org.rubato.math.module.morphism
Class ModuloMorphism

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

public class ModuloMorphism
extends ModuleMorphism

The function that takes an element i in Z^d to i mod n in Z_n^d. To create instances use the make(int) or make(int,int) methods.

Author:
Gérard Milmeister
See Also:
Serialized Form

Method Summary
 ModuleElement atZero()
          Returns the value of the morphism evaluated at the zero of the domain.
 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.
 int getDimension()
          Returns the dimension of the domain and codomain.
 java.lang.String getElementTypeName()
          Returns the value of the type attribute for this class.
 int getModulus()
          Returns the modulus of the codomain.
 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 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 ModuloMorphism make(int modulus)
          Creates a map that takes an integer i to i mod n.
static ModuloMorphism make(int dim, int modulus)
          Creates a map that takes an element i of Z^d to i mod n in Z_n^d.
 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
clone, composable, compose, difference, getCodomain, getConstantMorphism, getConstantMorphism, getDomain, getIdentityMorphism, inDomain, isIdentity, isRingMorphism, power, scaled, sum
 
Methods inherited from class java.lang.Object
getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Method Detail

make

public static ModuloMorphism make(int modulus)
Creates a map that takes an integer i to i mod n. The domain is ℤ, the codomain ℤn, where n is the specified modulus.

Parameters:
modulus - is at least 2, lower values will be set to 2

make

public static ModuloMorphism make(int dim,
                                  int modulus)
Creates a map that takes an element i of Z^d to i mod n in Z_n^d.

Parameters:
dim - is at least 0, lower values will be set to 0
modulus - is at least 2, lower values will be set to 2

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

isConstant

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

Overrides:
isConstant in class ModuleMorphism

getModulus

public final int getModulus()
Returns the modulus of the codomain.


getDimension

public final int getDimension()
Returns the dimension of the domain and codomain.


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

atZero

public ModuleElement atZero()
Description copied from class: ModuleMorphism
Returns the value of the morphism evaluated at the zero of the domain.

Overrides:
atZero 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

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.