[35aab3] | 1 | // emacs edit mode for this file is -*- C++ -*- |
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| 2 | /**************************************** |
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| 3 | * Computer Algebra System SINGULAR * |
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| 4 | ****************************************/ |
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| 5 | /* |
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| 6 | * ABSTRACT: interface between Singular and factory |
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| 7 | */ |
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| 8 | |
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[b963c5] | 9 | //#define FACTORIZE2_DEBUG |
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[af598e] | 10 | #include "config.h" |
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| 11 | #include <misc/auxiliary.h> |
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| 12 | |
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[22a09d] | 13 | #ifdef HAVE_FACTORY |
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[35aab3] | 14 | #define SI_DONT_HAVE_GLOBAL_VARS |
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[fea2af] | 15 | |
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[22a09d] | 16 | #include <factory/factory.h> |
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[fea2af] | 17 | |
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[67c1dc] | 18 | #ifdef HAVE_LIBFAC |
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[e65b1a4] | 19 | #include <factory/libfac/libfac.h> |
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[67c1dc] | 20 | #endif |
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[fea2af] | 21 | |
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[22a09d] | 22 | |
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[af598e] | 23 | #include <omalloc/omalloc.h> |
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| 24 | #include <coeffs/numbers.h> |
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| 25 | #include <coeffs/coeffs.h> |
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[24a9587] | 26 | #include <coeffs/bigintmat.h> |
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[af598e] | 27 | |
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| 28 | // #include <kernel/ffields.h> |
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| 29 | |
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| 30 | #include "monomials/ring.h" |
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| 31 | #include "simpleideals.h" |
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[35aab3] | 32 | |
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[9144617] | 33 | |
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[1f414c8] | 34 | //#include "polys.h" |
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| 35 | #define TRANSEXT_PRIVATES |
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| 36 | #include "ext_fields/transext.h" |
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| 37 | |
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[9144617] | 38 | |
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| 39 | #include "clapsing.h" |
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| 40 | #include "clapconv.h" |
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| 41 | // #include <kernel/clapconv.h> |
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[67c1dc] | 42 | |
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[9144617] | 43 | |
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[a86cda] | 44 | void out_cf(const char *s1,const CanonicalForm &f,const char *s2); |
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[35aab3] | 45 | |
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[abb4787] | 46 | static poly singclap_gcd_r ( poly f, poly g, const ring r ) |
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[35aab3] | 47 | { |
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| 48 | poly res=NULL; |
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| 49 | |
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[36586bb] | 50 | assume(f!=NULL); |
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| 51 | assume(g!=NULL); |
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| 52 | |
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| 53 | if((pNext(f)==NULL) && (pNext(g)==NULL)) |
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[9b9b5a] | 54 | { |
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[a934fc8] | 55 | poly p=p_One(r); |
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[36586bb] | 56 | for(int i=rVar(r);i>0;i--) |
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| 57 | p_SetExp(p,i,si_min(p_GetExp(f,i,r),p_GetExp(g,i,r)),r); |
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| 58 | p_Setm(p,r); |
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| 59 | return p; |
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[9b9b5a] | 60 | } |
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[35aab3] | 61 | |
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[ea48f7d] | 62 | Off(SW_RATIONAL); |
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[ce2576] | 63 | if (rField_is_Q(r) || (rField_is_Zp(r))) |
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| 64 | { |
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| 65 | setCharacteristic( rChar(r) ); |
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| 66 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g, r ) ); |
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| 67 | res=convFactoryPSingP( gcd( F, G ) , r); |
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| 68 | } |
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| 69 | // and over Q(a) / Fp(a) |
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| 70 | else if ( rField_is_Extension(r)) |
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| 71 | { |
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| 72 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
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| 73 | else setCharacteristic( rChar(r) ); |
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[dd668f] | 74 | if (r->cf->extRing->qideal!=NULL) |
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[ce2576] | 75 | { |
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| 76 | bool b1=isOn(SW_USE_QGCD); |
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| 77 | if ( rField_is_Q_a(r) ) On(SW_USE_QGCD); |
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[dd668f] | 78 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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[ce2576] | 79 | r->cf->extRing); |
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| 80 | Variable a=rootOf(mipo); |
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| 81 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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| 82 | G( convSingAPFactoryAP( g,a,r ) ); |
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| 83 | res= convFactoryAPSingAP( gcd( F, G ),r ); |
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| 84 | if (!b1) Off(SW_USE_QGCD); |
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| 85 | } |
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| 86 | else |
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| 87 | { |
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| 88 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
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| 89 | res= convFactoryPSingTrP( gcd( F, G ),r ); |
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| 90 | } |
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| 91 | } |
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| 92 | else |
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| 93 | WerrorS( feNotImplemented ); |
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[ea48f7d] | 94 | Off(SW_RATIONAL); |
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[35aab3] | 95 | return res; |
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| 96 | } |
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| 97 | |
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[cd964c] | 98 | void singclap_gcd_and_divide ( poly& f, poly& g, const ring r) |
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[91d0e6] | 99 | { |
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| 100 | poly res=NULL; |
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| 101 | |
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[ce3f53c] | 102 | if (f!=NULL) p_Cleardenom(f, r); |
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[cd964c] | 103 | if (g!=NULL) p_Cleardenom(g, r); |
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| 104 | else return; // g==0 => but do a p_Cleardenom(f) |
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| 105 | if (f==NULL) return; // f==0 => but do a p_Cleardenom(g) |
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| 106 | |
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| 107 | Off(SW_RATIONAL); |
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| 108 | CanonicalForm F,G,GCD; |
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| 109 | if (rField_is_Q(r) || (rField_is_Zp(r))) |
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| 110 | { |
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| 111 | bool b1=isOn(SW_USE_EZGCD_P); |
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| 112 | setCharacteristic( rChar(r) ); |
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| 113 | F=convSingPFactoryP( f,r ); |
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| 114 | G=convSingPFactoryP( g,r ); |
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| 115 | GCD=gcd(F,G); |
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| 116 | if (!GCD.isOne()) |
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| 117 | { |
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| 118 | p_Delete(&f,r); |
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| 119 | p_Delete(&g,r); |
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| 120 | f=convFactoryPSingP( F/GCD, r); |
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| 121 | g=convFactoryPSingP( G/GCD, r); |
