Changes between Version 2 and Version 6 of Ticket #26103


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Timestamp:
08/21/18 17:32:49 (4 years ago)
Author:
saraedum
Comment:

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  • Ticket #26103

    • Property Commit changed from to 14e6fdc6defb191b89e1eaf49ba6df681f6d1ba2
    • Property Dependencies changed from to #26105
    • Property Branch changed from to u/saraedum/26103
    • Property Summary changed from simple_model() on quotients of polynomial rings to absolute_field() for towers of finite fields
  • Ticket #26103 – Description

    v2 v6  
    11Towers of finite fields are hard to work with because they lose most of the nice functionality of simple extensions of prime finite fields and are also much slower.
    22
    3 Therefore it would be useful to have a method that turns a tower into a simple extension. More generally there should be a function `simple_model(base=None)` on polynomial quotient rings that returns an isomorphic simple extension of `base` together with isomorphisms. `base` should default to the prime subfield.
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    5 Initially this would only be implemented for trivial extensions and towers of finite fields.
    6 
    7 As an alternative, there could also be a `absolute_field()` method in the category of finite fields.
     3Therefore it would be useful to have a method that turns a tower into a simple extension.
    84
    95Note that there have been attempts to support relative extensions of finite fields in #21413 and that there is also `sage.coding.relative_finite_field_extension`, the state of which is unclear to me.