cc.redberry.rings.poly.multivar.AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>

cc.redberry.rings.poly.multivar.MultivariatePolynomialZp64

All Implemented Interfaces:: Stringifiable<MultivariatePolynomialZp64>, IPolynomial<MultivariatePolynomialZp64>, Serializable, Comparable<MultivariatePolynomialZp64>, Iterable<MonomialZp64>

public final class MultivariatePolynomialZp64
extends AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>

Multivariate polynomial over Zp ring with the modulus in the range (0, 2^62) (see MachineArithmetic.MAX_SUPPORTED_MODULUS). For details on polynomial data structure and properties see AMultivariatePolynomial.

Since:: 1.0
See Also:: AMultivariatePolynomial, Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type	Class	Description
`static class`	`MultivariatePolynomialZp64.HornerFormZp64`	A representation of multivariate polynomial specifically optimized for fast evaluation of given variables
`static class`	`MultivariatePolynomialZp64.lPrecomputedPowers`	cached powers used to save some time
`static class`	`MultivariatePolynomialZp64.lPrecomputedPowersHolder`	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

IntegersZp64 ring
The ring.

Fields inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial
monomialAlgebra, nVariables, ordering

Method Summary

Modifier and Type	Method	Description
`MultivariatePolynomialZp64`	`add(long oth)`	Adds `oth` to this polynomial and returns it
`static MultivariatePolynomialZp64`	`asMultivariate(UnivariatePolynomialZp64 poly, int nVariables, int variable, Comparator<DegreeVector> ordering)`	Converts univariate polynomial to multivariate.
`static MultivariatePolynomialZp64`	`asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomialZp64> poly)`	Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
`static MultivariatePolynomialZp64`	`asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomialZp64> poly, int[] coefficientVariables, int[] mainVariables)`	Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
`static MultivariatePolynomialZp64`	`asNormalMultivariate(MultivariatePolynomial<UnivariatePolynomialZp64> poly, int variable)`	Converts multivariate polynomial over univariate polynomial ring (Zp[variable][other_variables]) to a multivariate polynomial over coefficient ring (Zp[all_variables])
`MultivariatePolynomial<MultivariatePolynomialZp64>`	`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<MultivariatePolynomialZp64>`	`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<UnivariatePolynomialZp64>`	`asOverUnivariate(int variable)`	Converts this to a multivariate polynomial with coefficients being univariate polynomials over `variable`
`MultivariatePolynomial<UnivariatePolynomialZp64>`	`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)
`MultivariatePolynomial<BigInteger>`	`asPolyZ()`	Returns polynomial over Z formed from the coefficients of this
`MultivariatePolynomial<BigInteger>`	`asPolyZSymmetric()`	Returns polynomial over Z formed from the coefficients of this represented in symmetric modular form (`-modulus/2 <= cfx <= modulus/2`).
`UnivariatePolynomialZp64`	`asUnivariate()`	Converts this to univariate polynomial or throws exception if conversion is impossible (more than one variable have non zero exponents)
`long`	`cc()`	Returns the constant coefficient of this polynomial.
`MultivariatePolynomialZp64`	`ccAsPoly()`	Returns the constant coefficient as a constant poly
`MultivariatePolynomialZp64`	`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<MultivariatePolynomialZp64> stringifier)`	String representation of the coefficient ring of this
`long[]`	`coefficients()`	Returns array of polynomial coefficients
