Package edu.jas.ps

Class UnivPowerSeriesRing<C extends RingElem<C>>

java.lang.Object

edu.jas.ps.UnivPowerSeriesRing<C>

Type Parameters:

C - ring element type

All Implemented Interfaces:

AbelianGroupFactory<UnivPowerSeries<C>>, ElemFactory<UnivPowerSeries<C>>, MonoidFactory<UnivPowerSeries<C>>, RingFactory<UnivPowerSeries<C>>, java.io.Serializable

public class UnivPowerSeriesRing<C extends RingElem<C>>
extends java.lang.Object
implements RingFactory<UnivPowerSeries<C>>

Univariate power series ring implementation. Uses lazy evaluated generating function for coefficients.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
RingFactory<C>	coFac	Coefficient ring factory.
static java.lang.String	DEFAULT_NAME	Default variable name.
static int	DEFAULT_TRUNCATE	Default truncate.
UnivPowerSeries<C>	ONE	The constant power series 1 for this ring.
protected static java.util.Random	random	A default random sequence generator.
UnivPowerSeries<C>	ZERO	The constant power series 0 for this ring.

Constructor Summary

Constructors

Constructor	Description
UnivPowerSeriesRing(GenPolynomialRing<C> pfac)	Constructor.
UnivPowerSeriesRing(RingFactory<C> coFac)	Constructor.
UnivPowerSeriesRing(RingFactory<C> coFac, int truncate)	Constructor.
UnivPowerSeriesRing(RingFactory<C> cofac, int truncate, java.lang.String name)	Constructor.
UnivPowerSeriesRing(RingFactory<C> coFac, java.lang.String name)	Constructor.

Method Summary

Modifier and Type	Method	Description
java.math.BigInteger	characteristic()	Characteristic of this ring.
UnivPowerSeries<C>	copy(UnivPowerSeries<C> c)	Copy power series.
boolean	equals(java.lang.Object B)	Comparison with any other object.
UnivPowerSeries<C>	fixPoint(UnivPowerSeriesMap<C> map)	Fixed point construction.
UnivPowerSeries<C>	fromInteger(long a)	Get a (constant) UnivPowerSeries<C> from a long value.
UnivPowerSeries<C>	fromInteger(java.math.BigInteger a)	Get a (constant) UnivPowerSeries<C> from a java.math.BigInteger.
UnivPowerSeries<C>	fromPolynomial(GenPolynomial<C> a)	Get a UnivPowerSeries<C> from a GenPolynomial<C>.
UnivPowerSeries<C>	fromVector(GenVector<C> a)	Get a UnivPowerSeries<C> from a GenVector<C>.
UnivPowerSeries<C>	generate(java.util.function.IntFunction<C> gener)	Generate a power series via lambda expression.
java.util.List<UnivPowerSeries<C>>	generators()	Get a list of the generating elements.
UnivPowerSeries<C>	getCOS()	Get the power series of the cosine function.
UnivPowerSeries<C>	getEXP()	Get the power series of the exponential function.
UnivPowerSeries<C>	getONE()	Get the one element.
UnivPowerSeries<C>	getSIN()	Get the power series of the sinus function.
UnivPowerSeries<C>	getTAN()	Get the power series of the tangens function.
UnivPowerSeries<C>	getZERO()	Get the zero element.
int	hashCode()	Hash code for this .
boolean	isAssociative()	Query if this ring is associative.
boolean	isCommutative()	Is commutative.
boolean	isField()	Query if this ring is a field.
boolean	isFinite()	Is this structure finite or infinite.
UnivPowerSeries<C>	parse(java.io.Reader r)	Parse a power series.
UnivPowerSeries<C>	parse(java.lang.String s)	Parse a power series.
GenPolynomialRing<C>	polyRing()	Get the corresponding GenPolynomialRing<C>.
UnivPowerSeries<C>	random()	Generate a random power series with k = 5, d = 0.7.
UnivPowerSeries<C>	random(int k)	Generate a random power series with d = 0.7.
UnivPowerSeries<C>	random(int k, float d)	Generate a random power series.
UnivPowerSeries<C>	random(int k, float d, java.util.Random rnd)	Generate a random power series.
UnivPowerSeries<C>	random(int k, java.util.Random rnd)	Generate a random power series with d = 0.7.
UnivPowerSeries<C>	seriesOfTaylor(TaylorFunction<C> f, C a)	Taylor power series.
UnivPowerSeries<C>	solveODE(UnivPowerSeries<C> f, C c)	Solve an ordinary differential equation. y' = f(y) with y(0) = c.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	To String.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface edu.jas.structure.ElemFactory

valueOf

Field Detail

random

protected static final java.util.Random random

A default random sequence generator.

