#17715: AsymptoticTerm
-------------------------------------+-------------------------------------
Reporter: behackl | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.5
Component: symbolics | Resolution:
Keywords: asymptotics, | Merged in:
gsoc15 | Reviewers: Daniel Krenn
Authors: Benjamin Hackl, | Work issues:
Daniel Krenn | Commit:
Report Upstream: N/A | 7f2c5842f61d78663fd3c61e303cfe864fc558a1
Branch: | Stopgaps:
u/behackl/asy/asymptoticTerm |
Dependencies: #17600 |
-------------------------------------+-------------------------------------
Description changed by behackl:
Old description:
> Asymptotic terms are expressions like O(n^2^), 7 * n * 2^n^, or 42 * n *
> log(n). They build upon the asymptotic growth elements from #17600, which
> are elements like n^2^, n*2^n^ and n * log(n) (that is, they handle only
> the asymptotic growth).
>
> All asymptotic terms have an attribute 'growth' (which is some growth
> element), and then they may have additional information (like, for
> example, a coefficient in the case of exact terms).
>
> Currently, we implemented the following asymptotic terms (plus their
> monoid parents):
>
> !GenericTerm::
> Implements the base structure of asymptotic terms.
>
> OTerm::
> Class for big O terms. These terms may "absorb" other asymptotic
> terms with weaker or equal growth.
>
> !TermWithCoefficient::
> Generic base class for asymptotic terms with coefficient. Base class
> for asymptotic exact terms and asymptotic L terms.
>
> !ExactTerm::
> Class for asymptotic exact terms. These terms correspond to symbolic
> expressions like, for example, 2 * x^3^, 7 * x^-2/5^, or 42 * x^1/3^ *
> log(x).
>
> LTermGeneric::
> Base class for asymptotic L terms, that is, asymptotic terms that
> behave like an O term, but with a specified constant and starting point.
>
> Asymptotic terms may be multiplied and absorbed; addition will be handled
> by !AsymptoticExpression.
>
> See meta-ticket #17601 for the planned structure.
New description:
Asymptotic terms are expressions like O(n^2^), 7 * n * 2^n^, or 42 * n *
log(n). They build upon the asymptotic growth elements from #17600, which
are elements like n^2^, n*2^n^ and n * log(n) (that is, they handle only
the asymptotic growth).
All asymptotic terms have an attribute 'growth' (which is some growth
element), and then they may have additional information (like, for
example, a coefficient in the case of exact terms).
Currently, we implemented the following asymptotic terms (plus their
monoid parents):
!GenericTerm::
Implements the base structure of asymptotic terms.
OTerm::
Class for big O terms. These terms may "absorb" other asymptotic terms
with weaker or equal growth.
!TermWithCoefficient::
Generic base class for asymptotic terms with coefficient. Base class
for asymptotic exact terms and asymptotic L terms.
!ExactTerm::
Class for asymptotic exact terms. These terms correspond to symbolic
expressions like, for example, 2 * x^3^, 7 * x^-2/5^, or 42 * x^1/3^ *
log(x).
Asymptotic terms may be multiplied and absorbed; addition will be handled
by !AsymptoticExpression.
See meta-ticket #17601 for the planned structure.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/17715#comment:13>
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