`int`	`compareTo(MultivariatePolynomialZp64 oth)`
`long`	`content()`	Returns the content of this polynomial.
`MultivariatePolynomialZp64`	`contentAsPoly()`	Returns the content of this (gcd of coefficients) as a constant poly
`UnivariatePolynomialZp64`	`contentUnivariate(int variable)`	Gives the content of this considered as R[variable][other_variables]
`static MultivariatePolynomialZp64`	`create(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering, MonomialSet<MonomialZp64> terms)`	Creates multivariate polynomial from a set of monomials
`static MultivariatePolynomialZp64`	`create(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering, MonomialZp64... terms)`	Creates multivariate polynomial from a list of monomial terms
`static MultivariatePolynomialZp64`	`create(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering, Iterable<MonomialZp64> terms)`	Creates multivariate polynomial from a list of monomial terms
`MultivariatePolynomialZp64[]`	`createArray(int length)`	overcome Java generics...
`MultivariatePolynomialZp64[][]`	`createArray2d(int length)`	overcome Java generics...
`MultivariatePolynomialZp64[][]`	`createArray2d(int length1, int length2)`	overcome Java generics...
`MultivariatePolynomialZp64`	`createConstant(long val)`	Creates constant polynomial with specified value
`MultivariatePolynomialZp64`	`createConstantFromTerm(MonomialZp64 monomial)`	Creates multivariate polynomial over the same ring as this with the single constant element taken from given monomial
`MultivariatePolynomialZp64`	`createLinear(int variable, long cc, long lc)`	Creates linear polynomial of the form `cc + lc * variable`
`MultivariatePolynomialZp64`	`createOne()`	Returns the new instance of unit polynomial (with the same coefficient ring)
`MultivariatePolynomialZp64`	`createZero()`	Returns the new instance of zero polynomial (with the same coefficient ring)
`MultivariatePolynomialZp64`	`decrement()`	Subtracts 1 from this
`MultivariatePolynomialZp64`	`derivative(int variable, int order)`	Gives partial derivative of specified `order` with respect to specified variable (new instance created)
`MultivariatePolynomialZp64`	`divide(long factor)`	Divides this polynomial by a `factor`
`MultivariatePolynomialZp64`	`divideByLC(MultivariatePolynomialZp64 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()`.
`MultivariatePolynomialZp64`	`divideOrNull(MonomialZp64 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`.
`MultivariatePolynomialZp64`	`eliminate(int[] variables, long[] values)`	Returns a copy of this with `values` substituted for `variables`
`MultivariatePolynomialZp64`	`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`.
`MultivariatePolynomialZp64`	`evaluate(int[] variables, long[] values)`	Returns a copy of this with `values` substituted for `variables`
`MultivariatePolynomialZp64`	`evaluate(int variable, long value)`	Returns a copy of this with `value` substituted for `variable`
`MultivariatePolynomialZp64[]`	`evaluate(int variable, long... values)`	Evaluates this polynomial at specified points
`long`	`evaluate(long... values)`	Evaluates this polynomial at specified points
`MultivariatePolynomialZp64`	`evaluateAtRandom(int variable, org.apache.commons.math3.random.RandomGenerator rnd)`	Evaluates `poly` at random point
`MultivariatePolynomialZp64`	`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 long`	`evaluateDenseRecursiveForm(IUnivariatePolynomial recForm, long[] values)`	Evaluates polynomial given in a dense recursive form at a given points
`static long`	`evaluateSparseRecursiveForm(AMultivariatePolynomial recForm, long[] values)`	Evaluates polynomial given in a sparse recursive form at a given points
