Package cc.redberry.rings.poly.multivar

Class MultivariatePolynomial<E>

java.lang.Object

cc.redberry.rings.poly.multivar.AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

cc.redberry.rings.poly.multivar.MultivariatePolynomial<E>

All Implemented Interfaces:

Stringifiable<MultivariatePolynomial<E>>, IPolynomial<MultivariatePolynomial<E>>, Serializable, Comparable<MultivariatePolynomial<E>>, Iterable<Monomial<E>>

public final class MultivariatePolynomial<E>
extends AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Since:

1.0

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	MultivariatePolynomial.HornerForm<E>	A representation of multivariate polynomial specifically optimized for fast evaluation of given variables
static class	MultivariatePolynomial.PrecomputedPowersHolder<E>	holds an array of precomputed powers

Nested classes/interfaces inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial

AMultivariatePolynomial.PolynomialCollector<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>>

Field Summary

Fields

Modifier and Type	Field	Description
Ring<E>	ring	The coefficient ring

Fields inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial

monomialAlgebra, nVariables, ordering

Method Summary

Modifier and Type	Method	Description
MultivariatePolynomial<E>	add(E oth)	Adds oth to this polynomial
static <E> MultivariatePolynomial<E>	asMultivariate(UnivariatePolynomial<E> poly, int nVariables, int variable, Comparator<DegreeVector> ordering)	Converts univariate polynomial to multivariate.
static <E> MultivariatePolynomial<E>	asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly)	Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static <E> MultivariatePolynomial<E>	asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly, int[] coefficientVariables, int[] mainVariables)	Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static <E> MultivariatePolynomial<E>	asNormalMultivariate(MultivariatePolynomial<UnivariatePolynomial<E>> poly, int variable)	Converts multivariate polynomial over univariate polynomial ring (R[variable][other_variables]) to a multivariate polynomial over coefficient ring (R[variables])
MultivariatePolynomial<MultivariatePolynomial<E>>	asOverMultivariate(int... variables)	Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
MultivariatePolynomial<MultivariatePolynomial<E>>	asOverMultivariateEliminate(int[] variables, Comparator<DegreeVector> ordering)	Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
MultivariatePolynomial<UnivariatePolynomial<E>>	asOverUnivariate(int variable)	Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable
MultivariatePolynomial<UnivariatePolynomial<E>>	asOverUnivariateEliminate(int variable)	Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable, the resulting polynomial have (nVariable - 1) multivariate variables (specified variable is eliminated)
static MultivariatePolynomialZp64	asOverZp64(MultivariatePolynomial<BigInteger> poly)	Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers
static MultivariatePolynomialZp64	asOverZp64(MultivariatePolynomial<BigInteger> poly, IntegersZp64 ring)	Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers
static MultivariatePolynomial<BigInteger>	asPolyZ(MultivariatePolynomial<BigInteger> poly, boolean copy)	Returns Z[X] polynomial formed from the coefficients of the poly.
static MultivariatePolynomial<BigInteger>	asPolyZSymmetric(MultivariatePolynomial<BigInteger> poly)	Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
UnivariatePolynomial<E>	asUnivariate()	Converts this to univariate polynomial or throws exception if conversion is impossible (more than one variable have non zero exponents)
E	cc()	Returns the constant coefficient of this polynomial.
MultivariatePolynomial<E>	ccAsPoly()	Returns the constant coefficient as a constant poly
MultivariatePolynomial<E>	clone()	Deep copy of this
BigInteger	coefficientRingCardinality()	Returns cardinality of the coefficient ring of this poly
BigInteger	coefficientRingCharacteristic()	Returns characteristic of the coefficient ring of this poly
BigInteger	coefficientRingPerfectPowerBase()	Returns base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
BigInteger	coefficientRingPerfectPowerExponent()	Returns exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
String	coefficientRingToString(IStringifier<MultivariatePolynomial<E>> stringifier)	String representation of the coefficient ring of this
Iterable<E>	coefficients()	Returns iterable over polynomial coefficients
E[]	coefficientsArray()	Returns array of polynomial coefficients
int	compareTo(MultivariatePolynomial<E> oth)
E	content()	Returns the content of this polynomial.
MultivariatePolynomial<E>	contentAsPoly()	Returns the content of this (gcd of coefficients) as a constant poly
UnivariatePolynomial<E>	contentUnivariate(int variable)	Gives the content of this considered as R[variable][other_variables]
static <E> MultivariatePolynomial<E>	create(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering, Monomial<E>... terms)	Creates multivariate polynomial from a list of monomial terms
static <E> MultivariatePolynomial<E>	create(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering, Iterable<Monomial<E>> terms)	Creates multivariate polynomial from a list of monomial terms
MultivariatePolynomial<E>[]	createArray(int length)	overcome Java generics...
MultivariatePolynomial<E>[][]	createArray2d(int length)	overcome Java generics...
MultivariatePolynomial<E>[][]	createArray2d(int length1, int length2)	overcome Java generics...
MultivariatePolynomial<E>	createConstant(E val)	Creates constant polynomial with specified value
MultivariatePolynomial<E>	createConstantFromTerm(Monomial<E> monomial)	Creates multivariate polynomial over the same ring as this with the single constant element taken from given monomial
MultivariatePolynomial<E>	createLinear(int variable, E cc, E lc)	Creates linear polynomial of the form cc + lc * variable
MultivariatePolynomial<E>	createOne()	Returns the new instance of unit polynomial (with the same coefficient ring)
MultivariatePolynomial<E>	createZero()	Returns the new instance of zero polynomial (with the same coefficient ring)
MultivariatePolynomial<E>	decrement()	Subtracts 1 from this
MultivariatePolynomial<E>	derivative(int variable, int order)	Gives partial derivative of specified order with respect to specified variable (new instance created)
MultivariatePolynomial<E>	divideByLC(MultivariatePolynomial<E> other)	Divides this polynomial by the leading coefficient of other or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the other.lc().
MultivariatePolynomial<E>	divideExact(E factor)	Divides this polynomial by a factor or throws exception if exact division is not possible
MultivariatePolynomial<E>	divideOrNull(Monomial<E> monomial)	Divides this polynomial by a monomial or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the monomial.
MultivariatePolynomial<E>	divideOrNull(E factor)	Divides this polynomial by a factor or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the factor.
MultivariatePolynomial<E>	eliminate(int[] variables, E[] values)	Returns a copy of this with values substituted for variables
MultivariatePolynomial<E>	eliminate(int variable, long value)	Substitutes value for variable and eliminates variable from the list of variables so that the resulting polynomial has result.nVariables = this.nVariables - 1.
MultivariatePolynomial<E>	eliminate(int variable, E value)	Substitutes value for variable and eliminates variable from the list of variables so that the resulting polynomial has result.nVariables = this.nVariables - 1.
MultivariatePolynomial<E>	evaluate(int[] variables, E[] values)	Returns a copy of this with values substituted for variables.
MultivariatePolynomial<E>	evaluate(int variable, long value)	Returns a copy of this with value substituted for variable.
MultivariatePolynomial<E>	evaluate(int variable, E value)	Returns a copy of this with value substituted for variable.
MultivariatePolynomial<E>[]	evaluate(int variable, E... values)	Evaluates this polynomial at specified points
E	evaluate(E... values)	Evaluates this polynomial at specified points
MultivariatePolynomial<E>	evaluateAtRandom(int variable, org.apache.commons.math3.random.RandomGenerator rnd)	Evaluates poly at random point
MultivariatePolynomial<E>	evaluateAtRandomPreservingSkeleton(int variable, org.apache.commons.math3.random.RandomGenerator rnd)	Evaluates poly at random point chosen in such way that the skeleton of evaluated version is the same as of the original poly with respect to all except variable variables
