Package cc.redberry.rings.poly.univar

Interface IUnivariatePolynomial<Poly extends IUnivariatePolynomial<Poly>>

Type Parameters:

Poly - the type of polynomial (self type)

All Superinterfaces:

Comparable<Poly>, IPolynomial<Poly>, Serializable, Stringifiable<Poly>

All Known Implementing Classes:

UnivariatePolynomial, UnivariatePolynomialZ64, UnivariatePolynomialZp64

public interface IUnivariatePolynomial<Poly extends IUnivariatePolynomial<Poly>>
extends IPolynomial<Poly>

Parent interface for univariate polynomials. Dense representation (array of coefficients) is used to hold univariate polynomials. Positional operations treat index so that i-th coefficient corresponds to x^i monomial.

Since:

1.0

Method Summary

Modifier and Type	Method	Description
default AMultivariatePolynomial	asMultivariate()	Convert to multivariate polynomial
AMultivariatePolynomial	asMultivariate(Comparator<DegreeVector> ordering)	Convert to multivariate polynomial
Poly	clone()	Deep copy of this
AMultivariatePolynomial	composition(AMultivariatePolynomial value)	Calculates the composition of this(oth)
default Poly	composition(Ring<Poly> ring, Poly value)	Calculates the composition of this(oth) (new instance, so the content of this is not changed))
Poly	composition(Poly value)	Calculates the composition of this(oth) (new instance, so the content of this is not changed))
Poly	createMonomial(int degree)	Creates new monomial x^degree (with the same coefficient ring)
Poly	derivative()	Returns the formal derivative of this poly (new instance, so the content of this is not changed)
void	ensureInternalCapacity(int desiredCapacity)	ensures that internal storage has enough size to store desiredCapacity elements
default gnu.trove.set.hash.TIntHashSet	exponents()	Returns a set of exponents of non-zero terms
int	firstNonZeroCoefficientPosition()	Returns position of the first non-zero coefficient, that is common monomial exponent (e.g.
Poly	getAsPoly(int i)	Returns i-th coefficient of this as a constant polynomial
Poly	getRange(int from, int to)	Creates polynomial formed from the coefficients of this starting from from (inclusive) to to (exclusive)
default boolean	isLinearExactly()	Returns whether this polynomial is linear (i.e.
default boolean	isLinearOrConstant()	Returns whether this polynomial is linear (i.e.
boolean	isZeroAt(int i)	Returns whether i-th coefficient of this is zero
default boolean	isZeroCC()	Returns true if constant term is zero
default <E> UnivariatePolynomial<E>	mapCoefficientsAsPolys(Ring<E> ring, Function<Poly,E> mapper)
default int	nNonZeroTerms()	Returns the number of non zero terms in this poly
Poly	reverse()	Reverses the coefficients of this
Poly	setAndDestroy(Poly oth)	Sets the content of this with oth and destroys oth
Poly	setFrom(int indexInThis, Poly poly, int indexInPoly)	Sets i-th element of this by j-th element of other poly
Poly	setZero(int i)	Fills i-th element with zero
Poly	shiftLeft(int offset)	Returns the quotient this / x^offset, it is polynomial with coefficient list formed by shifting coefficients of this to the left by offset.
Poly	shiftRight(int offset)	Multiplies this by the x^offset.
default int	size()	Returns the degree of this polynomial
Stream<Poly>	streamAsPolys()	Stream polynomial coefficients as constant polynomials
Poly	truncate(int newDegree)	Returns the remainder this rem x^(newDegree + 1), it is polynomial formed by coefficients of this from zero to newDegree (both inclusive)

Methods inherited from interface java.lang.Comparable

compareTo

Methods inherited from interface cc.redberry.rings.poly.IPolynomial

add, add, assertSameCoefficientRingWith, canonical, ccAsPoly, coefficientRingCardinality, coefficientRingCharacteristic, coefficientRingPerfectPowerBase, coefficientRingPerfectPowerExponent, coefficientRingToString, coefficientRingToString, contentAsPoly, copy, createArray, createArray, createArray, createArray, createArray2d, createArray2d, createConstant, createOne, createZero, decrement, degree, divideByLC, increment, isConstant, isMonic, isMonomial, isOne, isOverField, isOverFiniteField, isOverPerfectPower, isOverZ, isUnitCC, isZero, lcAsPoly, monic, monicExact, monicWithLC, multiply, multiply, multiply, multiply, multiplyByBigInteger, multiplyByLC, negate, parsePoly, primitivePart, primitivePartSameSign, sameCoefficientRingWith, set, setCoefficientRingFrom, setCoefficientRingFromOptional, signumOfLC, square, subtract, subtract, toPositiveLC, toString, toZero

Methods inherited from interface cc.redberry.rings.io.Stringifiable

toString

Method Details

size

default int size()

Returns the degree of this polynomial

Specified by:

size in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>

Returns:

the degree of this polynomial

nNonZeroTerms

default int nNonZeroTerms()

