[1a80b4] | 1 | /////////////////////////////////////////////////////////////////////////////// |
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[36b7a3] | 2 | static const char * errmsg = "\nYou found a bug!\nPlease inform singular@mathematik.uni-kl.de\nPlease include above information and your input (the ideal/polynomial and characteristic) in your bug-report.\nThank you."; |
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[1a80b4] | 3 | /////////////////////////////////////////////////////////////////////////////// |
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| 4 | // FACTORY - Includes |
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| 5 | #include <factory.h> |
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[14b1e65] | 6 | #ifndef NOSTREAMIO |
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[e2ca88] | 7 | #ifdef HAVE_IOSTREAM |
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| 8 | #include <iostream> |
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| 9 | #define CERR std::cerr |
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| 10 | #define CIN std::cin |
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| 11 | #elif defined(HAVE_IOSTREAM_H) |
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[14b1e65] | 12 | #include <iostream.h> |
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[e2ca88] | 13 | #define CERR cerr |
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| 14 | #define CIN cin |
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| 15 | #endif |
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[14b1e65] | 16 | #endif |
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[1a80b4] | 17 | // Factor - Includes |
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| 18 | #include "tmpl_inst.h" |
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| 19 | #include "SqrFree.h" |
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| 20 | #include "helpstuff.h" |
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| 21 | #include "MVMultiHensel.h" |
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| 22 | #include "Truefactor.h" |
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| 23 | #include "homogfactor.h" |
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[3e55bc] | 24 | #include "interrupt.h" |
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[4a81ec] | 25 | // some CC's need this: |
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| 26 | #include "Factor.h" |
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| 27 | |
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[0be2bc] | 28 | #include "alg_factor.h" |
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[070c1b4] | 29 | void out_cf(const char *s1,const CanonicalForm &f,const char *s2); |
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[a38d45] | 30 | void out_cff(CFFList &L); |
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| 31 | |
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[0be2bc] | 32 | |
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[1a80b4] | 33 | #ifdef FACTORDEBUG |
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| 34 | # define DEBUGOUTPUT |
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| 35 | #else |
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| 36 | # undef DEBUGOUTPUT |
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| 37 | #endif |
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| 38 | |
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[d92d71] | 39 | #include <libfac/factor/debug.h> |
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[1a80b4] | 40 | #include "timing.h" |
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[be5dff] | 41 | TIMING_DEFINE_PRINT(factorize_time) |
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| 42 | TIMING_DEFINE_PRINT(sqrfree_time) |
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| 43 | TIMING_DEFINE_PRINT(discr_time) |
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| 44 | TIMING_DEFINE_PRINT(evaluate_time) |
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| 45 | TIMING_DEFINE_PRINT(hensel_time) |
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| 46 | TIMING_DEFINE_PRINT(truefactor_time) |
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[1a80b4] | 47 | |
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[1048e0c] | 48 | /* |
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| 49 | * a wrapper for factorize over algebraic extensions: |
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| 50 | * does a sanity check and, if nec., a conversion |
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| 51 | * before calling factorize(f,alpha) |
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| 52 | * ( in factorize, alpha.level() must be < 0 ) |
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| 53 | */ |
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[cd8141] | 54 | static |
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[5c4b32] | 55 | CFFList factorize2 ( const CanonicalForm & f, |
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[1048e0c] | 56 | const Variable & alpha, const CanonicalForm & mipo ) |
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| 57 | { |
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| 58 | if (alpha.level() <0) |
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[fb4f62e] | 59 | { |
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[f152c5] | 60 | return factorize(f,alpha); |
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[5c4b32] | 61 | } |
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[1048e0c] | 62 | else |
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| 63 | { |
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| 64 | //out_cf("f2 - factor:",f,"\n"); |
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| 65 | //out_cf("f2 - ext:",alpha,"\n"); |
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| 66 | //out_cf("f2 - mipo:",mipo,"\n"); |
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| 67 | Variable X=rootOf(mipo); |
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| 68 | CanonicalForm F=f; |
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[070c1b4] | 69 | F=replacevar(f,alpha,X); |
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[1048e0c] | 70 | //out_cf("call - factor:",F,"\n"); |
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| 71 | //out_cf("call - ext:",X,"\n"); |
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| 72 | //out_cf("call - mipo:",getMipo(X,'A'),"\n"); |
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| 73 | CFFList L=factorize(F,X); |
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| 74 | CFFListIterator i=L; |
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| 75 | { |
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| 76 | CFFList Outputlist; |
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| 77 | for(;i.hasItem(); i++ ) |
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| 78 | { |
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| 79 | Outputlist.append(CFFactor( |
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| 80 | replacevar(i.getItem().factor(),X,alpha), |
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| 81 | i.getItem().exp())); |
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| 82 | } |
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[070c1b4] | 83 | //out_cff(Outputlist); |
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[1048e0c] | 84 | return Outputlist; |
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| 85 | } |
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| 86 | } |
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| 87 | } |
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[1a80b4] | 88 | /////////////////////////////////////////////////////////////// |
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| 89 | // Choose a main variable if the user didn`t wish a // |
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| 90 | // special one. Returns level of main variable. // |
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| 91 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 92 | static int |
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[1a80b4] | 93 | choose_main_variable( const CanonicalForm & f, int Mainvar=0){ |
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| 94 | CanonicalForm remlc, newlc; |
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| 95 | int n= level(f), mainvar= Mainvar; |
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| 96 | |
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| 97 | if (mainvar != 0) return mainvar ; // We force use of the wished mainvar |
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| 98 | remlc= LC(f,n); mainvar = n; |
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| 99 | if ( totaldegree(remlc)==0 ){ remlc=f.genOne() ; } |
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[e2ca88] | 100 | DEBOUTLN(CERR, "remlc= " , remlc); |
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[aa7480c] | 101 | for ( int i=n-1; i>=1; i-- ) |
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| 102 | { |
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[1a80b4] | 103 | newlc= LC(f,i); |
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| 104 | if ( totaldegree(newlc)==0 ){ newlc=f.genOne() ; } |
