[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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[341696] | 5 | // $Id$ |
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[35aab3] | 6 | /* |
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| 7 | * ABSTRACT: interface between Singular and factory |
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| 8 | */ |
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| 9 | |
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[b963c5] | 10 | //#define FACTORIZE2_DEBUG |
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[599326] | 11 | #include <kernel/mod2.h> |
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[b1dfaf] | 12 | #include <omalloc/omalloc.h> |
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[35aab3] | 13 | #ifdef HAVE_FACTORY |
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| 14 | #define SI_DONT_HAVE_GLOBAL_VARS |
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[599326] | 15 | #include <kernel/structs.h> |
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| 16 | #include <kernel/clapsing.h> |
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| 17 | #include <kernel/numbers.h> |
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| 18 | #include <kernel/ring.h> |
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| 19 | #include <kernel/ideals.h> |
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| 20 | #include <kernel/ffields.h> |
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[b1dfaf] | 21 | #include <factory/factory.h> |
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[599326] | 22 | #include <kernel/clapconv.h> |
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[b1dfaf] | 23 | #include <libfac/factor.h> |
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[599326] | 24 | #include <kernel/ring.h> |
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[35aab3] | 25 | |
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[a86cda] | 26 | void out_cf(const char *s1,const CanonicalForm &f,const char *s2); |
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[35aab3] | 27 | |
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[6620d75] | 28 | poly singclap_gcd_r ( poly f, poly g, const ring r ) |
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[35aab3] | 29 | { |
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[a0d9be] | 30 | // assume p_Cleardenom is done |
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[6620d75] | 31 | // assume f!=0, g!=0 |
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[35aab3] | 32 | poly res=NULL; |
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| 33 | |
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[36586bb] | 34 | assume(f!=NULL); |
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| 35 | assume(g!=NULL); |
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| 36 | |
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| 37 | if((pNext(f)==NULL) && (pNext(g)==NULL)) |
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[9b9b5a] | 38 | { |
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[36586bb] | 39 | poly p=pOne(); |
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| 40 | for(int i=rVar(r);i>0;i--) |
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| 41 | p_SetExp(p,i,si_min(p_GetExp(f,i,r),p_GetExp(g,i,r)),r); |
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| 42 | p_Setm(p,r); |
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| 43 | return p; |
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[9b9b5a] | 44 | } |
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[35aab3] | 45 | |
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| 46 | // for now there is only the possibility to handle polynomials over |
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| 47 | // Q and Fp ... |
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[ea48f7d] | 48 | Off(SW_RATIONAL); |
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[6620d75] | 49 | if (rField_is_Q(r) || (rField_is_Zp(r))) |
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[35aab3] | 50 | { |
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[6620d75] | 51 | setCharacteristic( n_GetChar(r) ); |
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[64a88e] | 52 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g, r ) ); |
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[308898e] | 53 | res=convFactoryPSingP( gcd( F, G ) , r); |
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[35aab3] | 54 | } |
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| 55 | // and over Q(a) / Fp(a) |
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[de7a92] | 56 | else if ( rField_is_Extension(r)) |
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[35aab3] | 57 | { |
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[de7a92] | 58 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
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| 59 | else setCharacteristic( -n_GetChar(r) ); |
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[6620d75] | 60 | if (r->minpoly!=NULL) |
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[35aab3] | 61 | { |
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[de7a92] | 62 | bool b1=isOn(SW_USE_QGCD); |
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| 63 | bool b2=isOn(SW_USE_fieldGCD); |
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| 64 | if ( rField_is_Q_a() ) On(SW_USE_QGCD); |
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| 65 | else On(SW_USE_fieldGCD); |
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| 66 | CanonicalForm mipo=convSingPFactoryP(((lnumber)r->minpoly)->z, |
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[64a88e] | 67 | r->algring); |
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[de7a92] | 68 | Variable a=rootOf(mipo); |
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| 69 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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| 70 | G( convSingAPFactoryAP( g,a,r ) ); |
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| 71 | res= convFactoryAPSingAP( gcd( F, G ),currRing ); |
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| 72 | if (!b1) Off(SW_USE_QGCD); |
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| 73 | if (!b2) Off(SW_USE_fieldGCD); |
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[35aab3] | 74 | } |
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| 75 | else |
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| 76 | { |
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[6620d75] | 77 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
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| 78 | res= convFactoryPSingTrP( gcd( F, G ),r ); |
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[35aab3] | 79 | } |
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| 80 | } |
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| 81 | #if 0 |
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[6620d75] | 82 | else if (( n_GetChar(r)>1 )&&(r->parameter!=NULL)) /* GF(q) */ |
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[35aab3] | 83 | { |
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[6620d75] | 84 | int p=rChar(r); |
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[35aab3] | 85 | int n=2; |
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| 86 | int t=p*p; |
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[6620d75] | 87 | while (t!=n_Char(r)) { t*=p;n++; } |
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[35aab3] | 88 | setCharacteristic(p,n,'a'); |
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[6620d75] | 89 | CanonicalForm F( convSingGFFactoryGF( f,r ) ), G( convSingGFFactoryGF( g,r ) ); |
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| 90 | res= convFactoryGFSingGF( gcd( F, G ),r ); |
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[35aab3] | 91 | } |
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| 92 | #endif |
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| 93 | else |
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| 94 | WerrorS( feNotImplemented ); |
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| 95 | |
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[ea48f7d] | 96 | Off(SW_RATIONAL); |
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[35aab3] | 97 | return res; |
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| 98 | } |
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| 99 | |
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[6620d75] | 100 | poly singclap_gcd ( poly f, poly g ) |
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[91d0e6] | 101 | { |
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| 102 | poly res=NULL; |
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| 103 | |
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[f8ace52] | 104 | if (f!=NULL) p_Cleardenom(f, currRing); |
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| 105 | if (g!=NULL) p_Cleardenom(g, currRing); |
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| 106 | else return f; // g==0 => gcd=f (but do a p_Cleardenom) |
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| 107 | if (f==NULL) return g; // f==0 => gcd=g (but do a p_Cleardenom) |
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[91d0e6] | 108 | |
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[6620d75] | 109 | res=singclap_gcd_r(f,g,currRing); |
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| 110 | pDelete(&f); |
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| 111 | pDelete(&g); |
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[91d0e6] | 112 | return res; |
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| 113 | } |
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| 114 | |
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[c95632f] | 115 | /*2 find the maximal exponent of var(i) in poly p*/ |
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| 116 | int pGetExp_Var(poly p, int i) |
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| 117 | { |
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| 118 | int m=0; |
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| 119 | int mm; |
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| 120 | while (p!=NULL) |
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| 121 | { |
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| 122 | mm=pGetExp(p,i); |
