#12589: series yields wrong result
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Reporter: dkrenn | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: series, order, symbolics | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps: todo
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Comment (by rws):
Replying to [comment:11 dkrenn]:
> Being stucked with this bug is not an option either... What else can we
do?
Mathematically you are dealing with so-called "lacunar" or "super-sparse"
series. Changing from 32bit to 64bit does not resolve it in principle if
it were possible with existing Sage functionality, try this:
{{{
sage: R.<a>=QQ[[]]
sage: 2^33
8589934592
sage: a^8589934592-1
versus
sage: R.<x>=PolynomialRing(QQ,sparse=True)
sage: 2^65
36893488147419103232
sage: x^36893488147419103232-1
x^36893488147419103232 - 1
versus
sage: R.<x>=PowerSeriesRing(QQ,sparse=True)
sage: x^36893488147419103232-1
-1 + x^36893488147419103232
sage: x^36893488147419103232-1+O(x^5555555555555555555555)
OverflowError: Python int too large to convert to C long
sage: R.<q>=PowerSeriesRing(QQ,sparse=True)
sage: f=(q^13362120470/((q - 1)) +1)/(q^7635497409/((q - 1)) + 1)
MemoryError
}}}
so apparently Sage's sparse power series ring can represent monomials with
bigint degree but not a bigint series order term. Representing or
computing a full series lastly can involve memory problems for whatever
reason.
However, if you request `f.series(q,2)` you do not want a full series so
maybe lazy series could be your solution.
--
Ticket URL: <http://trac.sagemath.org/ticket/12589#comment:12>
Sage <http://www.sagemath.org>
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