MultiVarPowerSeries

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

Type Parameters:

C - ring element type

All Implemented Interfaces:

AbelianGroupElem<MultiVarPowerSeries<C>>, Element<MultiVarPowerSeries<C>>, MonoidElem<MultiVarPowerSeries<C>>, RingElem<MultiVarPowerSeries<C>>, java.io.Serializable, java.lang.Comparable<MultiVarPowerSeries<C>>
```
public class MultiVarPowerSeries<C extends RingElem<C>>
extends java.lang.Object
implements RingElem<MultiVarPowerSeries<C>>
```
Multivariate 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 methods which use the order() or orderExpVector() methods, like signum(), abs(), divide(), remainder() and gcd(). Note: Currently the term order is fixed to the order defined by the iterator over exponent vectors in class ExpVectorIterator.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

MultiVarPowerSeriesRing<C> ring
Power series ring factory.

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

Constructor Summary

Constructors
Constructor and Description
`MultiVarPowerSeries(MultiVarPowerSeriesRing<C> ring, MultiVarCoefficients<C> lazyCoeffs)` Constructor.
`MultiVarPowerSeries(MultiVarPowerSeriesRing<C> ring, MultiVarCoefficients<C> lazyCoeffs, int trunc)` Constructor.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`MultiVarPowerSeries<C>`	`abs()` Absolute value.
`GenPolynomial<C>`	`asPolynomial()` Get a GenPolynomial<C> from this.
`C`	`coefficient(ExpVector index)` Get coefficient.
`int`	`compareTo(MultiVarPowerSeries<C> ps)` Compare to.
`MultiVarPowerSeries<C>`	`copy()` Clone this power series.
`MultiVarPowerSeries<C>`	`differentiate(int r)` Differentiate with respect to variable r.
`MultiVarPowerSeries<C>`	`divide(MultiVarPowerSeries<C> ps)` Divide by another power series.
`long`	`ecart()` Ecart.
`MultiVarPowerSeries<C>[]`	`egcd(MultiVarPowerSeries<C> S)` Power series extended greatest common divisor.
`boolean`	`equals(java.lang.Object B)` Comparison with any other object.
`C`	`evaluate(java.util.List<C> a)` Evaluate at given point.
`MultiVarPowerSeriesRing<C>`	`factory()` Get the corresponding element factory.
`MultiVarPowerSeries<C>`	`gcd(MultiVarPowerSeries<C> ps)` Power series greatest common divisor.
`int`	`hashCode()` Hash code for this polynomial.
`GenPolynomial<C>`	`homogeneousPart(long tdeg)` Homogeneous part.
`MultiVarPowerSeries<C>`	`integrate(C c, int r)` Integrate with respect to variable r and with given constant.
`MultiVarPowerSeries<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.
`MultiVarPowerSeries<C>`	`map(UnaryFunctor<? super C,C> f)` Map a unary function to this power series.
`MultiVarPowerSeries<C>`	`monic()` Monic.
`MultiVarPowerSeries<C>`	`multiply(C a)` Multiply by coefficient.
`MultiVarPowerSeries<C>`	`multiply(C c, ExpVector k)` Multiply by exponent vector and coefficient.
`MultiVarPowerSeries<C>`	`multiply(MultiVarPowerSeries<C> ps)` Multiply by another power series.
`MultiVarPowerSeries<C>`	`negate()` Negate.
`int`	`order()` Order.
`ExpVector`	`orderExpVector()` Order ExpVector.
`java.util.Map.Entry<ExpVector,C>`	`orderMonomial()` Order monomial.
`MultiVarPowerSeries<C>`	`prepend(C h, int r)` Prepend a new leading coefficient.
`MultiVarPowerSeries<C>[]`	`quotientRemainder(MultiVarPowerSeries<C> S)` Quotient and remainder by division of this by S.
`MultiVarPowerSeries<C>`	`reductum()` Reductum.
`MultiVarPowerSeries<C>`	`reductum(int r)` Reductum.
`MultiVarPowerSeries<C>`	`remainder(MultiVarPowerSeries<C> ps)` Power series remainder.
`MultiVarPowerSeries<C>`	`select(Selector<? super C> sel)` Select coefficients.
`int`	`setTruncate(int t)` Set truncate.
`MultiVarPowerSeries<C>`	`shift(ExpVector k)` Shift coefficients.
`MultiVarPowerSeries<C>`	`shift(int k, int r)` Shift coefficients.
`MultiVarPowerSeries<C>`	`shiftSelect(Selector<? super C> sel)` Shift select coefficients.
`int`	`signum()` Signum.
`MultiVarPowerSeries<C>`	`subtract(C c, ExpVector k)` Subtract exponent vector and coefficient.
`MultiVarPowerSeries<C>`	`subtract(MultiVarPowerSeries<C> ps)` Subtract a another power series.
`MultiVarPowerSeries<C>`	`subtractZip(MultiVarPowerSeries<C> ps)` Subtraction of two power series, using zip().
`MultiVarPowerSeries<C>`	`sum(C c, ExpVector k)` Sum exponent vector and coefficient.
`MultiVarPowerSeries<C>`	`sum(java.util.Map.Entry<ExpVector,C> m)` Sum monomial.
`MultiVarPowerSeries<C>`	`sum(MultiVarCoefficients<C> mvc)` Sum exponent vector and coefficient.
`MultiVarPowerSeries<C>`	`sum(MultiVarPowerSeries<C> ps)` Sum a another power series.
`MultiVarPowerSeries<C>`	`sumZip(MultiVarPowerSeries<C> ps)` Sum of two power series, using zip().
`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 trunc)` To String with given truncate.
`int`	`truncate()` Truncate.
`MultiVarPowerSeries<C>`	`zip(BinaryFunctor<? super C,? super C,C> f, MultiVarPowerSeries<C> 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

