PolynomialRing.Polynomial (math 3.1.0 API)

java.lang.Object
- org.cryptimeleon.math.structures.rings.polynomial.PolynomialRing.Polynomial

All Implemented Interfaces:

UniqueByteRepresentable, Representable, Element, RingElement

Enclosing class:

PolynomialRing
```
public class PolynomialRing.Polynomial
extends java.lang.Object
implements RingElement
```
An element of PolynomialRing.

Field Summary

Fields
Modifier and Type Field and Description

protected RingElement[] coefficients
Coefficients of this polynomial, i.e.

protected int degree
The degree of this polynomial.

Fields
Modifier and Type	Field and Description
`protected RingElement[]`	`coefficients` Coefficients of this polynomial, i.e.
`protected int`	`degree` The degree of this polynomial.

Constructor Summary

Constructors
Constructor and Description
`Polynomial(int i)` Creates the polynomial \(X^i\).
`Polynomial(int i, RingElement a)` Creates the polynomial \(a \cdot X^i\).
`Polynomial(java.util.List<RingElement> coefficients)` Creates a polynomial with the given coefficients.
`Polynomial(RingElement... coefficients)` Creates a polynomial with the given coefficients.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`PolynomialRing.Polynomial`	`add(Element e)` Creates a new polynomial by adding the given polynomial to this.
`java.math.BigInteger`	`asInteger()` Interprets this element as an integer.
`protected void`	`computeDegree()` Sets the degree instance variable according to the coefficients.
`boolean`	`divides(RingElement e)` Checks whether this polynomial can be divided without remainder by the given polynomial.
`PolynomialRing.Polynomial[]`	`divideWithRemainder(RingElement e)` Performs polynomial division with remainder.
`protected void`	`ensureArrayNonNull()` Makes sure that the coefficients array does not contain null values at indices `i <= degree`.
`boolean`	`equals(java.lang.Object o)`
`RingElement`	`evaluate(Element x)` Return the value of the polynomial evaluated at `x`.
`RingElement[]`	`getCoefficients()`
`RingElementVector`	`getCoefficientVector()`
`int`	`getDegree()`
`java.math.BigInteger`	`getRank()` Implements the euclidean function of a euclidean domain.
`Representation`	`getRepresentation()` The representation of this object.
`PolynomialRing`	`getStructure()` Returns the `Structure` that this `Element` belongs to.
`int`	`hashCode()`
`Zp.ZpElement`	`innerProduct(PolynomialRing.Polynomial e)` Computes the inner product of the coefficient vectors.
`PolynomialRing.Polynomial`	`inv()` Inverts the constant polynomial by inverting the zero degree coefficient in its corresponding ring.
`PolynomialRing.Polynomial`	`mul(java.math.BigInteger k)` Multiplies each coefficient with the given integer.
`PolynomialRing.Polynomial`	`mul(Element e)` Multiplies the given polynomial with this using standard polynomial multiplication.
`PolynomialRing.Polynomial`	`neg()` Negates the polynomial by negating each coefficient.
`PolynomialRing.Polynomial`	`normalize()` Normalizes this polynomial by multiplying it with the inverse of the leading coefficient.
`PolynomialRing.Polynomial`	`scalarMul(Element elem)` Multiplies each coefficient of this polynomial with the given base ring element.
`PolynomialRing.Polynomial`	`sub(Element e)` Creates a new polynomial by subtracting the given polynomial from this.
`java.lang.String`	`toString()`
`ByteAccumulator`	`updateAccumulator(ByteAccumulator accumulator)` Updates the ByteAccumulator with the unique byte representation of this object.

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

Methods inherited from interface org.cryptimeleon.math.structures.rings.RingElement
div, isOne, isUnit, isZero, mul, pow, pow, square, toAdditiveGroupElement, toUnitGroupElement

Methods inherited from interface org.cryptimeleon.math.hash.UniqueByteRepresentable
getUniqueByteRepresentation

- Field Detail
  - coefficients
```
protected RingElement[] coefficients
```
    Coefficients of this polynomial, i.e. \(\text{this} = \sum coefficients[i] * x^i\).
    All entries with index i > degree may be null. This array always contains at least one element.
  - degree
```
protected int degree
```
    The degree of this polynomial.
- Constructor Detail
  - Polynomial
```
public Polynomial(RingElement... coefficients)
```
    Creates a polynomial with the given coefficients.
    For example, new Polynomial(1,2,3) returns \(1 + 2 \cdot X + 3 \cdot X^2\).
    
