Package edu.jas.poly

Class GenExteriorPolynomial<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.GenExteriorPolynomial<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

AbelianGroupElem<GenExteriorPolynomial<C>>, Element<GenExteriorPolynomial<C>>, MonoidElem<GenExteriorPolynomial<C>>, RingElem<GenExteriorPolynomial<C>>, java.io.Serializable, java.lang.Comparable<GenExteriorPolynomial<C>>, java.lang.Iterable<IndexListMonomial<C>>

public final class GenExteriorPolynomial<C extends RingElem<C>>
extends java.lang.Object
implements RingElem<GenExteriorPolynomial<C>>, java.lang.Iterable<IndexListMonomial<C>>

GenExteriorPolynomial generic polynomials implementing RingElem. Antisymmetric polynomials (in fact vectors) over C. Objects of this class are intended to be immutable. The implementation is based on TreeMap respectively SortedMap from index lists to coefficients. Only the coefficients are modeled with generic types, the "exponents" are fixed to IndexList. C can also be a non integral domain, e.g. a ModInteger, i.e. it may contain zero divisors, since multiply() does check for zero coefficients and index lists.

Author:

Heinz Kredel

See Also:

"masnc.DIPE.mi#EIVEPR from SAC2/MAS", Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
GenExteriorPolynomialRing<C>	ring	The factory for the polynomial ring.

Constructor Summary

Constructors

Modifier	Constructor	Description
	GenExteriorPolynomial(GenExteriorPolynomialRing<C> r)	Constructor for zero GenExteriorPolynomial.
	GenExteriorPolynomial(GenExteriorPolynomialRing<C> r, C c)	Constructor for GenExteriorPolynomial c * x0.
	GenExteriorPolynomial(GenExteriorPolynomialRing<C> r, C c, ExpVector e)	Constructor for GenExteriorPolynomial c * xe.
	GenExteriorPolynomial(GenExteriorPolynomialRing<C> r, C c, IndexList e)	Constructor for GenExteriorPolynomial c * xe.
	GenExteriorPolynomial(GenExteriorPolynomialRing<C> r, ExpVector e)	Constructor for GenExteriorPolynomial xe.
	GenExteriorPolynomial(GenExteriorPolynomialRing<C> r, IndexList e)	Constructor for GenExteriorPolynomial xe.
protected	GenExteriorPolynomial(GenExteriorPolynomialRing<C> r, java.util.SortedMap<IndexList,C> v)	Constructor for GenExteriorPolynomial.

