galois.are_coprime¶

galois.are_coprime(*values: int) → bool¶

galois.are_coprime(*values: Poly) → bool

Determines if the arguments are pairwise coprime.

Parameters

*values

Each argument must be an integer or polynomial.

Returns

True if the arguments are pairwise coprime.

See also

lcm, prod

Notes

A set of integers or polynomials are pairwise coprime if their LCM is equal to their product.

Examples

Integers

Determine if a set of integers are pairwise coprime.

In [1]: galois.are_coprime(3, 4, 5)
Out[1]: True

In [2]: galois.are_coprime(3, 7, 9, 11)
Out[2]: False

Polynomials

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

In [3]: GF = galois.GF(7)

In [4]: f1 = galois.irreducible_poly(7, 1); f1
Out[4]: Poly(x, GF(7))

In [5]: f2 = galois.irreducible_poly(7, 2); f2
Out[5]: Poly(x^2 + 1, GF(7))

In [6]: f3 = galois.irreducible_poly(7, 3); f3
Out[6]: Poly(x^3 + 2, GF(7))

Determine if combinations of the irreducible polynomials are pairwise coprime.

In [7]: galois.are_coprime(f1, f2, f3)
Out[7]: True

In [8]: galois.are_coprime(f1 * f2, f2, f3)
Out[8]: False