- Field Detail
  - ring
```
public final MultiVarPowerSeriesRing<C extends RingElem<C>> ring
```
    Power series ring factory.
- Constructor Detail
  - MultiVarPowerSeries
```
public MultiVarPowerSeries(MultiVarPowerSeriesRing<C> ring,
                           MultiVarCoefficients<C> lazyCoeffs)
```
    Constructor.
    
    Parameters:
    
    ring - power series ring.
    
    lazyCoeffs - generating function for coefficients.
  - MultiVarPowerSeries
```
public MultiVarPowerSeries(MultiVarPowerSeriesRing<C> ring,
                           MultiVarCoefficients<C> lazyCoeffs,
                           int trunc)
```
    Constructor.
    
    Parameters:
    
    ring - power series ring.
    
    lazyCoeffs - generating function for coefficients.
    
    trunc - truncate parameter for this power series.
- Method Detail
  - factory
```
public MultiVarPowerSeriesRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - copy
```
public MultiVarPowerSeries<C> copy()
```
    Clone this power series.
    
    Specified by:
    
    copy in interface Element<MultiVarPowerSeries<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 trunc)
```
    To String with given truncate.
    
    Parameters:
    
    trunc - truncate parameter for this power series.
    
    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<MultiVarPowerSeries<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<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - coefficient
```
public C coefficient(ExpVector index)
```
    Get coefficient.
    
    Parameters:
    
    index - number of requested coefficient.
    
    Returns:
    
    coefficient at index.
  - homogeneousPart
```
public GenPolynomial<C> homogeneousPart(long tdeg)
```
    Homogeneous part.
    
    Parameters:
    
    tdeg - requested degree.
    
    Returns:
    
    polynomial part of given degree.
  - asPolynomial
```
public GenPolynomial<C> asPolynomial()
```
    Get a GenPolynomial<C> from this.
    
    Returns:
    
    a GenPolynomial<C> from this up to truncate homogeneous parts.
  - leadingCoefficient
```
public C leadingCoefficient()
```
    Leading base coefficient.
    
    Returns:
    
    first coefficient.
  - reductum
```
public MultiVarPowerSeries<C> reductum(int r)
```
    Reductum.
    
    Parameters:
    
    r - variable for taking the reductum.
    
    Returns:
    
    this - leading monomial in the direction of r.
  - prepend
```
public MultiVarPowerSeries<C> prepend(C h,
                                      int r)
```
    Prepend a new leading coefficient.
    
    Parameters:
    
    r - variable for the direction.
    
    h - new coefficient.
    
    Returns:
    
    new power series.
  - shift
```
public MultiVarPowerSeries<C> shift(int k,
                                    int r)
```
    Shift coefficients.
    
    Parameters:
    
    k - shift index.
    
    r - variable for the direction.
    