Method Summary

Modifier and Type	Method	Description
GenExteriorPolynomial<C>	abs()	GenExteriorPolynomial absolute value, i.e. leadingCoefficient > 0.
C	coefficient(IndexList e)	Coefficient.
java.util.Iterator<C>	coefficientIterator()	Iterator over coefficients.
GenExteriorPolynomial<C>	coeffPrimitivePart()	GenExteriorPolynomial coefficient primitive part.
int	compareTo(GenExteriorPolynomial<C> b)	GenExteriorPolynomial comparison.
GenExteriorPolynomial<C>	copy()	Copy this GenExteriorPolynomial.
long	degree()	Index degree.
GenExteriorPolynomial<C>	divide(C s)	GenExteriorPolynomial division.
GenExteriorPolynomial<C>	divide(GenExteriorPolynomial<C> S)	GenExteriorPolynomial division.
void	doPutToMap(IndexList e, C c)	Put a IndexList to coefficient entry into the internal map of this GenExteriorPolynomial.
void	doPutToMap(java.util.SortedMap<IndexList,C> vals)	Put an a sorted map of index list to coefficients into the internal map of this GenExteriorPolynomial.
void	doRemoveFromMap(IndexList e, C c)	Remove a IndexList to coefficient entry from the internal map of this GenExteriorPolynomial.
GenExteriorPolynomial<C>[]	egcd(GenExteriorPolynomial<C> S)	GenExteriorPolynomial extended greatest common divisor.
boolean	equals(java.lang.Object B)	Comparison with any other object.
GenExteriorPolynomialRing<C>	factory()	Get the corresponding element factory.
GenExteriorPolynomial<C>	form(long k)	k-form part.
GenExteriorPolynomial<C>	gcd(GenExteriorPolynomial<C> S)	GenExteriorPolynomial greatest common divisor.
java.util.SortedMap<IndexList,C>	getMap()	IndexList to coefficient map of GenExteriorPolynomial.
int	hashCode()	Hash code for this polynomial.
GenExteriorPolynomial<C>	homogeneousPart(long tdeg)	Homogeneous part.
java.util.Iterator<IndexList>	indexListIterator()	Iterator over index lists.
GenExteriorPolynomial<C>	interiorLeftProduct(GenExteriorPolynomial<C> S)	GenExteriorPolynomial interior left multiplication.
GenExteriorPolynomial<C>	interiorRightProduct(GenExteriorPolynomial<C> S)	GenExteriorPolynomial interior right multiplication.
GenExteriorPolynomial<C>	inverse()	GenExteriorPolynomial inverse.
boolean	isConstant()	Is GenExteriorPolynomial<C> a constant.
boolean	isHomogeneous()	Is GenExteriorPolynomial<C> homogeneous.
boolean	isONE()	Is GenExteriorPolynomial<C> one.
boolean	isUnit()	Is GenExteriorPolynomial<C> a unit.
boolean	isZERO()	Is GenExteriorPolynomial<C> zero.
java.util.Iterator<IndexListMonomial<C>>	iterator()	Iterator over monomials.
C	leadingBaseCoefficient()	Leading base coefficient.
IndexList	leadingIndexList()	Leading index list.
java.util.Map.Entry<IndexList,C>	leadingMonomial()	Leading monomial.
int	length()	Length of GenExteriorPolynomial.
GenExteriorPolynomial<C>	map(UnaryFunctor<? super C,C> f)	Map a unary function to the coefficients.
long	maxDegree()	Index maximal degree.
C	maxNorm()	GenExteriorPolynomial maximum norm.
GenExteriorPolynomial<C>	monic()	GenExteriorPolynomial monic, i.e. leadingCoefficient == 1.
GenExteriorPolynomial<C>	multiply(C s)	GenExteriorPolynomial multiplication.
GenExteriorPolynomial<C>	multiply(C s, C t)	GenExteriorPolynomial multiplication.
GenExteriorPolynomial<C>	multiply(C s, IndexList e)	GenExteriorPolynomial multiplication.
GenExteriorPolynomial<C>	multiply(C s, IndexList e, C t, IndexList f)	GenExteriorPolynomial left and right multiplication.
GenExteriorPolynomial<C>	multiply(C s, IndexList e, IndexList f)	GenExteriorPolynomial left and right multiplication.
GenExteriorPolynomial<C>	multiply(GenExteriorPolynomial<C> S)	GenExteriorPolynomial multiplication.
GenExteriorPolynomial<C>	multiply(GenExteriorPolynomial<C> S, GenExteriorPolynomial<C> T)	GenExteriorPolynomial left and right multiplication.
GenExteriorPolynomial<C>	multiply(IndexList e)	GenExteriorPolynomial multiplication.
GenExteriorPolynomial<C>	multiply(IndexList e, IndexList f)	GenExteriorPolynomial left and right multiplication.
GenExteriorPolynomial<C>	multiply(java.util.Map.Entry<IndexList,C> m)	GenExteriorPolynomial multiplication.
GenExteriorPolynomial<C>	negate()	GenExteriorPolynomial negation.
int	numberOfVariables()	Number of variables.
GenExteriorPolynomial<C>[]	quotientRemainder(GenExteriorPolynomial<C> S)	GenExteriorPolynomial division with remainder.
GenExteriorPolynomial<C>	reductum()	Reductum.
GenExteriorPolynomial<C>	remainder(GenExteriorPolynomial<C> S)	GenExteriorPolynomial remainder.
GenExteriorPolynomial<C>	shiftIndex(int s)	GenExteriorPolynomial shift index.
int	signum()	GenExteriorPolynomial signum.
GenExteriorPolynomial<C>	subtract(C a)	GenExteriorPolynomial subtract.
GenExteriorPolynomial<C>	subtract(C a, IndexList e)	GenExteriorPolynomial subtraction.
GenExteriorPolynomial<C>	subtract(GenExteriorPolynomial<C> S)	GenExteriorPolynomial subtraction.
GenExteriorPolynomial<C>	sum(C a)	GenExteriorPolynomial addition.
GenExteriorPolynomial<C>	sum(C a, IndexList e)	GenExteriorPolynomial addition.
GenExteriorPolynomial<C>	sum(GenExteriorPolynomial<C> S)	GenExteriorPolynomial summation.
C	sumNorm()	GenExteriorPolynomial sum norm.
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 GenExteriorPolynomial.
C	trailingBaseCoefficient()	Trailing base coefficient.
IndexList	trailingIndexList()	Trailing index list.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.lang.Iterable

