| 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 1.2 1997-06-09 15:56:04 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 | |
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| 12 | #ifdef TRUEFACTORDEBUG |
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| 13 | # define DEBUGOUTPUT |
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| 14 | #else |
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| 15 | # undef DEBUGOUTPUT |
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| 16 | #endif |
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| 17 | |
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| 18 | #include "debug.h" |
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| 19 | #include "timing.h" |
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| 20 | |
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| 21 | #ifdef HAVE_SINGULAR |
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| 22 | extern void WerrorS(char *); |
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| 23 | #endif |
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| 24 | /////////////////////////////////////////////////////////////// |
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| 25 | // generate all different k-subsets of the set with n // |
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| 26 | // elements and return them in returnlist. // |
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| 27 | /////////////////////////////////////////////////////////////// |
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| 28 | static void |
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| 29 | combinat( int k, int n, List<IntList> & returnlist ){ |
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| 30 | ListIntList ListofLists; |
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| 31 | IntList intermediate,intermediate2; |
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| 32 | int value,j; |
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| 33 | |
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| 34 | if ( k == 1 ){ // k=1 |
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| 35 | for ( j=1; j<=n; j++) |
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| 36 | returnlist.append( IntList(j) ); |
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| 37 | } |
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| 38 | else{ // k-1 --> k |
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| 39 | combinat(k-1,n,returnlist); // generate (k-1,n) |
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| 40 | for ( ListIntListIterator l=returnlist; l.hasItem(); l++ ){ |
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| 41 | intermediate = l.getItem(); |
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| 42 | value = intermediate.getLast(); |
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| 43 | if ( value != n ) |
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| 44 | for ( j=value+1; j<=n; j++ ){ |
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| 45 | intermediate2 = intermediate; intermediate2.append(j); |
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| 46 | ListofLists.append( intermediate2 ); |
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| 47 | } |
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| 48 | } |
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| 49 | returnlist = ListofLists; |
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| 50 | } |
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| 51 | } |
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| 52 | |
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| 53 | /////////////////////////////////////////////////////////////// |
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| 54 | // Return the CanonicalForm number nr in Factorlist. // |
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| 55 | /////////////////////////////////////////////////////////////// |
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| 56 | static CanonicalForm |
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| 57 | getItemNr(int nr, const CFFList & Factorlist ){ |
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| 58 | ListIterator<CFFactor> i=Factorlist; |
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| 59 | int Nr=nr; |
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| 60 | |
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| 61 | for ( Nr=1; Nr<nr; Nr++ ) i++; |
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| 62 | return i.getItem().factor(); |
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| 63 | } |
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| 64 | |
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| 65 | /////////////////////////////////////////////////////////////// |
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| 66 | // Generate all sets of m factors out of LiftedFactors list. // |
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| 67 | /////////////////////////////////////////////////////////////// |
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| 68 | static CFFList |
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| 69 | combine( int m, const CFFList & LiftedFactors ){ |
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| 70 | CFFList result; |
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| 71 | ListIntList CombinatList; |
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| 72 | CanonicalForm intermediate; |
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| 73 | |
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| 74 | combinat(m, LiftedFactors.length(), CombinatList); |
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| 75 | for ( ListIntListIterator j=CombinatList ; j.hasItem(); j++ ){ |
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| 76 | intermediate=1; |
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| 77 | for ( IntListIterator k=j.getItem(); k.hasItem(); k++ ) |
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| 78 | intermediate *= getItemNr(k.getItem(), LiftedFactors); |
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| 79 | result.append(CFFactor(intermediate,1)); |
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| 80 | } |
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| 81 | return result; |
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| 82 | } |
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| 83 | |
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| 84 | /////////////////////////////////////////////////////////////// |
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| 85 | // Remove element elem from the list L. // |
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| 86 | /////////////////////////////////////////////////////////////// |
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| 87 | static CFFList |
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| 88 | Remove_from_List( const CFFList & L, const CanonicalForm & elem ){ |
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| 89 | CFFList Returnlist; |
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| 90 | |
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| 91 | DEBOUTLN(cout, "Remove_from_List called with L= ",L); |
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| 92 | DEBOUTLN(cout, " and elem= ",elem); |
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| 93 | for ( ListIterator<CFFactor> i = L ; i.hasItem(); i++) |
