Opened 7 years ago

#18122 new enhancement

Automatically choosing exactification algorithm

Reported by: gagern Owned by:
Priority: major Milestone: sage-6.6
Component: number fields Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #16222, #17886 Stopgaps:

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Description

#16222 will provide a method for computing an exact representation of an algebraic number based on the minimal polynomial of a symbolic expression. At the moment I plan to only make that approach available as a manual choice, but in the long run it would be nice if Sage could somehow automatically decide how to perform the exactification.

Since the main benefit of the symbolic exactification is a speed gain, #17886 should be taken into account as well, since that might drastically reduce the cost of “normal” exactification. At least if that ticket gets its decision-making right, which might be non-trivial.

So we have three possible approaches to exactification:

  1. number field unions and operations therein (implemented so far)
  2. minimal polynomials from symbolic expressions (#16222)
  3. minimal polynomials from resultants (#17886)

and we should here try to make the choices among these alternatives as good as we can.

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