java.lang.Object
- cc.redberry.rings.poly.multivar.AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
- - cc.redberry.rings.poly.multivar.MultivariatePolynomial<E>

All Implemented Interfaces:

Stringifiable<MultivariatePolynomial<E>>, IPolynomial<MultivariatePolynomial<E>>, Serializable, Comparable<MultivariatePolynomial<E>>, Iterable<Monomial<E>>
```
public final class MultivariatePolynomial<E>
extends AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
```
Since:

1.0

See Also:

Serialized Form

Nested Class Summary

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

Nested classes/interfaces inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial
AMultivariatePolynomial.PolynomialCollector<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>>

Field Summary

Fields
Modifier and Type Field Description

Ring<E> ring
The coefficient ring
- Fields inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial
  monomialAlgebra, nVariables, ordering

Method Summary

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

Methods inherited from class cc.redberry.rings.poly.multivar.AMultivariatePolynomial
add, add, add, add, ascendingIterator, asMultivariate, asMultivariate, asMultivariate, asOverMultivariateEliminate, asOverPoly, asUnivariate, asUnivariateEliminate, coefficientOf, coefficientOf, collection, composition, composition, composition, composition, composition, composition, content, contentExcept, create, create, create, create, createMonomial, degree, degree, degree, degreeMax, degrees, degrees, degreesRef, degreeSum, derivative, derivative, descendingIterator, divideDegreeVectorOrNull, dropCoefficientOf, dropSelectVariables, dropVariable, dropVariables, ecart, equals, evaluateAtZero, evaluateAtZero, first, getSkeleton, getSkeleton, getSkeletonDrop, getSkeletonExcept, hashCode, homogenize, insertVariable, insertVariable, isEffectiveUnivariate, isHomogeneous, isLinearExactly, isLinearOrConstant, isMonomial, isVariable, isZero, isZeroCC, iterator, joinNewVariable, joinNewVariables, last, lc, lt, lt, ltAsPoly, mapVariables, monomialContent, mt, multidegree, multiplyByDegreeVector, multiplyByMonomial, negate, nUsedVariables, 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, univariateVariable

Methods inherited from class java.lang.Object
finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface cc.redberry.rings.poly.IPolynomial
add, assertSameCoefficientRingWith, canonical, coefficientRingToString, copy, createArray, createArray, createArray, createConstant, monicExact, multiply, multiply, setCoefficientRingFromOptional, subtract, toPositiveLC, toString

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

- Field Detail
  - ring
```
public final Ring<E> ring
```
    The coefficient ring
- Method Detail
  - create
```
public static <E> MultivariatePolynomial<E> create(int nVariables,
                                                   Ring<E> ring,
                                                   Comparator<DegreeVector> ordering,
                                                   Iterable<Monomial<E>> terms)
```
    Creates multivariate polynomial from a list of monomial terms
    
    Parameters:
    
    ring - the ring
    
    ordering - term ordering
    
    terms - the monomial terms
    
    Returns:
    
    multivariate polynomial
  - create
```
public static <E> MultivariatePolynomial<E> create(int nVariables,
                                                   Ring<E> ring,
                                                   Comparator<DegreeVector> ordering,
                                                   Monomial<E>... terms)
```
    Creates multivariate polynomial from a list of monomial terms
    
    Parameters:
    
    ring - the ring
    
    ordering - term ordering
    
    terms - the monomial terms
    
    Returns:
    
    multivariate polynomial
  - zero
```
public static <E> MultivariatePolynomial<E> zero(int nVariables,
                                                 Ring<E> ring,
                                                 Comparator<DegreeVector> ordering)
```
    Creates zero polynomial.
    
    Parameters:
    
    nVariables - number of variables
    
    ring - the ring
    
    ordering - the ordering
    
    Returns:
    
    zero polynomial
  - one
```
public static <E> MultivariatePolynomial<E> one(int nVariables,
                                                Ring<E> ring,
                                                Comparator<DegreeVector> ordering)
```
    Creates unit polynomial.
    
    Parameters:
    
    nVariables - number of variables
    
    ring - the ring
    
    ordering - the ordering
    
    Returns:
    
    unit polynomial
  - parse
```
public static MultivariatePolynomial<BigInteger> parse(String string,
                                                       String... variables)
```
    Parse multivariate Z[X] polynomial from string.
    
    Parameters:
    
    string - the string
    
    variables - string variables that should be taken into account. For examples: parse("a", LEX) and parse("a", LEX, "a", "b") although give the same mathematical expressions are differ, since the first one is considered as Z[x], while the second as Z[x1,x2]
    
    Returns:
    
    multivariate Z[X] polynomial
  - parse
```
@Deprecated
public static MultivariatePolynomial<BigInteger> parse(String string)
```
    Deprecated.
    use #parse(string, ring, ordering, variables)
    
    Parse multivariate Z[X] polynomial from string.
    
    Parameters:
    
    string - the string
    
    Returns:
    
    multivariate Z[X] polynomial
  - parse
```
public static <E> MultivariatePolynomial<E> parse(String string,
                                                  Ring<E> ring,
                                                  String... variables)
```
    Parse multivariate polynomial from string.
    