`static MultivariatePolynomialZp64`	`fromDenseRecursiveForm(IUnivariatePolynomial recForm, int nVariables, Comparator<DegreeVector> ordering)`	Converts poly from a recursive univariate representation.
`static MultivariatePolynomialZp64`	`fromDenseRecursiveForm(IUnivariatePolynomial recForm, Comparator<DegreeVector> ordering)`	Converts poly from a recursive univariate representation.
`static MultivariatePolynomialZp64`	`fromSparseRecursiveForm(AMultivariatePolynomial recForm, int nVariables, Comparator<DegreeVector> ordering)`	Converts poly from a recursive univariate representation.
`static MultivariatePolynomialZp64`	`fromSparseRecursiveForm(AMultivariatePolynomial recForm, Comparator<DegreeVector> ordering)`	Converts poly from a sparse recursive univariate representation.
`MultivariatePolynomialZp64.HornerFormZp64`	`getHornerForm(int[] evaluationVariables)`	Gives data structure for fast Horner-like sparse evaluation of this multivariate polynomial
`MultivariatePolynomialZp64`	`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
`long`	`lc()`	Returns the leading coefficient of this polynomial that is coefficient of the largest term according to the ordering.
`long`	`lc(Comparator<DegreeVector> ordering)`	Returns the leading coefficient of this polynomial with respect to specified ordering
`MultivariatePolynomialZp64`	`lcAsPoly()`	Returns the leading coefficient as a constant poly
`MultivariatePolynomialZp64`	`lcAsPoly(Comparator<DegreeVector> ordering)`	Returns the leading coefficient with respect to specified ordering as a constant poly
`<T> MultivariatePolynomial<T>`	`mapCoefficients(Ring<T> newRing, LongFunction<T> mapper)`	Maps coefficients of this using specified mapping function
`<E> MultivariatePolynomial<E>`	`mapCoefficientsAsPolys(Ring<E> ring, Function<MultivariatePolynomialZp64,E> mapper)`
`MultivariatePolynomialZp64`	`mapTerms(IntegersZp64 newRing, Function<MonomialZp64,MonomialZp64> mapper)`	Maps terms of this using specified mapping function
`<T> MultivariatePolynomial<T>`	`mapTerms(Ring<T> newRing, Function<MonomialZp64,Monomial<T>> mapper)`	Maps terms of this using specified mapping function
`MultivariatePolynomialZp64.lPrecomputedPowersHolder`	`mkPrecomputedPowers(int[] variables, long[] values)`
`MultivariatePolynomialZp64.lPrecomputedPowersHolder`	`mkPrecomputedPowers(int variable, long value)`
`static MultivariatePolynomialZp64.lPrecomputedPowersHolder`	`mkPrecomputedPowers(int nVariables, IntegersZp64 ring, int[] variables, long[] values)`
`MultivariatePolynomialZp64.lPrecomputedPowersHolder`	`mkPrecomputedPowers(long[] values)`
`MultivariatePolynomialZp64`	`monic()`	Makes this polynomial monic
`MultivariatePolynomialZp64`	`monic(long factor)`	Sets `this` to its monic part (with respect to given ordering) multiplied by the given factor;
`MultivariatePolynomialZp64`	`monic(Comparator<DegreeVector> ordering)`	Make this poly monic considering leading term with respect to given ordering
`MultivariatePolynomialZp64`	`monic(Comparator<DegreeVector> ordering, long factor)`	Sets `this` to its monic part (with respect to given ordering) multiplied by the given factor;
`MultivariatePolynomialZp64`	`monicWithLC(MultivariatePolynomialZp64 other)`	Sets `this` to its monic part multiplied by the leading coefficient of `other`;
`MultivariatePolynomialZp64`	`monicWithLC(Comparator<DegreeVector> ordering, MultivariatePolynomialZp64 other)`	Sets `this` to its monic part multiplied by the leading coefficient of `other` with respect to given ordering
`MultivariatePolynomialZp64`	`multiply(long factor)`	Multiplies this by `factor`
`MultivariatePolynomialZp64`	`multiply(MonomialZp64 monomial)`	Multiplies `this` by the `monomial`
