**DeclareGaloisField**

declares a Galois field to be effective.

**IrreduciblePolynomial**

returns the coefficient list of an irreducible polynomial which is used for a extension field
of the argument.

**ExtensionDegree**

returns extension degree of a field of the argument.

**Order**

returns the order of the field.

returns the order of a element of Galois field if the argument is Galois field constant.

**BaseField**

returns the algebra name of the base field.

**ExtensionDegree**

returns the extension degree of an extension field.

**Characteristic**

returns the characterristic of a field.

**AlgebraName**

returns algebra names of variables which are contained in an expression .

**DeclareVariables**

declares symbols to be variables of a Galois field.

**NonZero**

declares variables to be nonzero elements.

**NonZeroQ**

returns TRUE if the given variable is a nonzero variable.

**NonZeroVariables**

returns the list of declared nonzero variables.

**DeclareAlgebraicVariables ( DeclareIndeterminates )**

declares symbols to be algebraic variables of a Galois field.

**MakeGaloisField**

makes a Galois field object as a file.

**ClearAlgebra**

clears all symboles which are related to a algebra name of the argument.

**ClearVariables**

clears variables of the arguments.

**PolynomialRepresentation**

convert a Galois field constant to its polynomial representation.

**RegularRepresentation**

convert a Galois field constant to its regular representation.

**VectorRepresentation**

convert a Galois field constant to its vector representation.

**ExponentRepresentation**

convert a Galois field constant to its exponential representation.

**PthRoot**

returns the p-th root of a Galois field constant.

**ShiftRegister**

is the process of a feedback shift register.

**Polynomialize**

the inverse process of the function CoefficientList.

**PolynomialExtendedGCD**

returns the gcd and coefficients of the extended GCD algorithm.

M**inimalPolynomial**

returns the minimal polynomial of a Galois field constant of the argument.

** PrimitiveQ**

returns TRUE if the argument is a primitive element of a Galois field.

**Variables**

does not out put Galois field constants.

**PolynomialGCD**

works on a polynomial over a Galois field.

**Factor**

works on a polynomial over a Galois field including an extension field.

**FactorList**

works on a polynomial over a Galois field.