    Parameters:
    
    string - the string
    
    ring - the ring
    
    variables - string variables that should be taken into account. For examples: parse("a", LEX) and parse("a", LEX, "a", "b") although give the same mathematical expressions are differ, since the first one is considered as Z[x], while the second as Z[x1,x2]
    
    Returns:
    
    multivariate polynomial
  - parse
```
@Deprecated
public static <E> MultivariatePolynomial<E> parse(String string,
                                                  Ring<E> ring)
```
    Deprecated.
    use #parse(string, ring, ordering, variables)
    
    Parse multivariate polynomial from string.
    
    Parameters:
    
    string - the string
    
    ring - the ring
    
    Returns:
    
    multivariate polynomial
  - parse
```
public static MultivariatePolynomial<BigInteger> parse(String string,
                                                       Comparator<DegreeVector> ordering,
                                                       String... variables)
```
    Parse multivariate Z[X] polynomial from string.
    
    Parameters:
    
    string - the string
    
    ordering - monomial order
    
    variables - string variables that should be taken into account. For examples: parse("a", LEX) and parse("a", LEX, "a", "b") although give the same mathematical expressions are differ, since the first one is considered as Z[x], while the second as Z[x1,x2]
    
    Returns:
    
    Z[X] multivariate polynomial
  - parse
```
@Deprecated
public static MultivariatePolynomial<BigInteger> parse(String string,
                                                       Comparator<DegreeVector> ordering)
```
    Deprecated.
    use #parse(string, ring, ordering, variables)
    
    Parse multivariate Z[X] polynomial from string.
    
    Parameters:
    
    string - the string
    
    ordering - monomial order
    
    Returns:
    
    Z[X] multivariate polynomial
  - parse
```
public static <E> MultivariatePolynomial<E> parse(String string,
                                                  Ring<E> ring,
                                                  Comparator<DegreeVector> ordering,
                                                  String... variables)
```
    Parse multivariate polynomial from string.
    
    Parameters:
    
    string - the string
    
    ring - the ring
    
    ordering - monomial order
    
    variables - string variables that should be taken into account. For examples: parse("a", LEX) and parse("a", LEX, "a", "b") although give the same mathematical expressions are different, since the first one is considered as Z[a], while the second as Z[a,b]
    
    Returns:
    
    multivariate polynomial
  - parse
```
@Deprecated
public static <E> MultivariatePolynomial<E> parse(String string,
                                                  Ring<E> ring,
                                                  Comparator<DegreeVector> ordering)
```
    Deprecated.
    use #parse(string, ring, ordering, variables)
    
    Parse multivariate polynomial from string.
    
    Parameters:
    
    string - the string
    
    ring - the ring
    
    ordering - monomial order
  - asOverZp64
```
public static MultivariatePolynomialZp64 asOverZp64(MultivariatePolynomial<BigInteger> poly)
```
    Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers
    
    Parameters:
    
    poly - the polynomial
    
    Returns:
    
    multivariate polynomial over machine sized modular integers
    
    Throws:
    
    IllegalArgumentException - if poly.ring is not Zp
    
    ArithmeticException - if some of coefficients will not exactly fit in a long.
  - asOverZp64
```
public static MultivariatePolynomialZp64 asOverZp64(MultivariatePolynomial<BigInteger> poly,
                                                    IntegersZp64 ring)
```
    Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers
    
    Parameters:
    
    poly - the polynomial
    
    ring - Zp64 ring
    
    Returns:
    
    multivariate polynomial over machine sized modular integers
    
    Throws:
    
    IllegalArgumentException - if poly.ring is not Zp
    
    ArithmeticException - if some of coefficients will not exactly fit in a long.
  - asMultivariate
```
public static <E> MultivariatePolynomial<E> asMultivariate(UnivariatePolynomial<E> poly,
                                                           int nVariables,
                                                           int variable,
                                                           Comparator<DegreeVector> ordering)
```
    Converts univariate polynomial to multivariate.
    
    Parameters:
    
    poly - univariate polynomial
    
    nVariables - number of variables in the result
    
    variable - variable that will be used as a primary variable
    
    ordering - monomial order
    
    Returns:
    
    multivariate polynomial
  - asUnivariate
```
public UnivariatePolynomial<E> asUnivariate()
```
    Description copied from class: AMultivariatePolynomial
    
    Converts this to univariate polynomial or throws exception if conversion is impossible (more than one variable have non zero exponents)
    
    Specified by:
    
    asUnivariate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Returns:
    
    univariate polynomial
  - asOverUnivariate
```
public MultivariatePolynomial<UnivariatePolynomial<E>> asOverUnivariate(int variable)
```
    Description copied from class: AMultivariatePolynomial
    
    Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable
    
    Specified by:
    
    asOverUnivariate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    variable - variable
    
    Returns:
    
    multivariate polynomial with coefficients being univariate polynomials over variable
  - asOverUnivariateEliminate
```
public MultivariatePolynomial<UnivariatePolynomial<E>> asOverUnivariateEliminate(int variable)
```
    Description copied from class: AMultivariatePolynomial
    
    Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable, the resulting polynomial have (nVariable - 1) multivariate variables (specified variable is eliminated)
    
