#1956: implement multivariate truncated power series arithmetic
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Reporter: was | Owner: pernici
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7
Component: commutative algebra | Keywords: multivariate
power series
Work_issues: | Upstream: N/A
Reviewer: Martin Albrecht, Simon King | Author: Niles Johnson
Merged: | Dependencies:
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Changes (by niles):
* status: needs_work => needs_review
Comment:
Replying to [comment:105 malb]:
Thanks for taking a look; sorry for the coverage negligence. I've added
the `#indirect notes`, and a docstring for `unpickle`. Now `sage
-coverage` returns 100% for both `multi_power_series` files. As a bonus,
I've added a docstring for the unpickle function of univariate power
series too.
I believe your other comments do not require changes -- I've elaborated
below. This means we are once again ready for review :)
>
> > 4. multi_power_series_ring.py: the code accurately does what it claims
to do (needs_review)
>
> Shouldn't ```def _element_constructor_(self,f)``` use the default
precision of the ring?
>
No, I believe not. Default precision is used only when absolutely
necessary to convert an infinite precision element to a finite precision
one (e.g. for inversion or reversion). But, for example, coercion of a
polynomial should result in an infinite precision element, not a finite
precision one. This is consistent with the behavior of univariate power
series rings:
{{{
sage: P = QQ[x]; P
Univariate Polynomial Ring in x over Rational Field
sage: S = P.completion(P.gen()); S
Power Series Ring in x over Rational Field
sage: S(P.random_element()).prec()
+Infinity
}}}
{{{
sage: P = QQ['x,y,z']; P
Multivariate Polynomial Ring in x, y, z over Rational Field
sage: S = P.completion(P.gens()); S
Multivariate Power Series Ring in x, y, z over Rational Field
sage: S(P.random_element()).prec()
+Infinity
}}}
> > 6. Integration with the rest of sage: construction and use of
`PowerSeriesRing`
> > works correctly, and parallels behavior of polynomial rings (needs
review)
>
> '''needs work'''
>
> The {{{default_prec}}} parameter does not seem to work as expected (or
is my expectation wrong?)
>
>
{{{
#!python
sage: P.<x,y> = PowerSeriesRing(GF(127),default_prec=20)
sage: x.prec()
+Infinity
}}}
I believe that your expectation is wrong, as described above. Note the
parallel behavior for univariate power series rings:
{{{
sage: P.<x> = PowerSeriesRing(GF(127),default_prec=20)
sage: x.prec()
+Infinity
}}}
> > 8. Coding: the code is free from obvious inefficiencies in error
handling, memory
> > management, etc. (needs review)
>
> If the performance is good (7), then I think we can just assume it's
okay. We can always come back and fix stuff later which is too slow.
so...I'm reading 'positive review', right? ;)
(free from *obvious* inefficiencies, etc.)
>
> I have to say that I don't like the excessive use of double underscore
attributes. It makes it harder to inherit from it or reach into the
internals (just as you have to write
{{{_PowerSeriesRing_generic__poly_ring}}}) I'd just use a single
underscore. I'll leave it up to you (i.e., not make my review dependent on
it) whether you insist on keeping them.
Excessive or not, each of the double underscore methods is necessary to
replace the corresponding method of `PowerSeries` or
`PowerSeriesRing_generic`, from which the `MPowerSeries*` classes inherit.
Here's a complete list of the double underscore attributes:
{{{
MPowerSeries.__init__
MPowerSeries.__reduce__
MPowerSeries.__call__
MPowerSeries.__getitem__
MPowerSeries.__invert__
MPowerSeries.__cmp__
MPowerSeries.__mod__
MPowerSeries.__lshift__
MPowerSeries.__rshift__
MPowerSeriesRing_generic.__init__
MPowerSeriesRing_generic.__reduce__
MPowerSeriesRing_generic.__cmp__
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:108>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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