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 .
  • The setting Modulus->0 specifies the full ring of integers.
  • Some functions require that Modulus be set to a prime, or a power of a prime. is a finite field when is prime.
  • Equations for Modulus can be given in Eliminate and related functions.


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Basic Examples  (1)

Solve equations:

Factor polynomials:

Compute inverse:

Scope  (6)

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:

Properties & Relations  (2)

Factor a polynomial over a finite field:

Factor a polynomial over a finite Extension of rationals:

Introduced in 1988