[70c40f] | 1 | // -*- c++ -*- |
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| 2 | //***************************************************************************** |
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| 3 | /** @file facNTLzzpEXGCD.cc |
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| 4 | * |
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| 5 | * @author Martin Lee |
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| 6 | * |
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| 7 | * @note the following code is slightly modified code out of |
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| 8 | * lzz_pEX.c from Victor Shoup's NTL. Below is NTL's copyright notice. |
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| 9 | * |
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| 10 | * Univariate GCD and extended GCD over Z/p[t]/(f)[x] for reducible f |
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| 11 | * |
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| 12 | * @par Copyright: |
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| 13 | * (c) by The SINGULAR Team, see LICENSE file |
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| 14 | * |
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| 15 | **/ |
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| 16 | //***************************************************************************** |
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| 17 | |
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| 18 | /** |
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| 19 | COPYRIGHT NOTICE |
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| 20 | for NTL 5.5 |
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| 21 | (modified for Singular 2-0-6 - 3-1) |
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| 22 | |
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| 23 | NTL -- A Library for Doing Number Theory |
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| 24 | Copyright (C) 1996-2009 Victor Shoup |
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| 25 | |
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| 26 | The most recent version of NTL is available at http://www.shoup.net |
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| 27 | |
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| 28 | This program is free software; you can redistribute it and/or |
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| 29 | modify it under the terms of the GNU General Public License |
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| 30 | as published by the Free Software Foundation; either version 2 |
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| 31 | of the License, or (at your option) any later version. |
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| 32 | |
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| 33 | This program is distributed in the hope that it will be useful, |
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| 34 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 35 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 36 | GNU General Public License for more details. |
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| 37 | |
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| 38 | You should have received a copy of the GNU General Public License |
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| 39 | along with this program; if not, write to the Free Software |
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| 40 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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| 41 | |
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| 42 | This entire copyright notice should be placed in an appropriately |
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| 43 | conspicuous place accompanying all distributions of software that |
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| 44 | make use of NTL. |
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| 45 | |
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| 46 | The above terms apply to all of the software modules distributed with NTL, |
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| 47 | i.e., all source files in either the ntl-xxx.tar.gz or WinNTL-xxx.zip |
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| 48 | distributions. In general, the individual files do not contain |
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| 49 | copyright notices. |
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| 50 | |
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| 51 | Note that the quad_float package is derived from the doubledouble package, |
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| 52 | originally developed by Keith Briggs, and also licensed unger the GNU GPL. |
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| 53 | The files quad_float.c and quad_float.h contain more detailed copyright |
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| 54 | notices. |
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| 55 | |
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| 56 | Note that the traditional long integer package used by NTL, lip.c, is derived |
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| 57 | from---and represents an extensive modification of--- |
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| 58 | a package originally developed and copyrighted by Arjen Lenstra, |
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| 59 | who has agreed to renounce any copyright claims on the particular |
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| 60 | version of the long integer package appearing in NTL, so that the |
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| 61 | this package now is covered by the GNU GPL as well. |
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| 62 | |
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| 63 | Note that the alternative long integer package used by NTL is GMP, |
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| 64 | which is written by Torbjorn Granlund <tege@swox.com>. |
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| 65 | GMP is licensed under the terms of the GNU Lesser General Public License. |
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| 66 | |
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| 67 | Note that NTL makes use of the RSA Data Security, Inc. MD5 Message |
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| 68 | Digest Algorithm. |
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| 69 | |
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| 70 | Note that prior to version 4.0, NTL was distributed under the following terms: |
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| 71 | NTL is freely available for research and educational purposes. |
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| 72 | I don't want to attach any legalistic licensing restrictions on |
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| 73 | users of NTL. |
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| 74 | However, NTL should not be linked in a commercial program |
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| 75 | (although using data in a commercial |
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| 76 | product produced by a program that used NTL is fine). |
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| 77 | |
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| 78 | The hope is that the GNU GPL is actually less restrictive than these |
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| 79 | older terms; however, in any circumstances such that GNU GPL is more |
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| 80 | restrictive, then the following rule is in force: |
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| 81 | versions prior to 4.0 may continue to be used under the old terms, |
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| 82 | but users of versions 4.0 or later should adhere to the terms of the GNU GPL. |
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| 83 | **/ |
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| 84 | |
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| 85 | |
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[d10821] | 86 | #include "config.h" |
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[70c40f] | 87 | |
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| 88 | #include "facNTLzzpEXGCD.h" |
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| 89 | |
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| 90 | #ifdef HAVE_NTL |
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| 91 | #include "NTLconvert.h" |
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| 92 | #endif |
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| 93 | |
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| 94 | #ifdef HAVE_NTL |
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| 95 | |
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| 96 | long InvModStatus (zz_pE& x, const zz_pE& a) |
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| 97 | { |
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| 98 | return InvModStatus(x._zz_pE__rep, a._zz_pE__rep, zz_pE::modulus()); |
