[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[341696] | 4 | /* $Id$ */ |
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[35aab3] | 5 | |
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| 6 | /* |
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| 7 | * ABSTRACT: resolutions |
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| 8 | */ |
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| 9 | |
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| 10 | |
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[599326] | 11 | #include <kernel/mod2.h> |
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[0f401f] | 12 | #include <misc/options.h> |
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[b1dfaf] | 13 | #include <omalloc/omalloc.h> |
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[210e07] | 14 | #include <polys/polys.h> |
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[599326] | 15 | #include <kernel/febase.h> |
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| 16 | #include <kernel/kstd1.h> |
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| 17 | #include <kernel/kutil.h> |
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| 18 | #include <kernel/stairc.h> |
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[210e07] | 19 | #include <misc/intvec.h> |
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[0f401f] | 20 | #include <coeffs/numbers.h> |
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[599326] | 21 | #include <kernel/ideals.h> |
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[210e07] | 22 | #include <misc/intvec.h> |
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| 23 | #include <polys/monomials/ring.h> |
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[599326] | 24 | #include <kernel/syz.h> |
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[76cfef] | 25 | #include <polys/prCopy.h> |
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[35aab3] | 26 | |
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[76cfef] | 27 | #include <polys/nc/sca.h> |
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[35aab3] | 28 | |
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| 29 | static intvec * syPrepareModComp(ideal arg,intvec ** w) |
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| 30 | { |
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| 31 | intvec *w1 = NULL; |
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| 32 | int i; |
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| 33 | BOOLEAN isIdeal=FALSE; |
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| 34 | |
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| 35 | if ((w==NULL) || (*w==NULL)) return w1; |
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| 36 | int maxxx = (*w)->length(); |
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| 37 | if (maxxx==1) |
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| 38 | { |
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| 39 | maxxx = 2; |
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| 40 | isIdeal = TRUE; |
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| 41 | } |
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| 42 | w1 = new intvec(maxxx+IDELEMS(arg)); |
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| 43 | if (!isIdeal) |
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| 44 | { |
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| 45 | for (i=0;i<maxxx;i++) |
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| 46 | { |
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| 47 | (*w1)[i] = (**w)[i]; |
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| 48 | } |
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| 49 | } |
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| 50 | for (i=maxxx;i<maxxx+IDELEMS(arg);i++) |
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| 51 | { |
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| 52 | if (arg->m[i-maxxx]!=NULL) |
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| 53 | { |
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[b50590] | 54 | (*w1)[i] = p_FDeg(arg->m[i-maxxx],currRing); |
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[35aab3] | 55 | if (pGetComp(arg->m[i-maxxx])!=0) |
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| 56 | { |
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| 57 | (*w1)[i]+=(**w)[pGetComp(arg->m[i-maxxx])-1]; |
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| 58 | } |
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| 59 | } |
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| 60 | } |
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| 61 | delete (*w); |
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| 62 | *w = new intvec(IDELEMS(arg)+1); |
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| 63 | for (i=0;i<IDELEMS(arg);i++) |
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| 64 | { |
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| 65 | (**w)[i+1] = (*w1)[i+maxxx]; |
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| 66 | } |
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| 67 | return w1; |
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| 68 | } |
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| 69 | |
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| 70 | static void syDeleteAbove(ideal up, int k) |
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| 71 | { |
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| 72 | if (up!=NULL) |
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| 73 | { |
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| 74 | for (int i=0;i<IDELEMS(up);i++) |
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| 75 | { |
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| 76 | if (up->m[i]!=NULL) |
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| 77 | pDeleteComp(&(up->m[i]),k+1); |
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| 78 | } |
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| 79 | } |
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| 80 | } |
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| 81 | |
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| 82 | /*2 |
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| 83 | *minimizes the module mod and cancel superfluous syzygies |
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| 84 | *from syz |
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| 85 | */ |
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| 86 | static void syMinStep(ideal mod,ideal syz,BOOLEAN final=FALSE,ideal up=NULL, |
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| 87 | tHomog h=isNotHomog) |
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| 88 | { |
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| 89 | ideal deg0=NULL; |
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| 90 | poly Unit1,Unit2,actWith; |
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| 91 | int len,i,j,ModComp,m,k,l; |
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| 92 | BOOLEAN searchUnit,existsUnit; |
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| 93 | |
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| 94 | if (TEST_OPT_PROT) PrintS("m"); |
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| 95 | if ((final) && (h==isHomog)) |
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| 96 | /*minim is TRUE, we are in the module: maxlength, maxlength <>0*/ |
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| 97 | { |
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| 98 | deg0=idJet(syz,0); |
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| 99 | idSkipZeroes(deg0); |
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| 100 | syz=deg0; |
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| 101 | } |
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| 102 | /*--cancels empty entees and their related components above--*/ |
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| 103 | j = IDELEMS(syz); |
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| 104 | while ((j>0) && (!syz->m[j-1])) j--; |
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| 105 | k = 0; |
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| 106 | while (k<j) |
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| 107 | { |
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| 108 | if (syz->m[k]!=NULL) |
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| 109 | k++; |
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| 110 | else |
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| 111 | { |
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| 112 | if (TEST_OPT_PROT) PrintS("."); |
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| 113 | for (l=k;l<j-1;l++) syz->m[l] = syz->m[l+1]; |
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| 114 | syz->m[j-1] = NULL; |
