#13125: Reals sets consisting of intervals and isolated points, supporting
integration.
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Reporter: ares | Owner: Ares Ribó
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.11
Component: calculus | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Volker Braun | Merged in:
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Volker Braun', 'oldvalue': u'Jordi Saludes and Ares
Rib\xf3'}):
* cc: kcrisman (added)
* status: new => needs_review
* author: Jordi Saludes and Ares Ribó => Volker Braun
Old description:
> This is based of previous work available from
> http://www.mail-archive.com/sage-
> [email protected]/msg21326.html
> but supporting now integration on real intervals and real sets.
>
> Laurent Claessens defined a class Interval that represents an interval
> (can be open, closed, half open, unbounded), and implemented union() and
> intersection() methods, as well as the __contains__() method that tests
> if a number is contained in the interval. Also defined the class
> ContinuousSet represening finite union and intersections of intervals by
> a list of disjoint intervals, and for this class ContinuousSet, union()
> and __contain__() methods were implemented.
>
> We extend the previous work of Laurent Claessens defining the class
> RealSet, that describes any real set as a list of disjoint intervals and
> a list of isolated points. We define the class RInterval of real
> intervals. A RInterval is now a RealSet, consituted as a list of disjoint
> intervals with a unique element and an empty list of isolated points. Our
> class RInterval is now always an open interval. The boundary/ies can be
> added as isolated point/s if necessary, constituting a RealSet.
>
> For the class RealSet, we implement the intersection(), union() and
> __contain__(). We implement the function subsets that, given two
> different real sets A and B, returns if A is a (proper) subset of B, and
> the function setdiff that returns the difference of two given real sets.
> We implement also the infimum and the supremum of a RealSet.
>
> Also we support definite integration over a RealSet.
New description:
Finite unions of open/closed/semi-closed subsets of the real line
For example
{{{
sage: RealSet(0,2) + RealSet.unbounded_above_closed(10)
(0, 2) + [10, +Infinity)
}}}
--
Comment:
I'm taking over this ticket since I need this for piecewise functions. I'm
not sure what happened with the originally proposed patch, but what was
attached here is not the actual code.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13125#comment:5>
Sage <http://www.sagemath.org>
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