UnivPowerSeries

java.lang.Object
- edu.jas.ps.UnivPowerSeries<C>

Type Parameters:

C - ring element type

All Implemented Interfaces:

AbelianGroupElem<UnivPowerSeries<C>>, Element<UnivPowerSeries<C>>, MonoidElem<UnivPowerSeries<C>>, RingElem<UnivPowerSeries<C>>, java.io.Serializable, java.lang.Comparable<UnivPowerSeries<C>>
```
public class UnivPowerSeries<C extends RingElem<C>>
extends java.lang.Object
implements RingElem<UnivPowerSeries<C>>
```
Univariate power series implementation. Uses inner classes and lazy evaluated generating function for coefficients. All ring element methods use lazy evaluation except where noted otherwise. Eager evaluated methods are toString(), compareTo(), equals(), evaluate(), or they use the order() method, like signum(), abs(), divide(), remainder() and gcd().

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

UnivPowerSeriesRing<C> ring
Power series ring factory.

Fields
Modifier and Type	Field and Description
`UnivPowerSeriesRing<C>`	`ring` Power series ring factory.

Constructor Summary

Constructors
Constructor and Description

UnivPowerSeries(UnivPowerSeriesRing<C> ring, Coefficients<C> lazyCoeffs)
Constructor.

Constructors
Constructor and Description
`UnivPowerSeries(UnivPowerSeriesRing<C> ring, Coefficients<C> lazyCoeffs)` Constructor.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`UnivPowerSeries<C>`	`abs()` Absolute value.
`GenPolynomial<C>`	`asPolynomial()` Get a GenPolynomial<C> from this.
`C`	`coefficient(int index)` Get coefficient.
`int`	`compareTo(UnivPowerSeries<C> ps)` Compare to.
`UnivPowerSeries<C>`	`copy()` Clone this power series.
`UnivPowerSeries<C>`	`differentiate()` Differentiate.
`UnivPowerSeries<C>`	`divide(UnivPowerSeries<C> ps)` Divide by another power series.
`UnivPowerSeries<C>[]`	`egcd(UnivPowerSeries<C> S)` Power series extended greatest common divisor.
`boolean`	`equals(java.lang.Object B)` Comparison with any other object.
`C`	`evaluate(C e)` Evaluate at given point.
`UnivPowerSeriesRing<C>`	`factory()` Get the corresponding element factory.
`UnivPowerSeries<C>`	`gcd(UnivPowerSeries<C> ps)` Power series greatest common divisor.
`int`	`hashCode()` Hash code for this polynomial.
`UnivPowerSeries<C>`	`integrate(C c)` Integrate with given constant.
`UnivPowerSeries<C>`	`inverse()` Inverse power series.
`boolean`	`isONE()` Is power series one.
`boolean`	`isUnit()` Is unit.
`boolean`	`isZERO()` Is power series zero.
`C`	`leadingCoefficient()` Leading base coefficient.
`UnivPowerSeries<C>`	`map(UnaryFunctor<? super C,C> f)` Map a unary function to this power series.
`UnivPowerSeries<C>`	`monic()` Monic.
`UnivPowerSeries<C>`	`multiply(C c)` Multiply by coefficient.
`UnivPowerSeries<C>`	`multiply(UnivPowerSeries<C> ps)` Multiply by another power series.
`UnivPowerSeries<C>`	`negate()` Negate.
`int`	`order()` Order.
`UnivPowerSeries<C>`	`prepend(C h)` Prepend a new leading coefficient.
`UnivPowerSeries<C>[]`	`quotientRemainder(UnivPowerSeries<C> S)` Quotient and remainder by division of this by S.
`UnivPowerSeries<C>`	`reductum()` Reductum.
`UnivPowerSeries<C>`	`remainder(UnivPowerSeries<C> ps)` Power series remainder.
`UnivPowerSeries<C>`	`select(Selector<? super C> sel)` Select coefficients.
`int`	`setTruncate(int t)` Set truncate.
`UnivPowerSeries<C>`	`shift(int k)` Shift coefficients.
`UnivPowerSeries<C>`	`shiftSelect(Selector<? super C> sel)` Shift select coefficients.
`int`	`signum()` Signum.
`UnivPowerSeries<C>`	`subtract(UnivPowerSeries<C> ps)` Subtraction of two power series.
`UnivPowerSeries<C>`	`sum(UnivPowerSeries<C> ps)` Sum of two power series.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toScriptFactory()` Get a scripting compatible string representation of the factory.
`java.lang.String`	`toString()` String representation of power series.
`java.lang.String`	`toString(int truncate)` To String with given truncate.
`int`	`truncate()` Truncate.
`<C2 extends RingElem<C2>> UnivPowerSeries<C>`	`zip(BinaryFunctor<? super C,? super C2,C> f, UnivPowerSeries<C2> ps)` Map a binary function to this and another power series.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface edu.jas.structure.RingElem
leftGcd, rightGcd

Methods inherited from interface edu.jas.structure.MonoidElem
leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

- Field Detail
  - ring
```
public final UnivPowerSeriesRing<C extends RingElem<C>> ring
```
    Power series ring factory.
- Constructor Detail
  - UnivPowerSeries
```
public UnivPowerSeries(UnivPowerSeriesRing<C> ring,
                       Coefficients<C> lazyCoeffs)
```
    Constructor.
    
