Package edu.jas.ps

Class MultiVarPowerSeries<C extends RingElem<C>>

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	Description
MultiVarPowerSeriesRing<C>	ring	Power series ring factory.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	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(int k, int r)	Shift coefficients.
MultiVarPowerSeries<C>	shift(ExpVector k)	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(MultiVarCoefficients<C> mvc)	Sum exponent vector and coefficient.
MultiVarPowerSeries<C>	sum(MultiVarPowerSeries<C> ps)	Sum a another power series.
MultiVarPowerSeries<C>	sum(java.util.Map.Entry<ExpVector,C> m)	Sum monomial.
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

Methods inherited from interface edu.jas.structure.MonoidElem

leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

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<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<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<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<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.

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(int r)

Reductum.

Parameters:

r - variable for taking the reductum.

Returns:

this - leading monomial in the direction of r.

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 , coefficient 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<C extends RingElem<C>>

Returns:

- this.

abs

public MultiVarPowerSeries<C> abs()

Absolute value.

Specified by:

abs in interface AbelianGroupElem<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<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 java.lang.Comparable<C extends RingElem<C>>

Specified by:

compareTo in interface Element<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<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<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<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<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<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<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<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<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<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<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<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.

Specified by:

quotientRemainder in interface MonoidElem<C extends RingElem<C>>

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<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<C extends RingElem<C>>

Parameters:

S - power series.

Returns:

[ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).