edu.jas.ps
Class MultiVarPowerSeriesRing<C extends RingElem<C>>

java.lang.Object
  edu.jas.ps.MultiVarPowerSeriesRing<C>

Type Parameters:

C - ring element type

All Implemented Interfaces:

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

public class MultiVarPowerSeriesRing<C extends RingElem<C>>
extends java.lang.Object
implements RingFactory<MultiVarPowerSeries<C>>

Multivariate 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 int	DEFAULT_TRUNCATE Default truncate.
ExpVector	EVZERO Zero ExpVector.
int	nvar The number of variables.
MultiVarPowerSeries<C>	ONE The constant power series 1 for this ring.
protected static java.util.Random	random A default random sequence generator.
protected java.lang.String[]	vars The names of the variables.
MultiVarPowerSeries<C>	ZERO The constant power series 0 for this ring.

Constructor Summary

MultiVarPowerSeriesRing(GenPolynomialRing<C> fac)
Constructor.

MultiVarPowerSeriesRing(RingFactory<C> coFac, int nv)
Constructor.

MultiVarPowerSeriesRing(RingFactory<C> coFac, int nv, int truncate)
Constructor.

MultiVarPowerSeriesRing(RingFactory<C> cofac, int nv, int truncate, java.lang.String[] names)
Constructor.

MultiVarPowerSeriesRing(RingFactory<C> cofac, int nv, java.lang.String[] names)
Constructor.

MultiVarPowerSeriesRing(RingFactory<C> coFac, java.lang.String[] names)
Constructor.

Method Summary

java.math.BigInteger	characteristic() Characteristic of this ring.
MultiVarPowerSeries<C>	copy(MultiVarPowerSeries<C> c) Copy power series.
boolean	equals(java.lang.Object B) Comparison with any other object.
MultiVarPowerSeries<C>	fixPoint(MultiVarPowerSeriesMap<C> map) Fixed point construction.
MultiVarPowerSeries<C>	fromInteger(java.math.BigInteger a) Get a (constant) MultiVarPowerSeries<C> from a java.math.BigInteger.
MultiVarPowerSeries<C>	fromInteger(long a) Get a (constant) MultiVarPowerSeries<C> from a long value.
MultiVarPowerSeries<C>	fromPolynomial(GenPolynomial<C> a) Get a MultiVarPowerSeries<C> from a GenPolynomial<C>.
java.util.List<MultiVarPowerSeries<C>>	fromPolynomial(java.util.List<GenPolynomial<C>> A) Get a list of MultiVarPowerSeries<C> from a list of GenPolynomial<C>.
MultiVarPowerSeries<C>	fromPowerSeries(UnivPowerSeries<C> ps, int r) Get a MultiVarPowerSeries<C> from a univariate power series.
java.util.List<MultiVarPowerSeries<C>>	generators() Get a list of the generating elements.
MultiVarPowerSeries<C>	getCOS(int r) Get the power series of the cosinus function.
MultiVarPowerSeries<C>	getEXP(int r) Get the power series of the exponential function.
MultiVarPowerSeries<C>	getONE() Get the one element.
MultiVarPowerSeries<C>	getSIN(int r) Get the power series of the sinus function.
MultiVarPowerSeries<C>	getTAN(int r) Get the power series of the tangens function.
java.lang.String[]	getVars() Get a variable names.
MultiVarPowerSeries<C>	getZERO() Get the zero element.
int	hashCode() Hash code for this .
boolean	isAssociative() Query if this ring is associative.
boolean	isCommutative() Query if this ring is commuative.
boolean	isField() Query if this ring is a field.
boolean	isFinite() Is this structure finite or infinite.
MultiVarPowerSeries<C>	parse(java.io.Reader r) Parse a power series.
MultiVarPowerSeries<C>	parse(java.lang.String s) Parse a power series.
GenPolynomialRing<C>	polyRing() Get the corresponding GenPolynomialRing<C>.
MultiVarPowerSeries<C>	random() Generate a random power series with k = 5, d = 0.7.
MultiVarPowerSeries<C>	random(int k) Generate a random power series with d = 0.7.
MultiVarPowerSeries<C>	random(int k, float d) Generate a random power series.
MultiVarPowerSeries<C>	random(int k, float d, java.util.Random rnd) Generate a random power series.
MultiVarPowerSeries<C>	random(int k, java.util.Random rnd) Generate a random power series with d = 0.7.
MultiVarPowerSeries<C>	seriesOfTaylor(TaylorFunction<C> f, java.util.List<C> a) Taylor power series.
int	setTruncate(int t) Set truncate.
MultiVarPowerSeries<C>	solvePDE(MultiVarPowerSeries<C> f, C c, int r) Solve an partial differential equation. y_r' = f(y_r) with y_r(0) = c.
java.lang.String	toScript() Get a scripting compatible string representation.
java.lang.String	toString() To String.
int	truncate() Truncate.
java.lang.String	varsToString() Get a String representation of the variable names.

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

EVZERO

public final ExpVector EVZERO

Zero ExpVector.

coFac

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

Coefficient ring factory.

nvar

public final int nvar

The number of variables.

vars

protected java.lang.String[] vars

The names of the variables. This value can be modified.

ONE

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

The constant power series 1 for this ring.

ZERO

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

The constant power series 0 for this ring.

Constructor Detail

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(GenPolynomialRing<C> fac)

Constructor.

