Class GaloisPolynomial

java.lang.Object
   |
   +----GaloisPolynomial

public class GaloisPolynomial
extends Object

A class for working with Polynomials.
The coefficients are elements taken from a galois field

See Also:: GaloisField, ExtendedGaloisField

ZEROCOEFS: An array of zero coefficients to construct a zero polynomial.

GaloisPolynomial(int[], char, GaloisField): Construct a polynomial.
GaloisPolynomial(String, char, GaloisField): Construct a polynomial.

allPolynomials(int, char, GaloisField): Returns a vector containing all possible polynomials degree 0 till [deg].
calcHorner(int): Evaluates the polynomial for a given galois element using the Horner scheme.
copy(): Returns a copy of this polynomial.
createConstant(int, char, GaloisField): Returns a constant 'polynomial'.
degree(): Returns the degree.
divide(GaloisPolynomial): Returns the quotient of 'this' and a given polynomial.
equals(GaloisPolynomial): Check if two polynomials are equal.
getAlfa(): Returns the variable.
getCoefficient(int): Returns the coefficient for position [pos].
getField(): Returns the coefficient's galois field.
irrMonomials(int, char, GaloisField): Returns a vector containing all the possible irreducible monomials.
minus(GaloisPolynomial): Returns the difference between 'this' and a given polynomial.
product(GaloisPolynomial): Returns the product of 'this' and a given polynomial.
product_one_term(int, int): Returns the product of 'this' and a 'one term polynomial'.
sum(GaloisPolynomial): Returns the sum of 'this' and a given polynomial.
toBase(): Converts the polynomial's coefficients into base-field elements.
toCoefficientString(int): Returns a string representation for this polynomial.
toExtended(GaloisField): Converts the polynomial's coefficients into elements of [fld2].
toString(): Returns a string representation for this polynomial.

ZEROCOEFS

  public final static int ZEROCOEFS[]

An array of zero coefficients to construct a zero polynomial.

GaloisPolynomial

  public GaloisPolynomial(int newcoef[],
                          char newalfa,
                          GaloisField newfield)

Construct a polynomial.

Parameters:: newcoef - An array containing the coefficients.; newalpha - The variable. For ex: 'x'.; newfield - The coefficient galois field.

GaloisPolynomial

  public GaloisPolynomial(String poly,
                          char newalfa,
                          GaloisField newfield) throws GaloisException

Construct a polynomial. Invoke the string parser.

Parameters:: poly - A string representation for the polynomial.; newalpha - The variable. For ex: 'x'.; newfield - The coefficient galois field.

createConstant

  public static GaloisPolynomial createConstant(int elem,
                                                char newalfa,
                                                GaloisField newfield)

Returns a constant 'polynomial'.

Parameters:: elem - The constants value.; newalpha - The variable. For ex: 'x'.; newfield - The coefficient galois field.

calcHorner

  public int calcHorner(int vl)

Evaluates the polynomial for a given galois element using the Horner scheme.

toBase

  public GaloisPolynomial toBase() throws GaloisException

Converts the polynomial's coefficients into base-field elements.

toExtended

  public GaloisPolynomial toExtended(GaloisField fld2) throws GaloisException

Converts the polynomial's coefficients into elements of [fld2].

Throws: GaloisException: If [fld2] is no superfield of getField().

toString

  public String toString()

Returns a string representation for this polynomial.
For ex: 1 + 3x + 4x^2.

Overrides:: toString in class Object

toCoefficientString

  public String toCoefficientString(int pwr)

Returns a string representation for this polynomial.
For ex: 11010001011 GF(2) (only the coefficients are given).
For ex: 11 01 00 01 11 GF(4)

degree

  public int degree()

Returns the degree.

equals

  public boolean equals(GaloisPolynomial b)

Check if two polynomials are equal. That is, if the coefficients are equal.

getCoefficient

  public int getCoefficient(int pos)

Returns the coefficient for position [pos].
getCoefficient(0) returns the constant coefficient.

copy

  public GaloisPolynomial copy()

Returns a copy of this polynomial.
You should never use this method because a polynomial can't change.
It uses value-semantics.

sum

  public GaloisPolynomial sum(GaloisPolynomial b)

Returns the sum of 'this' and a given polynomial.

minus

  public GaloisPolynomial minus(GaloisPolynomial b)

Returns the difference between 'this' and a given polynomial.

product

  public GaloisPolynomial product(GaloisPolynomial b)

Returns the product of 'this' and a given polynomial.

product_one_term

  public GaloisPolynomial product_one_term(int coef,
                                           int pwr)

Returns the product of 'this' and a 'one term polynomial'.
For ex: [coef]x^[pwr]

Parameters:: coef - The coefficient for the one-term.; pwr - The power for the one-term.

divide

  public GaloisPolynomial[] divide(GaloisPolynomial b) throws GaloisException

Returns the quotient of 'this' and a given polynomial.

Throws: GaloisException: On division by zero.

irrMonomials

  public static Vector irrMonomials(int deg,
                                    char alfa,
                                    GaloisField field)

Returns a vector containing all the possible irreducible monomials.
in the galois field [field].

Parameters:: deg - The degree of the monomials.; alfa - The variable. For ex: 'x'.; field - The galois field.

allPolynomials

  public static GaloisPolynomial[] allPolynomials(int deg,
                                                  char alfa,
                                                  GaloisField field)

Returns a vector containing all possible polynomials degree 0 till [deg].
in the galois field [field].

Parameters:: deg - The maximum degree of the polynomials.; alfa - The variable. For ex: 'x'.; field - The galois field.

getAlfa

  public char getAlfa()

Returns the variable. For ex: 'x'.

getField

  public GaloisField getField()

Returns the coefficient's galois field.