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

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

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

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(java.math.BigInteger a) Get a (constant) UnivPowerSeries<C> from a java.math.BigInteger.
UnivPowerSeries<C>	fromInteger(long a) Get a (constant) UnivPowerSeries<C> from a long value.
UnivPowerSeries<C>	fromPolynomial(GenPolynomial<C> a) Get a UnivPowerSeries<C> from a GenPolynomial<C>.
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

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<UnivPowerSeries<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<UnivPowerSeries<C extends RingElem<C>>>

Returns:

0 as UnivPowerSeries.

getONE

public UnivPowerSeries<C> getONE()

Get the one element.

Specified by:

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

Returns:

false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<UnivPowerSeries<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<UnivPowerSeries<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<UnivPowerSeries<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>.

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<UnivPowerSeries<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<UnivPowerSeries<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.

copy

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

Copy power series.

Specified by:

copy in interface ElemFactory<UnivPowerSeries<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<UnivPowerSeries<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<UnivPowerSeries<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.