| 1 | /* Copyright 1996 Michael Messollen. All rights reserved. */ |
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| 2 | /////////////////////////////////////////////////////////////////////////////// |
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| 3 | // emacs edit mode for this file is -*- C++ -*- |
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| 4 | //static char * rcsid = "@(#) $Id: Truefactor.cc,v 1.7 2001-08-06 08:32:54 Singular Exp $"; |
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| 5 | /////////////////////////////////////////////////////////////////////////////// |
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| 6 | // Factory - Includes |
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| 7 | #include <factory.h> |
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| 8 | // Factor - Includes |
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| 9 | #include "tmpl_inst.h" |
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| 10 | #include "helpstuff.h" |
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| 11 | // some CC's need this: |
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| 12 | #include "Truefactor.h" |
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| 13 | |
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| 14 | #ifdef SINGULAR |
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| 15 | # define HAVE_SINGULAR |
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| 16 | extern "C" { void WerrorS(char *); } |
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| 17 | #endif |
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| 18 | |
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| 19 | #ifdef TRUEFACTORDEBUG |
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| 20 | # define DEBUGOUTPUT |
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| 21 | #else |
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| 22 | # undef DEBUGOUTPUT |
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| 23 | #endif |
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| 24 | |
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| 25 | #include "debug.h" |
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| 26 | #include "timing.h" |
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| 27 | |
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| 28 | int hasAlgVar(const CanonicalForm &f, const Variable &v) |
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| 29 | { |
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| 30 | if (f.inBaseDomain()) return 0; |
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| 31 | if (f.inCoeffDomain()) |
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| 32 | { |
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| 33 | if (f.mvar()==v) return 1; |
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| 34 | return hasAlgVar(f.LC(),v); |
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| 35 | } |
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| 36 | if (f.inPolyDomain()) |
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| 37 | { |
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| 38 | if (hasAlgVar(f.LC(),v)) return 1; |
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| 39 | for( CFIterator i=f; i.hasTerms(); i++) |
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| 40 | { |
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| 41 | if (hasAlgVar(i.coeff(),v)) return 1; |
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| 42 | } |
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| 43 | } |
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| 44 | return 0; |
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| 45 | } |
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| 46 | |
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| 47 | int hasVar(const CanonicalForm &f, const Variable &v) |
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| 48 | { |
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| 49 | if (f.inBaseDomain()) return 0; |
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| 50 | if (f.inCoeffDomain()) |
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| 51 | { |
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| 52 | if (f.mvar()==v) return 1; |
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| 53 | return hasAlgVar(f.LC(),v); |
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| 54 | } |
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| 55 | if (f.inPolyDomain()) |
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| 56 | { |
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| 57 | if (f.mvar()==v) return 1; |
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| 58 | if (hasVar(f.LC(),v)) return 1; |
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| 59 | for( CFIterator i=f; i.hasTerms(); i++) |
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| 60 | { |
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| 61 | if (hasVar(i.coeff(),v)) return 1; |
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| 62 | } |
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| 63 | } |
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| 64 | return 0; |
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| 65 | } |
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| 66 | |
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| 67 | int hasAlgVar(const CanonicalForm &f) |
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| 68 | { |
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| 69 | if (f.inBaseDomain()) return 0; |
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| 70 | if (f.inCoeffDomain()) |
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| 71 | { |
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| 72 | if (f.level()!=0) |
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| 73 | { |
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| 74 | //cout << "hasAlgVar:" << f.mvar() <<endl; |
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| 75 | return 1; |
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| 76 | } |
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| 77 | return hasAlgVar(f.LC()); |
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| 78 | } |
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| 79 | if (f.inPolyDomain()) |
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| 80 | { |
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| 81 | if (hasAlgVar(f.LC())) return 1; |
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| 82 | for( CFIterator i=f; i.hasTerms(); i++) |
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| 83 | { |
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| 84 | if (hasAlgVar(i.coeff())) return 1; |
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| 85 | } |
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| 86 | } |
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| 87 | return 0; |
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| 88 | } |
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| 89 | |
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| 90 | /////////////////////////////////////////////////////////////// |
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| 91 | // generate all different k-subsets of the set with n // |
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| 92 | // elements and return them in returnlist. // |
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| 93 | /////////////////////////////////////////////////////////////// |
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| 94 | static void |
