#17600: AsymptoticGrowthElement
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Reporter: behackl | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.5
Component: symbolics | Resolution:
Keywords: asymptotics | Merged in:
Authors: Benjamin Hackl | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/behackl/asy/growthGroup | 278c1f740b54c3336e4624367332438a9dd9b1ba
Dependencies: | Stopgaps:
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Comment (by cheuberg):
Replying to [comment:6 vdelecroix]:
> Why is it a group and not a ring?
The `AsymptoticGrowthGroup` is only planned to handle the multiplicative
structure. Instead of the simplest example here, think about asymptotics
involving powers of `n` and `log(n)` for `n -> infinity`. Then this group
will be isomorphic to a cartesian product of `RR` with itself with
lexicographic order. In another example, where `|h|<= n^(3/4)` and
`n->infinity`, this group will again be a cartesian product of `RR` with
itself, but the partial order of the lexicographic order will be refined
by the additional rule, but not yet be a linear order because some of
these terms cannot be compared.
Handling of coefficients, addition of two terms and absorption of O terms
are rather independent of the growth group as outlined here. Thus they are
planned to be handeled by the `AsymptoticTerm` (#17715).
High level operations such as addition and multiplication of expressions
are still more general and will be part of the (yet unimplemented)
`AsymptoticExpression` (#17716).
> Why should there be, if any, a dedicated parent to an asymptotic term?
There is a natural coercion from an `AsymptoticGrowthGroup` in `n` to the
`AsymptoticGrowthGroup` in `n` and `log(n)`, for instance. Thus I think it
makes sense to use the coercion framework. This requires to have parents.
> What I see in the branch is only code that is working for itself which
is not very interesting and not very useful.
Therefore, all these tickets are still in status `new` and not
`needs_review`, because the `AsymptoticExpression` is still missing.
> You can not start building a cathedral without any serious roadmap.
There is a roadmap and the very brief version is in the meta ticket
#17601. The long version are notes made during long oral discussions.
Your comments here and on the meta ticket #17601 make it clear that the
abbreviated version is not sufficiently clear. Probably the long version
of the road map will also be of interest later on and could live in the
documentation of the asymptotic expression.
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Ticket URL: <http://trac.sagemath.org/ticket/17600#comment:7>
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