static <E> E	evaluateDenseRecursiveForm(UnivariatePolynomial recForm, int nVariables, E[] values)	Evaluates polynomial given in a dense recursive form at a given points
static <E> E	evaluateSparseRecursiveForm(AMultivariatePolynomial recForm, int nVariables, E[] values)	Evaluates polynomial given in a sparse recursive form at a given points
static <E> MultivariatePolynomial<E>	fromDenseRecursiveForm(UnivariatePolynomial recForm, int nVariables, Comparator<DegreeVector> ordering)	Converts poly from a recursive univariate representation.
static <E> MultivariatePolynomial<E>	fromSparseRecursiveForm(AMultivariatePolynomial recForm, int nVariables, Comparator<DegreeVector> ordering)	Converts poly from a recursive univariate representation.
MultivariatePolynomial.HornerForm	getHornerForm(int[] evaluationVariables)	Gives data structure for fast Horner-like sparse evaluation of this multivariate polynomial
MultivariatePolynomial<E>	increment()	Adds 1 to this
boolean	isConstant()	Returns true if this polynomial has only constant term
boolean	isMonic()	Returns true if this polynomial is monic
boolean	isOne()	Returns true if this is one
boolean	isOverField()	Returns whether the coefficient ring of this polynomial is a field
boolean	isOverFiniteField()	Returns whether the coefficient ring of this polynomial is a finite field
boolean	isOverPerfectPower()	Returns whether the coefficientRingCardinality() is a perfect power
boolean	isOverZ()	Returns whether the coefficient ring of this polynomial is Z
boolean	isUnitCC()	Returns true if constant term is equal to one
E	lc()	Returns the leading coefficient of this polynomial that is coefficient of the largest term according to the ordering.
E	lc(Comparator<DegreeVector> ordering)	Returns the leading coefficient of this polynomial with respect to specified ordering
MultivariatePolynomial<E>	lcAsPoly()	Returns the leading coefficient as a constant poly
MultivariatePolynomial<E>	lcAsPoly(Comparator<DegreeVector> ordering)	Returns the leading coefficient with respect to specified ordering as a constant poly
<T> MultivariatePolynomial<T>	mapCoefficients(Ring<T> newRing, Function<E,T> mapper)	Maps coefficients of this using specified mapping function
<T> MultivariatePolynomial<T>	mapCoefficientsAsPolys(Ring<T> ring, Function<MultivariatePolynomial<E>,T> mapper)
MultivariatePolynomialZp64	mapCoefficientsZp64(IntegersZp64 newDomain, ToLongFunction<E> mapper)	Maps coefficients of this using specified mapping function
<T> MultivariatePolynomial<T>	mapTerms(Ring<T> newRing, Function<Monomial<E>,Monomial<T>> mapper)	Maps terms of this using specified mapping function
E	maxAbsCoefficient()	Returns max absolute coefficient
MultivariatePolynomial.PrecomputedPowersHolder<E>	mkPrecomputedPowers(int[] variables, E[] values)
static <E> MultivariatePolynomial.PrecomputedPowersHolder<E>	mkPrecomputedPowers(int nVariables, Ring<E> ring, int[] variables, E[] values)
MultivariatePolynomial.PrecomputedPowersHolder<E>	mkPrecomputedPowers(int variable, E value)
MultivariatePolynomial.PrecomputedPowersHolder<E>	mkPrecomputedPowers(E[] values)
MultivariatePolynomial<E>	monic()	Makes this polynomial monic if possible, if not -- destroys this and returns null
MultivariatePolynomial<E>	monic(E factor)	Sets this to its monic part multiplied by the factor modulo modulus (that is monic(modulus).multiply(factor) ).
MultivariatePolynomial<E>	monic(Comparator<DegreeVector> ordering)	Make this poly monic considering leading term with respect to given ordering
MultivariatePolynomial<E>	monic(Comparator<DegreeVector> ordering, E factor)	Sets this to its monic part (with respect to given ordering) multiplied by the given factor;
MultivariatePolynomial<E>	monicWithLC(MultivariatePolynomial<E> other)	Sets this to its monic part multiplied by the leading coefficient of other;
MultivariatePolynomial<E>	monicWithLC(Comparator<DegreeVector> ordering, MultivariatePolynomial<E> other)	Sets this to its monic part multiplied by the leading coefficient of other with respect to given ordering
MultivariatePolynomial<E>	multiply(long factor)	Multiplies this by factor
MultivariatePolynomial<E>	multiply(Monomial<E> monomial)	Multiplies this by the monomial
MultivariatePolynomial<E>	multiply(MultivariatePolynomial<E> oth)	Multiplies this by oth
MultivariatePolynomial<E>	multiply(E factor)	Multiplies this by the factor
MultivariatePolynomial<E>	multiplyByBigInteger(BigInteger factor)	Multiplies this by factor
MultivariatePolynomial<E>	multiplyByLC(MultivariatePolynomial<E> other)	Multiply this by the leading coefficient of other
static <E> MultivariatePolynomial<E>	one(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering)	Creates unit polynomial.
static MultivariatePolynomial<BigInteger>	parse(String string)	Deprecated. use #parse(string, ring, ordering, variables)
static <E> MultivariatePolynomial<E>	parse(String string, Ring<E> ring)	Deprecated. use #parse(string, ring, ordering, variables)
static <E> MultivariatePolynomial<E>	parse(String string, Ring<E> ring, String... variables)	Parse multivariate polynomial from string.
static <E> MultivariatePolynomial<E>	parse(String string, Ring<E> ring, Comparator<DegreeVector> ordering)	Deprecated. use #parse(string, ring, ordering, variables)
static <E> MultivariatePolynomial<E>	parse(String string, Ring<E> ring, Comparator<DegreeVector> ordering, String... variables)	Parse multivariate polynomial from string.
static MultivariatePolynomial<BigInteger>	parse(String string, String... variables)	Parse multivariate Z[X] polynomial from string.
static MultivariatePolynomial<BigInteger>	parse(String string, Comparator<DegreeVector> ordering)	Deprecated. use #parse(string, ring, ordering, variables)
static MultivariatePolynomial<BigInteger>	parse(String string, Comparator<DegreeVector> ordering, String... variables)	Parse multivariate Z[X] polynomial from string.
MultivariatePolynomial<E>	parsePoly(String string)	Deprecated.
MultivariatePolynomial<E>	primitivePart()	Reduces poly to its primitive part (primitive part will always have positive l.c.)
MultivariatePolynomial<E>	primitivePart(int variable)	Gives primitive part of this considered as R[variable][other_variables]
MultivariatePolynomial<E>	primitivePartSameSign()	Reduces poly to its primitive part, so that primitive part will have the same signum as the initial poly
protected void	release()	release caches
boolean	sameCoefficientRingWith(MultivariatePolynomial<E> oth)	Returns whether oth and this have the same coefficient ring
MultivariatePolynomial<E>	seriesCoefficient(int variable, int order)	Gives (unevaluated) coefficient of Taylor series expansion for specified variable that is derivative(poly, variable, order) / order! , where the derivative is formal derivative and calculated with arithmetic performed in Z ring (to overcome possible zeros in Zp).
MultivariatePolynomial<E>	setCoefficientRingFrom(MultivariatePolynomial<E> poly)	Set the coefficient ring from specified poly
MultivariatePolynomial<E>	setLC(E val)	Sets the leading coefficient to the specified value
MultivariatePolynomial<E>	setRing(Ring<E> newRing)	Returns a copy of this with coefficient reduced to a newRing
MultivariatePolynomial<E>	setRingUnsafe(Ring<E> newRing)	internal API
MultivariatePolynomial<E>	shift(int[] variables, E[] shifts)	Returns a copy of this with variables -> variables + shifts
MultivariatePolynomial<E>	shift(int variable, long shift)	Returns a copy of this with variable -> variable + shift
MultivariatePolynomial<E>	shift(int variable, E shift)	Returns a copy of this with variable -> variable + shift
int	signumOfLC()	Gives signum of the leading coefficient
MultivariatePolynomial<E>	square()	Squares this
Stream<E>	stream()	Returns a stream of coefficients of this
MultivariatePolynomial<E>	substitute(int variable, MultivariatePolynomial<E> poly)	Returns a copy of this with poly substituted for variable.
MultivariatePolynomial<E>	subtract(E oth)	Subtracts oth from this polynomial
UnivariatePolynomial	toDenseRecursiveForm()	Gives a recursive univariate representation of this poly.
AMultivariatePolynomial	toSparseRecursiveForm()	Gives a recursive sparse univariate representation of this poly.
String	toString(IStringifier<MultivariatePolynomial<E>> stringifier)	convert this to string with the use of stringifier
static <E> MultivariatePolynomial<E>	zero(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering)	Creates zero polynomial.