    Returns:
    
    new power series with coefficient(i) = old.coefficient(i-k).
  - reductum
```
public MultiVarPowerSeries<C> reductum()
```
    Reductum.
    
    Returns:
    
    this - leading monomial.
  - shift
```
public MultiVarPowerSeries<C> shift(ExpVector k)
```
    Shift coefficients. Multiply by exponent vector.
    
    Parameters:
    
    k - shift ExpVector.
    
    Returns:
    
    new power series with coefficient(i) = old.coefficient(i-k).
  - multiply
```
public MultiVarPowerSeries<C> multiply(C c,
                                       ExpVector k)
```
    Multiply by exponent vector and coefficient.
    
    Parameters:
    
    k - shift ExpVector.
    
    c - coefficient multiplier.
    
    Returns:
    
    new power series with coefficient(i) = old.coefficient(i-k)*c.
  - sum
```
public MultiVarPowerSeries<C> sum(java.util.Map.Entry<ExpVector,C> m)
```
    Sum monomial.
    
    Parameters:
    
    m - ExpVector , coeffcient pair
    
    Returns:
    
    this + ONE.multiply(m.coefficient,m.exponent).
  - sum
```
public MultiVarPowerSeries<C> sum(C c,
                                  ExpVector k)
```
    Sum exponent vector and coefficient.
    
    Parameters:
    
    k - ExpVector.
    
    c - coefficient.
    
    Returns:
    
    this + ONE.multiply(c,k).
  - subtract
```
public MultiVarPowerSeries<C> subtract(C c,
                                       ExpVector k)
```
    Subtract exponent vector and coefficient.
    
    Parameters:
    
    k - ExpVector.
    
    c - coefficient.
    
    Returns:
    
    this - ONE.multiply(c,k).
  - sum
```
public MultiVarPowerSeries<C> sum(MultiVarCoefficients<C> mvc)
```
    Sum exponent vector and coefficient.
    
    Parameters:
    
    mvc - cached coefficients.
    
    Returns:
    
    this + mvc.
  - select
```
public MultiVarPowerSeries<C> select(Selector<? super C> sel)
```
    Select coefficients.
    
    Parameters:
    
    sel - selector functor.
    
    Returns:
    
