galois.lcm¶

galois.lcm(*values: int) → int¶

galois.lcm(*values: Poly) → Poly

Computes the least common multiple of the arguments.

Parameters

*values

Each argument must be an integer or polynomial.

Returns

The least common multiple of the arguments.

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]: f1 = galois.irreducible_poly(7, 1); f1
Out[3]: Poly(x, GF(7))

In [4]: f2 = galois.irreducible_poly(7, 2); f2
Out[4]: Poly(x^2 + 1, GF(7))

In [5]: f3 = galois.irreducible_poly(7, 3); f3
Out[5]: Poly(x^3 + 2, GF(7))

Compute the LCM of three polynomials \(f_1(x)^2 f_2(x)\), \(f_1(x) f_3(x)\), and \(f_2(x) f_3(x)\), which is \(f_1(x)^2 f_2(x) f_3(x)\).

In [6]: galois.lcm(f1**2 * f2, f1 * f3, f2 * f3)
Out[6]: Poly(x^7 + x^5 + 2x^4 + 2x^2, GF(7))

In [7]: f1**2 * f2 * f3
Out[7]: Poly(x^7 + x^5 + 2x^4 + 2x^2, GF(7))