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| 95 | combinat( int k, int n, List<IntList> & returnlist ){ |
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| 96 | ListIntList ListofLists; |
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| 97 | IntList intermediate,intermediate2; |
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| 98 | int value,j; |
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| 99 | |
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| 100 | if ( k == 1 ){ // k=1 |
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| 101 | for ( j=1; j<=n; j++) |
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| 102 | returnlist.append( IntList(j) ); |
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| 103 | } |
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| 104 | else{ // k-1 --> k |
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| 105 | combinat(k-1,n,returnlist); // generate (k-1,n) |
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| 106 | for ( ListIntListIterator l=returnlist; l.hasItem(); l++ ){ |
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| 107 | intermediate = l.getItem(); |
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| 108 | value = intermediate.getLast(); |
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| 109 | if ( value != n ) |
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| 110 | for ( j=value+1; j<=n; j++ ){ |
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| 111 | intermediate2 = intermediate; intermediate2.append(j); |
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| 112 | ListofLists.append( intermediate2 ); |
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| 113 | } |
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| 114 | } |
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| 115 | returnlist = ListofLists; |
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| 116 | } |
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| 117 | } |
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| 118 | |
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| 119 | /////////////////////////////////////////////////////////////// |
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| 120 | // Return the CanonicalForm number nr in Factorlist. // |
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| 121 | /////////////////////////////////////////////////////////////// |
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| 122 | static CanonicalForm |
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| 123 | getItemNr(int nr, const CFFList & Factorlist ){ |
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| 124 | ListIterator<CFFactor> i=Factorlist; |
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| 125 | int Nr=nr; |
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| 126 | |
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| 127 | for ( Nr=1; Nr<nr; Nr++ ) i++; |
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| 128 | return i.getItem().factor(); |
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| 129 | } |
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| 130 | |
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| 131 | /////////////////////////////////////////////////////////////// |
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| 132 | // Generate all sets of m factors out of LiftedFactors list. // |
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| 133 | /////////////////////////////////////////////////////////////// |
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| 134 | static CFFList |
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| 135 | combine( int m, const CFFList & LiftedFactors ){ |
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| 136 | CFFList result; |
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| 137 | ListIntList CombinatList; |
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| 138 | CanonicalForm intermediate; |
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| 139 | |
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| 140 | combinat(m, LiftedFactors.length(), CombinatList); |
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| 141 | for ( ListIntListIterator j=CombinatList ; j.hasItem(); j++ ){ |
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| 142 | intermediate=1; |
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| 143 | for ( IntListIterator k=j.getItem(); k.hasItem(); k++ ) |
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| 144 | intermediate *= getItemNr(k.getItem(), LiftedFactors); |
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| 145 | if (!hasAlgVar(intermediate)) |
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| 146 | result.append(CFFactor(intermediate,1)); |
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| 147 | } |
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| 148 | return result; |
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| 149 | } |
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| 150 | |
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| 151 | /////////////////////////////////////////////////////////////// |
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| 152 | // Remove element elem from the list L. // |
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| 153 | /////////////////////////////////////////////////////////////// |
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| 154 | static CFFList |
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| 155 | Remove_from_List( const CFFList & L, const CanonicalForm & elem ){ |
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| 156 | CFFList Returnlist; |
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| 157 | |
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| 158 | DEBOUTLN(cout, "Remove_from_List called with L= ",L); |
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| 159 | DEBOUTLN(cout, " and elem= ",elem); |
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| 160 | for ( ListIterator<CFFactor> i = L ; i.hasItem(); i++) |
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| 161 | if ( i.getItem().factor() != elem ) |
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| 162 | Returnlist.append( i.getItem() ); |
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| 163 | |
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| 164 | return Returnlist; |
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| 165 | } |
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| 166 | |
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| 167 | /////////////////////////////////////////////////////////////// |
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| 168 | // Here we solve: G= F mod ( P, S^h ) // |
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| 169 | /////////////////////////////////////////////////////////////// |
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| 170 | static CanonicalForm |
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| 171 | Multmod_power( const CanonicalForm & F, const SFormList & Substituionlist, int h, int levelF){ |
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| 172 | CanonicalForm G; |
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| 173 | |
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| 174 | G= change_poly(F, Substituionlist, 0); |
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| 175 | G= mod_power(G, h, levelF); |
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| 176 | G= change_poly(G, Substituionlist, 1); |
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| 177 | |
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| 178 | return G; |
