edu.stanford.math.plex4.streams.derived

Class HomStream<T,U>

java.lang.Object

edu.stanford.math.plex4.streams.derived.TensorStream<T,U>

edu.stanford.math.plex4.streams.derived.HomStream<T,U>

Type Parameters:

T - the underlying basis type of the first complex

U - the underlying basis type of the second complex

All Implemented Interfaces:

AbstractFilteredStream<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>, java.lang.Iterable<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>

public class HomStream<T,U>
extends TensorStream<T,U>

This implements the hom-complex from two filtered chain complexes. For the definition of the hom-complex, one is invited to look at the book "Homology" by Saunders Maclane. For the case of vector-space components, one can express the hom-complex in terms of the tensor product of the dualized first complex with the second. Elements of the hom-complex are of the form a* tensor b, for a in the first chain complex and b in the second chain complex. Thus in practice, we represent these as elements of type ObjectObjectPair.

Author:

Andrew Tausz

See Also:

TensorStream

Field Summary

Fields inherited from class edu.stanford.math.plex4.streams.derived.TensorStream

stream1, stream2

Constructor Summary

Constructors

Constructor and Description
HomStream(AbstractFilteredStream<T> domainStream, AbstractFilteredStream<U> codomainStream) This constructor initializes the hom-complexes from two existing chain complexes.

Method Summary

Methods

Modifier and Type	Method and Description
int	getDimension(edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U> element) This function returns the dimension of a basis element within the chain complex.
<R> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>>	getHomotopies()
<R> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.ObjectSparseFormalSum<R,edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>>	getHomotopies(edu.stanford.math.primitivelib.autogen.formal_sum.ObjectAlgebraicFreeModule<R,edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>> chainModule) This function returns the set of chain homotopies of between the domain and codomain chain complexes.
<R extends java.lang.Number> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>>	getHomotopiesAsDouble(edu.stanford.math.primitivelib.autogen.formal_sum.ObjectAlgebraicFreeModule<R,edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>> chainModule) This function returns the set of chain homotopies between the domain and codomain chain complexes as formal sums over pairs with double coefficients.
static <R extends java.lang.Number,M> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<M>>	toDoubleFormalSum(java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.ObjectSparseFormalSum<R,M>> objectFormalSumList) This function converts a list of ObjectSparseFormalSum objects to DoubleSparseFormalSum objects.
static <R extends java.lang.Number,M> edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<M>	toDoubleFormalSum(edu.stanford.math.primitivelib.autogen.formal_sum.ObjectSparseFormalSum<R,M> objectFormalSum) This function converts an ObjectSparseFormalSum to a DoubleSparseFormalSum object.

Methods inherited from class edu.stanford.math.plex4.streams.derived.TensorStream

containsElement, finalizeStream, getBasisComparator, getBoundary, getBoundaryCoefficients, getFiltrationIndex, getFiltrationValue, getMaximumFiltrationIndex, getMinimumFiltrationIndex, getSize, isFinalized, iterator, transform

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

HomStream

public HomStream(AbstractFilteredStream<T> domainStream,
         AbstractFilteredStream<U> codomainStream)

This constructor initializes the hom-complexes from two existing chain complexes.

Parameters:

domainStream - the domain complex

codomainStream - the codomain complex

Method Detail

getDimension

public int getDimension(edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U> element)

Description copied from interface: AbstractFilteredStream

This function returns the dimension of a basis element within the chain complex.

Specified by:

getDimension in interface AbstractFilteredStream<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>

Overrides:

getDimension in class TensorStream<T,U>

Parameters:

element - the element to get the dimension of

Returns:

the dimension of the basis element within the chain complex

getHomotopies

public <R> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>> getHomotopies()

getHomotopies

public <R> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.ObjectSparseFormalSum<R,edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>> getHomotopies(edu.stanford.math.primitivelib.autogen.formal_sum.ObjectAlgebraicFreeModule<R,edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>> chainModule)

This function returns the set of chain homotopies of between the domain and codomain chain complexes.

Type Parameters:

R - the underlying type of the ring in which to compute in

Parameters:

chainModule - the free module over pairs of type (T, U) with coefficients in R

Returns:

a list containing the set of chain homotopies

getHomotopiesAsDouble

public <R extends java.lang.Number> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>>> getHomotopiesAsDouble(edu.stanford.math.primitivelib.autogen.formal_sum.ObjectAlgebraicFreeModule<R,edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,U>> chainModule)

This function returns the set of chain homotopies between the domain and codomain chain complexes as formal sums over pairs with double coefficients.

Type Parameters:

R - the underlying type of the ring in which to compute in

Parameters:

chainModule - the free module over pairs of type (T, U) with coefficients in R

Returns:

a list containing the set of chain homotopies

toDoubleFormalSum

public static <R extends java.lang.Number,M> edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<M> toDoubleFormalSum(edu.stanford.math.primitivelib.autogen.formal_sum.ObjectSparseFormalSum<R,M> objectFormalSum)

This function converts an ObjectSparseFormalSum to a DoubleSparseFormalSum object.

Type Parameters:

R - the underlying type of the original coefficient field (must extend Number)

M - the type of the basis elements in the formal sumssum

Parameters:

objectFormalSum - the ObjectSparseFormalSum to convert

Returns:

a DoubleSparseFormalSum with the same objects as the one passed in, but with double coefficients

toDoubleFormalSum

public static <R extends java.lang.Number,M> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<M>> toDoubleFormalSum(java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.ObjectSparseFormalSum<R,M>> objectFormalSumList)

This function converts a list of ObjectSparseFormalSum objects to DoubleSparseFormalSum objects.

Type Parameters:

R - the underlying type of the original coefficient field (must extend Number)

M - the type of the basis elements in the formal sums

Parameters:

objectFormalSumList - the list of ObjectSparseFormalSum objects to convert

Returns:

the list of converted sums