Changes between Version 2 and Version 6 of Ticket #26103
- Timestamp:
- 08/21/18 17:32:49 (4 years ago)
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Ticket #26103
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14e6fdc6defb191b89e1eaf49ba6df681f6d1ba2
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#26105
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u/saraedum/26103
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simple_model() on quotients of polynomial rings
toabsolute_field() for towers of finite fields
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Ticket #26103 – Description
v2 v6 1 1 Towers 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. 2 2 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. 4 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. 3 Therefore it would be useful to have a method that turns a tower into a simple extension. 8 4 9 5 Note 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.