| 1 | // emacs edit mode for this file is -*- C++ -*- |
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| 2 | // $Id: fac_berlekamp.cc,v 1.3 1997-04-15 11:09:01 schmidt Exp $ |
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| 3 | |
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| 4 | /* |
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| 5 | $Log: not supported by cvs2svn $ |
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| 6 | Revision 1.2 1997/04/07 16:17:28 schmidt |
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| 7 | #include <config.h> added |
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| 8 | |
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| 9 | Revision 1.1 1997/03/27 09:34:59 schmidt |
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| 10 | debug output changed to DEBOUT |
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| 11 | |
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| 12 | Revision 1.0 1996/05/17 10:59:45 stobbe |
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| 13 | Initial revision |
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| 14 | |
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| 15 | */ |
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| 16 | |
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| 17 | #include <config.h> |
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| 18 | |
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| 19 | #include "assert.h" |
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| 20 | #include "debug.h" |
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| 21 | |
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| 22 | #include "cf_defs.h" |
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| 23 | #include "fac_berlekamp.h" |
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| 24 | #include "ffops.h" |
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| 25 | #include "gfops.h" |
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| 26 | #include "imm.h" |
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| 27 | #include "canonicalform.h" |
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| 28 | #include "cf_iter.h" |
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| 29 | #include "cf_generator.h" |
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| 30 | #include "fac_sqrfree.h" |
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| 31 | #include "cf_util.h" |
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| 32 | |
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| 33 | #ifdef DEBUGOUTPUT |
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| 34 | void QprintFF( int ** Q, int n ) |
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| 35 | { |
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| 36 | for ( int i = 0; i < n; i++ ) { |
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| 37 | for ( int j = 0; j < n; j++ ) |
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| 38 | cerr << Q[i][j] << " "; |
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| 39 | cerr << endl; |
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| 40 | } |
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| 41 | cerr << endl; |
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| 42 | } |
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| 43 | #endif /* DEBUGOUTPUT */ |
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| 44 | |
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| 45 | #ifdef DEBUGOUTPUT |
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| 46 | void QprintGF( int ** Q, int n ) |
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| 47 | { |
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| 48 | for ( int i = 0; i < n; i++ ) { |
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| 49 | for ( int j = 0; j < n; j++ ) { |
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| 50 | gf_print( cerr, Q[i][j] ); |
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| 51 | cerr << " "; |
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| 52 | } |
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| 53 | cerr << endl; |
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| 54 | } |
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| 55 | cerr << endl; |
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| 56 | } |
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| 57 | #endif /* DEBUGOUTPUT */ |
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| 58 | |
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| 59 | void QmatFF ( const CanonicalForm & f, int ** Q, int p ) |
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| 60 | { |
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| 61 | int n = degree( f ), nn = (n-1)*p + 1; |
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| 62 | int i, m, rn; |
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| 63 | int * a = new int [n]; |
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| 64 | int * r = new int [n]; |
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| 65 | int * q; |
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| 66 | |
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| 67 | q = Q[0]; *q = r[0] = 1; a[0] = 0; q++; |
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| 68 | |
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| 69 | for ( i = 1; i < n; i++, q++ ) |
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| 70 | *q = r[i] = a[i] = 0; |
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| 71 | CFIterator I = f; I++; |
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| 72 | while ( I.hasTerms() ) { |
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| 73 | a[I.exp()] = I.coeff().intval(); |
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| 74 | I++; |
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| 75 | } |
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| 76 | for ( m = 1; m < nn; m++ ) { |
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| 77 | rn = r[n-1]; |
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| 78 | for ( i = n-1; i > 0; i-- ) |
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| 79 | r[i] = ff_sub( r[i-1], ff_mul( rn, a[i] ) ); |
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| 80 | r[0] = ff_mul( ff_neg( rn ), a[0] ); |
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| 81 | if ( m % p == 0 ) { |
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| 82 | q = Q[m/p]; |
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| 83 | for ( i = 0; i < n; i++, q++ ) |
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| 84 | *q = r[i]; |