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| 123 | if (mm>m) m=mm; |
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| 124 | pIter(p); |
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| 125 | } |
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| 126 | return m; |
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| 127 | } |
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| 128 | |
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[9d9078] | 129 | // destroys f,g,x |
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[35aab3] | 130 | poly singclap_resultant ( poly f, poly g , poly x) |
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| 131 | { |
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[9d9078] | 132 | poly res=NULL; |
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[35aab3] | 133 | int i=pIsPurePower(x); |
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| 134 | if (i==0) |
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| 135 | { |
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| 136 | WerrorS("3rd argument must be a ring variable"); |
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[9d9078] | 137 | goto resultant_returns_res; |
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[35aab3] | 138 | } |
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| 139 | if ((f==NULL) || (g==NULL)) |
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[9d9078] | 140 | goto resultant_returns_res; |
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[35aab3] | 141 | // for now there is only the possibility to handle polynomials over |
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| 142 | // Q and Fp ... |
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[1629ab] | 143 | if (rField_is_Zp() || rField_is_Q()) |
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[35aab3] | 144 | { |
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| 145 | Variable X(i); |
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| 146 | setCharacteristic( nGetChar() ); |
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[46f6af6] | 147 | CanonicalForm F( convSingPFactoryP( f ) ), G( convSingPFactoryP( g ) ); |
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[9d9078] | 148 | res=convFactoryPSingP( resultant( F, G, X ) ); |
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[35aab3] | 149 | Off(SW_RATIONAL); |
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[9d9078] | 150 | goto resultant_returns_res; |
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[35aab3] | 151 | } |
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| 152 | // and over Q(a) / Fp(a) |
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[1629ab] | 153 | else if (rField_is_Extension()) |
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[35aab3] | 154 | { |
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[1629ab] | 155 | if (rField_is_Q_a()) setCharacteristic( 0 ); |
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[35aab3] | 156 | else setCharacteristic( -nGetChar() ); |
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[7c05ef] | 157 | Variable X(i+rPar(currRing)); |
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[35aab3] | 158 | if (currRing->minpoly!=NULL) |
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| 159 | { |
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[7c05ef] | 160 | //Variable X(i); |
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[6620d75] | 161 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
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[64a88e] | 162 | currRing->algring); |
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[35aab3] | 163 | Variable a=rootOf(mipo); |
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[cf74cd6] | 164 | CanonicalForm F( convSingAPFactoryAP( f,a,currRing ) ), |
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| 165 | G( convSingAPFactoryAP( g,a,currRing ) ); |
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[d1f231] | 166 | res= convFactoryAPSingAP( resultant( F, G, X ),currRing ); |
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[35aab3] | 167 | } |
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| 168 | else |
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| 169 | { |
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[7c05ef] | 170 | //Variable X(i+rPar(currRing)); |
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[c95632f] | 171 | number nf,ng; |
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[a0d9be] | 172 | p_Cleardenom_n(f, currRing,nf);p_Cleardenom_n(g, currRing,ng); |
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[c95632f] | 173 | int ef,eg; |
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| 174 | ef=pGetExp_Var(f,i); |
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| 175 | eg=pGetExp_Var(g,i); |
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[46f6af6] | 176 | CanonicalForm F( convSingTrPFactoryP( f ) ), G( convSingTrPFactoryP( g ) ); |
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| 177 | res= convFactoryPSingTrP( resultant( F, G, X ) ); |
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[c95632f] | 178 | if ((nf!=NULL)&&(!nIsOne(nf))&&(!nIsZero(nf))) |
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| 179 | { |
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| 180 | number n=nInvers(nf); |
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| 181 | while(eg>0) |
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| 182 | { |
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| 183 | res=pMult_nn(res,n); |
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| 184 | eg--; |
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| 185 | } |
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| 186 | nDelete(&n); |
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| 187 | } |
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| 188 | nDelete(&nf); |
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| 189 | if ((ng!=NULL)&&(!nIsOne(ng))&&(!nIsZero(ng))) |
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| 190 | { |
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| 191 | number n=nInvers(ng); |
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| 192 | while(ef>0) |
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| 193 | { |
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| 194 | res=pMult_nn(res,n); |
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| 195 | ef--; |
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| 196 | } |
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| 197 | nDelete(&n); |
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| 198 | } |
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| 199 | nDelete(&ng); |
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[35aab3] | 200 | } |
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| 201 | Off(SW_RATIONAL); |
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[9d9078] | 202 | goto resultant_returns_res; |
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[35aab3] | 203 | } |
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| 204 | else |
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| 205 | WerrorS( feNotImplemented ); |
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[9d9078] | 206 | resultant_returns_res: |
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| 207 | pDelete(&f); |
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| 208 | pDelete(&g); |
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| 209 | pDelete(&x); |
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| 210 | return res; |
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[35aab3] | 211 | } |
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| 212 | //poly singclap_resultant ( poly f, poly g , poly x) |
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| 213 | //{ |
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| 214 | // int i=pVar(x); |
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| 215 | // if (i==0) |
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| 216 | // { |
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| 217 | // WerrorS("ringvar expected"); |
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| 218 | // return NULL; |
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| 219 | // } |
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| 220 | // ideal I=idInit(1,1); |
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| 221 | // |
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| 222 | // // get the coeffs von f wrt. x: |
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| 223 | // I->m[0]=pCopy(f); |
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| 224 | // matrix ffi=mpCoeffs(I,i); |
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| 225 | // ffi->rank=1; |
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| 226 | // ffi->ncols=ffi->nrows; |
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| 227 | // ffi->nrows=1; |
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| 228 | // ideal fi=(ideal)ffi; |
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| 229 | // |
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| 230 | // // get the coeffs von g wrt. x: |
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| 231 | // I->m[0]=pCopy(g); |
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| 232 | // matrix ggi=mpCoeffs(I,i); |
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| 233 | // ggi->rank=1; |
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| 234 | // ggi->ncols=ggi->nrows; |
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| 235 | // ggi->nrows=1; |
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| 236 | // ideal gi=(ideal)ggi; |
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| 237 | // |
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| 238 | // // contruct the matrix: |
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| 239 | // int fn=IDELEMS(fi); //= deg(f,x)+1 |
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| 240 | // int gn=IDELEMS(gi); //= deg(g,x)+1 |
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| 241 | // matrix m=mpNew(fn+gn-2,fn+gn-2); |
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| 242 | // if(m==NULL) |
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| 243 | // { |
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| 244 | // return NULL; |
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| 245 | // } |
