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