galois.lcm¶

galois.lcm(*values)¶

Computes the least common multiple of the arguments.

Parameters¶

*values : int or galois.Poly

Each argument must be an integer or polynomial.

Returns¶

The least common multiple of the arguments.

Return type¶

int or galois.Poly

See also

gcd, egcd, prod

Examples

Integers

Compute the LCM of three integers.

In [1]: galois.lcm(2, 4, 14)
Out[1]: 28

Polynomials

Generate irreducible polynomials over \(\mathrm{GF}(7)\).

In [2]: GF = galois.GF(7)

In [3]: p1 = galois.irreducible_poly(7, 1); p1
Out[3]: Poly(x, GF(7))

In [4]: p2 = galois.irreducible_poly(7, 2); p2
Out[4]: Poly(x^2 + 1, GF(7))

In [5]: p3 = galois.irreducible_poly(7, 3); p3
Out[5]: Poly(x^3 + 2, GF(7))

Compute the LCM of three polynomials.

In [6]: a = p1**2 * p2; a
Out[6]: Poly(x^4 + x^2, GF(7))

In [7]: b = p1 * p3; b
Out[7]: Poly(x^4 + 2x, GF(7))

In [8]: c = p2 * p3; c
Out[8]: Poly(x^5 + x^3 + 2x^2 + 2, GF(7))

In [9]: galois.lcm(a, b, c)
Out[9]: Poly(x^7 + x^5 + 2x^4 + 2x^2, GF(7))

In [10]: p1**2 * p2 * p3
Out[10]: Poly(x^7 + x^5 + 2x^4 + 2x^2, GF(7))