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java.lang.Objectorg.rubato.math.module.Ring
public abstract class Ring
The abstract base class for rings. Rings always have dimension 1.
RingElement
,
Serialized FormConstructor Summary | |
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Ring()
|
Method Summary | |
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int |
compareTo(Module object)
Compares this module with object . |
Module |
getComponentModule(int i)
A ring has just one component module: itself. |
int |
getDimension()
Here, the dimension of a ring as a module is 1. |
abstract FreeModule |
getFreeModule(int dimension)
Returns the corresponding free module of dimension dim . |
ModuleMorphism |
getInjection(int index)
Returns a module morphism that injects a ring into the free module at the component index . |
abstract RingElement |
getOne()
Returns the unit element of this ring. |
ModuleMorphism |
getProjection(int index)
Returns a module morphism that projects the free module at the component index . |
Ring |
getRing()
The underlying ring of a ring as a module is itself. |
ModuleMorphism |
getTranslation(ModuleElement element)
Returns a morphism that translates by element . |
RingElement |
getUnitElement(int i)
Returns the unit vector with 1 at position i . |
abstract RingElement |
getZero()
Returns the zero element of this ring. |
abstract boolean |
isField()
Returns true if this ring is a field. |
boolean |
isNullModule()
Here, a ring is not a null-module. |
boolean |
isRing()
Returns true if this module is a ring. |
abstract RingElement |
parseString(java.lang.String s)
Creates an element in this module from a string representation. |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Methods inherited from interface org.rubato.math.module.FreeModule |
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isVectorspace |
Methods inherited from interface org.rubato.math.module.Module |
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cast, createElement, equals, getIdentityMorphism, getNullModule, hasElement, hashCode, toString, toVisualString |
Methods inherited from interface org.rubato.xml.XMLInputOutput |
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fromXML, getElementTypeName, toXML |
Constructor Detail |
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public Ring()
Method Detail |
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public abstract RingElement getZero()
getZero
in interface Module
public abstract RingElement getOne()
public RingElement getUnitElement(int i)
i
.
In the case of rings, this is simple the unit.
getUnitElement
in interface FreeModule
public ModuleMorphism getProjection(int index)
FreeModule
index
.
getProjection
in interface FreeModule
index
- the number of the component to project to,
the index will be clamped between 0 and the dimension-1 of
the free modulepublic ModuleMorphism getInjection(int index)
FreeModule
index
.
getInjection
in interface FreeModule
index
- the number of the component to project to,
the index will be clamped between 0 and the dimension-1 of
the free modulepublic abstract boolean isField()
public boolean isRing()
isRing
in interface Module
public abstract FreeModule getFreeModule(int dimension)
dim
.
public int getDimension()
getDimension
in interface Module
public Module getComponentModule(int i)
getComponentModule
in interface Module
public boolean isNullModule()
isNullModule
in interface Module
public Ring getRing()
getRing
in interface Module
public abstract RingElement parseString(java.lang.String s)
Module
parseString
in interface Module
public ModuleMorphism getTranslation(ModuleElement element)
element
.
getTranslation
in interface Module
public int compareTo(Module object)
Module
object
.
compareTo
in interface java.lang.Comparable<Module>
compareTo
in interface Module
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