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See:
Description
Class Summary | |
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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 | |
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CompositionException | Exception thrown if composition of morphisms fails. |
MappingException | Exception thrown when a module morphism fails to map an element. |
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.
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