forEach, spliterator

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 GenExteriorPolynomialRing<C extends RingElem<C>> ring

The factory for the polynomial ring.

Constructor Detail

GenExteriorPolynomial

public GenExteriorPolynomial(GenExteriorPolynomialRing<C> r)

Constructor for zero GenExteriorPolynomial.

Parameters:

r - polynomial ring factory.

GenExteriorPolynomial

public GenExteriorPolynomial(GenExteriorPolynomialRing<C> r,
                             C c,
                             IndexList e)

Constructor for GenExteriorPolynomial c * x_e.

Parameters:

r - polynomial ring factory.

c - coefficient.

e - word.

GenExteriorPolynomial

public GenExteriorPolynomial(GenExteriorPolynomialRing<C> r,
                             C c)

Constructor for GenExteriorPolynomial c * x₀.

Parameters:

r - polynomial ring factory.

c - coefficient.

GenExteriorPolynomial

public GenExteriorPolynomial(GenExteriorPolynomialRing<C> r,
                             IndexList e)

Constructor for GenExteriorPolynomial x_e.

Parameters:

r - polynomial ring factory.

e - index list.

GenExteriorPolynomial

public GenExteriorPolynomial(GenExteriorPolynomialRing<C> r,
                             ExpVector e)

Constructor for GenExteriorPolynomial x_e.

Parameters:

r - polynomial ring factory.

e - exponent vector.

GenExteriorPolynomial

public GenExteriorPolynomial(GenExteriorPolynomialRing<C> r,
                             C c,
                             ExpVector e)

Constructor for GenExteriorPolynomial c * x_e.

Parameters:

r - polynomial ring factory.

c - coefficient.

e - exponent vector.

GenExteriorPolynomial

protected GenExteriorPolynomial(GenExteriorPolynomialRing<C> r,
                                java.util.SortedMap<IndexList,C> v)

Constructor for GenExteriorPolynomial.

Parameters:

r - polynomial ring factory.

v - the SortedMap of some other polynomial.

Method Detail

factory

public GenExteriorPolynomialRing<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 GenExteriorPolynomial<C> copy()

Copy this GenExteriorPolynomial.

Specified by:

copy in interface Element<C extends RingElem<C>>

Returns:

copy of this.

length

public int length()

Length of GenExteriorPolynomial.

Returns:

number of coefficients of this GenExteriorPolynomial.

getMap

public java.util.SortedMap<IndexList,C> getMap()

IndexList to coefficient map of GenExteriorPolynomial.

Returns:

val as unmodifiable SortedMap.

doPutToMap

public void doPutToMap(IndexList e,
                       C c)

Put a IndexList to coefficient entry into the internal map of this GenExteriorPolynomial. Note: Do not use this method unless you are constructing a new polynomial. this is modified and breaks the immutability promise of this class.

Parameters:

c - coefficient.

e - index list.

doRemoveFromMap

public void doRemoveFromMap(IndexList e,
                            C c)

Remove a IndexList to coefficient entry from the internal map of this GenExteriorPolynomial. Note: Do not use this method unless you are constructing a new polynomial. this is modified and breaks the immutability promise of this class.