    Specified by:
    
    asOverUnivariateEliminate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    variable - the variable
    
    Returns:
    
    multivariate polynomial with coefficients being univariate polynomials over variable, the resulting polynomial have (nVariable - 1) multivariate variables
  - asOverMultivariate
```
public MultivariatePolynomial<MultivariatePolynomial<E>> asOverMultivariate(int... variables)
```
    Description copied from class: AMultivariatePolynomial
    
    Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
    
    Specified by:
    
    asOverMultivariate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    variables - the variables to separate
    
    Returns:
    
    multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
  - asOverMultivariateEliminate
```
public MultivariatePolynomial<MultivariatePolynomial<E>> asOverMultivariateEliminate(int[] variables,
                                                                                     Comparator<DegreeVector> ordering)
```
    Description copied from class: AMultivariatePolynomial
    
    Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
    
    Specified by:
    
    asOverMultivariateEliminate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    variables - the variables to separate
    
    ordering - monomial order to use for result
    
    Returns:
    
    multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
  - asNormalMultivariate
```
public static <E> MultivariatePolynomial<E> asNormalMultivariate(MultivariatePolynomial<UnivariatePolynomial<E>> poly,
                                                                 int variable)
```
    Converts multivariate polynomial over univariate polynomial ring (R[variable][other_variables]) to a multivariate polynomial over coefficient ring (R[variables])
    
    Parameters:
    
    poly - the polynomial
    
    variable - the variable to insert
    
    Returns:
    
    multivariate polynomial over normal coefficient ring
  - asNormalMultivariate
```
public static <E> MultivariatePolynomial<E> asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly)
```
    Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
    
    Parameters:
    
    poly - the polynomial
    
    Returns:
    
    multivariate polynomial over normal coefficient ring
  - asNormalMultivariate
```
public static <E> MultivariatePolynomial<E> asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly,
                                                                 int[] coefficientVariables,
                                                                 int[] mainVariables)
```
    Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
    
    Parameters:
    
    poly - the polynomial
    
    Returns:
    
    multivariate polynomial over normal coefficient ring
  - asPolyZ
```
public static MultivariatePolynomial<BigInteger> asPolyZ(MultivariatePolynomial<BigInteger> poly,
                                                         boolean copy)
```
    Returns Z[X] polynomial formed from the coefficients of the poly.
    
    Parameters:
    
    poly - the polynomial
    
    copy - whether to copy the internal data
    
    Returns:
    
    Z[X] version of the poly
  - asPolyZSymmetric
```
public static MultivariatePolynomial<BigInteger> asPolyZSymmetric(MultivariatePolynomial<BigInteger> poly)
```
    Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
    
    Parameters:
    
    poly - Zp polynomial
    
    Returns:
    
    Z[x] version of the poly with coefficients represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
    
    Throws:
    
    IllegalArgumentException - is poly.ring is not a IntegersZp
  - contentAsPoly
```
public MultivariatePolynomial<E> contentAsPoly()
```
    Description copied from interface: IPolynomial
    
    Returns the content of this (gcd of coefficients) as a constant poly
  - lcAsPoly
```
public MultivariatePolynomial<E> lcAsPoly()
```
    Description copied from interface: IPolynomial
    
    Returns the leading coefficient as a constant poly
  - lcAsPoly
```
public MultivariatePolynomial<E> lcAsPoly(Comparator<DegreeVector> ordering)
```
    Description copied from class: AMultivariatePolynomial
    
    Returns the leading coefficient with respect to specified ordering as a constant poly
    
    Specified by:
    
    lcAsPoly in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
  - ccAsPoly
```
public MultivariatePolynomial<E> ccAsPoly()
```
    Description copied from interface: IPolynomial
    
    Returns the constant coefficient as a constant poly
  - isOverField
```
public boolean isOverField()
```
    Description copied from interface: IPolynomial
    
    Returns whether the coefficient ring of this polynomial is a field
    
    Returns:
    
    whether the coefficient ring of this polynomial is a field
  - isOverFiniteField
```
public boolean isOverFiniteField()
```
    Description copied from interface: IPolynomial
    
    Returns whether the coefficient ring of this polynomial is a finite field
    
    Returns:
    
    whether the coefficient ring of this polynomial is a finite field
  - isOverZ
```
public boolean isOverZ()
```
    Description copied from interface: IPolynomial
    
    Returns whether the coefficient ring of this polynomial is Z
    
    Returns:
    
    whether the coefficient ring of this polynomial is Z
  - coefficientRingCardinality
```
public BigInteger coefficientRingCardinality()
```
    Description copied from interface: IPolynomial
    
    Returns cardinality of the coefficient ring of this poly
    
    Returns:
    
    cardinality of the coefficient ring
  - coefficientRingCharacteristic
```
public BigInteger coefficientRingCharacteristic()
```
    Description copied from interface: IPolynomial
    
    Returns characteristic of the coefficient ring of this poly
    
    Returns:
    
    characteristic of the coefficient ring
  - isOverPerfectPower
```
public boolean isOverPerfectPower()
```
    Description copied from interface: IPolynomial
    
