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