#13125: Reals sets consisting of intervals and isolated points
------------------------------------------------------------+---------------
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 , Jordi Saludes , Ares Ribó | Merged in:
Dependencies: | Stopgaps:
------------------------------------------------------------+---------------
Changes (by {'newvalue': u'Volker Braun , Jordi Saludes , Ares Rib\xf3',
'oldvalue': u'Volker Braun'}):
* author: Volker Braun => Volker Braun , Jordi Saludes , Ares Ribó
Old 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)
> }}}
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)
}}}
'''
Reals sets consisting of union of real intervals and isolated points.'''
This is based of previous work available from http://www.mail-
archive.com/[email protected]/msg21326.html
but supporting now integration on real intervals and real sets.
- Laurent Claessens (2010-12-10): Original Interval and ContinuousSet
from 'http://www.mail-archive.com/sage-
[email protected]/msg21326.html'.
Defined a class Interval that represents an interval (can be open,
closed, half open, unbounded), and implements 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 that represents
finite union and
intersections of intervals by a list of disjoint intervals. For
the class ContinuousSet, union() and __contain__() methods are
implemented.
- Ares Ribo (2011-10-24): Extended the previous work defining the
class RealSet, that describes any real set as a list of disjoint intervals
and a list of
isolated points. For this class, we implemented the intersection()
( union() and __contain__() as for ContinuousSets). We implemented the
function 'subsets'
which 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. Also we support definite integration over a RealSet, and we
implemented the infimum and the supremum of a RealSet. 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.
- Jordi Saludes (2011-12-10): Documentation and file reorganization.
Reimplementation of 'setdiff'. RInterval is now always an open interval.
The boundary/ies
can be added as isolated point/s if necessary, constituting a
RealSet.
The research leading to these results has received funding from the
European Union's Seventh Framework Programme (FP7/2007-2013) under grant
agreement
n° FP7-ICT-247914.
Examples
{{{
sage: A = RealSet([RInterval((1,2)),RInterval((3,4))],[1,2])
sage: A
[ 1 :: 2 ] + ] 3 :: 4 [
sage: B = RealSet([RInterval((2,3))],[1])
sage: B
] 2 :: 3 [ + {1}
}}}
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13125#comment:11>
Sage <http://www.sagemath.org>
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