org.rubato.math.module.morphism
Class GenericBasisMorphism

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

public class GenericBasisMorphism
extends ModuleMorphism

A generic basis morphism is defined by the values at the basis elements of the domain module.

Author:
Gérard Milmeister
See Also:
Serialized Form

Method Summary
 boolean equals(java.lang.Object object)
          Returns true iff this morphism is equal to object.
 GenericBasisMorphism 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 isLinear()
          Returns true iff this is a linear morphism.
 boolean isModuleHomomorphism()
          If true, then this is a module homomorphism.
 boolean isRingHomomorphism()
          If true, then this is a ring homomorphism.
static GenericBasisMorphism make(FreeModule domain, Module codomain, ModuleElement[] fi)
          Creates generic basis morphism with the free module domain and any codomain.
 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, isRingMorphism, power, scaled, sum
 
Methods inherited from class java.lang.Object
getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Method Detail

make

public static GenericBasisMorphism make(FreeModule domain,
                                        Module codomain,
                                        ModuleElement[] fi)
                                 throws DomainException
Creates generic basis morphism with the free module domain and any codomain. Both modules must be over the same ring. The array fi of module elements contains the element in the codomain that the vectors (0,0,0,0...), (1,0,0,0,...), (0,1,0,0,...), ... in this order are mapped to.

Throws:
DomainException - if rings don't match

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

isModuleHomomorphism

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

Overrides:
isModuleHomomorphism in class ModuleMorphism

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

isLinear

public boolean isLinear()
Description copied from class: ModuleMorphism
Returns true iff this is a linear morphism.

Overrides:
isLinear 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 GenericBasisMorphism 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.