Methods inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial

add, add, add, add, ascendingIterator, asMultivariate, asMultivariate, asMultivariate, asOverMultivariateEliminate, asOverPoly, asUnivariate, asUnivariateEliminate, coefficientOf, coefficientOf, collection, composition, composition, composition, composition, composition, composition, content, contentExcept, create, create, create, create, createMonomial, degree, degree, degree, degreeMax, degrees, degrees, degreesRef, degreeSum, derivative, derivative, descendingIterator, divideDegreeVectorOrNull, dropCoefficientOf, dropSelectVariables, dropVariable, dropVariables, ecart, equals, evaluateAtZero, evaluateAtZero, first, getSkeleton, getSkeleton, getSkeletonDrop, getSkeletonExcept, hashCode, homogenize, insertVariable, insertVariable, isEffectiveUnivariate, isHomogeneous, isLinearExactly, isLinearOrConstant, isMonomial, isVariable, isZero, isZeroCC, iterator, joinNewVariable, joinNewVariables, last, lc, lt, lt, ltAsPoly, mapVariables, monomialContent, mt, multidegree, multiplyByDegreeVector, multiplyByMonomial, negate, nUsedVariables, occurrences, put, renameVariables, renameVariables, renameVariables, sameSkeletonExceptQ, sameSkeletonQ, sameSkeletonQ, set, setAllCoefficientsToUnit, setLC, setNVariables, setOrdering, size, skeletonHashCode, sparsity, sparsity2, subtract, subtract, subtract, subtractLt, swapVariables, toArray, toString, totalDegree, toZero, uniqueOccurrences, univariateVariable

Methods inherited from class java.lang.Object

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

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

add, assertSameCoefficientRingWith, canonical, coefficientRingToString, copy, createArray, createArray, createArray, createConstant, monicExact, multiply, multiply, setCoefficientRingFromOptional, subtract, toPositiveLC, toString

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Details

ring

public final Ring<E> ring

The coefficient ring

Method Details

create

public static <E> MultivariatePolynomial<E> create(int nVariables,
Ring<E> ring,
Comparator<DegreeVector> ordering,
Iterable<Monomial<E>> terms)

Creates multivariate polynomial from a list of monomial terms

Parameters:

ring - the ring

ordering - term ordering

terms - the monomial terms

Returns:

multivariate polynomial

create

public static <E> MultivariatePolynomial<E> create(int nVariables,
Ring<E> ring,
Comparator<DegreeVector> ordering,
Monomial<E>... terms)

Creates multivariate polynomial from a list of monomial terms

Parameters:

ring - the ring

ordering - term ordering

terms - the monomial terms

Returns:

multivariate polynomial

zero

public static <E> MultivariatePolynomial<E> zero(int nVariables,
Ring<E> ring,
Comparator<DegreeVector> ordering)

Creates zero polynomial.

