IUnivariatePolynomial (rings 2.5 API)

Type Parameters:

Poly - the type of polynomial (self type)

All Superinterfaces:

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

All Known Implementing Classes:

UnivariatePolynomial, UnivariatePolynomialZ64, UnivariatePolynomialZp64
```
public interface IUnivariatePolynomial<Poly extends IUnivariatePolynomial<Poly>>
extends IPolynomial<Poly>
```
Parent interface for univariate polynomials. Dense representation (array of coefficients) is used to hold univariate polynomials. Positional operations treat index so that i-th coefficient corresponds to x^i monomial.

Since:

1.0

Method Summary

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

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

Methods inherited from interface java.lang.Comparable
compareTo

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

- Method Detail
  - size
```
default int size()
```
    Returns the degree of this polynomial
    
    Specified by:
    
    size in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>
    
    Returns:
    
    the degree of this polynomial
  - nNonZeroTerms
```
default int nNonZeroTerms()
```
    Returns the number of non zero terms in this poly
  - isZeroAt
```
boolean isZeroAt(int i)
```
    Returns whether i-th coefficient of this is zero
    
    Parameters:
    
    i - the position
    
    Returns:
    
    whether i-th coefficient of this is zero
  - isZeroCC
```
default boolean isZeroCC()
```
    Description copied from interface: IPolynomial
    
    Returns true if constant term is zero
    
    Specified by:
    
    isZeroCC in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>
    
    Returns:
    
    whether constant term is zero
  - setZero
```
Poly setZero(int i)
```
    Fills i-th element with zero
    
    Parameters:
    
    i - position
    
    Returns:
    
    self
  - setFrom
```
Poly setFrom(int indexInThis,
             Poly poly,
             int indexInPoly)
```
    Sets i-th element of this by j-th element of other poly
    
    Parameters:
    
    indexInThis - index in self
    
    poly - other polynomial
    
    indexInPoly - index in other polynomial
    
    Returns:
    
    self
  - getAsPoly
```
Poly getAsPoly(int i)
```
    Returns i-th coefficient of this as a constant polynomial
    
    Parameters:
    
    i - index in this
    
    Returns:
    
    i-th coefficient of this as a constant polynomial
  - exponents
```
default gnu.trove.set.hash.TIntHashSet exponents()
```
    Returns a set of exponents of non-zero terms
    
    Returns:
    
    a set of exponents of non-zero terms
  - firstNonZeroCoefficientPosition
```
int firstNonZeroCoefficientPosition()
```
    Returns position of the first non-zero coefficient, that is common monomial exponent (e.g. 2 for x^2 + x^3 + ...). In the case of zero polynomial, -1 returned
    
    Returns:
    
    position of the first non-zero coefficient or -1 if this is zero
  - shiftLeft
```
Poly shiftLeft(int offset)
```
    Returns the quotient this / x^offset, it is polynomial with coefficient list formed by shifting coefficients of this to the left by offset.
    
    Parameters:
    
    offset - shift amount
    
    Returns:
    
    the quotient this / x^offset
  - shiftRight
```
Poly shiftRight(int offset)
```
    Multiplies this by the x^offset.
    
    Parameters:
    
    offset - monomial exponent
    
    Returns:
    
    this * x^offset
  - truncate
```
Poly truncate(int newDegree)
```
    Returns the remainder this rem x^(newDegree + 1), it is polynomial formed by coefficients of this from zero to newDegree (both inclusive)
    
    Parameters:
    
    newDegree - new degree
    
    Returns:
    
    remainder this rem x^(newDegree + 1)
  - getRange
```
Poly getRange(int from,
              int to)
```
    Creates polynomial formed from the coefficients of this starting from from (inclusive) to to (exclusive)
    
    Parameters:
    
    from - the initial index of the range to be copied, inclusive
    
    to - the final index of the range to be copied, exclusive.
    
    Returns:
    
    polynomial formed from the range of coefficients of this
  - reverse
```
Poly reverse()
```
    Reverses the coefficients of this
    
    Returns:
    
    reversed polynomial
  - createMonomial
```
Poly createMonomial(int degree)
```
    Creates new monomial x^degree (with the same coefficient ring)
    
    Parameters:
    
    degree - monomial degree
    
    Returns:
    
    new monomial coefficient * x^degree
  - derivative
```
Poly derivative()
```
    Returns the formal derivative of this poly (new instance, so the content of this is not changed)
    
    Returns:
    
    the formal derivative
  - clone
```
Poly clone()
```
    Description copied from interface: IPolynomial
    
    Deep copy of this
    
    Specified by:
    
    clone in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>
    
    Returns:
    
    deep copy of this
  - setAndDestroy
```
Poly setAndDestroy(Poly oth)
```
    Sets the content of this with oth and destroys oth
    
    Parameters:
    
    oth - the polynomial (will be destroyed)
    
    Returns:
    
    this := oth
  - composition
```
Poly composition(Poly value)
```
    Calculates the composition of this(oth) (new instance, so the content of this is not changed))
    
    Parameters:
    
    value - polynomial
    
    Returns:
    
    composition this(oth)
  - composition
```
default Poly composition(Ring<Poly> ring,
                         Poly value)
```
    Calculates the composition of this(oth) (new instance, so the content of this is not changed))
    
    Parameters:
    
    value - polynomial
    
    Returns:
    
    composition this(oth)
  - streamAsPolys
```
Stream<Poly> streamAsPolys()
```
    Stream polynomial coefficients as constant polynomials
  - mapCoefficientsAsPolys
```
default <E> UnivariatePolynomial<E> mapCoefficientsAsPolys(Ring<E> ring,
                                                           Function<Poly,E> mapper)
```
  - composition
```
AMultivariatePolynomial composition(AMultivariatePolynomial value)
```
    Calculates the composition of this(oth)
    
    Parameters:
    
    value - polynomial
    
    Returns:
    
    composition this(oth)
  - asMultivariate
```
AMultivariatePolynomial asMultivariate(Comparator<DegreeVector> ordering)
```
    Convert to multivariate polynomial
  - asMultivariate
```
default AMultivariatePolynomial asMultivariate()
```
    Convert to multivariate polynomial
  - ensureInternalCapacity
```
void ensureInternalCapacity(int desiredCapacity)
```
    ensures that internal storage has enough size to store desiredCapacity elements
  - isLinearOrConstant
```
default boolean isLinearOrConstant()
```
    Description copied from interface: IPolynomial
    
    Returns whether this polynomial is linear (i.e. of the form a * X + b)
    
    Specified by:
    
    isLinearOrConstant in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>
  - isLinearExactly
```
default boolean isLinearExactly()
```
    Description copied from interface: IPolynomial
    
    Returns whether this polynomial is linear (i.e. of the form a * X + b with nonzero a)
    
    Specified by:
    
    isLinearExactly in interface IPolynomial<Poly extends IUnivariatePolynomial<Poly>>

Interface IUnivariatePolynomial<Poly extends IUnivariatePolynomial<Poly>>

Method Summary

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

Methods inherited from interface java.lang.Comparable

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

Method Detail

size

nNonZeroTerms

isZeroAt

isZeroCC

setZero

setFrom

getAsPoly

exponents

firstNonZeroCoefficientPosition

shiftLeft

shiftRight

truncate

getRange

reverse

createMonomial

derivative

clone

setAndDestroy

composition

composition

streamAsPolys

mapCoefficientsAsPolys

composition

asMultivariate

asMultivariate

ensureInternalCapacity

isLinearOrConstant

isLinearExactly