Parameters:

e - IndexList.

c - expected coefficient, null for ignore.

doPutToMap

public void doPutToMap(java.util.SortedMap<IndexList,C> vals)

Put an a sorted map of index list to coefficients into the internal map of this GenExteriorPolynomial. Note: Do not use this method unless you are constructing a new polynomial. this is modified and breaks the immutability promise of this class.

Parameters:

vals - sorted map of index list and coefficients.

toString

public java.lang.String toString()

String representation of GenExteriorPolynomial.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

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()

isZERO

public boolean isZERO()

Is GenExteriorPolynomial<C> zero.

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 GenExteriorPolynomial<C> one.

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()

isUnit

public boolean isUnit()

Is GenExteriorPolynomial<C> a unit.

Specified by:

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

Returns:

If this is a unit then true is returned, else false.

See Also:

MonoidElem.isUnit()

isConstant

public boolean isConstant()

Is GenExteriorPolynomial<C> a constant.

Returns:

If this is a constant polynomial then true is returned, else false.

isHomogeneous

public boolean isHomogeneous()

Is GenExteriorPolynomial<C> homogeneous.

Returns:

true, if this is homogeneous, else false.

form

public GenExteriorPolynomial<C> form(long k)

k-form part.

Parameters:

k - requested k-form part.

Returns:

k-form part of given degree of this.

homogeneousPart

public GenExteriorPolynomial<C> homogeneousPart(long tdeg)

Homogeneous part.

Parameters:

tdeg - requested degree of part.

Returns:

polynomial part of given degree.

equals

public boolean equals(java.lang.Object B)

Comparison with any other object.

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.

Specified by:

hashCode in interface Element<C extends RingElem<C>>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

compareTo

public int compareTo(GenExteriorPolynomial<C> b)

GenExteriorPolynomial comparison.

Specified by:

compareTo in interface java.lang.Comparable<C extends RingElem<C>>

Specified by:

compareTo in interface Element<C extends RingElem<C>>

Parameters:

b - GenExteriorPolynomial.

Returns:

sign(this-b).

signum

public int signum()

GenExteriorPolynomial signum.

Specified by:

signum in interface AbelianGroupElem<C extends RingElem<C>>

Returns:

sign(ldcf(this)).

numberOfVariables

public int numberOfVariables()

Number of variables.

Returns:

ring.ixfac.length().

leadingMonomial

public java.util.Map.Entry<IndexList,C> leadingMonomial()

Leading monomial.

Returns:

first map entry.

leadingIndexList

public IndexList leadingIndexList()

Leading index list.

Returns:

first highest index list.

trailingIndexList

public IndexList trailingIndexList()

Trailing index list.

Returns:

last lowest index list.

leadingBaseCoefficient

public C leadingBaseCoefficient()

Leading base coefficient.

Returns:

first coefficient.

trailingBaseCoefficient

public C trailingBaseCoefficient()

Trailing base coefficient.

Returns:

coefficient of constant term.

coefficient

public C coefficient(IndexList e)

Coefficient.

Parameters:

e - index list.

Returns:

coefficient for given index list.

reductum

public GenExteriorPolynomial<C> reductum()

Reductum.

Returns:

this - leading monomial.

degree

public long degree()

Index degree.

Returns:

maximal length of indexes.

maxDegree

public long maxDegree()

Index maximal degree.

Returns:

maximal degree of indexes.

maxNorm

public C maxNorm()

GenExteriorPolynomial maximum norm.

Returns:

||this||.

sumNorm

public C sumNorm()

GenExteriorPolynomial sum norm.

Returns:

sum of all absolute values of coefficients.

sum

public GenExteriorPolynomial<C> sum(GenExteriorPolynomial<C> S)

GenExteriorPolynomial summation.

Specified by:

sum in interface AbelianGroupElem<C extends RingElem<C>>

Parameters:

S - GenExteriorPolynomial.

Returns:

this+S.

sum

public GenExteriorPolynomial<C> sum(C a,
                                    IndexList e)

GenExteriorPolynomial addition. This method is not very efficient, since this is copied.