    Returns whether the coefficientRingCardinality() is a perfect power
    
    Returns:
    
    whether the coefficientRingCardinality() is a perfect power
  - coefficientRingPerfectPowerBase
```
public BigInteger coefficientRingPerfectPowerBase()
```
    Description copied from interface: IPolynomial
    
    Returns base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
    
    Returns:
    
    base so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
  - coefficientRingPerfectPowerExponent
```
public BigInteger coefficientRingPerfectPowerExponent()
```
    Description copied from interface: IPolynomial
    
    Returns exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
    
    Returns:
    
    exponent so that coefficientRingCardinality() == base^exponent or null if cardinality is not finite
  - createArray
```
public MultivariatePolynomial<E>[] createArray(int length)
```
    Description copied from interface: IPolynomial
    
    overcome Java generics...
  - createArray2d
```
public MultivariatePolynomial<E>[][] createArray2d(int length)
```
    Description copied from interface: IPolynomial
    
    overcome Java generics...
  - createArray2d
```
public MultivariatePolynomial<E>[][] createArray2d(int length1,
                                                   int length2)
```
    Description copied from interface: IPolynomial
    
    overcome Java generics...
  - sameCoefficientRingWith
```
public boolean sameCoefficientRingWith(MultivariatePolynomial<E> oth)
```
    Description copied from interface: IPolynomial
    
    Returns whether oth and this have the same coefficient ring
    
    Parameters:
    
    oth - other polynomial
    
    Returns:
    
    whether this and oth are over the same coefficient ring
  - setCoefficientRingFrom
```
public MultivariatePolynomial<E> setCoefficientRingFrom(MultivariatePolynomial<E> poly)
```
    Description copied from interface: IPolynomial
    
    Set the coefficient ring from specified poly
    
    Parameters:
    
    poly - the polynomial
    
    Returns:
    
    a copy of this with the coefficient ring taken from poly
  - release
```
protected void release()
```
    release caches
    
    Overrides:
    
    release in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
  - setRing
```
public MultivariatePolynomial<E> setRing(Ring<E> newRing)
```
    Returns a copy of this with coefficient reduced to a newRing
    
    Parameters:
    
    newRing - the new ring
    
    Returns:
    
    a copy of this reduced to the ring specified by newRing
  - setRingUnsafe
```
public MultivariatePolynomial<E> setRingUnsafe(Ring<E> newRing)
```
    internal API
  - createConstant
```
public MultivariatePolynomial<E> createConstant(E val)
```
    Creates constant polynomial with specified value
    
    Parameters:
    
    val - value
    
    Returns:
    
    constant polynomial with specified value
  - createConstantFromTerm
```
public MultivariatePolynomial<E> createConstantFromTerm(Monomial<E> monomial)
```
    Description copied from class: AMultivariatePolynomial
    
    Creates multivariate polynomial over the same ring as this with the single constant element taken from given monomial
    
    Specified by:
    
    createConstantFromTerm in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    monomial - the monomial
    
    Returns:
    
    multivariate polynomial
  - createZero
```
public MultivariatePolynomial<E> createZero()
```
    Description copied from interface: IPolynomial
    
    Returns the new instance of zero polynomial (with the same coefficient ring)
    
    Returns:
    
    new instance of 0
  - createOne
```
public MultivariatePolynomial<E> createOne()
```
    Description copied from interface: IPolynomial
    
    Returns the new instance of unit polynomial (with the same coefficient ring)
    
    Returns:
    
    new instance of 1
  - createLinear
```
public final MultivariatePolynomial<E> createLinear(int variable,
                                                    E cc,
                                                    E lc)
```
    Creates linear polynomial of the form cc + lc * variable
    
    Parameters:
    
    variable - the variable
    
    cc - the constant coefficient
    
    lc - the leading coefficient
    
    Returns:
    
    linear polynomial cc + lc * variable
  - isMonic
```
public boolean isMonic()
```
    Description copied from interface: IPolynomial
    
    Returns true if this polynomial is monic
    
    Returns:
    
    whether this is monic
  - signumOfLC
```
public int signumOfLC()
```
    Description copied from interface: IPolynomial
    
    Gives signum of the leading coefficient
    
    Returns:
    
    signum of the leading coefficient
  - isOne
```
public boolean isOne()
```
    Description copied from interface: IPolynomial
    
    Returns true if this is one
    
    Returns:
    
    whether this is one
  - isUnitCC
```
public boolean isUnitCC()
```
    Description copied from interface: IPolynomial
    
    Returns true if constant term is equal to one
    
    Returns:
    
    whether constant term is 1
  - isConstant
```
public boolean isConstant()
```
    Description copied from interface: IPolynomial
    
    Returns true if this polynomial has only constant term
    
    Returns:
    
    whether this is constant
  - maxAbsCoefficient
```
public E maxAbsCoefficient()
```
    Returns max absolute coefficient
  - lc
```
public E lc()
```
    Returns the leading coefficient of this polynomial that is coefficient of the largest term according to the ordering.
    
