alg_ext.h
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// -*- mode:C++ ; compile-command: "g++ -I.. -g -c alg_ext.cc" -*-
/*
* Copyright (C) 2001,2014 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_ALG_EXT_H
#define _GIAC_ALG_EXT_H
#include "first.h"
#include <string>
#include <map>
#include "global.h"
#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC
class gen;
struct unary_function_ptr;
struct symbolic;
bool proot_cached(const vecteur & v,double eps,vecteur & res);
bool proot_cache(const vecteur & v,double eps,const vecteur & res);
bool galoisconj_cached(const vecteur & v,vecteur & res);
bool galoisconj_cache(const vecteur & v,const vecteur & res);
vecteur galoisconj(const vecteur & v,GIAC_CONTEXT);
bool conj_in_nf(const vecteur & w,gen & g,GIAC_CONTEXT);
bool islesscomplex(const gen & a,const gen & b);
bool is_sqrt(const gen & a,gen & arg);
gen select_root(const vecteur & v,GIAC_CONTEXT);
gen in_select_root(const vecteur & a,bool reel,GIAC_CONTEXT,double eps=1e-14);
bool is_known_rootof(const vecteur & v,gen & symroot,GIAC_CONTEXT);
gen horner_rootof(const vecteur & p,const gen & g,GIAC_CONTEXT);
bool has_rootof_value(const gen & Pmin,gen & value,GIAC_CONTEXT);
gen alg_evalf(const gen & a,const gen &b,GIAC_CONTEXT);
gen approx_rootof(const gen & e,GIAC_CONTEXT);
gen common_EXT(gen & a,gen & b,const vecteur * l,GIAC_CONTEXT);
gen common_minimal_POLY(const gen & ga,const gen & gb, gen & a,gen & b,int &k,GIAC_CONTEXT);
gen algebraic_EXTension(const gen & a,const gen & v);
gen ext_reduce(const gen & a, const gen & v);
gen ext_reduce(const gen & e);
void clean_ext_reduce(vecteur & v);
void clean_ext_reduce(gen & g);
gen ext_add(const gen & a,const gen & b,GIAC_CONTEXT);
gen ext_sub(const gen & a,const gen & b,GIAC_CONTEXT);
gen ext_mul(const gen & a,const gen & b,GIAC_CONTEXT);
gen inv_EXT(const gen & a);
gen symb_rootof(const gen & p,const gen &pmin,GIAC_CONTEXT);
gen rootof(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_rootof ;
vecteur min_pol(gen & a);
// Return the signed subresultant Sturm sequence for a rational
// fraction g with respect to x
// A squarefree factorization is performed first
// Factors of even mult are discarded
// Factors of odd multiplicities generate one vecteur of dense
// polynomials (also coded as vecteur)
// The content of the numerator and denominator are returned as well
vecteur sturm(const gen &g,const gen & x,GIAC_CONTEXT);
extern const unary_function_ptr * const at_sturm ;
// Number of sign changes of g when x is inside the ]a,b[ interval
// Zeros of g of even multiplicities are not counted
// Zeros of g of odd multiplicites are counted once
// g must be a rational fraction with respect to x
// a should be < b
// If sturmab returns 0, then the sign is constant positive
// If sturmab returns -1, the sign is constant negative
int sturmab(const gen & g,const gen &x,const gen & a,const gen & b,GIAC_CONTEXT);
gen _sturmab(const gen & g_orig,GIAC_CONTEXT);
gen _sturm(const gen & g,GIAC_CONTEXT);
gen _sturmseq(const gen & g,GIAC_CONTEXT);
extern const unary_function_ptr * const at_sturmab ;
int sturmsign(const gen & a,bool strict,GIAC_CONTEXT);
// find extremals values of g, return type of g (0 nothing assumed, 1 real, 2 integer)
int find_range(const gen & g,vecteur & a,GIAC_CONTEXT);
// minmax=-1 min 0 both 1 max
gen fminmax(const gen & g,int minmax,GIAC_CONTEXT);
bool find_good_eval(const polynome & F,polynome & Fb,vecteur & b);
typedef std::map<gen,gen,comparegen > rootmap;
rootmap & symbolic_rootof_list();
rootmap & proot_list();
rootmap & galoisconj_list();
#ifndef NO_NAMESPACE_GIAC
} // namespace giac
#endif // ndef NO_NAMESPACE_GIAC
#endif // _GIAC_ALG_EXT_H