Parameters:

nVariables - number of variables

ring - the ring

ordering - the ordering

Returns:

zero polynomial

one

public static <E> MultivariatePolynomial<E> one(int nVariables,
Ring<E> ring,
Comparator<DegreeVector> ordering)

Creates unit polynomial.

Parameters:

nVariables - number of variables

ring - the ring

ordering - the ordering

Returns:

unit polynomial

parse

public static MultivariatePolynomial<BigInteger> parse(String string,
String... variables)

Parse multivariate Z[X] polynomial from string.

Parameters:

string - the string

variables - string variables that should be taken into account. For examples: parse("a", LEX) and parse("a", LEX, "a", "b") although give the same mathematical expressions are differ, since the first one is considered as Z[x], while the second as Z[x1,x2]

Returns:

multivariate Z[X] polynomial

parse

@Deprecated
public static MultivariatePolynomial<BigInteger> parse(String string)

Deprecated.

use #parse(string, ring, ordering, variables)

Parse multivariate Z[X] polynomial from string.

Parameters:

string - the string

Returns:

multivariate Z[X] polynomial

parse

public static <E> MultivariatePolynomial<E> parse(String string,
Ring<E> ring,
String... variables)

Parse multivariate polynomial from string.

Parameters:

string - the string

ring - the ring

variables - string variables that should be taken into account. For examples: parse("a", LEX) and parse("a", LEX, "a", "b") although give the same mathematical expressions are differ, since the first one is considered as Z[x], while the second as Z[x1,x2]

Returns:

multivariate polynomial

parse

@Deprecated
public static <E> MultivariatePolynomial<E> parse(String string,
Ring<E> ring)

Deprecated.

use #parse(string, ring, ordering, variables)

Parse multivariate polynomial from string.

Parameters:

string - the string

ring - the ring

Returns:

multivariate polynomial

parse

public static MultivariatePolynomial<BigInteger> parse(String string,
Comparator<DegreeVector> ordering,
String... variables)

Parse multivariate Z[X] polynomial from string.

Parameters:

string - the string

ordering - monomial order

variables - string variables that should be taken into account. For examples: parse("a", LEX) and parse("a", LEX, "a", "b") although give the same mathematical expressions are differ, since the first one is considered as Z[x], while the second as Z[x1,x2]

Returns:

Z[X] multivariate polynomial

parse

@Deprecated
public static MultivariatePolynomial<BigInteger> parse(String string,
Comparator<DegreeVector> ordering)

Deprecated.

use #parse(string, ring, ordering, variables)

Parse multivariate Z[X] polynomial from string.

Parameters:

string - the string

ordering - monomial order

Returns:

Z[X] multivariate polynomial

parse

public static <E> MultivariatePolynomial<E> parse(String string,
Ring<E> ring,
Comparator<DegreeVector> ordering,
String... variables)

Parse multivariate polynomial from string.

Parameters:

string - the string

ring - the ring

ordering - monomial order

variables - string variables that should be taken into account. For examples: parse("a", LEX) and parse("a", LEX, "a", "b") although give the same mathematical expressions are different, since the first one is considered as Z[a], while the second as Z[a,b]

Returns:

multivariate polynomial

parse

@Deprecated
public static <E> MultivariatePolynomial<E> parse(String string,
Ring<E> ring,
Comparator<DegreeVector> ordering)

Deprecated.

use #parse(string, ring, ordering, variables)

Parse multivariate polynomial from string.

Parameters:

string - the string

ring - the ring

ordering - monomial order

asOverZp64

public static MultivariatePolynomialZp64 asOverZp64(MultivariatePolynomial<BigInteger> poly)

Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers

Parameters:

poly - the polynomial

Returns:

multivariate polynomial over machine sized modular integers

Throws:

IllegalArgumentException - if poly.ring is not Zp

ArithmeticException - if some of coefficients will not exactly fit in a long.

asOverZp64

public static MultivariatePolynomialZp64 asOverZp64(MultivariatePolynomial<BigInteger> poly,
IntegersZp64 ring)

Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers

Parameters:

poly - the polynomial

ring - Zp64 ring

Returns:

multivariate polynomial over machine sized modular integers

Throws:

IllegalArgumentException - if poly.ring is not Zp

ArithmeticException - if some of coefficients will not exactly fit in a long.

asMultivariate

public static <E> MultivariatePolynomial<E> asMultivariate(UnivariatePolynomial<E> poly,
int nVariables,
int variable,
Comparator<DegreeVector> ordering)

Converts univariate polynomial to multivariate.

Parameters:

poly - univariate polynomial

nVariables - number of variables in the result

variable - variable that will be used as a primary variable

ordering - monomial order

Returns:

multivariate polynomial

asUnivariate

public UnivariatePolynomial<E> asUnivariate()

Description copied from class: AMultivariatePolynomial

Converts this to univariate polynomial or throws exception if conversion is impossible (more than one variable have non zero exponents)

Specified by:

asUnivariate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Returns:

univariate polynomial

asOverUnivariate

public MultivariatePolynomial<UnivariatePolynomial<E>> asOverUnivariate(int variable)

Description copied from class: AMultivariatePolynomial

Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable

Specified by:

asOverUnivariate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

variable - variable

Returns:

multivariate polynomial with coefficients being univariate polynomials over variable

asOverUnivariateEliminate

public MultivariatePolynomial<UnivariatePolynomial<E>> asOverUnivariateEliminate(int variable)

