[0f401f] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* $Id: ideals.cc 14320 2011-07-04 14:48:27Z hannes $ */ |
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| 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 <kernel/mod2.h> |
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| 11 | |
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| 12 | #ifndef NDEBUG |
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| 13 | # define MYTEST 0 |
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| 14 | #else /* ifndef NDEBUG */ |
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| 15 | # define MYTEST 1 |
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| 16 | #endif /* ifndef NDEBUG */ |
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| 17 | |
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| 18 | #include <misc/options.h> |
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| 19 | #include <omalloc/omalloc.h> |
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| 20 | #include <kernel/febase.h> |
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| 21 | #include <coefss/coeffs.h> |
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| 22 | #include <coefss/numbers.h> |
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| 23 | #include <kernel/longrat.h> |
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| 24 | #include <kernel/polys.h> |
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| 25 | #include <kernel/ring.h> |
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| 26 | #include <kernel/kstd1.h> |
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| 27 | #include <kernel/matpol.h> |
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| 28 | #include <kernel/weight.h> |
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| 29 | #include <kernel/intvec.h> |
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| 30 | #include <kernel/syz.h> |
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| 31 | #include <kernel/sparsmat.h> |
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| 32 | #include <kernel/ideals.h> |
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| 33 | #include <kernel/prCopy.h> |
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| 34 | #include <kernel/gring.h> |
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| 35 | |
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| 36 | |
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| 37 | omBin sip_sideal_bin = omGetSpecBin(sizeof(sip_sideal)); |
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| 38 | |
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| 39 | /* #define WITH_OLD_MINOR */ |
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| 40 | #define pCopy_noCheck(p) pCopy(p) |
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| 41 | |
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| 42 | static poly * idpower; |
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| 43 | /*collects the monomials in makemonoms, must be allocated befor*/ |
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| 44 | static int idpowerpoint; |
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| 45 | /*index of the actual monomial in idpower*/ |
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| 46 | static poly * givenideal; |
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| 47 | /*the ideal from which a power is computed*/ |
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| 48 | |
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| 49 | /*0 implementation*/ |
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| 50 | |
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| 51 | /*2 |
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| 52 | *returns a minimized set of generators of h1 |
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| 53 | */ |
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| 54 | ideal idMinBase (ideal h1) |
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| 55 | { |
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| 56 | ideal h2, h3,h4,e; |
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| 57 | int j,k; |
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| 58 | int i,l,ll; |
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| 59 | intvec * wth; |
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| 60 | BOOLEAN homog; |
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| 61 | |
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| 62 | homog = idHomModule(h1,currQuotient,&wth); |
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| 63 | if (rHasGlobalOrdering_currRing()) |
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| 64 | { |
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| 65 | if(!homog) |
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| 66 | { |
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| 67 | WarnS("minbase applies only to the local or homogeneous case"); |
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| 68 | e=idCopy(h1); |
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| 69 | return e; |
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| 70 | } |
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| 71 | else |
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| 72 | { |
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| 73 | ideal re=kMin_std(h1,currQuotient,(tHomog)homog,&wth,h2,NULL,0,3); |
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| 74 | idDelete(&re); |
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| 75 | return h2; |
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| 76 | } |
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| 77 | } |
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| 78 | e=idInit(1,h1->rank); |
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| 79 | if (idIs0(h1)) |
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| 80 | { |
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| 81 | return e; |
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| 82 | } |
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| 83 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
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| 84 | IDELEMS(e) = 16; |
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| 85 | h2 = kStd(h1,currQuotient,isNotHomog,NULL); |
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| 86 | h3 = idMaxIdeal(); |
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| 87 | h4=idMult(h2,h3); |
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| 88 | idDelete(&h3); |
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| 89 | h3=kStd(h4,currQuotient,isNotHomog,NULL); |
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| 90 | k = IDELEMS(h3); |
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| 91 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
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| 92 | j = -1; |
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| 93 | l = IDELEMS(h2); |
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| 94 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
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| 95 | for (i=l-1; i>=0; i--) |
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| 96 | { |
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| 97 | if (h2->m[i] != NULL) |
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| 98 | { |
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| 99 | ll = 0; |
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| 100 | while ((ll < k) && ((h3->m[ll] == NULL) |
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| 101 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
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| 102 | ll++; |
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| 103 | if (ll >= k) |
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| 104 | { |
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| 105 | j++; |
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| 106 | if (j > IDELEMS(e)-1) |
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| 107 | { |
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| 108 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
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| 109 | IDELEMS(e) += 16; |
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| 110 | } |
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| 111 | e->m[j] = pCopy(h2->m[i]); |
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| 112 | } |
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| 113 | } |
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| 114 | } |
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| 115 | idDelete(&h2); |
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| 116 | idDelete(&h3); |
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| 117 | idDelete(&h4); |
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| 118 | if (currQuotient!=NULL) |
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| 119 | { |
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| 120 | h3=idInit(1,e->rank); |
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| 121 | h2=kNF(h3,currQuotient,e); |
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| 122 | idDelete(&h3); |
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| 123 | idDelete(&e); |
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| 124 | e=h2; |
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| 125 | } |
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| 126 | idSkipZeroes(e); |
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| 127 | return e; |
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| 128 | } |
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| 129 | |
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| 130 | /*2 |
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| 131 | *the minimal index of used variables - 1 |
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| 132 | */ |
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| 133 | int pLowVar (poly p) |
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| 134 | { |
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| 135 | int k,l,lex; |
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| 136 | |
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| 137 | if (p == NULL) return -1; |
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| 138 | |
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| 139 | k = 32000;/*a very large dummy value*/ |
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| 140 | while (p != NULL) |
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| 141 | { |
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| 142 | l = 1; |
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| 143 | lex = pGetExp(p,l); |
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| 144 | while ((l < pVariables) && (lex == 0)) |
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| 145 | { |
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| 146 | l++; |
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| 147 | lex = pGetExp(p,l); |
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| 148 | } |
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| 149 | l--; |
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| 150 | if (l < k) k = l; |
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| 151 | pIter(p); |
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| 152 | } |
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| 153 | return k; |
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| 154 | } |
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| 155 | |
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| 156 | /*3 |
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| 157 | *multiplies p with t (!cas) or (t-1) |
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| 158 | *the index of t is:1, so we have to shift all variables |
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| 159 | *p is NOT in the actual ring, it has no t |
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| 160 | */ |
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| 161 | static poly pMultWithT (poly p,BOOLEAN cas) |
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| 162 | { |
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| 163 | /*qp is the working pointer in p*/ |
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| 164 | /*result is the result, qresult is the working pointer*/ |
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| 165 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
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| 166 | poly result,qp,pp; |
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| 167 | poly qresult=NULL; |
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| 168 | poly qpp=NULL; |
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| 169 | int i,j,lex; |
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| 170 | number n; |
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| 171 | |
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| 172 | pp = NULL; |
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| 173 | result = NULL; |
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| 174 | qp = p; |
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| 175 | while (qp != NULL) |
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| 176 | { |
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| 177 | i = 0; |
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| 178 | if (result == NULL) |
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| 179 | {/*first monomial*/ |
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| 180 | result = pInit(); |
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| 181 | qresult = result; |
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| 182 | } |
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| 183 | else |