    Returns:
    
    leading coefficient of this polynomial
  - lc
```
public E lc(Comparator<DegreeVector> ordering)
```
    Returns the leading coefficient of this polynomial with respect to specified ordering
    
    Returns:
    
    leading coefficient of this polynomial with respect to specified ordering
  - setLC
```
public MultivariatePolynomial<E> setLC(E val)
```
    Sets the leading coefficient to the specified value
    
    Parameters:
    
    val - new value for the lc
    
    Returns:
    
    the leading coefficient to the specified value
  - cc
```
public E cc()
```
    Returns the constant coefficient of this polynomial.
    
    Returns:
    
    constant coefficient of this polynomial
  - content
```
public E content()
```
    Returns the content of this polynomial.
    
    Returns:
    
    content of this polynomial
  - coefficients
```
public Iterable<E> coefficients()
```
    Returns iterable over polynomial coefficients
    
    Returns:
    
    iterable over polynomial coefficients
  - coefficientsArray
```
public E[] coefficientsArray()
```
    Returns array of polynomial coefficients
    
    Returns:
    
    array of polynomial coefficients
  - primitivePart
```
public MultivariatePolynomial<E> primitivePart(int variable)
```
    Description copied from class: AMultivariatePolynomial
    
    Gives primitive part of this considered as R[variable][other_variables]
    
    Specified by:
    
    primitivePart in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    variable - the variable
    
    Returns:
    
    primitive part of this considered as R[variable][other_variables]
  - contentUnivariate
```
public UnivariatePolynomial<E> contentUnivariate(int variable)
```
    Description copied from class: AMultivariatePolynomial
    
    Gives the content of this considered as R[variable][other_variables]
    
    Specified by:
    
    contentUnivariate in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    variable - the variable
    
    Returns:
    
    the content of this considered as R[variable][other_variables]
  - primitivePart
```
public MultivariatePolynomial<E> primitivePart()
```
    Description copied from interface: IPolynomial
    
    Reduces poly to its primitive part (primitive part will always have positive l.c.)
    
    Returns:
    
    primitive part (poly will be modified)
  - primitivePartSameSign
```
public MultivariatePolynomial<E> primitivePartSameSign()
```
    Description copied from interface: IPolynomial
    
    Reduces poly to its primitive part, so that primitive part will have the same signum as the initial poly
    
    Returns:
    
    primitive part (poly will be modified)
  - divideByLC
```
public MultivariatePolynomial<E> divideByLC(MultivariatePolynomial<E> other)
```
    Description copied from interface: IPolynomial
    
    Divides this polynomial by the leading coefficient of other or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the other.lc(). NOTE: if null is returned, the content of this is destroyed.
    
    Parameters:
    
    other - the polynomial
    
    Returns:
    
    this divided by the other.lc() or null if exact division is not possible
  - divideOrNull
```
public MultivariatePolynomial<E> divideOrNull(E factor)
```
    Divides this polynomial by a factor or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the factor. NOTE: if null is returned, the content of this is destroyed.
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this divided by the factor or null
  - divideExact
```
public MultivariatePolynomial<E> divideExact(E factor)
```
    Divides this polynomial by a factor or throws exception if exact division is not possible
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this divided by the factor
    
    Throws:
    
    ArithmeticException - if exact division is not possible
  - divideOrNull
```
public MultivariatePolynomial<E> divideOrNull(Monomial<E> monomial)
```
    Description copied from class: AMultivariatePolynomial
    
    Divides this polynomial by a monomial or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the monomial. NOTE: if null is returned, the content of this is destroyed.
    
    Specified by:
    
    divideOrNull in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    monomial - monomial degrees
    
    Returns:
    
    this divided by the factor * monomial or null
  - monic
```
public MultivariatePolynomial<E> monic()
```
    Makes this polynomial monic if possible, if not -- destroys this and returns null
    
    Returns:
    
    monic this or null if the ring does not support exact division by lc
  - monic
```
public MultivariatePolynomial<E> monic(Comparator<DegreeVector> ordering)
```
    Description copied from class: AMultivariatePolynomial
    
    Make this poly monic considering leading term with respect to given ordering
    
    Specified by:
    
    monic in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
  - monic
```
public MultivariatePolynomial<E> monic(E factor)
```
    Sets this to its monic part multiplied by the factor modulo modulus (that is monic(modulus).multiply(factor) ).
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this
  - monic
```
public MultivariatePolynomial<E> monic(Comparator<DegreeVector> ordering,
                                       E factor)
```
    Sets this to its monic part (with respect to given ordering) multiplied by the given factor;
  - monicWithLC
```
public MultivariatePolynomial<E> monicWithLC(MultivariatePolynomial<E> other)
```
    Description copied from interface: IPolynomial
    
    Sets this to its monic part multiplied by the leading coefficient of other;
    
    Parameters:
    
    other - other polynomial
    
    Returns:
    
    monic part multiplied by the leading coefficient of other or null if exact division by the reduced leading coefficient is not possible
  - monicWithLC
```
public MultivariatePolynomial<E> monicWithLC(Comparator<DegreeVector> ordering,
                                             MultivariatePolynomial<E> other)
```
    Description copied from class: AMultivariatePolynomial
    
    Sets this to its monic part multiplied by the leading coefficient of other with respect to given ordering
    
    Specified by:
    
    monicWithLC in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
  - toDenseRecursiveForm
```
public UnivariatePolynomial toDenseRecursiveForm()
```
    Gives a recursive univariate representation of this poly.
  - fromDenseRecursiveForm
```
public static <E> MultivariatePolynomial<E> fromDenseRecursiveForm(UnivariatePolynomial recForm,
                                                                   int nVariables,
                                                                   Comparator<DegreeVector> ordering)
```
    Converts poly from a recursive univariate representation.
    