`MultivariatePolynomialZp64`	`multiply(MultivariatePolynomialZp64 oth)`	Multiplies this by `oth`
`MultivariatePolynomialZp64`	`multiplyByBigInteger(BigInteger factor)`	Multiplies this by `factor`
`MultivariatePolynomialZp64`	`multiplyByLC(MultivariatePolynomialZp64 other)`	Multiply this by the leading coefficient of `other`
`static MultivariatePolynomialZp64`	`one(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering)`	Creates unit polynomial.
`static MultivariatePolynomialZp64`	`parse(String string, IntegersZp64 ring)`	Deprecated. use #parse(string, ring, ordering, variables)
`static MultivariatePolynomialZp64`	`parse(String string, IntegersZp64 ring, String... variables)`	Parse multivariate polynomial from string.
`static MultivariatePolynomialZp64`	`parse(String string, IntegersZp64 ring, Comparator<DegreeVector> ordering)`	Deprecated. use #parse(string, ring, ordering, variables)
`static MultivariatePolynomialZp64`	`parse(String string, IntegersZp64 ring, Comparator<DegreeVector> ordering, String... variables)`	Parse multivariate polynomial from string.
`MultivariatePolynomialZp64`	`parsePoly(String string)`	Deprecated.
`MultivariatePolynomialZp64`	`primitivePart()`	Reduces poly to its primitive part (primitive part will always have positive l.c.)
`MultivariatePolynomialZp64`	`primitivePart(int variable)`	Gives primitive part of this considered as R[variable][other_variables]
`MultivariatePolynomialZp64`	`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(MultivariatePolynomialZp64 oth)`	Returns whether `oth` and `this` have the same coefficient ring
`MultivariatePolynomialZp64`	`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).
`MultivariatePolynomialZp64`	`setCoefficientRingFrom(MultivariatePolynomialZp64 lMonomialTerms)`	Set the coefficient ring from specified poly
`MultivariatePolynomialZp64`	`setLC(long val)`	Sets the leading coefficient to the specified value
`MultivariatePolynomialZp64`	`setRing(long newModulus)`	Switches to another ring specified by `newModulus`
`MultivariatePolynomialZp64`	`setRing(IntegersZp64 newDomain)`	Switches to another ring specified by `newDomain`
`<E> MultivariatePolynomial<E>`	`setRing(Ring<E> newRing)`	Switches to another ring specified by `newRing`
`MultivariatePolynomialZp64`	`setRingUnsafe(IntegersZp64 newDomain)`	internal API
`MultivariatePolynomialZp64`	`shift(int[] variables, long[] shifts)`	Substitutes `variable -> variable + shift` for each variable from `variables` array
`MultivariatePolynomialZp64`	`shift(int variable, long shift)`	Returns a copy of this with `variable -> variable + shift`
`int`	`signumOfLC()`	Gives signum of the leading coefficient
`MultivariatePolynomialZp64`	`square()`	Squares `this`
`MultivariatePolynomialZp64`	`substitute(int variable, MultivariatePolynomialZp64 poly)`	Returns a copy of this with `poly` substituted for `variable`
`MultivariatePolynomialZp64`	`subtract(long oth)`	Subtracts `oth` from this polynomial and returns it
`MultivariatePolynomial<BigInteger>`	`toBigPoly()`	Returns polynomial over Z formed from the coefficients of this
`IUnivariatePolynomial`	`toDenseRecursiveForm()`	Gives a recursive univariate representation of this poly.
`AMultivariatePolynomial`	`toSparseRecursiveForm()`	Gives a recursive sparse univariate representation of this poly.
`String`	`toString(IStringifier<MultivariatePolynomialZp64> stringifier)`	convert this to string with the use of stringifier
`static MultivariatePolynomialZp64`	`zero(int nVariables, IntegersZp64 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, monicExact, multiply, multiply, setCoefficientRingFromOptional, subtract, toPositiveLC, toString