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| 184 | { |
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| 185 | qresult->next = pInit(); |
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| 186 | pIter(qresult); |
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| 187 | } |
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| 188 | for (j=pVariables-1; j>0; j--) |
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| 189 | { |
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| 190 | lex = pGetExp(qp,j); |
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| 191 | pSetExp(qresult,j+1,lex);/*copy all variables*/ |
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| 192 | } |
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| 193 | lex = pGetComp(qp); |
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| 194 | pSetComp(qresult,lex); |
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| 195 | n=nCopy(pGetCoeff(qp)); |
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| 196 | pSetCoeff0(qresult,n); |
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| 197 | qresult->next = NULL; |
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| 198 | pSetm(qresult); |
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| 199 | /*qresult is now qp brought into the actual ring*/ |
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| 200 | if (cas) |
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| 201 | { /*case: mult with t-1*/ |
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| 202 | pSetExp(qresult,1,0); |
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| 203 | pSetm(qresult); |
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| 204 | if (pp == NULL) |
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| 205 | { /*first monomial*/ |
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| 206 | pp = pCopy(qresult); |
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| 207 | qpp = pp; |
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| 208 | } |
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| 209 | else |
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| 210 | { |
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| 211 | qpp->next = pCopy(qresult); |
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| 212 | pIter(qpp); |
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| 213 | } |
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| 214 | pGetCoeff(qpp)=nNeg(pGetCoeff(qpp)); |
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| 215 | /*now qpp contains -1*qp*/ |
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| 216 | } |
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| 217 | pSetExp(qresult,1,1);/*this is mult. by t*/ |
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| 218 | pSetm(qresult); |
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| 219 | pIter(qp); |
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| 220 | } |
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| 221 | /* |
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| 222 | *now p is processed: |
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| 223 | *result contains t*p |
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| 224 | * if cas: pp contains -1*p (in the new ring) |
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| 225 | */ |
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| 226 | if (cas) qresult->next = pp; |
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| 227 | /* else qresult->next = NULL;*/ |
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| 228 | return result; |
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| 229 | } |
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| 230 | |
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| 231 | /*2 |
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| 232 | * verschiebt die Indizees der Modulerzeugenden um i |
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| 233 | */ |
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| 234 | void pShift (poly * p,int i) |
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| 235 | { |
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| 236 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
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| 237 | int j = pMaxComp(*p),k = pMinComp(*p); |
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| 238 | |
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| 239 | if (j+i < 0) return ; |
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| 240 | while (qp1 != NULL) |
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| 241 | { |
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| 242 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
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| 243 | { |
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| 244 | pAddComp(qp1,i); |
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| 245 | pSetmComp(qp1); |
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| 246 | qp2 = qp1; |
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| 247 | pIter(qp1); |
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| 248 | } |
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| 249 | else |
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| 250 | { |
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| 251 | if (qp2 == *p) |
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| 252 | { |
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| 253 | pIter(*p); |
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| 254 | pLmDelete(&qp2); |
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| 255 | qp2 = *p; |
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| 256 | qp1 = *p; |
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| 257 | } |
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| 258 | else |
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| 259 | { |
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| 260 | qp2->next = qp1->next; |
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| 261 | if (qp1!=NULL) pLmDelete(&qp1); |
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| 262 | qp1 = qp2->next; |
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| 263 | } |
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| 264 | } |
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| 265 | } |
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| 266 | } |
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| 267 | |
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| 268 | /*2 |
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| 269 | *initialized a field with r numbers between beg and end for the |
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| 270 | *procedure idNextChoise |
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| 271 | */ |
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| 272 | ideal idSectWithElim (ideal h1,ideal h2) |
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| 273 | // does not destroy h1,h2 |
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| 274 | { |
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| 275 | if (TEST_OPT_PROT) PrintS("intersect by elimination method\n"); |
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| 276 | assume(!idIs0(h1)); |
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| 277 | assume(!idIs0(h2)); |
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| 278 | assume(IDELEMS(h1)<=IDELEMS(h2)); |
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| 279 | assume(idRankFreeModule(h1)==0); |
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| 280 | assume(idRankFreeModule(h2)==0); |
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| 281 | // add a new variable: |
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| 282 | int j; |
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| 283 | ring origRing=currRing; |
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| 284 | ring r=rCopy0(origRing); |
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| 285 | r->N++; |
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| 286 | r->block0[0]=1; |
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| 287 | r->block1[0]= r->N; |
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| 288 | omFree(r->order); |
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| 289 | r->order=(int*)omAlloc0(3*sizeof(int*)); |
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| 290 | r->order[0]=ringorder_dp; |
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| 291 | r->order[1]=ringorder_C; |
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| 292 | char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr)); |
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| 293 | for (j=0;j<r->N-1;j++) names[j]=r->names[j]; |
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| 294 | names[r->N-1]=omStrDup("@"); |
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| 295 | omFree(r->names); |
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| 296 | r->names=names; |
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| 297 | rComplete(r,TRUE); |
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| 298 | // fetch h1, h2 |
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| 299 | ideal h; |
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| 300 | h1=idrCopyR(h1,origRing,r); |
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| 301 | h2=idrCopyR(h2,origRing,r); |
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| 302 | // switch to temp. ring r |
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| 303 | rChangeCurrRing(r); |
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| 304 | // create 1-t, t |
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| 305 | poly omt=pOne(); |
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| 306 | pSetExp(omt,r->N,1); |
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| 307 | poly t=pCopy(omt); |
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| 308 | pSetm(omt); |
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| 309 | omt=pNeg(omt); |
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| 310 | omt=pAdd(omt,pOne()); |
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| 311 | // compute (1-t)*h1 |
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| 312 | h1=(ideal)mpMultP((matrix)h1,omt); |
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| 313 | // compute t*h2 |
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| 314 | h2=(ideal)mpMultP((matrix)h2,pCopy(t)); |
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| 315 | // (1-t)h1 + t*h2 |
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| 316 | h=idInit(IDELEMS(h1)+IDELEMS(h2),1); |
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| 317 | int l; |
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| 318 | for (l=IDELEMS(h1)-1; l>=0; l--) |
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| 319 | { |
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| 320 | h->m[l] = h1->m[l]; h1->m[l]=NULL; |
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| 321 | } |
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| 322 | j=IDELEMS(h1); |
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| 323 | for (l=IDELEMS(h2)-1; l>=0; l--) |
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| 324 | { |
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| 325 | h->m[l+j] = h2->m[l]; h2->m[l]=NULL; |
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| 326 | } |
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| 327 | idDelete(&h1); |
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| 328 | idDelete(&h2); |
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| 329 | // eliminate t: |
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| 330 | |
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| 331 | ideal res=idElimination(h,t); |
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| 332 | // cleanup |
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| 333 | idDelete(&h); |
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| 334 | res=idrMoveR(res,r,origRing); |
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| 335 | rChangeCurrRing(origRing); |
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| 336 | rKill(r); |
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| 337 | return res; |
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| 338 | } |
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| 339 | /*2 |
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| 340 | * h3 := h1 intersect h2 |
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| 341 | */ |
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| 342 | ideal idSect (ideal h1,ideal h2) |
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| 343 | { |
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| 344 | int i,j,k,length; |
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| 345 | int flength = idRankFreeModule(h1); |
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| 346 | int slength = idRankFreeModule(h2); |
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| 347 | int rank=si_min(flength,slength); |
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| 348 | if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank); |
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| 349 | |
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| 350 | ideal first,second,temp,temp1,result; |
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| 351 | poly p,q; |
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| 352 | |
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| 353 | if (IDELEMS(h1)<IDELEMS(h2)) |
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| 354 | { |
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| 355 | first = h1; |
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| 356 | second = h2; |
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| 357 | } |