    Parameters:
    
    coefficients - coefficients for the new polynomial, in order from smallest to largest exponent
  - Polynomial
```
public Polynomial(java.util.List<RingElement> coefficients)
```
    Creates a polynomial with the given coefficients.
    For example, new Polynomial([1,2,3]) returns \(1 + 2 \cdot X + 3 \cdot X^2\).
    
    Parameters:
    
    coefficients - coefficients for the new polynomial, in order from smallest to largest exponents
  - Polynomial
```
public Polynomial(int i,
                  RingElement a)
```
    Creates the polynomial \(a \cdot X^i\).
  - Polynomial
```
public Polynomial(int i)
```
    Creates the polynomial \(X^i\).
- Method Detail
  - getCoefficients
```
public RingElement[] getCoefficients()
```
  - getCoefficientVector
```
public RingElementVector getCoefficientVector()
```
  - computeDegree
```
protected void computeDegree()
```
    Sets the degree instance variable according to the coefficients.
    This is done once when creating the polynomial.
  - ensureArrayNonNull
```
protected void ensureArrayNonNull()
```
    Makes sure that the coefficients array does not contain null values at indices i <= degree.
    
    Throws:
    
    java.lang.IllegalArgumentException - if any coefficient of the polynomial is null
  - getRepresentation
```
public Representation getRepresentation()
```
    Description copied from interface: Representable
    
    The representation of this object. Used for serialization. A convenient way to implement this is using @link ReprUtil
    
    Specified by:
    
    getRepresentation in interface Representable
    
    Returns:
    
    a Representation or null if an equal object can be recreated without any information.
    
    See Also:
    
    Representation
  - getStructure
```
public PolynomialRing getStructure()
```
    Description copied from interface: Element
    
    Returns the Structure that this Element belongs to.
    
    Specified by:
    
    getStructure in interface Element
    
    Specified by:
    
    getStructure in interface RingElement
  - evaluate
```
public RingElement evaluate(Element x)
```
    Return the value of the polynomial evaluated at x.
    Result is computes using the Horner scheme.
    
    Parameters:
    
    x - position to evaluate
    
    Returns:
    
    result of evaluation at position x
  - add
```
public PolynomialRing.Polynomial add(Element e)
```
    Creates a new polynomial by adding the given polynomial to this.
    Addition is done by adding the coefficients together. Degree of the resulting polynomial is the maximum degree of the two involved polynomials.
    
    Specified by:
    
    add in interface RingElement
    
    Parameters:
    
    e - the addend
    
    Returns:
    
    the resulting polynomial
  - neg
```
public PolynomialRing.Polynomial neg()
```
    Negates the polynomial by negating each coefficient.
    
    Specified by:
    
    neg in interface RingElement
    
    Returns:
    
    the negated polynomial
  - innerProduct
```
public Zp.ZpElement innerProduct(PolynomialRing.Polynomial e)
```
    Computes the inner product of the coefficient vectors.
  - sub
```
public PolynomialRing.Polynomial sub(Element e)
```
    Creates a new polynomial by subtracting the given polynomial from this.
    Subtraction is done by subtracting the coefficients of the given polynomial from this. Degree of the resulting polynomial is the maximum degree of the two involved polynomials.
    
    Specified by:
    
    sub in interface RingElement
    
    Parameters:
    
    e - the polynomial to subtract
    
    Returns:
    
    the resulting polynomial
  - mul
```
public PolynomialRing.Polynomial mul(Element e)
```
    Multiplies the given polynomial with this using standard polynomial multiplication.
    
    Specified by:
    
    mul in interface RingElement
    
    Parameters:
    
    e - the factor
    
    Returns:
    
    the result of the multiplication
  - mul
```
public PolynomialRing.Polynomial mul(java.math.BigInteger k)
```
    Multiplies each coefficient with the given integer.
    
    Specified by:
    
    mul in interface RingElement
    
    Parameters:
    
    k - the factor
    
    Returns:
    
    the resulting polynomial
  - inv
```
public PolynomialRing.Polynomial inv()
                              throws java.lang.UnsupportedOperationException
```
    Inverts the constant polynomial by inverting the zero degree coefficient in its corresponding ring.
    Does not work for polynomial of higher degree.
    