Parameters:

a - coefficient.

e - index list.

Returns:

this + a e.

sum

public GenExteriorPolynomial<C> sum(C a)

GenExteriorPolynomial addition. This method is not very efficient, since this is copied.

Parameters:

a - coefficient.

Returns:

this + a x₀.

subtract

public GenExteriorPolynomial<C> subtract(GenExteriorPolynomial<C> S)

GenExteriorPolynomial subtraction.

Specified by:

subtract in interface AbelianGroupElem<C extends RingElem<C>>

Parameters:

S - GenExteriorPolynomial.

Returns:

this-S.

subtract

public GenExteriorPolynomial<C> subtract(C a,
                                         IndexList e)

GenExteriorPolynomial subtraction. This method is not very efficient, since this is copied.

Parameters:

a - coefficient.

e - index list.

Returns:

this - a e.

subtract

public GenExteriorPolynomial<C> subtract(C a)

GenExteriorPolynomial subtract. This method is not very efficient, since this is copied.

Parameters:

a - coefficient.

Returns:

this + a x₀.

negate

public GenExteriorPolynomial<C> negate()

GenExteriorPolynomial negation.

Specified by:

negate in interface AbelianGroupElem<C extends RingElem<C>>

Returns:

-this.

abs

public GenExteriorPolynomial<C> abs()

GenExteriorPolynomial absolute value, i.e. leadingCoefficient > 0.

Specified by:

abs in interface AbelianGroupElem<C extends RingElem<C>>

Returns:

abs(this).

multiply

public GenExteriorPolynomial<C> multiply(GenExteriorPolynomial<C> S)

GenExteriorPolynomial multiplication.

Specified by:

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

Parameters:

S - GenExteriorPolynomial.

Returns:

this /\\ S.

interiorLeftProduct

public GenExteriorPolynomial<C> interiorLeftProduct(GenExteriorPolynomial<C> S)

GenExteriorPolynomial interior left multiplication.

Parameters:

S - GenExteriorPolynomial.

Returns:

this _| S.

interiorRightProduct

public GenExteriorPolynomial<C> interiorRightProduct(GenExteriorPolynomial<C> S)

GenExteriorPolynomial interior right multiplication.

Parameters:

S - GenExteriorPolynomial.

Returns:

this |_ S.

multiply

public GenExteriorPolynomial<C> multiply(GenExteriorPolynomial<C> S,
                                         GenExteriorPolynomial<C> T)

GenExteriorPolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - GenExteriorPolynomial.

T - GenExteriorPolynomial.

Returns:

S*this*T.

multiply

public GenExteriorPolynomial<C> multiply(C s)

GenExteriorPolynomial multiplication. Product with coefficient ring element.

Parameters:

s - coefficient.

Returns:

this*s.

multiply

public GenExteriorPolynomial<C> multiply(C s,
                                         C t)

GenExteriorPolynomial multiplication. Product with coefficient ring element.

Parameters:

s - coefficient.

t - coefficient.

Returns:

s*this*t.

monic

public GenExteriorPolynomial<C> monic()

GenExteriorPolynomial monic, i.e. leadingCoefficient == 1. If leadingCoefficient is not invertible returns this unmodified.

Returns:

monic(this).

multiply

public GenExteriorPolynomial<C> multiply(C s,
                                         IndexList e)

GenExteriorPolynomial multiplication. Product with ring element and index list.

Parameters:

s - coefficient.

e - left index list.

Returns:

this * s e.

multiply

public GenExteriorPolynomial<C> multiply(IndexList e,
                                         IndexList f)

GenExteriorPolynomial left and right multiplication. Product with ring element and two index lists.

Parameters:

e - left index list.

f - right index list.

Returns:

e * this * f.

multiply

public GenExteriorPolynomial<C> multiply(C s,
                                         IndexList e,
                                         IndexList f)

GenExteriorPolynomial left and right multiplication. Product with ring element and two index lists.

Parameters:

s - coefficient.

e - left index list.

f - right index list.