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| 115 | syDeleteAbove(up,k); |
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| 116 | j--; |
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| 117 | } |
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| 118 | } |
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| 119 | /*--searches for syzygies coming from superfluous elements |
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| 120 | * in the module below--*/ |
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| 121 | searchUnit = TRUE; |
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[b50590] | 122 | int curr_syz_limit = rGetCurrSyzLimit(currRing); |
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[35aab3] | 123 | while (searchUnit) |
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| 124 | { |
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| 125 | i=0; |
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| 126 | j=IDELEMS(syz); |
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| 127 | while ((j>0) && (syz->m[j-1]==NULL)) j--; |
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| 128 | existsUnit = FALSE; |
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[753f9d2] | 129 | if (rHasGlobalOrdering_currRing()) |
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[35aab3] | 130 | { |
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| 131 | while ((i<j) && (!existsUnit)) |
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| 132 | { |
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| 133 | existsUnit = pVectorHasUnitB(syz->m[i],&ModComp); |
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| 134 | i++; |
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| 135 | } |
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| 136 | } |
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| 137 | else |
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| 138 | { |
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| 139 | int I=0; |
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| 140 | l = 0; |
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| 141 | len=0; |
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| 142 | for (i=0;i<IDELEMS(syz);i++) |
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| 143 | { |
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| 144 | if (syz->m[i]!=NULL) |
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| 145 | { |
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| 146 | pVectorHasUnit(syz->m[i],&m, &l); |
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| 147 | if ((len==0) ||((l>0) && (l<len))) |
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| 148 | { |
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| 149 | len = l; |
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| 150 | ModComp = m; |
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| 151 | I = i; |
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| 152 | } |
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| 153 | } |
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| 154 | } |
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| 155 | //Print("Laenge ist: %d\n",len); |
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| 156 | if (len>0) existsUnit = TRUE; |
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| 157 | i = I+1; |
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| 158 | } |
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| 159 | if (existsUnit) |
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| 160 | { |
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| 161 | i--; |
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| 162 | //--takes out the founded syzygy-- |
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| 163 | if (TEST_OPT_PROT) PrintS("f"); |
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| 164 | actWith = syz->m[i]; |
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[3342df] | 165 | if (!rField_has_simple_inverse(currRing)) p_Cleardenom(actWith, currRing); |
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[35aab3] | 166 | //Print("actWith: ");pWrite(actWith); |
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| 167 | syz->m[i] = NULL; |
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| 168 | for (k=i;k<j-1;k++) syz->m[k] = syz->m[k+1]; |
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| 169 | syz->m[j-1] = NULL; |
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| 170 | syDeleteAbove(up,i); |
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| 171 | j--; |
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| 172 | //--makes Gauss alg. for the column ModComp-- |
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| 173 | Unit1 = pTakeOutComp(&(actWith), ModComp); |
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| 174 | //PrintS("actWith now: ");pWrite(actWith); |
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| 175 | //Print("Unit1: ");pWrite(Unit1); |
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| 176 | k=0; |
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| 177 | //Print("j= %d",j); |
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| 178 | while (k<j) |
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| 179 | { |
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| 180 | if (syz->m[k]!=NULL) |
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| 181 | { |
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| 182 | Unit2 = pTakeOutComp(&(syz->m[k]), ModComp); |
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| 183 | //Print("element %d: ",k);pWrite(syz->m[k]); |
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| 184 | //PrintS("Unit2: ");pWrite(Unit2); |
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[8049ad] | 185 | syz->m[k] = pMult(pCopy(Unit1),syz->m[k]); |
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[35aab3] | 186 | syz->m[k] = pSub(syz->m[k], |
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| 187 | pMult(Unit2,pCopy(actWith))); |
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| 188 | if (syz->m[k]==NULL) |
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| 189 | { |
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| 190 | for (l=k;l<j-1;l++) |
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| 191 | syz->m[l] = syz->m[l+1]; |
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| 192 | syz->m[j-1] = NULL; |
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| 193 | j--; |
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| 194 | syDeleteAbove(up,k); |
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| 195 | k--; |
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| 196 | } |
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| 197 | } |
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| 198 | k++; |
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| 199 | } |
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| 200 | pDelete(&actWith); |
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| 201 | pDelete(&Unit1); |
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| 202 | //--deletes superfluous elements from the module below--- |
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| 203 | pDelete(&(mod->m[ModComp-1 - curr_syz_limit])); |
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| 204 | for (k=ModComp-1 - curr_syz_limit;k<IDELEMS(mod)-1;k++) |
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| 205 | mod->m[k] = mod->m[k+1]; |
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| 206 | mod->m[IDELEMS(mod)-1] = NULL; |
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| 207 | } |
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| 208 | else |
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| 209 | searchUnit = FALSE; |
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| 210 | } |
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| 211 | if (TEST_OPT_PROT) PrintLn(); |
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| 212 | idSkipZeroes(mod); |
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| 213 | idSkipZeroes(syz); |
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| 214 | if (deg0!=NULL) |
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| 215 | idDelete(°0); |
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| 216 | } |
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| 217 | |
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| 218 | /*2 |
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| 219 | * make Gauss with the element elnum in the module component ModComp |
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| 220 | * for the generators from - till |
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| 221 | */ |
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| 222 | void syGaussForOne(ideal syz, int elnum, int ModComp,int from,int till) |
