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/* -*- mode:C++ ; compile-command: "g++ -I.. -g -c ezgcd.cc" -*- */
/* Multivariate GCD for large data not covered by the heuristic GCD algo
* Copyright (C) 2000,2014 B. Parisse, Institut Fourier, 38402 St Martin d'Heres
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef _GIAC_EZGCD_H_
#define _GIAC_EZGCD_H_
#include "first.h"
#include "gausspol.h"
#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC
void change_dim(polynome & p,int dim);
// Hensel quadratic lift
// Lift the equality p(b)=qb*rb [where b is a vecteur like for peval
// assumed to have p.dim-1 coordinates] to p=q*r mod (X-b)^deg
// Assuming that lcoeff(q)=lcp, lcoeff(r)=lcp, lcoeff(p)=lcp^2
// If you want to find factors of a poly P such that P(b)=Qb*Rb,
// if lcp is the leading coeff of P
// then p=P*lcp, qb=Qb*lcp(b)/lcoeff(Qb), rb=Rb*lcp(b)/lcoeff(Rb)
bool hensel_lift(const polynome & p, const polynome & lcp, const polynome & qb, const polynome & rb, const vecteur & b,polynome & q, polynome & r,bool linear_lift=true,double maxop=-1);
bool find_good_eval(const polynome & F,const polynome & G,polynome & Fb,polynome & Gb,vecteur & b,bool debuglog=false,const gen & mod=zero);
polynome peval_1(const polynome & p,const vecteur &v,const gen & mod);
// Replace the last coordinates of p with b instead of the first
gen peval_back(const polynome & p,const vecteur & b);
polynome unmodularize(const std::vector<int> & a);
// reduce_divrem does a mixed division: euclidean w.r.t. the first var
// and ascending power of X-v for the other vars
// FIXME: this implementation does not work currently, except if other
// depends only on the first var
bool bool reduce_divrem(const polynome & a,const polynome & other,const vecteur & v,int n,polynome & quo,polynome & rem) ;(const polynome & a,const polynome & other,const vecteur & v,int n,polynome & quo,polynome & rem) bool reduce_divrem(const polynome & a,const polynome & other,const vecteur & v,int n,polynome & quo,polynome & rem) ;
// find the "remainder of p mod (X-v)^degree"
// dim(p) = size(v)+1 (reduction for all variables of p except the main var)
polynome reduce_poly(const polynome & p,const vecteur & v,int degree);
bool try_sparse_factor(const polynome & pcur,const factorization & v0,int mult,factorization & f);
bool try_sparse_factor_bi(polynome & pcur,int mult,factorization & f);
bool try_hensel_lift_factor(const polynome & pcur,const polynome & F0,const factorization & v0,int mult,factorization & f);
// find u,v,d s.t. u*p+v*q=d by Hensel lift
bool try_hensel_egcd(const polynome & p,const polynome & q,polynome &u,polynome &v,polynome & d);
// max_gcddeg is used when ezgcd was not successfull to find
// the gcd even with 2 evaluations leading to the same gcd degree
// in this case ezgcd calls itself with a bound on the gcd degree
// is_sqff is true if we know that F_orig or G_orig is squarefree
// is_primitive is true if F_orig and G_orig is primitive
bool ezgcd(const polynome & F_orig,const polynome & G_orig,polynome & GCD,bool is_sqff=false,bool is_primitive=false,int max_gcddeg=0,double maxop=-1);
gen _ezgcd(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_ezgcd;
gen _modgcd(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_modgcd;
gen _heugcd(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_heugcd;
gen _psrgcd(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_psrgcd;
#ifndef NO_NAMESPACE_GIAC
} // namespace giac
#endif // NO_NAMESPACE_GIAC
#endif // _GIAC_EZGCD_H
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