org.rubato.math.module.morphism
Class GenericAffineMorphism

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

public final class GenericAffineMorphism
extends ModuleMorphism

This class handles affine morphisms between free modules over a given ring, that are not covered by specialized classes such as ZFreeAfineMorphism, etc.

Author:
Gérard Milmeister
See Also:
Serialized Form

Constructor Summary
GenericAffineMorphism(Ring ring, int dim, int codim)
          Creates an affine morphism from a free ring-module of dimension dim to a free ring-module of dimension codim.
 
Method Summary
 ModuleMorphism compose(ModuleMorphism morphism)
          Returns the composition this*morphism.
 ModuleMorphism difference(ModuleMorphism morphism)
          Returns the difference of this module morphism and morphism.
 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 isConstant()
          Returns true iff this morphism is constant.
 boolean isIdentity()
          Returns true iff this morphism is the identity morphism.
 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.
 ModuleElement map(ModuleElement x)
          Maps the element x.
 void setMatrix(int i, int j, RingElement element)
          Sets the i,j-element of the matrix to the specified element.
 void setVector(int i, RingElement element)
          Sets the i-th element of the translation vector to element.
 ModuleMorphism sum(ModuleMorphism morphism)
          Returns the sum of this module morphism and morphism.
 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, getCodomain, getConstantMorphism, getConstantMorphism, getDomain, getIdentityMorphism, inDomain, isRingMorphism, power, scaled
 
Methods inherited from class java.lang.Object
getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Constructor Detail

GenericAffineMorphism

public GenericAffineMorphism(Ring ring,
                             int dim,
                             int codim)
Creates an affine morphism from a free ring-module of dimension dim to a free ring-module of dimension codim. The morphism is the null morphism by default.

Method Detail

setMatrix

public void setMatrix(int i,
                      int j,
                      RingElement element)
Sets the i,j-element of the matrix to the specified element.


setVector

public void setVector(int i,
                      RingElement element)
Sets the i-th element of the translation vector to element.


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

isLinear

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

Overrides:
isLinear in class ModuleMorphism

isIdentity

public boolean isIdentity()
Description copied from class: ModuleMorphism
Returns true iff this morphism is the identity morphism.

Overrides:
isIdentity in class ModuleMorphism

isConstant

public boolean isConstant()
Description copied from class: ModuleMorphism
Returns true iff this morphism is constant.

Overrides:
isConstant in class ModuleMorphism

compose

public ModuleMorphism compose(ModuleMorphism morphism)
                       throws CompositionException
Description copied from class: ModuleMorphism
Returns the composition this*morphism.

Overrides:
compose in class ModuleMorphism
Throws:
CompositionException - if composition could not be performed

sum

public ModuleMorphism sum(ModuleMorphism morphism)
                   throws CompositionException
Description copied from class: ModuleMorphism
Returns the sum of this module morphism and morphism.

Overrides:
sum in class ModuleMorphism
Throws:
CompositionException - if sum could not be performed

difference

public ModuleMorphism difference(ModuleMorphism morphism)
                          throws CompositionException
Description copied from class: ModuleMorphism
Returns the difference of this module morphism and morphism.

Overrides:
difference in class ModuleMorphism
Throws:
CompositionException - if difference could not be performed

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.