#16014: Improvements to discriminant computation
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Reporter: gagern | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: algebra | Resolution:
Keywords: discriminant | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/gagern/ticket/16014 | 1892c84d6372e882fa0c39667d06ba83cc61f3be
Dependencies: | Stopgaps:
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Comment (by gagern):
Replying to [comment:5 pbruin]:
> I'm wondering if you couldn't be convinced to adopt John Cremona's
[https://groups.google.com/d/msg/sage-support/fABfhHyioa0/kPlhGN4Ri-EJ
proposal on sage-dev] to have a separate function
`generic_univariate_discriminant()` (or similar), which caches its output,
and hardcodes it for small degrees.
Sure I can be convinced, particularly if two people request something.
I've implemented the caching, but not the hardcoding so far. I wonder how
small “small” actually should be. Up to 7, things compute fairly quickly
so there seems to be little benefit from hardcoding, particularly since we
do caching. For higher degrees, computing them for hardcoding takes
considerable time, and writing down the hard code will take up quite a lot
of space in the source file. Should this really be implemented in Cython
code, or should we make some effort to obtain or compute discriminants up
to say 10 or so and store them in some kind of persistent data
representation instead of source code?
I also wonder how public this function should be. I prefer
`polynomial_element` over `invariant_theory` simply because it keeps all
my changes in one place. I've written a full docstring for the code, and
inside that docstring I had to import the function. Is this a reasonable
approach? Should I add the function to `sage.rings.polynomial.all`? Should
I prepend the function name with an underscore to mark it non-public?
I also have a question regarding my late import. I noticed the `cdef void
late_import` near the beginning of the module. I could add
`is_PowerSeriesRing` to that. But on the other hand, it seems as if that
function only gets called by `Polynomial.roots`. Which suggests that I
might not be able to rely on `is_PowertSeriesRing` if I were to follow
that approach. Do you agree with keeping the import where I have it so
far? Should the function `late_import` be renamed to something like
`late_import_for_root` to make it clearer that this does no general late
importing but specific to that method? Or should I add my imports to that
function and make sure to call `late_import` in `discriminant` as well?
Should I add myself as an author of that module, at the beginning of the
file?
--
Ticket URL: <http://trac.sagemath.org/ticket/16014#comment:7>
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