org.rubato.math.module.morphism
Class CastMorphism

java.lang.Object
  extended by org.rubato.math.module.morphism.ModuleMorphism
      extended by org.rubato.math.module.morphism.CastMorphism
All Implemented Interfaces:
java.io.Serializable, java.lang.Cloneable, java.lang.Comparable<ModuleMorphism>, XMLInputOutput<ModuleMorphism>

public abstract class CastMorphism
extends ModuleMorphism

Morphism that casts elements from a ring to another ring. The make(org.rubato.math.module.Ring, org.rubato.math.module.Ring) method is used to create a canonical morphism. Only proper cast morphisms are created, not identities, nor embeddings. Therefore casting morphism should generally not be created directly using this class, but through the CanonicalMorphism class, this also takes care of free modules.

Author:
Gérard Milmeister
See Also:
Serialized Form

Method Summary
 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()
          Casting morphisms are never module homomorphisms.
 boolean isRingHomomorphism()
          Casting morphisms are never ring homomorphisms.
static ModuleMorphism make(Ring domain, Ring codomain)
          Creates a casting morphism from domain to codomain.
 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, compareTo, 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

make

public static ModuleMorphism make(Ring domain,
                                  Ring codomain)
Creates a casting morphism from domain to codomain.

Returns:
null iff no such morphism could be created

map

public final ModuleElement map(ModuleElement x)
                        throws MappingException
Description copied from class: ModuleMorphism
Maps the element x. This must be implemented for each specific morphism type.

Specified by:
map in class ModuleMorphism
Returns:
the result of mapping element x
Throws:
MappingException - if mapping of element fails

mapValue

public abstract ModuleElement mapValue(ModuleElement element)
The low-level map method. This must be implemented by subclasses.


isModuleHomomorphism

public boolean isModuleHomomorphism()
Casting morphisms are never module homomorphisms.

Overrides:
isModuleHomomorphism in class ModuleMorphism

isRingHomomorphism

public boolean isRingHomomorphism()
Casting morphisms are never ring homomorphisms.

Overrides:
isRingHomomorphism in class ModuleMorphism

getRingMorphism

public ModuleMorphism getRingMorphism()
Description copied from class: ModuleMorphism
Returns the the ring morphism that transforms between the rings of the domain and codomain modules.

Specified by:
getRingMorphism in class ModuleMorphism

equals

public boolean equals(java.lang.Object object)
Description copied from class: ModuleMorphism
Returns true iff this morphism is equal to 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.

Specified by:
equals in class ModuleMorphism

toString

public java.lang.String toString()
Description copied from class: ModuleMorphism
Returns a string representation of this morphism. This string is used for generic comparison.

Specified by:
toString in class ModuleMorphism

toXML

public void toXML(XMLWriter writer)
Description copied from interface: XMLInputOutput
Outputs XML representation to writer.


fromXML

public ModuleMorphism fromXML(XMLReader reader,
                              org.w3c.dom.Element element)
Description copied from interface: XMLInputOutput
Reads XML representation from reader starting with element.

Returns:
an object of type T or null if parsing failed

getXMLInputOutput

public static XMLInputOutput<ModuleMorphism> getXMLInputOutput()

getElementTypeName

public java.lang.String getElementTypeName()
Description copied from interface: XMLInputOutput
Returns the value of the type attribute for this class.