Description copied from class: AMultivariatePolynomial

Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable, the resulting polynomial have (nVariable - 1) multivariate variables (specified variable is eliminated)

Specified by:

asOverUnivariateEliminate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

variable - the variable

Returns:

multivariate polynomial with coefficients being univariate polynomials over variable, the resulting polynomial have (nVariable - 1) multivariate variables

asOverMultivariate

public MultivariatePolynomial<MultivariatePolynomial<E>> asOverMultivariate(int... variables)

Description copied from class: AMultivariatePolynomial

Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]

Specified by:

asOverMultivariate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

variables - the variables to separate

Returns:

multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]

asOverMultivariateEliminate

public MultivariatePolynomial<MultivariatePolynomial<E>> asOverMultivariateEliminate(int[] variables,
Comparator<DegreeVector> ordering)

Description copied from class: AMultivariatePolynomial

Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]

Specified by:

asOverMultivariateEliminate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

variables - the variables to separate

ordering - monomial order to use for result

Returns:

multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]

asNormalMultivariate

public static <E> MultivariatePolynomial<E> asNormalMultivariate(MultivariatePolynomial<UnivariatePolynomial<E>> poly,
int variable)

Converts multivariate polynomial over univariate polynomial ring (R[variable][other_variables]) to a multivariate polynomial over coefficient ring (R[variables])

Parameters:

poly - the polynomial

variable - the variable to insert

Returns:

multivariate polynomial over normal coefficient ring

asNormalMultivariate

public static <E> MultivariatePolynomial<E> asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly)

Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring

Parameters:

poly - the polynomial

Returns:

multivariate polynomial over normal coefficient ring

asNormalMultivariate

public static <E> MultivariatePolynomial<E> asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly,
int[] coefficientVariables,
int[] mainVariables)

Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring

Parameters:

poly - the polynomial

Returns:

multivariate polynomial over normal coefficient ring

asPolyZ

public static MultivariatePolynomial<BigInteger> asPolyZ(MultivariatePolynomial<BigInteger> poly,
boolean copy)

Returns Z[X] polynomial formed from the coefficients of the poly.

Parameters:

poly - the polynomial

copy - whether to copy the internal data

Returns:

Z[X] version of the poly

asPolyZSymmetric

public static MultivariatePolynomial<BigInteger> asPolyZSymmetric(MultivariatePolynomial<BigInteger> poly)

Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).

Parameters:

poly - Zp polynomial

Returns:

Z[x] version of the poly with coefficients represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).

Throws:

IllegalArgumentException - is poly.ring is not a IntegersZp

contentAsPoly

public MultivariatePolynomial<E> contentAsPoly()

Description copied from interface: IPolynomial

Returns the content of this (gcd of coefficients) as a constant poly

lcAsPoly

public MultivariatePolynomial<E> lcAsPoly()

Description copied from interface: IPolynomial

Returns the leading coefficient as a constant poly

lcAsPoly

public MultivariatePolynomial<E> lcAsPoly(Comparator<DegreeVector> ordering)

Description copied from class: AMultivariatePolynomial

Returns the leading coefficient with respect to specified ordering as a constant poly

Specified by:

lcAsPoly in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

ccAsPoly

public MultivariatePolynomial<E> ccAsPoly()

Description copied from interface: IPolynomial

Returns the constant coefficient as a constant poly

isOverField

public boolean isOverField()

Description copied from interface: IPolynomial

Returns whether the coefficient ring of this polynomial is a field

Returns:

whether the coefficient ring of this polynomial is a field

isOverFiniteField

public boolean isOverFiniteField()

Description copied from interface: IPolynomial

Returns whether the coefficient ring of this polynomial is a finite field

Returns:

whether the coefficient ring of this polynomial is a finite field

isOverZ

public boolean isOverZ()

Description copied from interface: IPolynomial

Returns whether the coefficient ring of this polynomial is Z

Returns:

whether the coefficient ring of this polynomial is Z

coefficientRingCardinality

public BigInteger coefficientRingCardinality()

Description copied from interface: IPolynomial

Returns cardinality of the coefficient ring of this poly

Returns:

cardinality of the coefficient ring

coefficientRingCharacteristic

public BigInteger coefficientRingCharacteristic()

Description copied from interface: IPolynomial

Returns characteristic of the coefficient ring of this poly

Returns:

characteristic of the coefficient ring

isOverPerfectPower

public boolean isOverPerfectPower()

Description copied from interface: IPolynomial

Returns whether the coefficientRingCardinality() is a perfect power

Returns:

whether the coefficientRingCardinality() is a perfect power

coefficientRingPerfectPowerBase

public BigInteger coefficientRingPerfectPowerBase()

Description copied from interface: IPolynomial

Returns base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite

Returns:

base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite

coefficientRingPerfectPowerExponent

public BigInteger coefficientRingPerfectPowerExponent()

Description copied from interface: IPolynomial

Returns exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite

Returns:

exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite

createArray

public MultivariatePolynomial<E>[] createArray(int length)

Description copied from interface: IPolynomial

overcome Java generics...

createArray2d

public MultivariatePolynomial<E>[][] createArray2d(int length)

Description copied from interface: IPolynomial

overcome Java generics...

createArray2d

public MultivariatePolynomial<E>[][] createArray2d(int length1,
int length2)

Description copied from interface: IPolynomial

overcome Java generics...

sameCoefficientRingWith

public boolean sameCoefficientRingWith(MultivariatePolynomial<E> oth)

Description copied from interface: IPolynomial

Returns whether oth and this have the same coefficient ring

Parameters:

oth - other polynomial

Returns:

whether this and oth are over the same coefficient ring

setCoefficientRingFrom

public MultivariatePolynomial<E> setCoefficientRingFrom(MultivariatePolynomial<E> poly)

Description copied from interface: IPolynomial

Set the coefficient ring from specified poly

Parameters:

poly - the polynomial

Returns:

a copy of this with the coefficient ring taken from poly

release

protected void release()

release caches

Overrides:

release in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

setRing

public MultivariatePolynomial<E> setRing(Ring<E> newRing)

Returns a copy of this with coefficient reduced to a newRing

Parameters:

newRing - the new ring

Returns:

a copy of this reduced to the ring specified by newRing

setRingUnsafe

public MultivariatePolynomial<E> setRingUnsafe(Ring<E> newRing)

internal API

createConstant

public MultivariatePolynomial<E> createConstant(E val)