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Details
- ring
  
  public final IntegersZp64 ring
  
  The ring.
Method Details
- create
  
  public static MultivariatePolynomialZp64 create(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering, MonomialSet<MonomialZp64> terms)
  
  Creates multivariate polynomial from a set of monomials
  
  Parameters:
  
  nVariables - number of variables
  
  ring - the ring
  
  ordering - term ordering
  
  terms - the monomials
  
  Returns:
  
  multivariate polynomial
- create
  
  public static MultivariatePolynomialZp64 create(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering, Iterable<MonomialZp64> 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 MultivariatePolynomialZp64 create(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering, MonomialZp64... 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 MultivariatePolynomialZp64 zero(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering)
  
  Creates zero polynomial.
  
  Parameters:
  
  nVariables - number of variables
  
  ring - the ring
  
  ordering - the ordering
  
  Returns:
  
  zero
- one
  
  public static MultivariatePolynomialZp64 one(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering)
  
  Creates unit polynomial.
  
  Parameters:
  
  nVariables - number of variables
  
  ring - the ring
  
  ordering - the ordering
  
  Returns:
  
  unit
- parse
  
  public static MultivariatePolynomialZp64 parse(String string, IntegersZp64 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 MultivariatePolynomialZp64 parse(String string, IntegersZp64 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 MultivariatePolynomialZp64 parse(String string, IntegersZp64 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 differ, since the first one is considered as Z[x], while the second as Z[x1,x2]
  
  Returns:
  
  multivariate polynomial
- parse
  
  @Deprecated public static MultivariatePolynomialZp64 parse(String string, IntegersZp64 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
  
  Returns:
  
  multivariate polynomial
- asMultivariate
  
  public static MultivariatePolynomialZp64 asMultivariate(UnivariatePolynomialZp64 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 - the ordering
  
  Returns:
  
  multivariate polynomial
- asUnivariate
  
  public UnivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
  
  Returns:
  
  univariate polynomial
- asOverUnivariate
  
  public MultivariatePolynomial<UnivariatePolynomialZp64> 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<MonomialZp64,MultivariatePolynomialZp64>
  
  Parameters:
  
  variable - variable
  
  Returns:
  
  multivariate polynomial with coefficients being univariate polynomials over variable
- asOverUnivariateEliminate
  
  public MultivariatePolynomial<UnivariatePolynomialZp64> 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<MonomialZp64,MultivariatePolynomialZp64>
  
  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<MultivariatePolynomialZp64> 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<MonomialZp64,MultivariatePolynomialZp64>
  
  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<MultivariatePolynomialZp64> 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<MonomialZp64,MultivariatePolynomialZp64>
  
  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 MultivariatePolynomialZp64 asNormalMultivariate(MultivariatePolynomial<UnivariatePolynomialZp64> poly, int variable)
  
  Converts multivariate polynomial over univariate polynomial ring (Zp[variable][other_variables]) to a multivariate polynomial over coefficient ring (Zp[all_variables])
  
  Parameters:
  
  poly - the polynomial
  
  variable - the variable to insert
  
  Returns:
  
  multivariate polynomial over normal coefficient ring
- asNormalMultivariate
  
  public static MultivariatePolynomialZp64 asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomialZp64> 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 MultivariatePolynomialZp64 asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomialZp64> 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
- asPolyZSymmetric
  
  public MultivariatePolynomial<BigInteger> asPolyZSymmetric()
  
  Returns polynomial over Z formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
  
  Returns:
  
  Z[X] version of this with coefficients represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
- asPolyZ
  
  public MultivariatePolynomial<BigInteger> asPolyZ()
  
  Returns polynomial over Z formed from the coefficients of this
  
  Returns:
  
  Z[X] version of this
- toBigPoly
  
  public MultivariatePolynomial<BigInteger> toBigPoly()
  
  Returns polynomial over Z formed from the coefficients of this
  
  Returns:
  
  Z[X] version of this
- contentAsPoly
  
  public MultivariatePolynomialZp64 contentAsPoly()
  
  Description copied from interface: IPolynomial
  
  Returns the content of this (gcd of coefficients) as a constant poly
- lcAsPoly
  
  public MultivariatePolynomialZp64 lcAsPoly()
  
  Description copied from interface: IPolynomial
  
  Returns the leading coefficient as a constant poly
- lcAsPoly
  
  public MultivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
- ccAsPoly
  
  public MultivariatePolynomialZp64 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 MultivariatePolynomialZp64[] createArray(int length)
  
  Description copied from interface: IPolynomial
  
  overcome Java generics...
- createArray2d
  
  public MultivariatePolynomialZp64[][] createArray2d(int length)
  
  Description copied from interface: IPolynomial
  
  overcome Java generics...
- createArray2d
  
  public MultivariatePolynomialZp64[][] createArray2d(int length1, int length2)
  
  Description copied from interface: IPolynomial
  
  overcome Java generics...
- sameCoefficientRingWith
  
  public boolean sameCoefficientRingWith(MultivariatePolynomialZp64 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 MultivariatePolynomialZp64 setCoefficientRingFrom(MultivariatePolynomialZp64 lMonomialTerms)
  
  Description copied from interface: IPolynomial
  
  Set the coefficient ring from specified poly
  
  Parameters:
  
  lMonomialTerms - 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<MonomialZp64,MultivariatePolynomialZp64>
- setRing
  
  public MultivariatePolynomialZp64 setRing(long newModulus)
  
  Switches to another ring specified by newModulus
  
  Parameters:
  
  newModulus - the new modulus
  
  Returns:
  
  a copy of this reduced to the ring specified by newModulus
- setRing
  
  public MultivariatePolynomialZp64 setRing(IntegersZp64 newDomain)
  
