org.rubato.math.module.morphism
Class SplitMorphism

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

public class SplitMorphism
extends ModuleMorphism

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. For each part a morphism is given, in the example three morphisms f1:R^3->R^3, f2:R^2->R^2 and f3:R^4->R^4.

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[] getMorphisms()
          Returns the morphisms that make up this split morphism in the correct order.
 ModuleMorphism getRingMorphism()
          Returns the the ring morphism that transforms between the rings of the domain and codomain modules.
static XMLInputOutput<ModuleMorphism> getXMLInputOutput()
           
 boolean isModuleHomomorphism()
          If true, then this is a module homomorphism.
static ModuleMorphism make(FreeModule module, java.util.List<ModuleMorphism> morphisms)
          Creates a split morphism over module with the given list of morphisms.
 ModuleElement map(ModuleElement x)
          Maps the element x.
 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, isRingHomomorphism, 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(FreeModule module,
                                  java.util.List<ModuleMorphism> morphisms)
Creates a split morphism over module with the given list of morphisms.


map

public 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

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

isModuleHomomorphism

public boolean isModuleHomomorphism()
Description copied from class: ModuleMorphism
If true, then this is a module homomorphism.

Overrides:
isModuleHomomorphism in class ModuleMorphism

getMorphisms

public ModuleMorphism[] getMorphisms()
Returns the morphisms that make up this split morphism in the correct order.


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.