A framework for discrete valuations in Sage

[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
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.