#19999: Exponential growth group: q^x and (-q)^x are incomparable
-------------------------------------+-------------------------------------
Reporter: dkrenn | Owner:
Type: defect | Status: positive_review
Priority: major | Milestone: sage-7.1
Component: asymptotic | Resolution:
expansions | Merged in:
Keywords: | Reviewers: Clemens Heuberger
Authors: Benjamin Hackl | Work issues:
Report Upstream: N/A | Commit:
Branch: u/behackl/exp- | 7881bb3632dd40cb9add6ce3dfd3e6255e9f82be
growth-inf-loop | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by cheuberg):
* status: needs_review => positive_review
* reviewer: => Clemens Heuberger
Old description:
> {{{
> sage: 1 + (-1)^x + (1/2)^x
> }}}
> gives
> {{{
> RuntimeError: maximum recursion depth exceeded in __instancecheck__
> }}}
> But
> {{{
> sage: (-1)^x + (1/2)^x + 1
> 1 + (-1)^x + (1/2)^x
> }}}
> works.
New description:
Using `q^x` for negative `q` leads to errors.
{{{
sage: 1 + (-1)^x + (1/2)^x
}}}
gives
{{{
RuntimeError: maximum recursion depth exceeded in __instancecheck__
}}}
But
{{{
sage: (-1)^x + (1/2)^x + 1
1 + (-1)^x + (1/2)^x
}}}
works.
Thus make `q^x` and `(-q)^x` incomparable; also making cartesian products
of growth groups fit to have lexicographic products of non-linear orders.
--
Comment:
LGTM.
--
Ticket URL: <http://trac.sagemath.org/ticket/19999#comment:13>
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