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[e2ca88] | 105 | DEBOUTLN(CERR, "newlc= " , newlc); |
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[1a80b4] | 106 | if ( (remlc.isOne()) && (newlc.isOne()) ){ // take care of the degrees |
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| 107 | if ( degree(f,i) < degree(f,mainvar) ){ |
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[0be2bc] | 108 | remlc= newlc; |
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| 109 | mainvar= i; |
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[1a80b4] | 110 | } |
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| 111 | } |
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| 112 | else if ( (! remlc.isOne() ) && ( newlc.isOne() ) ){ |
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[0be2bc] | 113 | remlc= newlc; |
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[1a80b4] | 114 | mainvar= i; |
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| 115 | } |
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| 116 | } |
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| 117 | return mainvar; |
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| 118 | } |
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| 119 | |
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| 120 | /////////////////////////////////////////////////////////////// |
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| 121 | // Check if the derivative is nonzero for oldmainvar. // |
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| 122 | // Returns the level of the choosen main variable. // |
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| 123 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 124 | static int |
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[1a80b4] | 125 | necessary_condition( const CanonicalForm & F, int oldmainvar){ |
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| 126 | CanonicalForm g; |
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| 127 | int n=level(F); |
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| 128 | |
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[0be2bc] | 129 | g= swapvar(F,oldmainvar,n); |
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[1a80b4] | 130 | g= g.deriv(); |
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[0be2bc] | 131 | if ( g.isZero() ) |
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[52e543] | 132 | { |
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| 133 | for ( int i=n; i>=1; i-- ) |
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| 134 | { |
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[0be2bc] | 135 | g= swapvar(F,i,n); |
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[1a80b4] | 136 | g= g.deriv(); |
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| 137 | if ( ! g.isZero() ) return i; |
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| 138 | } |
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[52e543] | 139 | } |
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[1a80b4] | 140 | return oldmainvar; |
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| 141 | } |
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| 142 | |
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| 143 | /////////////////////////////////////////////////////////////// |
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| 144 | // Make F monic. Return monic polynomial. // |
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| 145 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 146 | static CanonicalForm |
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[7fa52c2] | 147 | make_monic( const CanonicalForm & F, const CanonicalForm & lt) |
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| 148 | { |
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[1a80b4] | 149 | CanonicalForm intermediatpoly,f; |
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| 150 | Variable x(level(F)); |
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| 151 | |
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| 152 | if ( degree(lt) == 0 ) f= 1/lt * F ; |
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[7fa52c2] | 153 | else |
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| 154 | { |
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[1a80b4] | 155 | intermediatpoly= power(lt,degree(F)-1); |
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| 156 | for ( int i=0; i<=degree(F); i++ ) |
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| 157 | if ( ! F[i].isZero()) |
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[0be2bc] | 158 | f+= (F[i] * intermediatpoly*power(x,i))/power(lt,i); |
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[1a80b4] | 159 | } |
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| 160 | return f; |
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| 161 | } |
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| 162 | |
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| 163 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 164 | // Decide whether num/denum (num,denum both from the // |
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[1a80b4] | 165 | // FiniteFielddomain) lies in the RationalDomain. // |
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| 166 | // If false, return num/denum else return the zero poly from // |
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| 167 | // the FiniteFielddomain. // |
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| 168 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 169 | static CanonicalForm |
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[1a80b4] | 170 | is_rational( const CanonicalForm & num, const CanonicalForm & denum ){ |
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| 171 | CanonicalForm a, b; |
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| 172 | int retvalue; |
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| 173 | |
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| 174 | retvalue= mydivremt(num,denum,a,b); |
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[e89e56] | 175 | if ( retvalue && b == num.genZero() ) // num/denum from FFdomain |
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[1a80b4] | 176 | return a; |
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| 177 | else // num/denum is rational |
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| 178 | return num.genZero(); |
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| 179 | } |
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| 180 | |
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| 181 | /////////////////////////////////////////////////////////////// |
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| 182 | // lt_is_product returns 1 iff lt is a product, 0 iff lt is // |
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| 183 | // a sum. // |
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| 184 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 185 | static int |
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[1a80b4] | 186 | lt_is_product( const CanonicalForm & lt ){ |
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| 187 | CFList result; |
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| 188 | |
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| 189 | result= get_Terms(lt); |
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| 190 | if ( result.length() > 1 ) return 0; |
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| 191 | else return 1; |
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| 192 | } |
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| 193 | |
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| 194 | /////////////////////////////////////////////////////////////// |
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| 195 | // Reverse the make_monic transformation. // |
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| 196 | // Return the list of factors. // |
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| 197 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 198 | static CFFList |
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[265aa7] | 199 | not_monic( const CFFList & TheList, const CanonicalForm & ltt, const CanonicalForm & F, int levelF) |
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| 200 | { |
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[1a80b4] | 201 | CFFList Returnlist,IntermediateList; |
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| 202 | CFFListIterator i; |
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| 203 | CanonicalForm intermediate,lt= ltt,savelc; |
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| 204 | CanonicalForm numerator,denumerator,test,a,b; |
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| 205 | Variable x(level(F)); |
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| 206 | int test1; |
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| 207 | |
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[aa7480c] | 208 | if ( lt.isOne() ) return TheList; // the poly was already monic |
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[265aa7] | 209 | if ( TheList.length() <= 1 ) // only one factor to substitute back |
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| 210 | { |
