org.rubato.math.module
Class PolynomialRing

java.lang.Object
  extended by org.rubato.math.module.Ring
      extended by org.rubato.math.module.PolynomialRing
All Implemented Interfaces:
java.io.Serializable, java.lang.Comparable<Module>, FreeModule, Module, PolynomialFreeModule, XMLInputOutput<Module>

public final class PolynomialRing
extends Ring
implements PolynomialFreeModule

The ring of polynomials with coefficients in a specified ring.

Author:
Gérard Milmeister
See Also:
PolynomialElement, Serialized Form

Method Summary
 PolynomialElement cast(ModuleElement element)
          Casts element to an element in this module if possible.
 int compareTo(Module object)
          Compares this module with object.
 PolynomialElement createElement(java.util.List<ModuleElement> elements)
          Creates an element in this module from a list of module elements.
 boolean equals(java.lang.Object object)
          Returns true iff this module is equals to object.
 Module fromXML(XMLReader reader, org.w3c.dom.Element element)
          Reads XML representation from reader starting with element.
 Ring getBaseRing()
           
 Ring getCoefficientRing()
          Returns the ring of the coefficients of the polynomials.
 java.lang.String getElementTypeName()
          Returns the value of the type attribute for this class.
 PolynomialFreeModule getFreeModule(int dimension)
          Returns the corresponding free module of dimension dim.
 ModuleMorphism getIdentityMorphism()
          Returns the identity morphism in this module.
 java.lang.String getIndeterminate()
          Returns the indeterminate of this polynomial module.
 java.util.List<java.lang.String> getIndeterminates()
           
 PolynomialFreeModule getNullModule()
          Returns the null-module corresponding to this module.
 PolynomialElement getOne()
          Returns the unit element of this ring.
static XMLInputOutput<Module> getXMLInputOutput()
           
 PolynomialElement getZero()
          Returns the zero element of this ring.
 boolean hasElement(ModuleElement element)
          Returns true iff element is an element of this module.
 int hashCode()
          Returns the hash code for this module.
 boolean hasIndeterminate(java.lang.String indet)
           
 boolean isField()
          Returns true if this ring is a field.
 boolean isVectorspace()
          Returns true if this free module is a vector space.
static PolynomialRing make(Ring coefficientRing, java.lang.String indeterminate)
           
 PolynomialElement parseString(java.lang.String string)
          Creates an element in this module from a string representation.
 java.lang.String toString()
          Returns a human readable string representation of this module.
 java.lang.String toVisualString()
          Returns a human readable string representation of this module.
 void toXML(XMLWriter writer)
          Outputs XML representation to writer.
 
Methods inherited from class org.rubato.math.module.Ring
getComponentModule, getDimension, getInjection, getProjection, getRing, getTranslation, getUnitElement, isNullModule, isRing
 
Methods inherited from class java.lang.Object
getClass, notify, notifyAll, wait, wait, wait
 
Methods inherited from interface org.rubato.math.module.FreeModule
getInjection, getProjection, getUnitElement
 
Methods inherited from interface org.rubato.math.module.Module
getComponentModule, getDimension, getRing, getTranslation, isNullModule, isRing
 

Method Detail

make

public static PolynomialRing make(Ring coefficientRing,
                                  java.lang.String indeterminate)

getIndeterminate

public java.lang.String getIndeterminate()
Description copied from interface: PolynomialFreeModule
Returns the indeterminate of this polynomial module.

Specified by:
getIndeterminate in interface PolynomialFreeModule

hasIndeterminate

public boolean hasIndeterminate(java.lang.String indet)

getIndeterminates

public java.util.List<java.lang.String> getIndeterminates()

getCoefficientRing

public Ring getCoefficientRing()
Description copied from interface: PolynomialFreeModule
Returns the ring of the coefficients of the polynomials.

