MultivariatePolynomialZp64 (rings 2.1 API)

java.lang.Object
- cc.redberry.rings.poly.multivar.AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>
- - cc.redberry.rings.poly.multivar.MultivariatePolynomialZp64

All Implemented Interfaces:

IPolynomial<MultivariatePolynomialZp64>, WithVariables, 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/interfaces inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial
  AMultivariatePolynomial.PolynomialCollector<Term extends DegreeVector<Term>,Poly extends AMultivariatePolynomial<Term,Poly>>

Field Summary

Fields
Modifier and Type Field and Description

IntegersZp64 ring
The ring.
- Fields inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial
  nVariables, ordering

Fields
Modifier and Type	Field and Description
`IntegersZp64`	`ring` The ring.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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)` 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()` 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, Iterable<MonomialZp64> terms)` Creates multivariate polynomial from a list of monomial terms
`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
`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`	`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)
`MonomialZp64`	`createTermWithUnitCoefficient(int[] exponents)` creates term with specified exponents and unit coefficient
`MonomialZp64`	`createUnitTerm()` creates a unit term
`MultivariatePolynomialZp64`	`createZero()` Returns the new instance of zero polynomial (with the same coefficient ring)
`MonomialZp64`	`createZeroTerm()` creates a zero term
`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 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... values)` Evaluates this polynomial at specified points
`MultivariatePolynomialZp64`	`evaluate(int variable, long value)` Returns a copy of this with `value` substituted for `variable`
`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
`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
`boolean`	`isZero()` Returns `true` if this is zero
`long`	`lc()` Returns the leading coefficient of this polynomial that is coefficient of the largest term according to the ordering.
`MultivariatePolynomialZp64`	`lcAsPoly()` Returns the leading coefficient as a constant poly
`MonomialZp64`	`lt()` Returns the leading term in this polynomial according to ordering
`<T> MultivariatePolynomial<T>`	`mapCoefficients(Ring<T> newRing, LongFunction<T> mapper)` Maps coefficients 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`	`monic()` Makes this polynomial monic
`MultivariatePolynomialZp64`	`monic(long factor)` Sets `this` to its monic part multiplied by the `factor` modulo `modulus` (that is `monic(modulus).multiply(factor)` ).
`MultivariatePolynomialZp64`	`monicWithLC(MultivariatePolynomialZp64 other)` Sets `this` to its monic part multiplied by the leading coefficient of `other`;
`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`
`MultivariatePolynomialZp64`	`negate()` Negates this and returns
`static MultivariatePolynomialZp64`	`one(int nVariables, IntegersZp64 ring, Comparator<DegreeVector> ordering)` Creates unit polynomial.
`static MultivariatePolynomialZp64`	`parse(String string, IntegersZp64 ring, Comparator<DegreeVector> ordering, String... variables)` Parse multivariate polynomial from string.
`static MultivariatePolynomialZp64`	`parse(String string, IntegersZp64 ring, String... variables)` Parse multivariate polynomial from string.
`MultivariatePolynomialZp64`	`parsePoly(String string)` Parse string representation of polynomial
`MultivariatePolynomialZp64`	`parsePoly(String string, String[] variables)` Parse string representation of polynomial
`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(IntegersZp64 newDomain)` Switches to another ring specified by `newDomain`
`MultivariatePolynomialZp64`	`setRing(long newModulus)` Switches to another ring specified by `newModulus`
`<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
`String`	`toString(String... vars)` Returns string representation of this using specified string representation for variables.
`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, asMultivariate, asMultivariate, asMultivariate, asUnivariate, asUnivariateEliminate, coefficientOf, coefficientOf, content, contentExcept, create, create, create, createMonomial, degree, degree, degreeMax, degrees, degrees, degreeSum, derivative, derivative, divideDegreeVectorOrNull, dropVariable, dropVariables, equals, evaluateAtZero, evaluateAtZero, getSkeleton, getSkeleton, getSkeletonExcept, hashCode, insertVariable, isEffectiveUnivariate, isMonomial, iterator, joinNewVariable, joinNewVariables, lc, monomialContent, multidegree, multiplyByDegreeVector, multiplyByMonomial, nUsedVariables, renameVariables, renameVariables, sameSkeletonExceptQ, sameSkeletonQ, sameSkeletonQ, set, setAllCoefficientsToUnit, setLC, setOrdering, size, sparsity, subtract, subtract, subtractLt, swapVariables, toString, toZero, 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, copy, createArray, monicExact, multiply, multiply, subtract

