k<=pVariables;k++) |
---|
| 3135 | IMATELEM(*imat,j,k) += pGetExp(actHead,k)-pGetExp(wPoint,k); |
---|
| 3136 | pIter(wPoint); |
---|
| 3137 | j++; |
---|
| 3138 | } |
---|
| 3139 | if ((i>=IDELEMS(id)) || (j>2*pVariables)) |
---|
| 3140 | { |
---|
| 3141 | ivTriangMat(imat,1,1); |
---|
| 3142 | j = ivFirstEmptyRow(imat); |
---|
| 3143 | if ((i>=IDELEMS(id)) || (j>pVariables)) notReady=FALSE; |
---|
| 3144 | } |
---|
| 3145 | } |
---|
| 3146 | intvec *result=NULL; |
---|
| 3147 | if (j<=pVariables) |
---|
| 3148 | { |
---|
| 3149 | result=ivSolveIntMat(imat); |
---|
| 3150 | } |
---|
| 3151 | //else |
---|
| 3152 | //{ |
---|
[da97958] | 3153 | // WerrorS("not homogeneous"); |
---|
[0e1846] | 3154 | //} |
---|
| 3155 | delete imat; |
---|
| 3156 | return result; |
---|
| 3157 | } |
---|
| 3158 | |
---|
[416465] | 3159 | /*3 |
---|
| 3160 | * searches for units in the components of the module arg and |
---|
| 3161 | * returns the first one |
---|
[0e1846] | 3162 | */ |
---|
[416465] | 3163 | static int idReadOutUnits(ideal arg,int* comp) |
---|
[0e1846] | 3164 | { |
---|
[416465] | 3165 | if (idIs0(arg)) return -1; |
---|
| 3166 | int i=0,j,rk_arg=idRankFreeModule(arg),generator=-1; |
---|
| 3167 | intvec * componentIsUsed =new intvec(rk_arg+1); |
---|
[0e1846] | 3168 | poly p,q; |
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| 3169 | |
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[416465] | 3170 | while ((i<IDELEMS(arg)) && (generator<0)) |
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[0e1846] | 3171 | { |
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[416465] | 3172 | for (j=rk_arg;j>=0;j--) |
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| 3173 | (*componentIsUsed)[j]=0; |
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| 3174 | p = arg->m[i]; |
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| 3175 | while (p!=NULL) |
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| 3176 | { |
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| 3177 | j = pGetComp(p); |
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| 3178 | if ((*componentIsUsed)[j]==0) |
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[0e1846] | 3179 | { |
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[416465] | 3180 | if (pIsConstantComp(p)) |
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[0e1846] | 3181 | { |
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[416465] | 3182 | generator = i; |
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| 3183 | (*componentIsUsed)[j] = 1; |
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| 3184 | } |
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| 3185 | else |
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| 3186 | { |
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| 3187 | (*componentIsUsed)[j] = -1; |
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[0e1846] | 3188 | } |
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| 3189 | } |
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[416465] | 3190 | else if ((*componentIsUsed)[j]>0) |
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| 3191 | { |
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| 3192 | ((*componentIsUsed)[j])++; |
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| 3193 | } |
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| 3194 | pIter(p); |
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[0e1846] | 3195 | } |
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[416465] | 3196 | i++; |
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| 3197 | } |
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| 3198 | i = 0; |
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| 3199 | *comp = -1; |
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| 3200 | for (j=0;j<=rk_arg;j++) |
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| 3201 | { |
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| 3202 | if ((*componentIsUsed)[j]>0) |
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[0e1846] | 3203 | { |
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[416465] | 3204 | if ((*comp==-1) || ((*componentIsUsed)[j]<i)) |
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[0e1846] | 3205 | { |
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[416465] | 3206 | *comp = j; |
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| 3207 | i= (*componentIsUsed)[j]; |
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[0e1846] | 3208 | } |
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[dc32d42] | 3209 | } |
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[416465] | 3210 | } |
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| 3211 | return generator; |
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| 3212 | } |
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| 3213 | |
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| 3214 | static void idDeleteComp(ideal arg,int red_comp) |
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| 3215 | { |
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| 3216 | int i,j; |
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| 3217 | poly p; |
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| 3218 | |
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| 3219 | for (i=IDELEMS(arg)-1;i>=0;i--) |
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| 3220 | { |
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| 3221 | p = arg->m[i]; |
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| 3222 | while (p!=NULL) |
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[dc32d42] | 3223 | { |
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[416465] | 3224 | j = pGetComp(p); |
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| 3225 | if (j>red_comp) |
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| 3226 | { |
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| 3227 | pSetComp(p,j-1); |
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| 3228 | pSetm(p); |
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| 3229 | } |
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| 3230 | pIter(p); |
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[0e1846] | 3231 | } |
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| 3232 | } |
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[416465] | 3233 | (arg->rank)--; |
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| 3234 | } |
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| 3235 | |
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| 3236 | /*2 |
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| 3237 | * returns the presentation of an isomorphic, minimally |
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| 3238 | * embedded module |
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| 3239 | */ |
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| 3240 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace) |
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| 3241 | { |
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| 3242 | if (idIs0(arg)) return idInit(1,arg->rank); |
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| 3243 | int next_gen,next_comp; |
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| 3244 | ideal res=arg; |
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| 3245 | |
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| 3246 | if (!inPlace) res = idCopy(arg); |
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| 3247 | loop |
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| 3248 | { |
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| 3249 | next_gen = idReadOutUnits(res,&next_comp); |
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| 3250 | if (next_gen<0) break; |
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| 3251 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
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| 3252 | idDeleteComp(res,next_comp); |
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| 3253 | } |
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| 3254 | idSkipZeroes(res); |
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[0e1846] | 3255 | return res; |
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| 3256 | } |
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[43580ac] | 3257 | |
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[dfc64d9] | 3258 | /*2 |
---|
| 3259 | * transpose a module |
---|
| 3260 | */ |
---|
| 3261 | ideal idTransp(ideal a) |
---|
| 3262 | { |
---|
| 3263 | int r = a->rank, c = IDELEMS(a); |
---|
| 3264 | ideal b = idInit(r,c); |
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| 3265 | |
---|
| 3266 | for (int i=c; i>0; i--) |
---|
| 3267 | { |
---|
| 3268 | poly p=a->m[i-1]; |
---|
| 3269 | while(p!=NULL) |
---|
| 3270 | { |
---|
| 3271 | poly h=pHead(p); |
---|
| 3272 | int co=pGetComp(h)-1; |
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| 3273 | pSetComp(h,i); |
---|
[66a672] | 3274 | pSetmComp(h); |
---|
[dfc64d9] | 3275 | b->m[co]=pAdd(b->m[co],h); |
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| 3276 | pIter(p); |
---|
| 3277 | } |
---|
| 3278 | } |
---|
| 3279 | return b; |
---|
| 3280 | } |
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| 3281 | |
---|