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| 122 | } |
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| 123 | if (!b1) Off (SW_USE_EZGCD_P); |
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| 124 | } |
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| 125 | // and over Q(a) / Fp(a) |
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| 126 | else if ( rField_is_Extension(r)) |
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| 127 | { |
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| 128 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
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| 129 | else setCharacteristic( rChar(r) ); |
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| 130 | if (r->cf->extRing->qideal!=NULL) |
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| 131 | { |
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| 132 | bool b1=isOn(SW_USE_QGCD); |
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| 133 | if ( rField_is_Q_a(r) ) On(SW_USE_QGCD); |
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| 134 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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| 135 | r->cf->extRing); |
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| 136 | Variable a=rootOf(mipo); |
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| 137 | F=( convSingAPFactoryAP( f,a,r ) ); |
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| 138 | G=( convSingAPFactoryAP( g,a,r ) ); |
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| 139 | GCD=gcd(F,G); |
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| 140 | if (!GCD.isOne()) |
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| 141 | { |
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| 142 | p_Delete(&f,r); |
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| 143 | p_Delete(&g,r); |
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| 144 | f= convFactoryAPSingAP( F/GCD,r ); |
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| 145 | g= convFactoryAPSingAP( G/GCD,r ); |
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| 146 | } |
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| 147 | if (!b1) Off(SW_USE_QGCD); |
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| 148 | } |
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| 149 | else |
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| 150 | { |
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| 151 | F=( convSingTrPFactoryP( f,r ) ); |
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| 152 | G=( convSingTrPFactoryP( g,r ) ); |
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| 153 | GCD=gcd(F,G); |
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| 154 | if (!GCD.isOne()) |
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| 155 | { |
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| 156 | p_Delete(&f,r); |
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| 157 | p_Delete(&g,r); |
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| 158 | f= convFactoryPSingTrP( F/GCD,r ); |
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| 159 | g= convFactoryPSingTrP( G/GCD,r ); |
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| 160 | } |
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| 161 | } |
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| 162 | } |
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| 163 | else |
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| 164 | WerrorS( feNotImplemented ); |
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| 165 | Off(SW_RATIONAL); |
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| 166 | } |
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| 167 | |
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| 168 | poly singclap_gcd ( poly f, poly g, const ring r) |
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| 169 | { |
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| 170 | poly res=NULL; |
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| 171 | |
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| 172 | if (f!=NULL) p_Cleardenom(f, r); |
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[ce3f53c] | 173 | if (g!=NULL) p_Cleardenom(g, r); |
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[f8ace52] | 174 | else return f; // g==0 => gcd=f (but do a p_Cleardenom) |
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| 175 | if (f==NULL) return g; // f==0 => gcd=g (but do a p_Cleardenom) |
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[91d0e6] | 176 | |
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[ce3f53c] | 177 | res=singclap_gcd_r(f,g,r); |
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| 178 | p_Delete(&f, r); |
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| 179 | p_Delete(&g, r); |
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[91d0e6] | 180 | return res; |
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| 181 | } |
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| 182 | |
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[c95632f] | 183 | /*2 find the maximal exponent of var(i) in poly p*/ |
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[ce3f53c] | 184 | int pGetExp_Var(poly p, int i, const ring r) |
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[c95632f] | 185 | { |
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| 186 | int m=0; |
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| 187 | int mm; |
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| 188 | while (p!=NULL) |
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| 189 | { |
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[ce3f53c] | 190 | mm=p_GetExp(p,i,r); |
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[c95632f] | 191 | if (mm>m) m=mm; |
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| 192 | pIter(p); |
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| 193 | } |
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| 194 | return m; |
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| 195 | } |
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| 196 | |
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[9d9078] | 197 | // destroys f,g,x |
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[ce3f53c] | 198 | poly singclap_resultant ( poly f, poly g , poly x, const ring r) |
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[35aab3] | 199 | { |
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[9d9078] | 200 | poly res=NULL; |
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[ce3f53c] | 201 | int i=p_IsPurePower(x, r); |
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[35aab3] | 202 | if (i==0) |
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| 203 | { |
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| 204 | WerrorS("3rd argument must be a ring variable"); |
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[9d9078] | 205 | goto resultant_returns_res; |
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[35aab3] | 206 | } |
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| 207 | if ((f==NULL) || (g==NULL)) |
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[9d9078] | 208 | goto resultant_returns_res; |
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[ce2576] | 209 | // for now there is only the possibility to handle polynomials over |
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| 210 | // Q and Fp ... |
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| 211 | if (rField_is_Zp(r) || rField_is_Q(r)) |
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| 212 | { |
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| 213 | Variable X(i); |
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| 214 | setCharacteristic( rChar(r) ); |
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| 215 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
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| 216 | res=convFactoryPSingP( resultant( F, G, X),r ); |
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[35aab3] | 217 | Off(SW_RATIONAL); |
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[ce2576] | 218 | goto resultant_returns_res; |
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[35aab3] | 219 | } |
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[ce2576] | 220 | // and over Q(a) / Fp(a) |
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| 221 | else if (rField_is_Extension(r)) |
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| 222 | { |
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| 223 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
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| 224 | else setCharacteristic( rChar(r) ); |
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| 225 | Variable X(i+rPar(r)); |
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[dd668f] | 226 | if (r->cf->extRing->qideal!=NULL) |
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[ce2576] | 227 | { |
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| 228 | //Variable X(i); |
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[dd668f] | 229 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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[ce2576] | 230 | r->cf->extRing); |
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| 231 | Variable a=rootOf(mipo); |
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| 232 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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| 233 | G( convSingAPFactoryAP( g,a,r ) ); |
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| 234 | res= convFactoryAPSingAP( resultant( F, G, X ),r ); |
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| 235 | } |
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| 236 | else |
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| 237 | { |
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| 238 | //Variable X(i+rPar(currRing)); |
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| 239 | number nf,ng; |
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| 240 | p_Cleardenom_n(f,r,nf);p_Cleardenom_n(g,r,ng); |
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| 241 | int ef,eg; |
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| 242 | ef=pGetExp_Var(f,i,r); |