Creates constant polynomial with specified value

Parameters:

val - value

Returns:

constant polynomial with specified value

createConstantFromTerm

public MultivariatePolynomial<E> createConstantFromTerm(Monomial<E> monomial)

Description copied from class: AMultivariatePolynomial

Creates multivariate polynomial over the same ring as this with the single constant element taken from given monomial

Specified by:

createConstantFromTerm in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

monomial - the monomial

Returns:

multivariate polynomial

createZero

public MultivariatePolynomial<E> createZero()

Description copied from interface: IPolynomial

Returns the new instance of zero polynomial (with the same coefficient ring)

Returns:

new instance of 0

createOne

public MultivariatePolynomial<E> createOne()

Description copied from interface: IPolynomial

Returns the new instance of unit polynomial (with the same coefficient ring)

Returns:

new instance of 1

createLinear

public final MultivariatePolynomial<E> createLinear(int variable,
E cc,
E lc)

Creates linear polynomial of the form cc + lc * variable

Parameters:

variable - the variable

cc - the constant coefficient

lc - the leading coefficient

Returns:

linear polynomial cc + lc * variable

isMonic

public boolean isMonic()

Description copied from interface: IPolynomial

Returns true if this polynomial is monic

Returns:

whether this is monic

signumOfLC

public int signumOfLC()

Description copied from interface: IPolynomial

Gives signum of the leading coefficient

Returns:

signum of the leading coefficient

isOne

public boolean isOne()

Description copied from interface: IPolynomial

Returns true if this is one

Returns:

whether this is one

isUnitCC

public boolean isUnitCC()

Description copied from interface: IPolynomial

Returns true if constant term is equal to one

Returns:

whether constant term is 1

isConstant

public boolean isConstant()

Description copied from interface: IPolynomial

Returns true if this polynomial has only constant term

Returns:

whether this is constant

maxAbsCoefficient

public E maxAbsCoefficient()

Returns max absolute coefficient

lc

public E lc()

Returns the leading coefficient of this polynomial that is coefficient of the largest term according to the ordering.

Returns:

leading coefficient of this polynomial

lc

public E lc(Comparator<DegreeVector> ordering)

Returns the leading coefficient of this polynomial with respect to specified ordering

Returns:

leading coefficient of this polynomial with respect to specified ordering

setLC

public MultivariatePolynomial<E> setLC(E val)

Sets the leading coefficient to the specified value

Parameters:

val - new value for the lc

Returns:

the leading coefficient to the specified value

cc

public E cc()

Returns the constant coefficient of this polynomial.

Returns:

constant coefficient of this polynomial

content

public E content()

Returns the content of this polynomial.

Returns:

content of this polynomial

coefficients

public Iterable<E> coefficients()

Returns iterable over polynomial coefficients

Returns:

iterable over polynomial coefficients

coefficientsArray

public E[] coefficientsArray()

Returns array of polynomial coefficients

Returns:

array of polynomial coefficients

primitivePart

public MultivariatePolynomial<E> primitivePart(int variable)

Description copied from class: AMultivariatePolynomial

Gives primitive part of this considered as R[variable][other_variables]

Specified by:

primitivePart in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

variable - the variable

Returns:

primitive part of this considered as R[variable][other_variables]

contentUnivariate

public UnivariatePolynomial<E> contentUnivariate(int variable)

Description copied from class: AMultivariatePolynomial

Gives the content of this considered as R[variable][other_variables]

Specified by:

contentUnivariate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

variable - the variable

Returns:

the content of this considered as R[variable][other_variables]

primitivePart

public MultivariatePolynomial<E> primitivePart()

Description copied from interface: IPolynomial

Reduces poly to its primitive part (primitive part will always have positive l.c.)

Returns:

primitive part (poly will be modified)

primitivePartSameSign

public MultivariatePolynomial<E> primitivePartSameSign()

Description copied from interface: IPolynomial

Reduces poly to its primitive part, so that primitive part will have the same signum as the initial poly

Returns:

primitive part (poly will be modified)

divideByLC

public MultivariatePolynomial<E> divideByLC(MultivariatePolynomial<E> other)

Description copied from interface: IPolynomial

Divides this polynomial by the leading coefficient of other or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the other.lc(). NOTE: if null is returned, the content of this is destroyed.

Parameters:

other - the polynomial

Returns:

this divided by the other.lc() or null if exact division is not possible

divideOrNull

public MultivariatePolynomial<E> divideOrNull(E factor)

Divides this polynomial by a factor or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the factor. NOTE: if null is returned, the content of this is destroyed.

Parameters:

factor - the factor

Returns:

this divided by the factor or null

divideExact

public MultivariatePolynomial<E> divideExact(E factor)

Divides this polynomial by a factor or throws exception if exact division is not possible

Parameters:

factor - the factor

Returns:

this divided by the factor

Throws:

ArithmeticException - if exact division is not possible

divideOrNull

public MultivariatePolynomial<E> divideOrNull(Monomial<E> monomial)

Description copied from class: AMultivariatePolynomial

Divides this polynomial by a monomial or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the monomial. NOTE: if null is returned, the content of this is destroyed.

Specified by:

divideOrNull in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

monomial - monomial degrees

Returns:

this divided by the factor * monomial or null

monic

public MultivariatePolynomial<E> monic()

Makes this polynomial monic if possible, if not -- destroys this and returns null

Returns:

monic this or null if the ring does not support exact division by lc

monic

public MultivariatePolynomial<E> monic(Comparator<DegreeVector> ordering)

Description copied from class: AMultivariatePolynomial

Make this poly monic considering leading term with respect to given ordering

Specified by:

monic in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

monic

public MultivariatePolynomial<E> monic(E factor)

Sets this to its monic part multiplied by the factor modulo modulus (that is monic(modulus).multiply(factor) ).

