John Cremona on Tue, 28 Mar 2023 12:49:18 +0200

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finite fields -- choice of defining polynomial

The documentation for ffinit(p,n)  does not seem to allow the user to specify their own irreducible polynomial (of degree n over Fp).  Is that right?

ffgen(k) does allow k to be an irreducible polynomial rather than the output of an ffinit().   If ffgen() is used with a polynomial, can one recover the associated ffinit structure, or in some other way do as much arithmetic in the field as with an ffinit?

More specifically, has anyone implemented Conway Polynomials in PARI/GP?

My reason for asking is that in the LMFDB we are intending to use Conway polynomials to define finite fields in a standard way, for use in several places including Dirichlet characters with values in finite fields, and we want to be able to carry out the associated constructions in all our favourite languages.  Both Sage and Magma use Conway polynomials by default in the construction of finite fields.