DEFAULT_TRUNCATE

public static final int DEFAULT_TRUNCATE

Default truncate.

See Also:

Constant Field Values

DEFAULT_NAME

public static final java.lang.String DEFAULT_NAME

Default variable name.

See Also:

Constant Field Values

coFac

public final RingFactory<C extends RingElem<C>> coFac

Coefficient ring factory.

ONE

public final UnivPowerSeries<C extends RingElem<C>> ONE

The constant power series 1 for this ring.

ZERO

public final UnivPowerSeries<C extends RingElem<C>> ZERO

The constant power series 0 for this ring.

Constructor Detail

UnivPowerSeriesRing

public UnivPowerSeriesRing(RingFactory<C> coFac)

Constructor.

Parameters:

coFac - coefficient ring factory.

UnivPowerSeriesRing

public UnivPowerSeriesRing(RingFactory<C> coFac,
                           int truncate)

Constructor.

Parameters:

coFac - coefficient ring factory.

truncate - index of truncation.

UnivPowerSeriesRing

public UnivPowerSeriesRing(RingFactory<C> coFac,
                           java.lang.String name)

Constructor.

Parameters:

coFac - coefficient ring factory.

name - of the variable.

UnivPowerSeriesRing

public UnivPowerSeriesRing(GenPolynomialRing<C> pfac)

Constructor.

Parameters:

pfac - polynomial ring factory.

UnivPowerSeriesRing

public UnivPowerSeriesRing(RingFactory<C> cofac,
                           int truncate,
                           java.lang.String name)

Constructor.

Parameters:

cofac - coefficient ring factory.

truncate - index of truncation.

name - of the variable.

Method Detail

fixPoint

public UnivPowerSeries<C> fixPoint(UnivPowerSeriesMap<C> map)

Fixed point construction.

Parameters:

map - a mapping of power series.

Returns:

fix point wrt map.

toString

public java.lang.String toString()

To String.

Overrides:

toString in class java.lang.Object

Returns:

string representation of this.

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<C extends RingElem<C>>

Returns:

script compatible representation for this ElemFactory.

See Also:

ElemFactory.toScript()

equals

public boolean equals(java.lang.Object B)

Comparison with any other object.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this .

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

getZERO

public UnivPowerSeries<C> getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<C extends RingElem<C>>

Returns:

0 as UnivPowerSeries.

getONE

public UnivPowerSeries<C> getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<C extends RingElem<C>>

Returns:

1 as UnivPowerSeries.

generators

public java.util.List<UnivPowerSeries<C>> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<C extends RingElem<C>>

Returns:

list of generators for the algebraic structure.

See Also:

ElemFactory.generators()

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

isFinite in interface ElemFactory<C extends RingElem<C>>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

getEXP

public UnivPowerSeries<C> getEXP()

Get the power series of the exponential function.

Returns:

exp(x) as UnivPowerSeries.

getSIN

public UnivPowerSeries<C> getSIN()

Get the power series of the sinus function.

Returns:

sin(x) as UnivPowerSeries.

getCOS

public UnivPowerSeries<C> getCOS()

Get the power series of the cosine function.

Returns:

cos(x) as UnivPowerSeries.

getTAN

public UnivPowerSeries<C> getTAN()

Get the power series of the tangens function.

Returns:

tan(x) as UnivPowerSeries.

solveODE

public UnivPowerSeries<C> solveODE(UnivPowerSeries<C> f,
                                   C c)

Solve an ordinary differential equation. y' = f(y) with y(0) = c.