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| 358 | else |
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| 359 | { |
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| 360 | first = h2; |
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| 361 | second = h1; |
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| 362 | int t=flength; flength=slength; slength=t; |
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| 363 | } |
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| 364 | length = si_max(flength,slength); |
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| 365 | if (length==0) |
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| 366 | { |
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| 367 | if ((currQuotient==NULL) |
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| 368 | && (currRing->OrdSgn==1) |
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| 369 | && (!rIsPluralRing(currRing)) |
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| 370 | && ((TEST_V_INTERSECT_ELIM) || (!TEST_V_INTERSECT_SYZ))) |
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| 371 | return idSectWithElim(first,second); |
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| 372 | else length = 1; |
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| 373 | } |
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| 374 | if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n"); |
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| 375 | j = IDELEMS(first); |
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| 376 | |
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| 377 | ring orig_ring=currRing; |
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| 378 | ring syz_ring=rCurrRingAssure_SyzComp(); |
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| 379 | rSetSyzComp(length); |
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| 380 | |
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| 381 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
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| 382 | temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j); |
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| 383 | k = 0; |
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| 384 | for (i=0;i<j;i++) |
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| 385 | { |
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| 386 | if (first->m[i]!=NULL) |
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| 387 | { |
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| 388 | if (syz_ring==orig_ring) |
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| 389 | temp->m[k] = pCopy(first->m[i]); |
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| 390 | else |
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| 391 | temp->m[k] = prCopyR(first->m[i], orig_ring); |
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| 392 | q = pOne(); |
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| 393 | pSetComp(q,i+1+length); |
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| 394 | pSetmComp(q); |
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| 395 | if (flength==0) pShift(&(temp->m[k]),1); |
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| 396 | p = temp->m[k]; |
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| 397 | while (pNext(p)!=NULL) pIter(p); |
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| 398 | pNext(p) = q; |
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| 399 | k++; |
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| 400 | } |
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| 401 | } |
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| 402 | for (i=0;i<IDELEMS(second);i++) |
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| 403 | { |
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| 404 | if (second->m[i]!=NULL) |
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| 405 | { |
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| 406 | if (syz_ring==orig_ring) |
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| 407 | temp->m[k] = pCopy(second->m[i]); |
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| 408 | else |
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| 409 | temp->m[k] = prCopyR(second->m[i], orig_ring); |
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| 410 | if (slength==0) pShift(&(temp->m[k]),1); |
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| 411 | k++; |
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| 412 | } |
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| 413 | } |
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| 414 | intvec *w=NULL; |
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| 415 | temp1 = kStd(temp,currQuotient,testHomog,&w,NULL,length); |
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| 416 | if (w!=NULL) delete w; |
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| 417 | idDelete(&temp); |
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| 418 | if(syz_ring!=orig_ring) |
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| 419 | rChangeCurrRing(orig_ring); |
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| 420 | |
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| 421 | result = idInit(IDELEMS(temp1),rank); |
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| 422 | j = 0; |
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| 423 | for (i=0;i<IDELEMS(temp1);i++) |
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| 424 | { |
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| 425 | if ((temp1->m[i]!=NULL) |
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| 426 | && (p_GetComp(temp1->m[i],syz_ring)>length)) |
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| 427 | { |
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| 428 | if(syz_ring==orig_ring) |
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| 429 | { |
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| 430 | p = temp1->m[i]; |
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| 431 | } |
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| 432 | else |
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| 433 | { |
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| 434 | p = prMoveR(temp1->m[i], syz_ring); |
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| 435 | } |
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| 436 | temp1->m[i]=NULL; |
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| 437 | while (p!=NULL) |
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| 438 | { |
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| 439 | q = pNext(p); |
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| 440 | pNext(p) = NULL; |
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| 441 | k = pGetComp(p)-1-length; |
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| 442 | pSetComp(p,0); |
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| 443 | pSetmComp(p); |
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| 444 | /* Warning! multiply only from the left! it's very important for Plural */ |
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| 445 | result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k]))); |
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| 446 | p = q; |
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| 447 | } |
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| 448 | j++; |
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| 449 | } |
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| 450 | } |
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| 451 | if(syz_ring!=orig_ring) |
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| 452 | { |
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| 453 | rChangeCurrRing(syz_ring); |
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| 454 | idDelete(&temp1); |
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| 455 | rChangeCurrRing(orig_ring); |
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| 456 | rKill(syz_ring); |
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| 457 | } |
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| 458 | else |
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| 459 | { |
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| 460 | idDelete(&temp1); |
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| 461 | } |
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| 462 | |
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| 463 | idSkipZeroes(result); |
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| 464 | if (TEST_OPT_RETURN_SB) |
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| 465 | { |
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| 466 | w=NULL; |
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| 467 | temp1=kStd(result,currQuotient,testHomog,&w); |
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| 468 | if (w!=NULL) delete w; |
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| 469 | idDelete(&result); |
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| 470 | idSkipZeroes(temp1); |
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| 471 | return temp1; |
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| 472 | } |
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| 473 | else //temp1=kInterRed(result,currQuotient); |
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| 474 | return result; |
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| 475 | } |
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| 476 | |
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| 477 | /*2 |
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| 478 | * ideal/module intersection for a list of objects |
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| 479 | * given as 'resolvente' |
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| 480 | */ |
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| 481 | ideal idMultSect(resolvente arg, int length) |
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| 482 | { |
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| 483 | int i,j=0,k=0,syzComp,l,maxrk=-1,realrki; |
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| 484 | ideal bigmat,tempstd,result; |
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| 485 | poly p; |
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| 486 | int isIdeal=0; |
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| 487 | intvec * w=NULL; |
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| 488 | |
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| 489 | /* find 0-ideals and max rank -----------------------------------*/ |
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| 490 | for (i=0;i<length;i++) |
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| 491 | { |
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| 492 | if (!idIs0(arg[i])) |
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| 493 | { |
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| 494 | realrki=idRankFreeModule(arg[i]); |
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| 495 | k++; |
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| 496 | j += IDELEMS(arg[i]); |
---|
| 497 | if (realrki>maxrk) maxrk = realrki; |
---|
| 498 | } |
---|
| 499 | else |
---|
| 500 | { |
---|
| 501 | if (arg[i]!=NULL) |
---|
| 502 | { |
---|
| 503 | return idInit(1,arg[i]->rank); |
---|
| 504 | } |
---|
| 505 | } |
---|
| 506 | } |
---|
| 507 | if (maxrk == 0) |
---|
| 508 | { |
---|
| 509 | isIdeal = 1; |
---|
| 510 | maxrk = 1; |
---|
| 511 | } |
---|
| 512 | /* init -----------------------------------------------------------*/ |
---|
| 513 | j += maxrk; |
---|
| 514 | syzComp = k*maxrk; |
---|
| 515 | |
---|
| 516 | ring orig_ring=currRing; |
---|
| 517 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 518 | rSetSyzComp(syzComp); |
---|
| 519 | |
---|
| 520 | bigmat = idInit(j,(k+1)*maxrk); |
---|
| 521 | /* create unit matrices ------------------------------------------*/ |
---|
| 522 | for (i=0;i<maxrk;i++) |
---|
| 523 | { |
---|
| 524 | for (j=0;j<=k;j++) |
---|
| 525 | { |
---|
| 526 | p = pOne(); |
---|
| 527 | pSetComp(p,i+1+j*maxrk); |
---|
| 528 | pSetmComp(p); |
---|
| 529 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
---|
| 530 | } |
---|
| 531 | } |
---|
| 532 | /* enter given ideals ------------------------------------------*/ |
---|
| 533 | i = maxrk; |
---|
| 534 | k = 0; |
---|
| 535 | for (j=0;j<length;j++) |
---|
| 536 | { |
---|
| 537 | if (arg[j]!=NULL) |
---|
| 538 | { |
---|
| 539 | for (l=0;l<IDELEMS(arg[j]);l++) |
---|
| 540 | { |
---|
| 541 | if (arg[j]->m[l]!=NULL) |
---|
| 542 | { |
---|
| 543 | if (syz_ring==orig_ring) |
---|
| 544 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
---|
| 545 | else |
---|
| 546 | bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring); |
---|
| 547 | pShift(&(bigmat->m[i]),k*maxrk+isIdeal); |
---|
| 548 | i++; |
---|
| 549 | } |
---|
| 550 | } |
---|
| 551 | k++; |
---|
| 552 | } |
---|
| 553 | } |
---|
| 554 | /* std computation --------------------------------------------*/ |
---|
| 555 | tempstd = kStd(bigmat,currQuotient,testHomog,&w,NULL,syzComp); |
---|
| 556 | if (w!=NULL) delete w; |
---|
| 557 | idDelete(&bigmat); |
---|
| 558 | |
---|
| 559 | if(syz_ring!=orig_ring) |
---|
| 560 | rChangeCurrRing(orig_ring); |
---|
| 561 | |
---|
| 562 | /* interprete result ----------------------------------------*/ |
---|
| 563 | result = idInit(IDELEMS(tempstd),maxrk); |
---|
| 564 | k = 0; |
---|
| 565 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
| 566 | { |
---|
| 567 | if ((tempstd->m[j]!=NULL) && (p_GetComp(tempstd->m[j],syz_ring)>syzComp)) |
---|
| 568 | { |
---|
| 569 | if (syz_ring==orig_ring) |
---|
| 570 | p = pCopy(tempstd->m[j]); |
---|
| 571 | else |
---|
| 572 | p = prCopyR(tempstd->m[j], syz_ring); |
---|
| 573 | pShift(&p,-syzComp-isIdeal); |
---|
| 574 | result->m[k] = p; |
---|
| 575 | k++; |