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| 94 | if ( i.getItem().factor() != elem ) |
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| 95 | Returnlist.append( i.getItem() ); |
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| 96 | |
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| 97 | return Returnlist; |
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| 98 | } |
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| 99 | |
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| 100 | /////////////////////////////////////////////////////////////// |
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| 101 | // Here we solve: G= F mod ( P, S^h ) // |
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| 102 | /////////////////////////////////////////////////////////////// |
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| 103 | static CanonicalForm |
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| 104 | Multmod_power( const CanonicalForm & F, const SFormList & Substituionlist, int h, int levelF){ |
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| 105 | CanonicalForm G; |
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| 106 | |
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| 107 | G= change_poly(F, Substituionlist, 0); |
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| 108 | G= mod_power(G, h, levelF); |
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| 109 | G= change_poly(G, Substituionlist, 1); |
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| 110 | |
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| 111 | return G; |
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| 112 | } |
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| 113 | |
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| 114 | /////////////////////////////////////////////////////////////// |
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| 115 | // Determine the right degree for the list of combinations // |
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| 116 | // of factors, i.e. delete any element from list CombL which // |
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| 117 | // degree in the main variable levelU exceeeds degU. // |
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| 118 | /////////////////////////////////////////////////////////////// |
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| 119 | static CFFList |
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| 120 | Rightdegree( const CFFList & CombL, int degU, int levelU ){ |
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| 121 | CFFList Returnlist; |
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| 122 | CFFactor factor; |
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| 123 | |
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| 124 | for ( ListIterator<CFFactor> i= CombL; i.hasItem(); i++ ){ |
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| 125 | factor= i.getItem(); |
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| 126 | if ( degree(factor.factor(), levelU) <= degU ) |
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| 127 | Returnlist.append(factor); |
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| 128 | } |
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| 129 | |
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| 130 | return Returnlist; |
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| 131 | } |
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| 132 | |
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| 133 | /////////////////////////////////////////////////////////////// |
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| 134 | // We have properly lifted all the specialized factors. See // |
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| 135 | // which one works. // |
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| 136 | // We use the (modified) algorithm TRUEFACTORS given by // |
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| 137 | // Paul S. Wang and Linda Preiss Rothschild: // |
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| 138 | // Factoring Multivariate Polynomials Over the Integers // |
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| 139 | // Math. Comp. V29 Nr131 (July 1975) p. 935-950 // |
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| 140 | /////////////////////////////////////////////////////////////// |
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| 141 | CFFList |
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| 142 | Truefactors( const CanonicalForm Ua, int levelU, const SFormList & SubstitutionList, const CFFList & PiList){ |
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| 143 | CanonicalForm U=Ua,a,b,Y; |
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| 144 | CFFactor factor; |
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| 145 | CFFList L,FAC,E_all; |
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| 146 | int c,r = PiList.length(),degU, onemore,M, h = subvardegree(Ua,levelU) + 1; |
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| 147 | ListIterator<CFFactor> i; |
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| 148 | |
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| 149 | // step 1: simply test the generated factors alone |
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| 150 | for ( i= PiList; i.hasItem();i++){ |
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| 151 | factor = i.getItem(); |
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| 152 | c= mydivremt(U,factor.factor(),a,b); |
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| 153 | if ( c && b == U.genZero()) { // factor.getFactor() divides U |
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| 154 | U= a; |
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| 155 | FAC.append(factor); |
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| 156 | } |
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| 157 | else{ |
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| 158 | L.append(factor); |
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| 159 | } |
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| 160 | } |
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| 161 | DEBOUTLN(cout,"Truefactors: (step1) L = ", L); |
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| 162 | DEBOUTLN(cout," FAC= ", FAC); |
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| 163 | |
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| 164 | // step 2: Do we have to check combinations? |
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| 165 | degU = L.length(); |
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| 166 | if ( degU == 0 ) // No elements: Return |
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| 167 | return FAC; |
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| 168 | else |
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| 169 | if ( degU < 4 ){ // Less then four elements: no combinations possible |
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| 170 | FAC.append( CFFactor(U,1) ); |
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| 171 | return FAC; |
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| 172 | } |
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| 173 | else { |
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| 174 | M = 1; r = r - FAC.length(); degU = degree(U, levelU)/2; |
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| 175 | } |
