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java.lang.Objectorg.rubato.math.module.morphism.ModuleMorphism
org.rubato.math.module.morphism.PowerMorphism
public final class PowerMorphism
Morphism that represents an iterated arbitrary morphism.
Method Summary | |
---|---|
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 . |
ModuleMorphism |
getBaseMorphism()
Returns the base morphism f of the power f^n. |
java.lang.String |
getElementTypeName()
Returns the value of the type attribute for this class. |
int |
getExponent()
Returns the exponent n of the power f^n. |
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. |
static ModuleMorphism |
make(ModuleMorphism f,
int exp)
Creates a morphism from f raised to power . |
ModuleElement |
map(ModuleElement x)
Maps the element x . |
ModuleMorphism |
power(int n)
Returns this module morphism raise to the power n . |
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, composable, compose, difference, getCodomain, getConstantMorphism, getConstantMorphism, getDomain, getIdentityMorphism, inDomain, isRingMorphism, scaled, sum |
Methods inherited from class java.lang.Object |
---|
getClass, hashCode, notify, notifyAll, wait, wait, wait |
Method Detail |
---|
public static ModuleMorphism make(ModuleMorphism f, int exp) throws CompositionException
f
raised to power
.
The resulting morphism h is such that h(x) = f(f(...(f(x))...)),
where there are exp
repetitions of f
.
This is a virtual constructor, so that simplifications can be made.
CompositionException
public 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 isIdentity()
ModuleMorphism
isIdentity
in class ModuleMorphism
public boolean isConstant()
ModuleMorphism
isConstant
in class ModuleMorphism
public ModuleMorphism getRingMorphism()
ModuleMorphism
getRingMorphism
in class ModuleMorphism
public ModuleMorphism getBaseMorphism()
public int getExponent()
public ModuleMorphism power(int n) throws CompositionException
ModuleMorphism
n
.
The power must be non-negative and the domain must be equal
to the codomain.
power
in class ModuleMorphism
CompositionException
- if power could not be performedpublic 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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