---|
| 576 | } |
---|
| 577 | } |
---|
| 578 | /* clean up ----------------------------------------------------*/ |
---|
| 579 | if(syz_ring!=orig_ring) |
---|
| 580 | rChangeCurrRing(syz_ring); |
---|
| 581 | idDelete(&tempstd); |
---|
| 582 | if(syz_ring!=orig_ring) |
---|
| 583 | { |
---|
| 584 | rChangeCurrRing(orig_ring); |
---|
| 585 | rKill(syz_ring); |
---|
| 586 | } |
---|
| 587 | idSkipZeroes(result); |
---|
| 588 | return result; |
---|
| 589 | } |
---|
| 590 | |
---|
| 591 | /*2 |
---|
| 592 | *computes syzygies of h1, |
---|
| 593 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
| 594 | *works always in a ring with ringorder_s |
---|
| 595 | */ |
---|
| 596 | static ideal idPrepare (ideal h1, tHomog hom, int syzcomp, intvec **w) |
---|
| 597 | { |
---|
| 598 | ideal h2, h3; |
---|
| 599 | int i; |
---|
| 600 | int j,jj=0,k; |
---|
| 601 | poly p,q; |
---|
| 602 | |
---|
| 603 | if (idIs0(h1)) return NULL; |
---|
| 604 | k = idRankFreeModule(h1); |
---|
| 605 | h2=idCopy(h1); |
---|
| 606 | i = IDELEMS(h2)-1; |
---|
| 607 | if (k == 0) |
---|
| 608 | { |
---|
| 609 | for (j=0; j<=i; j++) pShift(&(h2->m[j]),1); |
---|
| 610 | k = 1; |
---|
| 611 | } |
---|
| 612 | if (syzcomp<k) |
---|
| 613 | { |
---|
| 614 | Warn("syzcomp too low, should be %d instead of %d",k,syzcomp); |
---|
| 615 | syzcomp = k; |
---|
| 616 | rSetSyzComp(k); |
---|
| 617 | } |
---|
| 618 | h2->rank = syzcomp+i+1; |
---|
| 619 | |
---|
| 620 | //if (hom==testHomog) |
---|
| 621 | //{ |
---|
| 622 | // if(idHomIdeal(h1,currQuotient)) |
---|
| 623 | // { |
---|
| 624 | // hom=TRUE; |
---|
| 625 | // } |
---|
| 626 | //} |
---|
| 627 | |
---|
| 628 | #if MYTEST |
---|
| 629 | #ifdef RDEBUG |
---|
| 630 | Print("Prepare::h2: "); |
---|
| 631 | idPrint(h2); |
---|
| 632 | |
---|
| 633 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
| 634 | |
---|
| 635 | #endif |
---|
| 636 | #endif |
---|
| 637 | |
---|
| 638 | for (j=0; j<=i; j++) |
---|
| 639 | { |
---|
| 640 | p = h2->m[j]; |
---|
| 641 | q = pOne(); |
---|
| 642 | pSetComp(q,syzcomp+1+j); |
---|
| 643 | pSetmComp(q); |
---|
| 644 | if (p!=NULL) |
---|
| 645 | { |
---|
| 646 | while (pNext(p)) pIter(p); |
---|
| 647 | p->next = q; |
---|
| 648 | } |
---|
| 649 | else |
---|
| 650 | h2->m[j]=q; |
---|
| 651 | } |
---|
| 652 | |
---|
| 653 | #ifdef PDEBUG |
---|
| 654 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
| 655 | |
---|
| 656 | #if MYTEST |
---|
| 657 | #ifdef RDEBUG |
---|
| 658 | Print("Prepare::Input: "); |
---|
| 659 | idPrint(h2); |
---|
| 660 | |
---|
| 661 | Print("Prepare::currQuotient: "); |
---|
| 662 | idPrint(currQuotient); |
---|
| 663 | #endif |
---|
| 664 | #endif |
---|
| 665 | |
---|
| 666 | #endif |
---|
| 667 | |
---|
| 668 | idTest(h2); |
---|
| 669 | |
---|
| 670 | h3 = kStd(h2,currQuotient,hom,w,NULL,syzcomp); |
---|
| 671 | |
---|
| 672 | #if MYTEST |
---|
| 673 | #ifdef RDEBUG |
---|
| 674 | Print("Prepare::Output: "); |
---|
| 675 | idPrint(h3); |
---|
| 676 | for(j=0;j<IDELEMS(h2);j++) pTest(h3->m[j]); |
---|
| 677 | #endif |
---|
| 678 | #endif |
---|
| 679 | |
---|
| 680 | |
---|
| 681 | idDelete(&h2); |
---|
| 682 | return h3; |
---|
| 683 | } |
---|
| 684 | |
---|
| 685 | /*2 |
---|
| 686 | * compute the syzygies of h1 in R/quot, |
---|
| 687 | * weights of components are in w |
---|
| 688 | * if setRegularity, return the regularity in deg |
---|
| 689 | * do not change h1, w |
---|
| 690 | */ |
---|
| 691 | ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp, |
---|
| 692 | BOOLEAN setRegularity, int *deg) |
---|
| 693 | { |
---|
| 694 | ideal s_h1; |
---|
| 695 | poly p; |
---|
| 696 | int j, k, length=0,reg; |
---|
| 697 | BOOLEAN isMonomial=TRUE; |
---|
| 698 | int ii, idElemens_h1; |
---|
| 699 | |
---|
| 700 | assume(h1 != NULL); |
---|
| 701 | |
---|
| 702 | idElemens_h1=IDELEMS(h1); |
---|
| 703 | #ifdef PDEBUG |
---|
| 704 | for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]); |
---|
| 705 | #endif |
---|
| 706 | if (idIs0(h1)) |
---|
| 707 | { |
---|
| 708 | ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/); |
---|
| 709 | int curr_syz_limit=rGetCurrSyzLimit(); |
---|
| 710 | if (curr_syz_limit>0) |
---|
| 711 | for (ii=0;ii<idElemens_h1/*IDELEMS(h1)*/;ii++) |
---|
| 712 | { |
---|
| 713 | if (h1->m[ii]!=NULL) |
---|
| 714 | pShift(&h1->m[ii],curr_syz_limit); |
---|
| 715 | } |
---|
| 716 | return result; |
---|
| 717 | } |
---|
| 718 | int slength=(int)idRankFreeModule(h1); |
---|
| 719 | k=si_max(1,slength /*idRankFreeModule(h1)*/); |
---|
| 720 | |
---|
| 721 | assume(currRing != NULL); |
---|
| 722 | ring orig_ring=currRing; |
---|
| 723 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 724 | |
---|
| 725 | if (setSyzComp) |
---|
| 726 | rSetSyzComp(k); |
---|
| 727 | |
---|
| 728 | if (orig_ring != syz_ring) |
---|
| 729 | { |
---|
| 730 | s_h1=idrCopyR_NoSort(h1,orig_ring); |
---|
| 731 | } |
---|
| 732 | else |
---|
| 733 | { |
---|
| 734 | s_h1 = h1; |
---|
| 735 | } |
---|
| 736 | |
---|
| 737 | idTest(s_h1); |
---|
| 738 | |
---|
| 739 | ideal s_h3=idPrepare(s_h1,h,k,w); // main (syz) GB computation |
---|
| 740 | |
---|
| 741 | if (s_h3==NULL) |
---|
| 742 | { |
---|
| 743 | return idFreeModule( idElemens_h1 /*IDELEMS(h1)*/); |
---|
| 744 | } |
---|
| 745 | |
---|
| 746 | if (orig_ring != syz_ring) |
---|
| 747 | { |
---|
| 748 | idDelete(&s_h1); |
---|
| 749 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
| 750 | { |
---|
| 751 | if (s_h3->m[j] != NULL) |
---|
| 752 | { |
---|
| 753 | if (p_MinComp(s_h3->m[j],syz_ring) > k) |
---|
| 754 | pShift(&s_h3->m[j], -k); |
---|
| 755 | else |
---|
| 756 | pDelete(&s_h3->m[j]); |
---|
| 757 | } |
---|
| 758 | } |
---|
| 759 | idSkipZeroes(s_h3); |
---|
| 760 | s_h3->rank -= k; |
---|
| 761 | rChangeCurrRing(orig_ring); |
---|
| 762 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
| 763 | rKill(syz_ring); |
---|
| 764 | #ifdef HAVE_PLURAL |
---|
| 765 | if (rIsPluralRing(currRing)) |
---|
| 766 | { |
---|
| 767 | idDelMultiples(s_h3); |
---|
| 768 | idSkipZeroes(s_h3); |
---|
| 769 | } |
---|
| 770 | #endif |
---|
| 771 | idTest(s_h3); |
---|
| 772 | return s_h3; |
---|
| 773 | } |
---|
| 774 | |
---|
| 775 | ideal e = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
| 776 | |
---|
| 777 | for (j=IDELEMS(s_h3)-1; j>=0; j--) |
---|
| 778 | { |
---|
| 779 | if (s_h3->m[j] != NULL) |
---|
| 780 | { |
---|
| 781 | if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
| 782 | { |
---|
| 783 | e->m[j] = s_h3->m[j]; |
---|
| 784 | isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL); |
---|
| 785 | pDelete(&pNext(s_h3->m[j])); |
---|
| 786 | s_h3->m[j] = NULL; |
---|
| 787 | } |
---|
| 788 | } |
---|
| 789 | } |
---|
| 790 | |
---|
| 791 | idSkipZeroes(s_h3); |
---|
| 792 | idSkipZeroes(e); |
---|
| 793 | |
---|
| 794 | if ((deg != NULL) |
---|
| 795 | && (!isMonomial) |
---|
| 796 | && (!TEST_OPT_NOTREGULARITY) |
---|
| 797 | && (setRegularity) |
---|
| 798 | && (h==isHomog) |
---|
| 799 | && (!rIsPluralRing(currRing)) |
---|
| 800 | ) |
---|
| 801 | { |
---|
| 802 | ring dp_C_ring = rCurrRingAssure_dp_C(); |
---|
| 803 | if (dp_C_ring != syz_ring) |
---|
| 804 | e = idrMoveR_NoSort(e, syz_ring); |
---|
| 805 | resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE); |
---|
| 806 | intvec * dummy = syBetti(res,length,®, *w); |
---|
| 807 | *deg = reg+2; |
---|
| 808 | delete dummy; |
---|
| 809 | for (j=0;j<length;j++) |
---|
| 810 | { |
---|
| 811 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
| 812 | } |
---|
| 813 | omFreeSize((ADDRESS)res,length*sizeof(ideal)); |
---|
| 814 | idDelete(&e); |
---|
| 815 | if (dp_C_ring != syz_ring) |
---|
| 816 | { |
---|
| 817 | rChangeCurrRing(syz_ring); |
---|
| 818 | rKill(dp_C_ring); |
---|
| 819 | } |
---|
| 820 | } |
---|
| 821 | else |
---|
| 822 | { |
---|
| 823 | idDelete(&e); |
---|
| 824 | } |
---|
| 825 | idTest(s_h3); |
---|
| 826 | if (currQuotient != NULL) |
---|
| 827 | { |
---|
| 828 | ideal ts_h3=kStd(s_h3,currQuotient,h,w); |
---|
| 829 | idDelete(&s_h3); |
---|
| 830 | s_h3 = ts_h3; |
---|
| 831 | } |
---|
| 832 | return s_h3; |
---|
| 833 | } |
---|
| 834 | |
---|
| 835 | /*2 |
---|
| 836 | */ |
---|
| 837 | ideal idXXX (ideal h1, int k) |
---|
| 838 | { |
---|
| 839 | ideal s_h1; |
---|
| 840 | int j; |
---|
| 841 | intvec *w=NULL; |
---|
| 842 | |
---|
| 843 | assume(currRing != NULL); |
---|
| 844 | ring orig_ring=currRing; |
---|
| 845 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 846 | |
---|
| 847 | rSetSyzComp(k); |
---|
| 848 | |
---|
| 849 | if (orig_ring != syz_ring) |
---|
| 850 | { |
---|
| 851 | s_h1=idrCopyR_NoSort(h1,orig_ring); |
---|
| 852 | } |
---|
| 853 | else |
---|
| 854 | { |
---|
| 855 | s_h1 = h1; |
---|
| 856 | } |
---|
| 857 | |
---|
| 858 | ideal s_h3=kStd(s_h1,NULL,testHomog,&w,NULL,k); |
---|
| 859 | |
---|
| 860 | if (s_h3==NULL) |
---|
| 861 | { |
---|
| 862 | return idFreeModule(IDELEMS(h1)); |
---|
| 863 | } |
---|
| 864 | |
---|
| 865 | if (orig_ring != syz_ring) |
---|
| 866 | { |
---|
| 867 | idDelete(&s_h1); |
---|
| 868 | idSkipZeroes(s_h3); |
---|
| 869 | rChangeCurrRing(orig_ring); |
---|
| 870 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
| 871 | rKill(syz_ring); |
---|
| 872 | idTest(s_h3); |
---|
| 873 | return s_h3; |
---|
| 874 | } |
---|
| 875 | |
---|
| 876 | idSkipZeroes(s_h3); |
---|
| 877 | idTest(s_h3); |
---|
| 878 | return s_h3; |
---|
| 879 | } |
---|
| 880 | |
---|
| 881 | /* |
---|
| 882 | *computes a standard basis for h1 and stores the transformation matrix |
---|
| 883 | * in ma |
---|
| 884 | */ |
---|
| 885 | ideal idLiftStd (ideal h1, matrix* ma, tHomog hi, ideal * syz) |
---|
| 886 | { |
---|
| 887 | int i, j, k, t, inputIsIdeal=idRankFreeModule(h1); |
---|
| 888 | poly p=NULL, q, qq; |
---|
| 889 | intvec *w=NULL; |
---|
| 890 | |
---|
| 891 | idDelete((ideal*)ma); |
---|
| 892 | BOOLEAN lift3=FALSE; |
---|
| 893 | if (syz!=NULL) { lift3=TRUE; idDelete(syz); } |
---|
| 894 | if (idIs0(h1)) |
---|
| 895 | { |
---|
| 896 | *ma=mpNew(1,0); |
---|
| 897 | if (lift3) |
---|
| 898 | { |
---|
| 899 | *syz=idFreeModule(IDELEMS(h1)); |
---|
| 900 | int curr_syz_limit=rGetCurrSyzLimit(); |
---|
| 901 | if (curr_syz_limit>0) |
---|
| 902 | for (int ii=0;ii<IDELEMS(h1);ii++) |
---|
| 903 | { |
---|
| 904 | if (h1->m[ii]!=NULL) |
---|
| 905 | pShift(&h1->m[ii],curr_syz_limit); |
---|
| 906 | } |
---|
| 907 | } |
---|
| 908 | return idInit(1,h1->rank); |
---|
| 909 | } |
---|
| 910 | |
---|
| 911 | BITSET save_verbose=verbose; |
---|
| 912 | |
---|
| 913 | k=si_max(1,(int)idRankFreeModule(h1)); |
---|
| 914 | |
---|
| 915 | if ((k==1) && (!lift3)) verbose |=Sy_bit(V_IDLIFT); |
---|
| 916 | |
---|
| 917 | ring orig_ring = currRing; |
---|
| 918 | ring syz_ring = rCurrRingAssure_SyzComp(); |
---|
| 919 | rSetSyzComp(k); |
---|
| 920 | |
---|
| 921 | ideal s_h1=h1; |
---|
| 922 | |
---|
| 923 | if (orig_ring != syz_ring) |
---|
| 924 | s_h1 = idrCopyR_NoSort(h1,orig_ring); |
---|
| 925 | else |
---|
| 926 | s_h1 = h1; |
---|
| 927 | |
---|
| 928 | ideal s_h3=idPrepare(s_h1,hi,k,&w); // main (syz) GB computation |
---|
| 929 | |
---|
| 930 | ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
| 931 | |
---|
| 932 | if (lift3) (*syz)=idInit(IDELEMS(s_h3),IDELEMS(h1)); |
---|
| 933 | |
---|
| 934 | if (w!=NULL) delete w; |
---|
| 935 | i = 0; |
---|
| 936 | |
---|
| 937 | // now sort the result, SB : leave in s_h3 |
---|
| 938 | // T: put in s_h2 |
---|
| 939 | // syz: put in *syz |
---|
| 940 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
| 941 | { |
---|
| 942 | if (s_h3->m[j] != NULL) |
---|
| 943 | { |
---|
| 944 | //if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
| 945 | if (pGetComp(s_h3->m[j]) <= k) // syz_ring == currRing |
---|
| 946 | { |
---|
| 947 | i++; |
---|
| 948 | q = s_h3->m[j]; |
---|
| 949 | while (pNext(q) != NULL) |
---|
| 950 | { |
---|
| 951 | if (pGetComp(pNext(q)) > k) |
---|
| 952 | { |
---|
| 953 | s_h2->m[j] = pNext(q); |
---|
| 954 | pNext(q) = NULL; |
---|
| 955 | } |
---|
| 956 | else |
---|
| 957 | { |
---|
| 958 | pIter(q); |
---|
| 959 | } |
---|
| 960 | } |
---|
| 961 | if (!inputIsIdeal) pShift(&(s_h3->m[j]), -1); |
---|
| 962 | } |
---|
| 963 | else |
---|
| 964 | { |
---|
| 965 | // we a syzygy here: |
---|
| 966 | if (lift3) |
---|
| 967 | { |
---|
| 968 | pShift(&s_h3->m[j], -k); |
---|
| 969 | (*syz)->m[j]=s_h3->m[j]; |
---|
| 970 | s_h3->m[j]=NULL; |
---|
| 971 | } |
---|
| 972 | else |
---|
| 973 | pDelete(&(s_h3->m[j])); |
---|
| 974 | } |
---|
| 975 | } |
---|
| 976 | } |
---|
| 977 | idSkipZeroes(s_h3); |
---|
| 978 | //extern char * iiStringMatrix(matrix im, int dim,char ch); |
---|
| 979 | //PrintS("SB: ----------------------------------------\n"); |
---|
| 980 | //PrintS(iiStringMatrix((matrix)s_h3,k,'\n')); |
---|
| 981 | //PrintLn(); |
---|
| 982 | //PrintS("T: ----------------------------------------\n"); |
---|
| 983 | //PrintS(iiStringMatrix((matrix)s_h2,h1->rank,'\n')); |
---|
| 984 | //PrintLn(); |
---|
| 985 | |
---|
| 986 | if (lift3) idSkipZeroes(*syz); |
---|
| 987 | |
---|
| 988 | j = IDELEMS(s_h1); |
---|
| 989 | |
---|
| 990 | |
---|
| 991 | if (syz_ring!=orig_ring) |
---|
| 992 | { |
---|
| 993 | idDelete(&s_h1); |
---|
| 994 | rChangeCurrRing(orig_ring); |
---|
| 995 | } |
---|
| 996 | |
---|
| 997 | *ma = mpNew(j,i); |
---|
| 998 | |
---|
| 999 | i = 1; |
---|
| 1000 | for (j=0; j<IDELEMS(s_h2); j++) |
---|
| 1001 | { |
---|
| 1002 | if (s_h2->m[j] != NULL) |
---|
| 1003 | { |
---|
| 1004 | q = prMoveR( s_h2->m[j], syz_ring); |
---|
| 1005 | s_h2->m[j] = NULL; |
---|
| 1006 | |
---|
| 1007 | while (q != NULL) |
---|
| 1008 | { |
---|
| 1009 | p = q; |
---|
| 1010 | pIter(q); |
---|
| 1011 | pNext(p) = NULL; |
---|
| 1012 | t=pGetComp(p); |
---|
| 1013 | pSetComp(p,0); |
---|
| 1014 | pSetmComp(p); |
---|
| 1015 | MATELEM(*ma,t-k,i) = pAdd(MATELEM(*ma,t-k,i),p); |
---|
| 1016 | } |
---|
| 1017 | i++; |
---|
| 1018 | } |
---|
| 1019 | } |
---|
| 1020 | idDelete(&s_h2); |
---|
| 1021 | |
---|
| 1022 | for (i=0; i<IDELEMS(s_h3); i++) |
---|
| 1023 | { |
---|
| 1024 | s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], syz_ring); |