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| 246 | // |
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| 247 | // // enter the coeffs into m: |
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| 248 | // int j; |
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| 249 | // for(i=0;i<gn-1;i++) |
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| 250 | // { |
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| 251 | // for(j=0;j<fn;j++) |
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| 252 | // { |
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| 253 | // MATELEM(m,i+1,fn-j+i)=pCopy(fi->m[j]); |
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| 254 | // } |
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| 255 | // } |
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| 256 | // for(i=0;i<fn-1;i++) |
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| 257 | // { |
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| 258 | // for(j=0;j<gn;j++) |
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| 259 | // { |
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| 260 | // MATELEM(m,gn+i,gn-j+i)=pCopy(gi->m[j]); |
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| 261 | // } |
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| 262 | // } |
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| 263 | // |
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| 264 | // poly r=mpDet(m); |
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| 265 | // |
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| 266 | // idDelete(&fi); |
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| 267 | // idDelete(&gi); |
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| 268 | // idDelete((ideal *)&m); |
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| 269 | // return r; |
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| 270 | //} |
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| 271 | |
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| 272 | BOOLEAN singclap_extgcd ( poly f, poly g, poly &res, poly &pa, poly &pb ) |
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| 273 | { |
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| 274 | // for now there is only the possibility to handle univariate |
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| 275 | // polynomials over |
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| 276 | // Q and Fp ... |
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| 277 | res=NULL;pa=NULL;pb=NULL; |
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| 278 | On(SW_SYMMETRIC_FF); |
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[1629ab] | 279 | if (rField_is_Zp() || rField_is_Q()) |
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[35aab3] | 280 | { |
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| 281 | setCharacteristic( nGetChar() ); |
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[46f6af6] | 282 | CanonicalForm F( convSingPFactoryP( f ) ), G( convSingPFactoryP( g ) ); |
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[55e308] | 283 | CanonicalForm FpG=F+G; |
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| 284 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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| 285 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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[35aab3] | 286 | { |
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| 287 | Off(SW_RATIONAL); |
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| 288 | WerrorS("not univariate"); |
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| 289 | return TRUE; |
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| 290 | } |
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| 291 | CanonicalForm Fa,Gb; |
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| 292 | On(SW_RATIONAL); |
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[46f6af6] | 293 | res=convFactoryPSingP( extgcd( F, G, Fa, Gb ) ); |
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| 294 | pa=convFactoryPSingP(Fa); |
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| 295 | pb=convFactoryPSingP(Gb); |
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[35aab3] | 296 | Off(SW_RATIONAL); |
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| 297 | } |
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| 298 | // and over Q(a) / Fp(a) |
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[1629ab] | 299 | else if (rField_is_Extension()) |
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[35aab3] | 300 | { |
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[1629ab] | 301 | if (rField_is_Q_a()) setCharacteristic( 0 ); |
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[35aab3] | 302 | else setCharacteristic( -nGetChar() ); |
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| 303 | CanonicalForm Fa,Gb; |
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| 304 | if (currRing->minpoly!=NULL) |
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| 305 | { |
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[6620d75] | 306 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
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[64a88e] | 307 | currRing->algring); |
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[35aab3] | 308 | Variable a=rootOf(mipo); |
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[cf74cd6] | 309 | CanonicalForm F( convSingAPFactoryAP( f,a,currRing ) ), |
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| 310 | G( convSingAPFactoryAP( g,a,currRing ) ); |
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[55e308] | 311 | CanonicalForm FpG=F+G; |
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| 312 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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| 313 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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[35aab3] | 314 | { |
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| 315 | WerrorS("not univariate"); |
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| 316 | return TRUE; |
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| 317 | } |
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[d1f231] | 318 | res= convFactoryAPSingAP( extgcd( F, G, Fa, Gb ),currRing ); |
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| 319 | pa=convFactoryAPSingAP(Fa,currRing); |
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| 320 | pb=convFactoryAPSingAP(Gb,currRing); |
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[35aab3] | 321 | } |
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| 322 | else |
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| 323 | { |
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[46f6af6] | 324 | CanonicalForm F( convSingTrPFactoryP( f ) ), G( convSingTrPFactoryP( g ) ); |
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[55e308] | 325 | CanonicalForm FpG=F+G; |
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| 326 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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| 327 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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[35aab3] | 328 | { |
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| 329 | Off(SW_RATIONAL); |
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| 330 | WerrorS("not univariate"); |
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| 331 | return TRUE; |
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| 332 | } |
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[46f6af6] | 333 | res= convFactoryPSingTrP( extgcd( F, G, Fa, Gb ) ); |
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| 334 | pa=convFactoryPSingTrP(Fa); |
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| 335 | pb=convFactoryPSingTrP(Gb); |
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[35aab3] | 336 | } |
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| 337 | Off(SW_RATIONAL); |
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| 338 | } |
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| 339 | else |
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| 340 | { |
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| 341 | WerrorS( feNotImplemented ); |
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| 342 | return TRUE; |
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| 343 | } |
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[a86cda] | 344 | #ifndef NDEBUG |
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| 345 | // checking the result of extgcd: |
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| 346 | poly dummy; |
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| 347 | dummy=pSub(pAdd(pMult(pCopy(f),pCopy(pa)),pMult(pCopy(g),pCopy(pb))),pCopy(res)); |
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| 348 | if (dummy!=NULL) |
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| 349 | { |
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| 350 | PrintS("extgcd( ");pWrite(f);pWrite0(g);PrintS(" )\n"); |
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| 351 | PrintS("gcd, co-factors:");pWrite(res); pWrite(pa);pWrite(pb); |
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| 352 | pDelete(&dummy); |
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| 353 | } |
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[9d9078] | 354 | #endif |
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[35aab3] | 355 | return FALSE; |
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| 356 | } |
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| 357 | |
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[6620d75] | 358 | BOOLEAN singclap_extgcd_r ( poly f, poly g, poly &res, poly &pa, poly &pb, const ring r ) |
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| 359 | { |
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| 360 | // for now there is only the possibility to handle univariate |
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| 361 | // polynomials over |
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| 362 | // Q and Fp ... |
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| 363 | res=NULL;pa=NULL;pb=NULL; |
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| 364 | On(SW_SYMMETRIC_FF); |
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[de7a92] | 365 | if ( rField_is_Q(r) || rField_is_Zp(r) ) |
