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.
Examplesopen allclose all
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:
Wolfram Research (1988), Modulus, Wolfram Language function, https://reference.wolfram.com/language/ref/Modulus.html.
Wolfram Language. 1988. "Modulus." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Modulus.html.
Wolfram Language. (1988). Modulus. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Modulus.html