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| 243 | eg=pGetExp_Var(g,i,r); |
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| 244 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
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| 245 | res= convFactoryPSingTrP( resultant( F, G, X ),r ); |
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[a355723] | 246 | if ((nf!=NULL)&&(!n_IsOne(nf,r->cf))) |
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[ce2576] | 247 | { |
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| 248 | number n=n_Invers(nf,r->cf); |
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| 249 | while(eg>0) |
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| 250 | { |
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| 251 | res=p_Mult_nn(res,n,r); |
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| 252 | eg--; |
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| 253 | } |
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| 254 | n_Delete(&n,r->cf); |
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| 255 | } |
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| 256 | n_Delete(&nf,r->cf); |
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[a355723] | 257 | if ((ng!=NULL)&&(!n_IsOne(ng,r->cf))) |
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[ce2576] | 258 | { |
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| 259 | number n=n_Invers(ng,r->cf); |
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| 260 | while(ef>0) |
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| 261 | { |
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| 262 | res=p_Mult_nn(res,n,r); |
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| 263 | ef--; |
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| 264 | } |
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| 265 | n_Delete(&n,r->cf); |
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| 266 | } |
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| 267 | n_Delete(&ng,r->cf); |
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| 268 | } |
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| 269 | Off(SW_RATIONAL); |
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| 270 | goto resultant_returns_res; |
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| 271 | } |
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| 272 | else |
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| 273 | WerrorS( feNotImplemented ); |
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[9d9078] | 274 | resultant_returns_res: |
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[ce3f53c] | 275 | p_Delete(&f,r); |
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| 276 | p_Delete(&g,r); |
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| 277 | p_Delete(&x,r); |
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[9d9078] | 278 | return res; |
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[35aab3] | 279 | } |
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| 280 | //poly singclap_resultant ( poly f, poly g , poly x) |
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| 281 | //{ |
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| 282 | // int i=pVar(x); |
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| 283 | // if (i==0) |
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| 284 | // { |
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| 285 | // WerrorS("ringvar expected"); |
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| 286 | // return NULL; |
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| 287 | // } |
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| 288 | // ideal I=idInit(1,1); |
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| 289 | // |
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| 290 | // // get the coeffs von f wrt. x: |
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| 291 | // I->m[0]=pCopy(f); |
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| 292 | // matrix ffi=mpCoeffs(I,i); |
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| 293 | // ffi->rank=1; |
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| 294 | // ffi->ncols=ffi->nrows; |
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| 295 | // ffi->nrows=1; |
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| 296 | // ideal fi=(ideal)ffi; |
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| 297 | // |
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| 298 | // // get the coeffs von g wrt. x: |
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| 299 | // I->m[0]=pCopy(g); |
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| 300 | // matrix ggi=mpCoeffs(I,i); |
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| 301 | // ggi->rank=1; |
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| 302 | // ggi->ncols=ggi->nrows; |
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| 303 | // ggi->nrows=1; |
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| 304 | // ideal gi=(ideal)ggi; |
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| 305 | // |
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| 306 | // // contruct the matrix: |
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| 307 | // int fn=IDELEMS(fi); //= deg(f,x)+1 |
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| 308 | // int gn=IDELEMS(gi); //= deg(g,x)+1 |
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| 309 | // matrix m=mpNew(fn+gn-2,fn+gn-2); |
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| 310 | // if(m==NULL) |
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| 311 | // { |
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| 312 | // return NULL; |
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| 313 | // } |
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| 314 | // |
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| 315 | // // enter the coeffs into m: |
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| 316 | // int j; |
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| 317 | // for(i=0;i<gn-1;i++) |
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| 318 | // { |
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| 319 | // for(j=0;j<fn;j++) |
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| 320 | // { |
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| 321 | // MATELEM(m,i+1,fn-j+i)=pCopy(fi->m[j]); |
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| 322 | // } |
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| 323 | // } |
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| 324 | // for(i=0;i<fn-1;i++) |
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| 325 | // { |
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| 326 | // for(j=0;j<gn;j++) |
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| 327 | // { |
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| 328 | // MATELEM(m,gn+i,gn-j+i)=pCopy(gi->m[j]); |
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| 329 | // } |
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| 330 | // } |
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| 331 | // |
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| 332 | // poly r=mpDet(m); |
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| 333 | // |
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| 334 | // idDelete(&fi); |
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| 335 | // idDelete(&gi); |
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| 336 | // idDelete((ideal *)&m); |
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| 337 | // return r; |
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| 338 | //} |
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| 339 | |
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[ce3f53c] | 340 | BOOLEAN singclap_extgcd ( poly f, poly g, poly &res, poly &pa, poly &pb , const ring r) |
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[35aab3] | 341 | { |
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| 342 | // for now there is only the possibility to handle univariate |
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| 343 | // polynomials over |
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| 344 | // Q and Fp ... |
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| 345 | res=NULL;pa=NULL;pb=NULL; |
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| 346 | On(SW_SYMMETRIC_FF); |
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[ce2576] | 347 | if ( rField_is_Q(r) || rField_is_Zp(r) ) |
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[35aab3] | 348 | { |
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[ce2576] | 349 | setCharacteristic( rChar(r) ); |
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| 350 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r) ); |
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| 351 | CanonicalForm FpG=F+G; |
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| 352 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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| 353 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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| 354 | { |
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| 355 | Off(SW_RATIONAL); |
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| 356 | WerrorS("not univariate"); |
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| 357 | return TRUE; |
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| 358 | } |
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| 359 | CanonicalForm Fa,Gb; |
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| 360 | On(SW_RATIONAL); |
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| 361 | res=convFactoryPSingP( extgcd( F, G, Fa, Gb ),r ); |
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| 362 | pa=convFactoryPSingP(Fa,r); |
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| 363 | pb=convFactoryPSingP(Gb,r); |
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| 364 | Off(SW_RATIONAL); |
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| 365 | } |
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| 366 | // and over Q(a) / Fp(a) |
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| 367 | else if ( rField_is_Extension(r)) |
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| 368 | { |