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[1a80b4] | 211 | if ( totaldegree(lt) == 0 ) // lt is type numeric |
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| 212 | Returnlist.append( CFFactor(lt*TheList.getFirst().factor(), |
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[0be2bc] | 213 | TheList.getFirst().exp()) ); |
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[265aa7] | 214 | else |
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| 215 | { |
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[1a80b4] | 216 | intermediate = F(x*lt, levelF)/power(lt,degree(F,levelF)-1); |
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| 217 | Returnlist.append(CFFactor(intermediate,TheList.getFirst().exp())); |
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| 218 | } |
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| 219 | } |
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[265aa7] | 220 | else // more then one factor |
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| 221 | { |
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[1a80b4] | 222 | IntermediateList= TheList; |
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| 223 | if ( totaldegree(lt) == 0 ){ // lt is type numeric;(SqrFree-use, see above) |
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| 224 | Returnlist.append( CFFactor(lt*IntermediateList.getFirst().factor() |
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[0be2bc] | 225 | , IntermediateList.getFirst().exp()) ); |
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[1a80b4] | 226 | IntermediateList.removeFirst(); |
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| 227 | Returnlist= Union(Returnlist,IntermediateList); |
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| 228 | } |
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[265aa7] | 229 | else // lt is a) a product or b) a sum of terms |
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| 230 | { |
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| 231 | if ( lt_is_product(lt) ) // case a) |
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| 232 | { |
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[e2ca88] | 233 | DEBOUTLN(CERR, "lt_is_product: ", lt); |
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[0be2bc] | 234 | savelc= content(lt) ; // can we simplify to savelc= lc(lt); ? |
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| 235 | while ( getNumVars(savelc) != 0 ) |
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| 236 | savelc= content(savelc); |
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[265aa7] | 237 | for ( i=TheList; i.hasItem();i++ ) |
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| 238 | { |
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[0be2bc] | 239 | numerator= i.getItem().factor(); |
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| 240 | numerator= numerator(x*lt,levelF); // x <- x*lt |
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| 241 | denumerator= power(lt,degree(F,levelF)-1); // == lt^(1-degree(F,x) |
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[e89e56] | 242 | while (numerator.genZero() == is_rational(numerator, denumerator)) |
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[0be2bc] | 243 | numerator*= lt; |
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| 244 | intermediate= is_rational(numerator,denumerator); |
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| 245 | |
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| 246 | Returnlist.append( CFFactor(lc(content(intermediate))*intermediate/content(intermediate), i.getItem().exp() ) ); |
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| 247 | } |
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| 248 | // Now we add a test. If product(factors)/F is a multiple of |
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| 249 | // savelc, we have to add 1/multiplicity to the factors |
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| 250 | IntermediateList= Returnlist; |
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| 251 | intermediate= 1; |
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| 252 | for ( CFFListIterator j=IntermediateList; j.hasItem(); j++) |
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| 253 | intermediate*= j.getItem().factor(); |
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| 254 | test1= mydivremt( intermediate,F,a,b); |
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[e89e56] | 255 | if ( test1 && b == intermediate.genZero() ) // Yupp! |
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[265aa7] | 256 | { |
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[0be2bc] | 257 | IntermediateList.append(CFFactor(1/a,1)); |
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| 258 | Returnlist= IntermediateList; |
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| 259 | } |
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| 260 | else { Returnlist= IntermediateList; } |
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[1a80b4] | 261 | } |
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[265aa7] | 262 | else // case b) |
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| 263 | { |
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[e2ca88] | 264 | DEBOUTLN(CERR, "lt_is_sum: ", lt); |
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[0be2bc] | 265 | CanonicalForm save_denumerator= 1; |
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[265aa7] | 266 | for ( i=TheList; i.hasItem(); i++ ) |
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| 267 | { |
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[0be2bc] | 268 | numerator= i.getItem().factor(); |
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| 269 | numerator= numerator(x*lt,levelF); // x <- x*lt |
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| 270 | denumerator= power(lt,degree(numerator,levelF)); // == lt^(-degree(numerator,x) |
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| 271 | test= content(numerator,x); |
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| 272 | test1= mydivremt(denumerator,test,a,b); |
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[e89e56] | 273 | if ( test1 && b == numerator.genZero() ) // Yupp! |
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[265aa7] | 274 | { |
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[0be2bc] | 275 | save_denumerator*= a; |
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| 276 | Returnlist.append(CFFactor(numerator/test ,1)); |
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| 277 | } |
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[265aa7] | 278 | else |
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| 279 | { |
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[a13956] | 280 | factoryError("libfac: ERROR: not_monic1: case lt is a sum."); |
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[0be2bc] | 281 | } |
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| 282 | } |
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| 283 | // Now we add a test if we did the right thing: |
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| 284 | // save_denumerator should be a multiple of the leading coeff |
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| 285 | test1= mydivremt(save_denumerator,lt,a,b); |
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[e89e56] | 286 | if ( test1 && b == save_denumerator.genZero() ) // Yupp! |
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[0be2bc] | 287 | // We have to multiply one of the factors with |
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| 288 | // the multiplicity of the save_denumerator <-> lc |
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| 289 | // the following will do what we want |
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[e89e56] | 290 | Returnlist= myUnion( CFFList(CFFactor(1/a,1)),Returnlist) ; |
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[265aa7] | 291 | else |
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| 292 | { |
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[a13956] | 293 | factoryError("libfac: ERROR: not_monic2: case lt is a sum."); |
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[0be2bc] | 294 | } |
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[1a80b4] | 295 | } |
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| 296 | } |
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| 297 | } |
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[e2ca88] | 298 | DEBOUTLN(CERR,"Returnlist: ", Returnlist); |
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[1a80b4] | 299 | return Returnlist; |
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| 300 | } |
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| 301 | |
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| 302 | /////////////////////////////////////////////////////////////// |
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| 303 | // Substitute the (Variable,Value)-Pair(s) from Substitution-// |
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| 304 | // list into the polynomial F. Returns the resulting poly. // |
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| 305 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 306 | static CanonicalForm |
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[1a80b4] | 307 | substitutePoly( const CanonicalForm & F, const SFormList & Substitutionlist){ |