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| 223 | { |
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| 224 | int k,j,i,lu; |
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| 225 | poly unit1,unit2; |
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| 226 | poly actWith=syz->m[elnum]; |
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| 227 | |
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| 228 | if (from<0) from = 0; |
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| 229 | if ((till<=0) || (till>IDELEMS(syz))) till = IDELEMS(syz); |
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| 230 | syz->m[elnum] = NULL; |
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[3342df] | 231 | if (!rField_has_simple_inverse(currRing)) p_Cleardenom(actWith, currRing); |
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[35aab3] | 232 | /*--makes Gauss alg. for the column ModComp--*/ |
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| 233 | pTakeOutComp(&(actWith), ModComp, &unit1, &lu); |
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| 234 | while (from<till) |
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| 235 | { |
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[3705d5c] | 236 | poly tmp=syz->m[from]; |
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| 237 | if (/*syz->m[from]*/ tmp!=NULL) |
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[35aab3] | 238 | { |
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[3705d5c] | 239 | pTakeOutComp(&(tmp), ModComp, &unit2, &lu); |
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| 240 | tmp = pMult(pCopy(unit1),tmp); |
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| 241 | syz->m[from] = pSub(tmp, |
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[b6201e] | 242 | pMult(unit2,pCopy(actWith))); |
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[35aab3] | 243 | } |
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| 244 | from++; |
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| 245 | } |
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| 246 | pDelete(&actWith); |
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| 247 | pDelete(&unit1); |
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| 248 | } |
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| 249 | static void syDeleteAbove1(ideal up, int k) |
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| 250 | { |
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| 251 | poly p,pp; |
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| 252 | if (up!=NULL) |
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| 253 | { |
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| 254 | for (int i=0;i<IDELEMS(up);i++) |
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| 255 | { |
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| 256 | p = up->m[i]; |
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| 257 | while ((p!=NULL) && (pGetComp(p)==k)) |
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| 258 | { |
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[fe3266] | 259 | /* |
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[35aab3] | 260 | pp = pNext(p); |
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| 261 | pNext(p) = NULL; |
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| 262 | pDelete(&p); |
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| 263 | p = pp; |
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[fe3266] | 264 | */ |
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| 265 | pLmDelete(&p); |
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[35aab3] | 266 | } |
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| 267 | up->m[i] = p; |
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| 268 | if (p!=NULL) |
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| 269 | { |
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| 270 | while (pNext(p)!=NULL) |
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| 271 | { |
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| 272 | if (pGetComp(pNext(p))==k) |
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| 273 | { |
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[fe3266] | 274 | /* |
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[35aab3] | 275 | pp = pNext(pNext(p)); |
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| 276 | pNext(pNext(p)) = NULL; |
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| 277 | pDelete(&pNext(p)); |
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| 278 | pNext(p) = pp; |
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[fe3266] | 279 | */ |
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| 280 | pLmDelete(&pNext(p)); |
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[35aab3] | 281 | } |
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| 282 | else |
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| 283 | pIter(p); |
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| 284 | } |
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| 285 | } |
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| 286 | } |
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| 287 | } |
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| 288 | } |
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| 289 | /*2 |
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| 290 | *minimizes the resolution res |
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| 291 | *assumes homogeneous or local case |
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| 292 | */ |
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| 293 | static void syMinStep1(resolvente res, int length) |
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| 294 | { |
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| 295 | int i,j,k,l,index=0; |
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| 296 | poly p; |
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| 297 | ideal deg0=NULL,reddeg0=NULL; |
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| 298 | intvec *have_del=NULL,*to_del=NULL; |
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| 299 | |
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| 300 | while ((index<length) && (res[index]!=NULL)) |
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| 301 | { |
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| 302 | /*---we take out dependend elements from syz---------------------*/ |
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| 303 | if (res[index+1]!=NULL) |
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| 304 | { |
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| 305 | deg0 = idJet(res[index+1],0); |
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[e7c6b22] | 306 | reddeg0 = kInterRedOld(deg0); |
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[35aab3] | 307 | idDelete(°0); |
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| 308 | have_del = new intvec(IDELEMS(res[index])); |
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| 309 | for (i=0;i<IDELEMS(reddeg0);i++) |
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| 310 | { |
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| 311 | if (reddeg0->m[i]!=NULL) |
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| 312 | { |
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| 313 | j = pGetComp(reddeg0->m[i]); |
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| 314 | pDelete(&(res[index]->m[j-1])); |
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[fe3266] | 315 | /*res[index]->m[j-1] = NULL;*/ |
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[35aab3] | 316 | (*have_del)[j-1] = 1; |
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| 317 | } |
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| 318 | } |
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| 319 | idDelete(&reddeg0); |
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| 320 | } |
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| 321 | if (index>0) |
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| 322 | { |
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| 323 | /*--- we search for units and perform Gaussian elimination------*/ |
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| 324 | j = to_del->length(); |
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| 325 | while (j>0) |
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| 326 | { |
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| 327 | if ((*to_del)[j-1]==1) |
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| 328 | { |
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| 329 | k = 0; |
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| 330 | while (k<IDELEMS(res[index])) |
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| 331 | { |
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| 332 | p = res[index]->m[k]; |