    Specified by:
    
    inv in interface RingElement
    
    Returns:
    
    the inverted polynomial
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the degree of the polynomial to invert is greater than zero
  - scalarMul
```
public PolynomialRing.Polynomial scalarMul(Element elem)
```
    Multiplies each coefficient of this polynomial with the given base ring element.
  - normalize
```
public PolynomialRing.Polynomial normalize()
                                    throws java.lang.UnsupportedOperationException
```
    Normalizes this polynomial by multiplying it with the inverse of the leading coefficient.
    Results in a polynomial with coefficient one for the highest (leading) coefficient.
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the highest coefficient is not a unit, i.e. cannot be factored out
  - divides
```
public boolean divides(RingElement e)
                throws java.lang.UnsupportedOperationException
```
    Checks whether this polynomial can be divided without remainder by the given polynomial.
    
    Specified by:
    
    divides in interface RingElement
    
    Parameters:
    
    e - the divisor
    
    Returns:
    
    true if the remainder is zero, else false
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the divisors leading coefficient cannot be inverted
  - divideWithRemainder
```
public PolynomialRing.Polynomial[] divideWithRemainder(RingElement e)
                                                throws java.lang.UnsupportedOperationException
```
    Performs polynomial division with remainder.
    
    Specified by:
    
    divideWithRemainder in interface RingElement
    
    Parameters:
    
    e - the divisor
    
    Returns:
    
    a Polynomial array containing the quotient and remainder, in that order
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the divisors leading coefficient cannot be inverted
  - asInteger
```
public java.math.BigInteger asInteger()
                               throws java.lang.UnsupportedOperationException
```
    Description copied from interface: RingElement
    
    Interprets this element as an integer.
    Result will be between 0 and the ring's characteristic.
    Formally, this method shall return the inverse of Ring.getElement(BigInteger), i.e. x.getStructure().getElement(x.asInteger()).equals(x) (if asInteger() doesn't throw an exception).
    
    Specified by:
    
    asInteger in interface RingElement
    
    Returns:
    
    the integer corresponding to this element
    
    Throws:
    
    java.lang.UnsupportedOperationException - if no such element exists or cannot be efficiently computed
  - getRank
```
public java.math.BigInteger getRank()
                             throws java.lang.UnsupportedOperationException
```
    Description copied from interface: RingElement
    Implements the euclidean function of a euclidean domain.
    The euclidean function is a function from \(R \setminus \{0\}\) to \(\mathbb{N}_0\) such that
    - a.getRank() >= 0 for any a in the ring
    - a.mul(b).getRank() >= a.getRank() for any a, b != 0
    - the remainder rank after divideWithRemainder is less than the divisor's rank
    For example, for a polynomial ring this corresponds to the degree of the polynomial.
    The rank of the zero element is undefined (no guarantee as to what this method returns in that case).
    Specified by:
    
    getRank in interface RingElement
    
    Throws:
    
    java.lang.UnsupportedOperationException - if the ring is not a euclidean domain
  - getDegree
```
public int getDegree()
```
  - equals
```
public boolean equals(java.lang.Object o)
```
    Specified by:
    
    equals in interface Element
    
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Specified by:
    
    hashCode in interface Element
    
    Overrides:
    
    hashCode in class java.lang.Object
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - updateAccumulator
```
public ByteAccumulator updateAccumulator(ByteAccumulator accumulator)
```
    Description copied from interface: UniqueByteRepresentable
    
    Updates the ByteAccumulator with the unique byte representation of this object.
    The input to the accumulators update function is an injective (with respect to a given domain) byte encoding of this object.
    For many use-cases, the AnnotatedUbrUtil can be used to quickly implement this method.
    
    Specified by:
    
    updateAccumulator in interface UniqueByteRepresentable
    
    Returns:
    
    the same accumulator as was input

Class PolynomialRing.Polynomial

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.cryptimeleon.math.structures.rings.RingElement

Methods inherited from interface org.cryptimeleon.math.hash.UniqueByteRepresentable

Field Detail

coefficients

degree

Constructor Detail

Polynomial

Polynomial

Polynomial

Polynomial

Method Detail

getCoefficients

getCoefficientVector

computeDegree

ensureArrayNonNull

getRepresentation

getStructure

evaluate

add

neg

innerProduct

sub

mul

mul

inv

scalarMul

normalize

divides

divideWithRemainder

asInteger

getRank

getDegree

equals

hashCode

toString

updateAccumulator