Opened 5 years ago

Last modified 3 years ago

## #21869 closed enhancement

# A framework for discrete valuations in Sage — at Version 1

Reported by: | saraedum | Owned by: | |
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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 )

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

## Fix bugs in Sage

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

- Conversion from a Function Field to its Constant Field
- Conversion from a Function Field to its underlying Polynomial Ring
- Coercions between Function Fields
- Coercions are injective if the underlying map is
- Ring homomorphisms from Fields are injective
- The embedding of a ring into a polynomial ring over that ring is injective
- Morphisms of number fields are injective
- ZZ into QQ is injective
- ZZ into a Number Field is injective
- ZZ into an order of a Number Field is injective
- (some_elements() should return more than just [1] for most rings.)

## Add new features to Sage

New features that the code needs to work

- Factorization over iterated extensions of finite fields.
- principal_part() and sides() of a Newton Polygon

## Add the valuation code to Sage

i.e., add these files The files here https://github.com/saraedum/sage/tree/experimental/mac_lane to Sage.

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