#15306: partial_fraction_decomposition over QQ[] wrong
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Reporter: pong | Owner:
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.1
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by mmezzarobba):
* cc: Robert, Bradshaw (removed)
* cc: robertwb (added)
Comment:
It looks like `partial_fraction_decomposition` does not even attempt to
return numerators of degree smaller than that of the irreducible
polynomial in the denominator. The reason for that (I guess) is that
`partial_fraction_decomposition` is defined for all elements of parents
belonging to `QuotientFields()`, "the category of quotient fields over an
integral domain".
But while trying to fix the issue I realized that I am a bit confused:
* Is partial fraction decomposition really defined over the field of
fractions of any integral domain R? (I agree that it is when R is a PID,
but what about other cases?)
* In any case, isn't its ''computation'' going to require a Euclidean
domain?
* But in the Euclidean case, the stronger partial fraction decomposition
pong asks for is always defined, isn't it?
* What is the correct way to define methods that apply to all elements of
the field of fractions of a ''Euclidean'' domain? Conversely, should there
be a category of quotient fields over an integral (as opposed to
Euclidean) domain in Sage at all?...
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Ticket URL: <http://trac.sagemath.org/ticket/15306#comment:7>
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