Specified by:
getCoefficientRing in interface PolynomialFreeModule

getBaseRing

public Ring getBaseRing()

getZero

public PolynomialElement getZero()
Description copied from class: Ring
Returns the zero element of this ring.

Specified by:
getZero in interface Module
Specified by:
getZero in class Ring

getOne

public PolynomialElement getOne()
Description copied from class: Ring
Returns the unit element of this ring.

Specified by:
getOne in class Ring

getNullModule

public PolynomialFreeModule getNullModule()
Description copied from interface: Module
Returns the null-module corresponding to this module.

Specified by:
getNullModule in interface Module

isField

public boolean isField()
Description copied from class: Ring
Returns true if this ring is a field.

Specified by:
isField in class Ring

isVectorspace

public boolean isVectorspace()
Description copied from interface: FreeModule
Returns true if this free module is a vector space.

Specified by:
isVectorspace in interface FreeModule

getIdentityMorphism

public ModuleMorphism getIdentityMorphism()
Description copied from interface: Module
Returns the identity morphism in this module.

Specified by:
getIdentityMorphism in interface Module

hasElement

public boolean hasElement(ModuleElement element)
Description copied from interface: Module
Returns true iff element is an element of this module.

Specified by:
hasElement in interface Module

getFreeModule

public PolynomialFreeModule getFreeModule(int dimension)
Description copied from class: Ring
Returns the corresponding free module of dimension dim.

Specified by:
getFreeModule in class Ring

equals

public boolean equals(java.lang.Object object)
Description copied from interface: Module
Returns true iff this module is equals to object.

Specified by:
equals in interface Module
Overrides:
equals in class java.lang.Object

compareTo

public int compareTo(Module object)
Description copied from interface: Module
Compares this module with object.

Specified by:
compareTo in interface java.lang.Comparable<Module>
Specified by:
compareTo in interface Module
Overrides:
compareTo in class Ring

createElement

public PolynomialElement createElement(java.util.List<ModuleElement> elements)
Description copied from interface: Module
Creates an element in this module from a list of module elements.

Specified by:
createElement in interface Module
Returns:
null if no element in this module can be created from the arguments.

cast

public PolynomialElement cast(ModuleElement element)
Description copied from interface: Module
Casts element to an element in this module if possible.

Specified by:
cast in interface Module
Returns:
null if cast is not possible

toString

public java.lang.String toString()
Description copied from interface: Module
Returns a human readable string representation of this module. The representation is not meant to be parseable.

Specified by:
toString in interface Module
Overrides:
toString in class java.lang.Object

toVisualString

public java.lang.String toVisualString()
Description copied from interface: Module
Returns a human readable string representation of this module. The representation is not meant to be parseable. The string should be a short representation, possibly using Unicode characters.

Specified by:
toVisualString in interface Module

parseString

public PolynomialElement parseString(java.lang.String string)
Description copied from interface: Module
Creates an element in this module from a string representation.

Specified by:
parseString in interface Module
Specified by:
parseString in class Ring
Returns:
null if the string is in the wrong format

toXML

public void toXML(XMLWriter writer)
Description copied from interface: XMLInputOutput
Outputs XML representation to writer.

Specified by:
toXML in interface XMLInputOutput<Module>

fromXML

public Module fromXML(XMLReader reader,
                      org.w3c.dom.Element element)
Description copied from interface: XMLInputOutput
Reads XML representation from reader starting with element.

Specified by:
fromXML in interface XMLInputOutput<Module>
Returns:
an object of type T or null if parsing failed

getXMLInputOutput

public static XMLInputOutput<Module> getXMLInputOutput()

getElementTypeName

public java.lang.String getElementTypeName()
Description copied from interface: XMLInputOutput
Returns the value of the type attribute for this class.

Specified by:
getElementTypeName in interface XMLInputOutput<Module>

hashCode

public int hashCode()
Description copied from interface: Module
Returns the hash code for this module.

Specified by:
hashCode in interface Module
Overrides:
hashCode in class java.lang.Object