Parameters:

fac - polynomial ring factory.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> coFac,
                               int nv)

Constructor.

Parameters:

coFac - coefficient ring factory.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> coFac,
                               int nv,
                               int truncate)

Constructor.

Parameters:

coFac - coefficient ring factory.

truncate - index of truncation.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> coFac,
                               java.lang.String[] names)

Constructor.

Parameters:

coFac - coefficient ring factory.

names - of the variables.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> cofac,
                               int nv,
                               java.lang.String[] names)

Constructor.

Parameters:

cofac - coefficient ring factory.

nv - number of variables.

names - of the variables.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> cofac,
                               int nv,
                               int truncate,
                               java.lang.String[] names)

Constructor.

Parameters:

cofac - coefficient ring factory.

truncate - index of truncation.

names - of the variables.

Method Detail

fixPoint

public MultiVarPowerSeries<C> fixPoint(MultiVarPowerSeriesMap<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.

varsToString

public java.lang.String varsToString()

Get a String representation of the variable names.

Returns:

names seperated by commas.

getVars

public java.lang.String[] getVars()

Get a variable names.

Returns:

names.

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<MultiVarPowerSeries<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 MultiVarPowerSeries<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as MultiVarPowerSeries.

getONE

public MultiVarPowerSeries<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as MultiVarPowerSeries.

generators

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

Get a list of the generating elements.

Specified by:

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

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

truncate

public int truncate()

Truncate.

Returns:

truncate index of power series.

setTruncate

public int setTruncate(int t)

Set truncate.

Parameters:

t - new truncate index.

Returns:

old truncate index of power series.

getEXP

public MultiVarPowerSeries<C> getEXP(int r)

Get the power series of the exponential function.

Parameters:

r - variable for the direction.

Returns:

exp(x_r) as MultiVarPowerSeries.

getSIN

public MultiVarPowerSeries<C> getSIN(int r)

Get the power series of the sinus function.

Parameters:

r - variable for the direction.

Returns:

sin(x_r) as MultiVarPowerSeries.

getCOS

public MultiVarPowerSeries<C> getCOS(int r)

Get the power series of the cosinus function.

Parameters:

r - variable for the direction.

Returns:

cos(x_r) as MultiVarPowerSeries.

getTAN

public MultiVarPowerSeries<C> getTAN(int r)

Get the power series of the tangens function.

Parameters:

r - variable for the direction.

Returns:

tan(x_r) as MultiVarPowerSeries.

solvePDE

public MultiVarPowerSeries<C> solvePDE(MultiVarPowerSeries<C> f,
                                       C c,
                                       int r)

Solve an partial differential equation. y_r' = f(y_r) with y_r(0) = c.

Parameters:

f - a MultiVarPowerSeries.

c - integration constant.

r - variable for the direction.

Returns:

f.integrate(c).

isCommutative

public boolean isCommutative()

Query if this ring is commuative.

Specified by:

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

Returns:

false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

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

Returns:

characteristic of this ring.

fromInteger

public MultiVarPowerSeries<C> fromInteger(long a)

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

Specified by:

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

Parameters:

a - long.

Returns:

a MultiVarPowerSeries<C>.

fromInteger

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

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

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a MultiVarPowerSeries<C>.

polyRing

public GenPolynomialRing<C> polyRing()

Get the corresponding GenPolynomialRing<C>.

Returns:

GenPolynomialRing<C>.

fromPolynomial

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

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

Parameters:

a - GenPolynomial<C>.

Returns:

a MultiVarPowerSeries<C>.

fromPolynomial

public java.util.List<MultiVarPowerSeries<C>> fromPolynomial(java.util.List<GenPolynomial<C>> A)

Get a list of MultiVarPowerSeries<C> from a list of GenPolynomial<C>.

Parameters:

A - list of GenPolynomial<C>.

Returns:

a list of MultiVarPowerSeries<C>.

fromPowerSeries

public MultiVarPowerSeries<C> fromPowerSeries(UnivPowerSeries<C> ps,
                                              int r)

Get a MultiVarPowerSeries<C> from a univariate power series.

Parameters:

ps - UnivPowerSeries<C>.

r - variable for the direction.

Returns:

a MultiVarPowerSeries<C>.

random

public MultiVarPowerSeries<C> random()

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

Returns:

a random power series.

random

public MultiVarPowerSeries<C> random(int k)

Generate a random power series with d = 0.7.

Specified by:

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

Parameters:

k - bit-size of random coefficients.

Returns:

a random power series.

random

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

Generate a random power series with d = 0.7.

Specified by:

random in interface ElemFactory<MultiVarPowerSeries<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 MultiVarPowerSeries<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 MultiVarPowerSeries<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 MultiVarPowerSeries<C> copy(MultiVarPowerSeries<C> c)

Copy power series.

Specified by:

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

Parameters:

c - a power series.

Returns:

a copy of c.

parse

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

Parse a power series. Note: not implemented.

Specified by:

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

Parameters:

s - String.

Returns:

power series from s.

parse

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

Parse a power series. Note: not implemented.

Specified by:

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

Parameters:

r - Reader.

Returns:

next power series from r.

seriesOfTaylor

public MultiVarPowerSeries<C> seriesOfTaylor(TaylorFunction<C> f,
                                             java.util.List<C> a)

Taylor power series.

Parameters:

f - function.

a - expansion point.

Returns:

Taylor series of f.