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| 369 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
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| 370 | else setCharacteristic( rChar(r) ); |
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| 371 | CanonicalForm Fa,Gb; |
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[dd668f] | 372 | if (r->cf->extRing->qideal!=NULL) |
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[ce2576] | 373 | { |
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[dd668f] | 374 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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[ce2576] | 375 | r->cf->extRing); |
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| 376 | Variable a=rootOf(mipo); |
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| 377 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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| 378 | G( convSingAPFactoryAP( g,a,r ) ); |
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| 379 | CanonicalForm FpG=F+G; |
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| 380 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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| 381 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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| 382 | { |
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| 383 | WerrorS("not univariate"); |
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| 384 | return TRUE; |
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| 385 | } |
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| 386 | res= convFactoryAPSingAP( extgcd( F, G, Fa, Gb ),r ); |
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| 387 | pa=convFactoryAPSingAP(Fa,r); |
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| 388 | pb=convFactoryAPSingAP(Gb,r); |
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| 389 | } |
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| 390 | else |
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| 391 | { |
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| 392 | CanonicalForm F( convSingTrPFactoryP( f, r ) ), G( convSingTrPFactoryP( g, r ) ); |
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| 393 | CanonicalForm FpG=F+G; |
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| 394 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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| 395 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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| 396 | { |
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| 397 | Off(SW_RATIONAL); |
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| 398 | WerrorS("not univariate"); |
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| 399 | return TRUE; |
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| 400 | } |
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| 401 | res= convFactoryPSingTrP( extgcd( F, G, Fa, Gb ), r ); |
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| 402 | pa=convFactoryPSingTrP(Fa, r); |
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| 403 | pb=convFactoryPSingTrP(Gb, r); |
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| 404 | } |
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[35aab3] | 405 | Off(SW_RATIONAL); |
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[ce2576] | 406 | } |
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| 407 | else |
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| 408 | { |
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| 409 | WerrorS( feNotImplemented ); |
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[35aab3] | 410 | return TRUE; |
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| 411 | } |
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[a86cda] | 412 | #ifndef NDEBUG |
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| 413 | // checking the result of extgcd: |
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| 414 | poly dummy; |
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[ce3f53c] | 415 | dummy=p_Sub(p_Add_q(pp_Mult_qq(f,pa,r),pp_Mult_qq(g,pb,r),r),p_Copy(res,r),r); |
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[a86cda] | 416 | if (dummy!=NULL) |
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| 417 | { |
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[ce3f53c] | 418 | PrintS("extgcd( ");p_Write(f,r);p_Write0(g,r);PrintS(" )\n"); |
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[ce2576] | 419 | PrintS("extgcd( ");p_Write(f,r);p_Write0(g,r);PrintS(" )\n"); |
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[ce3f53c] | 420 | p_Delete(&dummy,r); |
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[a86cda] | 421 | } |
---|
[9d9078] | 422 | #endif |
---|
[35aab3] | 423 | return FALSE; |
---|
| 424 | } |
---|
| 425 | |
---|
[ce3f53c] | 426 | poly singclap_pdivide ( poly f, poly g, const ring r ) |
---|
[35aab3] | 427 | { |
---|
| 428 | poly res=NULL; |
---|
| 429 | On(SW_RATIONAL); |
---|
[ce2576] | 430 | if (rField_is_Zp(r) || rField_is_Q(r)) |
---|
| 431 | { |
---|
| 432 | setCharacteristic( rChar(r) ); |
---|
| 433 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
| 434 | res = convFactoryPSingP( F / G,r ); |
---|
| 435 | } |
---|
| 436 | else if (rField_is_Extension(r)) |
---|
| 437 | { |
---|
| 438 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
| 439 | else setCharacteristic( rChar(r) ); |
---|
[dd668f] | 440 | if (r->cf->extRing->qideal!=NULL) |
---|
[ce2576] | 441 | { |
---|
[dd668f] | 442 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
[ce2576] | 443 | r->cf->extRing); |
---|
| 444 | Variable a=rootOf(mipo); |
---|
| 445 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
| 446 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
| 447 | res= convFactoryAPSingAP( F / G, r ); |
---|
| 448 | } |
---|
| 449 | else |
---|
| 450 | { |
---|
| 451 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
| 452 | res= convFactoryPSingTrP( F / G,r ); |
---|
| 453 | } |
---|
| 454 | } |
---|
| 455 | #if 0 // not yet working |
---|
| 456 | else if (rField_is_GF()) |
---|
| 457 | { |
---|
| 458 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
| 459 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
| 460 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
| 461 | res = convFactoryGFSingGF( F / G ); |
---|
| 462 | } |
---|
| 463 | #endif |
---|
| 464 | else |
---|
| 465 | WerrorS( feNotImplemented ); |
---|
[d1f231] | 466 | Off(SW_RATIONAL); |
---|
| 467 | return res; |
---|
| 468 | } |
---|
| 469 | |
---|
[ce3f53c] | 470 | void singclap_divide_content ( poly f, const ring r ) |
---|
[35aab3] | 471 | { |
---|
| 472 | if ( f==NULL ) |
---|
| 473 | { |
---|
| 474 | return; |
---|
| 475 | } |
---|
| 476 | else if ( pNext( f ) == NULL ) |
---|
| 477 | { |
---|
[ce3f53c] | 478 | p_SetCoeff( f, n_Init( 1, r->cf ), r ); |
---|
[35aab3] | 479 | return; |
---|
| 480 | } |
---|
| 481 | else |
---|
| 482 | { |
---|
[ce3f53c] | 483 | if ( rField_is_Q_a(r) ) |
---|
[35aab3] | 484 | setCharacteristic( 0 ); |
---|
[ce3f53c] | 485 | else if ( rField_is_Zp_a(r) ) |
---|
| 486 | setCharacteristic( -rChar(r) ); |
---|
[35aab3] | 487 | else |
---|
| 488 | return; /* not implemented*/ |
---|
| 489 | |
---|
| 490 | CFList L; |
---|
| 491 | CanonicalForm g, h; |
---|
| 492 | poly p = pNext(f); |
---|
| 493 | |
---|
| 494 | // first attemp: find 2 smallest g: |
---|
| 495 | |
---|
| 496 | number g1=pGetCoeff(f); |
---|
| 497 | number g2=pGetCoeff(p); // p==pNext(f); |
---|
| 498 | pIter(p); |
---|
[ce3f53c] | 499 | int sz1=n_Size(g1, r->cf); |
---|
| 500 | int sz2=n_Size(g2, r->cf); |
---|
[35aab3] | 501 | if (sz1>sz2) |
---|
| 502 | { |
---|
| 503 | number gg=g1; |
---|
| 504 | g1=g2; g2=gg; |
---|
| 505 | int sz=sz1; |
---|
| 506 | sz1=sz2; sz2=sz; |
---|
| 507 | } |
---|
| 508 | while (p!=NULL) |
---|
| 509 | { |
---|
[ce3f53c] | 510 | int n_sz=n_Size(pGetCoeff(p),r->cf); |
---|
[35aab3] | 511 | if (n_sz<sz1) |
---|
| 512 | { |
---|
| 513 | sz2=sz1; |
---|
| 514 | g2=g1; |
---|
| 515 | g1=pGetCoeff(p); |
---|
| 516 | sz1=n_sz; |
---|
| 517 | if (sz1<=3) break; |
---|
| 518 | } |
---|
| 519 | else if(n_sz<sz2) |
---|
| 520 | { |
---|
| 521 | sz2=n_sz; |
---|
| 522 | g2=pGetCoeff(p); |
---|
| 523 | sz2=n_sz; |
---|
| 524 | } |
---|
| 525 | pIter(p); |
---|
| 526 | } |
---|
[7b2b05] | 527 | g = convSingPFactoryP( NUM(((fraction)g1)), r->cf->extRing ); |
---|
| 528 | g = gcd( g, convSingPFactoryP( NUM(((fraction)g2)) , r->cf->extRing)); |
---|
[35aab3] | 529 | |
---|
| 530 | // second run: gcd's |
---|
| 531 | |
---|
| 532 | p = f; |
---|
| 533 | while ( (p != NULL) && (g != 1) && ( g != 0)) |
---|
| 534 | { |
---|
[7b2b05] | 535 | h = convSingPFactoryP( NUM(((fraction)pGetCoeff(p))), r->cf->extRing ); |
---|
[35aab3] | 536 | pIter( p ); |
---|
| 537 | |
---|
| 538 | g = gcd( g, h ); |
---|
| 539 | |
---|
| 540 | L.append( h ); |
---|
| 541 | } |
---|
| 542 | if (( g == 1 ) || (g == 0)) |
---|
| 543 | { |
---|
| 544 | // pTest(f); |
---|
| 545 | return; |
---|
| 546 | } |
---|
| 547 | else |
---|
| 548 | { |
---|
| 549 | CFListIterator i; |
---|
| 550 | for ( i = L, p = f; i.hasItem(); i++, p=pNext(p) ) |
---|
| 551 | { |
---|
[7b2b05] | 552 | fraction c=(fraction)pGetCoeff(p); |
---|
| 553 | p_Delete(&(NUM(c)),r->cf->extRing); // 2nd arg used to be nacRing |
---|
| 554 | NUM(c)=convFactoryPSingP( i.getItem() / g, r->cf->extRing ); |
---|
[35aab3] | 555 | //nTest((number)c); |
---|
| 556 | //#ifdef LDEBUG |
---|
| 557 | //number cn=(number)c; |
---|
| 558 | //StringSetS(""); nWrite(nt); StringAppend(" ==> "); |
---|
[00d2a4] | 559 | //nWrite(cn);PrintS(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s); |
---|
[35aab3] | 560 | //#endif |
---|
| 561 | } |
---|
| 562 | } |
---|
| 563 | // pTest(f); |
---|
| 564 | } |
---|
| 565 | } |
---|
| 566 | |
---|
[ce3f53c] | 567 | BOOLEAN count_Factors(ideal I, intvec *v,int j, poly &f, poly fac, const ring r) |
---|
| 568 | { |
---|
| 569 | p_Test(f,r); |
---|
| 570 | p_Test(fac,r); |
---|
[0a55e5] | 571 | int e=0; |
---|
[ce3f53c] | 572 | if (!p_IsConstantPoly(fac,r)) |
---|
[0a55e5] | 573 | { |
---|
| 574 | #ifdef FACTORIZE2_DEBUG |
---|
[ce2576] | 575 | printf("start count_Factors(%d), Fdeg=%d, factor deg=%d\n",j,p_Totaldegree(f,r),p_Totaldegree(fac,r)); |
---|
[1db880] | 576 | p_wrp(fac,r);PrintLn(); |