  Switches to another ring specified by newDomain
  
  Parameters:
  
  newDomain - the new ring
  
  Returns:
  
  a copy of this reduced to the ring specified by newDomain
- setRing
  
  public <E> MultivariatePolynomial<E> setRing(Ring<E> newRing)
  
  Switches to another ring specified by newRing
  
  Parameters:
  
  newRing - the new ring
  
  Returns:
  
  a copy of this reduced to the ring specified by newRing
- setRingUnsafe
  
  public MultivariatePolynomialZp64 setRingUnsafe(IntegersZp64 newDomain)
  
  internal API
- createConstant
  
  public MultivariatePolynomialZp64 createConstant(long val)
  
  Creates constant polynomial with specified value
  
  Parameters:
  
  val - value
  
  Returns:
  
  constant polynomial with specified value
- createConstantFromTerm
  
  public MultivariatePolynomialZp64 createConstantFromTerm(MonomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
  
  Parameters:
  
  monomial - the monomial
  
  Returns:
  
  multivariate polynomial
- createZero
  
  public MultivariatePolynomialZp64 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 MultivariatePolynomialZp64 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 MultivariatePolynomialZp64 createLinear(int variable, long cc, long 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
- lc
  
  public long 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 long 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 MultivariatePolynomialZp64 setLC(long 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 long cc()
  
  Returns the constant coefficient of this polynomial.
  
  Returns:
  
  constant coefficient of this polynomial
- content
  
  public long content()
  
  Returns the content of this polynomial.
  
  Returns:
  
  content of this polynomial
- coefficients
  
  public long[] coefficients()
  
  Returns array of polynomial coefficients
  
  Returns:
  
  array of polynomial coefficients
- primitivePart
  
  public MultivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
  
  Parameters:
  
  variable - the variable
  
  Returns:
  
  primitive part of this considered as R[variable][other_variables]
- contentUnivariate
  
  public UnivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
  
  Parameters:
  
  variable - the variable
  
  Returns:
  
  the content of this considered as R[variable][other_variables]
- primitivePart
  
  public MultivariatePolynomialZp64 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 MultivariatePolynomialZp64 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 MultivariatePolynomialZp64 divideByLC(MultivariatePolynomialZp64 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
- divide
  
  public MultivariatePolynomialZp64 divide(long factor)
  
  Divides this polynomial by a factor
  
  Parameters:
  
  factor - the factor
  
  Returns:
  
  this / factor
- divideOrNull
  
  public MultivariatePolynomialZp64 divideOrNull(MonomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
  
  Parameters:
  
  monomial - monomial degrees
  
  Returns:
  
  this divided by the factor * monomial or null
- monic
  
  public MultivariatePolynomialZp64 monic()
  
  Makes this polynomial monic
  
  Returns:
  
  monic this
- monic
  
  public MultivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
- monic
  
  public MultivariatePolynomialZp64 monic(long factor)
  
  Sets this to its monic part (with respect to given ordering) multiplied by the given factor;
- monic
  
  public MultivariatePolynomialZp64 monic(Comparator<DegreeVector> ordering, long factor)
  
  Sets this to its monic part (with respect to given ordering) multiplied by the given factor;
- monicWithLC
  
  public MultivariatePolynomialZp64 monicWithLC(MultivariatePolynomialZp64 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 MultivariatePolynomialZp64 monicWithLC(Comparator<DegreeVector> ordering, MultivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
- toDenseRecursiveForm
  
  public IUnivariatePolynomial toDenseRecursiveForm()
  
  Gives a recursive univariate representation of this poly.
- fromDenseRecursiveForm
  
  public static MultivariatePolynomialZp64 fromDenseRecursiveForm(IUnivariatePolynomial recForm, Comparator<DegreeVector> ordering)
  
  Converts poly from a recursive univariate representation.
  