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| 176 | |
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| 177 | DEBOUTLN(cout,"Truefactors: (step2) M = ", M); |
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| 178 | DEBOUTLN(cout," r = ", r); |
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| 179 | DEBOUTLN(cout," degU= ", degU); |
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| 180 | |
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| 181 | // Now do the real work! |
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| 182 | // Test all the combinations of possible factors. |
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| 183 | |
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| 184 | onemore=1; |
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| 185 | // steps 3 to 6 |
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| 186 | while (1){ |
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| 187 | // step 3 iff onemore == 1 |
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| 188 | if ( onemore ) M+= 1; else onemore = 1; |
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| 189 | // step 4 |
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| 190 | if ( U == U.genOne() ) break; // Return FAC |
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| 191 | if ( ( r == 1 ) || ( M >= ( r-1 ) ) || ( M > degU ) ) { |
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| 192 | FAC.append( CFFactor(U,1) ); |
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| 193 | break; // Return FAC union {U} |
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| 194 | } |
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| 195 | // step 5 |
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| 196 | E_all = combine(M, L); // generate all combinations of M elements from L |
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| 197 | DEBOUTLN(cout,"Truefactors: (step5) E_all= ", E_all); |
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| 198 | // select combinations with the degree not to exceed degU: |
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| 199 | E_all = Rightdegree( E_all, degU, levelU ); |
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| 200 | DEBOUTLN(cout,"Truefactors: (step5) E_all(Rightdegree)= ", E_all); |
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| 201 | if ( E_all.length() == 0 ){ |
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| 202 | FAC.append( CFFactor(U,1) ); |
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| 203 | break; // Return FAC union {U} |
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| 204 | } |
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| 205 | for ( i=E_all; i.hasItem(); i++){ |
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| 206 | factor = i.getItem(); |
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| 207 | Y = Multmod_power( factor.factor(), SubstitutionList, h, levelU); |
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| 208 | DEBOUTLN(cout, "Truefactors: (step6) Testing Y = ", Y); |
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| 209 | c = mydivremt(U,Y,a,b); |
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| 210 | // if ( c && b == U.genZero()) { // Y divides U |
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| 211 | if ( c && b.isZero() ){ |
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| 212 | DEBOUT(cout,"Truefactors: (step6): ",Y ); |
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| 213 | DEBOUTLN(cout, " divides ",U); |
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| 214 | U = a; |
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| 215 | FAC.append(Y); // Y is a real factor |
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| 216 | onemore = 0; |
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| 217 | degU = degree(U, levelU)/2; // new degU |
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| 218 | // L = L \ {factor} |
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| 219 | // Hier ist noch etwas faul; wir muessen (f=prod(f_i)) die f_i |
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| 220 | // entfernen und nicht f! |
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| 221 | L = Remove_from_List( L, factor.factor() ); |
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| 222 | r -= 1; |
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| 223 | // delete from L any element with degree greater than degU |
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| 224 | L = Rightdegree( L, degU, levelU ); |
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| 225 | } |
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| 226 | } |
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| 227 | } |
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| 228 | |
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| 229 | return FAC; |
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| 230 | } |
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| 231 | |
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| 232 | /////////////////////////////////////////////////////////////// |
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| 233 | // Check if poly f is in Fp (returns true) or in Fp(a) // |
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| 234 | /////////////////////////////////////////////////////////////// |
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| 235 | bool |
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| 236 | is_in_Fp( const CanonicalForm & f ){ |
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| 237 | if ( f.inCoeffDomain() ) |
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| 238 | return f.inBaseDomain() ; |
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| 239 | else { |
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| 240 | CFIterator i=f; |
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| 241 | bool ok=true; |
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| 242 | while ( ok && i.hasTerms() ){ |
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| 243 | ok = is_in_Fp( i.coeff() ); |
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| 244 | i++ ; |
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| 245 | } |
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| 246 | return ok; |
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| 247 | } |
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| 248 | } |
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| 249 | |
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| 250 | /////////////////////////////////////////////////////////////// |
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| 251 | // We have factors which possibly lie in an extension of the // |
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| 252 | // base field. If one of these is not over the base field, // |
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| 253 | // find its norm by (the theoretically handicapped method // |
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| 254 | // of) multiplying by other elements. // |
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| 255 | /////////////////////////////////////////////////////////////// |
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| 256 | CFFList |
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| 257 | TakeNorms(const CFFList & PiList){ |
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| 258 | CFFList CopyPossibleFactors, PossibleFactors, TrueFactors; |