    Parameters:
    
    ring - power series ring.
    
    lazyCoeffs - generating function for coefficients.
- Method Detail
  - factory
```
public UnivPowerSeriesRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - copy
```
public UnivPowerSeries<C> copy()
```
    Clone this power series.
    
    Specified by:
    
    copy in interface Element<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    Creates and returns a copy of this Element.
    
    See Also:
    
    Object.clone()
  - toString
```
public java.lang.String toString()
```
    String representation of power series.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - toString
```
public java.lang.String toString(int truncate)
```
    To String with given truncate.
    
    Returns:
    
    string representation of this to given truncate.
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Specified by:
    
    toScript in interface Element<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    script compatible representation for this Element.
    
    See Also:
    
    Element.toScript()
  - toScriptFactory
```
public java.lang.String toScriptFactory()
```
    Get a scripting compatible string representation of the factory.
    
    Specified by:
    
    toScriptFactory in interface Element<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - coefficient
```
public C coefficient(int index)
```
    Get coefficient.
    
    Parameters:
    
    index - number of requested coefficient.
    
    Returns:
    
    coefficient at index.
  - asPolynomial
```
public GenPolynomial<C> asPolynomial()
```
    Get a GenPolynomial<C> from this.
    
    Returns:
    
    a GenPolynomial<C> from this up to truncate parts.
  - leadingCoefficient
```
public C leadingCoefficient()
```
    Leading base coefficient.
    
    Returns:
    
    first coefficient.
  - reductum
```
public UnivPowerSeries<C> reductum()
```
    Reductum.
    
    Returns:
    
    this - leading monomial.
  - prepend
```
public UnivPowerSeries<C> prepend(C h)
```
    Prepend a new leading coefficient.
    
    Parameters:
    
    h - new coefficient.
    
    Returns:
    
    new power series.
  - shift
```
public UnivPowerSeries<C> shift(int k)
```
    Shift coefficients.
    
    Parameters:
    
    k - shift index.
    
    Returns:
    
    new power series with coefficient(i) = old.coefficient(i-k).
  - select
```
public UnivPowerSeries<C> select(Selector<? super C> sel)
```
    Select coefficients.
    
    Parameters:
    
    sel - selector functor.
    
    Returns:
    
    new power series with selected coefficients.
  - shiftSelect
```
public UnivPowerSeries<C> shiftSelect(Selector<? super C> sel)
```
    Shift select coefficients. Not selected coefficients are removed from the result series.
    
    Parameters:
    
    sel - selector functor.
    
    Returns:
    
    new power series with shifted selected coefficients.
  - map
```
public UnivPowerSeries<C> map(UnaryFunctor<? super C,C> f)
```
    Map a unary function to this power series.
    
    Parameters:
    
    f - evaluation functor.
    
    Returns:
    
    new power series with coefficients f(this(i)).
  - zip
```
public <C2 extends RingElem<C2>> UnivPowerSeries<C> zip(BinaryFunctor<? super C,? super C2,C> f,
                                                        UnivPowerSeries<C2> ps)
```
    Map a binary function to this and another power series.
    
    Parameters:
    
    f - evaluation functor with coefficients f(this(i),other(i)).
    
    ps - other power series.
    
    Returns:
    
    new power series.
  - sum
```
public UnivPowerSeries<C> sum(UnivPowerSeries<C> ps)
```
    Sum of two power series.
    
    Specified by:
    
    sum in interface AbelianGroupElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - other power series.
    
    Returns:
    
    this + ps.
  - subtract
```
public UnivPowerSeries<C> subtract(UnivPowerSeries<C> ps)
```
    Subtraction of two power series.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - other power series.
    
    Returns:
    
    this - ps.
  - multiply
```
public UnivPowerSeries<C> multiply(C c)
```
    Multiply by coefficient.
    
    Parameters:
    
    c - coefficient.
    
    Returns:
    
    this * c.
  - monic
```
public UnivPowerSeries<C> monic()
```
    Monic.
    
    Returns:
    
    1/orderCoeff() * this.
  - negate
```
public UnivPowerSeries<C> negate()
```
    Negate.
    
    Specified by:
    
    negate in interface AbelianGroupElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    - this.
  - abs
```
public UnivPowerSeries<C> abs()
```
    Absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    abs(this).
  - evaluate
```
public C evaluate(C e)
```
    Evaluate at given point.
    
    Returns:
    
    ps(c).
  - order
```
public int order()
```
    Order.
    
    Returns:
    
    index of first non zero coefficient.
  - 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.
