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java.lang.Objectorg.rubato.math.module.morphism.ModuleMorphism
org.rubato.math.module.morphism.ModuloMorphism
public class ModuloMorphism
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.
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 |
---|
public static ModuloMorphism make(int modulus)
modulus
.
modulus
- is at least 2, lower values will be set to 2public static ModuloMorphism make(int dim, int modulus)
dim
- is at least 0, lower values will be set to 0modulus
- is at least 2, lower values will be set to 2public ModuleElement map(ModuleElement x) throws MappingException
ModuleMorphism
x
.
This must be implemented for each specific morphism type.
map
in class ModuleMorphism
x
MappingException
- if mapping of element fails
public boolean isModuleHomomorphism()
ModuleMorphism
isModuleHomomorphism
in class ModuleMorphism
public boolean isRingHomomorphism()
ModuleMorphism
isRingHomomorphism
in class ModuleMorphism
public boolean isLinear()
ModuleMorphism
isLinear
in class ModuleMorphism
public boolean isConstant()
ModuleMorphism
isConstant
in class ModuleMorphism
public final int getModulus()
public final int getDimension()
public ModuleMorphism getRingMorphism()
ModuleMorphism
getRingMorphism
in class ModuleMorphism
public ModuleElement atZero()
ModuleMorphism
atZero
in class ModuleMorphism
public int compareTo(ModuleMorphism object)
ModuleMorphism
compareTo
in interface java.lang.Comparable<ModuleMorphism>
compareTo
in class ModuleMorphism
public boolean equals(java.lang.Object object)
ModuleMorphism
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.
equals
in class ModuleMorphism
public java.lang.String toString()
ModuleMorphism
toString
in class ModuleMorphism
public void toXML(XMLWriter writer)
XMLInputOutput
writer
.
public ModuleMorphism fromXML(XMLReader reader, org.w3c.dom.Element element)
XMLInputOutput
reader
starting with element
.
public static XMLInputOutput<ModuleMorphism> getXMLInputOutput()
public java.lang.String getElementTypeName()
XMLInputOutput
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