---|
| 1025 | } |
---|
| 1026 | if (lift3) |
---|
| 1027 | { |
---|
| 1028 | for (i=0; i<IDELEMS(*syz); i++) |
---|
| 1029 | { |
---|
| 1030 | (*syz)->m[i] = prMoveR_NoSort((*syz)->m[i], syz_ring); |
---|
| 1031 | } |
---|
| 1032 | } |
---|
| 1033 | |
---|
| 1034 | if (syz_ring!=orig_ring) rKill(syz_ring); |
---|
| 1035 | verbose = save_verbose; |
---|
| 1036 | return s_h3; |
---|
| 1037 | } |
---|
| 1038 | |
---|
| 1039 | static void idPrepareStd(ideal s_temp, int k) |
---|
| 1040 | { |
---|
| 1041 | int j,rk=idRankFreeModule(s_temp); |
---|
| 1042 | poly p,q; |
---|
| 1043 | |
---|
| 1044 | if (rk == 0) |
---|
| 1045 | { |
---|
| 1046 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
| 1047 | { |
---|
| 1048 | if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1); |
---|
| 1049 | } |
---|
| 1050 | k = si_max(k,1); |
---|
| 1051 | } |
---|
| 1052 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
| 1053 | { |
---|
| 1054 | if (s_temp->m[j]!=NULL) |
---|
| 1055 | { |
---|
| 1056 | p = s_temp->m[j]; |
---|
| 1057 | q = pOne(); |
---|
| 1058 | //pGetCoeff(q)=nNeg(pGetCoeff(q)); //set q to -1 |
---|
| 1059 | pSetComp(q,k+1+j); |
---|
| 1060 | pSetmComp(q); |
---|
| 1061 | while (pNext(p)) pIter(p); |
---|
| 1062 | pNext(p) = q; |
---|
| 1063 | } |
---|
| 1064 | } |
---|
| 1065 | } |
---|
| 1066 | |
---|
| 1067 | /*2 |
---|
| 1068 | *computes a representation of the generators of submod with respect to those |
---|
| 1069 | * of mod |
---|
| 1070 | */ |
---|
| 1071 | |
---|
| 1072 | ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape, |
---|
| 1073 | BOOLEAN isSB, BOOLEAN divide, matrix *unit) |
---|
| 1074 | { |
---|
| 1075 | int lsmod =idRankFreeModule(submod), i, j, k; |
---|
| 1076 | int comps_to_add=0; |
---|
| 1077 | poly p; |
---|
| 1078 | |
---|
| 1079 | if (idIs0(submod)) |
---|
| 1080 | { |
---|
| 1081 | if (unit!=NULL) |
---|
| 1082 | { |
---|
| 1083 | *unit=mpNew(1,1); |
---|
| 1084 | MATELEM(*unit,1,1)=pOne(); |
---|
| 1085 | } |
---|
| 1086 | if (rest!=NULL) |
---|
| 1087 | { |
---|
| 1088 | *rest=idInit(1,mod->rank); |
---|
| 1089 | } |
---|
| 1090 | return idInit(1,mod->rank); |
---|
| 1091 | } |
---|
| 1092 | if (idIs0(mod)) /* and not idIs0(submod) */ |
---|
| 1093 | { |
---|
| 1094 | WerrorS("2nd module does not lie in the first"); |
---|
| 1095 | #if 0 |
---|
| 1096 | if (unit!=NULL) |
---|
| 1097 | { |
---|
| 1098 | i=IDELEMS(submod); |
---|
| 1099 | *unit=mpNew(i,i); |
---|
| 1100 | for (j=i;j>0;j--) |
---|
| 1101 | { |
---|
| 1102 | MATELEM(*unit,j,j)=pOne(); |
---|
| 1103 | } |
---|
| 1104 | } |
---|
| 1105 | if (rest!=NULL) |
---|
| 1106 | { |
---|
| 1107 | *rest=idCopy(submod); |
---|
| 1108 | } |
---|
| 1109 | return idInit(1,mod->rank); |
---|
| 1110 | #endif |
---|
| 1111 | return idInit(IDELEMS(submod),submod->rank); |
---|
| 1112 | } |
---|
| 1113 | if (unit!=NULL) |
---|
| 1114 | { |
---|
| 1115 | comps_to_add = IDELEMS(submod); |
---|
| 1116 | while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL)) |
---|
| 1117 | comps_to_add--; |
---|
| 1118 | } |
---|
| 1119 | k=si_max(idRankFreeModule(mod),idRankFreeModule(submod)); |
---|
| 1120 | if ((k!=0) && (lsmod==0)) lsmod=1; |
---|
| 1121 | k=si_max(k,(int)mod->rank); |
---|
| 1122 | if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; } |
---|
| 1123 | |
---|
| 1124 | ring orig_ring=currRing; |
---|
| 1125 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 1126 | rSetSyzComp(k); |
---|
| 1127 | |
---|
| 1128 | ideal s_mod, s_temp; |
---|
| 1129 | if (orig_ring != syz_ring) |
---|
| 1130 | { |
---|
| 1131 | s_mod = idrCopyR_NoSort(mod,orig_ring); |
---|
| 1132 | s_temp = idrCopyR_NoSort(submod,orig_ring); |
---|
| 1133 | } |
---|
| 1134 | else |
---|
| 1135 | { |
---|
| 1136 | s_mod = mod; |
---|
| 1137 | s_temp = idCopy(submod); |
---|
| 1138 | } |
---|
| 1139 | ideal s_h3; |
---|
| 1140 | if (isSB) |
---|
| 1141 | { |
---|
| 1142 | s_h3 = idCopy(s_mod); |
---|
| 1143 | idPrepareStd(s_h3, k+comps_to_add); |
---|
| 1144 | } |
---|
| 1145 | else |
---|
| 1146 | { |
---|
| 1147 | s_h3 = idPrepare(s_mod,(tHomog)FALSE,k+comps_to_add,NULL); |
---|
| 1148 | } |
---|
| 1149 | if (!goodShape) |
---|
| 1150 | { |
---|
| 1151 | for (j=0;j<IDELEMS(s_h3);j++) |
---|
| 1152 | { |
---|
| 1153 | if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k)) |
---|
| 1154 | pDelete(&(s_h3->m[j])); |
---|
| 1155 | } |
---|
| 1156 | } |
---|
| 1157 | idSkipZeroes(s_h3); |
---|
| 1158 | if (lsmod==0) |
---|
| 1159 | { |
---|
| 1160 | for (j=IDELEMS(s_temp);j>0;j--) |
---|
| 1161 | { |
---|
| 1162 | if (s_temp->m[j-1]!=NULL) |
---|
| 1163 | pShift(&(s_temp->m[j-1]),1); |
---|
| 1164 | } |
---|
| 1165 | } |
---|
| 1166 | if (unit!=NULL) |
---|
| 1167 | { |
---|
| 1168 | for(j = 0;j<comps_to_add;j++) |
---|
| 1169 | { |
---|
| 1170 | p = s_temp->m[j]; |
---|
| 1171 | if (p!=NULL) |
---|
| 1172 | { |
---|
| 1173 | while (pNext(p)!=NULL) pIter(p); |
---|
| 1174 | pNext(p) = pOne(); |
---|
| 1175 | pIter(p); |
---|
| 1176 | pSetComp(p,1+j+k); |
---|
| 1177 | pSetmComp(p); |
---|
| 1178 | p = pNeg(p); |
---|
| 1179 | } |
---|
| 1180 | } |
---|
| 1181 | } |
---|
| 1182 | ideal s_result = kNF(s_h3,currQuotient,s_temp,k); |
---|
| 1183 | s_result->rank = s_h3->rank; |
---|
| 1184 | ideal s_rest = idInit(IDELEMS(s_result),k); |
---|
| 1185 | idDelete(&s_h3); |
---|
| 1186 | idDelete(&s_temp); |
---|
| 1187 | |
---|
| 1188 | for (j=0;j<IDELEMS(s_result);j++) |
---|
| 1189 | { |
---|
| 1190 | if (s_result->m[j]!=NULL) |
---|
| 1191 | { |
---|
| 1192 | if (pGetComp(s_result->m[j])<=k) |
---|
| 1193 | { |
---|
| 1194 | if (!divide) |
---|
| 1195 | { |
---|
| 1196 | if (isSB) |
---|
| 1197 | { |
---|
| 1198 | WarnS("first module not a standardbasis\n" |
---|
| 1199 | "// ** or second not a proper submodule"); |
---|
| 1200 | } |
---|
| 1201 | else |
---|
| 1202 | WerrorS("2nd module does not lie in the first"); |
---|
| 1203 | idDelete(&s_result); |
---|
| 1204 | idDelete(&s_rest); |
---|
| 1205 | s_result=idInit(IDELEMS(submod),submod->rank); |
---|
| 1206 | break; |
---|
| 1207 | } |
---|
| 1208 | else |
---|
| 1209 | { |
---|
| 1210 | p = s_rest->m[j] = s_result->m[j]; |
---|
| 1211 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p); |
---|
| 1212 | s_result->m[j] = pNext(p); |
---|
| 1213 | pNext(p) = NULL; |
---|
| 1214 | } |
---|
| 1215 | } |
---|
| 1216 | pShift(&(s_result->m[j]),-k); |
---|
| 1217 | pNeg(s_result->m[j]); |
---|
| 1218 | } |
---|
| 1219 | } |
---|
| 1220 | if ((lsmod==0) && (!idIs0(s_rest))) |
---|
| 1221 | { |
---|
| 1222 | for (j=IDELEMS(s_rest);j>0;j--) |
---|
| 1223 | { |
---|
| 1224 | if (s_rest->m[j-1]!=NULL) |
---|
| 1225 | { |
---|
| 1226 | pShift(&(s_rest->m[j-1]),-1); |
---|
| 1227 | s_rest->m[j-1] = s_rest->m[j-1]; |
---|
| 1228 | } |
---|
| 1229 | } |
---|
| 1230 | } |
---|
| 1231 | if(syz_ring!=orig_ring) |
---|
| 1232 | { |
---|
| 1233 | idDelete(&s_mod); |
---|
| 1234 | rChangeCurrRing(orig_ring); |
---|
| 1235 | s_result = idrMoveR_NoSort(s_result, syz_ring); |
---|
| 1236 | s_rest = idrMoveR_NoSort(s_rest, syz_ring); |
---|
| 1237 | rKill(syz_ring); |
---|
| 1238 | } |
---|
| 1239 | if (rest!=NULL) |
---|
| 1240 | *rest = s_rest; |
---|
| 1241 | else |
---|
| 1242 | idDelete(&s_rest); |
---|
| 1243 | //idPrint(s_result); |
---|
| 1244 | if (unit!=NULL) |
---|
| 1245 | { |
---|
| 1246 | *unit=mpNew(comps_to_add,comps_to_add); |
---|
| 1247 | int i; |
---|
| 1248 | for(i=0;i<IDELEMS(s_result);i++) |
---|
| 1249 | { |
---|
| 1250 | poly p=s_result->m[i]; |
---|
| 1251 | poly q=NULL; |
---|
| 1252 | while(p!=NULL) |
---|
| 1253 | { |
---|
| 1254 | if(pGetComp(p)<=comps_to_add) |
---|
| 1255 | { |
---|
| 1256 | pSetComp(p,0); |
---|
| 1257 | if (q!=NULL) |
---|
| 1258 | { |
---|
| 1259 | pNext(q)=pNext(p); |
---|
| 1260 | } |
---|
| 1261 | else |
---|
| 1262 | { |
---|
| 1263 | pIter(s_result->m[i]); |
---|
| 1264 | } |
---|
| 1265 | pNext(p)=NULL; |
---|
| 1266 | MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p); |
---|
| 1267 | if(q!=NULL) p=pNext(q); |
---|
| 1268 | else p=s_result->m[i]; |
---|
| 1269 | } |
---|
| 1270 | else |
---|
| 1271 | { |
---|
| 1272 | q=p; |
---|
| 1273 | pIter(p); |
---|
| 1274 | } |
---|
| 1275 | } |
---|
| 1276 | pShift(&s_result->m[i],-comps_to_add); |
---|
| 1277 | } |
---|
| 1278 | } |
---|
| 1279 | return s_result; |
---|
| 1280 | } |
---|
| 1281 | |
---|
| 1282 | /*2 |
---|
| 1283 | *computes division of P by Q with remainder up to (w-weighted) degree n |
---|
| 1284 | *P, Q, and w are not changed |
---|
| 1285 | */ |
---|
| 1286 | void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,short *w) |
---|
| 1287 | { |
---|
| 1288 | long N=0; |
---|
| 1289 | int i; |
---|
| 1290 | for(i=IDELEMS(Q)-1;i>=0;i--) |
---|
| 1291 | if(w==NULL) |
---|
| 1292 | N=si_max(N,pDeg(Q->m[i])); |
---|
| 1293 | else |
---|
| 1294 | N=si_max(N,pDegW(Q->m[i],w)); |
---|
| 1295 | N+=n; |
---|
| 1296 | |
---|
| 1297 | T=mpNew(IDELEMS(Q),IDELEMS(P)); |
---|
| 1298 | R=idInit(IDELEMS(P),P->rank); |
---|
| 1299 | |
---|
| 1300 | for(i=IDELEMS(P)-1;i>=0;i--) |
---|
| 1301 | { |
---|
| 1302 | poly p; |
---|
| 1303 | if(w==NULL) |
---|
| 1304 | p=ppJet(P->m[i],N); |
---|
| 1305 | else |
---|
| 1306 | p=ppJetW(P->m[i],N,w); |
---|
| 1307 | |
---|
| 1308 | int j=IDELEMS(Q)-1; |
---|
| 1309 | while(p!=NULL) |
---|
| 1310 | { |
---|
| 1311 | if(pDivisibleBy(Q->m[j],p)) |
---|
| 1312 | { |
---|
| 1313 | poly p0=pDivideM(pHead(p),pHead(Q->m[j])); |
---|
| 1314 | if(w==NULL) |
---|
| 1315 | p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N); |
---|
| 1316 | else |
---|
| 1317 | p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w); |
---|
| 1318 | pNormalize(p); |
---|
| 1319 | if((w==NULL)&&(pDeg(p0)>n)||(w!=NULL)&&(pDegW(p0,w)>n)) |
---|
| 1320 | pDelete(&p0); |
---|
| 1321 | else |
---|
| 1322 | MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0); |
---|
| 1323 | j=IDELEMS(Q)-1; |
---|
| 1324 | } |
---|
| 1325 | else |
---|
| 1326 | { |
---|
| 1327 | if(j==0) |
---|
| 1328 | { |
---|
| 1329 | poly p0=p; |
---|
| 1330 | pIter(p); |
---|
| 1331 | pNext(p0)=NULL; |
---|
| 1332 | if(((w==NULL)&&(pDeg(p0)>n)) |
---|
| 1333 | ||((w!=NULL)&&(pDegW(p0,w)>n))) |
---|
| 1334 | pDelete(&p0); |
---|
| 1335 | else |
---|
| 1336 | R->m[i]=pAdd(R->m[i],p0); |
---|
| 1337 | j=IDELEMS(Q)-1; |
---|
| 1338 | } |
---|
| 1339 | else |
---|
| 1340 | j--; |
---|
| 1341 | } |
---|
| 1342 | } |
---|
| 1343 | } |
---|
| 1344 | } |
---|
| 1345 | |
---|
| 1346 | /*2 |
---|
| 1347 | *computes the quotient of h1,h2 : internal routine for idQuot |
---|
| 1348 | *BEWARE: the returned ideals may contain incorrectly ordered polys ! |
---|
| 1349 | * |
---|
| 1350 | */ |
---|
| 1351 | static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, |
---|
| 1352 | BOOLEAN *addOnlyOne, int *kkmax) |
---|
| 1353 | { |
---|
| 1354 | ideal temph1; |
---|
| 1355 | poly p,q = NULL; |
---|
| 1356 | int i,l,ll,k,kkk,kmax; |
---|
| 1357 | int j = 0; |
---|
| 1358 | int k1 = idRankFreeModule(h1); |
---|
| 1359 | int k2 = idRankFreeModule(h2); |
---|
| 1360 | tHomog hom=isNotHomog; |
---|
| 1361 | |
---|
| 1362 | k=si_max(k1,k2); |
---|
| 1363 | if (k==0) |
---|
| 1364 | k = 1; |
---|
| 1365 | if ((k2==0) && (k>1)) *addOnlyOne = FALSE; |
---|
| 1366 | |
---|
| 1367 | intvec * weights; |
---|
| 1368 | hom = (tHomog)idHomModule(h1,currQuotient,&weights); |
---|
| 1369 | if (/**addOnlyOne &&*/ (!h1IsStb)) |
---|
| 1370 | temph1 = kStd(h1,currQuotient,hom,&weights,NULL); |
---|
| 1371 | else |
---|
| 1372 | temph1 = idCopy(h1); |
---|
| 1373 | if (weights!=NULL) delete weights; |
---|
| 1374 | idTest(temph1); |
---|
| 1375 | /*--- making a single vector from h2 ---------------------*/ |
---|
| 1376 | for (i=0; i<IDELEMS(h2); i++) |
---|
| 1377 | { |
---|
| 1378 | if (h2->m[i] != NULL) |
---|
| 1379 | { |
---|
| 1380 | p = pCopy(h2->m[i]); |
---|
| 1381 | if (k2 == 0) |
---|
| 1382 | pShift(&p,j*k+1); |
---|
| 1383 | else |
---|
| 1384 | pShift(&p,j*k); |
---|
| 1385 | q = pAdd(q,p); |
---|
| 1386 | j++; |
---|
| 1387 | } |
---|
| 1388 | } |
---|
| 1389 | *kkmax = kmax = j*k+1; |
---|
| 1390 | /*--- adding a monomial for the result (syzygy) ----------*/ |
---|
| 1391 | p = q; |
---|
| 1392 | while (pNext(p)!=NULL) pIter(p); |
---|
| 1393 | pNext(p) = pOne(); |
---|
| 1394 | pIter(p); |
---|
| 1395 | pSetComp(p,kmax); |
---|
| 1396 | pSetmComp(p); |
---|
| 1397 | /*--- constructing the big matrix ------------------------*/ |
---|
| 1398 | ideal h4 = idInit(16,kmax+k-1); |
---|
| 1399 | h4->m[0] = q; |
---|
| 1400 | if (k2 == 0) |
---|
| 1401 | { |
---|
| 1402 | if (k > IDELEMS(h4)) |
---|
| 1403 | { |
---|
| 1404 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
| 1405 | IDELEMS(h4) = k; |
---|
| 1406 | } |
---|
| 1407 | for (i=1; i<k; i++) |
---|
| 1408 | { |
---|
| 1409 | if (h4->m[i-1]!=NULL) |
---|
| 1410 | { |
---|
| 1411 | p = pCopy_noCheck(h4->m[i-1]); |
---|
| 1412 | pShift(&p,1); |
---|
| 1413 | h4->m[i] = p; |
---|
| 1414 | } |
---|
| 1415 | } |
---|
| 1416 | } |
---|
| 1417 | idSkipZeroes(h4); |
---|
| 1418 | kkk = IDELEMS(h4); |
---|
| 1419 | i = IDELEMS(temph1); |
---|
| 1420 | for (l=0; l<i; l++) |
---|
| 1421 | { |
---|
| 1422 | if(temph1->m[l]!=NULL) |
---|
| 1423 | { |
---|
| 1424 | for (ll=0; ll<j; ll++) |
---|
| 1425 | { |
---|
| 1426 | p = pCopy(temph1->m[l]); |
---|
| 1427 | if (k1 == 0) |
---|
| 1428 | pShift(&p,ll*k+1); |
---|
| 1429 | else |
---|
| 1430 | pShift(&p,ll*k); |
---|
| 1431 | if (kkk >= IDELEMS(h4)) |
---|
| 1432 | { |
---|
| 1433 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
| 1434 | IDELEMS(h4) += 16; |
---|
| 1435 | } |
---|
| 1436 | h4->m[kkk] = p; |
---|
| 1437 | kkk++; |
---|
| 1438 | } |
---|
| 1439 | } |
---|
| 1440 | } |
---|
| 1441 | /*--- if h2 goes in as single vector - the h1-part is just SB ---*/ |
---|
| 1442 | if (*addOnlyOne) |
---|
| 1443 | { |
---|
| 1444 | idSkipZeroes(h4); |
---|
| 1445 | p = h4->m[0]; |
---|
| 1446 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
| 1447 | { |
---|
| 1448 | h4->m[i] = h4->m[i+1]; |
---|
| 1449 | } |
---|
| 1450 | h4->m[IDELEMS(h4)-1] = p; |
---|
| 1451 | test |= Sy_bit(OPT_SB_1); |
---|
| 1452 | } |
