70 lines
2.0 KiB
C++
70 lines
2.0 KiB
C++
// Copyright (c) 2006-2007 Max-Planck-Institute Saarbruecken (Germany).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org)
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Algebraic_foundations/include/CGAL/extended_euclidean_algorithm.h $
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// $Id: extended_euclidean_algorithm.h 52164b1 2019-10-19T15:34:59+02:00 Sébastien Loriot
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// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
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//
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// Author(s) : Michael Hemmer, Dominik Huelse
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//
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// ============================================================================
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#ifndef CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H
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#define CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H 1
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#include <CGAL/basic.h>
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#include <vector>
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namespace CGAL {
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// EEA computing the normalized gcd
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// Modern Computer Algebra (Hardcover)
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// by Joachim von zur Gathen (Author), Juergen Gerhard (Author)
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// Publisher: Cambridge University Press; 2 edition (September 1, 2003)
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// Language: English
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// ISBN-10: 0521826462
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// ISBN-13: 978-0521826464
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// pp.: 55
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template< class AS >
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AS extended_euclidean_algorithm(const AS& f, const AS& g, AS& s_, AS& t_){
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typename Algebraic_structure_traits<AS>::Integral_division idiv;
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typename Algebraic_structure_traits<AS>::Div div;
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typename Algebraic_structure_traits<AS>::Unit_part unit_part;
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std::vector<AS> p,r,s,t,q;
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p.push_back(unit_part(f));
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r.push_back(idiv(f,p[0]));
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s.push_back(idiv(AS(1),p[0]));
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t.push_back(AS(0));
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q.push_back(AS(0));
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p.push_back(unit_part(g));
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r.push_back(idiv(g,p[1]));
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s.push_back(AS(0));
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t.push_back(idiv(AS(1),p[1]));
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int i = 1;
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while(!is_zero(r[i])){
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q.push_back(div(r[i-1],r[i]));
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r.push_back(r[i-1]-q[i]*r[i]);
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p.push_back(unit_part(r[i+1]));
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r[i+1] = idiv(r[i+1],p[i+1]);
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s.push_back(idiv(s[i-1]-q[i]*s[i],p[i+1]));
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t.push_back(idiv(t[i-1]-q[i]*t[i],p[i+1]));
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i++;
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}
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s_=s[i-1];
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t_=t[i-1];
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AS h = r[i-1];
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CGAL_precondition( h == f*s_ + g*t_);
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return h;
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}
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} //namespace CGAL
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#endif // NiX_EXTENDED_EUCLIDEAN_ALGORITHM_H //
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