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java.lang.Objectorg.rubato.math.module.morphism.ModuleMorphism
org.rubato.math.module.morphism.EmbeddingMorphism
public abstract class EmbeddingMorphism
Morphism that embeds one module into another.
The following embeddings are covered:
- embeddings within the number hierarchy Z -> Q -> R -> C
- embeddings of number rings in polynomial rings
- embeddings between polynomial rings
- embeddings of number rings in string rings
- embeddings between string rings
- embeddings of rings in product rings
- embeddings between product rings
- embeddings between free modules if their rings embed
Method Summary | |
---|---|
int |
compareTo(ModuleMorphism object)
Compares two module morphisms. |
boolean |
equals(java.lang.Object object)
Returns true iff this morphism is equal to object . |
ModuleMorphism |
fromXML(XMLReader reader,
org.w3c.dom.Element element)
Reads XML representation from reader starting with element . |
java.lang.String |
getElementTypeName()
Returns the value of the type attribute for this class. |
ModuleMorphism |
getRingMorphism()
Returns the the ring morphism that transforms between the rings of the domain and codomain modules. |
static XMLInputOutput<ModuleMorphism> |
getXMLInputOutput()
|
boolean |
isModuleHomomorphism()
Embeddings are always module homomorphisms, except for embeddings of a Z_n ring into another ring. |
boolean |
isRingHomomorphism()
If true, then this is a ring homomorphism. |
static ModuleMorphism |
make(Module domain,
Module codomain)
Creates an embedding from a module domain
into a module codomain . |
static EmbeddingMorphism |
makeProductRingEmbedding(Ring domain,
ProductRing codomain,
int index)
Creates an embedding of a ring in a product ring, but only into one of the factors |
ModuleElement |
map(ModuleElement x)
Maps the element x . |
abstract ModuleElement |
mapValue(ModuleElement element)
The low-level map method. |
java.lang.String |
toString()
Returns a string representation of this morphism. |
void |
toXML(XMLWriter writer)
Outputs XML representation to writer . |
Methods inherited from class org.rubato.math.module.morphism.ModuleMorphism |
---|
atZero, clone, composable, compose, difference, getCodomain, getConstantMorphism, getConstantMorphism, getDomain, getIdentityMorphism, inDomain, isConstant, isIdentity, isLinear, isRingMorphism, power, scaled, sum |
Methods inherited from class java.lang.Object |
---|
getClass, hashCode, notify, notifyAll, wait, wait, wait |
Method Detail |
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public static ModuleMorphism make(Module domain, Module codomain)
domain
into a module codomain
.
public final ModuleElement map(ModuleElement x) throws MappingException
ModuleMorphism
x
.
This must be implemented for each specific morphism type.
map
in class ModuleMorphism
x
MappingException
- if mapping of element fails
public abstract ModuleElement mapValue(ModuleElement element)
public boolean isModuleHomomorphism()
isModuleHomomorphism
in class ModuleMorphism
public boolean isRingHomomorphism()
ModuleMorphism
isRingHomomorphism
in class ModuleMorphism
public ModuleMorphism getRingMorphism()
ModuleMorphism
getRingMorphism
in class ModuleMorphism
public final int compareTo(ModuleMorphism object)
ModuleMorphism
compareTo
in interface java.lang.Comparable<ModuleMorphism>
compareTo
in class ModuleMorphism
public final boolean equals(java.lang.Object object)
ModuleMorphism
object
.
In general it is not possible to determine whether to functions
are the same, so this returns true iff both morphisms have
the same structure.
equals
in class ModuleMorphism
public final java.lang.String toString()
ModuleMorphism
toString
in class ModuleMorphism
public void toXML(XMLWriter writer)
XMLInputOutput
writer
.
public ModuleMorphism fromXML(XMLReader reader, org.w3c.dom.Element element)
XMLInputOutput
reader
starting with element
.
public static XMLInputOutput<ModuleMorphism> getXMLInputOutput()
public java.lang.String getElementTypeName()
XMLInputOutput
public static final EmbeddingMorphism makeProductRingEmbedding(Ring domain, ProductRing codomain, int index)
domain
- a ringcodomain
- a product ringindex
- the index of the codomain factor where the ring should be embedded
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