---|
[0a55e5] | 577 | #endif |
---|
| 578 | On(SW_RATIONAL); |
---|
| 579 | CanonicalForm F, FAC,Q,R; |
---|
| 580 | Variable a; |
---|
[ce2576] | 581 | if (rField_is_Zp(r) || rField_is_Q(r)) |
---|
| 582 | { |
---|
| 583 | F=convSingPFactoryP( f,r ); |
---|
| 584 | FAC=convSingPFactoryP( fac,r ); |
---|
| 585 | } |
---|
| 586 | else if (rField_is_Extension(r)) |
---|
| 587 | { |
---|
[dd668f] | 588 | if (r->cf->extRing->qideal!=NULL) |
---|
[ce2576] | 589 | { |
---|
[dd668f] | 590 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
[ce2576] | 591 | r->cf->extRing); |
---|
| 592 | a=rootOf(mipo); |
---|
| 593 | F=convSingAPFactoryAP( f,a,r ); |
---|
| 594 | FAC=convSingAPFactoryAP( fac,a,r ); |
---|
| 595 | } |
---|
| 596 | else |
---|
| 597 | { |
---|
| 598 | F=convSingTrPFactoryP( f,r ); |
---|
| 599 | FAC=convSingTrPFactoryP( fac,r ); |
---|
| 600 | } |
---|
| 601 | } |
---|
| 602 | else |
---|
| 603 | WerrorS( feNotImplemented ); |
---|
[0a55e5] | 604 | |
---|
| 605 | poly q; |
---|
| 606 | loop |
---|
| 607 | { |
---|
| 608 | Q=F; |
---|
| 609 | Q/=FAC; |
---|
| 610 | R=Q; |
---|
| 611 | R*=FAC; |
---|
| 612 | R-=F; |
---|
| 613 | if (R.isZero()) |
---|
| 614 | { |
---|
[ce2576] | 615 | if (rField_is_Zp(r) || rField_is_Q(r)) |
---|
| 616 | { |
---|
| 617 | q = convFactoryPSingP( Q,r ); |
---|
| 618 | } |
---|
| 619 | else if (rField_is_Extension(r)) |
---|
| 620 | { |
---|
[dd668f] | 621 | if (r->cf->extRing->qideal!=NULL) |
---|
[ce2576] | 622 | { |
---|
| 623 | q= convFactoryAPSingAP( Q,r ); |
---|
| 624 | } |
---|
| 625 | else |
---|
| 626 | { |
---|
| 627 | q= convFactoryPSingTrP( Q,r ); |
---|
| 628 | } |
---|
| 629 | } |
---|
[ce3f53c] | 630 | e++; p_Delete(&f,r); f=q; q=NULL; F=Q; |
---|
[0a55e5] | 631 | } |
---|
| 632 | else |
---|
| 633 | { |
---|
| 634 | break; |
---|
| 635 | } |
---|
| 636 | } |
---|
| 637 | if (e==0) |
---|
| 638 | { |
---|
| 639 | Off(SW_RATIONAL); |
---|
| 640 | return FALSE; |
---|
| 641 | } |
---|
| 642 | } |
---|
| 643 | else e=1; |
---|
| 644 | I->m[j]=fac; |
---|
| 645 | if (v!=NULL) (*v)[j]=e; |
---|
| 646 | Off(SW_RATIONAL); |
---|
| 647 | return TRUE; |
---|
| 648 | } |
---|
| 649 | |
---|
[cd6df87] | 650 | #ifdef HAVE_FACTORY |
---|
[a5d9313] | 651 | int singclap_factorize_retry; |
---|
[5348866] | 652 | # ifdef HAVE_LIBFAC |
---|
| 653 | extern int libfac_interruptflag; |
---|
| 654 | # endif |
---|
[cd6df87] | 655 | #endif |
---|
[a5d9313] | 656 | |
---|
[ce3f53c] | 657 | ideal singclap_factorize ( poly f, intvec ** v , int with_exps, const ring r) |
---|
[93e7e91] | 658 | /* destroys f, sets *v */ |
---|
[35aab3] | 659 | { |
---|
[ce3f53c] | 660 | p_Test(f,r); |
---|
[0a55e5] | 661 | #ifdef FACTORIZE2_DEBUG |
---|
[ce2576] | 662 | printf("singclap_factorize, degree %ld\n",p_Totaldegree(f,r)); |
---|
[0a55e5] | 663 | #endif |
---|
[35aab3] | 664 | // with_exps: 3,1 return only true factors, no exponents |
---|
| 665 | // 2 return true factors and exponents |
---|
| 666 | // 0 return coeff, factors and exponents |
---|
[ee5d91] | 667 | BOOLEAN save_errorreported=errorreported; |
---|
[35aab3] | 668 | |
---|
| 669 | ideal res=NULL; |
---|
| 670 | |
---|
| 671 | // handle factorize(0) ========================================= |
---|
| 672 | if (f==NULL) |
---|
| 673 | { |
---|
| 674 | res=idInit(1,1); |
---|
| 675 | if (with_exps!=1) |
---|
| 676 | { |
---|
| 677 | (*v)=new intvec(1); |
---|
| 678 | (**v)[0]=1; |
---|
| 679 | } |
---|
| 680 | return res; |
---|
| 681 | } |
---|
| 682 | // handle factorize(mon) ========================================= |
---|
| 683 | if (pNext(f)==NULL) |
---|
| 684 | { |
---|
| 685 | int i=0; |
---|
| 686 | int n=0; |
---|
| 687 | int e; |
---|
[ce3f53c] | 688 | for(i=rVar(r);i>0;i--) if(p_GetExp(f,i,r)!=0) n++; |
---|
[35aab3] | 689 | if (with_exps==0) n++; // with coeff |
---|
| 690 | res=idInit(si_max(n,1),1); |
---|
| 691 | switch(with_exps) |
---|
| 692 | { |
---|
| 693 | case 0: // with coef & exp. |
---|
[ce3f53c] | 694 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
[35aab3] | 695 | // no break |
---|
| 696 | case 2: // with exp. |
---|
[54ff35] | 697 | (*v)=new intvec(si_max(1,n)); |
---|
[35aab3] | 698 | (**v)[0]=1; |
---|
| 699 | // no break |
---|
| 700 | case 1: ; |
---|
| 701 | #ifdef TEST |
---|
| 702 | default: ; |
---|
| 703 | #endif |
---|
| 704 | } |
---|
| 705 | if (n==0) |
---|
| 706 | { |
---|
[ce3f53c] | 707 | res->m[0]=p_One(r); |
---|
[35aab3] | 708 | // (**v)[0]=1; is already done |
---|
| 709 | } |
---|
[93e7e91] | 710 | else |
---|
[35aab3] | 711 | { |
---|
[ce3f53c] | 712 | for(i=rVar(r);i>0;i--) |
---|
[35aab3] | 713 | { |
---|
[ce3f53c] | 714 | e=p_GetExp(f,i,r); |
---|
[93e7e91] | 715 | if(e!=0) |
---|
| 716 | { |
---|
| 717 | n--; |
---|
[ce3f53c] | 718 | poly p=p_One(r); |
---|
| 719 | p_SetExp(p,i,1,r); |
---|
| 720 | p_Setm(p,r); |
---|
[93e7e91] | 721 | res->m[n]=p; |
---|
| 722 | if (with_exps!=1) (**v)[n]=e; |
---|
| 723 | } |
---|
[35aab3] | 724 | } |
---|
| 725 | } |
---|
[ce3f53c] | 726 | p_Delete(&f,r); |
---|
[35aab3] | 727 | return res; |
---|
| 728 | } |
---|
[ce2576] | 729 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
[54ff35] | 730 | // use factory/libfac in general ============================== |
---|
[35aab3] | 731 | Off(SW_RATIONAL); |
---|
| 732 | On(SW_SYMMETRIC_FF); |
---|
| 733 | #ifdef HAVE_NTL |
---|
| 734 | extern int prime_number; |
---|
[ce3f53c] | 735 | if(rField_is_Q(r)) prime_number=0; |
---|
[35aab3] | 736 | #endif |
---|
| 737 | CFFList L; |
---|
| 738 | number N=NULL; |
---|
[ffdd694] | 739 | number NN=NULL; |
---|
[ce3f53c] | 740 | number old_lead_coeff=n_Copy(pGetCoeff(f), r->cf); |
---|
[35aab3] | 741 | |
---|
[ce3f53c] | 742 | if (!rField_is_Zp(r) && !rField_is_Zp_a(r)) /* Q, Q(a) */ |
---|
[0a55e5] | 743 | { |
---|
| 744 | //if (f!=NULL) // already tested at start of routine |
---|
| 745 | { |
---|
[ce3f53c] | 746 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
[0a55e5] | 747 | if (with_exps==0) |
---|
[ce3f53c] | 748 | N=n_Copy(n0,r->cf); |
---|
| 749 | p_Cleardenom(f, r); |
---|
[ce2576] | 750 | //after here f should not have a denominator!! |
---|
| 751 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
[ce3f53c] | 752 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
| 753 | n_Delete(&n0,r->cf); |
---|
[0a55e5] | 754 | if (with_exps==0) |
---|
| 755 | { |
---|
[ce3f53c] | 756 | n_Delete(&N,r->cf); |
---|
| 757 | N=n_Copy(NN,r->cf); |
---|
[0a55e5] | 758 | } |
---|
| 759 | } |
---|
| 760 | } |
---|
[ce3f53c] | 761 | else if (rField_is_Zp_a(r)) |
---|
[35aab3] | 762 | { |
---|
[ffdd694] | 763 | //if (f!=NULL) // already tested at start of routine |
---|
[0a55e5] | 764 | if (singclap_factorize_retry==0) |
---|
[35aab3] | 765 | { |
---|
[ce3f53c] | 766 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
[ffdd694] | 767 | if (with_exps==0) |
---|
[ce3f53c] | 768 | N=n_Copy(n0,r->cf); |
---|
| 769 | p_Norm(f,r); |
---|
| 770 | p_Cleardenom(f, r); |
---|
| 771 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
| 772 | n_Delete(&n0,r->cf); |
---|
[ffdd694] | 773 | if (with_exps==0) |
---|
[35aab3] | 774 | { |
---|
[ce3f53c] | 775 | n_Delete(&N,r->cf); |
---|
| 776 | N=n_Copy(NN,r->cf); |
---|
[35aab3] | 777 | } |
---|
| 778 | } |
---|
[ffdd694] | 779 | } |
---|
[ce3f53c] | 780 | if (rField_is_Q(r) || rField_is_Zp(r)) |
---|
[ffdd694] | 781 | { |
---|
[ce3f53c] | 782 | setCharacteristic( rChar(r) ); |
---|
| 783 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
[34ceab] | 784 | L = factorize( F ); |
---|
[35aab3] | 785 | } |
---|
| 786 | // and over Q(a) / Fp(a) |
---|
[ce3f53c] | 787 | else if (rField_is_Extension(r)) |
---|
[35aab3] | 788 | { |
---|
[ce2576] | 789 | if (rField_is_Q_a (r)) setCharacteristic (0); |
---|
| 790 | else setCharacteristic( rChar(r) ); |
---|
[dd668f] | 791 | if (r->cf->extRing->qideal!=NULL) |
---|
[35aab3] | 792 | { |
---|
[dd668f] | 793 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
[6ccdd3a] | 794 | r->cf->extRing); |
---|
[35aab3] | 795 | Variable a=rootOf(mipo); |
---|
[ce2576] | 796 | CanonicalForm F( convSingAPFactoryAP( f, a, r ) ); |
---|
[ce3f53c] | 797 | if (rField_is_Zp_a(r)) |
---|
[35aab3] | 798 | { |
---|
| 799 | L = factorize( F, a ); |
---|
| 800 | } |
---|
| 801 | else |
---|
| 802 | { |
---|
[34ceab] | 803 | // over Q(a) |
---|
[fcf7587] | 804 | L= factorize (F, a); |
---|
[35aab3] | 805 | } |
---|
| 806 | } |
---|
| 807 | else |
---|
| 808 | { |
---|
[ce2576] | 809 | CanonicalForm F( convSingTrPFactoryP( f,r ) ); |
---|
[34ceab] | 810 | L = factorize( F ); |
---|
[35aab3] | 811 | } |
---|
| 812 | } |
---|
| 813 | else |
---|
| 814 | { |
---|
| 815 | goto notImpl; |
---|
| 816 | } |
---|
| 817 | { |
---|
[ce3f53c] | 818 | poly ff=p_Copy(f,r); // a copy for the retry stuff |
---|
[35aab3] | 819 | // the first factor should be a constant |
---|
| 820 | if ( ! L.getFirst().factor().inCoeffDomain() ) |
---|
| 821 | L.insert(CFFactor(1,1)); |
---|
| 822 | // convert into ideal |
---|
| 823 | int n = L.length(); |
---|
[91cb92] | 824 | if (n==0) n=1; |
---|
[35aab3] | 825 | CFFListIterator J=L; |
---|
| 826 | int j=0; |
---|
| 827 | if (with_exps!=1) |
---|
| 828 | { |
---|
| 829 | if ((with_exps==2)&&(n>1)) |
---|
| 830 | { |
---|
| 831 | n--; |
---|
| 832 | J++; |
---|
| 833 | } |
---|
| 834 | *v = new intvec( n ); |
---|
| 835 | } |
---|
| 836 | res = idInit( n ,1); |
---|
| 837 | for ( ; J.hasItem(); J++, j++ ) |
---|
| 838 | { |
---|
| 839 | if (with_exps!=1) (**v)[j] = J.getItem().exp(); |
---|
[ce3f53c] | 840 | if (rField_is_Zp(r) || rField_is_Q(r)) /* Q, Fp */ |
---|
[8fc55e2] | 841 | { |
---|
[46f6af6] | 842 | //count_Factors(res,*v,f, j, convFactoryPSingP( J.getItem().factor() ); |
---|
[ce3f53c] | 843 | res->m[j] = convFactoryPSingP( J.getItem().factor(),r ); |
---|
[8fc55e2] | 844 | } |
---|
[35aab3] | 845 | #if 0 |
---|
| 846 | else if (rField_is_GF()) |
---|
[46f6af6] | 847 | res->m[j] = convFactoryGFSingGF( J.getItem().factor() ); |
---|
[35aab3] | 848 | #endif |
---|
[ce3f53c] | 849 | else if (rField_is_Extension(r)) /* Q(a), Fp(a) */ |
---|
[35aab3] | 850 | { |
---|
[ea1d44c] | 851 | #ifndef NDEBUG |
---|
[5d491d] | 852 | intvec *w=NULL; |
---|
| 853 | if (v!=NULL) w=*v; |
---|
[ea1d44c] | 854 | #endif |
---|
[dd668f] | 855 | if (r->cf->extRing->qideal==NULL) |
---|
[8fc55e2] | 856 | { |
---|
[ea1d44c] | 857 | #ifdef NDEBUG |
---|
| 858 | res->m[j]= convFactoryPSingTrP( J.getItem().factor(),r ); |
---|