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| 308 | CanonicalForm f= F; |
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| 309 | |
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| 310 | for ( SFormListIterator i=Substitutionlist; i.hasItem(); i++ ) |
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| 311 | f= f(i.getItem().exp(),level(i.getItem().factor())); |
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| 312 | return f; |
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| 313 | } |
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| 314 | |
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| 315 | /////////////////////////////////////////////////////////////// |
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| 316 | // Find specialization values for the poly F. Returns 0 if // |
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| 317 | // procedure failed, 1 otherwise. On success Substitutionlist// |
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| 318 | // holds (Variable,Value)-pairs. On failure we only have a // |
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| 319 | // partitial list. // |
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| 320 | /////////////////////////////////////////////////////////////// |
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| 321 | // *** This is the version with extensions *** // |
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| 322 | /////////////////////////////////////////////////////////////// |
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| 323 | |
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| 324 | /////////////////////////////////////////////////////////////// |
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| 325 | // is CF g ok? // |
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| 326 | /////////////////////////////////////////////////////////////// |
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| 327 | static int |
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[aa7480c] | 328 | various_tests( const CanonicalForm & g, int deg, int vars_left) |
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| 329 | { |
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[1a80b4] | 330 | CFMap m; |
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| 331 | |
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| 332 | if ( degree(g) == deg ) // degrees match |
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| 333 | if ( level(compress(g,m)) == (vars_left) ) // exactly one variable less |
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[e89e56] | 334 | if ( SqrFreeTest(g,1) ) // poly is sqrfree |
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[aa7480c] | 335 | if ( gcd(g,g.deriv()).isOne() ) // Discriminante != 0 |
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[0be2bc] | 336 | return 1; |
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[1a80b4] | 337 | return 0; |
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| 338 | } |
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| 339 | |
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| 340 | /////////////////////////////////////////////////////////////// |
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| 341 | // specialize one variable over the given field. // |
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| 342 | /////////////////////////////////////////////////////////////// |
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[0be2bc] | 343 | // substitutes in poly f of degree deg with former |
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[1a80b4] | 344 | // former_nr_of_variables variables the variable nr_of_variable ; |
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| 345 | // this is done in the field of Char getCharacteristic() and |
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| 346 | // Extension given by Extgenerator. |
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| 347 | /////////////////////////////////////////////////////////////// |
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| 348 | static int |
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[b96e07] | 349 | specialize_variable( CanonicalForm & f, int deg, SFormList & Substitutionlist, int nr_of_variable, |
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| 350 | int former_nr_of_variables, CFGenerator & Extgenerator ){ |
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| 351 | CanonicalForm g; |
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| 352 | Variable x(nr_of_variable); |
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| 353 | |
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[e2ca88] | 354 | DEBOUTLN(CERR, "specialize_variable: called with: ", f); |
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[b96e07] | 355 | for ( Extgenerator.reset(); Extgenerator.hasItems(); Extgenerator.next() ){ |
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[e2ca88] | 356 | DEBOUTLN(CERR, " specialize_variable: trying: ", Extgenerator.item()); |
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[b96e07] | 357 | g= f( Extgenerator.item(), x ); |
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[e2ca88] | 358 | DEBOUTLN(CERR, " specialize_variable: resulting g= ", g); |
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[b96e07] | 359 | if ( various_tests(g,deg,former_nr_of_variables - nr_of_variable ) ){ |
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| 360 | Substitutionlist.insert(SForm(x,Extgenerator.item())); // append (Var,value) pair |
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| 361 | f= g; |
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| 362 | return 1; |
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| 363 | } |
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| 364 | } |
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| 365 | return 0; |
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| 366 | } |
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| 367 | static int |
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| 368 | specialize_agvariable( CanonicalForm & f, int deg, SFormList & Substitutionlist, int nr_of_variable, |
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| 369 | int former_nr_of_variables, AlgExtGenerator & Extgenerator ){ |
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[1a80b4] | 370 | CanonicalForm g; |
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| 371 | Variable x(nr_of_variable); |
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| 372 | |
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[e2ca88] | 373 | DEBOUTLN(CERR, "specialize_variable: called with: ", f); |
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[1a80b4] | 374 | for ( Extgenerator.reset(); Extgenerator.hasItems(); Extgenerator.next() ){ |
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[e2ca88] | 375 | DEBOUTLN(CERR, " specialize_variable: trying: ", Extgenerator.item()); |
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[1a80b4] | 376 | g= f( Extgenerator.item(), x ); |
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[e2ca88] | 377 | DEBOUTLN(CERR, " specialize_variable: resulting g= ", g); |
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[0be2bc] | 378 | if ( various_tests(g,deg,former_nr_of_variables - nr_of_variable ) ){ |
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[1a80b4] | 379 | Substitutionlist.insert(SForm(x,Extgenerator.item())); // append (Var,value) pair |
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| 380 | f= g; |
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| 381 | return 1; |
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| 382 | } |
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| 383 | } |
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| 384 | return 0; |
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| 385 | } |
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| 386 | |
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| 387 | /////////////////////////////////////////////////////////////// |
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| 388 | // generate a minpoly of degree degree_of_Extension in the // |
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| 389 | // field getCharacteristik()^Extension. // |
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| 390 | /////////////////////////////////////////////////////////////// |
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[4a81ec] | 391 | CanonicalForm |
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[1a80b4] | 392 | generate_mipo( int degree_of_Extension , const Variable & Extension ){ |
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[0be2bc] | 393 | FFRandom gen; |
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[21263cf] | 394 | if (degree (Extension) < 0) |
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| 395 | factoryError("libfac: evaluate: Extension not inFF() or inGF() !"); |
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[1a80b4] | 396 | return find_irreducible( degree_of_Extension, gen, Variable(1) ); |
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| 397 | } |
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| 398 | |
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| 399 | /////////////////////////////////////////////////////////////// |