  Parameters:
  
  recForm - recursive univariate representation
  
  ordering - monomial order
- fromDenseRecursiveForm
  
  public static MultivariatePolynomialZp64 fromDenseRecursiveForm(IUnivariatePolynomial 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 long evaluateDenseRecursiveForm(IUnivariatePolynomial recForm, long[] 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 MultivariatePolynomialZp64 fromSparseRecursiveForm(AMultivariatePolynomial recForm, Comparator<DegreeVector> ordering)
  
  Converts poly from a sparse recursive univariate representation.
  
  Parameters:
  
  recForm - recursive univariate representation
  
  ordering - monomial order
- fromSparseRecursiveForm
  
  public static MultivariatePolynomialZp64 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 long evaluateSparseRecursiveForm(AMultivariatePolynomial recForm, long[] values)
  
  Evaluates polynomial given in a sparse recursive form at a given points
- getHornerForm
  
  public MultivariatePolynomialZp64.HornerFormZp64 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 MultivariatePolynomialZp64 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))
- evaluate
  
  public MultivariatePolynomialZp64 evaluate(int[] variables, long[] 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))
- evaluate
  
  public long evaluate(long... values)
  
  Evaluates this polynomial at specified points
- evaluate
  
  public MultivariatePolynomialZp64[] evaluate(int variable, long... values)
  
  Evaluates this polynomial at specified points
- eliminate
  
  public MultivariatePolynomialZp64 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)
- eliminate
  
  public MultivariatePolynomialZp64 eliminate(int[] variables, long[] 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 MultivariatePolynomialZp64.lPrecomputedPowersHolder mkPrecomputedPowers(int variable, long value)
- mkPrecomputedPowers
  
  public MultivariatePolynomialZp64.lPrecomputedPowersHolder mkPrecomputedPowers(int[] variables, long[] values)
- mkPrecomputedPowers
  
  public static MultivariatePolynomialZp64.lPrecomputedPowersHolder mkPrecomputedPowers(int nVariables, IntegersZp64 ring, int[] variables, long[] values)
- mkPrecomputedPowers
  
  public MultivariatePolynomialZp64.lPrecomputedPowersHolder mkPrecomputedPowers(long[] values)
- substitute
  
  public MultivariatePolynomialZp64 substitute(int variable, MultivariatePolynomialZp64 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 MultivariatePolynomialZp64 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 MultivariatePolynomialZp64 shift(int[] variables, long[] shifts)
  
  Substitutes variable -> variable + shift for each variable from variables array
  
  Parameters:
  
  variables - the variables
  
  shifts - the corresponding shifts
  
  Returns:
  
  a copy of this with variable -> variable + shift
- add
  
  public MultivariatePolynomialZp64 add(long oth)
  
  Adds oth to this polynomial and returns it
  
  Parameters:
  
  oth - other polynomial
  
  Returns:
  
  this + oth
- subtract
  
  public MultivariatePolynomialZp64 subtract(long oth)
  
  Subtracts oth from this polynomial and returns it
  
  Parameters:
  
  oth - other polynomial
  
  Returns:
  
  this - oth
- increment
  
  public MultivariatePolynomialZp64 increment()
  
  Description copied from interface: IPolynomial
  
  Adds 1 to this
  
  Returns:
  
  this + 1
- decrement
  
  public MultivariatePolynomialZp64 decrement()
  
  Description copied from interface: IPolynomial
  
  Subtracts 1 from this
  
  Returns:
  
  this - 1
- multiply
  
  public MultivariatePolynomialZp64 multiply(long factor)
  
  Description copied from interface: IPolynomial
  
  Multiplies this by factor
  
  Parameters:
  
  factor - the factor
  
  Returns:
  
  this * factor
- multiplyByLC
  
  public MultivariatePolynomialZp64 multiplyByLC(MultivariatePolynomialZp64 other)
  
  Description copied from interface: IPolynomial
  
  Multiply this by the leading coefficient of other
  
  Parameters:
  
  other - polynomial
  
  Returns:
  
  this * lc(other)
- multiplyByBigInteger
  
  public MultivariatePolynomialZp64 multiplyByBigInteger(BigInteger factor)
  
  Description copied from interface: IPolynomial
  
  Multiplies this by factor
  
  Parameters:
  
  factor - the factor
  
  Returns:
  
  this * factor
- multiply
  
  public MultivariatePolynomialZp64 multiply(MonomialZp64 monomial)
  