| 859 | #else |
---|
[ce2576] | 860 | if(!count_Factors(res,w,j,ff,convFactoryPSingTrP( J.getItem().factor(),r ),r)) |
---|
[d499d1] | 861 | { |
---|
[a86cda] | 862 | if (w!=NULL) |
---|
[e080ab] | 863 | (*w)[j]=1; |
---|
[ce3f53c] | 864 | res->m[j]=p_One(r); |
---|
[d499d1] | 865 | } |
---|
[ea1d44c] | 866 | #endif |
---|
[8fc55e2] | 867 | } |
---|
[35aab3] | 868 | else |
---|
[8fc55e2] | 869 | { |
---|
[ea1d44c] | 870 | #ifdef NDEBUG |
---|
| 871 | res->m[j]= convFactoryAPSingAP( J.getItem().factor(),r ); |
---|
| 872 | #else |
---|
[ce2576] | 873 | if (!count_Factors(res,w,j,ff,convFactoryAPSingAP( J.getItem().factor(),r ),r)) |
---|
[d499d1] | 874 | { |
---|
[a86cda] | 875 | if (w!=NULL) |
---|
[e080ab] | 876 | (*w)[j]=1; |
---|
[ce3f53c] | 877 | res->m[j]=p_One(r); |
---|
[d499d1] | 878 | } |
---|
[ea1d44c] | 879 | #endif |
---|
[8fc55e2] | 880 | } |
---|
[0a55e5] | 881 | } |
---|
| 882 | } |
---|
[ea1d44c] | 883 | #ifndef NDEBUG |
---|
[ce3f53c] | 884 | if (rField_is_Extension(r) && (!p_IsConstantPoly(ff,r))) |
---|
[0a55e5] | 885 | { |
---|
| 886 | singclap_factorize_retry++; |
---|
| 887 | if (singclap_factorize_retry<3) |
---|
| 888 | { |
---|
| 889 | int jj; |
---|
| 890 | #ifdef FACTORIZE2_DEBUG |
---|
| 891 | printf("factorize_retry\n"); |
---|
| 892 | #endif |
---|
| 893 | intvec *ww=NULL; |
---|
[ce3f53c] | 894 | id_Test(res,r); |
---|
| 895 | ideal h=singclap_factorize ( ff, &ww , with_exps, r ); |
---|
| 896 | id_Test(h,r); |
---|
[0a55e5] | 897 | int l=(*v)->length(); |
---|
[91cb92] | 898 | (*v)->resize(l+ww->length()); |
---|
[0a55e5] | 899 | for(jj=0;jj<ww->length();jj++) |
---|
[91cb92] | 900 | (**v)[jj+l]=(*ww)[jj]; |
---|
[0a55e5] | 901 | delete ww; |
---|
| 902 | ideal hh=idInit(IDELEMS(res)+IDELEMS(h),1); |
---|
| 903 | for(jj=IDELEMS(res)-1;jj>=0;jj--) |
---|
| 904 | { |
---|
| 905 | hh->m[jj]=res->m[jj]; |
---|
| 906 | res->m[jj]=NULL; |
---|
| 907 | } |
---|
| 908 | for(jj=IDELEMS(h)-1;jj>=0;jj--) |
---|
| 909 | { |
---|
| 910 | hh->m[jj+IDELEMS(res)]=h->m[jj]; |
---|
| 911 | h->m[jj]=NULL; |
---|
| 912 | } |
---|
[ce3f53c] | 913 | id_Delete(&res,r); |
---|
| 914 | id_Delete(&h,r); |
---|
[0a55e5] | 915 | res=hh; |
---|
[ce3f53c] | 916 | id_Test(res,r); |
---|
[0a55e5] | 917 | ff=NULL; |
---|
| 918 | } |
---|
| 919 | else |
---|
| 920 | { |
---|
| 921 | WarnS("problem with factorize"); |
---|
[226dd7] | 922 | #if 0 |
---|
| 923 | pWrite(ff); |
---|
| 924 | idShow(res); |
---|
| 925 | #endif |
---|
[ce3f53c] | 926 | id_Delete(&res,r); |
---|
[226dd7] | 927 | res=idInit(2,1); |
---|
[ce3f53c] | 928 | res->m[0]=p_One(r); |
---|
[226dd7] | 929 | res->m[1]=ff; ff=NULL; |
---|
[35aab3] | 930 | } |
---|
| 931 | } |
---|
[ea1d44c] | 932 | #endif |
---|
[ce3f53c] | 933 | p_Delete(&ff,r); |
---|
[35aab3] | 934 | if (N!=NULL) |
---|
| 935 | { |
---|
[ce3f53c] | 936 | p_Mult_nn(res->m[0],N,r); |
---|
| 937 | n_Delete(&N,r->cf); |
---|
[ffdd694] | 938 | N=NULL; |
---|
[35aab3] | 939 | } |
---|
| 940 | // delete constants |
---|
| 941 | if (res!=NULL) |
---|
| 942 | { |
---|
| 943 | int i=IDELEMS(res)-1; |
---|
| 944 | int j=0; |
---|
| 945 | for(;i>=0;i--) |
---|
| 946 | { |
---|
| 947 | if ((res->m[i]!=NULL) |
---|
| 948 | && (pNext(res->m[i])==NULL) |
---|
[ce3f53c] | 949 | && (p_IsConstant(res->m[i],r))) |
---|
[35aab3] | 950 | { |
---|
| 951 | if (with_exps!=0) |
---|
| 952 | { |
---|
[ce3f53c] | 953 | p_Delete(&(res->m[i]),r); |
---|
[35aab3] | 954 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
| 955 | (**v)[i]=0; |
---|
| 956 | j++; |
---|
| 957 | } |
---|
| 958 | else if (i!=0) |
---|
| 959 | { |
---|
[d8932ed] | 960 | while ((v!=NULL) && ((*v)!=NULL) && ((**v)[i]>1)) |
---|
| 961 | { |
---|
[ce3f53c] | 962 | res->m[0]=p_Mult_q(res->m[0],p_Copy(res->m[i],r),r); |
---|
[d8932ed] | 963 | (**v)[i]--; |
---|
| 964 | } |
---|
[ce3f53c] | 965 | res->m[0]=p_Mult_q(res->m[0],res->m[i],r); |
---|
[35aab3] | 966 | res->m[i]=NULL; |
---|
| 967 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
[d499d1] | 968 | (**v)[i]=1; |
---|
[35aab3] | 969 | j++; |
---|
| 970 | } |
---|
| 971 | } |
---|
| 972 | } |
---|
| 973 | if (j>0) |
---|
| 974 | { |
---|
| 975 | idSkipZeroes(res); |
---|
| 976 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
| 977 | { |
---|
| 978 | intvec *w=*v; |
---|
[f12cd23] | 979 | int len=IDELEMS(res); |
---|
| 980 | *v = new intvec( len ); |
---|
[0a55e5] | 981 | for (i=0,j=0;i<si_min(w->length(),len);i++) |
---|
[35aab3] | 982 | { |
---|
| 983 | if((*w)[i]!=0) |
---|
| 984 | { |
---|
| 985 | (**v)[j]=(*w)[i]; j++; |
---|
| 986 | } |
---|
| 987 | } |
---|
| 988 | delete w; |
---|
| 989 | } |
---|
| 990 | } |
---|
| 991 | if (res->m[0]==NULL) |
---|
| 992 | { |
---|
[ce3f53c] | 993 | res->m[0]=p_One(r); |
---|
[35aab3] | 994 | } |
---|
| 995 | } |
---|
| 996 | } |
---|
[dd668f] | 997 | if (rField_is_Q_a(r) && (r->cf->extRing->qideal!=NULL)) |
---|
[35aab3] | 998 | { |
---|
| 999 | int i=IDELEMS(res)-1; |
---|
| 1000 | int stop=1; |
---|
| 1001 | if (with_exps!=0) stop=0; |
---|
| 1002 | for(;i>=stop;i--) |
---|
| 1003 | { |
---|
[ce3f53c] | 1004 | p_Norm(res->m[i],r); |
---|
[35aab3] | 1005 | } |
---|
[ce3f53c] | 1006 | if (with_exps==0) p_SetCoeff(res->m[0],old_lead_coeff,r); |
---|
| 1007 | else n_Delete(&old_lead_coeff,r->cf); |
---|
[35aab3] | 1008 | } |
---|
| 1009 | else |
---|
[ce3f53c] | 1010 | n_Delete(&old_lead_coeff,r->cf); |
---|
[ee5d91] | 1011 | errorreported=save_errorreported; |
---|
[35aab3] | 1012 | notImpl: |
---|
| 1013 | if (res==NULL) |
---|
| 1014 | WerrorS( feNotImplemented ); |
---|
[ffdd694] | 1015 | if (NN!=NULL) |
---|
[35aab3] | 1016 | { |
---|
[ce3f53c] | 1017 | n_Delete(&NN,r->cf); |
---|
[ffdd694] | 1018 | } |
---|
| 1019 | if (N!=NULL) |
---|
| 1020 | { |
---|
[ce3f53c] | 1021 | n_Delete(&N,r->cf); |
---|
[35aab3] | 1022 | } |
---|
[ce3f53c] | 1023 | if (f!=NULL) p_Delete(&f,r); |
---|
[35aab3] | 1024 | //PrintS("......S\n"); |
---|
| 1025 | return res; |
---|
| 1026 | } |
---|
[feed237] | 1027 | #ifdef HAVE_NTL |
---|
| 1028 | ideal singclap_absBiFactorize ( poly f, ideal & mipos, intvec ** exps, int & numFactors, const ring r) |
---|
| 1029 | { |
---|
| 1030 | p_Test(f, r); |
---|
| 1031 | |
---|
| 1032 | ideal res=NULL; |
---|
| 1033 | |
---|
| 1034 | int offs = rPar(r); |
---|
| 1035 | if (f==NULL) |
---|
| 1036 | { |
---|
| 1037 | res= idInit (1, 1); |
---|
| 1038 | mipos= idInit (1, 1); |
---|
| 1039 | mipos->m[0]= convFactoryPSingTrP (Variable (offs), r); //overkill |
---|
| 1040 | (*exps)=new intvec (1); |
---|
| 1041 | (**exps)[0]= 1; |
---|
| 1042 | numFactors= 0; |
---|
| 1043 | return res; |
---|
| 1044 | } |
---|
| 1045 | CanonicalForm F( convSingTrPFactoryP( f, r) ); |
---|
| 1046 | |
---|
| 1047 | if (getNumVars (F) > 2) |
---|
| 1048 | { |
---|
| 1049 | WerrorS( feNotImplemented ); |
---|
| 1050 | return res; |
---|
| 1051 | } |
---|
| 1052 | CFAFList absFactors= absFactorize (F); |
---|
| 1053 | |
---|
| 1054 | int n= absFactors.length(); |
---|
| 1055 | *exps=new intvec (n); |
---|
| 1056 | |
---|
| 1057 | res= idInit (n, 1); |
---|
| 1058 | |
---|
| 1059 | mipos= idInit (n, 1); |
---|
| 1060 | |
---|
| 1061 | Variable x= Variable (offs); |
---|
| 1062 | Variable alpha; |
---|
| 1063 | int i= 0; |
---|
| 1064 | numFactors= 0; |
---|
| 1065 | int count; |
---|
| 1066 | CFAFListIterator iter= absFactors; |
---|
| 1067 | CanonicalForm lead= iter.getItem().factor(); |
---|
| 1068 | if (iter.getItem().factor().inCoeffDomain()) |
---|
| 1069 | { |
---|
| 1070 | i++; |
---|
| 1071 | iter++; |
---|
| 1072 | } |
---|
| 1073 | for (; iter.hasItem(); iter++, i++) |
---|
| 1074 | { |
---|
| 1075 | (**exps)[i]= iter.getItem().exp(); |
---|
| 1076 | alpha= iter.getItem().minpoly().mvar(); |
---|
| 1077 | if (iter.getItem().minpoly().isOne()) //TODO make sure isOn (SW_RATIONAL) == true |
---|
| 1078 | lead /= bCommonDen (iter.getItem().factor()); |
---|
| 1079 | else |
---|
| 1080 | lead /= power (bCommonDen (iter.getItem().factor()), degree (iter.getItem().minpoly())); |
---|
| 1081 | res->m[i]= convFactoryPSingTrP (replacevar (iter.getItem().factor()*bCommonDen (iter.getItem().factor()), alpha, x), r); |
---|
| 1082 | if (iter.getItem().minpoly().isOne()) |
---|
| 1083 | { |
---|
| 1084 | count= iter.getItem().exp(); |
---|
| 1085 | mipos->m[i]= convFactoryPSingTrP (x,r); |
---|
| 1086 | } |
---|
| 1087 | else |
---|
| 1088 | { |
---|
| 1089 | count= iter.getItem().exp()*degree (iter.getItem().minpoly()); |
---|
| 1090 | mipos->m[i]= convFactoryPSingTrP (replacevar (iter.getItem().minpoly(), alpha, x), r); |
---|
| 1091 | } |
---|
| 1092 | numFactors += count; |
---|
| 1093 | } |
---|
| 1094 | |
---|
| 1095 | (**exps)[0]= 1; |
---|
| 1096 | res->m[0]= convFactoryPSingTrP (lead, r); |
---|
| 1097 | mipos->m[0]= convFactoryPSingTrP (x, r); |
---|
| 1098 | return res; |
---|
| 1099 | } |
---|
| 1100 | #endif |
---|
[3ef9c8] | 1101 | ideal singclap_sqrfree ( poly f, intvec ** v , int with_exps, const ring r) |
---|
[0dd641] | 1102 | { |
---|
[ce3f53c] | 1103 | p_Test(f,r); |
---|
[0dd641] | 1104 | #ifdef FACTORIZE2_DEBUG |
---|
| 1105 | printf("singclap_sqrfree, degree %d\n",pTotaldegree(f)); |
---|
| 1106 | #endif |
---|
| 1107 | // with_exps: 3,1 return only true factors, no exponents |
---|
| 1108 | // 2 return true factors and exponents |
---|
| 1109 | // 0 return coeff, factors and exponents |
---|
| 1110 | BOOLEAN save_errorreported=errorreported; |
---|
| 1111 | |
---|
| 1112 | ideal res=NULL; |
---|
| 1113 | |
---|
| 1114 | // handle factorize(0) ========================================= |
---|
| 1115 | if (f==NULL) |
---|
| 1116 | { |
---|
| 1117 | res=idInit(1,1); |
---|
[c92097b] | 1118 | if (with_exps!=1 && with_exps!=3) |
---|
[3ef9c8] | 1119 | { |
---|
| 1120 | (*v)=new intvec(1); |
---|
| 1121 | (**v)[0]=1; |
---|
| 1122 | } |
---|
[0dd641] | 1123 | return res; |
---|
| 1124 | } |
---|
| 1125 | // handle factorize(mon) ========================================= |
---|
| 1126 | if (pNext(f)==NULL) |
---|
| 1127 | { |
---|
| 1128 | int i=0; |
---|
| 1129 | int n=0; |
---|
| 1130 | int e; |
---|
[ce3f53c] | 1131 | for(i=rVar(r);i>0;i--) if(p_GetExp(f,i,r)!=0) n++; |
---|
[c92097b] | 1132 | if (with_exps==0 || with_exps==3) n++; // with coeff |
---|
[0dd641] | 1133 | res=idInit(si_max(n,1),1); |
---|
[3ef9c8] | 1134 | switch(with_exps) |
---|
| 1135 | { |
---|
| 1136 | case 0: // with coef & exp. |
---|
| 1137 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
| 1138 | // no break |
---|
