Hom< Source, Target, Enabled > Class Template Reference

map element of source ring(field) to target ringAn instance of Hom is a homomorphism from a ring of type Source to a ring (usually field) of type Target. More...

#include <hom.h>

Public Member Functions
	Hom (const Source &S, const Target &T)
	Construct a homomorphism from a specific source ring S and target field T with Hom(S, T). More...
Elt &	image (Elt &t, const SrcElt &s)
	image(t, s) implements the homomorphism, assigning the t the value of the image of s under the mapping. More...
SrcElt &	preimage (SrcElt &s, const Elt &t)
	If possible, preimage(s,t) assigns a value to s such that the image of s is t. More...

Detailed Description

template<class Source, class Target, class Enabled = void>
class LinBox::Hom< Source, Target, Enabled >

map element of source ring(field) to target ring

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.

Constructor & Destructor Documentation

Hom()

Hom ( const Source &  S, const Target &  T  )

inline

Construct a homomorphism from a specific source ring S and target field T with Hom(S, T).

Specializations define all actual homomorphisms.

Member Function Documentation

image()

Elt& image ( Elt &  t, const SrcElt &  s  )

inline

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.

preimage()

SrcElt& preimage ( SrcElt &  s, const Elt &  t  )

inline

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.

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The documentation for this class was generated from the following file:

• hom.h