Parameters:

factor - the factor

Returns:

this

monic

public MultivariatePolynomial<E> monic(Comparator<DegreeVector> ordering,
E factor)

Sets this to its monic part (with respect to given ordering) multiplied by the given factor;

monicWithLC

public MultivariatePolynomial<E> monicWithLC(MultivariatePolynomial<E> other)

Description copied from interface: IPolynomial

Sets this to its monic part multiplied by the leading coefficient of other;

Parameters:

other - other polynomial

Returns:

monic part multiplied by the leading coefficient of other or null if exact division by the reduced leading coefficient is not possible

monicWithLC

public MultivariatePolynomial<E> monicWithLC(Comparator<DegreeVector> ordering,
MultivariatePolynomial<E> other)

Description copied from class: AMultivariatePolynomial

Sets this to its monic part multiplied by the leading coefficient of other with respect to given ordering

Specified by:

monicWithLC in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

toDenseRecursiveForm

public UnivariatePolynomial toDenseRecursiveForm()

Gives a recursive univariate representation of this poly.

fromDenseRecursiveForm

public static <E> MultivariatePolynomial<E> fromDenseRecursiveForm(UnivariatePolynomial recForm,
int nVariables,
Comparator<DegreeVector> ordering)

Converts poly from a recursive univariate representation.

Parameters:

recForm - recursive univariate representation

nVariables - number of variables in multivariate polynomial

ordering - monomial order

evaluateDenseRecursiveForm

public static <E> E evaluateDenseRecursiveForm(UnivariatePolynomial recForm,
int nVariables,
E[] values)

Evaluates polynomial given in a dense recursive form at a given points

toSparseRecursiveForm

public AMultivariatePolynomial toSparseRecursiveForm()

Gives a recursive sparse univariate representation of this poly.

fromSparseRecursiveForm

public static <E> MultivariatePolynomial<E> fromSparseRecursiveForm(AMultivariatePolynomial recForm,
int nVariables,
Comparator<DegreeVector> ordering)

Converts poly from a recursive univariate representation.

Parameters:

recForm - recursive univariate representation

nVariables - number of variables in multivariate polynomial

ordering - monomial order

evaluateSparseRecursiveForm

public static <E> E evaluateSparseRecursiveForm(AMultivariatePolynomial recForm,
int nVariables,
E[] values)

Evaluates polynomial given in a sparse recursive form at a given points

getHornerForm

public MultivariatePolynomial.HornerForm getHornerForm(int[] evaluationVariables)

Gives data structure for fast Horner-like sparse evaluation of this multivariate polynomial

Parameters:

evaluationVariables - variables which will be substituted

evaluate

public MultivariatePolynomial<E> evaluate(int variable,
E value)

Returns a copy of this with value substituted for variable.

Parameters:

variable - the variable

value - the value

Returns:

a new multivariate polynomial with value substituted for variable but still with the same AMultivariatePolynomial.nVariables (though the effective number of variables is nVariables - 1, compare to eliminate(int, Object))

See Also:

eliminate(int, Object)

evaluate

public E evaluate(E... values)

Evaluates this polynomial at specified points

evaluate

public MultivariatePolynomial<E> evaluate(int[] variables,
E[] values)

Returns a copy of this with values substituted for variables.

Parameters:

variables - the variables

values - the values

Returns:

a new multivariate polynomial with value substituted for variable but still with the same AMultivariatePolynomial.nVariables (though the effective number of variables is nVariables - 1, compare to eliminate(int, Object))

See Also:

eliminate(int, Object)

evaluate

public MultivariatePolynomial<E>[] evaluate(int variable,
E... values)

Evaluates this polynomial at specified points

evaluate

public MultivariatePolynomial<E> evaluate(int variable,
long value)

Returns a copy of this with value substituted for variable.

Parameters:

variable - the variable

value - the value

Returns:

a new multivariate polynomial with value substituted for variable but still with the same AMultivariatePolynomial.nVariables (though the effective number of variables is nVariables - 1, compare to eliminate(int, long))

See Also:

eliminate(int, long)

eliminate

public MultivariatePolynomial<E> eliminate(int variable,
E value)

Substitutes value for variable and eliminates variable from the list of variables so that the resulting polynomial has result.nVariables = this.nVariables - 1.

Parameters:

variable - the variable

value - the value

Returns:

a new multivariate polynomial with value substituted for variable and nVariables = nVariables - 1)

See Also:

evaluate(int, Object)

eliminate

public MultivariatePolynomial<E> eliminate(int variable,
long value)

Substitutes value for variable and eliminates variable from the list of variables so that the resulting polynomial has result.nVariables = this.nVariables - 1.

Parameters:

variable - the variable

value - the value

Returns:

a new multivariate polynomial with value substituted for variable and nVariables = nVariables - 1)

See Also:

evaluate(int, long)

eliminate

public MultivariatePolynomial<E> eliminate(int[] variables,
E[] values)

Returns a copy of this with values substituted for variables

Parameters:

variables - the variables

values - the values

Returns:

a new multivariate polynomial with value substituted for variable but still with the same AMultivariatePolynomial.nVariables (though the effective number of variables is nVariables - 1, compare to eliminate(int, long))

mkPrecomputedPowers

public MultivariatePolynomial.PrecomputedPowersHolder<E> mkPrecomputedPowers(int variable,
E value)

mkPrecomputedPowers

public MultivariatePolynomial.PrecomputedPowersHolder<E> mkPrecomputedPowers(int[] variables,
E[] values)

mkPrecomputedPowers

public static <E>
MultivariatePolynomial.PrecomputedPowersHolder<E> mkPrecomputedPowers(int nVariables,
Ring<E> ring,
int[] variables,
E[] values)

mkPrecomputedPowers

public MultivariatePolynomial.PrecomputedPowersHolder<E> mkPrecomputedPowers(E[] values)

substitute

public MultivariatePolynomial<E> substitute(int variable,
MultivariatePolynomial<E> poly)

Returns a copy of this with poly substituted for variable.

