MultiVarPowerSeriesRing

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

Fields
Modifier and Type	Field and Description
`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

Constructors
Constructor and Description
`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

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`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.
`MultiVarPowerSeries<C>`	`generate(java.util.function.Function<ExpVector,C> gener)` Generate a power series via lambda expression.
`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 the 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 separated by commas.
  - getVars
```
public java.lang.String[] getVars()
```
    Get the 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:
    
    true if this ring is a field, else 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.
  - generate
```
public MultiVarPowerSeries<C> generate(java.util.function.Function<ExpVector,C> gener)
```
    Generate a power series via lambda expression.
    
    Parameters:
    
    gener - lambda expression.
    
    Returns:
    
    a generated 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.

Class MultiVarPowerSeriesRing<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

random

DEFAULT_TRUNCATE

EVZERO

coFac

nvar

vars

ONE

ZERO

Constructor Detail

MultiVarPowerSeriesRing

MultiVarPowerSeriesRing

MultiVarPowerSeriesRing

MultiVarPowerSeriesRing

MultiVarPowerSeriesRing

MultiVarPowerSeriesRing

Method Detail

fixPoint

toString

varsToString

getVars

toScript

equals

hashCode

getZERO

getONE

generators

isFinite

truncate

setTruncate

getEXP

getSIN

getCOS

getTAN

solvePDE

isCommutative

isAssociative

isField

characteristic

fromInteger

fromInteger

polyRing

fromPolynomial

fromPolynomial

fromPowerSeries

random

random

random

random

random

generate

copy

parse

parse

seriesOfTaylor