[c92097b] | 1139 | case 3: // with coef & exp. |
---|
| 1140 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
| 1141 | // no break |
---|
[3ef9c8] | 1142 | case 2: // with exp. |
---|
| 1143 | (*v)=new intvec(si_max(1,n)); |
---|
| 1144 | (**v)[0]=1; |
---|
| 1145 | // no break |
---|
| 1146 | case 1: ; |
---|
| 1147 | #ifdef TEST |
---|
| 1148 | default: ; |
---|
| 1149 | #endif |
---|
| 1150 | } |
---|
[ce3f53c] | 1151 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
[0dd641] | 1152 | if (n==0) |
---|
| 1153 | { |
---|
[ce3f53c] | 1154 | res->m[0]=p_One(r); |
---|
[0dd641] | 1155 | // (**v)[0]=1; is already done |
---|
| 1156 | } |
---|
[3ef9c8] | 1157 | else |
---|
[0dd641] | 1158 | { |
---|
[3ef9c8] | 1159 | for(i=rVar(r);i>0;i--) |
---|
[0dd641] | 1160 | { |
---|
[3ef9c8] | 1161 | e=p_GetExp(f,i,r); |
---|
| 1162 | if(e!=0) |
---|
| 1163 | { |
---|
| 1164 | n--; |
---|
| 1165 | poly p=p_One(r); |
---|
| 1166 | p_SetExp(p,i,1,r); |
---|
| 1167 | p_Setm(p,r); |
---|
| 1168 | res->m[n]=p; |
---|
| 1169 | if (with_exps!=1) (**v)[n]=e; |
---|
| 1170 | } |
---|
[0dd641] | 1171 | } |
---|
| 1172 | } |
---|
[3ef9c8] | 1173 | p_Delete(&f,r); |
---|
[0dd641] | 1174 | return res; |
---|
| 1175 | } |
---|
| 1176 | //PrintS("S:");pWrite(f);PrintLn(); |
---|
| 1177 | // use factory/libfac in general ============================== |
---|
| 1178 | Off(SW_RATIONAL); |
---|
| 1179 | On(SW_SYMMETRIC_FF); |
---|
| 1180 | #ifdef HAVE_NTL |
---|
| 1181 | extern int prime_number; |
---|
[ce3f53c] | 1182 | if(rField_is_Q(r)) prime_number=0; |
---|
[0dd641] | 1183 | #endif |
---|
| 1184 | CFFList L; |
---|
[3ef9c8] | 1185 | number N=NULL; |
---|
| 1186 | number NN=NULL; |
---|
[f78374] | 1187 | number old_lead_coeff=n_Copy(pGetCoeff(f), r->cf); |
---|
[0dd641] | 1188 | |
---|
[ce3f53c] | 1189 | if (!rField_is_Zp(r) && !rField_is_Zp_a(r)) /* Q, Q(a) */ |
---|
[0dd641] | 1190 | { |
---|
| 1191 | //if (f!=NULL) // already tested at start of routine |
---|
[3ef9c8] | 1192 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
[c92097b] | 1193 | if (with_exps==0 || with_exps==3) |
---|
[3ef9c8] | 1194 | N=n_Copy(n0,r->cf); |
---|
| 1195 | p_Cleardenom(f, r); |
---|
| 1196 | //after here f should not have a denominator!! |
---|
| 1197 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
| 1198 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
| 1199 | n_Delete(&n0,r->cf); |
---|
[c92097b] | 1200 | if (with_exps==0 || with_exps==3) |
---|
[0dd641] | 1201 | { |
---|
[3ef9c8] | 1202 | n_Delete(&N,r->cf); |
---|
| 1203 | N=n_Copy(NN,r->cf); |
---|
[0dd641] | 1204 | } |
---|
| 1205 | } |
---|
[ce3f53c] | 1206 | else if (rField_is_Zp_a(r)) |
---|
[0dd641] | 1207 | { |
---|
| 1208 | //if (f!=NULL) // already tested at start of routine |
---|
| 1209 | if (singclap_factorize_retry==0) |
---|
| 1210 | { |
---|
[3ef9c8] | 1211 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
[c92097b] | 1212 | if (with_exps==0 || with_exps==3) |
---|
[3ef9c8] | 1213 | N=n_Copy(n0,r->cf); |
---|
[ce3f53c] | 1214 | p_Norm(f,r); |
---|
| 1215 | p_Cleardenom(f, r); |
---|
[3ef9c8] | 1216 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
| 1217 | n_Delete(&n0,r->cf); |
---|
[c92097b] | 1218 | if (with_exps==0 || with_exps==3) |
---|
[3ef9c8] | 1219 | { |
---|
| 1220 | n_Delete(&N,r->cf); |
---|
| 1221 | N=n_Copy(NN,r->cf); |
---|
| 1222 | } |
---|
[0dd641] | 1223 | } |
---|
| 1224 | } |
---|
[ce3f53c] | 1225 | if (rField_is_Q(r) || rField_is_Zp(r)) |
---|
[0dd641] | 1226 | { |
---|
[ce3f53c] | 1227 | setCharacteristic( rChar(r) ); |
---|
| 1228 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
[85194f2] | 1229 | L = sqrFree( F ); |
---|
[0dd641] | 1230 | } |
---|
[3ef9c8] | 1231 | else if (rField_is_Extension(r)) |
---|
| 1232 | { |
---|
| 1233 | if (rField_is_Q_a (r)) setCharacteristic (0); |
---|
| 1234 | else setCharacteristic( rChar(r) ); |
---|
[dd668f] | 1235 | if (r->cf->extRing->qideal!=NULL) |
---|
[3ef9c8] | 1236 | { |
---|
[dd668f] | 1237 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
[3ef9c8] | 1238 | r->cf->extRing); |
---|
| 1239 | Variable a=rootOf(mipo); |
---|
| 1240 | CanonicalForm F( convSingAPFactoryAP( f, a, r ) ); |
---|
| 1241 | L= sqrFree (F); |
---|
| 1242 | } |
---|
| 1243 | else |
---|
| 1244 | { |
---|
| 1245 | CanonicalForm F( convSingTrPFactoryP( f,r ) ); |
---|
| 1246 | L = sqrFree( F ); |
---|
| 1247 | } |
---|
| 1248 | } |
---|
[0dd641] | 1249 | #if 0 |
---|
| 1250 | else if (rField_is_GF()) |
---|
| 1251 | { |
---|
[ce3f53c] | 1252 | int c=rChar(r); |
---|
[0dd641] | 1253 | setCharacteristic( c, primepower(c) ); |
---|
| 1254 | CanonicalForm F( convSingGFFactoryGF( f ) ); |
---|
| 1255 | if (F.isUnivariate()) |
---|
| 1256 | { |
---|
| 1257 | L = factorize( F ); |
---|
| 1258 | } |
---|
| 1259 | else |
---|
| 1260 | { |
---|
| 1261 | goto notImpl; |
---|
| 1262 | } |
---|
| 1263 | } |
---|
| 1264 | #endif |
---|
| 1265 | else |
---|
| 1266 | { |
---|
| 1267 | goto notImpl; |
---|
| 1268 | } |
---|
| 1269 | { |
---|
| 1270 | // convert into ideal |
---|
| 1271 | int n = L.length(); |
---|
| 1272 | if (n==0) n=1; |
---|
| 1273 | CFFListIterator J=L; |
---|
| 1274 | int j=0; |
---|
[3ef9c8] | 1275 | if (with_exps!=1) |
---|
| 1276 | { |
---|
| 1277 | if ((with_exps==2)&&(n>1)) |
---|
| 1278 | { |
---|
| 1279 | n--; |
---|
| 1280 | J++; |
---|
| 1281 | } |
---|
| 1282 | *v = new intvec( n ); |
---|
| 1283 | } |
---|
[c92097b] | 1284 | else if (L.getFirst().factor().inCoeffDomain() && with_exps!=3) |
---|
[3ef9c8] | 1285 | { |
---|
| 1286 | n--; |
---|
| 1287 | J++; |
---|
| 1288 | } |
---|
[0dd641] | 1289 | res = idInit( n ,1); |
---|
| 1290 | for ( ; J.hasItem(); J++, j++ ) |
---|
| 1291 | { |
---|
[c92097b] | 1292 | if (with_exps!=1 && with_exps!=3) (**v)[j] = J.getItem().exp(); |
---|
[3ef9c8] | 1293 | if (rField_is_Zp(r) || rField_is_Q(r)) |
---|
| 1294 | res->m[j] = convFactoryPSingP( J.getItem().factor(),r ); |
---|
| 1295 | else if (rField_is_Extension(r)) /* Q(a), Fp(a) */ |
---|
| 1296 | { |
---|
[dd668f] | 1297 | if (r->cf->extRing->qideal==NULL) |
---|
[3ef9c8] | 1298 | res->m[j]=convFactoryPSingTrP( J.getItem().factor(),r ); |
---|
| 1299 | else |
---|
| 1300 | res->m[j]=convFactoryAPSingAP( J.getItem().factor(),r ); |
---|
| 1301 | } |
---|
[0dd641] | 1302 | } |
---|
| 1303 | if (res->m[0]==NULL) |
---|
| 1304 | { |
---|
[ce3f53c] | 1305 | res->m[0]=p_One(r); |
---|
[0dd641] | 1306 | } |
---|
[f78374] | 1307 | if (N!=NULL) |
---|
| 1308 | { |
---|
| 1309 | p_Mult_nn(res->m[0],N,r); |
---|
| 1310 | n_Delete(&N,r->cf); |
---|
| 1311 | N=NULL; |
---|
| 1312 | } |
---|
[0dd641] | 1313 | } |
---|
[dd668f] | 1314 | if (rField_is_Q_a(r) && (r->cf->extRing->qideal!=NULL)) |
---|
[f78374] | 1315 | { |
---|
| 1316 | int i=IDELEMS(res)-1; |
---|
| 1317 | int stop=1; |
---|
[c92097b] | 1318 | if (with_exps!=0 || with_exps==3) stop=0; |
---|
[f78374] | 1319 | for(;i>=stop;i--) |
---|
| 1320 | { |
---|
| 1321 | p_Norm(res->m[i],r); |
---|
| 1322 | } |
---|
[c92097b] | 1323 | if (with_exps==0 || with_exps==3) p_SetCoeff(res->m[0],old_lead_coeff,r); |
---|
[f78374] | 1324 | else n_Delete(&old_lead_coeff,r->cf); |
---|
| 1325 | } |
---|
| 1326 | else |
---|
| 1327 | n_Delete(&old_lead_coeff,r->cf); |
---|
[ce3f53c] | 1328 | p_Delete(&f,r); |
---|
[0dd641] | 1329 | errorreported=save_errorreported; |
---|
| 1330 | notImpl: |
---|
| 1331 | if (res==NULL) |
---|
| 1332 | WerrorS( feNotImplemented ); |
---|
[f78374] | 1333 | if (NN!=NULL) |
---|
| 1334 | { |
---|
| 1335 | n_Delete(&NN,r->cf); |
---|
| 1336 | } |
---|
| 1337 | if (N!=NULL) |
---|
| 1338 | { |
---|
| 1339 | n_Delete(&N,r->cf); |
---|
| 1340 | } |
---|
[0dd641] | 1341 | return res; |
---|
| 1342 | } |
---|
[ce3f53c] | 1343 | |
---|
[67c1dc] | 1344 | #ifdef HAVE_LIBFAC |
---|
| 1345 | matrix singclap_irrCharSeries ( ideal I, const ring r) |
---|
[35aab3] | 1346 | { |
---|
| 1347 | if (idIs0(I)) return mpNew(1,1); |
---|
| 1348 | |
---|
| 1349 | // for now there is only the possibility to handle polynomials over |
---|
| 1350 | // Q and Fp ... |
---|
| 1351 | matrix res=NULL; |
---|
| 1352 | int i; |
---|
| 1353 | Off(SW_RATIONAL); |
---|
| 1354 | On(SW_SYMMETRIC_FF); |
---|
| 1355 | CFList L; |
---|
| 1356 | ListCFList LL; |
---|
[ce3f53c] | 1357 | if (((rChar(r) == 0) || (rChar(r) > 1) ) |
---|
| 1358 | && (rPar(r)==0)) |
---|
[35aab3] | 1359 | { |
---|
[ce3f53c] | 1360 | setCharacteristic( rChar(r) ); |
---|
[35aab3] | 1361 | for(i=0;i<IDELEMS(I);i++) |
---|
| 1362 | { |
---|
| 1363 | poly p=I->m[i]; |
---|
| 1364 | if (p!=NULL) |
---|
| 1365 | { |
---|
[ce3f53c] | 1366 | p=p_Copy(p,r); |
---|
| 1367 | p_Cleardenom(p, r); |
---|
| 1368 | L.append(convSingPFactoryP(p,r)); |
---|
[35aab3] | 1369 | } |
---|
| 1370 | } |
---|
| 1371 | } |
---|
| 1372 | // and over Q(a) / Fp(a) |
---|
[ce3f53c] | 1373 | else if (( rChar(r)==1 ) // Q(a) |
---|
| 1374 | || (rChar(r) <-1)) // Fp(a) |
---|
[35aab3] | 1375 | { |
---|
[ce3f53c] | 1376 | if (rChar(r)==1) setCharacteristic( 0 ); |
---|
| 1377 | else setCharacteristic( -rChar(r) ); |
---|
[35aab3] | 1378 | for(i=0;i<IDELEMS(I);i++) |
---|
| 1379 | { |
---|
| 1380 | poly p=I->m[i]; |
---|
| 1381 | if (p!=NULL) |
---|
| 1382 | { |
---|
[ce3f53c] | 1383 | p=p_Copy(p,r); |
---|
| 1384 | p_Cleardenom(p, r); |
---|
| 1385 | L.append(convSingTrPFactoryP(p,r)); |
---|
[35aab3] | 1386 | } |
---|
| 1387 | } |
---|
| 1388 | } |
---|
| 1389 | else |
---|
| 1390 | { |
---|
| 1391 | WerrorS( feNotImplemented ); |
---|
| 1392 | return res; |
---|
| 1393 | } |
---|
| 1394 | |
---|
| 1395 | // a very bad work-around --- FIX IT in libfac |
---|
| 1396 | // should be fixed as of 2001/6/27 |
---|
| 1397 | int tries=0; |
---|
| 1398 | int m,n; |
---|
| 1399 | ListIterator<CFList> LLi; |
---|
| 1400 | loop |
---|
| 1401 | { |
---|
| 1402 | LL=IrrCharSeries(L); |
---|
| 1403 | m= LL.length(); // Anzahl Zeilen |
---|
| 1404 | n=0; |
---|
| 1405 | for ( LLi = LL; LLi.hasItem(); LLi++ ) |
---|
| 1406 | { |
---|
| 1407 | n = si_max(LLi.getItem().length(),n); |
---|
| 1408 | } |
---|
| 1409 | if ((m!=0) && (n!=0)) break; |
---|
| 1410 | tries++; |
---|
| 1411 | if (tries>=5) break; |
---|
| 1412 | } |
---|
| 1413 | if ((m==0) || (n==0)) |
---|
| 1414 | { |
---|
| 1415 | Warn("char_series returns %d x %d matrix from %d input polys (%d)", |
---|
| 1416 | m,n,IDELEMS(I)+1,LL.length()); |
---|
[fc2746] | 1417 | iiWriteMatrix((matrix)I,"I",2,r,0); |
---|
[35aab3] | 1418 | m=si_max(m,1); |
---|
