GCD (Built-in Mathematica Symbol)

GCD[n_1, n_2, ...] gives the greatest common divisor of the n_i.

ExtendedGCD (Built-in Mathematica Symbol)

ExtendedGCD[n_1, n_2, ...] gives the extended greatest common divisor of the integers n_i.

PolynomialGCD (Built-in Mathematica Symbol)

PolynomialGCD[poly_1, poly_2, ...] gives the greatest common divisor of the polynomials poly_i. PolynomialGCD[poly_1, poly_2, ..., Modulus -> p] evaluates the GCD modulo the ...

PolynomialExtendedGCD (Built-in Mathematica Symbol)

PolynomialExtendedGCD[poly_1, poly_2, x] gives the extended GCD of poly_1 and poly_2 treated as univariate polynomials in x.PolynomialExtendedGCD[poly_1, poly_2, x, Modulus ...

Polynomials Modulo Primes (Mathematica Tutorial)

Mathematica can work with polynomials whose coefficients are in the finite field Z_p of integers modulo a prime p. Functions for manipulating polynomials over finite fields. ...

HermiteDecomposition (Built-in Mathematica Symbol)

HermiteDecomposition[m] gives the Hermite normal form decomposition of an integer matrix m.

Algebraic Operations on Polynomials (Mathematica Tutorial)

For many kinds of practical calculations, the only operations you will need to perform on polynomials are essentially structural ones. If you do more advanced algebra with ...

Number Theoretic Functions (Mathematica Guide)

Mathematica contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.

Integer and Number Theoretic Functions (Mathematica Tutorial)

Some integer functions. The remainder on dividing 17 by 3. The integer part of 17/3.

Matrix Decompositions (Mathematica Guide)