  Description copied from class: AMultivariatePolynomial
  
  Multiplies this by the monomial
  
  Specified by:
  
  multiply in class AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>
  
  Parameters:
  
  monomial - the monomial
  
  Returns:
  
  this multiplied by the monomial
- multiply
  
  public MultivariatePolynomialZp64 multiply(MultivariatePolynomialZp64 oth)
  
  Description copied from interface: IPolynomial
  
  Multiplies this by oth
  
  Parameters:
  
  oth - the polynomial
  
  Returns:
  
  this * oth
- square
  
  public MultivariatePolynomialZp64 square()
  
  Description copied from interface: IPolynomial
  
  Squares this
  
  Returns:
  
  this * this
- evaluateAtRandom
  
  public MultivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
- evaluateAtRandomPreservingSkeleton
  
  public MultivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
- derivative
  
  public MultivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
  
  Parameters:
  
  variable - the variable
  
  order - derivative order
  
  Returns:
  
  partial derivative of specified order with respect to specified variable
- seriesCoefficient
  
  public MultivariatePolynomialZp64 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<MonomialZp64,MultivariatePolynomialZp64>
  
  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)
- mapTerms
  
  public <T> MultivariatePolynomial<T> mapTerms(Ring<T> newRing, Function<MonomialZp64,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
- mapTerms
  
  public MultivariatePolynomialZp64 mapTerms(IntegersZp64 newRing, Function<MonomialZp64,MonomialZp64> mapper)
  
  Maps terms of this using specified mapping function
  
  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, LongFunction<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)
- mapCoefficientsAsPolys
  
  public <E> MultivariatePolynomial<E> mapCoefficientsAsPolys(Ring<E> ring, Function<MultivariatePolynomialZp64,E> mapper)
  
  Specified by:
  
  mapCoefficientsAsPolys in class AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>
- compareTo
  
  public int compareTo(MultivariatePolynomialZp64 oth)
- clone
  
  public MultivariatePolynomialZp64 clone()
  
  Description copied from interface: IPolynomial
  
  Deep copy of this
  
  Specified by:
  
  clone in interface IPolynomial<MultivariatePolynomialZp64>
  
  Specified by:
  
  clone in class AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>
  
  Returns:
  
  deep copy of this
- parsePoly
  
  @Deprecated public MultivariatePolynomialZp64 parsePoly(String string)
  
  Deprecated.
- toString
  
  public String toString(IStringifier<MultivariatePolynomialZp64> stringifier)
  
  Description copied from interface: Stringifiable
  
  convert this to string with the use of stringifier
- coefficientRingToString
  
  public String coefficientRingToString(IStringifier<MultivariatePolynomialZp64> stringifier)
  
  Description copied from interface: IPolynomial
  
  String representation of the coefficient ring of this

Class MultivariatePolynomialZp64

Nested Class Summary

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

Field Summary

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

Method Summary

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

Methods inherited from class java.lang.Object

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

Methods inherited from interface java.lang.Iterable

Field Details

ring

Method Details

create

create

create

zero

one

parse

parse

parse

parse

asMultivariate

asUnivariate

asOverUnivariate

asOverUnivariateEliminate

asOverMultivariate

asOverMultivariateEliminate

asNormalMultivariate

asNormalMultivariate

asNormalMultivariate

asPolyZSymmetric

asPolyZ

toBigPoly

contentAsPoly

lcAsPoly

lcAsPoly

ccAsPoly

isOverField

isOverFiniteField

isOverZ

coefficientRingCardinality

coefficientRingCharacteristic

isOverPerfectPower

coefficientRingPerfectPowerBase

coefficientRingPerfectPowerExponent

createArray

createArray2d

createArray2d

sameCoefficientRingWith

setCoefficientRingFrom

release

setRing

setRing

setRing

setRingUnsafe

createConstant

createConstantFromTerm

createZero

createOne

createLinear

isMonic

signumOfLC

isOne

isUnitCC

isConstant

lc

lc

setLC

cc

content

coefficients

primitivePart

contentUnivariate

primitivePart

primitivePartSameSign

divideByLC

divide

divideOrNull

monic