---|
| 1453 | idDelete(&temph1); |
---|
| 1454 | return h4; |
---|
| 1455 | } |
---|
| 1456 | /*2 |
---|
| 1457 | *computes the quotient of h1,h2 |
---|
| 1458 | */ |
---|
| 1459 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal) |
---|
| 1460 | { |
---|
| 1461 | // first check for special case h1:(0) |
---|
| 1462 | if (idIs0(h2)) |
---|
| 1463 | { |
---|
| 1464 | ideal res; |
---|
| 1465 | if (resultIsIdeal) |
---|
| 1466 | { |
---|
| 1467 | res = idInit(1,1); |
---|
| 1468 | res->m[0] = pOne(); |
---|
| 1469 | } |
---|
| 1470 | else |
---|
| 1471 | res = idFreeModule(h1->rank); |
---|
| 1472 | return res; |
---|
| 1473 | } |
---|
| 1474 | BITSET old_test=test; |
---|
| 1475 | int i,l,ll,k,kkk,kmax; |
---|
| 1476 | BOOLEAN addOnlyOne=TRUE; |
---|
| 1477 | tHomog hom=isNotHomog; |
---|
| 1478 | intvec * weights1; |
---|
| 1479 | |
---|
| 1480 | ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax); |
---|
| 1481 | |
---|
| 1482 | hom = (tHomog)idHomModule(s_h4,currQuotient,&weights1); |
---|
| 1483 | |
---|
| 1484 | ring orig_ring=currRing; |
---|
| 1485 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 1486 | rSetSyzComp(kmax-1); |
---|
| 1487 | if (orig_ring!=syz_ring) |
---|
| 1488 | // s_h4 = idrMoveR_NoSort(s_h4,orig_ring); |
---|
| 1489 | s_h4 = idrMoveR(s_h4,orig_ring); |
---|
| 1490 | idTest(s_h4); |
---|
| 1491 | #if 0 |
---|
| 1492 | void ipPrint_MA0(matrix m, const char *name); |
---|
| 1493 | matrix m=idModule2Matrix(idCopy(s_h4)); |
---|
| 1494 | PrintS("start:\n"); |
---|
| 1495 | ipPrint_MA0(m,"Q"); |
---|
| 1496 | idDelete((ideal *)&m); |
---|
| 1497 | PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn(); |
---|
| 1498 | #endif |
---|
| 1499 | ideal s_h3; |
---|
| 1500 | if (addOnlyOne) |
---|
| 1501 | { |
---|
| 1502 | s_h3 = kStd(s_h4,currQuotient,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1); |
---|
| 1503 | } |
---|
| 1504 | else |
---|
| 1505 | { |
---|
| 1506 | s_h3 = kStd(s_h4,currQuotient,hom,&weights1,NULL,kmax-1); |
---|
| 1507 | } |
---|
| 1508 | test = old_test; |
---|
| 1509 | #if 0 |
---|
| 1510 | // only together with the above debug stuff |
---|
| 1511 | idSkipZeroes(s_h3); |
---|
| 1512 | m=idModule2Matrix(idCopy(s_h3)); |
---|
| 1513 | Print("result, kmax=%d:\n",kmax); |
---|
| 1514 | ipPrint_MA0(m,"S"); |
---|
| 1515 | idDelete((ideal *)&m); |
---|
| 1516 | #endif |
---|
| 1517 | idTest(s_h3); |
---|
| 1518 | if (weights1!=NULL) delete weights1; |
---|
| 1519 | idDelete(&s_h4); |
---|
| 1520 | |
---|
| 1521 | for (i=0;i<IDELEMS(s_h3);i++) |
---|
| 1522 | { |
---|
| 1523 | if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax)) |
---|
| 1524 | { |
---|
| 1525 | if (resultIsIdeal) |
---|
| 1526 | pShift(&s_h3->m[i],-kmax); |
---|
| 1527 | else |
---|
| 1528 | pShift(&s_h3->m[i],-kmax+1); |
---|
| 1529 | } |
---|
| 1530 | else |
---|
| 1531 | pDelete(&s_h3->m[i]); |
---|
| 1532 | } |
---|
| 1533 | if (resultIsIdeal) |
---|
| 1534 | s_h3->rank = 1; |
---|
| 1535 | else |
---|
| 1536 | s_h3->rank = h1->rank; |
---|
| 1537 | if(syz_ring!=orig_ring) |
---|
| 1538 | { |
---|
| 1539 | rChangeCurrRing(orig_ring); |
---|
| 1540 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
| 1541 | rKill(syz_ring); |
---|
| 1542 | } |
---|
| 1543 | idSkipZeroes(s_h3); |
---|
| 1544 | idTest(s_h3); |
---|
| 1545 | return s_h3; |
---|
| 1546 | } |
---|
| 1547 | |
---|
| 1548 | /*2 |
---|
| 1549 | * eliminate delVar (product of vars) in h1 |
---|
| 1550 | */ |
---|
| 1551 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
| 1552 | { |
---|
| 1553 | int i,j=0,k,l; |
---|
| 1554 | ideal h,hh, h3; |
---|
| 1555 | int *ord,*block0,*block1; |
---|
| 1556 | int ordersize=2; |
---|
| 1557 | int **wv; |
---|
| 1558 | tHomog hom; |
---|
| 1559 | intvec * w; |
---|
| 1560 | ring tmpR; |
---|
| 1561 | ring origR = currRing; |
---|
| 1562 | |
---|
| 1563 | if (delVar==NULL) |
---|
| 1564 | { |
---|
| 1565 | return idCopy(h1); |
---|
| 1566 | } |
---|
| 1567 | if ((currQuotient!=NULL) && rIsPluralRing(origR)) |
---|
| 1568 | { |
---|
| 1569 | WerrorS("cannot eliminate in a qring"); |
---|
| 1570 | return idCopy(h1); |
---|
| 1571 | } |
---|
| 1572 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
| 1573 | #ifdef HAVE_PLURAL |
---|
| 1574 | if (rIsPluralRing(origR)) |
---|
| 1575 | /* in the NC case, we have to check the admissibility of */ |
---|
| 1576 | /* the subalgebra to be intersected with */ |
---|
| 1577 | { |
---|
| 1578 | if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */ |
---|
| 1579 | { |
---|
| 1580 | if (nc_CheckSubalgebra(delVar,origR)) |
---|
| 1581 | { |
---|
| 1582 | WerrorS("no elimination is possible: subalgebra is not admissible"); |
---|
| 1583 | return idCopy(h1); |
---|
| 1584 | } |
---|
| 1585 | } |
---|
| 1586 | } |
---|
| 1587 | #endif |
---|
| 1588 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
| 1589 | h3=idInit(16,h1->rank); |
---|
| 1590 | for (k=0;; k++) |
---|
| 1591 | { |
---|
| 1592 | if (origR->order[k]!=0) ordersize++; |
---|
| 1593 | else break; |
---|
| 1594 | } |
---|
| 1595 | #if 0 |
---|
| 1596 | if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed |
---|
| 1597 | // for G-algebra |
---|
| 1598 | { |
---|
| 1599 | for (k=0;k<ordersize-1; k++) |
---|
| 1600 | { |
---|
| 1601 | block0[k+1] = origR->block0[k]; |
---|
| 1602 | block1[k+1] = origR->block1[k]; |
---|
| 1603 | ord[k+1] = origR->order[k]; |
---|
| 1604 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
| 1605 | } |
---|
| 1606 | } |
---|
| 1607 | else |
---|
| 1608 | { |
---|
| 1609 | block0[1] = 1; |
---|
| 1610 | block1[1] = pVariables; |
---|
| 1611 | if (origR->OrdSgn==1) ord[1] = ringorder_wp; |
---|
| 1612 | else ord[1] = ringorder_ws; |
---|
| 1613 | wv[1]=(int*)omAlloc0(pVariables*sizeof(int)); |
---|
| 1614 | double wNsqr = (double)2.0 / (double)pVariables; |
---|
| 1615 | wFunctional = wFunctionalBuch; |
---|
| 1616 | int *x= (int * )omAlloc(2 * (pVariables + 1) * sizeof(int)); |
---|
| 1617 | int sl=IDELEMS(h1) - 1; |
---|
| 1618 | wCall(h1->m, sl, x, wNsqr); |
---|
| 1619 | for (sl = pVariables; sl!=0; sl--) |
---|
| 1620 | wv[1][sl-1] = x[sl + pVariables + 1]; |
---|
| 1621 | omFreeSize((ADDRESS)x, 2 * (pVariables + 1) * sizeof(int)); |
---|
| 1622 | |
---|
| 1623 | ord[2]=ringorder_C; |
---|
| 1624 | ord[3]=0; |
---|
| 1625 | } |
---|
| 1626 | #else |
---|
| 1627 | #endif |
---|
| 1628 | if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR))) |
---|
| 1629 | { |
---|
| 1630 | #if 1 |
---|
| 1631 | // we change to an ordering: |
---|
| 1632 | // aa(1,1,1,...,0,0,0),wp(...),C |
---|
| 1633 | // this seems to be better than version 2 below, |
---|
| 1634 | // according to Tst/../elimiate_[3568].tat (- 17 %) |
---|
| 1635 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1636 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1637 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1638 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
| 1639 | block0[0] = block0[1] = 1; |
---|
| 1640 | block1[0] = block1[1] = rVar(origR); |
---|
| 1641 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1642 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
| 1643 | // ignore it |
---|
| 1644 | ord[0] = ringorder_aa; |
---|
| 1645 | for (j=0;j<rVar(origR);j++) |
---|
| 1646 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
| 1647 | BOOLEAN wp=FALSE; |
---|
| 1648 | for (j=0;j<rVar(origR);j++) |
---|
| 1649 | if (pWeight(j+1,origR)!=1) { wp=TRUE;break; } |
---|
| 1650 | if (wp) |
---|
| 1651 | { |
---|
| 1652 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1653 | for (j=0;j<rVar(origR);j++) |
---|
| 1654 | wv[1][j]=pWeight(j+1,origR); |
---|
| 1655 | ord[1] = ringorder_wp; |
---|
| 1656 | } |
---|
| 1657 | else |
---|
| 1658 | ord[1] = ringorder_dp; |
---|
| 1659 | #else |
---|
| 1660 | // we change to an ordering: |
---|
| 1661 | // a(w1,...wn),wp(1,...0.....),C |
---|
| 1662 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1663 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1664 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1665 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
| 1666 | block0[0] = block0[1] = 1; |
---|
| 1667 | block1[0] = block1[1] = rVar(origR); |
---|
| 1668 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1669 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1670 | ord[0] = ringorder_a; |
---|
| 1671 | for (j=0;j<rVar(origR);j++) |
---|
| 1672 | wv[0][j]=pWeight(j+1,origR); |
---|
| 1673 | ord[1] = ringorder_wp; |
---|
| 1674 | for (j=0;j<rVar(origR);j++) |
---|
| 1675 | if (pGetExp(delVar,j+1)!=0) wv[1][j]=1; |
---|
| 1676 | #endif |
---|
| 1677 | ord[2] = ringorder_C; |
---|
| 1678 | ord[3] = 0; |
---|
| 1679 | } |
---|
| 1680 | else |
---|
| 1681 | { |
---|
| 1682 | // we change to an ordering: |
---|
| 1683 | // aa(....),orig_ordering |
---|
| 1684 | ord=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
| 1685 | block0=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
| 1686 | block1=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
| 1687 | wv=(int**) omAlloc0(ordersize*sizeof(int**)); |
---|
| 1688 | for (k=0;k<ordersize-1; k++) |
---|
| 1689 | { |
---|
| 1690 | block0[k+1] = origR->block0[k]; |
---|
| 1691 | block1[k+1] = origR->block1[k]; |
---|
| 1692 | ord[k+1] = origR->order[k]; |
---|
| 1693 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
| 1694 | } |
---|
| 1695 | block0[0] = 1; |
---|
| 1696 | block1[0] = rVar(origR); |
---|
| 1697 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1698 | for (j=0;j<rVar(origR);j++) |
---|
| 1699 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
| 1700 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
| 1701 | // ignore it |
---|
| 1702 | ord[0] = ringorder_aa; |
---|
| 1703 | } |
---|
| 1704 | // fill in tmp ring to get back the data later on |
---|
| 1705 | tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL |
---|
| 1706 | //rUnComplete(tmpR); |
---|
| 1707 | tmpR->p_Procs=NULL; |
---|
| 1708 | tmpR->order = ord; |
---|
| 1709 | tmpR->block0 = block0; |
---|
| 1710 | tmpR->block1 = block1; |
---|
| 1711 | tmpR->wvhdl = wv; |
---|
| 1712 | rComplete(tmpR, 1); |
---|
| 1713 | |
---|
| 1714 | #ifdef HAVE_PLURAL |
---|
| 1715 | /* update nc structure on tmpR */ |
---|
| 1716 | if (rIsPluralRing(origR)) |
---|
| 1717 | { |
---|
| 1718 | if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal! |
---|
| 1719 | { |
---|
| 1720 | Werror("no elimination is possible: ordering condition is violated"); |
---|
| 1721 | // cleanup |
---|
| 1722 | rDelete(tmpR); |
---|
| 1723 | if (w!=NULL) |
---|
| 1724 | delete w; |
---|
| 1725 | return idCopy(h1); |
---|
| 1726 | } |
---|
| 1727 | } |
---|
| 1728 | #endif |
---|
| 1729 | // change into the new ring |
---|
| 1730 | //pChangeRing(pVariables,currRing->OrdSgn,ord,block0,block1,wv); |
---|
| 1731 | rChangeCurrRing(tmpR); |
---|
| 1732 | |
---|
| 1733 | //h = idInit(IDELEMS(h1),h1->rank); |
---|
| 1734 | // fetch data from the old ring |
---|
| 1735 | //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR); |
---|
| 1736 | h=idrCopyR(h1,origR,currRing); |
---|
| 1737 | if (origR->qideal!=NULL) |
---|
| 1738 | { |
---|
| 1739 | WarnS("eliminate in q-ring: experimental"); |
---|
| 1740 | ideal q=idrCopyR(origR->qideal,origR,currRing); |
---|
| 1741 | ideal s=idSimpleAdd(h,q); |
---|
| 1742 | idDelete(&h); |
---|
| 1743 | idDelete(&q); |
---|
| 1744 | h=s; |
---|
| 1745 | } |
---|
| 1746 | // compute kStd |
---|
| 1747 | #if 1 |
---|
| 1748 | //rWrite(tmpR);PrintLn(); |
---|
| 1749 | BITSET save=test; |
---|
| 1750 | //test |=1; |
---|
| 1751 | //Print("h: %d gen, rk=%d\n",IDELEMS(h),h->rank); |
---|
| 1752 | //extern char * showOption(); |
---|
| 1753 | //Print("%s\n",showOption()); |
---|
| 1754 | hh = kStd(h,NULL,hom,&w,hilb); |
---|
| 1755 | test=save; |
---|
| 1756 | idDelete(&h); |
---|
| 1757 | #else |
---|
| 1758 | extern ideal kGroebner(ideal F, ideal Q); |
---|
| 1759 | hh=kGroebner(h,NULL); |
---|
| 1760 | #endif |
---|
| 1761 | // go back to the original ring |
---|
| 1762 | rChangeCurrRing(origR); |
---|
| 1763 | i = IDELEMS(hh)-1; |
---|
| 1764 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
| 1765 | j = -1; |
---|
| 1766 | // fetch data from temp ring |
---|
| 1767 | for (k=0; k<=i; k++) |
---|
| 1768 | { |
---|
| 1769 | l=pVariables; |
---|
| 1770 | while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--; |
---|
| 1771 | if (l==0) |
---|
| 1772 | { |
---|
| 1773 | j++; |
---|
| 1774 | if (j >= IDELEMS(h3)) |
---|
| 1775 | { |
---|
| 1776 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
| 1777 | IDELEMS(h3) += 16; |
---|
| 1778 | } |
---|
| 1779 | h3->m[j] = prMoveR( hh->m[k], tmpR); |
---|
| 1780 | hh->m[k] = NULL; |
---|
| 1781 | } |
---|
| 1782 | } |
---|
| 1783 | id_Delete(&hh, tmpR); |
---|
| 1784 | idSkipZeroes(h3); |
---|
| 1785 | rDelete(tmpR); |
---|
| 1786 | if (w!=NULL) |
---|
| 1787 | delete w; |
---|
| 1788 | return h3; |
---|
| 1789 | } |
---|
| 1790 | |
---|
| 1791 | /*2 |
---|
| 1792 | * compute the which-th ar-minor of the matrix a |
---|
| 1793 | */ |
---|
| 1794 | poly idMinor(matrix a, int ar, unsigned long which, ideal R) |
---|
| 1795 | { |
---|
| 1796 | int i,j,k,size; |
---|
| 1797 | unsigned long curr; |
---|
| 1798 | int *rowchoise,*colchoise; |
---|
| 1799 | BOOLEAN rowch,colch; |
---|
| 1800 | ideal result; |
---|
| 1801 | matrix tmp; |
---|
| 1802 | poly p,q; |
---|
| 1803 | |
---|
| 1804 | i = binom(a->rows(),ar); |
---|
| 1805 | j = binom(a->cols(),ar); |
---|
| 1806 | |
---|
| 1807 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1808 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1809 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
| 1810 | else size=i*j; |
---|
| 1811 | result=idInit(size,1); |
---|
| 1812 | tmp=mpNew(ar,ar); |
---|
| 1813 | k = 0; /* the index in result*/ |
---|
| 1814 | curr = 0; /* index of current minor */ |
---|
| 1815 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
| 1816 | while (!rowch) |
---|
| 1817 | { |
---|
| 1818 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
| 1819 | while (!colch) |
---|
| 1820 | { |
---|
| 1821 | if (curr == which) |