  - signum
```
public int signum()
```
    Signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    sign of first non zero coefficient.
  - compareTo
```
public int compareTo(UnivPowerSeries<C> ps)
```
    Compare to. Note: compare only up to truncate.
    
    Specified by:
    
    compareTo in interface Element<UnivPowerSeries<C extends RingElem<C>>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    sign of first non zero coefficient of this-ps.
  - isZERO
```
public boolean isZERO()
```
    Is power series zero. Note: compare only up to truncate.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    If this is 0 then true is returned, else false.
    
    See Also:
    
    AbelianGroupElem.isZERO()
  - isONE
```
public boolean isONE()
```
    Is power series one. Note: compare only up to truncate.
    
    Specified by:
    
    isONE in interface MonoidElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    If this is 1 then true is returned, else false.
    
    See Also:
    
    MonoidElem.isONE()
  - equals
```
public boolean equals(java.lang.Object B)
```
    Comparison with any other object. Note: compare only up to truncate.
    
    Specified by:
    
    equals in interface Element<UnivPowerSeries<C extends RingElem<C>>>
    
    Overrides:
    
    equals in class java.lang.Object
    
    Returns:
    
    true if this is equal to b, else false.
    
    See Also:
    
    Object.equals(java.lang.Object)
  - hashCode
```
public int hashCode()
```
    Hash code for this polynomial. Note: only up to truncate.
    
    Specified by:
    
    hashCode in interface Element<UnivPowerSeries<C extends RingElem<C>>>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
    
    See Also:
    
    Object.hashCode()
  - isUnit
```
public boolean isUnit()
```
    Is unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    true, if this power series is invertible, else false.
  - multiply
```
public UnivPowerSeries<C> multiply(UnivPowerSeries<C> ps)
```
    Multiply by another power series.
    
    Specified by:
    
    multiply in interface MonoidElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    this * ps.
  - inverse
```
public UnivPowerSeries<C> inverse()
```
    Inverse power series.
    
    Specified by:
    
    inverse in interface MonoidElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    ps with this * ps = 1.
  - divide
```
public UnivPowerSeries<C> divide(UnivPowerSeries<C> ps)
```
    Divide by another power series.
    
    Specified by:
    
    divide in interface MonoidElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    this / ps.
  - remainder
```
public UnivPowerSeries<C> remainder(UnivPowerSeries<C> ps)
```
    Power series remainder.
    
    Specified by:
    
    remainder in interface MonoidElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - nonzero power series with invertible leading coefficient.
    
    Returns:
    
    remainder with this = quotient * ps + remainder.
  - quotientRemainder
```
public UnivPowerSeries<C>[] quotientRemainder(UnivPowerSeries<C> S)
```
    Quotient and remainder by division of this by S.
    
    Specified by:
    
    quotientRemainder in interface MonoidElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    S - a UnivPowerSeries
    
    Returns:
    
    [this/S, this - (this/S)*S].
  - differentiate
```
public UnivPowerSeries<C> differentiate()
```
    Differentiate.
    
    Returns:
    
    differentiate(this).
  - integrate
```
public UnivPowerSeries<C> integrate(C c)
```
    Integrate with given constant.
    
    Parameters:
    
    c - integration constant.
    
    Returns:
    
    integrate(this).
  - gcd
```
public UnivPowerSeries<C> gcd(UnivPowerSeries<C> ps)
```
    Power series greatest common divisor.
    
    Specified by:
    
    gcd in interface RingElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - power series.
    
    Returns:
    
    gcd(this,ps).
  - egcd
```
public UnivPowerSeries<C>[] egcd(UnivPowerSeries<C> S)
```
    Power series extended greatest common divisor. Note: not implemented.
    
    Specified by:
    
    egcd in interface RingElem<UnivPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    S - power series.
    
    Returns:
    
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).

Class UnivPowerSeries<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface edu.jas.structure.RingElem

Methods inherited from interface edu.jas.structure.MonoidElem

Field Detail

ring

Constructor Detail

UnivPowerSeries

Method Detail

factory

copy

toString

toString

toScript

toScriptFactory

coefficient

asPolynomial

leadingCoefficient

reductum

prepend

shift

select

shiftSelect

map

zip

sum

subtract

multiply

monic

negate

abs

evaluate

order

truncate

setTruncate

signum

compareTo

isZERO

isONE

equals

hashCode

isUnit

multiply

inverse

divide

remainder

quotientRemainder

differentiate

integrate

gcd

egcd