Parameters:

f - a UnivPowerSeries.

c - integration constant.

Returns:

f.integrate(c).

isCommutative

public boolean isCommutative()

Is commutative.

Specified by:

isCommutative in interface MonoidFactory<C extends RingElem<C>>

Returns:

true, if this ring is commutative, else false.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<C extends RingElem<C>>

Returns:

true if this ring is associative, else false.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<C extends RingElem<C>>

Returns:

false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<C extends RingElem<C>>

Returns:

characteristic of this ring.

fromInteger

public UnivPowerSeries<C> fromInteger(long a)

Get a (constant) UnivPowerSeries<C> from a long value.

Specified by:

fromInteger in interface ElemFactory<C extends RingElem<C>>

Parameters:

a - long.

Returns:

a UnivPowerSeries<C>.

fromInteger

public UnivPowerSeries<C> fromInteger(java.math.BigInteger a)

Get a (constant) UnivPowerSeries<C> from a java.math.BigInteger.

Specified by:

fromInteger in interface ElemFactory<C extends RingElem<C>>

Parameters:

a - BigInteger.

Returns:

a UnivPowerSeries<C>.

polyRing

public GenPolynomialRing<C> polyRing()

Get the corresponding GenPolynomialRing<C>.

Returns:

GenPolynomialRing<C>.

fromPolynomial

public UnivPowerSeries<C> fromPolynomial(GenPolynomial<C> a)

Get a UnivPowerSeries<C> from a GenPolynomial<C>.

Parameters:

a - GenPolynomial<C>.

Returns:

a UnivPowerSeries<C>.

fromVector

public UnivPowerSeries<C> fromVector(GenVector<C> a)

Get a UnivPowerSeries<C> from a GenVector<C>.

Parameters:

a - GenVector<C>.

Returns:

a UnivPowerSeries<C>.

random

public UnivPowerSeries<C> random()

Generate a random power series with k = 5, d = 0.7.

Returns:

a random power series.

random

public UnivPowerSeries<C> random(int k)

Generate a random power series with d = 0.7.

Specified by:

random in interface ElemFactory<C extends RingElem<C>>

Parameters:

k - bitsize of random coefficients.

Returns:

a random power series.

random

public UnivPowerSeries<C> random(int k,
                                 java.util.Random rnd)

Generate a random power series with d = 0.7.

Specified by:

random in interface ElemFactory<C extends RingElem<C>>

Parameters:

k - bit-size of random coefficients.

rnd - is a source for random bits.

Returns:

a random power series.

random

public UnivPowerSeries<C> random(int k,
                                 float d)

Generate a random power series.

Parameters:

k - bit-size of random coefficients.

d - density of non-zero coefficients.

Returns:

a random power series.

random

public UnivPowerSeries<C> random(int k,
                                 float d,
                                 java.util.Random rnd)

Generate a random power series.

Parameters:

k - bit-size of random coefficients.

d - density of non-zero coefficients.

rnd - is a source for random bits.

Returns:

a random power series.

generate

public UnivPowerSeries<C> generate(java.util.function.IntFunction<C> gener)

Generate a power series via lambda expression.

Parameters:

gener - lambda expression.

Returns:

a generated power series.

copy

public UnivPowerSeries<C> copy(UnivPowerSeries<C> c)

Copy power series.

Specified by:

copy in interface ElemFactory<C extends RingElem<C>>

Parameters:

c - a power series.

Returns:

a copy of c.

parse

public UnivPowerSeries<C> parse(java.lang.String s)

Parse a power series. Note: not implemented.

Specified by:

parse in interface ElemFactory<C extends RingElem<C>>

Parameters:

s - String.

Returns:

power series from s.

parse

public UnivPowerSeries<C> parse(java.io.Reader r)

Parse a power series. Note: not implemented.

Specified by:

parse in interface ElemFactory<C extends RingElem<C>>

Parameters:

r - Reader.

Returns:

next power series from r.

seriesOfTaylor

public UnivPowerSeries<C> seriesOfTaylor(TaylorFunction<C> f,
                                         C a)

Taylor power series.

Parameters:

f - function.

a - expansion point.

Returns:

Taylor series of f.