/usr/include/linbox/field/hom.h is in liblinbox-dev 1.4.2-5build1.
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* Copyright(C) LinBox
* Written by David Saunders
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*.
*/
#ifndef __LINBOX_hom_H
#define __LINBOX_hom_H
#include "linbox/linbox-config.h"
#include "linbox/util/error.h"
#include "linbox/integer.h"
#include <givaro/givcaster.h>
#include <givaro/givrational.h>
#include <givaro/modular.h>
#include <givaro/zring.h>
#ifdef __LINBOX_HAVE_NTL
#include "linbox/ring/ntl/ntl-zz.h"
#endif //__LINBOX_HAVE_NTL
#include "givaro/givrational.h"
namespace LinBox
{
/// Error object for attempt to establish a Hom that cannot exist.
class NoHomError {};
/** \brief map element of source ring(field) to target ring
\ingroup field
* An instance of Hom is a homomorphism from a ring of type Source
* to a ring (usually field) of type Target. The intended use is that
* it will be a natural mapping. For instance:
*
* Hom<Unparametric<Integers>, Givaro::Modular<integer> >(Z, Zp) nat; // is the mod p mapping.
*
* Hom<<NTL_ZZp, Givaro::Modular<integer> >(Zp, Mp) nat;
*
* // is an isomorphism, provided the Zp and Mp have same characteristic.
* Hom<Unparametric<NTL_ZZp, Unparameteric<NTL_ZZpEx> >(Z3, Z27) nat;
* // is the embedding of the prime field in the extension.
*/
template< class Source, class Target, class Enabled = void > // Enabled is just for std::enable_if
class Hom {
public:
typedef typename Source::Element SrcElt;
typedef typename Target::Element Elt;
//Hom(){}
/**
* Construct a homomorphism from a specific source ring S and target
* field T with Hom(S, T).
* Specializations define all actual homomorphisms.
*/
Hom(const Source& S, const Target& T) :
_source(S), _target(T)
{ }
/**
* image(t, s) implements the homomorphism, assigning the
* t the value of the image of s under the mapping.
*
* The default behaviour goes through integers.
*/
Elt& image(Elt& t, const SrcElt& s) {
return _target.init(t, _source.convert(tmp,s));
}
/** If possible, preimage(s,t) assigns a value to s such that
* the image of s is t. Otherwise behaviour is unspecified.
* An error may be thrown, a conventional value may be set, or
* an arb value set.
*
* The default behaviour goes through integers.
*/
SrcElt& preimage(SrcElt& s, const Elt& t) {
return _source.init(s, _target.convert(tmp,t));
}
const Source& source() { return _source;}
const Target& target() { return _target;}
private:
integer tmp;
const Source& _source;
const Target& _target;
}; // end Hom
// specialization for equal domain TYPES
// WARNING this FORBIDS same type homomorphism
template <class Source>
class Hom<Source, Source> {
public:
typedef Source Target;
typedef typename Source::Element SrcElt;
typedef typename Target::Element Elt;
Hom(const Source& S, const Target& T) :
_source (S)
{}
Elt& image(Elt& t, const SrcElt& s)
{
_source.assign (t, s);
return t;
}
SrcElt& preimage(SrcElt& s, const Elt& t)
{
_source.assign (s, t);
return s;
}
const Source& source() { return _source;}
const Target& target() { return _source;}
protected:
const Source& _source;
};
}
// // Specialization to modular
// namespace LinBox
// {
// // GENERIC SPECIALISATION FOR MODULAR HOMORMOPHISM
// // The enable_if is to protect undetermination with Hom<Source, Source>
// template<typename T1, typename C1, typename T2, typename C2>
// class Hom<Givaro::Modular<T1, C1>, Givaro::Modular<T2, C2>,
// typename std::enable_if<!std::is_same<Givaro::Modular<T1, C1>, Givaro::Modular<T2, C2>>::value>::type>
// {
// public:
// using Element1 = typename Givaro::Modular<T1, C1>::Element;
// using Element2 = typename Givaro::Modular<T2, C2>::Element;
// Hom(const Givaro::Modular<T1, C1>& S, const Givaro::Modular<T2, C2>& T)
// {
// integer ps, pt;
// if (S.characteristic(ps) != T.characteristic(pt)) throw NoHomError();
// }
// inline Element2& image(Element2& t, const Element1& s) const
// {
// return Givaro::Caster<Element2,Element1>(t,s);
// }
// // assumes t normalized.