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[6620d75] | 366 | { |
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| 367 | setCharacteristic( n_GetChar(r) ); |
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[64a88e] | 368 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r) ); |
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[6620d75] | 369 | CanonicalForm FpG=F+G; |
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| 370 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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| 371 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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| 372 | { |
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| 373 | Off(SW_RATIONAL); |
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| 374 | WerrorS("not univariate"); |
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| 375 | return TRUE; |
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| 376 | } |
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| 377 | CanonicalForm Fa,Gb; |
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| 378 | On(SW_RATIONAL); |
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| 379 | res=convFactoryPSingP( extgcd( F, G, Fa, Gb ),r ); |
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| 380 | pa=convFactoryPSingP(Fa,r); |
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| 381 | pb=convFactoryPSingP(Gb,r); |
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| 382 | Off(SW_RATIONAL); |
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| 383 | } |
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| 384 | // and over Q(a) / Fp(a) |
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[9d9078] | 385 | else if ( rField_is_Extension(r)) |
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[6620d75] | 386 | { |
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[de7a92] | 387 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
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[6620d75] | 388 | else setCharacteristic( -n_GetChar(r) ); |
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| 389 | CanonicalForm Fa,Gb; |
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| 390 | if (r->minpoly!=NULL) |
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| 391 | { |
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| 392 | CanonicalForm mipo=convSingPFactoryP(((lnumber)r->minpoly)->z, |
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[64a88e] | 393 | r->algring); |
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[6620d75] | 394 | Variable a=rootOf(mipo); |
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[cf74cd6] | 395 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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| 396 | G( convSingAPFactoryAP( g,a,r ) ); |
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[6620d75] | 397 | CanonicalForm FpG=F+G; |
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| 398 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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| 399 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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| 400 | { |
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| 401 | WerrorS("not univariate"); |
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| 402 | return TRUE; |
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| 403 | } |
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[d1f231] | 404 | res= convFactoryAPSingAP( extgcd( F, G, Fa, Gb ),currRing ); |
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| 405 | pa=convFactoryAPSingAP(Fa,currRing); |
---|
| 406 | pb=convFactoryAPSingAP(Gb,currRing); |
---|
[6620d75] | 407 | } |
---|
| 408 | else |
---|
| 409 | { |
---|
| 410 | CanonicalForm F( convSingTrPFactoryP( f, r ) ), G( convSingTrPFactoryP( g, r ) ); |
---|
| 411 | CanonicalForm FpG=F+G; |
---|
| 412 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
---|
| 413 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
---|
| 414 | { |
---|
| 415 | Off(SW_RATIONAL); |
---|
| 416 | WerrorS("not univariate"); |
---|
| 417 | return TRUE; |
---|
| 418 | } |
---|
| 419 | res= convFactoryPSingTrP( extgcd( F, G, Fa, Gb ), r ); |
---|
| 420 | pa=convFactoryPSingTrP(Fa, r); |
---|
| 421 | pb=convFactoryPSingTrP(Gb, r); |
---|
| 422 | } |
---|
| 423 | Off(SW_RATIONAL); |
---|
| 424 | } |
---|
| 425 | else |
---|
| 426 | { |
---|
| 427 | WerrorS( feNotImplemented ); |
---|
| 428 | return TRUE; |
---|
| 429 | } |
---|
| 430 | return FALSE; |
---|
| 431 | } |
---|
| 432 | |
---|
[35aab3] | 433 | poly singclap_pdivide ( poly f, poly g ) |
---|
| 434 | { |
---|
| 435 | poly res=NULL; |
---|
| 436 | On(SW_RATIONAL); |
---|
[1629ab] | 437 | if (rField_is_Zp() || rField_is_Q()) |
---|
[35aab3] | 438 | { |
---|
| 439 | setCharacteristic( nGetChar() ); |
---|
[46f6af6] | 440 | CanonicalForm F( convSingPFactoryP( f ) ), G( convSingPFactoryP( g ) ); |
---|
| 441 | res = convFactoryPSingP( F / G ); |
---|
[35aab3] | 442 | } |
---|
[1629ab] | 443 | else if (rField_is_Extension()) |
---|
[35aab3] | 444 | { |
---|
[1629ab] | 445 | if (rField_is_Q_a()) setCharacteristic( 0 ); |
---|
[35aab3] | 446 | else setCharacteristic( -nGetChar() ); |
---|
| 447 | if (currRing->minpoly!=NULL) |
---|
| 448 | { |
---|
[6620d75] | 449 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
---|
[64a88e] | 450 | currRing->algring); |
---|
[35aab3] | 451 | Variable a=rootOf(mipo); |
---|
[cf74cd6] | 452 | CanonicalForm F( convSingAPFactoryAP( f,a,currRing ) ), |
---|
| 453 | G( convSingAPFactoryAP( g,a,currRing ) ); |
---|
[d1f231] | 454 | res= convFactoryAPSingAP( F / G,currRing ); |
---|
[35aab3] | 455 | } |
---|
| 456 | else |
---|
| 457 | { |
---|
[46f6af6] | 458 | CanonicalForm F( convSingTrPFactoryP( f ) ), G( convSingTrPFactoryP( g ) ); |
---|
| 459 | res= convFactoryPSingTrP( F / G ); |
---|
[35aab3] | 460 | } |
---|
| 461 | } |
---|
[5d68a6] | 462 | #if 0 // not yet working |
---|
| 463 | else if (rField_is_GF()) |
---|
| 464 | { |
---|
| 465 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
| 466 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
| 467 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
| 468 | res = convFactoryGFSingGF( F / G ); |
---|
| 469 | } |
---|
| 470 | #endif |
---|
[35aab3] | 471 | else |
---|
| 472 | WerrorS( feNotImplemented ); |
---|
| 473 | Off(SW_RATIONAL); |
---|
| 474 | return res; |
---|
| 475 | } |
---|
| 476 | |
---|
[d1f231] | 477 | poly singclap_pdivide_r ( poly f, poly g, const ring r ) |
---|
| 478 | { |
---|
| 479 | poly res=NULL; |
---|
| 480 | On(SW_RATIONAL); |
---|
| 481 | if (rField_is_Zp(r) || rField_is_Q(r)) |
---|
| 482 | { |
---|
| 483 | setCharacteristic( n_GetChar(r) ); |
---|
| 484 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
| 485 | res = convFactoryPSingP( F / G,r ); |
---|
| 486 | } |
---|
| 487 | else if (rField_is_Extension(r)) |
---|
| 488 | { |
---|
| 489 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
| 490 | else setCharacteristic( -n_GetChar(r) ); |
---|
| 491 | if (r->minpoly!=NULL) |
---|
| 492 | { |
---|
| 493 | CanonicalForm mipo=convSingPFactoryP(((lnumber)r->minpoly)->z, |
---|
| 494 | r->algring); |
---|
| 495 | Variable a=rootOf(mipo); |
---|
| 496 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
| 497 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
| 498 | res= convFactoryAPSingAP( F / G, r ); |
---|
| 499 | } |
---|
| 500 | else |
---|
| 501 | { |
---|
| 502 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
| 503 | res= convFactoryPSingTrP( F / G,r ); |
---|
| 504 | } |
---|
| 505 | } |
---|
| 506 | #if 0 // not yet working |
---|
| 507 | else if (rField_is_GF()) |
---|
| 508 | { |
---|
| 509 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
| 510 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
| 511 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
| 512 | res = convFactoryGFSingGF( F / G ); |
---|
| 513 | } |
---|
| 514 | #endif |
---|
| 515 | else |
---|
| 516 | WerrorS( feNotImplemented ); |
---|
| 517 | Off(SW_RATIONAL); |
---|
| 518 | return res; |
---|
| 519 | } |
---|
| 520 | |
---|
[35aab3] | 521 | void singclap_divide_content ( poly f ) |
---|
| 522 | { |
---|
| 523 | if ( f==NULL ) |
---|
| 524 | { |
---|
| 525 | return; |
---|
| 526 | } |
---|
| 527 | else if ( pNext( f ) == NULL ) |
---|
| 528 | { |
---|
| 529 | pSetCoeff( f, nInit( 1 ) ); |
---|
| 530 | return; |
---|
| 531 | } |
---|
| 532 | else |
---|
| 533 | { |
---|
[1629ab] | 534 | if ( rField_is_Q_a() ) |
---|
[35aab3] | 535 | setCharacteristic( 0 ); |
---|
[1629ab] | 536 | else if ( rField_is_Zp_a() ) |
---|
[35aab3] | 537 | setCharacteristic( -nGetChar() ); |
---|
| 538 | else |
---|
| 539 | return; /* not implemented*/ |
---|
| 540 | |
---|
| 541 | CFList L; |
---|
| 542 | CanonicalForm g, h; |
---|
| 543 | poly p = pNext(f); |
---|
| 544 | |
---|
| 545 | // first attemp: find 2 smallest g: |
---|
| 546 | |
---|
| 547 | number g1=pGetCoeff(f); |
---|
| 548 | number g2=pGetCoeff(p); // p==pNext(f); |
---|
| 549 | pIter(p); |
---|
| 550 | int sz1=nSize(g1); |
---|
| 551 | int sz2=nSize(g2); |
---|
| 552 | if (sz1>sz2) |
---|
| 553 | { |
---|
| 554 | number gg=g1; |
---|
| 555 | g1=g2; g2=gg; |
---|
| 556 | int sz=sz1; |
---|
| 557 | sz1=sz2; sz2=sz; |
---|
| 558 | } |
---|
| 559 | while (p!=NULL) |
---|
| 560 | { |
---|
| 561 | int n_sz=nSize(pGetCoeff(p)); |
---|
| 562 | if (n_sz<sz1) |
---|
| 563 | { |
---|
| 564 | sz2=sz1; |
---|
| 565 | g2=g1; |
---|
| 566 | g1=pGetCoeff(p); |
---|
| 567 | sz1=n_sz; |
---|
| 568 | if (sz1<=3) break; |
---|
| 569 | } |
---|
| 570 | else if(n_sz<sz2) |
---|
| 571 | { |
---|
| 572 | sz2=n_sz; |
---|
| 573 | g2=pGetCoeff(p); |
---|
| 574 | sz2=n_sz; |
---|
| 575 | } |
---|
| 576 | pIter(p); |
---|
| 577 | } |
---|
[64a88e] | 578 | g = convSingPFactoryP( ((lnumber)g1)->z, currRing->algring ); |
---|
| 579 | g = gcd( g, convSingPFactoryP( ((lnumber)g2)->z , currRing->algring)); |
---|
[35aab3] | 580 | |
---|
| 581 | // second run: gcd's |
---|
| 582 | |
---|
| 583 | p = f; |
---|
| 584 | while ( (p != NULL) && (g != 1) && ( g != 0)) |
---|
| 585 | { |
---|
[64a88e] | 586 | h = convSingPFactoryP( ((lnumber)pGetCoeff(p))->z, currRing->algring ); |
---|
[35aab3] | 587 | pIter( p ); |
---|
| 588 | |
---|
| 589 | g = gcd( g, h ); |
---|
| 590 | |
---|
| 591 | L.append( h ); |
---|
| 592 | } |
---|
| 593 | if (( g == 1 ) || (g == 0)) |
---|
| 594 | { |
---|
| 595 | // pTest(f); |
---|
| 596 | return; |
---|
| 597 | } |
---|
| 598 | else |
---|
| 599 | { |
---|
| 600 | CFListIterator i; |
---|
| 601 | for ( i = L, p = f; i.hasItem(); i++, p=pNext(p) ) |
---|
| 602 | { |
---|
| 603 | lnumber c=(lnumber)pGetCoeff(p); |
---|
[661c214] | 604 | p_Delete(&c->z,currRing->algring); // 2nd arg used to be nacRing |
---|
[6620d75] | 605 | c->z=convFactoryPSingP( i.getItem() / g, currRing->algring ); |
---|
[35aab3] | 606 | //nTest((number)c); |
---|
| 607 | //#ifdef LDEBUG |
---|
| 608 | //number cn=(number)c; |
---|
| 609 | //StringSetS(""); nWrite(nt); StringAppend(" ==> "); |
---|
| 610 | //nWrite(cn);PrintS(StringAppend("\n")); |
---|
| 611 | //#endif |
---|
| 612 | } |
---|
| 613 | } |
---|
| 614 | // pTest(f); |
---|
| 615 | } |
---|
| 616 | } |
---|
| 617 | |
---|
[0a55e5] | 618 | BOOLEAN count_Factors(ideal I, intvec *v,int j, poly &f, poly fac) |
---|
| 619 | { |
---|
| 620 | pTest(f); |
---|
| 621 | pTest(fac); |
---|
| 622 | int e=0; |
---|
| 623 | if (!pIsConstantPoly(fac)) |
---|
| 624 | { |
---|
| 625 | #ifdef FACTORIZE2_DEBUG |
---|
| 626 | printf("start count_Factors(%d), Fdeg=%d, factor deg=%d\n",j,pTotaldegree(f),pTotaldegree(fac)); |
---|
| 627 | p_wrp(fac,currRing);PrintLn(); |
---|
| 628 | #endif |
---|
| 629 | On(SW_RATIONAL); |
---|
| 630 | CanonicalForm F, FAC,Q,R; |
---|
| 631 | Variable a; |
---|
[1629ab] | 632 | if (rField_is_Zp() || rField_is_Q()) |
---|
[0a55e5] | 633 | { |
---|
[46f6af6] | 634 | F=convSingPFactoryP( f ); |
---|
| 635 | FAC=convSingPFactoryP( fac ); |
---|
[0a55e5] | 636 | } |
---|
[1629ab] | 637 | else if (rField_is_Extension()) |
---|
[0a55e5] | 638 | { |
---|
| 639 | if (currRing->minpoly!=NULL) |
---|
| 640 | { |
---|
[6620d75] | 641 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
---|
[64a88e] | 642 | currRing->algring); |
---|
[0a55e5] | 643 | a=rootOf(mipo); |
---|
[cf74cd6] | 644 | F=convSingAPFactoryAP( f,a,currRing ); |
---|
| 645 | FAC=convSingAPFactoryAP( fac,a,currRing ); |
---|
[0a55e5] | 646 | } |
---|
| 647 | else |
---|
| 648 | { |
---|
[46f6af6] | 649 | F=convSingTrPFactoryP( f ); |
---|
| 650 | FAC=convSingTrPFactoryP( fac ); |
---|
[0a55e5] | 651 | } |
---|
| 652 | } |
---|
| 653 | else |
---|
| 654 | WerrorS( feNotImplemented ); |
---|
| 655 | |
---|
| 656 | poly q; |
---|
| 657 | loop |
---|
| 658 | { |
---|
| 659 | Q=F; |
---|
| 660 | Q/=FAC; |
---|
| 661 | R=Q; |
---|
| 662 | R*=FAC; |
---|
| 663 | R-=F; |
---|
| 664 | if (R.isZero()) |
---|
| 665 | { |
---|
[1629ab] | 666 | if (rField_is_Zp() || rField_is_Q()) |
---|
[0a55e5] | 667 | { |
---|
[46f6af6] | 668 | q = convFactoryPSingP( Q ); |
---|
[0a55e5] | 669 | } |
---|
[1629ab] | 670 | else if (rField_is_Extension()) |
---|
[0a55e5] | 671 | { |
---|
| 672 | if (currRing->minpoly!=NULL) |
---|
| 673 | { |
---|
[d1f231] | 674 | q= convFactoryAPSingAP( Q,currRing ); |
---|
[0a55e5] | 675 | } |
---|
| 676 | else |
---|
| 677 | { |
---|
[46f6af6] | 678 | q= convFactoryPSingTrP( Q ); |
---|
[0a55e5] | 679 | } |
---|
| 680 | } |
---|
| 681 | e++; pDelete(&f); f=q; q=NULL; F=Q; |
---|
| 682 | } |
---|
| 683 | else |
---|
| 684 | { |
---|
| 685 | break; |
---|
| 686 | } |
---|
| 687 | } |
---|
| 688 | if (e==0) |
---|
| 689 | { |
---|
| 690 | Off(SW_RATIONAL); |
---|
| 691 | return FALSE; |
---|
| 692 | } |
---|
| 693 | } |
---|
| 694 | else e=1; |
---|
| 695 | I->m[j]=fac; |
---|
| 696 | if (v!=NULL) (*v)[j]=e; |
---|
| 697 | Off(SW_RATIONAL); |
---|
| 698 | return TRUE; |
---|
| 699 | } |
---|
| 700 | |
---|
[a5d9313] | 701 | int singclap_factorize_retry; |
---|
[0a55e5] | 702 | extern int libfac_interruptflag; |
---|
[a5d9313] | 703 | |
---|
[35aab3] | 704 | ideal singclap_factorize ( poly f, intvec ** v , int with_exps) |
---|
[93e7e91] | 705 | /* destroys f, sets *v */ |
---|
[35aab3] | 706 | { |
---|
[0a55e5] | 707 | pTest(f); |
---|
| 708 | #ifdef FACTORIZE2_DEBUG |
---|
[99bdcf] | 709 | printf("singclap_factorize, degree %ld\n",pTotaldegree(f)); |
---|
[0a55e5] | 710 | #endif |
---|
[35aab3] | 711 | // with_exps: 3,1 return only true factors, no exponents |
---|
| 712 | // 2 return true factors and exponents |
---|
| 713 | // 0 return coeff, factors and exponents |
---|
[ee5d91] | 714 | BOOLEAN save_errorreported=errorreported; |
---|
[35aab3] | 715 | |
---|
| 716 | ideal res=NULL; |
---|
| 717 | |
---|
| 718 | // handle factorize(0) ========================================= |
---|
| 719 | if (f==NULL) |
---|
| 720 | { |
---|
| 721 | res=idInit(1,1); |
---|
| 722 | if (with_exps!=1) |
---|
| 723 | { |
---|
| 724 | (*v)=new intvec(1); |
---|
| 725 | (**v)[0]=1; |
---|
| 726 | } |
---|
| 727 | return res; |
---|
| 728 | } |
---|
| 729 | // handle factorize(mon) ========================================= |
---|
| 730 | if (pNext(f)==NULL) |
---|
| 731 | { |
---|
| 732 | int i=0; |
---|
| 733 | int n=0; |
---|
| 734 | int e; |
---|
| 735 | for(i=pVariables;i>0;i--) if(pGetExp(f,i)!=0) n++; |
---|
| 736 | if (with_exps==0) n++; // with coeff |
---|
| 737 | res=idInit(si_max(n,1),1); |
---|
| 738 | switch(with_exps) |
---|
| 739 | { |
---|
| 740 | case 0: // with coef & exp. |
---|
[2abbb60] | 741 | res->m[0]=pNSet(nCopy(pGetCoeff(f))); |
---|
[35aab3] | 742 | // no break |
---|
| 743 | case 2: // with exp. |
---|
[54ff35] | 744 | (*v)=new intvec(si_max(1,n)); |
---|
[35aab3] | 745 | (**v)[0]=1; |
---|
| 746 | // no break |
---|
| 747 | case 1: ; |
---|
| 748 | #ifdef TEST |
---|
| 749 | default: ; |
---|
| 750 | #endif |
---|
| 751 | } |
---|
| 752 | if (n==0) |
---|
| 753 | { |
---|
| 754 | res->m[0]=pOne(); |
---|
| 755 | // (**v)[0]=1; is already done |
---|
| 756 | } |
---|
[93e7e91] | 757 | else |
---|
[35aab3] | 758 | { |
---|
[93e7e91] | 759 | for(i=pVariables;i>0;i--) |
---|
[35aab3] | 760 | { |
---|
[93e7e91] | 761 | e=pGetExp(f,i); |
---|
| 762 | if(e!=0) |
---|
| 763 | { |
---|
| 764 | n--; |
---|
| 765 | poly p=pOne(); |
---|
| 766 | pSetExp(p,i,1); |
---|
| 767 | pSetm(p); |
---|
| 768 | res->m[n]=p; |
---|
| 769 | if (with_exps!=1) (**v)[n]=e; |
---|
| 770 | } |
---|
[35aab3] | 771 | } |
---|
| 772 | } |
---|
[93e7e91] | 773 | pDelete(&f); |
---|
[35aab3] | 774 | return res; |
---|
| 775 | } |
---|
| 776 | //PrintS("S:");pWrite(f);PrintLn(); |
---|
[54ff35] | 777 | // use factory/libfac in general ============================== |
---|
[35aab3] | 778 | Off(SW_RATIONAL); |
---|
| 779 | On(SW_SYMMETRIC_FF); |
---|
| 780 | #ifdef HAVE_NTL |
---|
| 781 | extern int prime_number; |
---|
| 782 | if(rField_is_Q()) prime_number=0; |
---|
| 783 | #endif |
---|
| 784 | CFFList L; |
---|
| 785 | number N=NULL; |
---|
[ffdd694] | 786 | number NN=NULL; |
---|
[35aab3] | 787 | number old_lead_coeff=nCopy(pGetCoeff(f)); |
---|
| 788 | |
---|
[0a55e5] | 789 | if (!rField_is_Zp() && !rField_is_Zp_a()) /* Q, Q(a) */ |
---|
| 790 | { |
---|
| 791 | //if (f!=NULL) // already tested at start of routine |
---|
| 792 | { |
---|
| 793 | number n0=nCopy(pGetCoeff(f)); |
---|
| 794 | if (with_exps==0) |
---|
| 795 | N=nCopy(n0); |
---|
[a0d9be] | 796 | p_Cleardenom(f, currRing); |
---|
[0a55e5] | 797 | NN=nDiv(n0,pGetCoeff(f)); |
---|
| 798 | nDelete(&n0); |
---|
| 799 | if (with_exps==0) |
---|
| 800 | { |
---|
| 801 | nDelete(&N); |
---|
| 802 | N=nCopy(NN); |
---|
| 803 | } |
---|
| 804 | } |
---|
| 805 | } |
---|
| 806 | else if (rField_is_Zp_a()) |
---|
[35aab3] | 807 | { |
---|
[ffdd694] | 808 | //if (f!=NULL) // already tested at start of routine |
---|
[0a55e5] | 809 | if (singclap_factorize_retry==0) |
---|
[35aab3] | 810 | { |
---|
[ffdd694] | 811 | number n0=nCopy(pGetCoeff(f)); |
---|
| 812 | if (with_exps==0) |
---|
| 813 | N=nCopy(n0); |
---|
[0a55e5] | 814 | pNorm(f); |
---|
[a0d9be] | 815 | p_Cleardenom(f, currRing); |
---|
[ffdd694] | 816 | NN=nDiv(n0,pGetCoeff(f)); |
---|
| 817 | nDelete(&n0); |
---|
| 818 | if (with_exps==0) |
---|
[35aab3] | 819 | { |
---|
[ffdd694] | 820 | nDelete(&N); |
---|
| 821 | N=nCopy(NN); |
---|
[35aab3] | 822 | } |
---|
| 823 | } |
---|
[ffdd694] | 824 | } |
---|
| 825 | if (rField_is_Q() || rField_is_Zp()) |
---|
| 826 | { |
---|
| 827 | setCharacteristic( nGetChar() ); |
---|
[46f6af6] | 828 | CanonicalForm F( convSingPFactoryP( f ) ); |
---|
[34ceab] | 829 | L = factorize( F ); |
---|
[35aab3] | 830 | } |
---|
| 831 | #if 0 |
---|
| 832 | else if (rField_is_GF()) |
---|
| 833 | { |
---|
| 834 | int c=rChar(currRing); |
---|
| 835 | setCharacteristic( c, primepower(c) ); |
---|
[46f6af6] | 836 | CanonicalForm F( convSingGFFactoryGF( f ) ); |
---|
[35aab3] | 837 | if (F.isUnivariate()) |
---|
| 838 | { |
---|
| 839 | L = factorize( F ); |
---|
| 840 | } |
---|
| 841 | else |
---|
| 842 | { |
---|
| 843 | goto notImpl; |
---|
| 844 | } |
---|
| 845 | } |
---|
| 846 | #endif |
---|
| 847 | // and over Q(a) / Fp(a) |
---|
| 848 | else if (rField_is_Extension()) |
---|
| 849 | { |
---|
| 850 | if (rField_is_Q_a()) setCharacteristic( 0 ); |
---|
| 851 | else setCharacteristic( -nGetChar() ); |
---|
| 852 | if (currRing->minpoly!=NULL) |
---|
| 853 | { |
---|
[6620d75] | 854 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
---|
[64a88e] | 855 | currRing->algring); |
---|
[35aab3] | 856 | Variable a=rootOf(mipo); |
---|
[cf74cd6] | 857 | CanonicalForm F( convSingAPFactoryAP( f,a,currRing ) ); |
---|
[34ceab] | 858 | if (rField_is_Zp_a()) |
---|
[35aab3] | 859 | { |
---|
| 860 | L = factorize( F, a ); |
---|
| 861 | } |
---|
| 862 | else |
---|
| 863 | { |
---|
[34ceab] | 864 | // over Q(a) |
---|
[59a7ca1] | 865 | if (F.isUnivariate()) |
---|
[8de151] | 866 | { |
---|
[59a7ca1] | 867 | L= factorize (F, a); |
---|
| 868 | } |
---|
| 869 | else |
---|
| 870 | { |
---|
| 871 | CanonicalForm G( convSingTrPFactoryP( f ) ); |
---|
| 872 | do |
---|
| 873 | { |
---|
| 874 | libfac_interruptflag=0; |
---|
| 875 | L=Factorize2(G, mipo); |
---|
| 876 | } |
---|
| 877 | while ((libfac_interruptflag!=0) ||(L.isEmpty())); |
---|
| 878 | #ifdef FACTORIZE2_DEBUG |
---|
| 879 | printf("while okay\n"); |
---|
| 880 | #endif |
---|
[0a55e5] | 881 | libfac_interruptflag=0; |
---|
[8de151] | 882 | } |
---|
[35aab3] | 883 | } |
---|
| 884 | } |
---|
| 885 | else |
---|
| 886 | { |
---|
[46f6af6] | 887 | CanonicalForm F( convSingTrPFactoryP( f ) ); |
---|
[34ceab] | 888 | L = factorize( F ); |
---|
[35aab3] | 889 | } |
---|
| 890 | } |
---|
| 891 | else |
---|
| 892 | { |
---|
| 893 | goto notImpl; |
---|
| 894 | } |
---|
| 895 | { |
---|
[0a55e5] | 896 | poly ff=pCopy(f); // a copy for the retry stuff |
---|
[35aab3] | 897 | // the first factor should be a constant |
---|
| 898 | if ( ! L.getFirst().factor().inCoeffDomain() ) |
---|
| 899 | L.insert(CFFactor(1,1)); |
---|
| 900 | // convert into ideal |
---|
| 901 | int n = L.length(); |
---|
[91cb92] | 902 | if (n==0) n=1; |
---|
[35aab3] | 903 | CFFListIterator J=L; |
---|
| 904 | int j=0; |
---|
| 905 | if (with_exps!=1) |
---|
| 906 | { |
---|
| 907 | if ((with_exps==2)&&(n>1)) |
---|
| 908 | { |
---|
| 909 | n--; |
---|
| 910 | J++; |
---|
| 911 | } |
---|
| 912 | *v = new intvec( n ); |
---|
| 913 | } |
---|
| 914 | res = idInit( n ,1); |
---|
| 915 | for ( ; J.hasItem(); J++, j++ ) |
---|
| 916 | { |
---|
| 917 | if (with_exps!=1) (**v)[j] = J.getItem().exp(); |
---|
| 918 | if (rField_is_Zp() || rField_is_Q()) /* Q, Fp */ |
---|
[8fc55e2] | 919 | { |
---|
[46f6af6] | 920 | //count_Factors(res,*v,f, j, convFactoryPSingP( J.getItem().factor() ); |
---|
| 921 | res->m[j] = convFactoryPSingP( J.getItem().factor() ); |
---|
[8fc55e2] | 922 | } |
---|
[35aab3] | 923 | #if 0 |
---|
| 924 | else if (rField_is_GF()) |
---|
[46f6af6] | 925 | res->m[j] = convFactoryGFSingGF( J.getItem().factor() ); |
---|
[35aab3] | 926 | #endif |
---|
| 927 | else if (rField_is_Extension()) /* Q(a), Fp(a) */ |
---|
| 928 | { |
---|
[5d491d] | 929 | intvec *w=NULL; |
---|
| 930 | if (v!=NULL) w=*v; |
---|
[35aab3] | 931 | if (currRing->minpoly==NULL) |
---|
[8fc55e2] | 932 | { |
---|
| 933 | if(!count_Factors(res,w,j,ff,convFactoryPSingTrP( J.getItem().factor() ))) |
---|
[d499d1] | 934 | { |
---|
[a86cda] | 935 | if (w!=NULL) |
---|
[e080ab] | 936 | (*w)[j]=1; |
---|
[8fc55e2] | 937 | res->m[j]=pOne(); |
---|
[d499d1] | 938 | } |
---|
[8fc55e2] | 939 | } |
---|
[35aab3] | 940 | else |
---|
[8fc55e2] | 941 | { |
---|
[d1f231] | 942 | if (!count_Factors(res,w,j,ff,convFactoryAPSingAP( J.getItem().factor(),currRing ))) |
---|
[d499d1] | 943 | { |
---|
[a86cda] | 944 | if (w!=NULL) |
---|
[e080ab] | 945 | (*w)[j]=1; |
---|
[8fc55e2] | 946 | res->m[j]=pOne(); |
---|
[d499d1] | 947 | } |
---|
[8fc55e2] | 948 | } |
---|
[0a55e5] | 949 | } |
---|
| 950 | } |
---|
| 951 | if (rField_is_Extension() && (!pIsConstantPoly(ff))) |
---|
| 952 | { |
---|
| 953 | singclap_factorize_retry++; |
---|
| 954 | if (singclap_factorize_retry<3) |
---|
| 955 | { |
---|
| 956 | int jj; |
---|
| 957 | #ifdef FACTORIZE2_DEBUG |
---|
| 958 | printf("factorize_retry\n"); |
---|
| 959 | #endif |
---|
| 960 | intvec *ww=NULL; |
---|
| 961 | idTest(res); |
---|
| 962 | ideal h=singclap_factorize ( ff, &ww , with_exps); |
---|
| 963 | idTest(h); |
---|
| 964 | int l=(*v)->length(); |
---|
[91cb92] | 965 | (*v)->resize(l+ww->length()); |
---|
[0a55e5] | 966 | for(jj=0;jj<ww->length();jj++) |
---|
[91cb92] | 967 | (**v)[jj+l]=(*ww)[jj]; |
---|
[0a55e5] | 968 | delete ww; |
---|
| 969 | ideal hh=idInit(IDELEMS(res)+IDELEMS(h),1); |
---|
| 970 | for(jj=IDELEMS(res)-1;jj>=0;jj--) |
---|
| 971 | { |
---|
| 972 | hh->m[jj]=res->m[jj]; |
---|
| 973 | res->m[jj]=NULL; |
---|
| 974 | } |
---|
| 975 | for(jj=IDELEMS(h)-1;jj>=0;jj--) |
---|
| 976 | { |
---|
| 977 | hh->m[jj+IDELEMS(res)]=h->m[jj]; |
---|
| 978 | h->m[jj]=NULL; |
---|
| 979 | } |
---|
| 980 | idDelete(&res); |
---|
| 981 | idDelete(&h); |
---|
| 982 | res=hh; |
---|
| 983 | idTest(res); |
---|
| 984 | ff=NULL; |
---|
| 985 | } |
---|
| 986 | else |
---|
| 987 | { |
---|
| 988 | WarnS("problem with factorize"); |
---|
[226dd7] | 989 | #if 0 |
---|
| 990 | pWrite(ff); |
---|
| 991 | idShow(res); |
---|
| 992 | #endif |
---|
| 993 | idDelete(&res); |
---|
| 994 | res=idInit(2,1); |
---|
| 995 | res->m[0]=pOne(); |
---|
| 996 | res->m[1]=ff; ff=NULL; |
---|
[35aab3] | 997 | } |
---|
| 998 | } |
---|
[0a55e5] | 999 | pDelete(&ff); |
---|
[35aab3] | 1000 | if (N!=NULL) |
---|
| 1001 | { |
---|
| 1002 | pMult_nn(res->m[0],N); |
---|
[ffdd694] | 1003 | nDelete(&N); |
---|
| 1004 | N=NULL; |
---|
[35aab3] | 1005 | } |
---|
| 1006 | // delete constants |
---|
| 1007 | if (res!=NULL) |
---|
| 1008 | { |
---|
| 1009 | int i=IDELEMS(res)-1; |
---|
| 1010 | int j=0; |
---|
| 1011 | for(;i>=0;i--) |
---|
| 1012 | { |
---|
| 1013 | if ((res->m[i]!=NULL) |
---|
| 1014 | && (pNext(res->m[i])==NULL) |
---|
| 1015 | && (pIsConstant(res->m[i]))) |
---|
| 1016 | { |
---|
| 1017 | if (with_exps!=0) |
---|
| 1018 | { |
---|
| 1019 | pDelete(&(res->m[i])); |
---|
| 1020 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
| 1021 | (**v)[i]=0; |
---|
| 1022 | j++; |
---|
| 1023 | } |
---|
| 1024 | else if (i!=0) |
---|
| 1025 | { |
---|
[d8932ed] | 1026 | while ((v!=NULL) && ((*v)!=NULL) && ((**v)[i]>1)) |
---|
| 1027 | { |
---|
| 1028 | res->m[0]=pMult(res->m[0],pCopy(res->m[i])); |
---|
| 1029 | (**v)[i]--; |
---|
| 1030 | } |
---|
[35aab3] | 1031 | res->m[0]=pMult(res->m[0],res->m[i]); |
---|
| 1032 | res->m[i]=NULL; |
---|
| 1033 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
[d499d1] | 1034 | (**v)[i]=1; |
---|
[35aab3] | 1035 | j++; |
---|
| 1036 | } |
---|
| 1037 | } |
---|
| 1038 | } |
---|
| 1039 | if (j>0) |
---|
| 1040 | { |
---|
| 1041 | idSkipZeroes(res); |
---|
| 1042 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
| 1043 | { |
---|
| 1044 | intvec *w=*v; |
---|
[f12cd23] | 1045 | int len=IDELEMS(res); |
---|
| 1046 | *v = new intvec( len ); |
---|
[0a55e5] | 1047 | for (i=0,j=0;i<si_min(w->length(),len);i++) |
---|
[35aab3] | 1048 | { |
---|
| 1049 | if((*w)[i]!=0) |
---|
| 1050 | { |
---|
| 1051 | (**v)[j]=(*w)[i]; j++; |
---|
| 1052 | } |
---|
| 1053 | } |
---|
| 1054 | delete w; |
---|
| 1055 | } |
---|
| 1056 | } |
---|
| 1057 | if (res->m[0]==NULL) |
---|
| 1058 | { |
---|
| 1059 | res->m[0]=pOne(); |
---|
| 1060 | } |
---|
| 1061 | } |
---|
| 1062 | } |
---|
| 1063 | if (rField_is_Q_a() && (currRing->minpoly!=NULL)) |
---|
| 1064 | { |
---|
| 1065 | int i=IDELEMS(res)-1; |
---|
| 1066 | int stop=1; |
---|
| 1067 | if (with_exps!=0) stop=0; |
---|
| 1068 | for(;i>=stop;i--) |
---|
| 1069 | { |
---|
| 1070 | pNorm(res->m[i]); |
---|
| 1071 | } |
---|
| 1072 | if (with_exps==0) pSetCoeff(res->m[0],old_lead_coeff); |
---|
| 1073 | else nDelete(&old_lead_coeff); |
---|
| 1074 | } |
---|
| 1075 | else |
---|
| 1076 | nDelete(&old_lead_coeff); |
---|
[ee5d91] | 1077 | errorreported=save_errorreported; |
---|
[35aab3] | 1078 | notImpl: |
---|
| 1079 | if (res==NULL) |
---|
| 1080 | WerrorS( feNotImplemented ); |
---|
[ffdd694] | 1081 | if (NN!=NULL) |
---|
[35aab3] | 1082 | { |
---|
| 1083 | nDelete(&NN); |
---|
[ffdd694] | 1084 | } |
---|
| 1085 | if (N!=NULL) |
---|
| 1086 | { |
---|
[35aab3] | 1087 | nDelete(&N); |
---|
| 1088 | } |
---|
[93e7e91] | 1089 | if (f!=NULL) pDelete(&f); |
---|
[35aab3] | 1090 | //PrintS("......S\n"); |
---|
| 1091 | return res; |
---|
| 1092 | } |
---|
[0dd641] | 1093 | ideal singclap_sqrfree ( poly f) |
---|
| 1094 | { |
---|
| 1095 | pTest(f); |
---|
| 1096 | #ifdef FACTORIZE2_DEBUG |
---|
| 1097 | printf("singclap_sqrfree, degree %d\n",pTotaldegree(f)); |
---|
| 1098 | #endif |
---|
| 1099 | // with_exps: 3,1 return only true factors, no exponents |
---|
| 1100 | // 2 return true factors and exponents |
---|
| 1101 | // 0 return coeff, factors and exponents |
---|
| 1102 | BOOLEAN save_errorreported=errorreported; |
---|
| 1103 | |
---|
| 1104 | ideal res=NULL; |
---|
| 1105 | |
---|
| 1106 | // handle factorize(0) ========================================= |
---|
| 1107 | if (f==NULL) |
---|
| 1108 | { |
---|
| 1109 | res=idInit(1,1); |
---|
| 1110 | return res; |
---|
| 1111 | } |
---|
| 1112 | // handle factorize(mon) ========================================= |
---|
| 1113 | if (pNext(f)==NULL) |
---|
| 1114 | { |
---|
| 1115 | int i=0; |
---|
| 1116 | int n=0; |
---|
| 1117 | int e; |
---|
| 1118 | for(i=pVariables;i>0;i--) if(pGetExp(f,i)!=0) n++; |
---|
| 1119 | n++; // with coeff |
---|
| 1120 | res=idInit(si_max(n,1),1); |
---|
[2abbb60] | 1121 | res->m[0]=pNSet(nCopy(pGetCoeff(f))); |
---|
[0dd641] | 1122 | if (n==0) |
---|
| 1123 | { |
---|
| 1124 | res->m[0]=pOne(); |
---|
| 1125 | // (**v)[0]=1; is already done |
---|
| 1126 | return res; |
---|
| 1127 | } |
---|
| 1128 | for(i=pVariables;i>0;i--) |
---|
| 1129 | { |
---|
| 1130 | e=pGetExp(f,i); |
---|
| 1131 | if(e!=0) |
---|
| 1132 | { |
---|
| 1133 | n--; |
---|
| 1134 | poly p=pOne(); |
---|
| 1135 | pSetExp(p,i,1); |
---|
| 1136 | pSetm(p); |
---|
| 1137 | res->m[n]=p; |
---|
| 1138 | } |
---|
| 1139 | } |
---|
| 1140 | return res; |
---|
| 1141 | } |
---|
| 1142 | //PrintS("S:");pWrite(f);PrintLn(); |
---|
| 1143 | // use factory/libfac in general ============================== |
---|
| 1144 | Off(SW_RATIONAL); |
---|
| 1145 | On(SW_SYMMETRIC_FF); |
---|
| 1146 | #ifdef HAVE_NTL |
---|
| 1147 | extern int prime_number; |
---|
| 1148 | if(rField_is_Q()) prime_number=0; |
---|
| 1149 | #endif |
---|
| 1150 | CFFList L; |
---|
| 1151 | |
---|
| 1152 | if (!rField_is_Zp() && !rField_is_Zp_a()) /* Q, Q(a) */ |
---|
| 1153 | { |
---|
| 1154 | //if (f!=NULL) // already tested at start of routine |
---|
| 1155 | { |
---|
[a0d9be] | 1156 | p_Cleardenom(f, currRing); |
---|
[0dd641] | 1157 | } |
---|
| 1158 | } |
---|
| 1159 | else if (rField_is_Zp_a()) |
---|
| 1160 | { |
---|
| 1161 | //if (f!=NULL) // already tested at start of routine |
---|
| 1162 | if (singclap_factorize_retry==0) |
---|
| 1163 | { |
---|
| 1164 | pNorm(f); |
---|
[a0d9be] | 1165 | p_Cleardenom(f, currRing); |
---|
[0dd641] | 1166 | } |
---|
| 1167 | } |
---|
| 1168 | if (rField_is_Q() || rField_is_Zp()) |
---|
| 1169 | { |
---|
| 1170 | setCharacteristic( nGetChar() ); |
---|
| 1171 | CanonicalForm F( convSingPFactoryP( f ) ); |
---|
[85194f2] | 1172 | L = sqrFree( F ); |
---|
[0dd641] | 1173 | } |
---|
| 1174 | #if 0 |
---|
| 1175 | else if (rField_is_GF()) |
---|
| 1176 | { |
---|
| 1177 | int c=rChar(currRing); |
---|
| 1178 | setCharacteristic( c, primepower(c) ); |
---|
| 1179 | CanonicalForm F( convSingGFFactoryGF( f ) ); |
---|
| 1180 | if (F.isUnivariate()) |
---|
| 1181 | { |
---|
| 1182 | L = factorize( F ); |
---|
| 1183 | } |
---|
| 1184 | else |
---|
| 1185 | { |
---|
| 1186 | goto notImpl; |
---|
| 1187 | } |
---|
| 1188 | } |
---|
| 1189 | #endif |
---|
| 1190 | // and over Q(a) / Fp(a) |
---|
| 1191 | else if (rField_is_Extension()) |
---|
| 1192 | { |
---|
| 1193 | if (rField_is_Q_a()) setCharacteristic( 0 ); |
---|
| 1194 | else setCharacteristic( -nGetChar() ); |
---|
| 1195 | if (currRing->minpoly!=NULL) |
---|
| 1196 | { |
---|
[6620d75] | 1197 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
---|
[64a88e] | 1198 | currRing->algring); |
---|
[0dd641] | 1199 | Variable a=rootOf(mipo); |
---|
[cf74cd6] | 1200 | CanonicalForm F( convSingAPFactoryAP( f,a,currRing ) ); |
---|
[85194f2] | 1201 | CFFList SqrFreeMV( const CanonicalForm & f , const CanonicalForm & mipo=0) ; |
---|
| 1202 | |
---|
| 1203 | L = SqrFreeMV( F,mipo ); |
---|