    Parameters:
    
    recForm - recursive univariate representation
    
    nVariables - number of variables in multivariate polynomial
    
    ordering - monomial order
  - evaluateDenseRecursiveForm
```
public static <E> E evaluateDenseRecursiveForm(UnivariatePolynomial recForm,
                                               int nVariables,
                                               E[] values)
```
    Evaluates polynomial given in a dense recursive form at a given points
  - toSparseRecursiveForm
```
public AMultivariatePolynomial toSparseRecursiveForm()
```
    Gives a recursive sparse univariate representation of this poly.
  - fromSparseRecursiveForm
```
public static <E> MultivariatePolynomial<E> fromSparseRecursiveForm(AMultivariatePolynomial recForm,
                                                                    int nVariables,
                                                                    Comparator<DegreeVector> ordering)
```
    Converts poly from a recursive univariate representation.
    
    Parameters:
    
    recForm - recursive univariate representation
    
    nVariables - number of variables in multivariate polynomial
    
    ordering - monomial order
  - evaluateSparseRecursiveForm
```
public static <E> E evaluateSparseRecursiveForm(AMultivariatePolynomial recForm,
                                                int nVariables,
                                                E[] values)
```
    Evaluates polynomial given in a sparse recursive form at a given points
  - getHornerForm
```
public MultivariatePolynomial.HornerForm getHornerForm(int[] evaluationVariables)
```
    Gives data structure for fast Horner-like sparse evaluation of this multivariate polynomial
    
    Parameters:
    
    evaluationVariables - variables which will be substituted
  - evaluate
```
public MultivariatePolynomial<E> evaluate(int variable,
                                          E value)
```
    Returns a copy of this with value substituted for variable.
    
    Parameters:
    
    variable - the variable
    
    value - the value
    
    Returns:
    
    a new multivariate polynomial with value substituted for variable but still with the same AMultivariatePolynomial.nVariables (though the effective number of variables is nVariables - 1, compare to eliminate(int, Object))
    
    See Also:
    
    eliminate(int, Object)
  - evaluate
```
public E evaluate(E... values)
```
    Evaluates this polynomial at specified points
  - evaluate
```
public MultivariatePolynomial<E> evaluate(int[] variables,
                                          E[] values)
```
    Returns a copy of this with values substituted for variables.
    
    Parameters:
    
    variables - the variables
    
    values - the values
    
    Returns:
    
    a new multivariate polynomial with value substituted for variable but still with the same AMultivariatePolynomial.nVariables (though the effective number of variables is nVariables - 1, compare to eliminate(int, Object))
    
    See Also:
    
    eliminate(int, Object)
  - evaluate
```
public MultivariatePolynomial<E>[] evaluate(int variable,
                                            E... values)
```
    Evaluates this polynomial at specified points
  - evaluate
```
public MultivariatePolynomial<E> evaluate(int variable,
                                          long value)
```
    Returns a copy of this with value substituted for variable.
    
    Parameters:
    
    variable - the variable
    
    value - the value
    
    Returns:
    
    a new multivariate polynomial with value substituted for variable but still with the same AMultivariatePolynomial.nVariables (though the effective number of variables is nVariables - 1, compare to eliminate(int, long))
    
    See Also:
    
    eliminate(int, long)
  - eliminate
```
public MultivariatePolynomial<E> eliminate(int variable,
                                           E value)
```
    Substitutes value for variable and eliminates variable from the list of variables so that the resulting polynomial has result.nVariables = this.nVariables - 1.
    
    Parameters:
    
    variable - the variable
    
    value - the value
    
    Returns:
    
    a new multivariate polynomial with value substituted for variable and nVariables = nVariables - 1)
    
    See Also:
    
    evaluate(int, Object)
  - eliminate
```
public MultivariatePolynomial<E> eliminate(int variable,
                                           long value)
```
    Substitutes value for variable and eliminates variable from the list of variables so that the resulting polynomial has result.nVariables = this.nVariables - 1.
    