// inline Element1& preimage(Element1& s, const Element2& t) const
// {
// return Givaro::Caster<Element1,Element2>(s,t);
// }
// };
// }// namespace LinBox
namespace LinBox
{
template<class _Source>
class Hom<_Source, Givaro::ZRing<Integer> > {
public:
typedef Givaro::ZRing<Integer> Target;
typedef _Source Source;
typedef typename Source::Element SrcElt;
typedef Integer Elt;
Hom(const Source& S, const Target& T) :
_source (S), _target (T)
{}
inline Integer& image(Integer& t, const SrcElt& s)
{
return Givaro::Caster(t,s);
}
inline SrcElt& preimage(SrcElt& s, const Integer& t)
{
return Givaro::Caster(s,t);
}
const Source& source() { return _source;}
const Target& target() { return _target;}
protected:
const Source& _source;
const Target& _target;
}; // end Hom
template<class _Target>
class Hom<Givaro::ZRing<Integer>, _Target> {
public:
typedef Givaro::ZRing<Integer> Source;
typedef _Target Target;
typedef typename Source::Element SrcElt;
typedef typename Target::Element Elt;
Hom(const Source& S, const Target& T) :
_source (S), _target (T)
{}
inline Elt& image(Elt& t, const SrcElt& s)
{
_target. init (t, s);
return t;
}
inline SrcElt& preimage(SrcElt& s, const Elt& t)
{
_target. convert (s, t);
return s;
}
const Source& source() { return _source;}
const Target& target() { return _target;}
protected:
const Source& _source;
const Target& _target;
}; // end Hom
template<>
class Hom<Givaro::ZRing<Integer>, Givaro::ZRing<Integer> > {
public:
typedef Givaro::ZRing<Integer> Source;
typedef Source Target;
typedef Integer SrcElt;
typedef Integer Elt;
Hom(const Source& S, const Target& T) :
_source (S), _target (T)
{}
inline Elt& image(Elt& t, const SrcElt& s)
{
return t=s;
}
inline SrcElt& preimage(SrcElt& s, const Elt& t)
{
return s=t;
}
const Source& source() { return _source;}
const Target& target() { return _target;}
protected:
const Source& _source;
const Target& _target;
}; // end Hom
template <class _Target>
class Hom<Givaro::QField<Givaro::Rational>, _Target> {
public:
typedef Givaro::QField<Givaro::Rational> Source;
typedef _Target Target;
typedef typename Source::Element SrcElt;
typedef typename Target::Element Elt;
Hom(const Source& S, const Target& T) :
_source (S), _target(T)
{ }
Elt& image(Elt& t, const SrcElt& s) {
if (_source.isOne(s.deno())) {
return _target.init(t,s.nume());
}
else if (_source.isOne(s.nume())) {
_target.init(t,s.deno());
return _target.invin(t);
}
else {
_target. init (tmp, s.deno());
_target. init (t, s.nume());
return _target. divin (t, tmp);
}
}
// Warning, by default convert only the numerator
SrcElt& preimage(SrcElt& s, const Elt& t) {
_target. convert (s.nume(), t);
_source. init (s, s.nume());
return s;
}
const Source& source() { return _source;}
const Target& target() { return _target;}
protected:
Elt tmp;
Source _source;
Target _target;
}; // end Hom
} // namespace LinBox
#ifdef __LINBOX_HAVE_NTL
namespace LinBox
{
template<class _Target >
class Hom <NTL_ZZ , _Target> {
public:
typedef NTL_ZZ Source;
typedef _Target Target;
typedef typename Source::Element SrcElt;
typedef typename Target::Element Elt;
Hom(const Source& S, const Target& T) :
_source(S), _target(T)
{}
inline Elt& image(Elt& t, const SrcElt& s) {
return _target. init (t, _source. convert (tmp, s));
}
inline SrcElt& preimage(SrcElt& s, const Elt& t) {
return _source. init (s, _target. convert (tmp, t) );
}
const Source& source() { return _source;}
const Target& target() { return _target;}
protected:
Integer tmp;
Source _source;
Target _target;
}; // end Hom
template<>
class Hom <NTL_ZZ , NTL_ZZ> {
public:
typedef NTL_ZZ Source;
typedef NTL_ZZ Target;
typedef Source::Element SrcElt;
typedef Target::Element Elt;
Hom(const Source& S, const Target& T) :
_source(S), _target(T)
{}
inline Elt& image(Elt& t, const SrcElt& s) {
return _target.assign(t, s);
}
inline SrcElt& preimage(SrcElt& s, const Elt& t) {
return _source.assign(s, t);
}