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| 333 | while ((p!=NULL) && ((!pLmIsConstantComp(p)) || (pGetComp(p)!=j))) |
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| 334 | pIter(p); |
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| 335 | if ((p!=NULL) && (pLmIsConstantComp(p)) && (pGetComp(p)==j)) break; |
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| 336 | k++; |
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| 337 | } |
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| 338 | if (k>=IDELEMS(res[index])) |
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| 339 | { |
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| 340 | PrintS("out of range\n"); |
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| 341 | } |
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| 342 | syGaussForOne(res[index],k,j); |
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| 343 | if (res[index+1]!=NULL) |
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| 344 | syDeleteAbove1(res[index+1],k+1); |
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| 345 | (*to_del)[j-1] = 0; |
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| 346 | } |
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| 347 | j--; |
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| 348 | } |
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| 349 | } |
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| 350 | if (to_del!=NULL) delete to_del; |
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| 351 | to_del = have_del; |
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| 352 | have_del = NULL; |
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| 353 | index++; |
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| 354 | } |
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| 355 | if (TEST_OPT_PROT) PrintLn(); |
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| 356 | syKillEmptyEntres(res,length); |
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| 357 | } |
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| 358 | |
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| 359 | void syMinimizeResolvente(resolvente res, int length, int first) |
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| 360 | { |
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| 361 | int syzIndex=first; |
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| 362 | intvec *dummy; |
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| 363 | |
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| 364 | if (syzIndex<1) syzIndex=1; |
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| 365 | if ((syzIndex==1) && (idHomModule(res[0],currQuotient,&dummy)) && (!rIsPluralRing(currRing))) |
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| 366 | { |
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| 367 | syMinStep1(res,length); |
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| 368 | delete dummy; |
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| 369 | return; |
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| 370 | } |
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| 371 | while ((syzIndex<length-1) && (res[syzIndex]!=NULL) && (res[syzIndex+1]!=NULL)) |
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| 372 | { |
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| 373 | syMinStep(res[syzIndex-1],res[syzIndex],FALSE,res[syzIndex+1]); |
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| 374 | syzIndex++; |
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| 375 | } |
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| 376 | if (res[syzIndex]!=NULL) |
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| 377 | syMinStep(res[syzIndex-1],res[syzIndex]); |
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| 378 | if (!idIs0(res[0])) |
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| 379 | idMinEmbedding(res[0],TRUE); |
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| 380 | } |
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| 381 | |
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| 382 | /*2 |
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| 383 | * resolution of ideal/module arg, <=maxlength steps, (r[0..maxlength]) |
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| 384 | * no limitation in length if maxlength==0 |
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| 385 | * input:arg |
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| 386 | * minim: TRUE means mres cmd, FALSE nres cmd. |
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| 387 | * if *len!=0: module weights: weights[0] |
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| 388 | * (and weights is defined:weights[0..len-1] |
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| 389 | * |
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| 390 | * output:resolvente r[0..length-1], |
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| 391 | * module weights: weights[0..length-1] |
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| 392 | */ |
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| 393 | resolvente syResolvente(ideal arg, int maxlength, int * length, |
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| 394 | intvec *** weights, BOOLEAN minim) |
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| 395 | { |
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| 396 | resolvente res; |
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| 397 | resolvente newres; |
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| 398 | tHomog hom=isNotHomog; |
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| 399 | ideal temp=NULL; |
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| 400 | intvec *w = NULL,**tempW; |
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[7b25fe] | 401 | int i,k,syzIndex = 0,j,rk_arg=si_max(1,(int)id_RankFreeModule(arg,currRing)); |
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[35aab3] | 402 | int Kstd1_OldDeg=Kstd1_deg; |
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| 403 | BOOLEAN completeMinim; |
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| 404 | BOOLEAN oldDegBound=TEST_OPT_DEGBOUND; |
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| 405 | BOOLEAN setRegularity=TRUE; |
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| 406 | int wlength=*length; |
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| 407 | |
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| 408 | if (maxlength!=-1) *length = maxlength+1; |
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| 409 | else *length = 5; |
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| 410 | if ((wlength!=0) && (*length!=wlength)) |
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| 411 | { |
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| 412 | intvec **wtmp = (intvec**)omAlloc0((*length)*sizeof(intvec*)); |
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| 413 | wtmp[0]=(*weights)[0]; |
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| 414 | omFreeSize((ADDRESS)*weights,wlength*sizeof(intvec*)); |
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| 415 | *weights=wtmp; |
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| 416 | } |
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| 417 | res = (resolvente)omAlloc0((*length)*sizeof(ideal)); |
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| 418 | |
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| 419 | /*--- initialize the syzygy-ring -----------------------------*/ |
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| 420 | ring origR = currRing; |
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| 421 | ring syz_ring = rCurrRingAssure_SyzComp(); |
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| 422 | rSetSyzComp(rk_arg); |
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| 423 | |
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| 424 | if (syz_ring != origR) |
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| 425 | { |
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| 426 | res[0] = idrCopyR_NoSort(arg, origR); |
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| 427 | } |
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| 428 | else |
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| 429 | { |
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| 430 | res[0] = idCopy(arg); |
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| 431 | } |
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| 432 | |
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| 433 | /*--- creating weights for the module components ---------------*/ |
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[a63c24] | 434 | if ((weights!=NULL) && (*weights!=NULL)&& ((*weights)[0]!=NULL)) |
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| 435 | { |
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| 436 | if (!idTestHomModule(res[0],currQuotient,(*weights)[0])) |