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| 179 | } |
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| 180 | |
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| 181 | /////////////////////////////////////////////////////////////// |
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| 182 | // Determine the right degree for the list of combinations // |
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| 183 | // of factors, i.e. delete any element from list CombL which // |
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| 184 | // degree in the main variable levelU exceeeds degU. // |
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| 185 | /////////////////////////////////////////////////////////////// |
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| 186 | static CFFList |
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| 187 | Rightdegree( const CFFList & CombL, int degU, int levelU ){ |
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| 188 | CFFList Returnlist; |
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| 189 | CFFactor factor; |
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| 190 | |
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| 191 | for ( ListIterator<CFFactor> i= CombL; i.hasItem(); i++ ){ |
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| 192 | factor= i.getItem(); |
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| 193 | if ( degree(factor.factor(), levelU) <= degU ) |
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| 194 | Returnlist.append(factor); |
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| 195 | } |
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| 196 | |
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| 197 | return Returnlist; |
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| 198 | } |
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| 199 | |
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| 200 | /////////////////////////////////////////////////////////////// |
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| 201 | // We have properly lifted all the specialized factors. See // |
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| 202 | // which one works. // |
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| 203 | // We use the (modified) algorithm TRUEFACTORS given by // |
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| 204 | // Paul S. Wang and Linda Preiss Rothschild: // |
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| 205 | // Factoring Multivariate Polynomials Over the Integers // |
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| 206 | // Math. Comp. V29 Nr131 (July 1975) p. 935-950 // |
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| 207 | /////////////////////////////////////////////////////////////// |
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| 208 | CFFList |
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| 209 | Truefactors( const CanonicalForm Ua, int levelU, const SFormList & SubstitutionList, const CFFList & PiList){ |
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| 210 | CanonicalForm U=Ua,a,b,Y; |
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| 211 | CFFactor factor; |
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| 212 | CFFList L,FAC,E_all; |
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| 213 | int c,r = PiList.length(),degU, onemore,M, h = subvardegree(Ua,levelU) + 1; |
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| 214 | ListIterator<CFFactor> i; |
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| 215 | |
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| 216 | //cout << "SubstitutionList="<< SubstitutionList<<endl; |
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| 217 | // step 1: simply test the generated factors alone |
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| 218 | for ( i= PiList; i.hasItem();i++){ |
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| 219 | factor = i.getItem(); |
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| 220 | //CanonicalForm test_f=change_poly(factor.factor(),SubstitutionList,0); |
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| 221 | CanonicalForm test_f=factor.factor(); |
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| 222 | //cout <<"f:" << factor.factor() << " -> test_f:"<<test_f <<endl; |
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| 223 | //cout << " 1:" << change_poly(factor.factor(),SubstitutionList,1) <<endl; |
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| 224 | c= mydivremt(U,test_f,a,b); |
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| 225 | if ( c && b == U.genZero() && !hasAlgVar(test_f)) |
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| 226 | // factor.getFactor() divides U |
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| 227 | { |
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| 228 | //cout << " teilt:" << test_f <<endl; |
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| 229 | U= a; |
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| 230 | FAC.append(factor); |
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| 231 | } |
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| 232 | else{ |
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| 233 | //cout << " teilt nicht:" << test_f <<endl; |
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| 234 | L.append(factor); |
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| 235 | } |
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| 236 | } |
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| 237 | DEBOUTLN(cout,"Truefactors: (step1) L = ", L); |
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| 238 | DEBOUTLN(cout," FAC= ", FAC); |
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| 239 | |
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| 240 | // step 2: Do we have to check combinations? |
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| 241 | degU = L.length(); |
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| 242 | if ( degU == 0 ) // No elements: Return |
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| 243 | return FAC; |
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| 244 | else |
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| 245 | if ( degU < 4 ){ // Less then four elements: no combinations possible |
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| 246 | FAC.append( CFFactor(U,1) ); |
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| 247 | return FAC; |
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| 248 | } |
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| 249 | else { |
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| 250 | M = 1; r = r - FAC.length(); degU = degree(U, levelU)/2; |
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| 251 | } |
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| 252 | |
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| 253 | DEBOUTLN(cout,"Truefactors: (step2) M = ", M); |
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| 254 | DEBOUTLN(cout," r = ", r); |
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| 255 | DEBOUTLN(cout," degU= ", degU); |
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| 256 | |
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| 257 | // Now do the real work! |
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| 258 | // Test all the combinations of possible factors. |
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| 259 | |
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| 260 | onemore=1; |
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| 261 | // steps 3 to 6 |