---|
| 1822 | { |
---|
| 1823 | for (i=1; i<=ar; i++) |
---|
| 1824 | { |
---|
| 1825 | for (j=1; j<=ar; j++) |
---|
| 1826 | { |
---|
| 1827 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
| 1828 | } |
---|
| 1829 | } |
---|
| 1830 | p = mpDetBareiss(tmp); |
---|
| 1831 | if (p!=NULL) |
---|
| 1832 | { |
---|
| 1833 | if (R!=NULL) |
---|
| 1834 | { |
---|
| 1835 | q = p; |
---|
| 1836 | p = kNF(R,currQuotient,q); |
---|
| 1837 | pDelete(&q); |
---|
| 1838 | } |
---|
| 1839 | /*delete the matrix tmp*/ |
---|
| 1840 | for (i=1; i<=ar; i++) |
---|
| 1841 | { |
---|
| 1842 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
| 1843 | } |
---|
| 1844 | idDelete((ideal*)&tmp); |
---|
| 1845 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
| 1846 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
| 1847 | return (p); |
---|
| 1848 | } |
---|
| 1849 | } |
---|
| 1850 | curr++; |
---|
| 1851 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
| 1852 | } |
---|
| 1853 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
| 1854 | } |
---|
| 1855 | return (poly) 1; |
---|
| 1856 | } |
---|
| 1857 | |
---|
| 1858 | #ifdef WITH_OLD_MINOR |
---|
| 1859 | /*2 |
---|
| 1860 | * compute all ar-minors of the matrix a |
---|
| 1861 | */ |
---|
| 1862 | ideal idMinors(matrix a, int ar, ideal R) |
---|
| 1863 | { |
---|
| 1864 | int i,j,k,size; |
---|
| 1865 | int *rowchoise,*colchoise; |
---|
| 1866 | BOOLEAN rowch,colch; |
---|
| 1867 | ideal result; |
---|
| 1868 | matrix tmp; |
---|
| 1869 | poly p,q; |
---|
| 1870 | |
---|
| 1871 | i = binom(a->rows(),ar); |
---|
| 1872 | j = binom(a->cols(),ar); |
---|
| 1873 | |
---|
| 1874 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1875 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1876 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
| 1877 | else size=i*j; |
---|
| 1878 | result=idInit(size,1); |
---|
| 1879 | tmp=mpNew(ar,ar); |
---|
| 1880 | k = 0; /* the index in result*/ |
---|
| 1881 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
| 1882 | while (!rowch) |
---|
| 1883 | { |
---|
| 1884 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
| 1885 | while (!colch) |
---|
| 1886 | { |
---|
| 1887 | for (i=1; i<=ar; i++) |
---|
| 1888 | { |
---|
| 1889 | for (j=1; j<=ar; j++) |
---|
| 1890 | { |
---|
| 1891 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
| 1892 | } |
---|
| 1893 | } |
---|
| 1894 | p = mpDetBareiss(tmp); |
---|
| 1895 | if (p!=NULL) |
---|
| 1896 | { |
---|
| 1897 | if (R!=NULL) |
---|
| 1898 | { |
---|
| 1899 | q = p; |
---|
| 1900 | p = kNF(R,currQuotient,q); |
---|
| 1901 | pDelete(&q); |
---|
| 1902 | } |
---|
| 1903 | if (p!=NULL) |
---|
| 1904 | { |
---|
| 1905 | if (k>=size) |
---|
| 1906 | { |
---|
| 1907 | pEnlargeSet(&result->m,size,32); |
---|
| 1908 | size += 32; |
---|
| 1909 | } |
---|
| 1910 | result->m[k] = p; |
---|
| 1911 | k++; |
---|
| 1912 | } |
---|
| 1913 | } |
---|
| 1914 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
| 1915 | } |
---|
| 1916 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
| 1917 | } |
---|
| 1918 | /*delete the matrix tmp*/ |
---|
| 1919 | for (i=1; i<=ar; i++) |
---|
| 1920 | { |
---|
| 1921 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
| 1922 | } |
---|
| 1923 | idDelete((ideal*)&tmp); |
---|
| 1924 | if (k==0) |
---|
| 1925 | { |
---|
| 1926 | k=1; |
---|
| 1927 | result->m[0]=NULL; |
---|
| 1928 | } |
---|
| 1929 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
| 1930 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
| 1931 | pEnlargeSet(&result->m,size,k-size); |
---|
| 1932 | IDELEMS(result) = k; |
---|
| 1933 | return (result); |
---|
| 1934 | } |
---|
| 1935 | #else |
---|
| 1936 | /*2 |
---|
| 1937 | * compute all ar-minors of the matrix a |
---|
| 1938 | * the caller of mpRecMin |
---|
| 1939 | * the elements of the result are not in R (if R!=NULL) |
---|
| 1940 | */ |
---|
| 1941 | ideal idMinors(matrix a, int ar, ideal R) |
---|
| 1942 | { |
---|
| 1943 | int elems=0; |
---|
| 1944 | int r=a->nrows,c=a->ncols; |
---|
| 1945 | int i; |
---|
| 1946 | matrix b; |
---|
| 1947 | ideal result,h; |
---|
| 1948 | ring origR; |
---|
| 1949 | ring tmpR; |
---|
| 1950 | long bound; |
---|
| 1951 | |
---|
| 1952 | if((ar<=0) || (ar>r) || (ar>c)) |
---|
| 1953 | { |
---|
| 1954 | Werror("%d-th minor, matrix is %dx%d",ar,r,c); |
---|
| 1955 | return NULL; |
---|
| 1956 | } |
---|
| 1957 | h = idMatrix2Module(mpCopy(a)); |
---|
| 1958 | bound = smExpBound(h,c,r,ar); |
---|
| 1959 | idDelete(&h); |
---|
| 1960 | tmpR=smRingChange(&origR,bound); |
---|
| 1961 | b = mpNew(r,c); |
---|
| 1962 | for (i=r*c-1;i>=0;i--) |
---|
| 1963 | { |
---|
| 1964 | if (a->m[i]) |
---|
| 1965 | b->m[i] = prCopyR(a->m[i],origR); |
---|
| 1966 | } |
---|
| 1967 | if (R!=NULL) |
---|
| 1968 | { |
---|
| 1969 | R = idrCopyR(R,origR); |
---|
| 1970 | //if (ar>1) // otherwise done in mpMinorToResult |
---|
| 1971 | //{ |
---|
| 1972 | // matrix bb=(matrix)kNF(R,currQuotient,(ideal)b); |
---|
| 1973 | // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols; |
---|
| 1974 | // idDelete((ideal*)&b); b=bb; |
---|
| 1975 | //} |
---|
| 1976 | } |
---|
| 1977 | result=idInit(32,1); |
---|
| 1978 | if(ar>1) mpRecMin(ar-1,result,elems,b,r,c,NULL,R); |
---|
| 1979 | else mpMinorToResult(result,elems,b,r,c,R); |
---|
| 1980 | idDelete((ideal *)&b); |
---|
| 1981 | if (R!=NULL) idDelete(&R); |
---|
| 1982 | idSkipZeroes(result); |
---|
| 1983 | rChangeCurrRing(origR); |
---|
| 1984 | result = idrMoveR(result,tmpR); |
---|
| 1985 | smKillModifiedRing(tmpR); |
---|
| 1986 | idTest(result); |
---|
| 1987 | return result; |
---|
| 1988 | } |
---|
| 1989 | #endif |
---|
| 1990 | |
---|
| 1991 | /*2 |
---|
| 1992 | *returns TRUE if id1 is a submodule of id2 |
---|
| 1993 | */ |
---|
| 1994 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
| 1995 | { |
---|
| 1996 | int i; |
---|
| 1997 | poly p; |
---|
| 1998 | |
---|
| 1999 | if (idIs0(id1)) return TRUE; |
---|
| 2000 | for (i=0;i<IDELEMS(id1);i++) |
---|
| 2001 | { |
---|
| 2002 | if (id1->m[i] != NULL) |
---|
| 2003 | { |
---|
| 2004 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
| 2005 | if (p != NULL) |
---|
| 2006 | { |
---|
| 2007 | pDelete(&p); |
---|
| 2008 | return FALSE; |
---|
| 2009 | } |
---|
| 2010 | } |
---|
| 2011 | } |
---|
| 2012 | return TRUE; |
---|
| 2013 | } |
---|
| 2014 | |
---|
| 2015 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
| 2016 | { |
---|
| 2017 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
| 2018 | if (idIs0(m)) return TRUE; |
---|
| 2019 | |
---|
| 2020 | int cmax=-1; |
---|
| 2021 | int i; |
---|
| 2022 | poly p=NULL; |
---|
| 2023 | int length=IDELEMS(m); |
---|
| 2024 | polyset P=m->m; |
---|
| 2025 | for (i=length-1;i>=0;i--) |
---|
| 2026 | { |
---|
| 2027 | p=P[i]; |
---|
| 2028 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
| 2029 | } |
---|
| 2030 | if (w != NULL) |
---|
| 2031 | if (w->length()+1 < cmax) |
---|
| 2032 | { |
---|
| 2033 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
| 2034 | return FALSE; |
---|
| 2035 | } |
---|
| 2036 | |
---|
| 2037 | if(w!=NULL) |
---|
| 2038 | pSetModDeg(w); |
---|
| 2039 | |
---|
| 2040 | for (i=length-1;i>=0;i--) |
---|
| 2041 | { |
---|
| 2042 | p=P[i]; |
---|
| 2043 | poly q=p; |
---|
| 2044 | if (p!=NULL) |
---|
| 2045 | { |
---|
| 2046 | int d=pFDeg(p,currRing); |
---|
| 2047 | loop |
---|
| 2048 | { |
---|
| 2049 | pIter(p); |
---|
| 2050 | if (p==NULL) break; |
---|
| 2051 | if (d!=pFDeg(p,currRing)) |
---|
| 2052 | { |
---|
| 2053 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
| 2054 | if(w!=NULL) |
---|
| 2055 | pSetModDeg(NULL); |
---|
| 2056 | return FALSE; |
---|
| 2057 | } |
---|
| 2058 | } |
---|
| 2059 | } |
---|
| 2060 | } |
---|
| 2061 | |
---|
| 2062 | if(w!=NULL) |
---|
| 2063 | pSetModDeg(NULL); |
---|
| 2064 | |
---|
| 2065 | return TRUE; |
---|
| 2066 | } |
---|
| 2067 | |
---|
| 2068 | int idMinDegW(ideal M,intvec *w) |
---|
| 2069 | { |
---|
| 2070 | int d=-1; |
---|
| 2071 | for(int i=0;i<IDELEMS(M);i++) |
---|
| 2072 | { |
---|
| 2073 | int d0=pMinDeg(M->m[i],w); |
---|
| 2074 | if(-1<d0&&(d0<d||d==-1)) |
---|
| 2075 | d=d0; |
---|
| 2076 | } |
---|
| 2077 | return d; |
---|
| 2078 | } |
---|
| 2079 | |
---|
| 2080 | ideal idSeries(int n,ideal M,matrix U,intvec *w) |
---|
| 2081 | { |
---|
| 2082 | for(int i=IDELEMS(M)-1;i>=0;i--) |
---|
| 2083 | { |
---|
| 2084 | if(U==NULL) |
---|
| 2085 | M->m[i]=pSeries(n,M->m[i],NULL,w); |
---|
| 2086 | else |
---|
| 2087 | { |
---|
| 2088 | M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w); |
---|
| 2089 | MATELEM(U,i+1,i+1)=NULL; |
---|
| 2090 | } |
---|
| 2091 | } |
---|
| 2092 | if(U!=NULL) |
---|
| 2093 | idDelete((ideal*)&U); |
---|
| 2094 | return M; |
---|
| 2095 | } |
---|
| 2096 | |
---|
| 2097 | matrix idDiff(matrix i, int k) |
---|
| 2098 | { |
---|
| 2099 | int e=MATCOLS(i)*MATROWS(i); |
---|
| 2100 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
| 2101 | r->rank=i->rank; |
---|
| 2102 | int j; |
---|
| 2103 | for(j=0; j<e; j++) |
---|
| 2104 | { |
---|
| 2105 | r->m[j]=pDiff(i->m[j],k); |
---|
| 2106 | } |
---|
| 2107 | return r; |
---|
| 2108 | } |
---|
| 2109 | |
---|
| 2110 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
| 2111 | { |
---|
| 2112 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
| 2113 | int i,j; |
---|
| 2114 | for(i=0; i<IDELEMS(I); i++) |
---|
| 2115 | { |
---|
| 2116 | for(j=0; j<IDELEMS(J); j++) |
---|
| 2117 | { |
---|
| 2118 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
| 2119 | } |
---|
| 2120 | } |
---|
| 2121 | return r; |
---|
| 2122 | } |
---|
| 2123 | |
---|
| 2124 | /*3 |
---|
| 2125 | *handles for some ideal operations the ring/syzcomp managment |
---|
| 2126 | *returns all syzygies (componentwise-)shifted by -syzcomp |
---|
| 2127 | *or -syzcomp-1 (in case of ideals as input) |
---|
| 2128 | static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE) |
---|
| 2129 | { |
---|
| 2130 | ring orig_ring=currRing; |
---|
| 2131 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 2132 | rSetSyzComp(length); |
---|
| 2133 | |
---|
| 2134 | ideal s_temp; |
---|
| 2135 | if (orig_ring!=syz_ring) |
---|
| 2136 | s_temp=idrMoveR_NoSort(arg,orig_ring); |
---|
| 2137 | else |
---|
| 2138 | s_temp=arg; |
---|
| 2139 | |
---|
| 2140 | ideal s_temp1 = kStd(s_temp,currQuotient,testHomog,&w,NULL,length); |
---|
| 2141 | if (w!=NULL) delete w; |
---|
| 2142 | |
---|
| 2143 | if (syz_ring!=orig_ring) |
---|
| 2144 | { |
---|
| 2145 | idDelete(&s_temp); |
---|
| 2146 | rChangeCurrRing(orig_ring); |
---|
| 2147 | } |
---|
| 2148 | |
---|
| 2149 | idDelete(&temp); |
---|
| 2150 | ideal temp1=idRingCopy(s_temp1,syz_ring); |
---|
| 2151 | |
---|
| 2152 | if (syz_ring!=orig_ring) |
---|
| 2153 | { |
---|
| 2154 | rChangeCurrRing(syz_ring); |
---|
| 2155 | idDelete(&s_temp1); |
---|
| 2156 | rChangeCurrRing(orig_ring); |
---|
| 2157 | rKill(syz_ring); |
---|
| 2158 | } |
---|
| 2159 | |
---|
| 2160 | for (i=0;i<IDELEMS(temp1);i++) |
---|
| 2161 | { |
---|
| 2162 | if ((temp1->m[i]!=NULL) |
---|
| 2163 | && (pGetComp(temp1->m[i])<=length)) |
---|
| 2164 | { |
---|
| 2165 | pDelete(&(temp1->m[i])); |
---|
| 2166 | } |
---|
| 2167 | else |
---|
| 2168 | { |
---|
| 2169 | pShift(&(temp1->m[i]),-length); |
---|
| 2170 | } |
---|
| 2171 | } |
---|
| 2172 | temp1->rank = rk; |
---|
| 2173 | idSkipZeroes(temp1); |
---|
| 2174 | |
---|
| 2175 | return temp1; |
---|
| 2176 | } |
---|
| 2177 | */ |
---|
| 2178 | /*2 |
---|
| 2179 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
| 2180 | */ |
---|
| 2181 | //ideal idModulo (ideal h2,ideal h1) |
---|
| 2182 | ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w) |
---|
| 2183 | { |
---|
| 2184 | intvec *wtmp=NULL; |
---|
| 2185 | |
---|
| 2186 | int i,j,k,rk,flength=0,slength,length; |
---|
| 2187 | poly p,q; |
---|
| 2188 | |
---|
| 2189 | if (idIs0(h2)) |
---|
| 2190 | return idFreeModule(si_max(1,h2->ncols)); |
---|
| 2191 | if (!idIs0(h1)) |
---|
| 2192 | flength = idRankFreeModule(h1); |
---|
| 2193 | slength = idRankFreeModule(h2); |
---|
| 2194 | length = si_max(flength,slength); |
---|
| 2195 | if (length==0) |
---|
| 2196 | { |
---|
| 2197 | length = 1; |
---|
| 2198 | } |
---|
| 2199 | ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2)); |
---|
| 2200 | if ((w!=NULL)&&((*w)!=NULL)) |
---|
| 2201 | { |
---|
| 2202 | //Print("input weights:");(*w)->show(1);PrintLn(); |
---|
| 2203 | int d; |
---|
| 2204 | int k; |
---|
| 2205 | wtmp=new intvec(length+IDELEMS(h2)); |
---|
| 2206 | for (i=0;i<length;i++) |
---|
| 2207 | ((*wtmp)[i])=(**w)[i]; |
---|
| 2208 | for (i=0;i<IDELEMS(h2);i++) |
---|
| 2209 | { |
---|
| 2210 | poly p=h2->m[i]; |
---|
| 2211 | if (p!=NULL) |
---|
| 2212 | { |
---|
| 2213 | d = pDeg(p); |
---|
| 2214 | k= pGetComp(p); |
---|
| 2215 | if (slength>0) k--; |
---|
| 2216 | d +=((**w)[k]); |
---|
| 2217 | ((*wtmp)[i+length]) = d; |
---|
| 2218 | } |
---|
| 2219 | } |
---|
| 2220 | //Print("weights:");wtmp->show(1);PrintLn(); |
---|
| 2221 | } |
---|
| 2222 | for (i=0;i<IDELEMS(h2);i++) |
---|
| 2223 | { |
---|
| 2224 | temp->m[i] = pCopy(h2->m[i]); |
---|
| 2225 | q = pOne(); |
---|
| 2226 | pSetComp(q,i+1+length); |
---|
| 2227 | pSetmComp(q); |
---|
| 2228 | if(temp->m[i]!=NULL) |
---|
| 2229 | { |
---|
| 2230 | if (slength==0) pShift(&(temp->m[i]),1); |
---|
| 2231 | p = temp->m[i]; |
---|
| 2232 | while (pNext(p)!=NULL) pIter(p); |
---|
| 2233 | pNext(p) = q; |
---|
| 2234 | } |
---|
| 2235 | else |
---|
| 2236 | temp->m[i]=q; |
---|
| 2237 | } |
---|
| 2238 | rk = k = IDELEMS(h2); |
---|
| 2239 | if (!idIs0(h1)) |
---|
| 2240 | { |
---|
| 2241 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
| 2242 | IDELEMS(temp) += IDELEMS(h1); |
---|
| 2243 | for (i=0;i<IDELEMS(h1);i++) |
---|
| 2244 | { |
---|
| 2245 | if (h1->m[i]!=NULL) |
---|
| 2246 | { |
---|
| 2247 | temp->m[k] = pCopy(h1->m[i]); |
---|
| 2248 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
| 2249 | k++; |
---|
| 2250 | } |
---|
| 2251 | } |
---|
| 2252 | } |
---|
| 2253 | |
---|
| 2254 | ring orig_ring=currRing; |
---|