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| 99 | } |
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| 100 | |
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| 101 | static |
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| 102 | void SetSize(vec_zz_pX& x, long n, long m) |
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| 103 | { |
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| 104 | x.SetLength(n); |
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| 105 | long i; |
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| 106 | for (i = 0; i < n; i++) |
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| 107 | x[i].rep.SetMaxLength(m); |
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| 108 | } |
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| 109 | |
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| 110 | void tryPlainRem(zz_pEX& r, const zz_pEX& a, const zz_pEX& b, vec_zz_pX& x, |
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| 111 | bool& fail) |
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| 112 | { |
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| 113 | long da, db, dq, i, j, LCIsOne; |
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| 114 | const zz_pE *bp; |
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| 115 | zz_pX *xp; |
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| 116 | |
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| 117 | |
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| 118 | zz_pE LCInv, t; |
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| 119 | zz_pX s; |
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| 120 | |
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| 121 | da = deg(a); |
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| 122 | db = deg(b); |
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| 123 | |
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| 124 | if (db < 0) Error("zz_pEX: division by zero"); |
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| 125 | |
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| 126 | if (da < db) { |
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| 127 | r = a; |
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| 128 | return; |
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| 129 | } |
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| 130 | |
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| 131 | bp = b.rep.elts(); |
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| 132 | |
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| 133 | if (IsOne(bp[db])) |
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| 134 | LCIsOne = 1; |
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| 135 | else { |
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| 136 | LCIsOne = 0; |
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| 137 | fail= InvModStatus (LCInv, bp[db]); |
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| 138 | //inv(LCInv, bp[db]); |
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| 139 | if (fail) |
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| 140 | return; |
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| 141 | } |
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| 142 | |
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| 143 | for (i = 0; i <= da; i++) |
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| 144 | x[i] = rep(a.rep[i]); |
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| 145 | |
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| 146 | xp = x.elts(); |
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| 147 | |
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| 148 | dq = da - db; |
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| 149 | |
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| 150 | for (i = dq; i >= 0; i--) { |
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| 151 | conv(t, xp[i+db]); |
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| 152 | if (!LCIsOne) |
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| 153 | mul(t, t, LCInv); |
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| 154 | NTL::negate(t, t); |
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| 155 | |
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| 156 | for (j = db-1; j >= 0; j--) { |
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| 157 | mul(s, rep(t), rep(bp[j])); |
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| 158 | add(xp[i+j], xp[i+j], s); |
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| 159 | } |
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| 160 | } |
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| 161 | |
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| 162 | r.rep.SetLength(db); |
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| 163 | for (i = 0; i < db; i++) |
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| 164 | conv(r.rep[i], xp[i]); |
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| 165 | r.normalize(); |
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| 166 | } |
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| 167 | |
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| 168 | void tryPlainDivRem(zz_pEX& q, zz_pEX& r, const zz_pEX& a, const zz_pEX& b, |
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| 169 | bool& fail) |
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| 170 | { |
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| 171 | long da, db, dq, i, j, LCIsOne; |
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| 172 | const zz_pE *bp; |
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| 173 | zz_pE *qp; |
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| 174 | zz_pX *xp; |
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| 175 | |
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| 176 | |
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| 177 | zz_pE LCInv, t; |
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| 178 | zz_pX s; |
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| 179 | |
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| 180 | da = deg(a); |
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| 181 | db = deg(b); |
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| 182 | |
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| 183 | if (db < 0) Error("zz_pEX: division by zero"); |
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| 184 | |
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| 185 | if (da < db) { |
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| 186 | r = a; |
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| 187 | clear(q); |
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| 188 | return; |
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| 189 | } |
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| 190 | |
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| 191 | zz_pEX lb; |
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| 192 | |
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| 193 | if (&q == &b) { |
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| 194 | lb = b; |
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| 195 | bp = lb.rep.elts(); |
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| 196 | } |
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| 197 | else |
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| 198 | bp = b.rep.elts(); |
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| 199 | |
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| 200 | if (IsOne(bp[db])) |
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| 201 | LCIsOne = 1; |
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| 202 | else { |
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| 203 | LCIsOne = 0; |
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| 204 | fail= InvModStatus (LCInv, bp[db]); |
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| 205 | //inv(LCInv, bp[db]); |
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| 206 | if (fail) |
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| 207 | return; |
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| 208 | } |
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| 209 | |
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| 210 | vec_zz_pX x; |
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| 211 | |
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| 212 | SetSize(x, da+1, 2*zz_pE::degree()); |
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| 213 | |
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| 214 | for (i = 0; i <= da; i++) |
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| 215 | x[i] = rep(a.rep[i]); |
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| 216 | |
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| 217 | xp = x.elts(); |
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| 218 | |
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| 219 | dq = da - db; |
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| 220 | q.rep.SetLength(dq+1); |
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| 221 | qp = q.rep.elts(); |
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| 222 | |
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| 223 | for (i = dq; i >= 0; i--) { |