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| 262 | while (1){ |
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| 263 | // step 3 iff onemore == 1 |
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| 264 | if ( onemore ) M+= 1; else onemore = 1; |
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| 265 | // step 4 |
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| 266 | if ( U == U.genOne() ) break; // Return FAC |
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| 267 | if ( ( r == 1 ) || ( M >= ( r-1 ) ) || ( M > degU ) ) { |
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| 268 | FAC.append( CFFactor(U,1) ); |
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| 269 | break; // Return FAC union {U} |
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| 270 | } |
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| 271 | // step 5 |
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| 272 | E_all = combine(M, L); // generate all combinations of M elements from L |
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| 273 | DEBOUTLN(cout,"Truefactors: (step5) E_all= ", E_all); |
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| 274 | // select combinations with the degree not to exceed degU: |
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| 275 | E_all = Rightdegree( E_all, degU, levelU ); |
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| 276 | DEBOUTLN(cout,"Truefactors: (step5) E_all(Rightdegree)= ", E_all); |
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| 277 | if ( E_all.length() == 0 ){ |
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| 278 | FAC.append( CFFactor(U,1) ); |
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| 279 | break; // Return FAC union {U} |
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| 280 | } |
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| 281 | for ( i=E_all; i.hasItem(); i++){ |
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| 282 | factor = i.getItem(); |
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| 283 | Y = Multmod_power( factor.factor(), SubstitutionList, h, levelU); |
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| 284 | DEBOUTLN(cout, "Truefactors: (step6) Testing Y = ", Y); |
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| 285 | c = mydivremt(U,Y,a,b); |
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| 286 | // if ( c && b == U.genZero()) { // Y divides U |
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| 287 | if ( c && b.isZero() ){ |
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| 288 | DEBOUT(cout,"Truefactors: (step6): ",Y ); |
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| 289 | DEBOUTLN(cout, " divides ",U); |
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| 290 | U = a; |
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| 291 | FAC.append(Y); // Y is a real factor |
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| 292 | onemore = 0; |
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| 293 | degU = degree(U, levelU)/2; // new degU |
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| 294 | // L = L \ {factor} |
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| 295 | // Hier ist noch etwas faul; wir muessen (f=prod(f_i)) die f_i |
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| 296 | // entfernen und nicht f! |
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| 297 | L = Remove_from_List( L, factor.factor() ); |
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| 298 | r -= 1; |
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| 299 | // delete from L any element with degree greater than degU |
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| 300 | L = Rightdegree( L, degU, levelU ); |
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| 301 | } |
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| 302 | } |
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| 303 | } |
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| 304 | |
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| 305 | return FAC; |
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| 306 | } |
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| 307 | |
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| 308 | /////////////////////////////////////////////////////////////// |
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| 309 | // Check if poly f is in Fp (returns true) or in Fp(a) // |
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| 310 | /////////////////////////////////////////////////////////////// |
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| 311 | static bool |
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| 312 | is_in_Fp( const CanonicalForm & f ){ |
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| 313 | if ( f.inCoeffDomain() ) |
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| 314 | return f.inBaseDomain() ; |
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| 315 | else { |
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| 316 | CFIterator i=f; |
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| 317 | bool ok=true; |
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| 318 | while ( ok && i.hasTerms() ){ |
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| 319 | ok = is_in_Fp( i.coeff() ); |
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| 320 | i++ ; |
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| 321 | } |
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| 322 | return ok; |
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| 323 | } |
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| 324 | } |
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| 325 | |
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| 326 | /////////////////////////////////////////////////////////////// |
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| 327 | // We have factors which possibly lie in an extension of the // |
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| 328 | // base field. If one of these is not over the base field, // |
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| 329 | // find its norm by (the theoretically handicapped method // |
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| 330 | // of) multiplying by other elements. // |
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| 331 | /////////////////////////////////////////////////////////////// |
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| 332 | CFFList |
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| 333 | TakeNorms(const CFFList & PiList){ |
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| 334 | CFFList CopyPossibleFactors, PossibleFactors, TrueFactors; |
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| 335 | CFFListIterator i; |
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| 336 | CFFactor Factor; |
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| 337 | CanonicalForm intermediate; |
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| 338 | ListIntList CombinatList; |
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| 339 | ListIntListIterator j; |
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| 340 | IntListIterator k; |
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| 341 | |
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| 342 | // First check if the factors in PiList already lie in Fp-Domain |
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| 343 | for ( i=PiList; i.hasItem(); i++ ){ |
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| 344 | Factor = i.getItem(); |
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| 345 | if ( is_in_Fp( Factor.factor() ) ) |