| 1419 | n=si_max(n,1); |
---|
| 1420 | } |
---|
| 1421 | res=mpNew(m,n); |
---|
| 1422 | CFListIterator Li; |
---|
| 1423 | for ( m=1, LLi = LL; LLi.hasItem(); LLi++, m++ ) |
---|
| 1424 | { |
---|
| 1425 | for (n=1, Li = LLi.getItem(); Li.hasItem(); Li++, n++) |
---|
| 1426 | { |
---|
[ce3f53c] | 1427 | if ( (rChar(r) == 0) || (rChar(r) > 1) ) |
---|
| 1428 | MATELEM(res,m,n)=convFactoryPSingP(Li.getItem(),r); |
---|
[35aab3] | 1429 | else |
---|
[ce3f53c] | 1430 | MATELEM(res,m,n)=convFactoryPSingTrP(Li.getItem(),r); |
---|
[35aab3] | 1431 | } |
---|
| 1432 | } |
---|
| 1433 | Off(SW_RATIONAL); |
---|
| 1434 | return res; |
---|
[67c1dc] | 1435 | } |
---|
[35aab3] | 1436 | |
---|
[3aa9b6] | 1437 | char* singclap_neworder ( ideal I, const ring r) |
---|
[35aab3] | 1438 | { |
---|
| 1439 | int i; |
---|
| 1440 | Off(SW_RATIONAL); |
---|
| 1441 | On(SW_SYMMETRIC_FF); |
---|
| 1442 | CFList L; |
---|
[ce3f53c] | 1443 | if (((rChar(r) == 0) || (rChar(r) > 1) ) |
---|
| 1444 | && (rPar(r)==0)) |
---|
[35aab3] | 1445 | { |
---|
[ce3f53c] | 1446 | setCharacteristic( rChar(r) ); |
---|
[35aab3] | 1447 | for(i=0;i<IDELEMS(I);i++) |
---|
| 1448 | { |
---|
[ce3f53c] | 1449 | L.append(convSingPFactoryP(I->m[i],r)); |
---|
[35aab3] | 1450 | } |
---|
| 1451 | } |
---|
| 1452 | // and over Q(a) / Fp(a) |
---|
[ce3f53c] | 1453 | else if (( rChar(r)==1 ) // Q(a) |
---|
| 1454 | || (rChar(r) <-1)) // Fp(a) |
---|
[35aab3] | 1455 | { |
---|
[ce3f53c] | 1456 | if (rChar(r)==1) setCharacteristic( 0 ); |
---|
| 1457 | else setCharacteristic( -rChar(r) ); |
---|
[35aab3] | 1458 | for(i=0;i<IDELEMS(I);i++) |
---|
| 1459 | { |
---|
[ce3f53c] | 1460 | L.append(convSingTrPFactoryP(I->m[i],r)); |
---|
[35aab3] | 1461 | } |
---|
| 1462 | } |
---|
| 1463 | else |
---|
| 1464 | { |
---|
| 1465 | WerrorS( feNotImplemented ); |
---|
| 1466 | return NULL; |
---|
| 1467 | } |
---|
| 1468 | |
---|
| 1469 | List<int> IL=neworderint(L); |
---|
| 1470 | ListIterator<int> Li; |
---|
| 1471 | StringSetS(""); |
---|
| 1472 | Li = IL; |
---|
[ce3f53c] | 1473 | int offs=rPar(r); |
---|
| 1474 | int* mark=(int*)omAlloc0((rVar(r)+offs)*sizeof(int)); |
---|
| 1475 | int cnt=rVar(r)+offs; |
---|
[35aab3] | 1476 | loop |
---|
| 1477 | { |
---|
| 1478 | if(! Li.hasItem()) break; |
---|
| 1479 | BOOLEAN done=TRUE; |
---|
| 1480 | i=Li.getItem()-1; |
---|
| 1481 | mark[i]=1; |
---|
| 1482 | if (i<offs) |
---|
| 1483 | { |
---|
| 1484 | done=FALSE; |
---|
[ce3f53c] | 1485 | //StringAppendS(r->parameter[i]); |
---|
[35aab3] | 1486 | } |
---|
| 1487 | else |
---|
| 1488 | { |
---|
[ce3f53c] | 1489 | StringAppendS(r->names[i-offs]); |
---|
[35aab3] | 1490 | } |
---|
| 1491 | Li++; |
---|
| 1492 | cnt--; |
---|
| 1493 | if(cnt==0) break; |
---|
| 1494 | if (done) StringAppendS(","); |
---|
| 1495 | } |
---|
[ce3f53c] | 1496 | for(i=0;i<rVar(r)+offs;i++) |
---|
[35aab3] | 1497 | { |
---|
| 1498 | BOOLEAN done=TRUE; |
---|
| 1499 | if(mark[i]==0) |
---|
| 1500 | { |
---|
| 1501 | if (i<offs) |
---|
| 1502 | { |
---|
| 1503 | done=FALSE; |
---|
[ce3f53c] | 1504 | //StringAppendS(r->parameter[i]); |
---|
[35aab3] | 1505 | } |
---|
| 1506 | else |
---|
| 1507 | { |
---|
[ce3f53c] | 1508 | StringAppendS(r->names[i-offs]); |
---|
[35aab3] | 1509 | } |
---|
| 1510 | cnt--; |
---|
| 1511 | if(cnt==0) break; |
---|
| 1512 | if (done) StringAppendS(","); |
---|
| 1513 | } |
---|
| 1514 | } |
---|
[538512] | 1515 | char * s=StringEndS(); |
---|
[35aab3] | 1516 | if (s[strlen(s)-1]==',') s[strlen(s)-1]='\0'; |
---|
| 1517 | return s; |
---|
[67c1dc] | 1518 | } |
---|
| 1519 | #endif /*HAVE_LIBFAC*/ |
---|
[35aab3] | 1520 | |
---|
[ce3f53c] | 1521 | BOOLEAN singclap_isSqrFree(poly f, const ring r) |
---|
[35aab3] | 1522 | { |
---|
| 1523 | BOOLEAN b=FALSE; |
---|
[abb4787] | 1524 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
| 1525 | if((r->cf->type==n_Zp)&&(!F.isUnivariate())) |
---|
[35aab3] | 1526 | goto err; |
---|
[abb4787] | 1527 | b=(BOOLEAN)isSqrFree(F); |
---|
| 1528 | Off(SW_RATIONAL); |
---|
[35aab3] | 1529 | return b; |
---|
[abb4787] | 1530 | err: |
---|
| 1531 | WerrorS( feNotImplemented ); |
---|
| 1532 | return 0; |
---|
[35aab3] | 1533 | } |
---|
| 1534 | |
---|
[ce3f53c] | 1535 | poly singclap_det( const matrix m, const ring s ) |
---|
[35aab3] | 1536 | { |
---|
| 1537 | int r=m->rows(); |
---|
| 1538 | if (r!=m->cols()) |
---|
| 1539 | { |
---|
| 1540 | Werror("det of %d x %d matrix",r,m->cols()); |
---|
| 1541 | return NULL; |
---|
| 1542 | } |
---|
| 1543 | poly res=NULL; |
---|
[abb4787] | 1544 | CFMatrix M(r,r); |
---|
| 1545 | int i,j; |
---|
| 1546 | for(i=r;i>0;i--) |
---|
[35aab3] | 1547 | { |
---|
[abb4787] | 1548 | for(j=r;j>0;j--) |
---|
[35aab3] | 1549 | { |
---|
[abb4787] | 1550 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s); |
---|
[35aab3] | 1551 | } |
---|
| 1552 | } |
---|
[abb4787] | 1553 | res= convFactoryPSingP( determinant(M,r),s ) ; |
---|
[35aab3] | 1554 | Off(SW_RATIONAL); |
---|
| 1555 | return res; |
---|
| 1556 | } |
---|
| 1557 | |
---|
[2e4ec14] | 1558 | int singclap_det_i( intvec * m, const ring /*r*/) |
---|
[35aab3] | 1559 | { |
---|
[9d5ba2] | 1560 | // assume( r == currRing ); // Anything else is not guaranted to work! |
---|
| 1561 | |
---|
| 1562 | setCharacteristic( 0 ); // ? |
---|
[35aab3] | 1563 | CFMatrix M(m->rows(),m->cols()); |
---|
| 1564 | int i,j; |
---|
| 1565 | for(i=m->rows();i>0;i--) |
---|
| 1566 | { |
---|
| 1567 | for(j=m->cols();j>0;j--) |
---|
| 1568 | { |
---|
| 1569 | M(i,j)=IMATELEM(*m,i,j); |
---|
| 1570 | } |
---|
| 1571 | } |
---|
[ce3f53c] | 1572 | int res= convFactoryISingI( determinant(M,m->rows()) ) ; |
---|
[24a9587] | 1573 | return res; |
---|
| 1574 | } |
---|
| 1575 | |
---|
| 1576 | number singclap_det_bi( bigintmat * m, const coeffs cf) |
---|
| 1577 | { |
---|
| 1578 | assume(m->basecoeffs()==cf); |
---|
| 1579 | CFMatrix M(m->rows(),m->cols()); |
---|
| 1580 | int i,j; |
---|
| 1581 | BOOLEAN setchar=TRUE; |
---|
| 1582 | for(i=m->rows();i>0;i--) |
---|
| 1583 | { |
---|
| 1584 | for(j=m->cols();j>0;j--) |
---|
| 1585 | { |
---|
| 1586 | M(i,j)=cf->convSingNFactoryN(BIMATELEM(*m,i,j),setchar,cf); |
---|
| 1587 | setchar=FALSE; |
---|
| 1588 | } |
---|
| 1589 | } |
---|
| 1590 | number res= cf->convFactoryNSingN( determinant(M,m->rows()),cf ) ; |
---|
[35aab3] | 1591 | return res; |
---|
| 1592 | } |
---|
[c74d6a] | 1593 | |
---|
[2072126] | 1594 | #ifdef HAVE_NTL |
---|
[895b31c] | 1595 | #if 1 |
---|
[ce3f53c] | 1596 | matrix singntl_HNF(matrix m, const ring s ) |
---|
[9d9078] | 1597 | { |
---|
[af8863] | 1598 | int r=m->rows(); |
---|
| 1599 | if (r!=m->cols()) |
---|
| 1600 | { |
---|
| 1601 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
| 1602 | return NULL; |
---|
| 1603 | } |
---|
[895b31c] | 1604 | |
---|
| 1605 | matrix res=mp_New(r,r); |
---|
| 1606 | |
---|
[ce3f53c] | 1607 | if (rField_is_Q(s)) |
---|
[af8863] | 1608 | { |
---|
[9d9078] | 1609 | |
---|
[af8863] | 1610 | CFMatrix M(r,r); |
---|
| 1611 | int i,j; |
---|
| 1612 | for(i=r;i>0;i--) |
---|
| 1613 | { |
---|
| 1614 | for(j=r;j>0;j--) |
---|
| 1615 | { |
---|
[ce3f53c] | 1616 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s ); |
---|
[af8863] | 1617 | } |
---|
| 1618 | } |
---|
| 1619 | CFMatrix *MM=cf_HNF(M); |
---|
| 1620 | for(i=r;i>0;i--) |
---|
| 1621 | { |
---|
| 1622 | for(j=r;j>0;j--) |
---|
[9d9078] | 1623 | { |
---|
[ce3f53c] | 1624 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j),s); |
---|
[af8863] | 1625 | } |
---|
| 1626 | } |
---|
| 1627 | delete MM; |
---|
| 1628 | } |
---|
| 1629 | return res; |
---|
| 1630 | } |
---|
[895b31c] | 1631 | |
---|
| 1632 | intvec* singntl_HNF(intvec* m, const ring) |
---|
[af8863] | 1633 | { |
---|
| 1634 | int r=m->rows(); |
---|
| 1635 | if (r!=m->cols()) |
---|
| 1636 | { |
---|
| 1637 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
| 1638 | return NULL; |
---|
| 1639 | } |
---|
| 1640 | setCharacteristic( 0 ); |
---|
| 1641 | CFMatrix M(r,r); |
---|
| 1642 | int i,j; |
---|
| 1643 | for(i=r;i>0;i--) |
---|
| 1644 | { |
---|
| 1645 | for(j=r;j>0;j--) |
---|
| 1646 | { |
---|
| 1647 | M(i,j)=IMATELEM(*m,i,j); |
---|
| 1648 | } |
---|
| 1649 | } |
---|
| 1650 | CFMatrix *MM=cf_HNF(M); |
---|
| 1651 | intvec *mm=ivCopy(m); |
---|
| 1652 | for(i=r;i>0;i--) |
---|
| 1653 | { |
---|
| 1654 | for(j=r;j>0;j--) |
---|
| 1655 | { |
---|
| 1656 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
| 1657 | } |
---|
| 1658 | } |
---|
| 1659 | delete MM; |
---|
| 1660 | return mm; |
---|
| 1661 | } |
---|
[895b31c] | 1662 | |
---|
[ce3f53c] | 1663 | matrix singntl_LLL(matrix m, const ring s ) |
---|
[9d9078] | 1664 | { |
---|
[9c0b20a] | 1665 | int r=m->rows(); |
---|
| 1666 | int c=m->cols(); |
---|
[895b31c] | 1667 | matrix res=mp_New(r,c); |
---|
[ce3f53c] | 1668 | if (rField_is_Q(s)) |
---|
[9c0b20a] | 1669 | { |
---|
| 1670 | CFMatrix M(r,c); |
---|
| 1671 | int i,j; |
---|
| 1672 | for(i=r;i>0;i--) |
---|
| 1673 | { |
---|
| 1674 | for(j=c;j>0;j--) |
---|
| 1675 | { |
---|
[ce3f53c] | 1676 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s); |
---|
[9c0b20a] | 1677 | } |
---|
| 1678 | } |
---|
| 1679 | CFMatrix *MM=cf_LLL(M); |
---|
| 1680 | for(i=r;i>0;i--) |
---|
| 1681 | { |
---|
| 1682 | for(j=c;j>0;j--) |
---|
[9d9078] | 1683 | { |
---|
[ce3f53c] | 1684 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j),s); |
---|
[9c0b20a] | 1685 | } |
---|
| 1686 | } |
---|
| 1687 | delete MM; |
---|
| 1688 | } |
---|
| 1689 | return res; |
---|
| 1690 | } |
---|
[895b31c] | 1691 | |
---|
| 1692 | intvec* singntl_LLL(intvec* m, const ring) |
---|
[9c0b20a] | 1693 | { |
---|
| 1694 | int r=m->rows(); |
---|
| 1695 | int c=m->cols(); |
---|
| 1696 | setCharacteristic( 0 ); |
---|
| 1697 | CFMatrix M(r,c); |
---|
| 1698 | int i,j; |
---|
| 1699 | for(i=r;i>0;i--) |
---|
| 1700 | { |
---|
| 1701 | for(j=r;j>0;j--) |
---|
| 1702 | { |
---|
| 1703 | M(i,j)=IMATELEM(*m,i,j); |
---|
| 1704 | } |
---|
| 1705 | } |
---|
| 1706 | CFMatrix *MM=cf_LLL(M); |
---|
| 1707 | intvec *mm=ivCopy(m); |
---|
| 1708 | for(i=r;i>0;i--) |
---|
| 1709 | { |
---|
| 1710 | for(j=c;j>0;j--) |
---|
| 1711 | { |
---|
| 1712 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
| 1713 | } |
---|
| 1714 | } |
---|
| 1715 | delete MM; |
---|
| 1716 | return mm; |
---|
| 1717 | } |
---|
[c74d6a] | 1718 | #endif |
---|
[686f46] | 1719 | #endif |
---|
[c74d6a] | 1720 | |
---|
[fea2af] | 1721 | |
---|
| 1722 | #endif /* HAVE_FACTORY */ |
---|