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| 400 | // Try to find a specialization for f over the field of char // |
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| 401 | // f.getCharacteristic() and (possible) extension defined by // |
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| 402 | // the variable Extension . // |
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| 403 | // Returns 1 iff specialisation was found, 0 otherwise. // |
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| 404 | // If 0 is returned there are variables left to substitute. // |
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| 405 | // We check if Substitutionlist.length() > 0, i.e. we // |
---|
| 406 | // previously tried to find specialization values for some // |
---|
| 407 | // values. We take them and work with the resulting poly. // |
---|
| 408 | /////////////////////////////////////////////////////////////// |
---|
| 409 | static int |
---|
[38e7b3] | 410 | try_specializePoly(const CanonicalForm & f, const Variable & Extension, int deg, SFormList & Substitutionlist, int ii,int j) |
---|
| 411 | { |
---|
[1a80b4] | 412 | int ok,i= ii; |
---|
| 413 | CanonicalForm ff= f; |
---|
| 414 | |
---|
| 415 | if ( Substitutionlist.length() > 0 ){ // we formerly tried to specialize |
---|
| 416 | ff= substitutePoly(f,Substitutionlist); // substitute found values |
---|
| 417 | i= Substitutionlist.length() + 1; |
---|
| 418 | } |
---|
| 419 | |
---|
[38e7b3] | 420 | if ( degree(Extension) > 0 ) |
---|
| 421 | { // working over Extensions |
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[e2ca88] | 422 | DEBOUTLN(CERR, "try_specializePoly: working over Extensions: ", Extension); |
---|
[38e7b3] | 423 | if (Extension.level() > 0) |
---|
| 424 | { |
---|
| 425 | // AlgExtGenerator g(Extension,minpoly ); |
---|
| 426 | // for ( int k=i ; k<j ; k++ ) // try to find specialization for all |
---|
| 427 | // { // variables (# = k ) beginning with the |
---|
| 428 | // // starting value i |
---|
| 429 | // ok= specialize_agvariable( ff, deg, Substitutionlist, k, j, g ); |
---|
| 430 | // if ( ! ok ) return 0; // we failed |
---|
| 431 | // } |
---|
[52e543] | 432 | #ifndef NDEBUG |
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[7cb56a9] | 433 | //printf("libfac: try_specializePoly: extension level >0\n"); |
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[52e543] | 434 | #endif |
---|
[38e7b3] | 435 | return 0; // we failed |
---|
| 436 | } |
---|
| 437 | else |
---|
| 438 | { |
---|
| 439 | AlgExtGenerator g(Extension); |
---|
| 440 | for ( int k=i ; k<j ; k++ ) // try to find specialization for all |
---|
| 441 | { // variables (# = k ) beginning with the |
---|
[1a80b4] | 442 | // starting value i |
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[38e7b3] | 443 | ok= specialize_agvariable( ff, deg, Substitutionlist, k, j, g ); |
---|
| 444 | if ( ! ok ) return 0; // we failed |
---|
| 445 | } |
---|
[1a80b4] | 446 | } |
---|
| 447 | } |
---|
| 448 | else{ // working over the ground-field |
---|
| 449 | FFGenerator g; |
---|
[e2ca88] | 450 | DEBOUTMSG(CERR, "try_specializePoly: working over the ground-field."); |
---|
[1a80b4] | 451 | for ( int k=i ; k<j ; k++ ){ |
---|
| 452 | ok= specialize_variable( ff, deg, Substitutionlist, k, j, g ); |
---|
| 453 | if ( ! ok ) return 0; // we failed |
---|
| 454 | } |
---|
| 455 | } |
---|
| 456 | return 1; |
---|
| 457 | } |
---|
| 458 | |
---|
| 459 | static int |
---|
[070c1b4] | 460 | specializePoly(const CanonicalForm & f, Variable & Extension, int deg, SFormList & Substitutionlist, int i,int j) |
---|
| 461 | { |
---|
[1a80b4] | 462 | Variable minpoly= Extension; |
---|
| 463 | int ok,extended= degree(Extension), working_over_extension; |
---|
| 464 | |
---|
| 465 | // Remember if we are working over an extension-field |
---|
| 466 | if ( extended >= 2 ) { working_over_extension = 1; } |
---|
| 467 | else { working_over_extension = 0; extended = 1; } |
---|
| 468 | // First try: |
---|
| 469 | ok = try_specializePoly(f,minpoly,deg,Substitutionlist,i,j); |
---|
[070c1b4] | 470 | while ( ! ok ) // we have to extend! |
---|
| 471 | { |
---|
| 472 | SFormList origS=Substitutionlist; |
---|
[1a80b4] | 473 | extended+= 1; |
---|
[070c1b4] | 474 | if ( ! working_over_extension ) |
---|
| 475 | { |
---|
[21263cf] | 476 | if (!hasMipo(Extension)) |
---|
| 477 | minpoly= rootOf (generate_mipo (extended, Extension)); |
---|
| 478 | else |
---|
| 479 | { |
---|
| 480 | setReduce (Extension, false); |
---|
| 481 | setMipo (minpoly, generate_mipo ( extended, Extension)); |
---|
| 482 | setReduce (Extension, true); |
---|
| 483 | } |
---|
[1a80b4] | 484 | Extension= minpoly; |
---|
| 485 | ok= try_specializePoly(f,minpoly,deg,Substitutionlist,i,j); |
---|
[070c1b4] | 486 | if (!ok) |
---|
| 487 | Substitutionlist=origS; |
---|
[1a80b4] | 488 | } |
---|
[a13956] | 489 | else |
---|
| 490 | { |
---|
| 491 | factoryError("libfac: spezializePoly ERROR: Working over given extension-field not yet implemented!"); |
---|
[1a80b4] | 492 | return 0; |
---|
| 493 | } |
---|
| 494 | } |
---|
| 495 | return 1; |
---|
| 496 | } |
---|
| 497 | |
---|
| 498 | |
---|
| 499 | // This is a procedure to play with: lot's of parameters! |
---|
| 500 | // returns: 0 iff no success (possibly because Extension isn't great enough |
---|
| 501 | // >0 iff g (univariate) splits into n factors; |
---|
| 502 | // if n>0 BestEvaluationpoint contains the choice of values for the variables |
---|
| 503 | // |
---|
| 504 | // tries to find at least maxtries evaluation points |
---|
| 505 | // if g factored sametries into the same number of poly's the procedure stops |
---|
| 506 | // if we tried failtries evaluations not found valid, we stop. Perhaps |
---|
| 507 | // Extension isn't big enough! |
---|
| 508 | static int |
---|
[1048e0c] | 509 | evaluate( int maxtries, int sametries, int failtries, const CanonicalForm &f , const Variable & Extension, const CanonicalForm &mipo, SFormList & BestEvaluationpoint, CFFList & BestFactorisation ){ |
---|
[1a80b4] | 510 | int minfactors=degree(f),degf=degree(f),n=level(f.mvar())-1; |
---|
| 511 | SFormList minEvaluation; |
---|
| 512 | CFFList minFactorisation; |
---|
| 513 | int samefactors=0, failedfactor=0, tried=0; |
---|
| 514 | FFRandom gen; |
---|
| 515 | CFFList unilist; |
---|
| 516 | |
---|
[0be2bc] | 517 | if ( degree(Extension) >0 ) GFRandom gen; |
---|
[a13956] | 518 | else |
---|
| 519 | { |
---|
| 520 | if ( degree(Extension) == 0 ) FFRandom gen; |
---|
| 521 | else |
---|
| 522 | { |
---|
| 523 | factoryError("libfac: evaluate: Extension not inFF() or inGF() !"); |
---|
| 524 | } |
---|
| 525 | } |
---|
[1a80b4] | 526 | REvaluation k(1,n,gen); |
---|
[4a81ec] | 527 | k.nextpoint(); |
---|
[a13956] | 528 | for ( int i=1; i<=maxtries ; i++) |
---|
| 529 | { |
---|
[4a81ec] | 530 | // k.nextpoint(); |
---|
[1a80b4] | 531 | SFormList Substitutionlist; |
---|
| 532 | for ( int j=1; j<=n; j++ ) |
---|
[0be2bc] | 533 | Substitutionlist.insert(SForm(Variable(j),k[j])); |
---|
[1a80b4] | 534 | k.nextpoint(); |
---|
| 535 | CanonicalForm g=substitutePoly(f,Substitutionlist); |
---|
[a13956] | 536 | if ( various_tests(g, degf,1) ) |
---|
| 537 | { // found a valid point |
---|
[1a80b4] | 538 | failedfactor = 0; tried += 1; |
---|
| 539 | if ( degree(Extension) == 0 ) |
---|
[0be2bc] | 540 | unilist = factorize(g,1); // poly is sqr-free! |
---|
[1a80b4] | 541 | else |
---|
[b4ea1d] | 542 | { |
---|
[1048e0c] | 543 | unilist = factorize2(g,Extension,mipo); |
---|
| 544 | } |
---|
[aa7480c] | 545 | if (unilist.length() <= minfactors ) |
---|
| 546 | { |
---|
[0be2bc] | 547 | minfactors=unilist.length(); |
---|
| 548 | minEvaluation=Substitutionlist; |
---|
| 549 | minFactorisation=unilist; |
---|
[1a80b4] | 550 | } |
---|
| 551 | else samefactors +=1; |
---|
| 552 | |
---|
[aa7480c] | 553 | if (unilist.length() == 1 ) // wow! we found f is irreducible! |
---|
| 554 | { |
---|
[0be2bc] | 555 | BestEvaluationpoint=minEvaluation; |
---|
| 556 | BestFactorisation=minFactorisation; |
---|
| 557 | return 1; |
---|
[1a80b4] | 558 | } |
---|
| 559 | |
---|
[aa7480c] | 560 | if ( samefactors >= sametries ) // now we stop ( maybe polynomial *has* |
---|
| 561 | // minfactors factors? ) |
---|
| 562 | { |
---|
[0be2bc] | 563 | BestEvaluationpoint=minEvaluation; |
---|
| 564 | BestFactorisation=minFactorisation; |
---|
| 565 | return minfactors; |
---|
[1a80b4] | 566 | } |
---|
| 567 | |
---|
| 568 | } |
---|
[aa7480c] | 569 | else |
---|
| 570 | failedfactor += 1; |
---|
[1a80b4] | 571 | |
---|
[aa7480c] | 572 | if ( failedfactor >= failtries ) // now we stop ( perhaps Extension isn't |
---|
| 573 | // big enough ) |
---|
| 574 | { |
---|
[1a80b4] | 575 | if ( tried == 0 ) |
---|
[0be2bc] | 576 | return 0; |
---|
[aa7480c] | 577 | else |
---|
| 578 | { |
---|
[0be2bc] | 579 | BestEvaluationpoint=minEvaluation; |
---|
| 580 | BestFactorisation=minFactorisation; |
---|
| 581 | return minfactors; |
---|
[1a80b4] | 582 | } |
---|
| 583 | } |
---|
| 584 | } |
---|
| 585 | BestEvaluationpoint=minEvaluation; |
---|
| 586 | BestFactorisation=minFactorisation; |
---|
| 587 | return minfactors; |
---|
| 588 | } |
---|
| 589 | |
---|
| 590 | /////////////////////////////////////////////////////////////// |
---|
| 591 | // A factorization routine for a sqrfree polynomial. // |
---|
| 592 | // Returns the list of factors. // |
---|
