Changes between Version 97 and Version 100 of Ticket #8335

07/29/13 12:08:49 (8 years ago)

Besides everything else, the latest patch moves _coerce_map_from_() from the various finite field implementations to the FiniteField base class; it is now implementation-independent. For this reason, this ticket now depends on #12142. Various other changes have been made.

The syntax for constructing finite fields using Conway polynomials that admit automatic coercion is now

sage: F.<a> = FiniteField(5^3, conway=True, prefix='z')

This is not too pretty, but it is meant as a temporary solution until we have algebraic closures of finite fields.

Older patches on this ticket contained various changes that were in older attachments and that do not seem immediately relevant to this ticket. I deleted those changes that seemed superfluous and kept those that I thought could be necessary after all.

This ticket should be reviewed once #14958 is done.

For patchbot:

apply trac_8335-finite_field_coerce-5.11.b3.patch


  • Ticket #8335

    • Property Status changed from needs_work to needs_info
    • Property Dependencies changed from #14958 to #14958, #12142
    • Property Work issues changed from rebase to wait for #14958
  • Ticket #8335 – Description

    v97 v100  
    4 sage: k = GF(9)
    5 sage: l = GF(27)
     4sage: k = GF(9, conway=True, prefix='z')
     5sage: l = GF(27, conway=True, prefix='z')
    66sage: x = k.gen() + l.gen(); x
    77z6^5 + 2*z6^4 + 2*z6^3 + z6^2 + 2*z6 + 1
    1212This feature is implemented for fields outside the range of the Conway polynomial database by the implementation of a function for finding pseudo-Conway polynomials: polynomials that satisfy all of the algebraic constraints on Conway polynomials without the lexicographic constraint that imposes uniqueness.
    14 For the time being, finite fields still require an explicit variable name (so the above code snippet won't work exactly as shown); in the future, a variant is planned that no longer requires a variable name.
     14When using the `conway` and `prefix` parameters, one does not need to specify an explicit variable name; if no variable name is given, it is constructed from the `prefix` and the degree (as in the above code snippet).
     16In the future, the functionality of this ticket will be incorporated into that for algebraic closures of finite fields.
     18Apply: [attachment:trac_8335-finite_field_coerce-5.11.b3.patch]