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| 85 | } |
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| 86 | } |
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| 87 | for ( i = 0; i < n; i++ ) |
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| 88 | Q[i][i] = ff_sub( Q[i][i], 1 ); |
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| 89 | |
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| 90 | delete [] a; |
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| 91 | delete [] r; |
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| 92 | } |
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| 93 | |
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| 94 | void QmatGF ( const CanonicalForm & f, int ** Q, int p ) |
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| 95 | { |
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| 96 | int n = degree( f ), nn = (n-1)*p + 1; |
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| 97 | int i, m, rn; |
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| 98 | int * a = new int [n]; |
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| 99 | int * r = new int [n]; |
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| 100 | int * q; |
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| 101 | |
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| 102 | q = Q[0]; *q = r[0] = gf_one(); a[0] = gf_zero(); q++; |
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| 103 | |
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| 104 | for ( i = 1; i < n; i++, q++ ) |
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| 105 | *q = r[i] = a[i] = gf_zero(); |
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| 106 | CFIterator I = f; I++; |
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| 107 | while ( I.hasTerms() ) { |
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| 108 | a[I.exp()] = imm2int( I.coeff().getval() ); |
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| 109 | I++; |
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| 110 | } |
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| 111 | for ( m = 1; m < nn; m++ ) { |
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| 112 | rn = r[n-1]; |
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| 113 | for ( i = n-1; i > 0; i-- ) |
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| 114 | r[i] = gf_sub( r[i-1], gf_mul( rn, a[i] ) ); |
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| 115 | r[0] = gf_mul( gf_neg( rn ), a[0] ); |
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| 116 | if ( m % p == 0 ) { |
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| 117 | q = Q[m/p]; |
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| 118 | for ( i = 0; i < n; i++, q++ ) |
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| 119 | *q = r[i]; |
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| 120 | } |
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| 121 | } |
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| 122 | for ( i = 0; i < n; i++ ) |
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| 123 | Q[i][i] = gf_sub( Q[i][i], gf_one() ); |
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| 124 | |
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| 125 | delete [] a; |
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| 126 | delete [] r; |
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| 127 | } |
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| 128 | |
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| 129 | int nullSpaceFF ( int ** Q, int ** b, int n ) |
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| 130 | { |
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| 131 | int * c = new int[n]; |
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| 132 | int r, i, j, k, h, s, d; |
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| 133 | |
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| 134 | r = 0; |
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| 135 | for ( s = 0; s < n; s++ ) c[s] = -1; |
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| 136 | for ( h = 0; h < n; h++ ) { |
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| 137 | j = 0; |
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| 138 | while ( j < n && ! ( Q[h][j] != 0 && c[j] < 0 ) ) j++; |
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| 139 | if ( j < n ) { |
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| 140 | d = ff_neg( ff_inv( Q[h][j] ) ); |
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| 141 | for ( s = 0; s < n; s++ ) |
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| 142 | Q[s][j] = ff_mul( d, Q[s][j] ); |
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| 143 | for ( i = 0; i < n; i++ ) { |
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| 144 | if ( i != j ) { |
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| 145 | d = Q[h][i]; |
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| 146 | for ( s = 0; s < n; s++ ) |
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| 147 | Q[s][i] = ff_add( ff_mul( d, Q[s][j] ), Q[s][i] ); |
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| 148 | } |
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| 149 | } |
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| 150 | c[j] = h; |
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| 151 | } |
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| 152 | else { |
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| 153 | b[r] = new int[n]; |
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| 154 | for ( j = 0; j < n; j++ ) { |
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| 155 | if ( j == h ) |
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| 156 | b[r][j] = 1; |
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| 157 | else { |
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| 158 | k = 0; |
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| 159 | while ( k < n && c[k] != j ) k++; |
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| 160 | if ( k < n ) |
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| 161 | b[r][j] = Q[h][k]; |
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| 162 | else |
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| 163 | b[r][j] = 0; |
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| 164 | } |
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| 165 | } |
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| 166 | r++; |
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| 167 | } |
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| 168 | } |
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| 169 | delete [] c; |
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| 170 | return r; |
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| 171 | } |
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| 172 | |
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| 173 | int nullSpaceGF ( int ** Q, int ** b, int n ) |
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| 174 | { |
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| 175 | int * c = new int[n]; |
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| 176 | int r, i, j, k, h, s, d; |
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| 177 | |
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| 178 | r = 0; |
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| 179 | for ( s = 0; s < n; s++ ) c[s] = -1; |
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| 180 | for ( h = 0; h < n; h++ ) { |
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| 181 | j = 0; |
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| 182 | while ( j < n && ! ( ! gf_iszero( Q[h][j] ) && c[j] < 0 ) ) j++; |
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| 183 | if ( j < n ) { |
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| 184 | d = gf_neg( gf_inv( Q[h][j] ) ); |
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| 185 | for ( s = 0; s < n; s++ ) |
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| 186 | Q[s][j] = gf_mul( d, Q[s][j] ); |
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| 187 | for ( i = 0; i < n; i++ ) { |
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| 188 | if ( i != j ) { |
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| 189 | d = Q[h][i]; |
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| 190 | for ( s = 0; s < n; s++ ) |
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| 191 | Q[s][i] = gf_add( gf_mul( d, Q[s][j] ), Q[s][i] ); |
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| 192 | } |
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| 193 | } |
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| 194 | c[j] = h; |
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| 195 | } |
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| 196 | else { |
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| 197 | b[r] = new int[n]; |
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| 198 | for ( j = 0; j < n; j++ ) { |
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| 199 | if ( j == h ) |
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| 200 | b[r][j] = gf_one(); |
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| 201 | else { |
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| 202 | k = 0; |
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| 203 | while ( k < n && c[k] != j ) k++; |
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| 204 | if ( k < n ) |
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| 205 | b[r][j] = Q[h][k]; |
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| 206 | else |
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| 207 | b[r][j] = gf_zero(); |
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| 208 | } |
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| 209 | } |
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| 210 | r++; |
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| 211 | } |
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| 212 | } |
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| 213 | delete [] c; |
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| 214 | return r; |
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| 215 | } |
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| 216 | |
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| 217 | CanonicalForm cfFromIntVec( int * a, int n, const Variable & x ) |
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| 218 | { |
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| 219 | CanonicalForm result = power( x, n-1 ) * a[n-1]; |
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| 220 | for ( int i = n-2; i >= 0; i-- ) |
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| 221 | if ( a[i] != 0 ) |
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| 222 | result += power( x, i ) * a[i]; |
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| 223 | return result; |
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| 224 | } |
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| 225 | |
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| 226 | CanonicalForm cfFromGFVec( int * a, int n, const Variable & x ) |
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| 227 | { |
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| 228 | CanonicalForm result = power( x, n-1 ) * CanonicalForm( int2imm_gf( a[n-1] ) ); |
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| 229 | for ( int i = n-2; i >= 0; i-- ) |
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| 230 | if ( ! gf_iszero( a[i] ) ) |
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| 231 | result += power( x, i ) * CanonicalForm( int2imm_gf( a[i] ) ); |
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| 232 | return result; |
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| 233 | } |
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| 234 | |
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| 235 | typedef int * intptr; |
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| 236 | |
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| 237 | CFFList BerlekampFactorFF ( const CanonicalForm & f ) |
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| 238 | { |
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| 239 | CFFList F; |
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| 240 | int p = getCharacteristic(); |
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| 241 | int r, s, len, i, k, n = degree( f ); |
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| 242 | Variable x = f.mvar(); |
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| 243 | CanonicalForm u, g; |
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| 244 | intptr* Q = new intptr [n]; |
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| 245 | intptr* B = new intptr [n]; |
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| 246 | for ( i = 0; i < n; i++ ) |
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| 247 | Q[i] = new int[n]; |
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| 248 | QmatFF( f, Q, p ); |
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| 249 | #ifdef DEBUGOUTPUT |
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| 250 | DEBOUTLN( cerr, "Q = " ); |
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| 251 | QprintFF( Q, n ); |
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| 252 | #endif /* DEBUGOUTPUT */ |
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| 253 | k = nullSpaceFF( Q, B, n ); |
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| 254 | #ifdef DEBUGOUTPUT |
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| 255 | DEBOUTLN( cerr, "Q = " ); |
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| 256 | QprintFF( Q, n ); |
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| 257 | #endif /* DEBUGOUTPUT */ |
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| 258 | F.insert( CFFactor( f, 1 ) ); |
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| 259 | r = 1; |
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| 260 | len = 1; |
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| 261 | while ( len < k ) { |
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| 262 | ASSERT( r < k, "fatal fatal" ); |
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| 263 | ListIterator<CFFactor> I = F; |
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| 264 | while ( I.hasItem() && len < k ) { |
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| 265 | u = I.getItem().factor(); |
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| 266 | for ( s = 0; s < p && len < k; s++ ) { |
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| 267 | g = gcd( cfFromIntVec( B[r], n, x ) - s, u ); |
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| 268 | if ( degree( g ) > 0 && g != u ) { |
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| 269 | u /= g; |
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| 270 | I.append( CFFactor( g, 1 ) ); |
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| 271 | I.append( CFFactor( u, 1 ) ); |
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| 272 | I.remove( 1 ); |
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| 273 | len++; |
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| 274 | } |
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| 275 | } |
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| 276 | I++; |
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| 277 | } |
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| 278 | r++; |
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| 279 | } |
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| 280 | for ( i = 0; i < n; i++ ) |
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| 281 | delete [] Q[i]; |
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| 282 | for ( i = 0; i < r; i++ ) |
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| 283 | delete [] B[i]; |
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| 284 | delete [] B; |
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| 285 | delete [] Q; |
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| 286 | return F; |
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| 287 | } |
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| 288 | |
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| 289 | CFFList BerlekampFactorGF ( const CanonicalForm & f ) |
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| 290 | { |
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| 291 | CFFList F; |
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| 292 | int r, len, i, k, n = degree( f ); |
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| 293 | Variable x = f.mvar(); |
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| 294 | CanonicalForm u, g; |
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| 295 | intptr* Q = new intptr [n]; |
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| 296 | intptr* B = new intptr [n]; |
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| 297 | for ( i = 0; i < n; i++ ) |
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| 298 | Q[i] = new int[n]; |
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| 299 | QmatGF( f, Q, gf_q ); |
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| 300 | #ifdef DEBUGOUTPUT |
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| 301 | DEBOUTLN( cerr, "Q = " ); |
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| 302 | QprintGF( Q, n ); |
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| 303 | #endif /* DEBUGOUTPUT */ |
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| 304 | k = nullSpaceGF( Q, B, n ); |
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| 305 | #ifdef DEBUGOUTPUT |
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| 306 | DEBOUTLN( cerr, "Q = " ); |
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| 307 | QprintFF( Q, n ); |
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| 308 | #endif /* DEBUGOUTPUT */ |
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| 309 | F.insert( CFFactor( f, 1 ) ); |
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| 310 | r = 1; |
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| 311 | len = 1; |
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| 312 | GFGenerator s; |
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| 313 | while ( len < k ) { |
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| 314 | ASSERT( r < k, "fatal fatal" ); |
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| 315 | ListIterator<CFFactor> I = F; |
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| 316 | while ( I.hasItem() && len < k ) { |
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| 317 | u = I.getItem().factor(); |
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| 318 | for ( s.reset(); s.hasItems() && len < k; s++ ) { |
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| 319 | g = gcd( cfFromGFVec( B[r], n, x ) - s.item(), u ); |
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| 320 | if ( degree( g ) > 0 && g != u ) { |
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| 321 | u /= g; |
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| 322 | I.append( CFFactor( g, 1 ) ); |
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| 323 | I.append( CFFactor( u, 1 ) ); |
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| 324 | I.remove( 1 ); |
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| 325 | len++; |
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| 326 | } |
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| 327 | } |
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| 328 | I++; |
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| 329 | } |
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| 330 | r++; |
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| 331 | } |
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| 332 | for ( i = 0; i < n; i++ ) |
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| 333 | delete [] Q[i]; |