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| 437 | { |
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[e6a019] | 438 | WarnS("wrong weights given(1):"); (*weights)[0]->show();PrintLn(); |
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[a63c24] | 439 | idHomModule(res[0],currQuotient,&w); |
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| 440 | w->show();PrintLn(); |
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| 441 | *weights=NULL; |
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| 442 | } |
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| 443 | } |
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| 444 | |
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[35aab3] | 445 | if ((weights==NULL) || (*weights==NULL) || ((*weights)[0]==NULL)) |
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| 446 | { |
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| 447 | hom=(tHomog)idHomModule(res[0],currQuotient,&w); |
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| 448 | if (hom==isHomog) |
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| 449 | { |
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| 450 | *weights = (intvec**)omAlloc0((*length)*sizeof(intvec*)); |
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| 451 | if (w!=NULL) (*weights)[0] = ivCopy(w); |
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| 452 | } |
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| 453 | } |
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| 454 | else |
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| 455 | { |
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| 456 | if ((weights!=NULL) && (*weights!=NULL)&& ((*weights)[0]!=NULL)) |
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| 457 | { |
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| 458 | w = ivCopy((*weights)[0]); |
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| 459 | hom = isHomog; |
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| 460 | } |
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| 461 | } |
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[b1dfaf] | 462 | |
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| 463 | #ifdef HAVE_PLURAL |
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[d07546] | 464 | if (rIsPluralRing(currRing) && !rIsSCA(currRing) ) |
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[750e70] | 465 | { |
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[d07546] | 466 | // quick solution; need theory to apply homog GB stuff for G-Algebras |
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| 467 | hom = isNotHomog; |
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| 468 | } |
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[b1dfaf] | 469 | #endif // HAVE_PLURAL |
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| 470 | |
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[35aab3] | 471 | if (hom==isHomog) |
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| 472 | { |
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| 473 | intvec *w1 = syPrepareModComp(res[0],&w); |
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| 474 | if (w!=NULL) { delete w;w=NULL; } |
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| 475 | w = w1; |
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| 476 | j = 0; |
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| 477 | while ((j<IDELEMS(res[0])) && (res[0]->m[j]==NULL)) j++; |
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| 478 | if (j<IDELEMS(res[0])) |
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| 479 | { |
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[b50590] | 480 | if (p_FDeg(res[0]->m[j],currRing)!=pTotaldegree(res[0]->m[j])) |
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[35aab3] | 481 | setRegularity = FALSE; |
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| 482 | } |
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| 483 | } |
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| 484 | else |
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| 485 | { |
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| 486 | setRegularity = FALSE; |
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| 487 | } |
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| 488 | |
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| 489 | /*--- the main loop --------------------------------------*/ |
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| 490 | while ((!idIs0(res[syzIndex])) && |
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| 491 | ((maxlength==-1) || (syzIndex<=maxlength))) |
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| 492 | // (syzIndex<maxlength+(int)minim))) |
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| 493 | /*--- compute one step more for minimizing-----------------*/ |
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| 494 | { |
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| 495 | if (Kstd1_deg!=0) Kstd1_deg++; |
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| 496 | if (syzIndex+1==*length) |
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| 497 | { |
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| 498 | newres = (resolvente)omAlloc0((*length+5)*sizeof(ideal)); |
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| 499 | tempW = (intvec**)omAlloc0((*length+5)*sizeof(intvec*)); |
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| 500 | for (j=0;j<*length;j++) |
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| 501 | { |
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| 502 | newres[j] = res[j]; |
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| 503 | if (*weights!=NULL) tempW[j] = (*weights)[j]; |
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| 504 | /*else tempW[j] = NULL;*/ |
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| 505 | } |
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| 506 | omFreeSize((ADDRESS)res,*length*sizeof(ideal)); |
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| 507 | if (*weights != NULL) omFreeSize((ADDRESS)*weights,*length*sizeof(intvec*)); |
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| 508 | *length += 5; |
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| 509 | res=newres; |
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| 510 | *weights = tempW; |
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| 511 | } |
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| 512 | /*--- interreducing first -----------------------------------*/ |
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| 513 | if (syzIndex>0) |
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| 514 | { |
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[7b25fe] | 515 | int rkI=id_RankFreeModule(res[syzIndex],currRing); |
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[35aab3] | 516 | rSetSyzComp(rkI); |
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| 517 | } |
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[750e70] | 518 | if(! TEST_OPT_NO_SYZ_MINIM ) |
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[35aab3] | 519 | if (minim || (syzIndex!=0)) |
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| 520 | { |
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[e7c6b22] | 521 | temp = kInterRedOld(res[syzIndex],currQuotient); |
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[35aab3] | 522 | idDelete(&res[syzIndex]); |
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| 523 | idSkipZeroes(temp); |
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| 524 | res[syzIndex] = temp; |
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| 525 | } |
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| 526 | temp = NULL; |
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| 527 | /*--- computing the syzygy modules --------------------------------*/ |
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| 528 | if ((currQuotient==NULL)&&(syzIndex==0)&& (!TEST_OPT_DEGBOUND)) |
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| 529 | { |
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| 530 | res[/*syzIndex+*/1] = idSyzygies(res[0/*syzIndex*/],hom,&w,FALSE,setRegularity,&Kstd1_deg); |
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| 531 | if ((!TEST_OPT_NOTREGULARITY) && (Kstd1_deg>0)) test |= Sy_bit(OPT_DEGBOUND); |
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| 532 | } |
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| 533 | else |
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| 534 | { |
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| 535 | res[syzIndex+1] = idSyzygies(res[syzIndex],hom,&w,FALSE); |
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| 536 | } |
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| 537 | completeMinim=(syzIndex!=maxlength) || (maxlength ==-1) || (hom!=isHomog); |
