galois.is_monic¶

galois.is_monic(poly: Poly) → bool¶

Determines whether the polynomial is monic.

Parameters¶

poly: Poly¶

A polynomial over a Galois field.

Returns¶

True if the polynomial is monic.

See also

is_irreducible, is_primitive

Notes

A monic polynomial has its highest-degree, non-zero coefficient with value 1.

Examples

A monic polynomial over \(\mathrm{GF}(7)\).

In [1]: GF = galois.GF(7)

In [2]: p = galois.Poly([1, 0, 4, 5], field=GF); p
Out[2]: Poly(x^3 + 4x + 5, GF(7))

In [3]: galois.is_monic(p)
Out[3]: True

A non-monic polynomial over \(\mathrm{GF}(7)\).

In [4]: GF = galois.GF(7)

In [5]: p = galois.Poly([3, 0, 4, 5], field=GF); p
Out[5]: Poly(3x^3 + 4x + 5, GF(7))

In [6]: galois.is_monic(p)
Out[6]: False