const Source& source() { return _source;}
const Target& target() { return _target;}
protected:
Source _source;
Target _target;
}; // end Hom
}
#endif //__LINBOX_HAVE_NTL
#ifdef __LINBOX_field_gf2_H
namespace LinBox
{
template <>
class Hom<GF2,GF2> {
public:
typedef GF2 Target;
typedef GF2 Source;
typedef Source::Element SrcElt;
typedef Target::Element Elt;
Hom(const Source& S, const Target& ) :
_source (S)
{}
Elt& image(Elt& t, const SrcElt& s)
{
return _source.assign (t, s);
}
SrcElt& preimage(SrcElt& s, const Elt& t)
{
return _source.assign (s, t);
}
const Source& source()
{
return _source;
}
const Target& target()
{
return _source;
}
protected:
Source _source;
};
template<class Target >
class Hom<GF2, Target > {
public:
typedef GF2 Source;
typedef typename GF2::Element SrcElt;
typedef typename Target::Element Elt;
Hom(const Source& S, const Target& T) :
_source(S), _target(T)
{ }
Elt& image(Elt& t, const SrcElt& s)
{
return _source.convert(t,s);
}
SrcElt& preimage(SrcElt& s, const Elt& t)
{
return _target.convert(s,t);
}
stdBitReference preimage(stdBitReference s, const Elt& t) const
{
int ts;
return s = _target.convert(ts, t);
}
const Source& source()
{
return _source;
}
const Target& target()
{
return _target;
}
private:
Source _source;
Target _target;
}; // end Hom
}
#include <givaro/extension.h>
namespace LinBox
{
template<>
class Hom < GF2, Givaro::Extension<GF2> > {
typedef GF2 Source;
typedef Givaro::Extension<GF2> Target;
public:
typedef Source::Element SrcElt;
typedef Target::Element Elt;
//Hom(){}
/**
* Construct a homomorphism from a specific source ring S and target
* field T with Hom(S, T). The default behaviour is error.
* Specializations define all actual homomorphisms.
*/
Hom(const Source& S, const Target& T) :
_source(S), _target(T)
{}
/**
* image(t, s) implements the homomorphism, assigning the
* t the value of the image of s under the mapping.
*
* The default behaviour is a no-op.
*/
Elt& image(Elt& t, const SrcElt& s) const
{
return _target.assign(t,s);
}
/** If possible, preimage(s,t) assigns a value to s such that
* the image of s is t. Otherwise behaviour is unspecified.
* An error may be thrown, a conventional value may be set, or
* an arb value set.
*
* The default behaviour is a no-op.
*/
SrcElt& preimage(SrcElt& s, const Elt& t) const
{
return _target.convert(s, t);
}
stdBitReference preimage(stdBitReference s, const Elt& t) const
{
bool ts;
return s = _target.convert(ts, t);
}
const Source& source() const
{
return _source;
}
const Target& target() const
{
return _target;
}
private:
Source _source;
Target _target;
}; // end Hom
}
#endif // __LINBOX_field_gf2_H
#ifdef __LINBOX_field_givaro_gfq_H
namespace LinBox
{
template<>
class Hom <Givaro::GFq,Givaro::GFq> {
public:
typedef Givaro::GFq Source;
typedef Givaro::GFq Target;
typedef Source::Element SrcElt;
typedef Target::Element Elt;
//Hom(){}
/**
* Construct a homomorphism from a specific source ring S and target
* field T with Hom(S, T).
* Specializations define all actual homomorphisms.
*/
Hom(const Source& S, const Target& T) :
_source(S), _target(T)
{ }
/**
* image(t, s) implements the homomorphism, assigning the
* t the value of the image of s under the mapping.
*
* The default behaviour goes through Integers.
*/
Elt& image(Elt& t, const SrcElt& s)
{
return _target.init(t, _source.convert(tmp,s));
}
/** If possible, preimage(s,t) assigns a value to s such that
* the image of s is t. Otherwise behaviour is unspecified.
* An error may be thrown, a conventional value may be set, or
* an arb value set.
*
* The default behaviour goes through Integers.
*/
SrcElt& preimage(SrcElt& s, const Elt& t)
{
return _source.init(s, _target.convert(tmp,t));
}
const Source& source() { return _source;}
const Target& target() { return _target;}
private:
Integer tmp;
Source _source;
Target _target;
}; // end Hom
}
#endif
#endif // __LINBOX_hom_H
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