Opened 3 years ago

Last modified 10 months ago

#21869 closed enhancement

A framework for discrete valuations in Sage — at Version 26

Reported by: saraedum Owned by:
Priority: major Milestone: sage-7.5
Component: commutative algebra Keywords: discrete valuations, valuations, p-adics, function fields, number fields, smooth projective curves, Mac Lane algorithm, Montes algorithm, sd87
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by saraedum)

This is a meta-ticket to keep track of the progress of integrating https://github.com/saraedum/mac_lane into Sage.

Fix bugs in Sage

There are a number of trivial bugs that get fixed by monkey-patches in https://github.com/saraedum/mac_lane/blob/master/__init__.py

  1. Conversion from a Function Field to its Constant Field #21872
  2. Conversion from a Function Field to its underlying Polynomial Ring #23166
  3. Coercions between Function Fields #23167
  4. Coercions are injective if the underlying map is #21879
  5. Ring homomorphisms from Fields are injective #21879
  6. Polynomial rings embed into their fraction fields #23185
  7. The embedding of a ring into a polynomial ring over that ring is injective #23203, #23204, #23211
  8. p-adic rings embed into their fraction fields #23188
  9. Morphisms of number fields are injective #21879
  10. ZZ into QQ is injective #21879
  11. quotients of polynomial rings are injective/surjective #23190
  12. ZZ into a Number Field is injective #21879
  13. ZZ into an order of a Number Field is injective #21879
  14. ZZ does not map onto QQ #23186
  15. ZpCA shifts are broken
  16. add default implementation of inverse_of_unit() #23191

Add new features to Sage

New features that the code needs to work

  1. Factorization over iterated extensions of finite fields. #21996
  2. principal_part() and sides() of a Newton Polygon (patch this in the calling code instead.)
  3. (cached_in_argument_method #22034)

Make tests non-trivial

  1. (some_elements() should be non-trivial for number fields/orders) #23192
  2. (some_elements() should be non-trivial/deterministic for rational function fields and their extensions) #23193
  3. (some_elements() should be non-trivial for fraction_fields of polynomial rings) #23194

Add the valuation code to Sage

i.e., add these files https://github.com/saraedum/mac_lane to Sage.

Change History (26)

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