Package org.rubato.math.module.morphism

This package provides classes implementing morphisms between modules.

See:
          Description

Class Summary
CAbstractMorphism The abstract base class for morphisms in C.
CAffineMorphism Affine morphism in C.
CanonicalMorphism Canonical morphisms are the "simplest" morphisms that map an element from the domain to the codomain, e.g, identities, embeddings or casts.
CastMorphism Morphism that casts elements from a ring to another ring.
CFreeAbstractMorphism The abstract base class for morphisms in a free C-module.
CFreeAffineMorphism Affine morphism in a free C-module.
CompositionMorphism Morphism that represents the composition of two arbitrary morphisms.
ConjugationMorphism The function that takes a complex number (or vector) to its conjugate.
ConstantMorphism Constant mappings between modules.
DifferenceMorphism Morphism that represents the difference of two arbitrary morphisms.
DirectSumAbstractMorphism The abstract base class for morphisms in a composite module.
EmbeddingMorphism Morphism that embeds one module into another.
FoldingMorphism Morphism that represents the folding of a set of ModuleElements.
GenericAffineMorphism This class handles affine morphisms between free modules over a given ring, that are not covered by specialized classes such as ZFreeAfineMorphism, etc.
GenericBasisMorphism A generic basis morphism is defined by the values at the basis elements of the domain module.
IdentityMorphism Identity mappings on a module.
ModuleMorphism The abstract base class for morphisms in modules.
ModuloMorphism The function that takes an element i in Z^d to i mod n in Z_n^d.
PolynomialMorphism Polynomial mappings.
PowerMorphism Morphism that represents an iterated arbitrary morphism.
ProductMorphism Morphism that represents the product of two morphisms with the same domains and codomains, respectively, provided that the codomain is a ring.
ProjectionMorphism A projection from a ProductRing to one its factors.
QAbstractMorphism The abstract base class for morphisms in Q.
QAffineMorphism Affine morphism in Q.
QFreeAbstractMorphism The abstract base class for morphisms in a free Q-module.
QFreeAffineMorphism Affine morphism in a free Q-module.
RAbstractMorphism The abstract base class for morphisms in R.
RAffineMorphism Affine morphism in R.
ReorderMorphism These are generalized projections, i.e., factors of a product ring are reordered, deleted or duplicated.
RFreeAbstractMorphism The abstract base class for morphisms in a free R-module.
RFreeAffineMorphism Affine morphism in a free R-module.
ScaledMorphism Morphism that represents a scaled arbitrary morphism.
ShuffleMorphism This morphism reorders the components of an element of the domain.
SplitMorphism A split morphism describes a morphism from a free module into itself, where the module is split into several parts, for example a R^9 into R^3, R^2 and R^4.
SumMorphism Morphism that represents the sum of two arbitrary morphisms.
TranslationMorphism Morphism that represents a translation in an arbitrary module.
ZAbstractMorphism The abstract base class for morphisms in Z.
ZAffineMorphism Affine morphism in the Z.
ZFreeAbstractMorphism The abstract base class for morphisms in a free Z-module.
ZFreeAffineMorphism Affine morphism in a free Z module.
ZnAbstractMorphism The abstract base class for morphisms in Zn.
ZnAffineMorphism Affine morphism in Zn.
ZnFreeAbstractMorphism The abstract base class for morphisms in a free Zn-module.
ZnFreeAffineMorphism Affine morphism in a free Zn-module.
 

Exception Summary
CompositionException Exception thrown if composition of morphisms fails.
MappingException Exception thrown when a module morphism fails to map an element.
 

Package org.rubato.math.module.morphism Description

This package provides classes implementing morphisms between modules.

The provided morphisms are mostly affine morphisms. Included are methods for building new morphisms from existing ones, such as the difference, the sum, the composition and the power of morphisms.

There are also identity and constant morphisms, as well as morphisms translated by an element.