| 593 | /////////////////////////////////////////////////////////////// |
---|
[0be2bc] | 594 | CFFList |
---|
[8de151] | 595 | Factorized( const CanonicalForm & F, const CanonicalForm & alpha, int Mainvar) |
---|
| 596 | { |
---|
[1a80b4] | 597 | CanonicalForm f,lt,ff,ffuni; |
---|
[639047e] | 598 | Variable Extension=alpha.mvar(); |
---|
[1a80b4] | 599 | CFFList Outputlist,UnivariateFactorlist,Outputlist2; |
---|
| 600 | SFormList Substitutionlist, Evaluationpoint; |
---|
| 601 | CFFactor copy; |
---|
| 602 | int mainvar=Mainvar,success,oldmainvar; |
---|
| 603 | CFMap m; |
---|
| 604 | |
---|
[3e55bc] | 605 | // INTERRUPTHANDLER |
---|
| 606 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 607 | // INTERRUPTHANDLER |
---|
| 608 | |
---|
[924d8f] | 609 | if (F.inCoeffDomain()) { return CFFList(CFFactor(F,1)); } |
---|
[8de151] | 610 | if ( F.isUnivariate() ) // could have lost one Variable elsewhere |
---|
| 611 | { |
---|
| 612 | if ( degree(Extension) == 0 ) |
---|
| 613 | { |
---|
[1a80b4] | 614 | TIMING_START(evaluate_time); |
---|
| 615 | Outputlist = factorize(F,1); // poly is sqr-free |
---|
| 616 | TIMING_END(evaluate_time); |
---|
| 617 | return Outputlist; |
---|
| 618 | } |
---|
[8de151] | 619 | else |
---|
| 620 | { |
---|
[1048e0c] | 621 | if (Extension.level()<0) |
---|
[e2ca88] | 622 | DEBOUTLN(CERR, "Univ. Factorization over extension of degree ", |
---|
[0be2bc] | 623 | degree(getMipo(Extension,'x')) ); |
---|
[5c4b32] | 624 | else |
---|
[e2ca88] | 625 | DEBOUTLN(CERR, "Univ. Factorization over extension of level ??", |
---|
[1048e0c] | 626 | Extension.level()); |
---|
[1a80b4] | 627 | TIMING_START(evaluate_time); |
---|
[f152c5] | 628 | Outputlist = factorize2(F,Extension,alpha); |
---|
[1a80b4] | 629 | TIMING_END(evaluate_time); |
---|
| 630 | return Outputlist; |
---|
| 631 | } |
---|
| 632 | } |
---|
| 633 | |
---|
| 634 | if ( Mainvar ) oldmainvar=Mainvar; else oldmainvar=level(F); |
---|
| 635 | // First choose a main variable; this may be revisted in the next step |
---|
| 636 | mainvar = choose_main_variable(F); |
---|
| 637 | // Let`s look if @f/@mainvar is nonzero |
---|
| 638 | mainvar = necessary_condition(F,mainvar); |
---|
| 639 | // Now we have definetly choosen a main variable |
---|
| 640 | // swap poly such that the mainvar has highest level |
---|
| 641 | f=swapvar(F,mainvar,level(F)); |
---|
[0be2bc] | 642 | |
---|
[3e55bc] | 643 | // INTERRUPTHANDLER |
---|
| 644 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 645 | // INTERRUPTHANDLER |
---|
| 646 | |
---|
[1a80b4] | 647 | if ( oldmainvar != mainvar ){ |
---|
[e2ca88] | 648 | DEBOUTSL(CERR); DEBOUT(CERR,"Swapped poly ", F); |
---|
| 649 | DEBOUT(CERR, " in ", f); DEBOUTNL(CERR); |
---|
| 650 | DEBOUTSL(CERR); DEBOUT(CERR,"Swapped ", oldmainvar ); |
---|
| 651 | DEBOUT(CERR, " <-- ", mainvar ); DEBOUT(CERR, " Mainvar= ", f.mvar()); |
---|
| 652 | DEBOUTNL(CERR); |
---|
[1a80b4] | 653 | ff = f.deriv(); |
---|
| 654 | TIMING_START(discr_time); |
---|
[38e7b3] | 655 | ffuni = gcd(f,ff); |
---|
[1a80b4] | 656 | TIMING_END(discr_time); |
---|
[20722e4] | 657 | if ( !(ffuni.isOne()) ){ //discriminante nonzero: split poly |
---|
[e2ca88] | 658 | DEBOUTLN(CERR,"Nontrivial GCD of f= ", f); |
---|
| 659 | DEBOUTLN(CERR," and @f= ", ff); |
---|
| 660 | DEBOUTLN(CERR," GCD(f,@f)= ", ffuni); |
---|
[1a80b4] | 661 | ff=f/ffuni; |
---|
| 662 | CFFList Outputlist_a, Outputlist_b; |
---|
| 663 | Outputlist_a = Factorized(ff,alpha); |
---|
[e2ca88] | 664 | DEBOUTLN(CERR, "Outputlist_a = ", Outputlist_a); |
---|
[1a80b4] | 665 | Outputlist_b = Factorized(ffuni,alpha); |
---|
[e2ca88] | 666 | DEBOUTLN(CERR, "Outputlist_b = ", Outputlist_b); |
---|
[e89e56] | 667 | Outputlist = myUnion(Outputlist_a, Outputlist_b); |
---|
[1a80b4] | 668 | // have to back-swapvar the factors.... |
---|
| 669 | for ( CFFListIterator i=Outputlist; i.hasItem(); i++ ){ |
---|
[0be2bc] | 670 | copy=i.getItem(); |
---|
| 671 | Outputlist2.append(CFFactor(swapvar(copy.factor(),oldmainvar,mainvar),copy.exp())); |
---|
[1a80b4] | 672 | } |
---|
[e2ca88] | 673 | DEBOUTLN(CERR, "Outputlist2 (a+b swapped) (to return) = ", Outputlist2); |
---|
[1a80b4] | 674 | return Outputlist2; |
---|
| 675 | } |
---|
| 676 | } |
---|
| 677 | |
---|
| 678 | // Check special cases |
---|
| 679 | for ( int i=1; i<=level(F); i++) |
---|
[aa7480c] | 680 | { |
---|
[8e0cdf] | 681 | if ( degree(f,Variable(i) ) == 1 ) |
---|
[aa7480c] | 682 | //test trivial case; only true iff F is primitiv w.r.t every variable; else check (if F=ax+b) gcd(a,b)=1 ? |
---|
| 683 | { |
---|
[e2ca88] | 684 | DEBOUTLN(CERR, "Trivial case: ", F); |
---|
[1a80b4] | 685 | Outputlist.append(CFFactor(F,1)); |
---|
| 686 | return Outputlist; |
---|
| 687 | } |
---|
[aa7480c] | 688 | } |
---|
[1a80b4] | 689 | |
---|
| 690 | // Look at the leading term: |
---|
| 691 | lt = LC(f); |
---|
[e2ca88] | 692 | DEBOUTLN(CERR, "Leading term: ", lt); |
---|
[aa7480c] | 693 | //if ( lt != f.genOne() ) |
---|
| 694 | if ( !lt.isOne() ) |
---|
[38e7b3] | 695 | { |
---|
[1a80b4] | 696 | // make the polynomial monic in the main variable |
---|
| 697 | ff = make_monic(f,lt); ffuni = ff; |
---|
[e2ca88] | 698 | DEBOUTLN(CERR, "make_monic returned: ", ff); |
---|
[1a80b4] | 699 | } |
---|
| 700 | else{ ff= f; ffuni= ff; } |
---|
| 701 | |
---|
| 702 | TIMING_START(evaluate_time); |
---|
[1048e0c] | 703 | success=evaluate(min(10,max(degree(ff), 5)), min(degree(ff),3), min(degree(ff),3), ff, Extension, alpha, Substitutionlist,UnivariateFactorlist); |
---|
[e2ca88] | 704 | DEBOUTLN(CERR, "Returned from evaluate: success: ", success); |
---|
[38e7b3] | 705 | for ( SFormListIterator ii=Substitutionlist; ii.hasItem(); ii++ ) |
---|
| 706 | { |
---|
[e2ca88] | 707 | DEBOUTLN(CERR, "Substituting ", ii.getItem().factor()); |
---|
| 708 | DEBOUTLN(CERR, " with value: ", ii.getItem().exp()); |
---|
[1a80b4] | 709 | } |
---|
| 710 | |
---|
[38e7b3] | 711 | if ( success==0 ) // evalute wasn't successfull |
---|
| 712 | { |
---|
[1a80b4] | 713 | success= specializePoly(ffuni,Extension,degree(ff),Substitutionlist,1,getNumVars(compress(ff,m))); |
---|
[e2ca88] | 714 | DEBOUTLN(CERR, "Returned from specializePoly: success: ", success); |
---|
[38e7b3] | 715 | if (success == 0 ) // No spezialisation could be found |
---|
| 716 | { |
---|
[a13956] | 717 | factoryError("libfac: Factorize: ERROR: Not able to find a valid specialization!"); |
---|
[1a80b4] | 718 | Outputlist.append(CFFactor(F,1)); |
---|
| 719 | return Outputlist; |
---|
| 720 | } |
---|
[3e55bc] | 721 | |
---|
| 722 | // INTERRUPTHANDLER |
---|
| 723 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 724 | // INTERRUPTHANDLER |
---|
| 725 | |
---|
[1a80b4] | 726 | ffuni = substitutePoly(ff,Substitutionlist); |
---|
| 727 | // We now have an univariat poly; factorize that |
---|
[38e7b3] | 728 | if ( degree(Extension) == 0 ) |
---|
| 729 | { |
---|
[e2ca88] | 730 | DEBOUTMSG(CERR, "Univ. Factorization over the ground field"); |
---|
[1a80b4] | 731 | UnivariateFactorlist = factorize(ffuni,1); // univ. poly is sqr-free! |
---|
| 732 | } |
---|
[38e7b3] | 733 | else |
---|
| 734 | { |
---|
[e2ca88] | 735 | DEBOUTLN(CERR, "Univ. Factorization over extension of degree ", |
---|
[0be2bc] | 736 | degree(getMipo(Extension,'x')) ); |
---|
[1048e0c] | 737 | UnivariateFactorlist = factorize2(ffuni,Extension,alpha); |
---|
[1a80b4] | 738 | } |
---|
| 739 | } |
---|
[38e7b3] | 740 | else |
---|
| 741 | { |
---|
[0be2bc] | 742 | ffuni = substitutePoly(ff,Substitutionlist); |
---|
[1a80b4] | 743 | } |
---|
| 744 | TIMING_END(evaluate_time); |
---|
[38e7b3] | 745 | if (UnivariateFactorlist.length() == 1) |
---|
| 746 | { // poly is irreduzibel |
---|
[e2ca88] | 747 | DEBOUTLN(CERR, "Univ. poly is irreduzible: ", UnivariateFactorlist); |
---|
[1a80b4] | 748 | Outputlist.append(CFFactor(F,1)); |
---|
| 749 | return Outputlist; |
---|
| 750 | } |
---|
[38e7b3] | 751 | else |
---|
| 752 | { // we have factors |
---|
[e2ca88] | 753 | DEBOUTSL(CERR); |
---|
| 754 | DEBOUT(CERR, "Univariate poly has " , UnivariateFactorlist.length()); |
---|
| 755 | DEBOUT(CERR, " factors: ", ffuni); |
---|
| 756 | DEBOUT(CERR, " = ", UnivariateFactorlist); DEBOUTNL(CERR); |
---|
[1a80b4] | 757 | |
---|
[3e55bc] | 758 | // INTERRUPTHANDLER |
---|
| 759 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 760 | // INTERRUPTHANDLER |
---|
| 761 | |
---|
[1a80b4] | 762 | TIMING_START(hensel_time); |
---|
[8de151] | 763 | Outputlist = MultiHensel(ff,UnivariateFactorlist,Substitutionlist, alpha); |
---|
[e2ca88] | 764 | DEBOUTLN(CERR, "Outputlist after MultiHensel: ", Outputlist); |
---|
[1a80b4] | 765 | TIMING_END(hensel_time); |
---|
| 766 | |
---|
[3e55bc] | 767 | // INTERRUPTHANDLER |
---|
| 768 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 769 | // INTERRUPTHANDLER |
---|
| 770 | |
---|
[1a80b4] | 771 | TIMING_START(truefactor_time); |
---|
| 772 | Outputlist = Truefactors(ff, level(ff), Substitutionlist, Outputlist); |
---|
[e2ca88] | 773 | DEBOUTLN(CERR, "Outputlist after Truefactors: ", Outputlist); |
---|
[1a80b4] | 774 | TIMING_END(truefactor_time); |
---|
| 775 | |
---|
[3e55bc] | 776 | // INTERRUPTHANDLER |
---|
| 777 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 778 | // INTERRUPTHANDLER |
---|
| 779 | |
---|
[aa7480c] | 780 | //if ( lt != f.genOne() ) |
---|
| 781 | if ( !lt.isOne() ) |
---|
[52e543] | 782 | { |
---|
[1a80b4] | 783 | Outputlist = not_monic(Outputlist,lt,ff,level(ff)); |
---|
[e2ca88] | 784 | DEBOUTLN(CERR, "not_monic returned: ", Outputlist); |