| 1204 | //WarnS("L = sqrFree( F,mipo );"); |
---|
| 1205 | //L = sqrFree( F ); |
---|
[0dd641] | 1206 | } |
---|
| 1207 | else |
---|
| 1208 | { |
---|
| 1209 | CanonicalForm F( convSingTrPFactoryP( f ) ); |
---|
[85194f2] | 1210 | L = sqrFree( F ); |
---|
[0dd641] | 1211 | } |
---|
| 1212 | } |
---|
| 1213 | else |
---|
| 1214 | { |
---|
| 1215 | goto notImpl; |
---|
| 1216 | } |
---|
| 1217 | { |
---|
| 1218 | // convert into ideal |
---|
| 1219 | int n = L.length(); |
---|
| 1220 | if (n==0) n=1; |
---|
| 1221 | CFFListIterator J=L; |
---|
| 1222 | int j=0; |
---|
| 1223 | res = idInit( n ,1); |
---|
| 1224 | for ( ; J.hasItem(); J++, j++ ) |
---|
| 1225 | { |
---|
| 1226 | if (rField_is_Zp() || rField_is_Q()) /* Q, Fp */ |
---|
| 1227 | //count_Factors(res,*v,f, j, convFactoryPSingP( J.getItem().factor() ); |
---|
| 1228 | res->m[j] = convFactoryPSingP( J.getItem().factor() ); |
---|
| 1229 | #if 0 |
---|
| 1230 | else if (rField_is_GF()) |
---|
| 1231 | res->m[j] = convFactoryGFSingGF( J.getItem().factor() ); |
---|
| 1232 | #endif |
---|
| 1233 | else if (rField_is_Extension()) /* Q(a), Fp(a) */ |
---|
| 1234 | { |
---|
| 1235 | if (currRing->minpoly==NULL) |
---|
| 1236 | res->m[j]=convFactoryPSingTrP( J.getItem().factor() ); |
---|
| 1237 | else |
---|
[d1f231] | 1238 | res->m[j]=convFactoryAPSingAP( J.getItem().factor(),currRing ); |
---|
[0dd641] | 1239 | } |
---|
| 1240 | } |
---|
| 1241 | if (res->m[0]==NULL) |
---|
| 1242 | { |
---|
| 1243 | res->m[0]=pOne(); |
---|
| 1244 | } |
---|
| 1245 | } |
---|
[c53b8af] | 1246 | pDelete(&f); |
---|
[0dd641] | 1247 | errorreported=save_errorreported; |
---|
| 1248 | notImpl: |
---|
| 1249 | if (res==NULL) |
---|
| 1250 | WerrorS( feNotImplemented ); |
---|
| 1251 | return res; |
---|
| 1252 | } |
---|
[35aab3] | 1253 | matrix singclap_irrCharSeries ( ideal I) |
---|
| 1254 | { |
---|
| 1255 | if (idIs0(I)) return mpNew(1,1); |
---|
| 1256 | |
---|
| 1257 | // for now there is only the possibility to handle polynomials over |
---|
| 1258 | // Q and Fp ... |
---|
| 1259 | matrix res=NULL; |
---|
| 1260 | int i; |
---|
| 1261 | Off(SW_RATIONAL); |
---|
| 1262 | On(SW_SYMMETRIC_FF); |
---|
| 1263 | CFList L; |
---|
| 1264 | ListCFList LL; |
---|
| 1265 | if (((nGetChar() == 0) || (nGetChar() > 1) ) |
---|
| 1266 | && (currRing->parameter==NULL)) |
---|
| 1267 | { |
---|
| 1268 | setCharacteristic( nGetChar() ); |
---|
| 1269 | for(i=0;i<IDELEMS(I);i++) |
---|
| 1270 | { |
---|
| 1271 | poly p=I->m[i]; |
---|
| 1272 | if (p!=NULL) |
---|
| 1273 | { |
---|
| 1274 | p=pCopy(p); |
---|
[a0d9be] | 1275 | p_Cleardenom(p, currRing); |
---|
[46f6af6] | 1276 | L.append(convSingPFactoryP(p)); |
---|
[35aab3] | 1277 | } |
---|
| 1278 | } |
---|
| 1279 | } |
---|
| 1280 | // and over Q(a) / Fp(a) |
---|
| 1281 | else if (( nGetChar()==1 ) /* Q(a) */ |
---|
| 1282 | || (nGetChar() <-1)) /* Fp(a) */ |
---|
| 1283 | { |
---|
| 1284 | if (nGetChar()==1) setCharacteristic( 0 ); |
---|
| 1285 | else setCharacteristic( -nGetChar() ); |
---|
| 1286 | for(i=0;i<IDELEMS(I);i++) |
---|
| 1287 | { |
---|
| 1288 | poly p=I->m[i]; |
---|
| 1289 | if (p!=NULL) |
---|
| 1290 | { |
---|
| 1291 | p=pCopy(p); |
---|
[a0d9be] | 1292 | p_Cleardenom(p, currRing); |
---|
[46f6af6] | 1293 | L.append(convSingTrPFactoryP(p)); |
---|
[35aab3] | 1294 | } |
---|
| 1295 | } |
---|
| 1296 | } |
---|
| 1297 | else |
---|
| 1298 | { |
---|
| 1299 | WerrorS( feNotImplemented ); |
---|
| 1300 | return res; |
---|
| 1301 | } |
---|
| 1302 | |
---|
| 1303 | // a very bad work-around --- FIX IT in libfac |
---|
| 1304 | // should be fixed as of 2001/6/27 |
---|
| 1305 | int tries=0; |
---|
| 1306 | int m,n; |
---|
| 1307 | ListIterator<CFList> LLi; |
---|
| 1308 | loop |
---|
| 1309 | { |
---|
| 1310 | LL=IrrCharSeries(L); |
---|
| 1311 | m= LL.length(); // Anzahl Zeilen |
---|
| 1312 | n=0; |
---|
| 1313 | for ( LLi = LL; LLi.hasItem(); LLi++ ) |
---|
| 1314 | { |
---|
| 1315 | n = si_max(LLi.getItem().length(),n); |
---|
| 1316 | } |
---|
| 1317 | if ((m!=0) && (n!=0)) break; |
---|
| 1318 | tries++; |
---|
| 1319 | if (tries>=5) break; |
---|
| 1320 | } |
---|
| 1321 | if ((m==0) || (n==0)) |
---|
| 1322 | { |
---|
| 1323 | Warn("char_series returns %d x %d matrix from %d input polys (%d)", |
---|
| 1324 | m,n,IDELEMS(I)+1,LL.length()); |
---|
| 1325 | iiWriteMatrix((matrix)I,"I",2,0); |
---|
| 1326 | m=si_max(m,1); |
---|
| 1327 | n=si_max(n,1); |
---|
| 1328 | } |
---|
| 1329 | res=mpNew(m,n); |
---|
| 1330 | CFListIterator Li; |
---|
| 1331 | for ( m=1, LLi = LL; LLi.hasItem(); LLi++, m++ ) |
---|
| 1332 | { |
---|
| 1333 | for (n=1, Li = LLi.getItem(); Li.hasItem(); Li++, n++) |
---|
| 1334 | { |
---|
| 1335 | if ( (nGetChar() == 0) || (nGetChar() > 1) ) |
---|
[46f6af6] | 1336 | MATELEM(res,m,n)=convFactoryPSingP(Li.getItem()); |
---|
[35aab3] | 1337 | else |
---|
[46f6af6] | 1338 | MATELEM(res,m,n)=convFactoryPSingTrP(Li.getItem()); |
---|
[35aab3] | 1339 | } |
---|
| 1340 | } |
---|
| 1341 | Off(SW_RATIONAL); |
---|
| 1342 | return res; |
---|
| 1343 | } |
---|
| 1344 | |
---|
| 1345 | char* singclap_neworder ( ideal I) |
---|
| 1346 | { |
---|
| 1347 | int i; |
---|
| 1348 | Off(SW_RATIONAL); |
---|
| 1349 | On(SW_SYMMETRIC_FF); |
---|
| 1350 | CFList L; |
---|
| 1351 | if (((nGetChar() == 0) || (nGetChar() > 1) ) |
---|
| 1352 | && (currRing->parameter==NULL)) |
---|
| 1353 | { |
---|
| 1354 | setCharacteristic( nGetChar() ); |
---|
| 1355 | for(i=0;i<IDELEMS(I);i++) |
---|
| 1356 | { |
---|
[46f6af6] | 1357 | L.append(convSingPFactoryP(I->m[i])); |
---|
[35aab3] | 1358 | } |
---|
| 1359 | } |
---|
| 1360 | // and over Q(a) / Fp(a) |
---|
| 1361 | else if (( nGetChar()==1 ) /* Q(a) */ |
---|
| 1362 | || (nGetChar() <-1)) /* Fp(a) */ |
---|
| 1363 | { |
---|
| 1364 | if (nGetChar()==1) setCharacteristic( 0 ); |
---|
| 1365 | else setCharacteristic( -nGetChar() ); |
---|
| 1366 | for(i=0;i<IDELEMS(I);i++) |
---|
| 1367 | { |
---|
[46f6af6] | 1368 | L.append(convSingTrPFactoryP(I->m[i])); |
---|
[35aab3] | 1369 | } |
---|
| 1370 | } |
---|
| 1371 | else |
---|
| 1372 | { |
---|
| 1373 | WerrorS( feNotImplemented ); |
---|
| 1374 | return NULL; |
---|
| 1375 | } |
---|
| 1376 | |
---|
| 1377 | List<int> IL=neworderint(L); |
---|
| 1378 | ListIterator<int> Li; |
---|
| 1379 | StringSetS(""); |
---|
| 1380 | Li = IL; |
---|
| 1381 | int offs=rPar(currRing); |
---|
| 1382 | int* mark=(int*)omAlloc0((pVariables+offs)*sizeof(int)); |
---|
| 1383 | int cnt=pVariables+offs; |
---|
| 1384 | loop |
---|
| 1385 | { |
---|
| 1386 | if(! Li.hasItem()) break; |
---|
| 1387 | BOOLEAN done=TRUE; |
---|
| 1388 | i=Li.getItem()-1; |
---|
| 1389 | mark[i]=1; |
---|
| 1390 | if (i<offs) |
---|
| 1391 | { |
---|
| 1392 | done=FALSE; |
---|
| 1393 | //StringAppendS(currRing->parameter[i]); |
---|
| 1394 | } |
---|
| 1395 | else |
---|
| 1396 | { |
---|
| 1397 | StringAppendS(currRing->names[i-offs]); |
---|
| 1398 | } |
---|
| 1399 | Li++; |
---|
| 1400 | cnt--; |
---|
| 1401 | if(cnt==0) break; |
---|
| 1402 | if (done) StringAppendS(","); |
---|
| 1403 | } |
---|
| 1404 | for(i=0;i<pVariables+offs;i++) |
---|
| 1405 | { |
---|
| 1406 | BOOLEAN done=TRUE; |
---|
| 1407 | if(mark[i]==0) |
---|
| 1408 | { |
---|
| 1409 | if (i<offs) |
---|
| 1410 | { |
---|
| 1411 | done=FALSE; |
---|
| 1412 | //StringAppendS(currRing->parameter[i]); |
---|
| 1413 | } |
---|
| 1414 | else |
---|
| 1415 | { |
---|
| 1416 | StringAppendS(currRing->names[i-offs]); |
---|
| 1417 | } |
---|
| 1418 | cnt--; |
---|
| 1419 | if(cnt==0) break; |
---|
| 1420 | if (done) StringAppendS(","); |
---|
| 1421 | } |
---|
| 1422 | } |
---|
| 1423 | char * s=omStrDup(StringAppendS("")); |
---|
| 1424 | if (s[strlen(s)-1]==',') s[strlen(s)-1]='\0'; |
---|
| 1425 | return s; |
---|
| 1426 | } |
---|
| 1427 | |
---|
| 1428 | BOOLEAN singclap_isSqrFree(poly f) |
---|
| 1429 | { |
---|
| 1430 | BOOLEAN b=FALSE; |
---|
| 1431 | Off(SW_RATIONAL); |
---|
| 1432 | // Q / Fp |
---|
| 1433 | if (((nGetChar() == 0) || (nGetChar() > 1) ) |
---|
| 1434 | &&(currRing->parameter==NULL)) |
---|
| 1435 | { |
---|
| 1436 | setCharacteristic( nGetChar() ); |
---|
[46f6af6] | 1437 | CanonicalForm F( convSingPFactoryP( f ) ); |
---|
[35aab3] | 1438 | if((nGetChar()>1)&&(!F.isUnivariate())) |
---|
| 1439 | goto err; |
---|
| 1440 | b=(BOOLEAN)isSqrFree(F); |
---|
| 1441 | } |
---|
| 1442 | // and over Q(a) / Fp(a) |
---|
| 1443 | else if (( nGetChar()==1 ) /* Q(a) */ |
---|
| 1444 | || (nGetChar() <-1)) /* Fp(a) */ |
---|
| 1445 | { |
---|
| 1446 | if (nGetChar()==1) setCharacteristic( 0 ); |
---|
| 1447 | else setCharacteristic( -nGetChar() ); |
---|
| 1448 | //if (currRing->minpoly!=NULL) |
---|
| 1449 | //{ |
---|
[6620d75] | 1450 | // CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
---|
[64a88e] | 1451 | // currRing->algring); |
---|
[35aab3] | 1452 | // Variable a=rootOf(mipo); |
---|
[46f6af6] | 1453 | // CanonicalForm F( convSingAPFactoryAP( f,a ) ); |
---|
[35aab3] | 1454 | // ... |
---|
| 1455 | //} |
---|
| 1456 | //else |
---|
| 1457 | { |
---|
[46f6af6] | 1458 | CanonicalForm F( convSingTrPFactoryP( f ) ); |
---|
[35aab3] | 1459 | b=(BOOLEAN)isSqrFree(F); |
---|
| 1460 | } |
---|
| 1461 | Off(SW_RATIONAL); |
---|
| 1462 | } |
---|
| 1463 | else |
---|
| 1464 | { |
---|
| 1465 | err: |
---|
| 1466 | WerrorS( feNotImplemented ); |
---|
| 1467 | } |
---|
| 1468 | return b; |
---|
| 1469 | } |
---|
| 1470 | |
---|
| 1471 | poly singclap_det( const matrix m ) |
---|
| 1472 | { |
---|
| 1473 | int r=m->rows(); |
---|
| 1474 | if (r!=m->cols()) |
---|
| 1475 | { |
---|
| 1476 | Werror("det of %d x %d matrix",r,m->cols()); |
---|
| 1477 | return NULL; |
---|
| 1478 | } |
---|
| 1479 | poly res=NULL; |
---|
| 1480 | if (( nGetChar() == 0 || nGetChar() > 1 ) |
---|
| 1481 | && (currRing->parameter==NULL)) |
---|
| 1482 | { |
---|
| 1483 | setCharacteristic( nGetChar() ); |
---|
| 1484 | CFMatrix M(r,r); |
---|
| 1485 | int i,j; |
---|
| 1486 | for(i=r;i>0;i--) |
---|
| 1487 | { |
---|
| 1488 | for(j=r;j>0;j--) |
---|
| 1489 | { |
---|
[46f6af6] | 1490 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j)); |
---|
[35aab3] | 1491 | } |
---|
| 1492 | } |
---|
[46f6af6] | 1493 | res= convFactoryPSingP( determinant(M,r) ) ; |
---|
[35aab3] | 1494 | } |
---|
| 1495 | // and over Q(a) / Fp(a) |
---|
| 1496 | else if (( nGetChar()==1 ) /* Q(a) */ |
---|
| 1497 | || (nGetChar() <-1)) /* Fp(a) */ |
---|
| 1498 | { |
---|
| 1499 | if (nGetChar()==1) setCharacteristic( 0 ); |
---|
| 1500 | else setCharacteristic( -nGetChar() ); |
---|
| 1501 | CFMatrix M(r,r); |
---|
| 1502 | poly res; |
---|
| 1503 | if (currRing->minpoly!=NULL) |