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| 334 | for ( i = 0; i < r; i++ ) |
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| 335 | delete [] B[i]; |
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| 336 | delete [] B; |
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| 337 | delete [] Q; |
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| 338 | return F; |
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| 339 | } |
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| 340 | // { |
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| 341 | // CFFList F; |
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| 342 | // int p = getCharacteristic(); |
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| 343 | // int r, len, k, n = degree( f ); |
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| 344 | // Variable x = f.mvar(); |
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| 345 | // CanonicalForm u, g; |
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| 346 | // intptr* Q = new intptr [n]; |
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| 347 | // for ( int i = 0; i < n; i++ ) |
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| 348 | // Q[i] = new int[n]; |
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| 349 | // QmatGF( f, Q, p ); |
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| 350 | // // Qprint( Q, n ); |
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| 351 | // k = nullSpaceGF( Q, n ); |
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| 352 | // // Qprint( Q, n ); |
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| 353 | // F.insert( CFFactor( f, 1 ) ); |
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| 354 | // r = 1; |
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| 355 | // len = 1; |
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| 356 | // GFIterator s; |
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| 357 | // while ( len < k ) { |
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| 358 | // ListIterator<CFFactor> I = F; |
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| 359 | // while ( I.hasItem() && len < k ) { |
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| 360 | // u = I.getItem().factor(); |
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| 361 | // for ( s.reset(); s.hasItems() && len < k; s++ ) { |
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| 362 | // g = gcd( cfFromGFVec( Q[r], n, x ) - s.item(), u ); |
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| 363 | // if ( degree( g ) > 0 && g != u ) { |
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| 364 | // u /= g; |
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| 365 | // I.append( CFFactor( g, 1 ) ); |
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| 366 | // I.append( CFFactor( u, 1 ) ); |
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| 367 | // I.remove( 1 ); |
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| 368 | // len++; |
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| 369 | // } |
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| 370 | // } |
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| 371 | // I++; |
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| 372 | // } |
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| 373 | // r++; |
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| 374 | // } |
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| 375 | // for ( i = 0; i < n; i++ ) |
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| 376 | // delete [] Q[i]; |
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| 377 | // return F; |
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| 378 | // } |
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| 379 | |
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| 380 | CFFList FpFactorizeUnivariateB( const CanonicalForm& f, bool issqrfree ) |
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| 381 | { |
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| 382 | CFFList F, G, H; |
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| 383 | CanonicalForm fac; |
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| 384 | ListIterator<CFFactor> i, k; |
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| 385 | int d; |
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| 386 | bool galoisfield = getGFDegree() > 1; |
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| 387 | |
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| 388 | if ( LC( f ).isOne() ) |
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| 389 | if ( issqrfree ) |
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| 390 | F.append( CFFactor( f, 1 ) ); |
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| 391 | else |
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| 392 | F = sqrFreeFp( f ); |
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| 393 | else { |
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| 394 | H.append( LC( f ) ); |
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| 395 | if ( issqrfree ) |
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| 396 | F.append( CFFactor( f / LC( f ), 1 ) ); |
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| 397 | else |
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| 398 | F = sqrFreeFp( f / LC( f ) ); |
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| 399 | } |
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| 400 | for ( i = F; i.hasItem(); ++i ) { |
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| 401 | d = i.getItem().exp(); |
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| 402 | fac = i.getItem().factor(); |
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| 403 | if ( galoisfield ) |
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| 404 | G = BerlekampFactorGF( fac / LC( fac ) ); |
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| 405 | else |
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| 406 | G = BerlekampFactorFF( fac / LC( fac ) ); |
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| 407 | for ( k = G; k.hasItem(); ++k ) { |
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| 408 | fac = k.getItem().factor(); |
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| 409 | H.append( CFFactor( fac / LC( fac ), d ) ); |
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| 410 | } |
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| 411 | } |
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| 412 | return H; |
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| 413 | } |
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