---|
[1a80b4] | 785 | } |
---|
| 786 | |
---|
| 787 | // have to back-swapvar the factors.... |
---|
[52e543] | 788 | for ( CFFListIterator i=Outputlist; i.hasItem(); i++ ) |
---|
| 789 | { |
---|
| 790 | copy=i.getItem(); |
---|
| 791 | Outputlist2.append(CFFactor(swapvar(copy.factor(),oldmainvar,mainvar),copy.exp())); |
---|
[1a80b4] | 792 | } |
---|
| 793 | |
---|
| 794 | return Outputlist2; |
---|
| 795 | } |
---|
| 796 | } |
---|
| 797 | |
---|
[5299b6] | 798 | int cmpCF( const CFFactor & f, const CFFactor & g ); |
---|
| 799 | |
---|
[1a80b4] | 800 | /////////////////////////////////////////////////////////////// |
---|
| 801 | // The user front-end for a uni/multivariate factorization // |
---|
| 802 | // routine. F needs not to be SqrFree. // |
---|
| 803 | // Option of * choosing a main variable (n.y.i.) // |
---|
| 804 | // * choosing an algebraic extension (n.y.u.) // |
---|
| 805 | // * ensuring poly is sqrfree (n.y.i.) // |
---|
[b4ea1d] | 806 | // use Factorize(F,alpha,is_SqrFree) if not over Zp[x]/Q[x] // |
---|
[1a80b4] | 807 | /////////////////////////////////////////////////////////////// |
---|
[b6249e] | 808 | int find_mvar(const CanonicalForm &f); |
---|
[38e7b3] | 809 | CFFList Factorize(const CanonicalForm & F, int is_SqrFree ) |
---|
| 810 | { |
---|
[ee586a] | 811 | //out_cf("Factorize ",F,"\n"); |
---|
[9e47237] | 812 | CFFList Outputlist; |
---|
[1a80b4] | 813 | |
---|
[3e55bc] | 814 | // INTERRUPTHANDLER |
---|
| 815 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 816 | // INTERRUPTHANDLER |
---|
| 817 | |
---|
[e2ca88] | 818 | DEBINCLEVEL(CERR, "Factorize"); |
---|
| 819 | DEBOUTLN(CERR, "Called with F= ", F); |
---|
[9e9b7c] | 820 | if (( getCharacteristic() == 0 ) || (F.isUnivariate())) |
---|
[38e7b3] | 821 | { // char == 0 |
---|
[1a80b4] | 822 | TIMING_START(factorize_time); |
---|
[e2ca88] | 823 | //CERR << "Factoring in char=0 of " << F << " = " << Outputlist << "\n"; |
---|
[1a80b4] | 824 | Outputlist= factorize(F); |
---|
[3e55bc] | 825 | // Factorization in char=0 doesn't sometimes return at least two elements!!! |
---|
[0be2bc] | 826 | if ( getNumVars(Outputlist.getFirst().factor()) != 0 ) |
---|
[3e55bc] | 827 | Outputlist.insert(CFFactor(1,1)); |
---|
[e2ca88] | 828 | //CERR << " Factorize in char=0: returning with: " << Outputlist << "\n"; |
---|
[3e55bc] | 829 | TIMING_END(factorize_time); |
---|
[e2ca88] | 830 | DEBDECLEVEL(CERR, "Factorize"); |
---|
[3e55bc] | 831 | TIMING_PRINT(factorize_time, "\ntime used for factorization : "); |
---|
| 832 | return Outputlist; |
---|
[1a80b4] | 833 | } |
---|
[9e47237] | 834 | CFFList SqrFreeList,Intermediatelist,Outputlist2; |
---|
| 835 | ListIterator<CFFactor> i,j; |
---|
| 836 | CanonicalForm g=1,unit=1,r=1; |
---|
| 837 | Variable minpoly; // dummy |
---|
| 838 | int exp; |
---|
| 839 | CFMap m; |
---|
[1a80b4] | 840 | TIMING_START(factorize_time); |
---|
[b6249e] | 841 | // search an "optimal" main variavble |
---|
| 842 | int mv=F.level(); |
---|
[9e9b7c] | 843 | if ((mv != LEVELBASE) /* && (! F.isUnivariate()) */) |
---|
[b6249e] | 844 | { |
---|
| 845 | mv=find_mvar(F); |
---|
| 846 | if (mv!=F.level()) |
---|
| 847 | { |
---|
| 848 | swapvar(F,Variable(mv),F.mvar()); |
---|
| 849 | } |
---|
| 850 | } |
---|
| 851 | |
---|
[1a80b4] | 852 | /////// |
---|
| 853 | // Maybe it`s better to add a sqrfree-test before? |
---|
| 854 | // (If gcd is fast...) |
---|
| 855 | /////// |
---|
[e89e56] | 856 | // if ( ! SqrFreeTest(F) ){ |
---|
[38e7b3] | 857 | if ( ! is_SqrFree ) |
---|
| 858 | { |
---|
[3e55bc] | 859 | TIMING_START(sqrfree_time); |
---|
[e89e56] | 860 | SqrFreeList = SqrFreeMV(F) ; // first sqrfree the polynomial |
---|
| 861 | // don't use sqrFree(F), factory's internal sqrFree for multiv. |
---|
| 862 | // Polynomials; it's wrong!! Ex.: char=p f= x^p*(y+1); |
---|
| 863 | // SqrFreeMV(f)= ( y+1, (x)^p ), sqrFree(f)= ( y+1 ) . |
---|
[3e55bc] | 864 | TIMING_END(sqrfree_time); |
---|
| 865 | |
---|
| 866 | // INTERRUPTHANDLER |
---|
| 867 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 868 | // INTERRUPTHANDLER |
---|
| 869 | |
---|
[1a80b4] | 870 | } |
---|
[0be2bc] | 871 | else |
---|
[3e55bc] | 872 | SqrFreeList.append(CFFactor(F,1)); |
---|
[9e9b7c] | 873 | |
---|
[e89e56] | 874 | DEBOUTLN(CERR, "SqrFreeMV= ", SqrFreeList); |
---|
[38e7b3] | 875 | for ( i=SqrFreeList; i.hasItem(); i++ ) |
---|
| 876 | { |
---|
[e2ca88] | 877 | DEBOUTLN(CERR, "Factor under consideration: ", i.getItem().factor()); |
---|
[1a80b4] | 878 | // We need a compress on each list item ! Maybe we have less variables! |
---|
[0be2bc] | 879 | g =compress(i.getItem().factor(),m); |
---|
[1a80b4] | 880 | exp = i.getItem().exp(); |
---|
| 881 | if ( getNumVars(g) ==0 ) // a constant; Exp==1 |
---|
| 882 | Outputlist.append( CFFactor(g,1) ) ; |
---|
| 883 | else// a real polynomial |
---|
[38e7b3] | 884 | if ( g.isUnivariate() ) |
---|
| 885 | { |
---|
[ee586a] | 886 | //out_cf("univ. poly: ",g,"\n"); |
---|
[0be2bc] | 887 | Intermediatelist=factorize(g,1); // poly is sqr-free! |
---|
| 888 | for ( j=Intermediatelist; j.hasItem(); j++ ) |
---|
| 889 | //Normally j.getItem().exp() should be 1 |
---|
| 890 | Outputlist.append( CFFactor( m(j.getItem().factor()),exp*j.getItem().exp())); |
---|
[1a80b4] | 891 | } |
---|
[38e7b3] | 892 | else |
---|
| 893 | { // multivariate polynomial |
---|
| 894 | if ( g.isHomogeneous() ) |
---|
| 895 | { |
---|
[e2ca88] | 896 | DEBOUTLN(CERR, "Poly is homogeneous! : ", g); |
---|
[0be2bc] | 897 | // Now we can substitute one variable to 1, factorize and then |
---|
| 898 | // look on the resulting factors and their monomials for |
---|
| 899 | // backsubstitution of the substituted variable. |
---|
| 900 | Intermediatelist = HomogFactor(g, minpoly, 0); |
---|
| 901 | } |
---|
| 902 | else // not homogeneous |
---|
| 903 | Intermediatelist = Factorized(g, minpoly, 0); |
---|
| 904 | |
---|
| 905 | // INTERRUPTHANDLER |
---|
| 906 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 907 | // INTERRUPTHANDLER |
---|
| 908 | |
---|
| 909 | for ( j=Intermediatelist; j.hasItem(); j++ ) |
---|
| 910 | //Normally j.getItem().exp() should be 1 |
---|
[e89e56] | 911 | Outputlist= myappend( Outputlist, CFFactor(m(j.getItem().factor()),exp*j.getItem().exp())); |
---|
[1a80b4] | 912 | } |
---|
| 913 | } |
---|
| 914 | g=1; unit=1; |
---|
[e2ca88] | 915 | DEBOUTLN(CERR, "Outputlist is ", Outputlist); |
---|
[1a80b4] | 916 | for ( i=Outputlist; i.hasItem(); i++ ) |
---|
[38e7b3] | 917 | if ( level(i.getItem().factor()) > 0 ) |
---|
| 918 | { |
---|
[1a80b4] | 919 | unit = lc(i.getItem().factor()); |
---|
[38e7b3] | 920 | if ( getNumVars(unit) == 0 ) |
---|
| 921 | { // a constant; possibly 1 |
---|
[0be2bc] | 922 | Outputlist2.append(CFFactor(i.getItem().factor()/unit , i.getItem().exp())); |
---|
| 923 | g *=power(i.getItem().factor()/unit,i.getItem().exp()); |
---|
[1a80b4] | 924 | } |
---|
[38e7b3] | 925 | else |
---|
| 926 | { |
---|
[0be2bc] | 927 | Outputlist2.append(i.getItem()); |
---|
| 928 | g *=power(i.getItem().factor(),i.getItem().exp()); |
---|
[1a80b4] | 929 | } |
---|
| 930 | } |
---|
[0be2bc] | 931 | |
---|
| 932 | r=F/g; |
---|
[1a80b4] | 933 | Outputlist2.insert(CFFactor(r,1)); |
---|
[0be2bc] | 934 | |
---|
[b6249e] | 935 | if ((mv!=F.level()) && (! F.isUnivariate() )) |
---|
| 936 | { |
---|
| 937 | CFFListIterator J=Outputlist2; |
---|
| 938 | for ( ; J.hasItem(); J++) |
---|
| 939 | { |
---|
| 940 | swapvar(J.getItem().factor(),Variable(mv),F.mvar()); |
---|
| 941 | } |
---|
| 942 | swapvar(F,Variable(mv),F.mvar()); |
---|
| 943 | } |
---|
[e2ca88] | 944 | DEBDECLEVEL(CERR, "Factorize"); |
---|
[1a80b4] | 945 | TIMING_END(factorize_time); |
---|
| 946 | |
---|
| 947 | TIMING_PRINT(sqrfree_time, "\ntime used for sqrfree : "); |
---|
| 948 | TIMING_PRINT(discr_time, "time used for discriminante : "); |
---|
| 949 | TIMING_PRINT(evaluate_time, "time used for evaluation and univ. factorization : "); |
---|
| 950 | TIMING_PRINT(hensel_time, "time used for hensel-lift : "); |
---|
| 951 | TIMING_PRINT(truefactor_time, "time used for truefactors : "); |
---|
| 952 | TIMING_PRINT(factorize_time, "\ntime used for factorization : "); |
---|
[5299b6] | 953 | |
---|
| 954 | if(isOn(SW_USE_NTL_SORT)) Outputlist2.sort(cmpCF); |
---|
| 955 | |
---|
[1a80b4] | 956 | return Outputlist2; |
---|
| 957 | } |
---|
| 958 | |
---|
[b4ea1d] | 959 | /////////////////////////////////////////////////////////////// |
---|
| 960 | // The user front-end for a uni/multivariate factorization // |
---|
| 961 | // routine. F needs not to be SqrFree. // |
---|
| 962 | // Option of * choosing a main variable (n.y.i.) // |
---|
| 963 | // * choosing an algebraic extension (n.y.u.) // |
---|
| 964 | // * ensuring poly is sqrfree (n.y.i.) // |
---|
| 965 | /////////////////////////////////////////////////////////////// |
---|
[52e543] | 966 | static bool fdivides2(const CanonicalForm &F, const CanonicalForm &G, const CanonicalForm &minpoly) |
---|
| 967 | { |
---|
[8e0cdf] | 968 | if (!minpoly.isZero()) |
---|
[52e543] | 969 | { |
---|
| 970 | #if 0 |
---|
| 971 | Variable Alpha=minpoly.mvar(); |
---|
| 972 | Variable X=rootOf(minpoly); |
---|
| 973 | CanonicalForm rF=replacevar(F,Alpha,X); |
---|
| 974 | CanonicalForm rG=replacevar(G,Alpha,X); |
---|
| 975 | return fdivides(rF,rG);; |
---|
| 976 | #else |
---|
[304e26] | 977 | if (degree(F,F.mvar()) > degree(G,F.mvar())) return false; |
---|
| 978 | return true; |
---|
| 979 | //CanonicalForm a,b; |