Methods inherited from interface cc.redberry.rings.WithVariables
defaultVars

Methods inherited from interface java.lang.Iterable
forEach, spliterator

- Field Detail
  - ring
```
public final IntegersZp64 ring
```
    The ring.
- Method Detail
  - 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
```
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
  - 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)
```
    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
    
    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
  - ccAsPoly
```
public MultivariatePolynomialZp64 ccAsPoly()
```
    Description copied from interface: IPolynomial
    
    Returns the constant coefficient as a constant poly
  - createTermWithUnitCoefficient
```
public MonomialZp64 createTermWithUnitCoefficient(int[] exponents)
```
    Description copied from class: AMultivariatePolynomial
    
    creates term with specified exponents and unit coefficient
    
    Specified by:
    
    createTermWithUnitCoefficient in class AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>
  - createUnitTerm
```
public MonomialZp64 createUnitTerm()
```
    Description copied from class: AMultivariatePolynomial
    
    creates a unit term
    
    Specified by:
    
    createUnitTerm in class AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>
  - createZeroTerm
```
public MonomialZp64 createZeroTerm()
```
    Description copied from class: AMultivariatePolynomial
    
    creates a zero term
    
    Specified by:
    
    createZeroTerm in class AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>
  - 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
  - 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
  - isZero
```
public boolean isZero()
```
    Description copied from interface: IPolynomial
    
    Returns true if this is zero
    
    Returns:
    
    whether this is zero
  - 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
  - lt
```
public MonomialZp64 lt()
```
    Description copied from class: AMultivariatePolynomial
    
    Returns the leading term in this polynomial according to ordering
    
    Specified by:
    
    lt in class AMultivariatePolynomial<MonomialZp64,MultivariatePolynomialZp64>
    
    Returns:
    
    the leading term in this polynomial according to ordering
  - 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
  - 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(long 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
  - 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
  - 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 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)
  - 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
  - negate
```
public MultivariatePolynomialZp64 negate()
```
    Description copied from interface: IPolynomial
    
    Negates this and returns
    
    Returns:
    
    this negated
  - 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
  - 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)
  - 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
```
public MultivariatePolynomialZp64 parsePoly(String string)
```
    Description copied from interface: IPolynomial
    
    Parse string representation of polynomial
    
    Parameters:
    
    string - string
    
    Returns:
    
    the polynomial corresponding to specified string
  - parsePoly
```
public MultivariatePolynomialZp64 parsePoly(String string,
                                            String[] variables)
```
    Description copied from interface: IPolynomial
    
    Parse string representation of polynomial
    
    Parameters:
    
    string - string
    
    variables - names of variables
    
    Returns:
    
    the polynomial corresponding to specified string
  - toString
```
public String toString(String... vars)
```
    Description copied from interface: WithVariables
    
    Returns string representation of this using specified string representation for variables.
    
    Parameters:
    
    vars - string values of variables
    
    Returns:
    
    string representation of this
  - coefficientRingToString
```
public String coefficientRingToString()
```
    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 cc.redberry.rings.WithVariables

Methods inherited from interface java.lang.Iterable

Field Detail

ring

Method Detail

create

create

create

zero

one

parse

parse

asMultivariate

asUnivariate

asOverUnivariate

asOverUnivariateEliminate

asOverMultivariate

asOverMultivariateEliminate

asNormalMultivariate

asNormalMultivariate

asNormalMultivariate

asPolyZSymmetric

asPolyZ

toBigPoly

contentAsPoly

lcAsPoly

ccAsPoly

createTermWithUnitCoefficient

createUnitTerm

createZeroTerm

isOverField

isOverFiniteField

isOverZ

coefficientRingCardinality

coefficientRingCharacteristic

isOverPerfectPower

coefficientRingPerfectPowerBase

coefficientRingPerfectPowerExponent

createArray

createArray2d

createArray2d

sameCoefficientRingWith

setCoefficientRingFrom

release

setRing

setRing

setRing

setRingUnsafe

createConstant

createZero

createOne

createLinear

isMonic

signumOfLC

isZero

isOne

isUnitCC

isConstant

lt

lc

setLC

cc

content

coefficients

primitivePart

contentUnivariate

primitivePart

primitivePartSameSign

divideByLC

divide

divideOrNull