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| 259 | CFFListIterator i; |
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| 260 | CFFactor Factor; |
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| 261 | CanonicalForm intermediate; |
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| 262 | ListIntList CombinatList; |
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| 263 | ListIntListIterator j; |
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| 264 | IntListIterator k; |
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| 265 | |
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| 266 | // First check if the factors in PiList already lie in Fp-Domain |
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| 267 | for ( i=PiList; i.hasItem(); i++ ){ |
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| 268 | Factor = i.getItem(); |
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| 269 | if ( is_in_Fp( Factor.factor() ) ) |
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| 270 | TrueFactors.append(Factor); |
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| 271 | else |
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| 272 | PossibleFactors.append(Factor); |
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| 273 | } |
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| 274 | // Now we have to check if combinations of the remaining factors |
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| 275 | // (now in PossibleFactors) do lie in Fp-Domain |
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| 276 | if ( PossibleFactors.length() > 0 ){ // there are (at least two) items |
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| 277 | int n=2; |
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| 278 | if ( PossibleFactors.length() < n ) { // a little check |
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| 279 | #ifdef HAVE_SINGULAR |
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| 280 | WerrorS("libfac: ERROR: TakeNorms less then two items remaining!"); |
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| 281 | #else |
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| 282 | cerr << "libfac: ERROR: TakeNorms less then two items remaining! " |
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| 283 | << endl; |
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| 284 | #endif |
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| 285 | } |
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| 286 | while ( n < PossibleFactors.length() ){ |
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| 287 | // generate all combinations of n elements |
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| 288 | combinat(n, PossibleFactors.length(), CombinatList); |
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| 289 | for ( j=CombinatList ; j.hasItem(); j++ ){ |
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| 290 | intermediate=1; |
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| 291 | for ( k=j.getItem(); k.hasItem(); k++ ) |
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| 292 | intermediate *= getItemNr( k.getItem(), PossibleFactors ); |
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| 293 | if ( is_in_Fp( intermediate ) ){ |
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| 294 | TrueFactors.append(intermediate); // found a true factor |
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| 295 | CopyPossibleFactors=PossibleFactors; // save list |
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| 296 | for ( k=j.getItem(); k.hasItem(); k++ ) |
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| 297 | //remove combined factors from PossibleFactors |
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| 298 | PossibleFactors=Remove_from_List(PossibleFactors, |
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| 299 | getItemNr( k.getItem(), CopyPossibleFactors )); |
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| 300 | n-=1; // look for the same number of combined factors: |
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| 301 | break; |
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| 302 | } |
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| 303 | else { |
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| 304 | //cout << "Schade!" << endl; |
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| 305 | } |
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| 306 | DEBOUT(cout, "Truefactor: Combined ", n); |
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| 307 | DEBOUTLN(cout, " factors to: ", intermediate); |
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| 308 | } |
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| 309 | n += 1; |
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| 310 | } |
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| 311 | // All remaining factors in PossibleFactors multiplied |
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| 312 | // should lie in Fp domain |
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| 313 | if ( PossibleFactors.length() >=1 ){ |
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| 314 | for ( i=PossibleFactors; i.hasItem(); i++ ) |
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| 315 | intermediate *= i.getItem().factor(); |
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| 316 | // a last check: |
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| 317 | if ( is_in_Fp(intermediate) ){ |
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| 318 | TrueFactors.append(CFFactor(intermediate,1)); |
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| 319 | } |
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| 320 | else{ |
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| 321 | #ifdef HAVE_SINGULAR |
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| 322 | WerrorS("libfac: TakeNorms: somethings wrong with remaining factors!"); |
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| 323 | #else |
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| 324 | cerr << "libfac: TakeNorms: somethings wrong with remaining factors!" |
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| 325 | << endl; |
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| 326 | #endif |
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| 327 | } |
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| 328 | } |
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| 329 | } |
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| 330 | return TrueFactors; |
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| 331 | } |
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| 332 | |
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| 333 | //////////////////////////////////////////////////////////// |
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| 334 | /* |
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| 335 | $Log: not supported by cvs2svn $ |
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| 336 | Revision 1.3 1997/04/25 22:39:11 michael |
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| 337 | changed cerr and cout messages for use with Singular |
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| 338 | Version for libfac-0.2.1 |
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| 339 | |
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| 340 | */ |
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