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Mathematica > Mathematics and Algorithms > Polynomial Algebra > Modulus >

BUILT-IN MATHEMATICA SYMBOL

Modulus

Modulus->n
is an option that can be given in certain algebraic functions to specify that integers should be treated modulo n.

Modulus appears as an option in Solve, Reduce, Factor, PolynomialGCD, and PolynomialLCM, as well as in linear algebra functions such as Inverse, LinearSolve, and Det.

Arithmetic is usually done over the full ring of integers; setting the option Modulus specifies that arithmetic should instead be done in the finite ring .

Some functions require that Modulus be set to a prime, or a power of a prime. is a finite field when is prime.

Solve equations:

Factor polynomials:

Compute inverse:

Solve equations:

Out[1]=

Factor polynomials:

Out[2]=

Compute inverse:

Out[3]=

Compute PolynomialGCD over the integers modulo 2:

Factor a polynomial over the integers modulo 3:

Find a GroebnerBasis over the integers modulo 5:

Reduce equations over the integers modulo 7:

Compute the determinant of a matrix modulo 8:

Find a modulus for which a system of equations has a solution:

Factor a polynomial over a finite field:

Factor a polynomial over a finite Extension of rationals: