#18940: Polynomials ignore the step argument in __getitem__
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Reporter: pbruin | Owner:
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.10
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pbruin/18940-getitem_step | 1c56779b3140d12fbe5d0973cdcad0ac9dbb8054
Dependencies: #19409 | Stopgaps:
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Comment (by jhpalmieri):
Mathematically, I can certainly imagine wanting the part of the polynomial
between degrees 2 and 5: I might want this:
{{{
sage: f
-10*x^6 + 1/2*x^5 - x^4 + 7*x^3 - 2*x^2 + x - 3
sage: f[2:6]
1/2*x^5 - x^4 + 7*x^3 - 2*x^2
}}}
I don't know if I would ever want `f[2:6]` to return the polynomial with
same coefficients but translated down in degree (i.e., `1/2*x^3 - x^2 +
7*x - 2`). Computationally, though, if I have that second result, I can
easily get back to the first one by multiplying by `x^2`. If I have the
first, I can get to the second by dividing, but that puts the result in
the fraction field, which is probably not what I want. Alternatively, I
can also get to the second by creating a polynomial from `list(f)[2:6]`,
which is not as intuitive, but not too hard.
Surely different mathematicians will have different points of view on
this.
I think this is the issue for me: do we want
{{{
sage: list(pol[5:]) == list(pol)[5:]
True
}}}
or do we want
{{{
sage: pol[:5] + pol[5:] == pol
True
}}}
We can't have both, right? I prefer the second. That is, I tend to think
of polynomials as graded objects and slicing is returning some of their
homogeneous components, and it seems most natural to do this without
regrading the result: if a term is in degree 3 in the original polynomial,
it should still be in degree 3 after slicing. I would also like this:
{{{
sage: pol[0:10:2] + pol[1:10:2] == pol[0:10]
True
}}}
Adding the even terms to the odd terms should yield the original
polynomial.
A related question: should `f[2]` return `-2` or `-2 * x^2`?
-----------
When it comes down to it, I'm not sure I care which option is implemented
as `__getitem__`, but perhaps both should be implemented as methods which
are visible via tab-completion, or as a single method with a keyword which
determines which option to use.
--
Ticket URL: <http://trac.sagemath.org/ticket/18940#comment:32>
Sage <http://www.sagemath.org>
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