    new power series with selected coefficients.
  - shiftSelect
```
public MultiVarPowerSeries<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 MultiVarPowerSeries<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 MultiVarPowerSeries<C> zip(BinaryFunctor<? super C,? super C,C> f,
                                  MultiVarPowerSeries<C> 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.
  - sumZip
```
public MultiVarPowerSeries<C> sumZip(MultiVarPowerSeries<C> ps)
```
    Sum of two power series, using zip().
    
    Parameters:
    
    ps - other power series.
    
    Returns:
    
    this + ps.
  - subtractZip
```
public MultiVarPowerSeries<C> subtractZip(MultiVarPowerSeries<C> ps)
```
    Subtraction of two power series, using zip().
    
    Parameters:
    
    ps - other power series.
    
    Returns:
    
    this - ps.
  - multiply
```
public MultiVarPowerSeries<C> multiply(C a)
```
    Multiply by coefficient.
    
    Parameters:
    
    a - coefficient.
    
    Returns:
    
    this * a.
  - monic
```
public MultiVarPowerSeries<C> monic()
```
    Monic.
    
    Returns:
    
    1/orderCoeff() * this.
  - negate
```
public MultiVarPowerSeries<C> negate()
```
    Negate.
    
    Specified by:
    
    negate in interface AbelianGroupElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    - this.
  - abs
```
public MultiVarPowerSeries<C> abs()
```
    Absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    abs(this).
  - evaluate
```
public C evaluate(java.util.List<C> a)
```
    Evaluate at given point.
    
    Returns:
    
    ps(a).
  - order
```
public int order()
```
    Order.
    
    Returns:
    
    index of first non zero coefficient.
  - orderExpVector
```
public ExpVector orderExpVector()
```
    Order ExpVector.
    
    Returns:
    
    ExpVector of first non zero coefficient.
  - orderMonomial
```
public java.util.Map.Entry<ExpVector,C> orderMonomial()
```
    Order monomial.
    
    Returns:
    
    first map entry or null.
  - 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.
  - ecart
```
public long ecart()
```
    Ecart.
    
    Returns:
    
    ecart.
  - signum
```
public int signum()
```
    Signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    sign of first non zero coefficient.
  - compareTo
```
public int compareTo(MultiVarPowerSeries<C> ps)
```
    Compare to. Note: compare only up to max(truncates).
    
    Specified by:
    
    compareTo in interface Element<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<MultiVarPowerSeries<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<MultiVarPowerSeries<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<MultiVarPowerSeries<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<MultiVarPowerSeries<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<MultiVarPowerSeries<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<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    true, if this power series is invertible, else false.
  - sum
```
public MultiVarPowerSeries<C> sum(MultiVarPowerSeries<C> ps)
```
    Sum a another power series.
    
    Specified by:
    
    sum in interface AbelianGroupElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - other power series.
    
    Returns:
    
    this + ps.
  - subtract
```
public MultiVarPowerSeries<C> subtract(MultiVarPowerSeries<C> ps)
```
    Subtract a another power series.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - other power series.
    
    Returns:
    
    this - ps.
  - multiply
```
public MultiVarPowerSeries<C> multiply(MultiVarPowerSeries<C> ps)
```
    Multiply by another power series.
    
    Specified by:
    
    multiply in interface MonoidElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - other power series.
    
    Returns:
    
    this * ps.
  - inverse
```
public MultiVarPowerSeries<C> inverse()
```
    Inverse power series.
    
    Specified by:
    
    inverse in interface MonoidElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Returns:
    
    ps with this * ps = 1.
  - divide
```
public MultiVarPowerSeries<C> divide(MultiVarPowerSeries<C> ps)
```
    Divide by another power series.
    
    Specified by:
    
    divide in interface MonoidElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - nonzero power series with invertible coefficient.
    
    Returns:
    
    this / ps.
  - remainder
```
public MultiVarPowerSeries<C> remainder(MultiVarPowerSeries<C> ps)
```
    Power series remainder.
    
    Specified by:
    
    remainder in interface MonoidElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - nonzero power series with invertible leading coefficient.
    
    Returns:
    
    remainder with this = quotient * ps + remainder.
  - quotientRemainder
```
public MultiVarPowerSeries<C>[] quotientRemainder(MultiVarPowerSeries<C> S)
```
    Quotient and remainder by division of this by S.
    
    Parameters:
    
    S - a MultiVarPowerSeries
    
    Returns:
    
    [this/S, this - (this/S)*S].
  - differentiate
```
public MultiVarPowerSeries<C> differentiate(int r)
```
    Differentiate with respect to variable r.
    
    Parameters:
    
    r - variable for the direction.
    
    Returns:
    
    differentiate(this).
  - integrate
```
public MultiVarPowerSeries<C> integrate(C c,
                                        int r)
```
    Integrate with respect to variable r and with given constant.
    
    Parameters:
    
    c - integration constant.
    
    r - variable for the direction.
    
    Returns:
    
    integrate(this).
  - gcd
```
public MultiVarPowerSeries<C> gcd(MultiVarPowerSeries<C> ps)
```
    Power series greatest common divisor.
    
    Specified by:
    
    gcd in interface RingElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    ps - power series.
    
    Returns:
    
    gcd(this,ps).
  - egcd
```
public MultiVarPowerSeries<C>[] egcd(MultiVarPowerSeries<C> S)
```
    Power series extended greatest common divisor. Note: not implemented.
    
    Specified by:
    
    egcd in interface RingElem<MultiVarPowerSeries<C extends RingElem<C>>>
    
    Parameters:
    
    S - power series.
    
    Returns:
    
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).

Class MultiVarPowerSeries<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

Constructor Detail

MultiVarPowerSeries

MultiVarPowerSeries

Method Detail

factory

copy

toString

toString

toScript

toScriptFactory

coefficient

homogeneousPart

asPolynomial

leadingCoefficient

reductum

prepend

shift

reductum

shift

multiply

sum

sum

subtract

sum

select

shiftSelect

map

zip

sumZip

subtractZip

multiply

monic

negate

abs

evaluate

order

orderExpVector

orderMonomial

truncate

setTruncate

ecart

signum

compareTo

isZERO

isONE

equals

hashCode

isUnit

sum

subtract

multiply

inverse

divide

remainder

quotientRemainder

differentiate

integrate

gcd

egcd