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| 538 | syzIndex++; |
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| 539 | if (TEST_OPT_PROT) Print("[%d]\n",syzIndex); |
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[750e70] | 540 | |
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| 541 | if(! TEST_OPT_NO_SYZ_MINIM ) |
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[35aab3] | 542 | { |
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[750e70] | 543 | if ((minim)||(syzIndex>1)) |
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| 544 | syMinStep(res[syzIndex-1],res[syzIndex],!completeMinim,NULL,hom); |
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| 545 | if (!completeMinim) |
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| 546 | /*minim is TRUE, we are in the module: maxlength, maxlength <>0*/ |
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| 547 | { |
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| 548 | idDelete(&res[syzIndex]); |
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| 549 | } |
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[35aab3] | 550 | } |
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| 551 | /*---creating the iterated weights for module components ---------*/ |
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| 552 | if ((hom == isHomog) && (!idIs0(res[syzIndex]))) |
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| 553 | { |
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| 554 | //Print("die %d Modulegewichte sind:\n",w1->length()); |
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| 555 | //w1->show(); |
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| 556 | //PrintLn(); |
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[7b25fe] | 557 | int max_comp = id_RankFreeModule(res[syzIndex],currRing); |
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[b50590] | 558 | k = max_comp - rGetCurrSyzLimit(currRing); |
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[35aab3] | 559 | assume(w != NULL); |
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| 560 | if (w != NULL) |
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| 561 | w->resize(max_comp+IDELEMS(res[syzIndex])); |
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| 562 | else |
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| 563 | w = new intvec(max_comp+IDELEMS(res[syzIndex])); |
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| 564 | (*weights)[syzIndex] = new intvec(k); |
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| 565 | for (i=0;i<k;i++) |
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| 566 | { |
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| 567 | if (res[syzIndex-1]->m[i]!=NULL) // hs |
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| 568 | { |
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[b50590] | 569 | (*w)[i + rGetCurrSyzLimit(currRing)] = p_FDeg(res[syzIndex-1]->m[i],currRing); |
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[35aab3] | 570 | if (pGetComp(res[syzIndex-1]->m[i])>0) |
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[b50590] | 571 | (*w)[i + rGetCurrSyzLimit(currRing)] |
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[35aab3] | 572 | += (*w)[pGetComp(res[syzIndex-1]->m[i])-1]; |
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[b50590] | 573 | (*((*weights)[syzIndex]))[i] = (*w)[i+rGetCurrSyzLimit(currRing)]; |
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[35aab3] | 574 | } |
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| 575 | } |
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| 576 | for (i=k;i<k+IDELEMS(res[syzIndex]);i++) |
---|
| 577 | { |
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| 578 | if (res[syzIndex]->m[i-k]!=NULL) |
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[b50590] | 579 | (*w)[i+rGetCurrSyzLimit(currRing)] = p_FDeg(res[syzIndex]->m[i-k],currRing) |
---|
[35aab3] | 580 | +(*w)[pGetComp(res[syzIndex]->m[i-k])-1]; |
---|
| 581 | } |
---|
| 582 | } |
---|
| 583 | } |
---|
| 584 | /*--- end of the main loop --------------------------------------*/ |
---|
| 585 | /*--- deleting the temporare data structures --------------------*/ |
---|
| 586 | if ((syzIndex!=0) && (res[syzIndex]!=NULL) && (idIs0(res[syzIndex]))) |
---|
| 587 | idDelete(&res[syzIndex]); |
---|
| 588 | if (w !=NULL) delete w; |
---|
| 589 | |
---|
| 590 | Kstd1_deg=Kstd1_OldDeg; |
---|
| 591 | if (!oldDegBound) |
---|
| 592 | test &= ~Sy_bit(OPT_DEGBOUND); |
---|
| 593 | |
---|
| 594 | for (i=1; i<=syzIndex; i++) |
---|
| 595 | { |
---|
| 596 | if (! idIs0(res[i])) |
---|
| 597 | { |
---|
| 598 | for (j=0; j<IDELEMS(res[i]); j++) |
---|
| 599 | { |
---|
[861529] | 600 | p_Shift(&res[i]->m[j], -rGetMaxSyzComp(i),currRing); |
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[35aab3] | 601 | } |
---|
| 602 | } |
---|
| 603 | } |
---|
| 604 | /*--- going back to the original ring -------------------------*/ |
---|
| 605 | if (origR != syz_ring) |
---|
| 606 | { |
---|
| 607 | rChangeCurrRing(origR); |
---|
| 608 | for (i=0; i<=syzIndex; i++) |
---|
| 609 | { |
---|
| 610 | res[i] = idrMoveR_NoSort(res[i], syz_ring); |
---|
| 611 | } |
---|
| 612 | rKill(syz_ring); |
---|
| 613 | } |
---|
| 614 | return res; |
---|
| 615 | } |
---|
| 616 | |
---|
| 617 | syStrategy syResolution(ideal arg, int maxlength,intvec * w, BOOLEAN minim) |
---|
| 618 | { |
---|
[8b09ef] | 619 | |
---|
[90adb6a] | 620 | #ifdef HAVE_PLURAL |
---|
[8b09ef] | 621 | |
---|
[57bfa2] | 622 | const ideal idSaveCurrQuotient = currQuotient; |
---|
| 623 | const ideal idSaveCurrRingQuotient = currRing->qideal; |
---|
[8b09ef] | 624 | |
---|
[90adb6a] | 625 | if( rIsSCA(currRing) ) |
---|
| 626 | { |
---|
[e65ce5] | 627 | |
---|
| 628 | #ifdef RDEBUG |
---|
| 629 | // rWrite(currRing); |
---|
| 630 | // rDebugPrint(currRing); |
---|
| 631 | #endif |
---|
[8b09ef] | 632 | |
---|
[57bfa2] | 633 | if( ncExtensions(TESTSYZSCAMASK) ) |
---|
| 634 | { |
---|
| 635 | currQuotient = SCAQuotient(currRing); |
---|
| 636 | currRing->qideal = currQuotient; |
---|
| 637 | } |
---|
[90adb6a] | 638 | |
---|
| 639 | const unsigned int m_iFirstAltVar = scaFirstAltVar(currRing); |
---|
| 640 | const unsigned int m_iLastAltVar = scaLastAltVar(currRing); |
---|
[750e70] | 641 | |
---|
[e2efe91] | 642 | arg = id_KillSquares(arg, m_iFirstAltVar, m_iLastAltVar, currRing, false); // kill suares in input! |
---|
[90adb6a] | 643 | } |
---|
| 644 | #endif |
---|
[750e70] | 645 | |
---|
[35aab3] | 646 | int typ0; |
---|
| 647 | syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy)); |
---|
| 648 | |
---|
[90adb6a] | 649 | if ((w!=NULL) && (!idTestHomModule(arg,currQuotient,w))) // is this right in SCA case??? |
---|
[a63c24] | 650 | { |
---|
[e6a019] | 651 | WarnS("wrong weights given(2):");w->show();PrintLn(); |
---|
[a63c24] | 652 | idHomModule(arg,currQuotient,&w); |
---|
| 653 | w->show();PrintLn(); |
---|
| 654 | w=NULL; |
---|
| 655 | } |
---|
[35aab3] | 656 | if (w!=NULL) |
---|
| 657 | { |
---|
[835d83] | 658 | result->weights = (intvec**)omAlloc0Bin(char_ptr_bin); |
---|
[35aab3] | 659 | (result->weights)[0] = ivCopy(w); |
---|
| 660 | result->length = 1; |
---|
| 661 | } |
---|
| 662 | resolvente fr = syResolvente(arg,maxlength,&(result->length),&(result->weights),minim),fr1; |
---|
| 663 | if (minim) |
---|
| 664 | { |
---|
| 665 | result->minres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal)); |
---|
| 666 | fr1 = result->minres; |
---|
| 667 | } |
---|
| 668 | else |
---|
| 669 | { |
---|
| 670 | result->fullres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal)); |
---|
| 671 | fr1 = result->fullres; |
---|
| 672 | } |
---|
| 673 | for (int i=result->length-1;i>=0;i--) |
---|
| 674 | { |
---|
| 675 | if (fr[i]!=NULL) |
---|
| 676 | fr1[i] = fr[i]; |
---|
| 677 | fr[i] = NULL; |
---|
| 678 | } |
---|
| 679 | omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal)); |
---|
[90adb6a] | 680 | |
---|
| 681 | |
---|
| 682 | #ifdef HAVE_PLURAL |
---|
| 683 | if( rIsSCA(currRing) ) |
---|
| 684 | { |
---|
[8b09ef] | 685 | |
---|
[57bfa2] | 686 | if( ncExtensions(TESTSYZSCAMASK) ) |
---|
| 687 | { |
---|
[750e70] | 688 | currQuotient = idSaveCurrQuotient; |
---|
[57bfa2] | 689 | currRing->qideal = idSaveCurrRingQuotient; |
---|
| 690 | } |
---|
[90adb6a] | 691 | |
---|
| 692 | id_Delete(&arg, currRing); |
---|
| 693 | } |
---|
| 694 | #endif |
---|
| 695 | |
---|
| 696 | |
---|
[35aab3] | 697 | return result; |
---|
| 698 | } |
---|
| 699 | |
---|
| 700 | static poly sypCopyConstant(poly inp) |
---|
| 701 | { |
---|
| 702 | poly outp=NULL,q; |
---|
| 703 | |
---|
| 704 | while (inp!=NULL) |
---|
| 705 | { |
---|
| 706 | if (pLmIsConstantComp(inp)) |
---|
| 707 | { |
---|
| 708 | if (outp==NULL) |
---|
| 709 | { |
---|
| 710 | q = outp = pHead(inp); |
---|
| 711 | } |
---|
| 712 | else |
---|
| 713 | { |
---|
| 714 | pNext(q) = pHead(inp); |
---|
| 715 | pIter(q); |
---|
| 716 | } |