---|
| 1504 | { |
---|
[6620d75] | 1505 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
---|
[64a88e] | 1506 | currRing->algring); |
---|
[35aab3] | 1507 | Variable a=rootOf(mipo); |
---|
| 1508 | int i,j; |
---|
| 1509 | for(i=r;i>0;i--) |
---|
| 1510 | { |
---|
| 1511 | for(j=r;j>0;j--) |
---|
| 1512 | { |
---|
[cf74cd6] | 1513 | M(i,j)=convSingAPFactoryAP(MATELEM(m,i,j),a,currRing); |
---|
[35aab3] | 1514 | } |
---|
| 1515 | } |
---|
[d1f231] | 1516 | res= convFactoryAPSingAP( determinant(M,r),currRing ) ; |
---|
[35aab3] | 1517 | } |
---|
| 1518 | else |
---|
| 1519 | { |
---|
| 1520 | int i,j; |
---|
| 1521 | for(i=r;i>0;i--) |
---|
| 1522 | { |
---|
| 1523 | for(j=r;j>0;j--) |
---|
| 1524 | { |
---|
[46f6af6] | 1525 | M(i,j)=convSingTrPFactoryP(MATELEM(m,i,j)); |
---|
[35aab3] | 1526 | } |
---|
| 1527 | } |
---|
[46f6af6] | 1528 | res= convFactoryPSingTrP( determinant(M,r) ); |
---|
[35aab3] | 1529 | } |
---|
| 1530 | } |
---|
| 1531 | else |
---|
| 1532 | WerrorS( feNotImplemented ); |
---|
| 1533 | Off(SW_RATIONAL); |
---|
| 1534 | return res; |
---|
| 1535 | } |
---|
| 1536 | |
---|
| 1537 | int singclap_det_i( intvec * m ) |
---|
| 1538 | { |
---|
| 1539 | setCharacteristic( 0 ); |
---|
| 1540 | CFMatrix M(m->rows(),m->cols()); |
---|
| 1541 | int i,j; |
---|
| 1542 | for(i=m->rows();i>0;i--) |
---|
| 1543 | { |
---|
| 1544 | for(j=m->cols();j>0;j--) |
---|
| 1545 | { |
---|
| 1546 | M(i,j)=IMATELEM(*m,i,j); |
---|
| 1547 | } |
---|
| 1548 | } |
---|
[46f6af6] | 1549 | int res= convFactoryISingI( determinant(M,m->rows())) ; |
---|
[35aab3] | 1550 | Off(SW_RATIONAL); |
---|
| 1551 | return res; |
---|
| 1552 | } |
---|
[2072126] | 1553 | #ifdef HAVE_NTL |
---|
[af8863] | 1554 | matrix singntl_HNF(matrix m ) |
---|
[9d9078] | 1555 | { |
---|
[af8863] | 1556 | int r=m->rows(); |
---|
| 1557 | if (r!=m->cols()) |
---|
| 1558 | { |
---|
| 1559 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
| 1560 | return NULL; |
---|
| 1561 | } |
---|
| 1562 | matrix res=mpNew(r,r); |
---|
| 1563 | if (rField_is_Q(currRing)) |
---|
| 1564 | { |
---|
[9d9078] | 1565 | |
---|
[af8863] | 1566 | CFMatrix M(r,r); |
---|
| 1567 | int i,j; |
---|
| 1568 | for(i=r;i>0;i--) |
---|
| 1569 | { |
---|
| 1570 | for(j=r;j>0;j--) |
---|
| 1571 | { |
---|
| 1572 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j)); |
---|
| 1573 | } |
---|
| 1574 | } |
---|
| 1575 | CFMatrix *MM=cf_HNF(M); |
---|
| 1576 | for(i=r;i>0;i--) |
---|
| 1577 | { |
---|
| 1578 | for(j=r;j>0;j--) |
---|
[9d9078] | 1579 | { |
---|
[af8863] | 1580 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j)); |
---|
| 1581 | } |
---|
| 1582 | } |
---|
| 1583 | delete MM; |
---|
| 1584 | } |
---|
| 1585 | return res; |
---|
| 1586 | } |
---|
| 1587 | intvec* singntl_HNF(intvec* m ) |
---|
| 1588 | { |
---|
| 1589 | int r=m->rows(); |
---|
| 1590 | if (r!=m->cols()) |
---|
| 1591 | { |
---|
| 1592 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
| 1593 | return NULL; |
---|
| 1594 | } |
---|
| 1595 | setCharacteristic( 0 ); |
---|
| 1596 | CFMatrix M(r,r); |
---|
| 1597 | int i,j; |
---|
| 1598 | for(i=r;i>0;i--) |
---|
| 1599 | { |
---|
| 1600 | for(j=r;j>0;j--) |
---|
| 1601 | { |
---|
| 1602 | M(i,j)=IMATELEM(*m,i,j); |
---|
| 1603 | } |
---|
| 1604 | } |
---|
| 1605 | CFMatrix *MM=cf_HNF(M); |
---|
| 1606 | intvec *mm=ivCopy(m); |
---|
| 1607 | for(i=r;i>0;i--) |
---|
| 1608 | { |
---|
| 1609 | for(j=r;j>0;j--) |
---|
| 1610 | { |
---|
| 1611 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
| 1612 | } |
---|
| 1613 | } |
---|
| 1614 | delete MM; |
---|
| 1615 | return mm; |
---|
| 1616 | } |
---|
[9c0b20a] | 1617 | matrix singntl_LLL(matrix m ) |
---|
[9d9078] | 1618 | { |
---|
[9c0b20a] | 1619 | int r=m->rows(); |
---|
| 1620 | int c=m->cols(); |
---|
| 1621 | matrix res=mpNew(r,c); |
---|
| 1622 | if (rField_is_Q(currRing)) |
---|
| 1623 | { |
---|
| 1624 | CFMatrix M(r,c); |
---|
| 1625 | int i,j; |
---|
| 1626 | for(i=r;i>0;i--) |
---|
| 1627 | { |
---|
| 1628 | for(j=c;j>0;j--) |
---|
| 1629 | { |
---|
| 1630 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j)); |
---|
| 1631 | } |
---|
| 1632 | } |
---|
| 1633 | CFMatrix *MM=cf_LLL(M); |
---|
| 1634 | for(i=r;i>0;i--) |
---|
| 1635 | { |
---|
| 1636 | for(j=c;j>0;j--) |
---|
[9d9078] | 1637 | { |
---|
[9c0b20a] | 1638 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j)); |
---|
| 1639 | } |
---|
| 1640 | } |
---|
| 1641 | delete MM; |
---|
| 1642 | } |
---|
| 1643 | return res; |
---|
| 1644 | } |
---|
| 1645 | intvec* singntl_LLL(intvec* m ) |
---|
| 1646 | { |
---|
| 1647 | int r=m->rows(); |
---|
| 1648 | int c=m->cols(); |
---|
| 1649 | setCharacteristic( 0 ); |
---|
| 1650 | CFMatrix M(r,c); |
---|
| 1651 | int i,j; |
---|
| 1652 | for(i=r;i>0;i--) |
---|
| 1653 | { |
---|
| 1654 | for(j=r;j>0;j--) |
---|
| 1655 | { |
---|
| 1656 | M(i,j)=IMATELEM(*m,i,j); |
---|
| 1657 | } |
---|
| 1658 | } |
---|
| 1659 | CFMatrix *MM=cf_LLL(M); |
---|
| 1660 | intvec *mm=ivCopy(m); |
---|
| 1661 | for(i=r;i>0;i--) |
---|
| 1662 | { |
---|
| 1663 | for(j=c;j>0;j--) |
---|
| 1664 | { |
---|
| 1665 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
| 1666 | } |
---|
| 1667 | } |
---|
| 1668 | delete MM; |
---|
| 1669 | return mm; |
---|
| 1670 | } |
---|
[2072126] | 1671 | #endif |
---|
[af8863] | 1672 | |
---|
[35aab3] | 1673 | napoly singclap_alglcm ( napoly f, napoly g ) |
---|
| 1674 | { |
---|
| 1675 | |
---|
| 1676 | // over Q(a) / Fp(a) |
---|
| 1677 | if (nGetChar()==1) setCharacteristic( 0 ); |
---|
| 1678 | else setCharacteristic( -nGetChar() ); |
---|
| 1679 | napoly res; |
---|
| 1680 | |
---|
| 1681 | if (currRing->minpoly!=NULL) |
---|
| 1682 | { |
---|
[6620d75] | 1683 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
---|
[64a88e] | 1684 | currRing->algring); |
---|
[35aab3] | 1685 | Variable a=rootOf(mipo); |
---|
[cf74cd6] | 1686 | CanonicalForm F( convSingAFactoryA( f,a, currRing ) ), |
---|
| 1687 | G( convSingAFactoryA( g,a, currRing ) ); |
---|
[35aab3] | 1688 | CanonicalForm GCD; |
---|
| 1689 | |
---|
| 1690 | // calculate gcd |
---|
| 1691 | GCD = gcd( F, G ); |
---|
| 1692 | |
---|
| 1693 | // calculate lcm |
---|
[d1f231] | 1694 | res= convFactoryASingA( (F/GCD)*G,currRing ); |
---|
[35aab3] | 1695 | } |
---|
| 1696 | else |
---|
| 1697 | { |
---|
[64a88e] | 1698 | CanonicalForm F( convSingPFactoryP( f,currRing->algring ) ), |
---|
| 1699 | G( convSingPFactoryP( g,currRing->algring ) ); |
---|
[35aab3] | 1700 | CanonicalForm GCD; |
---|
| 1701 | // calculate gcd |
---|
| 1702 | GCD = gcd( F, G ); |
---|
| 1703 | |
---|
| 1704 | // calculate lcm |
---|
[6620d75] | 1705 | res= convFactoryPSingP( (F/GCD)*G, currRing->algring ); |
---|
[35aab3] | 1706 | } |
---|
| 1707 | |
---|
| 1708 | Off(SW_RATIONAL); |
---|
| 1709 | return res; |
---|
| 1710 | } |
---|
| 1711 | |
---|
| 1712 | void singclap_algdividecontent ( napoly f, napoly g, napoly &ff, napoly &gg ) |
---|
| 1713 | { |
---|
| 1714 | // over Q(a) / Fp(a) |
---|
| 1715 | if (nGetChar()==1) setCharacteristic( 0 ); |
---|
| 1716 | else setCharacteristic( -nGetChar() ); |
---|
| 1717 | ff=gg=NULL; |
---|
| 1718 | On(SW_RATIONAL); |
---|
| 1719 | |
---|
| 1720 | if (currRing->minpoly!=NULL) |
---|
| 1721 | { |
---|
[6620d75] | 1722 | CanonicalForm mipo=convSingPFactoryP(((lnumber)currRing->minpoly)->z, |
---|
[64a88e] | 1723 | currRing->algring); |
---|
[35aab3] | 1724 | Variable a=rootOf(mipo); |
---|
[cf74cd6] | 1725 | CanonicalForm F( convSingAFactoryA( f,a, currRing ) ), |
---|
| 1726 | G( convSingAFactoryA( g,a, currRing ) ); |
---|
[35aab3] | 1727 | CanonicalForm GCD; |
---|
| 1728 | |
---|
| 1729 | GCD=gcd( F, G ); |
---|
| 1730 | |
---|
| 1731 | if ((GCD!=1) && (GCD!=0)) |
---|
| 1732 | { |
---|
[d1f231] | 1733 | ff= convFactoryASingA( F/ GCD, currRing ); |
---|
| 1734 | gg= convFactoryASingA( G/ GCD, currRing ); |
---|
[35aab3] | 1735 | } |
---|
| 1736 | } |
---|
| 1737 | else |
---|
| 1738 | { |
---|
[64a88e] | 1739 | CanonicalForm F( convSingPFactoryP( f,currRing->algring ) ), |
---|
| 1740 | G( convSingPFactoryP( g,currRing->algring ) ); |
---|
[35aab3] | 1741 | CanonicalForm GCD; |
---|
| 1742 | |
---|
| 1743 | GCD=gcd( F, G ); |
---|
| 1744 | |
---|
| 1745 | if ((GCD!=1) && (GCD!=0)) |
---|
| 1746 | { |
---|
[6620d75] | 1747 | ff= convFactoryPSingP( F/ GCD, currRing->algring ); |
---|
| 1748 | gg= convFactoryPSingP( G/ GCD, currRing->algring ); |
---|
[35aab3] | 1749 | } |
---|
| 1750 | } |
---|
| 1751 | |
---|
| 1752 | Off(SW_RATIONAL); |
---|
| 1753 | } |
---|
| 1754 | |
---|
| 1755 | #if 0 |
---|
| 1756 | lists singclap_chineseRemainder(lists x, lists q) |
---|
| 1757 | { |
---|
| 1758 | //assume(x->nr == q->nr); |
---|
| 1759 | //assume(x->nr >= 0); |
---|
| 1760 | int n=x->nr+1; |
---|
| 1761 | if ((x->nr<0) || (x->nr!=q->nr)) |
---|
| 1762 | { |
---|
| 1763 | WerrorS("list are empty or not of equal length"); |
---|
| 1764 | return NULL; |
---|
| 1765 | } |
---|
| 1766 | lists res=(lists)omAlloc0Bin(slists_bin); |
---|
| 1767 | CFArray X(1,n), Q(1,n); |
---|
| 1768 | int i; |
---|
| 1769 | for(i=0; i<n; i++) |
---|
| 1770 | { |
---|
| 1771 | if (x->m[i-1].Typ()==INT_CMD) |
---|
| 1772 | { |
---|
| 1773 | X[i]=(int)x->m[i-1].Data(); |
---|
| 1774 | } |
---|
| 1775 | else if (x->m[i-1].Typ()==NUMBER_CMD) |
---|
| 1776 | { |
---|
| 1777 | number N=(number)x->m[i-1].Data(); |
---|
[46f6af6] | 1778 | X[i]=convSingNFactoryN(N); |
---|
[35aab3] | 1779 | } |
---|
| 1780 | else |
---|
| 1781 | { |
---|
| 1782 | WerrorS("illegal type in chineseRemainder"); |
---|
| 1783 | omFreeBin(res,slists_bin); |
---|
| 1784 | return NULL; |
---|
| 1785 | } |
---|
| 1786 | if (q->m[i-1].Typ()==INT_CMD) |
---|
| 1787 | { |
---|
| 1788 | Q[i]=(int)q->m[i-1].Data(); |
---|
| 1789 | } |
---|
| 1790 | else if (q->m[i-1].Typ()==NUMBER_CMD) |
---|
| 1791 | { |
---|
| 1792 | number N=(number)x->m[i-1].Data(); |
---|
[46f6af6] | 1793 | Q[i]=convSingNFactoryN(N); |
---|
[35aab3] | 1794 | } |
---|
| 1795 | else |
---|
| 1796 | { |
---|
| 1797 | WerrorS("illegal type in chineseRemainder"); |
---|
| 1798 | omFreeBin(res,slists_bin); |
---|
| 1799 | return NULL; |
---|
| 1800 | } |
---|
| 1801 | } |
---|
| 1802 | CanonicalForm r, prod; |
---|
| 1803 | chineseRemainder( X, Q, r, prod ); |
---|
| 1804 | res->Init(2); |
---|
| 1805 | res->m[0].rtyp=NUMBER_CMD; |
---|
| 1806 | res->m[1].rtyp=NUMBER_CMD; |
---|
[46f6af6] | 1807 | res->m[0].data=(char *)convFactoryNSingN( r ); |
---|
| 1808 | res->m[1].data=(char *)convFactoryNSingN( prod ); |
---|
[35aab3] | 1809 | return res; |
---|
| 1810 | } |
---|
| 1811 | #endif |
---|
| 1812 | #endif |
---|