    Parameters:
    
    variable - the variable
    
    value - the value
    
    Returns:
    
    a new multivariate polynomial with value substituted for variable and nVariables = nVariables - 1)
    
    See Also:
    
    evaluate(int, long)
  - eliminate
```
public MultivariatePolynomial<E> eliminate(int[] variables,
                                           E[] values)
```
    Returns a copy of this with values substituted for variables
    
    Parameters:
    
    variables - the variables
    
    values - the values
    
    Returns:
    
    a new multivariate polynomial with value substituted for variable but still with the same AMultivariatePolynomial.nVariables (though the effective number of variables is nVariables - 1, compare to eliminate(int, long))
  - mkPrecomputedPowers
```
public MultivariatePolynomial.PrecomputedPowersHolder<E> mkPrecomputedPowers(int variable,
                                                                             E value)
```
  - mkPrecomputedPowers
```
public MultivariatePolynomial.PrecomputedPowersHolder<E> mkPrecomputedPowers(int[] variables,
                                                                             E[] values)
```
  - mkPrecomputedPowers
```
public static <E> MultivariatePolynomial.PrecomputedPowersHolder<E> mkPrecomputedPowers(int nVariables,
                                                                                        Ring<E> ring,
                                                                                        int[] variables,
                                                                                        E[] values)
```
  - mkPrecomputedPowers
```
public MultivariatePolynomial.PrecomputedPowersHolder<E> mkPrecomputedPowers(E[] values)
```
  - substitute
```
public MultivariatePolynomial<E> substitute(int variable,
                                            MultivariatePolynomial<E> poly)
```
    Returns a copy of this with poly substituted for variable.
    
    Parameters:
    
    variable - the variable
    
    poly - the replacement for the variable
    
    Returns:
    
    a copy of this with variable -> poly
  - shift
```
public MultivariatePolynomial<E> shift(int variable,
                                       long shift)
```
    Returns a copy of this with variable -> variable + shift
    
    Parameters:
    
    variable - the variable
    
    shift - shift amount
    
    Returns:
    
    a copy of this with variable -> variable + shift
  - shift
```
public MultivariatePolynomial<E> shift(int variable,
                                       E shift)
```
    Returns a copy of this with variable -> variable + shift
    
    Parameters:
    
    variable - the variable
    
    shift - shift amount
    
    Returns:
    
    a copy of this with variable -> variable + shift
  - shift
```
public MultivariatePolynomial<E> shift(int[] variables,
                                       E[] shifts)
```
    Returns a copy of this with variables -> variables + shifts
    
    Parameters:
    
    variables - the variables
    
    shifts - the corresponding shifts
    
    Returns:
    
    a copy of this with variables -> variables + shifts
  - add
```
public MultivariatePolynomial<E> add(E oth)
```
    Adds oth to this polynomial
    
    Parameters:
    
    oth - other polynomial
    
    Returns:
    
    this + oth
  - subtract
```
public MultivariatePolynomial<E> subtract(E oth)
```
    Subtracts oth from this polynomial
    
    Parameters:
    
    oth - other polynomial
    
    Returns:
    
    this - oth
  - increment
```
public MultivariatePolynomial<E> increment()
```
    Description copied from interface: IPolynomial
    
    Adds 1 to this
    
    Returns:
    
    this + 1
  - decrement
```
public MultivariatePolynomial<E> decrement()
```
    Description copied from interface: IPolynomial
    
    Subtracts 1 from this
    
    Returns:
    
    this - 1
  - multiply
```
public MultivariatePolynomial<E> multiply(E factor)
```
    Multiplies this by the factor
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this multiplied by the factor
  - multiplyByLC
```
public MultivariatePolynomial<E> multiplyByLC(MultivariatePolynomial<E> other)
```
    Description copied from interface: IPolynomial
    
    Multiply this by the leading coefficient of other
    
    Parameters:
    
    other - polynomial
    
    Returns:
    
    this * lc(other)
  - multiply
```
public MultivariatePolynomial<E> multiply(Monomial<E> monomial)
```
    Description copied from class: AMultivariatePolynomial
    
    Multiplies this by the monomial
    
    Specified by:
    
    multiply in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    monomial - the monomial
    
    Returns:
    
    this multiplied by the monomial
  - multiply
```
public MultivariatePolynomial<E> multiply(long factor)
```
    Description copied from interface: IPolynomial
    
    Multiplies this by factor
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this * factor
  - multiplyByBigInteger
```
public MultivariatePolynomial<E> multiplyByBigInteger(BigInteger factor)
```
    Description copied from interface: IPolynomial
    
    Multiplies this by factor
    
    Parameters:
    
    factor - the factor
    
    Returns:
    
    this * factor
  - multiply
```
public MultivariatePolynomial<E> multiply(MultivariatePolynomial<E> oth)
```
    Description copied from interface: IPolynomial
    
    Multiplies this by oth
    
    Parameters:
    
    oth - the polynomial
    
    Returns:
    
    this * oth
  - square
```
public MultivariatePolynomial<E> square()
```
    Description copied from interface: IPolynomial
    
    Squares this
    
    Returns:
    
    this * this
  - evaluateAtRandom
```
public MultivariatePolynomial<E> evaluateAtRandom(int variable,
                                                  org.apache.commons.math3.random.RandomGenerator rnd)
```
    Description copied from class: AMultivariatePolynomial
    
    Evaluates poly at random point
    
    Specified by:
    
    evaluateAtRandom in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
  - evaluateAtRandomPreservingSkeleton
```
public MultivariatePolynomial<E> evaluateAtRandomPreservingSkeleton(int variable,
                                                                    org.apache.commons.math3.random.RandomGenerator rnd)
```
    Description copied from class: AMultivariatePolynomial
    
    Evaluates poly at random point chosen in such way that the skeleton of evaluated version is the same as of the original poly with respect to all except variable variables
    
