galois.conway_poly¶

galois.conway_poly(characteristic, degree)[source]¶

Returns the Conway polynomial for \(\mathrm{GF}(p^m)\).

This function uses Frank Luebeck’s Conway polynomial database. See: http://www.math.rwth-aachen.de/~Frank.Luebeck/data/ConwayPol/index.html.

Parameters

characteristic (int) – The prime characteristic \(p\) of the field \(\mathrm{GF}(p^m)\).
degree (int) – The prime characteristic’s degree \(m\) of the field \(\mathrm{GF}(p^m)\).

Returns

The degree-\(m\) polynomial in \(\mathrm{GF}(p)[x]\).

Return type

galois.Poly

Note

If the \(\mathrm{GF}(p)\) field hasn’t already been created, it will be created in this function since it’s needed in the return polynomial.

Examples

In [5]: galois.conway_poly(2, 100)
Out[5]: Poly(x^100 + x^57 + x^56 + x^55 + x^52 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^41 + x^37 + x^36 + x^35 + x^34 + x^31 + x^30 + x^27 + x^25 + x^24 + x^22 + x^20 + x^19 + x^16 + x^15 + x^11 + x^9 + x^8 + x^6 + x^5 + x^3 + 1, GF2)

In [6]: galois.conway_poly(7, 13)
Out[6]: Poly(x^13 + 6x^2 + 4, GF7)