---|
| 717 | } |
---|
| 718 | pIter(inp); |
---|
| 719 | } |
---|
| 720 | return outp; |
---|
| 721 | } |
---|
| 722 | int syDetect(ideal id,int index,BOOLEAN homog,int * degrees,int * tocancel) |
---|
| 723 | { |
---|
| 724 | int i, j, k, ModComp,subFromRank=0, lu; |
---|
| 725 | poly p, q, qq, Unit1, Unit2; |
---|
| 726 | ideal temp; |
---|
| 727 | |
---|
| 728 | if (idIs0(id)) return 0; |
---|
| 729 | temp = idInit(IDELEMS(id),id->rank); |
---|
| 730 | for (i=0;i<IDELEMS(id);i++) |
---|
| 731 | { |
---|
| 732 | temp->m[i] = sypCopyConstant(id->m[i]); |
---|
| 733 | } |
---|
| 734 | i = IDELEMS(id); |
---|
| 735 | while ((i>0) && (temp->m[i-1]==NULL)) i--; |
---|
| 736 | if (i==0) |
---|
| 737 | { |
---|
| 738 | idDelete(&temp); |
---|
| 739 | return 0; |
---|
| 740 | } |
---|
| 741 | j = 0; |
---|
| 742 | p = NULL; |
---|
| 743 | while ((j<i) && (temp->m[j]==NULL)) j++; |
---|
| 744 | while (j<i) |
---|
| 745 | { |
---|
| 746 | if (homog) |
---|
| 747 | { |
---|
[b50590] | 748 | if (index==0) k = p_FDeg(temp->m[j],currRing)+degrees[pGetComp(temp->m[j])]; |
---|
[b130fb] | 749 | else k = degrees[pGetComp(temp->m[j])]; |
---|
[35aab3] | 750 | if (k>=index) tocancel[k-index]++; |
---|
| 751 | if ((k>=0) && (index==0)) subFromRank++; |
---|
| 752 | } |
---|
| 753 | else |
---|
| 754 | { |
---|
| 755 | tocancel[0]--; |
---|
| 756 | } |
---|
| 757 | syGaussForOne(temp,j,pGetComp(temp->m[j]),j+1,i); |
---|
| 758 | j++; |
---|
| 759 | while ((j<i) && (temp->m[j]==NULL)) j++; |
---|
| 760 | } |
---|
| 761 | idDelete(&temp); |
---|
| 762 | return subFromRank; |
---|
| 763 | } |
---|
| 764 | |
---|
| 765 | void syDetect(ideal id,int index,int rsmin, BOOLEAN homog, |
---|
| 766 | intvec * degrees,intvec * tocancel) |
---|
| 767 | { |
---|
| 768 | int * deg=NULL; |
---|
| 769 | int * tocan=(int*) omAlloc0(tocancel->length()*sizeof(int)); |
---|
| 770 | int i; |
---|
| 771 | |
---|
| 772 | if (homog) |
---|
| 773 | { |
---|
| 774 | deg = (int*) omAlloc0(degrees->length()*sizeof(int)); |
---|
| 775 | for (i=degrees->length();i>0;i--) |
---|
| 776 | deg[i-1] = (*degrees)[i-1]-rsmin; |
---|
| 777 | } |
---|
| 778 | int dummy=syDetect(id,index,homog,deg,tocan); |
---|
| 779 | for (i=tocancel->length();i>0;i--) |
---|
| 780 | (*tocancel)[i-1] = tocan[i-1]; |
---|
| 781 | if (homog) |
---|
| 782 | omFreeSize((ADDRESS)deg,degrees->length()*sizeof(int)); |
---|
| 783 | omFreeSize((ADDRESS)tocan,tocancel->length()*sizeof(int)); |
---|
| 784 | } |
---|
| 785 | |
---|
| 786 | /*2 |
---|
| 787 | * computes the betti numbers from a given resolution |
---|
| 788 | * of length 'length' (0..length-1), not necessairily minimal, |
---|
| 789 | * (if weights are given, they are used) |
---|
| 790 | * returns the int matrix of betti numbers |
---|
| 791 | * and the regularity |
---|
| 792 | */ |
---|
| 793 | intvec * syBetti(resolvente res,int length, int * regularity, |
---|
| 794 | intvec* weights,BOOLEAN tomin,int * row_shift) |
---|
| 795 | { |
---|
| 796 | //#define BETTI_WITH_ZEROS |
---|
| 797 | //tomin = FALSE; |
---|
| 798 | int i,j=0,k=0,l,rows,cols,mr; |
---|
| 799 | int *temp1,*temp2,*temp3;/*used to compute degrees*/ |
---|
| 800 | int *tocancel; /*(BOOLEAN)tocancel[i]=element is superfluous*/ |
---|
| 801 | int r0_len; |
---|
| 802 | |
---|
| 803 | /*------ compute size --------------*/ |
---|
| 804 | *regularity = -1; |
---|
| 805 | cols = length; |
---|
| 806 | while ((cols>0) |
---|
| 807 | && ((res[cols-1]==NULL) |
---|
| 808 | || (idIs0(res[cols-1])))) |
---|
| 809 | { |
---|
| 810 | cols--; |
---|
| 811 | } |
---|
| 812 | intvec * result; |
---|
| 813 | if (idIs0(res[0])) |
---|
| 814 | { |
---|
| 815 | if (res[0]==NULL) |
---|
| 816 | result = new intvec(1,1,1); |
---|
| 817 | else |
---|
| 818 | result = new intvec(1,1,res[0]->rank); |
---|
| 819 | return result; |
---|
| 820 | } |
---|
| 821 | intvec *w=NULL; |
---|
[a63c24] | 822 | if (weights!=NULL) |
---|
| 823 | { |
---|
| 824 | if (!idTestHomModule(res[0],currQuotient,weights)) |
---|
| 825 | { |
---|
[e6a019] | 826 | WarnS("wrong weights given(3):");weights->show();PrintLn(); |
---|
[a63c24] | 827 | idHomModule(res[0],currQuotient,&w); |
---|
| 828 | if (w!=NULL) { w->show();PrintLn();} |
---|
| 829 | weights=NULL; |
---|
| 830 | } |
---|
| 831 | } |
---|
[8ebd1a0] | 832 | #if 0 |
---|
| 833 | if (idHomModule(res[0],currQuotient,&w)!=isHomog) |
---|
| 834 | { |
---|
| 835 | Warn("betti-command: Input is not homogeneous!"); |
---|
| 836 | weights=NULL; |
---|
| 837 | } |
---|
| 838 | #endif |
---|
[a63c24] | 839 | if (weights==NULL) weights=w; |
---|
| 840 | else delete w; |
---|
| 841 | r0_len=IDELEMS(res[0]); |
---|
| 842 | while ((r0_len>0) && (res[0]->m[r0_len-1]==NULL)) r0_len--; |
---|
| 843 | #ifdef SHOW_W |
---|
[192b522] | 844 | PrintS("weights:");if (weights!=NULL) weights->show(); else Print("NULL"); PrintLn(); |
---|
[a63c24] | 845 | #endif |
---|
[7b25fe] | 846 | int rkl=l = si_max(id_RankFreeModule(res[0],currRing),res[0]->rank); |
---|
[35aab3] | 847 | i = 0; |
---|
| 848 | while ((i<length) && (res[i]!=NULL)) |
---|
| 849 | { |
---|
| 850 | if (IDELEMS(res[i])>l) l = IDELEMS(res[i]); |
---|
| 851 | i++; |
---|
| 852 | } |
---|
| 853 | temp1 = (int*)omAlloc0((l+1)*sizeof(int)); |
---|
| 854 | temp2 = (int*)omAlloc((l+1)*sizeof(int)); |
---|
| 855 | rows = 1; |
---|
| 856 | mr = 1; |
---|
| 857 | cols++; |
---|
| 858 | for (i=0;i<cols-1;i++) |
---|
| 859 | { |
---|
[b44f5e] | 860 | if ((i==0) && (weights!=NULL)) p_SetModDeg(weights, currRing); |
---|
[35aab3] | 861 | memset(temp2,0,(l+1)*sizeof(int)); |
---|
| 862 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
| 863 | { |
---|
| 864 | if (res[i]->m[j]!=NULL) |
---|
| 865 | { |
---|
| 866 | if ((pGetComp(res[i]->m[j])>l) |
---|
| 867 | || ((i>1) && (res[i-1]->m[pGetComp(res[i]->m[j])-1]==NULL))) |
---|
| 868 | { |
---|
| 869 | WerrorS("input not a resolvent"); |
---|
| 870 | omFreeSize((ADDRESS)temp1,(l+1)*sizeof(int)); |
---|
| 871 | omFreeSize((ADDRESS)temp2,(l+1)*sizeof(int)); |
---|
| 872 | return NULL; |
---|
| 873 | } |
---|
[b50590] | 874 | temp2[j+1] = p_FDeg(res[i]->m[j],currRing)+temp1[pGetComp(res[i]->m[j])]; |
---|
[35aab3] | 875 | if (temp2[j+1]-i>rows) rows = temp2[j+1]-i; |
---|
| 876 | if (temp2[j+1]-i<mr) mr = temp2[j+1]-i; |
---|
| 877 | } |
---|
| 878 | } |
---|
[b44f5e] | 879 | if ((i==0) && (weights!=NULL)) p_SetModDeg(NULL, currRing); |
---|
[35aab3] | 880 | temp3 = temp1; |
---|
| 881 | temp1 = temp2; |
---|
| 882 | temp2 = temp3; |
---|
| 883 | } |
---|
| 884 | mr--; |
---|
[3e1bc9] | 885 | if (weights!=NULL) |
---|
| 886 | { |
---|
| 887 | for(j=0;j<weights->length();j++) |
---|
| 888 | { |
---|
| 889 | if (rows <(*weights)[j]+1) rows=(-mr)+(*weights)[j]+1; |
---|
| 890 | } |
---|
| 891 | } |
---|
[35aab3] | 892 | /*------ computation betti numbers --------------*/ |
---|
| 893 | rows -= mr; |
---|
[a63c24] | 894 | result = new intvec(rows+1,cols,0); |
---|
| 895 | if (weights!=NULL) |
---|
| 896 | { |
---|
| 897 | for(j=0;j<weights->length();j++) |
---|
| 898 | { |
---|
| 899 | IMATELEM((*result),(-mr)+(*weights)[j]+1,1) ++; |
---|
[192b522] | 900 | //Print("imat(%d,%d)++ -> %d\n",(-mr)+(*weights)[j]+1, 1, IMATELEM((*result),(-mr)+(*weights)[j]+1,1)); |
---|
[a63c24] | 901 | } |
---|
| 902 | } |
---|
| 903 | else |
---|
| 904 | { |
---|
| 905 | (*result)[(-mr)*cols] = /*idRankFreeModule(res[0])*/ rkl; |
---|
| 906 | if ((!idIs0(res[0])) && ((*result)[(-mr)*cols]==0)) |
---|
| 907 | (*result)[(-mr)*cols] = 1; |
---|
| 908 | } |
---|
[35aab3] | 909 | tocancel = (int*)omAlloc0((rows+1)*sizeof(int)); |
---|
| 910 | memset(temp1,0,(l+1)*sizeof(int)); |
---|
[a63c24] | 911 | if (weights!=NULL) |
---|
| 912 | { |
---|
| 913 | memset(temp2,0,l*sizeof(int)); |
---|
[b44f5e] | 914 | p_SetModDeg(weights, currRing); |
---|
[a63c24] | 915 | } |
---|
| 916 | else |
---|
| 917 | memset(temp2,0,l*sizeof(int)); |
---|
[35aab3] | 918 | int dummy = syDetect(res[0],0,TRUE,temp2,tocancel); |
---|
[b44f5e] | 919 | if (weights!=NULL) p_SetModDeg(NULL, currRing); |
---|
[35aab3] | 920 | if (tomin) |
---|
[a63c24] | 921 | { |
---|
| 922 | //(*result)[(-mr)*cols] -= dummy; |
---|
| 923 | for(j=0;j<=rows+mr;j++) |
---|
| 924 | { |
---|
[192b522] | 925 | //Print("tocancel[%d]=%d imat(%d,%d)=%d\n",j,tocancel[j],(-mr)+j+1,1,IMATELEM((*result),(-mr)+j+1,1)); |
---|
[a63c24] | 926 | IMATELEM((*result),(-mr)+j+1,1) -= tocancel[j]; |
---|
| 927 | } |
---|
| 928 | } |
---|
[35aab3] | 929 | for (i=0;i<cols-1;i++) |
---|
| 930 | { |
---|
[b44f5e] | 931 | if ((i==0) && (weights!=NULL)) p_SetModDeg(weights, currRing); |
---|
[35aab3] | 932 | memset(temp2,0,l*sizeof(int)); |
---|
| 933 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
| 934 | { |
---|
| 935 | if (res[i]->m[j]!=NULL) |
---|
| 936 | { |
---|
[b50590] | 937 | temp2[j+1] = p_FDeg(res[i]->m[j],currRing)+temp1[pGetComp(res[i]->m[j])]; |
---|
[35aab3] | 938 | //(*result)[i+1+(temp2[j+1]-i-1)*cols]++; |
---|
| 939 | //if (temp2[j+1]>i) IMATELEM((*result),temp2[j+1]-i-mr,i+2)++; |
---|