    Specified by:
    
    evaluateAtRandomPreservingSkeleton in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
  - derivative
```
public MultivariatePolynomial<E> derivative(int variable,
                                            int order)
```
    Description copied from class: AMultivariatePolynomial
    
    Gives partial derivative of specified order with respect to specified variable (new instance created)
    
    Specified by:
    
    derivative in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    variable - the variable
    
    order - derivative order
    
    Returns:
    
    partial derivative of specified order with respect to specified variable
  - seriesCoefficient
```
public MultivariatePolynomial<E> seriesCoefficient(int variable,
                                                   int order)
```
    Description copied from class: AMultivariatePolynomial
    
    Gives (unevaluated) coefficient of Taylor series expansion for specified variable that is derivative(poly, variable, order) / order!, where the derivative is formal derivative and calculated with arithmetic performed in Z ring (to overcome possible zeros in Zp).
    
    Specified by:
    
    seriesCoefficient in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Parameters:
    
    variable - the variable
    
    order - derivative order
    
    Returns:
    
    derivative(poly, variable, order) / order! , where the derivative is formal derivative and calculated with arithmetic performed in Z ring (to overcome possible zeros in Zp)
  - stream
```
public Stream<E> stream()
```
    Returns a stream of coefficients of this
    
    Returns:
    
    stream of coefficients
  - mapTerms
```
public <T> MultivariatePolynomial<T> mapTerms(Ring<T> newRing,
                                              Function<Monomial<E>,Monomial<T>> mapper)
```
    Maps terms of this using specified mapping function
    
    Type Parameters:
    
    T - new element type
    
    Parameters:
    
    newRing - the new ring
    
    mapper - mapping
    
    Returns:
    
    a new polynomial with terms obtained by applying mapper to this terms
  - mapCoefficients
```
public <T> MultivariatePolynomial<T> mapCoefficients(Ring<T> newRing,
                                                     Function<E,T> mapper)
```
    Maps coefficients of this using specified mapping function
    
    Type Parameters:
    
    T - new element type
    
    Parameters:
    
    newRing - the new ring
    
    mapper - mapping
    
    Returns:
    
    a new polynomial with terms obtained by applying mapper to this terms (only coefficients are changed)
  - mapCoefficients
```
public MultivariatePolynomialZp64 mapCoefficients(IntegersZp64 newDomain,
                                                  ToLongFunction<E> mapper)
```
    Maps coefficients of this using specified mapping function
    
    Parameters:
    
    newDomain - the new ring
    
    mapper - mapping
    
    Returns:
    
    a new polynomial with terms obtained by applying mapper to this terms (only coefficients are changed)
  - mapCoefficientsAsPolys
```
public <T> MultivariatePolynomial<T> mapCoefficientsAsPolys(Ring<T> ring,
                                                            Function<MultivariatePolynomial<E>,T> mapper)
```
    Specified by:
    
    mapCoefficientsAsPolys in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
  - compareTo
```
public int compareTo(MultivariatePolynomial<E> oth)
```
  - clone
```
public MultivariatePolynomial<E> clone()
```
    Description copied from interface: IPolynomial
    
    Deep copy of this
    
    Specified by:
    
    clone in interface IPolynomial<E>
    
    Specified by:
    
    clone in class AMultivariatePolynomial<Monomial<E>,MultivariatePolynomial<E>>
    
    Returns:
    
    deep copy of this
  - parsePoly
```
@Deprecated
public MultivariatePolynomial<E> parsePoly(String string)
```
    Deprecated.
  - toString
```
public String toString(IStringifier<MultivariatePolynomial<E>> stringifier)
```
    Description copied from interface: Stringifiable
    
    convert this to string with the use of stringifier
  - coefficientRingToString
```
public String coefficientRingToString(IStringifier<MultivariatePolynomial<E>> stringifier)
```
    Description copied from interface: IPolynomial
    
    String representation of the coefficient ring of this

Class MultivariatePolynomial<E>

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 Detail

ring

Method Detail

create

create

zero

one

parse

parse

parse

parse

parse

parse

parse

parse

asOverZp64

asOverZp64

asMultivariate

asUnivariate

asOverUnivariate

asOverUnivariateEliminate

asOverMultivariate

asOverMultivariateEliminate

asNormalMultivariate

asNormalMultivariate

asNormalMultivariate

asPolyZ

asPolyZSymmetric

contentAsPoly

lcAsPoly

lcAsPoly

ccAsPoly

isOverField

isOverFiniteField

isOverZ

coefficientRingCardinality

coefficientRingCharacteristic

isOverPerfectPower

coefficientRingPerfectPowerBase

coefficientRingPerfectPowerExponent

createArray

createArray2d

createArray2d

sameCoefficientRingWith

setCoefficientRingFrom

release

setRing

setRingUnsafe

createConstant

createConstantFromTerm

createZero

createOne

createLinear

isMonic

signumOfLC

isOne

isUnitCC

isConstant

maxAbsCoefficient

lc

lc

setLC

cc

content

coefficients

coefficientsArray

primitivePart

contentUnivariate

primitivePart

primitivePartSameSign