Returns:

e * this * s * f.

multiply

public GenExteriorPolynomial<C> multiply(C s,
                                         IndexList e,
                                         C t,
                                         IndexList f)

GenExteriorPolynomial left and right multiplication. Product with ring element and two index lists.

Parameters:

s - coefficient.

e - left index list.

t - coefficient.

f - right index list.

Returns:

s * e * this * t * f.

multiply

public GenExteriorPolynomial<C> multiply(IndexList e)

GenExteriorPolynomial multiplication. Product with index list.

Parameters:

e - index list (!= null).

Returns:

this * e.

multiply

public GenExteriorPolynomial<C> multiply(java.util.Map.Entry<IndexList,C> m)

GenExteriorPolynomial multiplication. Product with 'monomial'.

Parameters:

m - 'monomial'.

Returns:

this * m.

divide

public GenExteriorPolynomial<C> divide(C s)

GenExteriorPolynomial division. Division by coefficient ring element. Fails, if exact division is not possible.

Parameters:

s - coefficient.

Returns:

this/s.

coeffPrimitivePart

public GenExteriorPolynomial<C> coeffPrimitivePart()

GenExteriorPolynomial coefficient primitive part. Division by gcd of coefficients.

Returns:

this/gcd(coeff(this)).

quotientRemainder

public GenExteriorPolynomial<C>[] quotientRemainder(GenExteriorPolynomial<C> S)

GenExteriorPolynomial division with remainder. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.

Specified by:

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

Parameters:

S - nonzero GenExteriorPolynomial with invertible leading coefficient.

Returns:

[ quotient , remainder ] with this = quotient * S + remainder and deg(remainder) < deg(S) or remainder = 0.

See Also:

.

divide

public GenExteriorPolynomial<C> divide(GenExteriorPolynomial<C> S)

GenExteriorPolynomial division. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.

Specified by:

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

Parameters:

S - nonzero GenExteriorPolynomial with invertible leading coefficient.

Returns:

quotient with this = quotient * S + remainder.

See Also:

.

remainder

public GenExteriorPolynomial<C> remainder(GenExteriorPolynomial<C> S)

GenExteriorPolynomial remainder. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.

Specified by:

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

Parameters:

S - nonzero GenExteriorPolynomial with invertible leading coefficient.

Returns:

remainder with this = quotient * S + remainder.

See Also:

.

gcd

public GenExteriorPolynomial<C> gcd(GenExteriorPolynomial<C> S)

GenExteriorPolynomial greatest common divisor. Note: not implemented.

Specified by:

gcd in interface RingElem<C extends RingElem<C>>

Parameters:

S - GenExteriorPolynomial.

Returns:

gcd(this,S).

egcd

public GenExteriorPolynomial<C>[] egcd(GenExteriorPolynomial<C> S)

GenExteriorPolynomial extended greatest common divisor. Note: not implemented.

Specified by:

egcd in interface RingElem<C extends RingElem<C>>

Parameters:

S - GenExteriorPolynomial.

Returns:

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

inverse

public GenExteriorPolynomial<C> inverse()

GenExteriorPolynomial inverse. Required by RingElem. Throws not invertible exception.

Specified by:

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

Returns:

x with this * x = 1, if it exists.

shiftIndex

public GenExteriorPolynomial<C> shiftIndex(int s)

GenExteriorPolynomial shift index. Add number to each index.

Parameters:

s - shift index by this number.

Returns:

this.shift(s).

coefficientIterator

public java.util.Iterator<C> coefficientIterator()

Iterator over coefficients.

Returns:

val.values().iterator().

indexListIterator

public java.util.Iterator<IndexList> indexListIterator()

Iterator over index lists.

Returns:

val.keySet().iterator().

iterator

public java.util.Iterator<IndexListMonomial<C>> iterator()

Iterator over monomials.

Specified by:

iterator in interface java.lang.Iterable<C extends RingElem<C>>

Returns:

a PolyIterator.

map

public GenExteriorPolynomial<C> map(UnaryFunctor<? super C,C> f)

Map a unary function to the coefficients.

Parameters:

f - evaluation functor.

Returns:

new polynomial with coefficients f(this(e)).