Parameters:

variable - the variable

poly - the replacement for the variable

Returns:

a copy of this with variable -> poly

shift

public MultivariatePolynomial<E> shift(int variable,
long shift)

Returns a copy of this with variable -> variable + shift

Parameters:

variable - the variable

shift - shift amount

Returns:

a copy of this with variable -> variable + shift

shift

public MultivariatePolynomial<E> shift(int variable,
E shift)

Returns a copy of this with variable -> variable + shift

Parameters:

variable - the variable

shift - shift amount

Returns:

a copy of this with variable -> variable + shift

shift

public MultivariatePolynomial<E> shift(int[] variables,
E[] shifts)

Returns a copy of this with variables -> variables + shifts

Parameters:

variables - the variables

shifts - the corresponding shifts

Returns:

a copy of this with variables -> variables + shifts

add

public MultivariatePolynomial<E> add(E oth)

Adds oth to this polynomial

Parameters:

oth - other polynomial

Returns:

this + oth

subtract

public MultivariatePolynomial<E> subtract(E oth)

Subtracts oth from this polynomial

Parameters:

oth - other polynomial

Returns:

this - oth

increment

public MultivariatePolynomial<E> increment()

Description copied from interface: IPolynomial

Adds 1 to this

Returns:

this + 1

decrement

public MultivariatePolynomial<E> decrement()

Description copied from interface: IPolynomial

Subtracts 1 from this

Returns:

this - 1

multiply

public MultivariatePolynomial<E> multiply(E factor)

Multiplies this by the factor

Parameters:

factor - the factor

Returns:

this multiplied by the factor

multiplyByLC

public MultivariatePolynomial<E> multiplyByLC(MultivariatePolynomial<E> other)

Description copied from interface: IPolynomial

Multiply this by the leading coefficient of other

Parameters:

other - polynomial

Returns:

this * lc(other)

multiply

public MultivariatePolynomial<E> multiply(Monomial<E> monomial)

Description copied from class: AMultivariatePolynomial

Multiplies this by the monomial

Specified by:

multiply in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

monomial - the monomial

Returns:

this multiplied by the monomial

multiply

public MultivariatePolynomial<E> multiply(long factor)

Description copied from interface: IPolynomial

Multiplies this by factor

Parameters:

factor - the factor

Returns:

this * factor

multiplyByBigInteger

public MultivariatePolynomial<E> multiplyByBigInteger(BigInteger factor)

Description copied from interface: IPolynomial

Multiplies this by factor

Parameters:

factor - the factor

Returns:

this * factor

multiply

public MultivariatePolynomial<E> multiply(MultivariatePolynomial<E> oth)

Description copied from interface: IPolynomial

Multiplies this by oth

Parameters:

oth - the polynomial

Returns:

this * oth

square

public MultivariatePolynomial<E> square()

Description copied from interface: IPolynomial

Squares this

Returns:

this * this

evaluateAtRandom

public MultivariatePolynomial<E> evaluateAtRandom(int variable,
org.apache.commons.math3.random.RandomGenerator rnd)

Description copied from class: AMultivariatePolynomial

Evaluates poly at random point

Specified by:

evaluateAtRandom in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

evaluateAtRandomPreservingSkeleton

public MultivariatePolynomial<E> evaluateAtRandomPreservingSkeleton(int variable,
org.apache.commons.math3.random.RandomGenerator rnd)

Description copied from class: AMultivariatePolynomial

Evaluates poly at random point chosen in such way that the skeleton of evaluated version is the same as of the original poly with respect to all except variable variables

Specified by:

evaluateAtRandomPreservingSkeleton in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

derivative

public MultivariatePolynomial<E> derivative(int variable,
int order)

Description copied from class: AMultivariatePolynomial

Gives partial derivative of specified order with respect to specified variable (new instance created)

Specified by:

derivative in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

variable - the variable

order - derivative order

Returns:

partial derivative of specified order with respect to specified variable

seriesCoefficient

public MultivariatePolynomial<E> seriesCoefficient(int variable,
int order)

Description copied from class: AMultivariatePolynomial

Gives (unevaluated) coefficient of Taylor series expansion for specified variable that is derivative(poly, variable, order) / order! , where the derivative is formal derivative and calculated with arithmetic performed in Z ring (to overcome possible zeros in Zp).

Specified by:

seriesCoefficient in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Parameters:

variable - the variable

order - derivative order

Returns:

derivative(poly, variable, order) / order! , where the derivative is formal derivative and calculated with arithmetic performed in Z ring (to overcome possible zeros in Zp)

stream

public Stream<E> stream()

Returns a stream of coefficients of this

Returns:

stream of coefficients

mapTerms

public <T> MultivariatePolynomial<T> mapTerms(Ring<T> newRing,
Function<Monomial<E>,Monomial<T>> mapper)

Maps terms of this using specified mapping function

Type Parameters:

T - new element type

Parameters:

newRing - the new ring

mapper - mapping

Returns:

a new polynomial with terms obtained by applying mapper to this terms

mapCoefficients

public <T> MultivariatePolynomial<T> mapCoefficients(Ring<T> newRing,
Function<E,T> mapper)

Maps coefficients of this using specified mapping function

Type Parameters:

T - new element type

Parameters:

newRing - the new ring

mapper - mapping

Returns:

a new polynomial with terms obtained by applying mapper to this terms (only coefficients are changed)

mapCoefficientsZp64

public MultivariatePolynomialZp64 mapCoefficientsZp64(IntegersZp64 newDomain,
ToLongFunction<E> mapper)

Maps coefficients of this using specified mapping function

Parameters:

newDomain - the new ring

mapper - mapping

Returns:

a new polynomial with terms obtained by applying mapper to this terms (only coefficients are changed)

mapCoefficientsAsPolys

public <T> MultivariatePolynomial<T> mapCoefficientsAsPolys(Ring<T> ring,
Function<MultivariatePolynomial<E>,T> mapper)

Specified by:

mapCoefficientsAsPolys in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

compareTo

public int compareTo(MultivariatePolynomial<E> oth)

clone

public MultivariatePolynomial<E> clone()

Description copied from interface: IPolynomial

Deep copy of this

Specified by:

clone in interface IPolynomial<E>

Specified by:

clone in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>

Returns:

deep copy of this

parsePoly

@Deprecated
public MultivariatePolynomial<E> parsePoly(String string)

Deprecated.

toString

public String toString(IStringifier<MultivariatePolynomial<E>> stringifier)

Description copied from interface: Stringifiable

convert this to string with the use of stringifier

coefficientRingToString

public String coefficientRingToString(IStringifier<MultivariatePolynomial<E>> stringifier)

Description copied from interface: IPolynomial

String representation of the coefficient ring of this