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| 346 | TrueFactors.append(Factor); |
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| 347 | else |
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| 348 | PossibleFactors.append(Factor); |
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| 349 | } |
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| 350 | // Now we have to check if combinations of the remaining factors |
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| 351 | // (now in PossibleFactors) do lie in Fp-Domain |
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| 352 | if ( PossibleFactors.length() > 0 ){ // there are (at least two) items |
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| 353 | int n=2; |
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| 354 | if ( PossibleFactors.length() < n ) { // a little check |
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| 355 | #ifdef HAVE_SINGULAR |
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| 356 | WerrorS("libfac: ERROR: TakeNorms less then two items remaining!"); |
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| 357 | #else |
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| 358 | cerr << "libfac: ERROR: TakeNorms less then two items remaining! " |
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| 359 | << endl; |
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| 360 | #endif |
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| 361 | } |
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| 362 | while ( n < PossibleFactors.length() ){ |
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| 363 | // generate all combinations of n elements |
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| 364 | combinat(n, PossibleFactors.length(), CombinatList); |
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| 365 | for ( j=CombinatList ; j.hasItem(); j++ ){ |
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| 366 | intermediate=1; |
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| 367 | for ( k=j.getItem(); k.hasItem(); k++ ) |
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| 368 | intermediate *= getItemNr( k.getItem(), PossibleFactors ); |
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| 369 | if ( is_in_Fp( intermediate ) ){ |
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| 370 | TrueFactors.append(intermediate); // found a true factor |
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| 371 | CopyPossibleFactors=PossibleFactors; // save list |
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| 372 | for ( k=j.getItem(); k.hasItem(); k++ ) |
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| 373 | //remove combined factors from PossibleFactors |
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| 374 | PossibleFactors=Remove_from_List(PossibleFactors, |
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| 375 | getItemNr( k.getItem(), CopyPossibleFactors )); |
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| 376 | n-=1; // look for the same number of combined factors: |
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| 377 | break; |
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| 378 | } |
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| 379 | else { |
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| 380 | //cout << "Schade!" << endl; |
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| 381 | } |
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| 382 | DEBOUT(cout, "Truefactor: Combined ", n); |
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| 383 | DEBOUTLN(cout, " factors to: ", intermediate); |
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| 384 | } |
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| 385 | n += 1; |
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| 386 | } |
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| 387 | // All remaining factors in PossibleFactors multiplied |
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| 388 | // should lie in Fp domain |
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| 389 | if ( PossibleFactors.length() >=1 ){ |
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| 390 | for ( i=PossibleFactors; i.hasItem(); i++ ) |
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| 391 | intermediate *= i.getItem().factor(); |
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| 392 | // a last check: |
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| 393 | if ( is_in_Fp(intermediate) ){ |
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| 394 | TrueFactors.append(CFFactor(intermediate,1)); |
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| 395 | } |
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| 396 | else{ |
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| 397 | #ifdef HAVE_SINGULAR |
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| 398 | WerrorS("libfac: TakeNorms: somethings wrong with remaining factors!"); |
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| 399 | #else |
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| 400 | cerr << "libfac: TakeNorms: somethings wrong with remaining factors!" |
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| 401 | << endl; |
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| 402 | #endif |
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| 403 | } |
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| 404 | } |
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| 405 | } |
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| 406 | return TrueFactors; |
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| 407 | } |
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| 408 | |
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| 409 | //////////////////////////////////////////////////////////// |
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| 410 | /* |
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| 411 | $Log: not supported by cvs2svn $ |
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| 412 | Revision 1.6 2001/06/27 13:58:06 Singular |
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| 413 | *hannes/GP: debug newfactoras, char_series, ... |
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| 414 | |
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| 415 | Revision 1.5 2001/06/21 14:57:06 Singular |
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| 416 | *hannes/GP: Factorize, newfactoras, ... |
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| 417 | |
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| 418 | Revision 1.4 1997/11/18 16:39:07 Singular |
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| 419 | * hannes: moved WerrorS from C++ to C |
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| 420 | (Factor.cc MVMultiHensel.cc SqrFree.cc Truefactor.cc) |
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| 421 | |
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| 422 | Revision 1.3 1997/09/12 07:19:52 Singular |
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| 423 | * hannes/michael: libfac-0.3.0 |
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| 424 | |
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| 425 | Revision 1.3 1997/04/25 22:39:11 michael |
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| 426 | changed cerr and cout messages for use with Singular |
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| 427 | Version for libfac-0.2.1 |
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| 428 | |
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| 429 | */ |
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