| 2255 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
| 2256 | rSetSyzComp(length); |
---|
| 2257 | ideal s_temp; |
---|
| 2258 | |
---|
| 2259 | if (syz_ring != orig_ring) |
---|
| 2260 | { |
---|
| 2261 | s_temp = idrMoveR_NoSort(temp, orig_ring); |
---|
| 2262 | } |
---|
| 2263 | else |
---|
| 2264 | { |
---|
| 2265 | s_temp = temp; |
---|
| 2266 | } |
---|
| 2267 | |
---|
| 2268 | idTest(s_temp); |
---|
| 2269 | ideal s_temp1 = kStd(s_temp,currQuotient,hom,&wtmp,NULL,length); |
---|
| 2270 | |
---|
| 2271 | //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn(); |
---|
| 2272 | if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL)) |
---|
| 2273 | { |
---|
| 2274 | delete *w; |
---|
| 2275 | *w=new intvec(IDELEMS(h2)); |
---|
| 2276 | for (i=0;i<IDELEMS(h2);i++) |
---|
| 2277 | ((**w)[i])=(*wtmp)[i+length]; |
---|
| 2278 | } |
---|
| 2279 | if (wtmp!=NULL) delete wtmp; |
---|
| 2280 | |
---|
| 2281 | for (i=0;i<IDELEMS(s_temp1);i++) |
---|
| 2282 | { |
---|
| 2283 | if ((s_temp1->m[i]!=NULL) |
---|
| 2284 | && (pGetComp(s_temp1->m[i])<=length)) |
---|
| 2285 | { |
---|
| 2286 | pDelete(&(s_temp1->m[i])); |
---|
| 2287 | } |
---|
| 2288 | else |
---|
| 2289 | { |
---|
| 2290 | pShift(&(s_temp1->m[i]),-length); |
---|
| 2291 | } |
---|
| 2292 | } |
---|
| 2293 | s_temp1->rank = rk; |
---|
| 2294 | idSkipZeroes(s_temp1); |
---|
| 2295 | |
---|
| 2296 | if (syz_ring!=orig_ring) |
---|
| 2297 | { |
---|
| 2298 | rChangeCurrRing(orig_ring); |
---|
| 2299 | s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring); |
---|
| 2300 | rKill(syz_ring); |
---|
| 2301 | // Hmm ... here seems to be a memory leak |
---|
| 2302 | // However, simply deleting it causes memory trouble |
---|
| 2303 | // idDelete(&s_temp); |
---|
| 2304 | } |
---|
| 2305 | else |
---|
| 2306 | { |
---|
| 2307 | idDelete(&temp); |
---|
| 2308 | } |
---|
| 2309 | idTest(s_temp1); |
---|
| 2310 | return s_temp1; |
---|
| 2311 | } |
---|
| 2312 | |
---|
| 2313 | int idElem(const ideal F) |
---|
| 2314 | { |
---|
| 2315 | int i=0,j=IDELEMS(F)-1; |
---|
| 2316 | |
---|
| 2317 | while(j>=0) |
---|
| 2318 | { |
---|
| 2319 | if ((F->m)[j]!=NULL) i++; |
---|
| 2320 | j--; |
---|
| 2321 | } |
---|
| 2322 | return i; |
---|
| 2323 | } |
---|
| 2324 | |
---|
| 2325 | /* |
---|
| 2326 | *computes module-weights for liftings of homogeneous modules |
---|
| 2327 | */ |
---|
| 2328 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
| 2329 | { |
---|
| 2330 | if (idIs0(mod)) return new intvec(2); |
---|
| 2331 | int i=IDELEMS(mod); |
---|
| 2332 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
| 2333 | intvec *result = new intvec(i+1); |
---|
| 2334 | while (i>0) |
---|
| 2335 | { |
---|
| 2336 | (*result)[i]=pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])]; |
---|
| 2337 | } |
---|
| 2338 | return result; |
---|
| 2339 | } |
---|
| 2340 | |
---|
| 2341 | /*2 |
---|
| 2342 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
| 2343 | *with x_max,...,x_1) |
---|
| 2344 | */ |
---|
| 2345 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
| 2346 | { |
---|
| 2347 | int i; |
---|
| 2348 | ideal result; |
---|
| 2349 | |
---|
| 2350 | if (idIs0(kBase)) return NULL; |
---|
| 2351 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
| 2352 | *convert = idSort(kBase,FALSE); |
---|
| 2353 | for (i=0;i<(*convert)->length();i++) |
---|
| 2354 | { |
---|
| 2355 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
| 2356 | } |
---|
| 2357 | return result; |
---|
| 2358 | } |
---|
| 2359 | |
---|
| 2360 | /*2 |
---|
| 2361 | *returns the index of a given monom in the list of the special kbase |
---|
| 2362 | */ |
---|
| 2363 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
| 2364 | { |
---|
| 2365 | int j=IDELEMS(kbase); |
---|
| 2366 | |
---|
| 2367 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
| 2368 | if (j==0) return -1; |
---|
| 2369 | int i=pVariables; |
---|
| 2370 | while (i>0) |
---|
| 2371 | { |
---|
| 2372 | loop |
---|
| 2373 | { |
---|
| 2374 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
| 2375 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
| 2376 | j--; |
---|
| 2377 | if (j==0) return -1; |
---|
| 2378 | } |
---|
| 2379 | if (i==1) |
---|
| 2380 | { |
---|
| 2381 | while(j>0) |
---|
| 2382 | { |
---|
| 2383 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
| 2384 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
| 2385 | j--; |
---|
| 2386 | } |
---|
| 2387 | } |
---|
| 2388 | i--; |
---|
| 2389 | } |
---|
| 2390 | return -1; |
---|
| 2391 | } |
---|
| 2392 | |
---|
| 2393 | /*2 |
---|
| 2394 | *decomposes the monom in a part of coefficients described by the |
---|
| 2395 | *complement of how and a monom in variables occuring in how, the |
---|
| 2396 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
| 2397 | *exists) |
---|
| 2398 | */ |
---|
| 2399 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
| 2400 | { |
---|
| 2401 | int i; |
---|
| 2402 | poly coeff=pOne(), base=pOne(); |
---|
| 2403 | |
---|
| 2404 | for (i=1;i<=pVariables;i++) |
---|
| 2405 | { |
---|
| 2406 | if (pGetExp(how,i)>0) |
---|
| 2407 | { |
---|
| 2408 | pSetExp(base,i,pGetExp(monom,i)); |
---|
| 2409 | } |
---|
| 2410 | else |
---|
| 2411 | { |
---|
| 2412 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
| 2413 | } |
---|
| 2414 | } |
---|
| 2415 | pSetComp(base,pGetComp(monom)); |
---|
| 2416 | pSetm(base); |
---|
| 2417 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
| 2418 | pSetm(coeff); |
---|
| 2419 | *pos = idIndexOfKBase(base,kbase); |
---|
| 2420 | if (*pos<0) |
---|
| 2421 | pDelete(&coeff); |
---|
| 2422 | pDelete(&base); |
---|
| 2423 | return coeff; |
---|
| 2424 | } |
---|
| 2425 | |
---|
| 2426 | /*2 |
---|
| 2427 | *returns a matrix A of coefficients with kbase*A=arg |
---|
| 2428 | *if all monomials in variables of how occur in kbase |
---|
| 2429 | *the other are deleted |
---|
| 2430 | */ |
---|
| 2431 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
| 2432 | { |
---|
| 2433 | matrix result; |
---|
| 2434 | ideal tempKbase; |
---|
| 2435 | poly p,q; |
---|
| 2436 | intvec * convert; |
---|
| 2437 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
| 2438 | #if 0 |
---|
| 2439 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
| 2440 | if (idIs0(arg)) |
---|
| 2441 | return mpNew(i,1); |
---|
| 2442 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
| 2443 | result = mpNew(i,j); |
---|
| 2444 | #else |
---|
| 2445 | result = mpNew(i, j); |
---|
| 2446 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
| 2447 | #endif |
---|
| 2448 | |
---|
| 2449 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
| 2450 | for (k=0;k<j;k++) |
---|
| 2451 | { |
---|
| 2452 | p = arg->m[k]; |
---|
| 2453 | while (p!=NULL) |
---|
| 2454 | { |
---|
| 2455 | q = idDecompose(p,how,tempKbase,&pos); |
---|
| 2456 | if (pos>=0) |
---|
| 2457 | { |
---|
| 2458 | MATELEM(result,(*convert)[pos],k+1) = |
---|
| 2459 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
| 2460 | } |
---|
| 2461 | else |
---|
| 2462 | pDelete(&q); |
---|
| 2463 | pIter(p); |
---|
| 2464 | } |
---|
| 2465 | } |
---|
| 2466 | idDelete(&tempKbase); |
---|
| 2467 | return result; |
---|
| 2468 | } |
---|
| 2469 | |
---|
| 2470 | static void idDeleteComps(ideal arg,int* red_comp,int del) |
---|
| 2471 | // red_comp is an array [0..args->rank] |
---|
| 2472 | { |
---|
| 2473 | int i,j; |
---|
| 2474 | poly p; |
---|
| 2475 | |
---|
| 2476 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
| 2477 | { |
---|
| 2478 | p = arg->m[i]; |
---|
| 2479 | while (p!=NULL) |
---|
| 2480 | { |
---|
| 2481 | j = pGetComp(p); |
---|
| 2482 | if (red_comp[j]!=j) |
---|
| 2483 | { |
---|
| 2484 | pSetComp(p,red_comp[j]); |
---|
| 2485 | pSetmComp(p); |
---|
| 2486 | } |
---|
| 2487 | pIter(p); |
---|
| 2488 | } |
---|
| 2489 | } |
---|
| 2490 | (arg->rank) -= del; |
---|
| 2491 | } |
---|
| 2492 | |
---|
| 2493 | /*2 |
---|
| 2494 | * returns the presentation of an isomorphic, minimally |
---|
| 2495 | * embedded module (arg represents the quotient!) |
---|
| 2496 | */ |
---|
| 2497 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w) |
---|
| 2498 | { |
---|
| 2499 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
| 2500 | int i,next_gen,next_comp; |
---|
| 2501 | ideal res=arg; |
---|
| 2502 | if (!inPlace) res = idCopy(arg); |
---|
| 2503 | res->rank=si_max(res->rank,idRankFreeModule(res)); |
---|
| 2504 | int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int)); |
---|
| 2505 | for (i=res->rank;i>=0;i--) red_comp[i]=i; |
---|
| 2506 | |
---|
| 2507 | int del=0; |
---|
| 2508 | loop |
---|
| 2509 | { |
---|
| 2510 | next_gen = idReadOutPivot(res,&next_comp); |
---|
| 2511 | if (next_gen<0) break; |
---|
| 2512 | del++; |
---|
| 2513 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
---|
| 2514 | for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--; |
---|
| 2515 | if ((w !=NULL)&&(*w!=NULL)) |
---|
| 2516 | { |
---|
| 2517 | for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i]; |
---|
| 2518 | } |
---|
| 2519 | } |
---|
| 2520 | |
---|
| 2521 | idDeleteComps(res,red_comp,del); |
---|
| 2522 | idSkipZeroes(res); |
---|
| 2523 | omFree(red_comp); |
---|
| 2524 | |
---|
| 2525 | if ((w !=NULL)&&(*w!=NULL) &&(del>0)) |
---|
| 2526 | { |
---|
| 2527 | intvec *wtmp=new intvec((*w)->length()-del); |
---|
| 2528 | for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i]; |
---|
| 2529 | delete *w; |
---|
| 2530 | *w=wtmp; |
---|
| 2531 | } |
---|
| 2532 | return res; |
---|
| 2533 | } |
---|
| 2534 | |
---|
| 2535 | #include <kernel/clapsing.h> |
---|
| 2536 | |
---|
| 2537 | #ifdef HAVE_FACTORY |
---|
| 2538 | poly id_GCD(poly f, poly g, const ring r) |
---|
| 2539 | { |
---|
| 2540 | ring save_r=currRing; |
---|
| 2541 | rChangeCurrRing(r); |
---|
| 2542 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
| 2543 | intvec *w = NULL; |
---|
| 2544 | ideal S=idSyzygies(I,testHomog,&w); |
---|
| 2545 | if (w!=NULL) delete w; |
---|
| 2546 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
| 2547 | idDelete(&S); |
---|
| 2548 | poly gcd_p=singclap_pdivide(f,gg); |
---|
| 2549 | pDelete(&gg); |
---|
| 2550 | rChangeCurrRing(save_r); |
---|
| 2551 | return gcd_p; |
---|
| 2552 | } |
---|
| 2553 | #endif |
---|
| 2554 | |
---|
| 2555 | /*2 |
---|
| 2556 | * xx,q: arrays of length 0..rl-1 |
---|
| 2557 | * xx[i]: SB mod q[i] |
---|
| 2558 | * assume: char=0 |
---|
| 2559 | * assume: q[i]!=0 |
---|
| 2560 | * destroys xx |
---|
| 2561 | */ |
---|
| 2562 | #ifdef HAVE_FACTORY |
---|
| 2563 | ideal idChineseRemainder(ideal *xx, number *q, int rl) |
---|
| 2564 | { |
---|
| 2565 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
| 2566 | ideal result=idInit(cnt,xx[0]->rank); |
---|
| 2567 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
| 2568 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
| 2569 | int i,j; |
---|
| 2570 | poly r,h,hh,res_p; |
---|
| 2571 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
| 2572 | for(i=cnt-1;i>=0;i--) |
---|
| 2573 | { |
---|
| 2574 | res_p=NULL; |
---|
| 2575 | loop |
---|
| 2576 | { |
---|
| 2577 | r=NULL; |
---|
| 2578 | for(j=rl-1;j>=0;j--) |
---|
| 2579 | { |
---|
| 2580 | h=xx[j]->m[i]; |
---|
| 2581 | if ((h!=NULL) |
---|
| 2582 | &&((r==NULL)||(pLmCmp(r,h)==-1))) |
---|
| 2583 | r=h; |
---|
| 2584 | } |
---|
| 2585 | if (r==NULL) break; |
---|
| 2586 | h=pHead(r); |
---|
| 2587 | for(j=rl-1;j>=0;j--) |
---|
| 2588 | { |
---|
| 2589 | hh=xx[j]->m[i]; |
---|
| 2590 | if ((hh!=NULL) && (pLmCmp(r,hh)==0)) |
---|
| 2591 | { |
---|
| 2592 | x[j]=pGetCoeff(hh); |
---|
| 2593 | hh=pLmFreeAndNext(hh); |
---|
| 2594 | xx[j]->m[i]=hh; |
---|
| 2595 | } |
---|
| 2596 | else |
---|
| 2597 | x[j]=nlInit(0, currRing); |
---|
| 2598 | } |
---|
| 2599 | number n=nlChineseRemainder(x,q,rl); |
---|
| 2600 | for(j=rl-1;j>=0;j--) |
---|
| 2601 | { |
---|
| 2602 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
| 2603 | } |
---|
| 2604 | if (nlIsZero(n)) pDelete(&h); |
---|
| 2605 | else |
---|
| 2606 | { |
---|
| 2607 | pSetCoeff(h,n); |
---|
| 2608 | //Print("new mon:");pWrite(h); |
---|
| 2609 | res_p=pAdd(res_p,h); |
---|
| 2610 | } |
---|
| 2611 | } |
---|
| 2612 | result->m[i]=res_p; |
---|
| 2613 | } |
---|
| 2614 | omFree(x); |
---|
| 2615 | for(i=rl-1;i>=0;i--) idDelete(&(xx[i])); |
---|
| 2616 | omFree(xx); |
---|
| 2617 | return result; |
---|
| 2618 | } |
---|
| 2619 | #endif |
---|
| 2620 | /* currently unsed: |
---|
| 2621 | ideal idChineseRemainder(ideal *xx, intvec *iv) |
---|
| 2622 | { |
---|
| 2623 | int rl=iv->length(); |
---|
| 2624 | number *q=(number *)omAlloc(rl*sizeof(number)); |
---|
| 2625 | int i; |
---|
| 2626 | for(i=0; i<rl; i++) |
---|
| 2627 | { |
---|
| 2628 | q[i]=nInit((*iv)[i]); |
---|
| 2629 | } |
---|
| 2630 | return idChineseRemainder(xx,q,rl); |
---|
| 2631 | } |
---|
| 2632 | */ |
---|
| 2633 | /* |
---|
| 2634 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
---|
| 2635 | */ |
---|
| 2636 | ideal idFarey(ideal x, number N) |
---|
| 2637 | { |
---|
| 2638 | int cnt=IDELEMS(x)*x->nrows; |
---|
| 2639 | ideal result=idInit(cnt,x->rank); |
---|
| 2640 | result->nrows=x->nrows; // for lifting matrices |
---|
| 2641 | result->ncols=x->ncols; // for lifting matrices |
---|
| 2642 | |
---|
| 2643 | int i; |
---|
| 2644 | for(i=cnt-1;i>=0;i--) |
---|
| 2645 | { |
---|
| 2646 | poly h=pCopy(x->m[i]); |
---|
| 2647 | result->m[i]=h; |
---|
| 2648 | while(h!=NULL) |
---|
| 2649 | { |
---|
| 2650 | number c=pGetCoeff(h); |
---|
| 2651 | pSetCoeff0(h,nlFarey(c,N)); |
---|
| 2652 | nDelete(&c); |
---|
| 2653 | pIter(h); |
---|
| 2654 | } |
---|
| 2655 | while((result->m[i]!=NULL)&&(nIsZero(pGetCoeff(result->m[i])))) |
---|
| 2656 | { |
---|
| 2657 | pLmDelete(&(result->m[i])); |
---|
| 2658 | } |
---|
| 2659 | h=result->m[i]; |
---|
| 2660 | while((h!=NULL) && (pNext(h)!=NULL)) |
---|
| 2661 | { |
---|
| 2662 | if(nIsZero(pGetCoeff(pNext(h)))) |
---|
| 2663 | { |
---|
| 2664 | pLmDelete(&pNext(h)); |
---|
| 2665 | } |
---|
| 2666 | else pIter(h); |
---|
| 2667 | } |
---|
| 2668 | } |
---|
| 2669 | return result; |
---|
| 2670 | } |
---|