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| 224 | conv(t, xp[i+db]); |
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| 225 | if (!LCIsOne) |
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| 226 | mul(t, t, LCInv); |
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| 227 | qp[i] = t; |
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| 228 | NTL::negate(t, t); |
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| 229 | |
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| 230 | for (j = db-1; j >= 0; j--) { |
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| 231 | mul(s, rep(t), rep(bp[j])); |
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| 232 | add(xp[i+j], xp[i+j], s); |
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| 233 | } |
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| 234 | } |
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| 235 | |
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| 236 | r.rep.SetLength(db); |
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| 237 | for (i = 0; i < db; i++) |
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| 238 | conv(r.rep[i], xp[i]); |
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| 239 | r.normalize(); |
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| 240 | } |
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| 241 | |
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| 242 | |
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| 243 | void tryNTLGCD(zz_pEX& x, const zz_pEX& a, const zz_pEX& b, bool& fail) |
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| 244 | { |
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| 245 | zz_pE t; |
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| 246 | |
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| 247 | if (IsZero(b)) |
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| 248 | x = a; |
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| 249 | else if (IsZero(a)) |
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| 250 | x = b; |
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| 251 | else { |
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| 252 | long n = max(deg(a),deg(b)) + 1; |
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| 253 | zz_pEX u(INIT_SIZE, n), v(INIT_SIZE, n); |
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| 254 | |
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| 255 | vec_zz_pX tmp; |
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| 256 | SetSize(tmp, n, 2*zz_pE::degree()); |
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| 257 | |
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| 258 | u = a; |
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| 259 | v = b; |
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| 260 | do { |
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| 261 | tryPlainRem(u, u, v, tmp, fail); |
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| 262 | if (fail) |
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| 263 | return; |
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| 264 | swap(u, v); |
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| 265 | } while (!IsZero(v)); |
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| 266 | |
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| 267 | x = u; |
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| 268 | } |
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| 269 | |
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| 270 | if (IsZero(x)) return; |
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| 271 | if (IsOne(LeadCoeff(x))) return; |
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| 272 | |
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| 273 | /* make gcd monic */ |
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| 274 | |
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| 275 | |
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| 276 | fail= InvModStatus (t, LeadCoeff(x)); |
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| 277 | if (fail) |
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| 278 | return; |
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| 279 | mul(x, x, t); |
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| 280 | } |
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| 281 | |
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| 282 | void tryNTLXGCD(zz_pEX& d, zz_pEX& s, zz_pEX& t, const zz_pEX& a, |
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| 283 | const zz_pEX& b, bool& fail) |
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| 284 | { |
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| 285 | zz_pE z; |
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| 286 | |
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| 287 | |
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| 288 | if (IsZero(b)) { |
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| 289 | set(s); |
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| 290 | clear(t); |
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| 291 | d = a; |
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| 292 | } |
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| 293 | else if (IsZero(a)) { |
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| 294 | clear(s); |
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| 295 | set(t); |
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| 296 | d = b; |
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| 297 | } |
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| 298 | else { |
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| 299 | long e = max(deg(a), deg(b)) + 1; |
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| 300 | |
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| 301 | zz_pEX temp(INIT_SIZE, e), u(INIT_SIZE, e), v(INIT_SIZE, e), |
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| 302 | u0(INIT_SIZE, e), v0(INIT_SIZE, e), |
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| 303 | u1(INIT_SIZE, e), v1(INIT_SIZE, e), |
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| 304 | u2(INIT_SIZE, e), v2(INIT_SIZE, e), q(INIT_SIZE, e); |
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| 305 | |
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| 306 | |
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| 307 | set(u1); clear(v1); |
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| 308 | clear(u2); set(v2); |
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| 309 | u = a; v = b; |
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| 310 | |
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| 311 | do { |
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| 312 | fail= InvModStatus (z, LeadCoeff(v)); |
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| 313 | if (fail) |
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| 314 | return; |
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| 315 | DivRem(q, u, u, v); |
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| 316 | swap(u, v); |
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| 317 | u0 = u2; |
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| 318 | v0 = v2; |
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| 319 | mul(temp, q, u2); |
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| 320 | sub(u2, u1, temp); |
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| 321 | mul(temp, q, v2); |
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| 322 | sub(v2, v1, temp); |
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| 323 | u1 = u0; |
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| 324 | v1 = v0; |
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| 325 | } while (!IsZero(v)); |
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| 326 | |
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| 327 | d = u; |
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| 328 | s = u1; |
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| 329 | t = v1; |
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| 330 | } |
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| 331 | |
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| 332 | if (IsZero(d)) return; |
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| 333 | if (IsOne(LeadCoeff(d))) return; |
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| 334 | |
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| 335 | /* make gcd monic */ |
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| 336 | |
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| 337 | fail= InvModStatus (z, LeadCoeff(d)); |
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| 338 | if (fail) |
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| 339 | return; |
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| 340 | mul(d, d, z); |
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| 341 | mul(s, s, z); |
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| 342 | mul(t, t, z); |
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| 343 | } |
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| 344 | #endif |
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| 345 | |
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