Returns the number of non zero terms in this poly

isZeroAt

boolean isZeroAt(int i)

Returns whether i-th coefficient of this is zero

Parameters:

i - the position

Returns:

whether i-th coefficient of this is zero

isZeroCC

default boolean isZeroCC()

Description copied from interface: IPolynomial

Returns true if constant term is zero

Specified by:

isZeroCC in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>

Returns:

whether constant term is zero

setZero

Poly setZero(int i)

Fills i-th element with zero

Parameters:

i - position

Returns:

self

setFrom

Poly setFrom(int indexInThis,
Poly poly,
int indexInPoly)

Sets i-th element of this by j-th element of other poly

Parameters:

indexInThis - index in self

poly - other polynomial

indexInPoly - index in other polynomial

Returns:

self

getAsPoly

Poly getAsPoly(int i)

Returns i-th coefficient of this as a constant polynomial

Parameters:

i - index in this

Returns:

i-th coefficient of this as a constant polynomial

exponents

default gnu.trove.set.hash.TIntHashSet exponents()

Returns a set of exponents of non-zero terms

Returns:

a set of exponents of non-zero terms

firstNonZeroCoefficientPosition

int firstNonZeroCoefficientPosition()

Returns position of the first non-zero coefficient, that is common monomial exponent (e.g. 2 for x^2 + x^3 + ...). In the case of zero polynomial, -1 returned

Returns:

position of the first non-zero coefficient or -1 if this is zero

shiftLeft

Poly shiftLeft(int offset)

Returns the quotient this / x^offset, it is polynomial with coefficient list formed by shifting coefficients of this to the left by offset.

Parameters:

offset - shift amount

Returns:

the quotient this / x^offset

shiftRight

Poly shiftRight(int offset)

Multiplies this by the x^offset.

Parameters:

offset - monomial exponent

Returns:

this * x^offset

truncate

Poly truncate(int newDegree)

Returns the remainder this rem x^(newDegree + 1), it is polynomial formed by coefficients of this from zero to newDegree (both inclusive)

Parameters:

newDegree - new degree

Returns:

remainder this rem x^(newDegree + 1)

getRange

Poly getRange(int from,
int to)

Creates polynomial formed from the coefficients of this starting from from (inclusive) to to (exclusive)

Parameters:

from - the initial index of the range to be copied, inclusive

to - the final index of the range to be copied, exclusive.

Returns:

polynomial formed from the range of coefficients of this

reverse

Poly reverse()

Reverses the coefficients of this

Returns:

reversed polynomial

createMonomial

Poly createMonomial(int degree)

Creates new monomial x^degree (with the same coefficient ring)

Parameters:

degree - monomial degree

Returns:

new monomial coefficient * x^degree

derivative

Poly derivative()

Returns the formal derivative of this poly (new instance, so the content of this is not changed)

Returns:

the formal derivative

clone

Poly clone()

Description copied from interface: IPolynomial

Deep copy of this

Specified by:

clone in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>

Returns:

deep copy of this

setAndDestroy

Poly setAndDestroy(Poly oth)

Sets the content of this with oth and destroys oth

Parameters:

oth - the polynomial (will be destroyed)

Returns:

this := oth

composition

Poly composition(Poly value)

Calculates the composition of this(oth) (new instance, so the content of this is not changed))

Parameters:

value - polynomial

Returns:

composition this(oth)

composition

default Poly composition(Ring<Poly> ring,
Poly value)

Calculates the composition of this(oth) (new instance, so the content of this is not changed))

Parameters:

value - polynomial

Returns:

composition this(oth)

streamAsPolys

Stream<Poly> streamAsPolys()

Stream polynomial coefficients as constant polynomials

mapCoefficientsAsPolys

default <E> UnivariatePolynomial<E> mapCoefficientsAsPolys(Ring<E> ring,
Function<Poly,E> mapper)

composition

AMultivariatePolynomial composition(AMultivariatePolynomial value)

Calculates the composition of this(oth)

Parameters:

value - polynomial

Returns:

composition this(oth)

asMultivariate

AMultivariatePolynomial asMultivariate(Comparator<DegreeVector> ordering)

Convert to multivariate polynomial

asMultivariate

default AMultivariatePolynomial asMultivariate()

Convert to multivariate polynomial

ensureInternalCapacity

void ensureInternalCapacity(int desiredCapacity)

ensures that internal storage has enough size to store desiredCapacity elements

isLinearOrConstant

default boolean isLinearOrConstant()

Description copied from interface: IPolynomial

Returns whether this polynomial is linear (i.e. of the form a * X + b)

Specified by:

isLinearOrConstant in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>

isLinearExactly

default boolean isLinearExactly()

Description copied from interface: IPolynomial

Returns whether this polynomial is linear (i.e. of the form a * X + b with nonzero a)

Specified by:

isLinearExactly in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>