org.rubato.math.module.morphism
Class ReorderMorphism

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

public class ReorderMorphism
extends ModuleMorphism

These are generalized projections, i.e., factors of a product ring are reordered, deleted or duplicated. A common example is the twisting morphism that switches positions in pairs. An ordering is an array of integers a: The codomain product ring as a factor for each entry ai which gives the factor of domain. Instances are created using the make(ProductRing,int[]) and make(Ring,int) methods.

Author:
Gérard Milmeister
See Also:
ProductRing, Serialized Form

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.
 int[] getOrdering()
          Returns ordering specifcation.
 ModuleMorphism getRingMorphism()
          Returns the the ring morphism that transforms between the rings of the domain and codomain modules.
static XMLInputOutput<ModuleMorphism> getXMLInputOutput()
           
 boolean isRingHomomorphism()
          If true, then this is a ring homomorphism.
static ModuleMorphism make(ProductRing domain, int[] ordering)
          Creates a reordering of the domain using the ordering specification.
static ModuleMorphism make(Ring ring, int fc)
          Creates a morphism that "blows up" a ring into a product ring with fc factors equal to ring.
 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, composable, compose, difference, getCodomain, getConstantMorphism, getConstantMorphism, getDomain, getIdentityMorphism, inDomain, isConstant, isIdentity, isLinear, isModuleHomomorphism, 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(ProductRing domain,
                                  int[] ordering)
Creates a reordering of the domain using the ordering specification. If ordering is null or the length of ordering is 0, an identity morphism is returned.


make

public static ModuleMorphism make(Ring ring,
                                  int fc)
Creates a morphism that "blows up" a ring into a product ring with fc factors equal to ring. This simply copies the value in the domain to the factors of the codomain.


getOrdering

public final int[] getOrdering()
Returns ordering specifcation.


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

isRingHomomorphism

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

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

compareTo

public int compareTo(ModuleMorphism object)
Description copied from class: ModuleMorphism
Compares two module morphisms. Checks first for equality. The default comparison is on names, subclasses may implement a more meaningful comparison.

Specified by:
compareTo in interface java.lang.Comparable<ModuleMorphism>
Overrides:
compareTo 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.