| 940 | IMATELEM((*result),temp2[j+1]-i-mr,i+2)++; |
---|
| 941 | } |
---|
| 942 | else if (i==0) |
---|
| 943 | { |
---|
| 944 | if (j<r0_len) IMATELEM((*result),-mr,2)++; |
---|
| 945 | } |
---|
| 946 | } |
---|
| 947 | /*------ computation betti numbers, if res not minimal --------------*/ |
---|
| 948 | if (tomin) |
---|
| 949 | { |
---|
| 950 | for (j=mr;j<rows+mr;j++) |
---|
| 951 | { |
---|
| 952 | //(*result)[i+1+j*cols] -= tocancel[j+1]; |
---|
| 953 | IMATELEM((*result),j+1-mr,i+2) -= tocancel[j+1]; |
---|
| 954 | } |
---|
| 955 | if ((i<length-1) && (res[i+1]!=NULL)) |
---|
| 956 | { |
---|
| 957 | memset(tocancel,0,(rows+1)*sizeof(int)); |
---|
| 958 | dummy = syDetect(res[i+1],i+1,TRUE,temp2,tocancel); |
---|
| 959 | for (j=0;j<rows;j++) |
---|
| 960 | { |
---|
| 961 | //(*result)[i+1+j*cols] -= tocancel[j]; |
---|
| 962 | IMATELEM((*result),j+1,i+2) -= tocancel[j]; |
---|
| 963 | } |
---|
| 964 | } |
---|
| 965 | } |
---|
| 966 | temp3 = temp1; |
---|
| 967 | temp1 = temp2; |
---|
| 968 | temp2 = temp3; |
---|
[a63c24] | 969 | for (j=0;j<=rows;j++) |
---|
[35aab3] | 970 | { |
---|
| 971 | // if (((*result)[i+1+j*cols]!=0) && (j>*regularity)) *regularity = j; |
---|
| 972 | if ((IMATELEM((*result),j+1,i+2)!=0) && (j>*regularity)) *regularity = j; |
---|
| 973 | } |
---|
[b44f5e] | 974 | if ((i==0) && (weights!=NULL)) p_SetModDeg(NULL, currRing); |
---|
[35aab3] | 975 | } |
---|
[a63c24] | 976 | // Print("nach minim:\n"); result->show(); PrintLn(); |
---|
[35aab3] | 977 | /*------ clean up --------------*/ |
---|
| 978 | omFreeSize((ADDRESS)tocancel,(rows+1)*sizeof(int)); |
---|
| 979 | omFreeSize((ADDRESS)temp1,(l+1)*sizeof(int)); |
---|
| 980 | omFreeSize((ADDRESS)temp2,(l+1)*sizeof(int)); |
---|
| 981 | if ((tomin) && (mr<0)) // deletes the first (zero) line |
---|
| 982 | { |
---|
[a63c24] | 983 | for (j=1;j<=rows+mr+1;j++) |
---|
[35aab3] | 984 | { |
---|
| 985 | for (k=1;k<=cols;k++) |
---|
| 986 | { |
---|
| 987 | IMATELEM((*result),j,k) = IMATELEM((*result),j-mr,k); |
---|
| 988 | } |
---|
| 989 | } |
---|
[a63c24] | 990 | for (j=rows+mr+1;j<=rows+1;j++) |
---|
[35aab3] | 991 | { |
---|
| 992 | for (k=1;k<=cols;k++) |
---|
| 993 | { |
---|
| 994 | IMATELEM((*result),j,k) = 0; |
---|
| 995 | } |
---|
| 996 | } |
---|
| 997 | } |
---|
| 998 | j = 0; |
---|
| 999 | k = 0; |
---|
[a63c24] | 1000 | for (i=1;i<=result->rows();i++) |
---|
[35aab3] | 1001 | { |
---|
[a63c24] | 1002 | for(l=1;l<=result->cols();l++) |
---|
| 1003 | if (IMATELEM((*result),i,l) != 0) |
---|
[35aab3] | 1004 | { |
---|
[a63c24] | 1005 | j = si_max(j, i-1); |
---|
| 1006 | k = si_max(k, l-1); |
---|
[35aab3] | 1007 | } |
---|
| 1008 | } |
---|
| 1009 | intvec * exactresult=new intvec(j+1,k+1,0); |
---|
| 1010 | for (i=0;i<exactresult->rows();i++) |
---|
| 1011 | { |
---|
| 1012 | for (j=0;j<exactresult->cols();j++) |
---|
| 1013 | { |
---|
| 1014 | IMATELEM(*exactresult,i+1,j+1) = IMATELEM(*result,i+1,j+1); |
---|
| 1015 | } |
---|
| 1016 | } |
---|
| 1017 | if (row_shift!=NULL) *row_shift = mr; |
---|
| 1018 | delete result; |
---|
| 1019 | return exactresult; |
---|
| 1020 | } |
---|
| 1021 | |
---|
| 1022 | /*2 |
---|
| 1023 | * minbare via syzygies |
---|
| 1024 | */ |
---|
| 1025 | ideal syMinBase(ideal arg) |
---|
| 1026 | { |
---|
| 1027 | intvec ** weights=NULL; |
---|
| 1028 | int leng; |
---|
| 1029 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
| 1030 | resolvente res=syResolvente(arg,1,&leng,&weights,TRUE); |
---|
| 1031 | ideal result=res[0]; |
---|
| 1032 | omFreeSize((ADDRESS)res,leng*sizeof(ideal)); |
---|
| 1033 | if (weights!=NULL) |
---|
| 1034 | { |
---|
| 1035 | if (*weights!=NULL) |
---|
| 1036 | { |
---|
| 1037 | delete (*weights); |
---|
| 1038 | *weights=NULL; |
---|
| 1039 | } |
---|
| 1040 | if ((leng>=1) && (*(weights+1)!=NULL)) |
---|
| 1041 | { |
---|
| 1042 | delete *(weights+1); |
---|
| 1043 | *(weights+1)=NULL; |
---|
| 1044 | } |
---|
| 1045 | } |
---|
| 1046 | idSkipZeroes(result); |
---|
| 1047 | return result; |
---|
| 1048 | } |
---|
| 1049 | |
---|
[f815bd7] | 1050 | #if 0 /* currently used: syBetti */ |
---|
[35aab3] | 1051 | /*2 |
---|
| 1052 | * computes Betti-numbers from a resolvente of |
---|
| 1053 | * (non-)homogeneous objects |
---|
| 1054 | * the numbers of entrees !=NULL in res and weights must be equal |
---|
| 1055 | * and < length |
---|
| 1056 | */ |
---|
| 1057 | intvec * syNewBetti(resolvente res, intvec ** weights, int length) |
---|
| 1058 | { |
---|
| 1059 | intvec * result,*tocancel; |
---|
| 1060 | int i,j,k,rsmin=0,rsmax=0,rs=0; |
---|
| 1061 | BOOLEAN homog=TRUE; |
---|
| 1062 | |
---|
| 1063 | if (weights!=NULL) //---homogeneous Betti numbers |
---|
| 1064 | { |
---|
| 1065 | /*--------------computes size of the field----------------------*/ |
---|
| 1066 | for (i=1;i<length;i++) |
---|
| 1067 | { |
---|
| 1068 | if (weights[i] != NULL) |
---|
| 1069 | { |
---|
| 1070 | for (j=1;j<(weights[i])->length();j++) |
---|
| 1071 | { |
---|
| 1072 | if ((*(weights[i]))[j]-i<rsmin) rsmin = (*(weights[i]))[j]-i; |
---|
| 1073 | if ((*(weights[i]))[j]-i>rsmax) rsmax = (*(weights[i]))[j]-i; |
---|
| 1074 | } |
---|
| 1075 | } |
---|
| 1076 | } |
---|
| 1077 | i = 0; |
---|
| 1078 | while (weights[i] != NULL) i++; |
---|
| 1079 | i--; |
---|
| 1080 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
| 1081 | { |
---|
| 1082 | if (res[i]->m[j]!=NULL) |
---|
| 1083 | { |
---|
[b50590] | 1084 | k = p_FDeg(res[i]->m[j],currRing)+(*(weights[i]))[pGetComp(res[i]->m[j])]-i-1; |
---|
[35aab3] | 1085 | if (k>rsmax) rsmax = k; |
---|
| 1086 | if (k<rsmin) rsmin = k; |
---|
| 1087 | } |
---|
| 1088 | } |
---|
| 1089 | for (j=1;j<(weights[0])->length();j++) |
---|
| 1090 | { |
---|
| 1091 | if ((*weights[0])[j]>rsmax) rsmax = (*weights[0])[j]; |
---|
| 1092 | if ((*weights[0])[j]<rsmin) rsmin = (*weights[0])[j]; |
---|
| 1093 | } |
---|
| 1094 | //Print("rsmax = %d\n",rsmax); |
---|
| 1095 | //Print("rsmin = %d\n",rsmin); |
---|
| 1096 | rs = rsmax-rsmin+1; |
---|
| 1097 | result = new intvec(rs,i+2,0); |
---|
| 1098 | tocancel = new intvec(rs); |
---|
| 1099 | /*-----------enter the Betti numbers-------------------------------*/ |
---|
| 1100 | if (/*idRankFreeModule(res[0])*/ res[0]->rank==0) |
---|
| 1101 | { |
---|
| 1102 | IMATELEM(*result,1-rsmin,1)=1; |
---|
| 1103 | } |
---|
| 1104 | else |
---|
| 1105 | { |
---|
| 1106 | for (i=1;i<(weights[0])->length();i++) |
---|
| 1107 | IMATELEM(*result,(*weights[0])[i]+1-rsmin,1)++; |
---|
| 1108 | } |
---|
| 1109 | i = 1; |
---|
| 1110 | while (weights[i]!=NULL) |
---|
| 1111 | { |
---|
| 1112 | for (j=1;j<(weights[i])->length();j++) |
---|
| 1113 | { |
---|
| 1114 | IMATELEM(*result,(*(weights[i]))[j]-i+1-rsmin,i+1)++; |
---|
| 1115 | } |
---|
| 1116 | i++; |
---|
| 1117 | } |
---|
| 1118 | i--; |
---|
| 1119 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
| 1120 | { |
---|
| 1121 | if (res[i]->m[j]!=NULL) |
---|
| 1122 | { |
---|
[b50590] | 1123 | k = p_FDeg(res[i]->m[j],currRing)+(*(weights[i]))[pGetComp(res[i]->m[j])]-i; |
---|
[35aab3] | 1124 | IMATELEM(*result,k-rsmin,i+2)++; |
---|
| 1125 | } |
---|
| 1126 | } |
---|
| 1127 | } |
---|
| 1128 | else //-----the non-homgeneous case |
---|
| 1129 | { |
---|
| 1130 | homog = FALSE; |
---|
| 1131 | tocancel = new intvec(1); |
---|
| 1132 | k = length; |
---|
| 1133 | while ((k>0) && (idIs0(res[k-1]))) k--; |
---|
| 1134 | result = new intvec(1,k+1,0); |
---|
| 1135 | (*result)[0] = res[0]->rank; |
---|
| 1136 | for (i=0;i<length;i++) |
---|
| 1137 | { |
---|
| 1138 | if (res[i]!=NULL) |
---|
| 1139 | { |
---|
| 1140 | for (j=0;j<IDELEMS(res[i]);j++) |
---|
| 1141 | { |
---|
| 1142 | if (res[i]->m[j]!=NULL) (*result)[i+1]++; |
---|
| 1143 | } |
---|
| 1144 | } |
---|
| 1145 | } |
---|
| 1146 | } |
---|
| 1147 | /*--------computes the Betti numbers for the minimized reolvente----*/ |
---|
| 1148 | |
---|
| 1149 | i = 1; |
---|
| 1150 | while ((res[i]!=NULL) && (weights[i]!=NULL)) |
---|
| 1151 | { |
---|
| 1152 | syDetect(res[i],i,rsmin,homog,weights[i],tocancel); |
---|
| 1153 | if (homog) |
---|
| 1154 | { |
---|
| 1155 | for (j=0;j<rs-1;j++) |
---|
| 1156 | { |
---|
| 1157 | IMATELEM((*result),j+1,i+1) -= (*tocancel)[j]; |
---|
| 1158 | IMATELEM((*result),j+1,i+2) -= (*tocancel)[j+1]; |
---|
| 1159 | } |
---|
| 1160 | IMATELEM((*result),rs,i+1) -= (*tocancel)[rs-1]; |
---|
| 1161 | } |
---|
| 1162 | else |
---|
| 1163 | { |
---|
| 1164 | (*result)[i+1] -= (*tocancel)[0]; |
---|
| 1165 | (*result)[i+2] -= (*tocancel)[0]; |
---|
| 1166 | } |
---|
| 1167 | i++; |
---|
| 1168 | } |
---|
| 1169 | |
---|
| 1170 | /*--------print Betti numbers for control---------------------------*/ |
---|
| 1171 | for(i=rsmin;i<=rsmax;i++) |
---|
| 1172 | { |
---|
| 1173 | Print("%2d:",i); |
---|
| 1174 | for(j=1;j<=result->cols();j++) |
---|
| 1175 | { |
---|
| 1176 | Print(" %5d",IMATELEM(*result,i-rsmin+1,j)); |
---|
| 1177 | } |
---|
| 1178 | PrintLn(); |
---|
| 1179 | } |
---|
| 1180 | return result; |
---|
| 1181 | } |
---|
[f815bd7] | 1182 | #endif |
---|
| 1183 | |
---|