---|
| 980 | //mydivrem(G,F,a,b); |
---|
| 981 | //if (b.isZero()) return true; |
---|
| 982 | //else return false; |
---|
[52e543] | 983 | #endif |
---|
| 984 | } |
---|
| 985 | else |
---|
| 986 | return fdivides(F,G); |
---|
| 987 | } |
---|
[927b7e] | 988 | |
---|
[b4ea1d] | 989 | CFFList |
---|
[38e7b3] | 990 | Factorize(const CanonicalForm & F, const CanonicalForm & minpoly, int is_SqrFree ) |
---|
| 991 | { |
---|
[a38d45] | 992 | //out_cf("Factorize: F=",F,"\n"); |
---|
| 993 | //out_cf(" minpoly:",minpoly,"\n"); |
---|
[b4ea1d] | 994 | CFFList Outputlist,SqrFreeList,Intermediatelist,Outputlist2; |
---|
| 995 | ListIterator<CFFactor> i,j; |
---|
| 996 | CanonicalForm g=1,unit=1,r=1; |
---|
| 997 | //Variable minpoly; // reserved (-> Factorisation over algebraic Extensions) |
---|
| 998 | int exp; |
---|
| 999 | CFMap m; |
---|
| 1000 | |
---|
| 1001 | // INTERRUPTHANDLER |
---|
| 1002 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 1003 | // INTERRUPTHANDLER |
---|
| 1004 | |
---|
[e2ca88] | 1005 | DEBINCLEVEL(CERR, "Factorize"); |
---|
| 1006 | DEBOUTLN(CERR, "Called with F= ", F); |
---|
[639047e] | 1007 | if ( getCharacteristic() == 0 ) |
---|
| 1008 | { // char == 0 |
---|
[b4ea1d] | 1009 | TIMING_START(factorize_time); |
---|
[e2ca88] | 1010 | //CERR << "Factoring in char=0 of " << F << " = " << Outputlist << "\n"; |
---|
[639047e] | 1011 | #if 0 |
---|
[93a6da3] | 1012 | // SHOULD: Outputlist= factorize(F,minpoly); |
---|
| 1013 | Outputlist= factorize(F); |
---|
[639047e] | 1014 | #else |
---|
[8e0cdf] | 1015 | if (!minpoly.isZero()) |
---|
[639047e] | 1016 | { |
---|
[a38d45] | 1017 | if ( F.isHomogeneous() ) |
---|
[6036eb2] | 1018 | { |
---|
[a38d45] | 1019 | DEBOUTLN(CERR, "Poly is homogeneous! : ", F); |
---|
| 1020 | // Now we can substitute one variable to 1, factorize and then |
---|
| 1021 | // look on the resulting factors and their monomials for |
---|
| 1022 | // backsubstitution of the substituted variable. |
---|
| 1023 | Outputlist=HomogFactor(F, minpoly, 0); |
---|
| 1024 | } |
---|
| 1025 | else |
---|
| 1026 | { |
---|
| 1027 | CFList as(minpoly); |
---|
[8e0cdf] | 1028 | //CFFList sqF=sqrFree(F); // sqrFreeZ |
---|
| 1029 | CFFList sqF=SqrFreeMV(F,minpoly); |
---|
[f152c5] | 1030 | if (sqF.isEmpty()) sqF=sqrFree(F); |
---|
[a38d45] | 1031 | CFFList G,H; |
---|
| 1032 | CanonicalForm fac; |
---|
| 1033 | int d; |
---|
| 1034 | ListIterator<CFFactor> i,k; |
---|
| 1035 | for ( i = sqF; i.hasItem(); ++i ) |
---|
[6036eb2] | 1036 | { |
---|
[a38d45] | 1037 | d = i.getItem().exp(); |
---|
| 1038 | fac = i.getItem().factor(); |
---|
[adfb22] | 1039 | int success=1; |
---|
| 1040 | G = newfactoras( fac, as, success); |
---|
[a38d45] | 1041 | for ( k = G; k.hasItem(); ++k ) |
---|
| 1042 | { |
---|
| 1043 | fac = k.getItem().factor(); |
---|
| 1044 | int dd = k.getItem().exp(); |
---|
| 1045 | H.append( CFFactor( fac , d*dd ) ); |
---|
| 1046 | } |
---|
[6036eb2] | 1047 | } |
---|
[a38d45] | 1048 | Outputlist = H; |
---|
[6036eb2] | 1049 | } |
---|
[639047e] | 1050 | } |
---|
[8e0cdf] | 1051 | else // minpoly==0 |
---|
[639047e] | 1052 | Outputlist=factorize(F); |
---|
| 1053 | #endif |
---|
[b4ea1d] | 1054 | // Factorization in char=0 doesn't sometimes return at least two elements!!! |
---|
| 1055 | if ( getNumVars(Outputlist.getFirst().factor()) != 0 ) |
---|
| 1056 | Outputlist.insert(CFFactor(1,1)); |
---|
[e2ca88] | 1057 | //CERR << " Factorize in char=0: returning with: " << Outputlist << "\n"; |
---|
[b4ea1d] | 1058 | TIMING_END(factorize_time); |
---|
[e2ca88] | 1059 | DEBDECLEVEL(CERR, "Factorize"); |
---|
[b4ea1d] | 1060 | TIMING_PRINT(factorize_time, "\ntime used for factorization : "); |
---|
[a38d45] | 1061 | //out_cff(Outputlist); |
---|
[b4ea1d] | 1062 | return Outputlist; |
---|
| 1063 | } |
---|
| 1064 | TIMING_START(factorize_time); |
---|
| 1065 | // search an "optimal" main variavble |
---|
| 1066 | int mv=F.level(); |
---|
| 1067 | if (mv != LEVELBASE && ! F.isUnivariate() ) |
---|
| 1068 | { |
---|
| 1069 | mv=find_mvar(F); |
---|
| 1070 | if (mv!=F.level()) |
---|
| 1071 | { |
---|
| 1072 | swapvar(F,Variable(mv),F.mvar()); |
---|
| 1073 | } |
---|
| 1074 | } |
---|
| 1075 | |
---|
| 1076 | /////// |
---|
| 1077 | // Maybe it`s better to add a sqrfree-test before? |
---|
| 1078 | // (If gcd is fast...) |
---|
| 1079 | /////// |
---|
[e89e56] | 1080 | // if ( ! SqrFreeTest(F) ){ |
---|
[10697c] | 1081 | if ( ! is_SqrFree ) |
---|
| 1082 | { |
---|
[b4ea1d] | 1083 | TIMING_START(sqrfree_time); |
---|
[e89e56] | 1084 | SqrFreeList = SqrFreeMV(F, minpoly) ; // first sqrfree the polynomial |
---|
| 1085 | // don't use sqrFree(F), factory's internal sqrFree for multiv. |
---|
| 1086 | // Polynomials; it's wrong!! Ex.: char=p f= x^p*(y+1); |
---|
| 1087 | // SqrFreeMV(f)= ( y+1, (x)^p ), sqrFree(f)= ( y+1 ) . |
---|
[b4ea1d] | 1088 | TIMING_END(sqrfree_time); |
---|
| 1089 | |
---|
| 1090 | // INTERRUPTHANDLER |
---|
| 1091 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 1092 | // INTERRUPTHANDLER |
---|
| 1093 | |
---|
| 1094 | } |
---|
| 1095 | else |
---|
| 1096 | SqrFreeList.append(CFFactor(F,1)); |
---|
[e89e56] | 1097 | DEBOUTLN(CERR, "SqrFreeMV= ", SqrFreeList); |
---|
[10697c] | 1098 | for ( i=SqrFreeList; i.hasItem(); i++ ) |
---|
| 1099 | { |
---|
[e2ca88] | 1100 | DEBOUTLN(CERR, "Factor under consideration: ", i.getItem().factor()); |
---|
[b4ea1d] | 1101 | // We need a compress on each list item ! Maybe we have less variables! |
---|
| 1102 | g =compress(i.getItem().factor(),m); |
---|
| 1103 | exp = i.getItem().exp(); |
---|
| 1104 | if ( getNumVars(g) ==0 ) // a constant; Exp==1 |
---|
| 1105 | Outputlist.append( CFFactor(g,1) ) ; |
---|
| 1106 | else// a real polynomial |
---|
[8de151] | 1107 | { |
---|
[10697c] | 1108 | if ( g.isUnivariate() ) |
---|
| 1109 | { |
---|
[639047e] | 1110 | Variable alpha=rootOf(minpoly); |
---|
[1048e0c] | 1111 | Intermediatelist=factorize2(g,alpha,minpoly); // poly is sqr-free! |
---|
[b4ea1d] | 1112 | for ( j=Intermediatelist; j.hasItem(); j++ ) |
---|
| 1113 | //Normally j.getItem().exp() should be 1 |
---|
[639047e] | 1114 | Outputlist.append( |
---|
| 1115 | CFFactor( m(replacevar(j.getItem().factor(),alpha,minpoly.mvar())), |
---|
| 1116 | exp*j.getItem().exp())); |
---|
[b4ea1d] | 1117 | } |
---|
[10697c] | 1118 | else // multivariate polynomial |
---|
| 1119 | { |
---|
| 1120 | if ( g.isHomogeneous() ) |
---|
[52e543] | 1121 | { |
---|
[e2ca88] | 1122 | DEBOUTLN(CERR, "Poly is homogeneous! : ", g); |
---|
[b4ea1d] | 1123 | // Now we can substitute one variable to 1, factorize and then |
---|
| 1124 | // look on the resulting factors and their monomials for |
---|
| 1125 | // backsubstitution of the substituted variable. |
---|
| 1126 | Intermediatelist = HomogFactor(g, minpoly, 0); |
---|
| 1127 | } |
---|
| 1128 | else // not homogeneous |
---|
| 1129 | Intermediatelist = Factorized(g, minpoly, 0); |
---|
| 1130 | |
---|
| 1131 | // INTERRUPTHANDLER |
---|
| 1132 | if ( interrupt_handle() ) return CFFList() ; |
---|
| 1133 | // INTERRUPTHANDLER |
---|
| 1134 | |
---|
| 1135 | for ( j=Intermediatelist; j.hasItem(); j++ ) |
---|
| 1136 | //Normally j.getItem().exp() should be 1 |
---|
[e89e56] | 1137 | Outputlist= myappend( Outputlist, CFFactor(m(j.getItem().factor()),exp*j.getItem().exp())); |
---|
[b4ea1d] | 1138 | } |
---|
[8de151] | 1139 | } |
---|
[b4ea1d] | 1140 | } |
---|
| 1141 | g=1; unit=1; |
---|
[e2ca88] | 1142 | DEBOUTLN(CERR, "Outputlist is ", Outputlist); |
---|
[b4ea1d] | 1143 | for ( i=Outputlist; i.hasItem(); i++ ) |
---|
[8e0cdf] | 1144 | if ( level(i.getItem().factor()) > 0 ) |
---|
| 1145 | { |
---|
[b4ea1d] | 1146 | unit = lc(i.getItem().factor()); |
---|
| 1147 | if ( getNumVars(unit) == 0 ){ // a constant; possibly 1 |
---|
| 1148 | Outputlist2.append(CFFactor(i.getItem().factor()/unit , i.getItem().exp())); |
---|
| 1149 | g *=power(i.getItem().factor()/unit,i.getItem().exp()); |
---|
| 1150 | } |
---|
[8e0cdf] | 1151 | else |
---|
| 1152 | { |
---|
[b4ea1d] | 1153 | Outputlist2.append(i.getItem()); |
---|
| 1154 | g *=power(i.getItem().factor(),i.getItem().exp()); |
---|
| 1155 | } |
---|
| 1156 | } |
---|
| 1157 | |
---|
| 1158 | r=F/g; |
---|
| 1159 | Outputlist2.insert(CFFactor(r,1)); |
---|
| 1160 | |
---|
| 1161 | if ((mv!=F.level()) && (! F.isUnivariate() )) |
---|
| 1162 | { |
---|
| 1163 | CFFListIterator J=Outputlist2; |
---|
| 1164 | for ( ; J.hasItem(); J++) |
---|
| 1165 | { |
---|
| 1166 | swapvar(J.getItem().factor(),Variable(mv),F.mvar()); |
---|
| 1167 | } |
---|
| 1168 | swapvar(F,Variable(mv),F.mvar()); |
---|
| 1169 | } |
---|
[1048e0c] | 1170 | |
---|
[e2ca88] | 1171 | DEBDECLEVEL(CERR, "Factorize"); |
---|
[b4ea1d] | 1172 | TIMING_END(factorize_time); |
---|
| 1173 | |
---|
| 1174 | TIMING_PRINT(sqrfree_time, "\ntime used for sqrfree : "); |
---|
| 1175 | TIMING_PRINT(discr_time, "time used for discriminante : "); |
---|
| 1176 | TIMING_PRINT(evaluate_time, "time used for evaluation and univ. factorization : "); |
---|
| 1177 | TIMING_PRINT(hensel_time, "time used for hensel-lift : "); |
---|
| 1178 | TIMING_PRINT(truefactor_time, "time used for truefactors : "); |
---|
| 1179 | TIMING_PRINT(factorize_time, "\ntime used for factorization : "); |
---|
[5299b6] | 1180 | |
---|
| 1181 | if(isOn(SW_USE_NTL_SORT)) Outputlist2.sort(cmpCF); |
---|
| 1182 | |
---|
[a38d45] | 1183 | //out_cff(Outputlist2); |
---|
[b4ea1d] | 1184 | return Outputlist2; |
---|
| 1185 | } |
---|
| 1186 | |
---|