Changes between Version 5 and Version 11 of Ticket #13125


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Timestamp:
06/22/13 10:53:46 (9 years ago)
Author:
ares
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  • Ticket #13125

    • Property Summary changed from Reals sets consisting of intervals and isolated points, supporting integration. to Reals sets consisting of intervals and isolated points
    • Property Authors changed from Volker Braun to Volker Braun , Jordi Saludes , Ares Ribó
  • Ticket #13125 – Description

    v5 v11  
    66    (0, 2) + [10, +Infinity)
    77}}}
     8'''
     9Reals sets consisting of union of real intervals and isolated points.'''
     10   
     11    This is based of previous work available from http://www.mail-archive.com/sage-support@googlegroups.com/msg21326.html
     12    but supporting now integration on real intervals and real sets.
     13   
     14    - Laurent Claessens (2010-12-10): Original Interval and ContinuousSet from 'http://www.mail-archive.com/sage-support@googlegroups.com/msg21326.html'.
     15        Defined a class Interval that represents an interval (can be open, closed, half open, unbounded), and implements union() and intersection() methods, as well
     16        as the __contains__() method that tests if a number is contained in the interval. Also defined the class ContinuousSet that represents finite union and
     17        intersections of intervals by a list of disjoint intervals. For the class ContinuousSet, union() and __contain__() methods are implemented.
     18
     19    - 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     
     20        isolated points. For this class, we implemented the intersection() ( union() and __contain__() as for ContinuousSets). We implemented the function 'subsets'
     21        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
     22        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
     23        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.
     24
     25    - Jordi Saludes (2011-12-10): Documentation and file reorganization. Reimplementation of 'setdiff'. RInterval is now always an open interval. The boundary/ies
     26        can be added as isolated point/s if necessary, constituting a RealSet.
     27
     28    The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement
     29    n° FP7-ICT-247914.
     30     
     31    Examples
     32{{{
     33    sage: A = RealSet([RInterval((1,2)),RInterval((3,4))],[1,2])
     34
     35    sage: A
     36    [ 1 :: 2 ] + ] 3 :: 4 [
     37
     38    sage: B = RealSet([RInterval((2,3))],[1])
     39
     40    sage: B
     41    ] 2 :: 3 [ + {1}
     42}}}
     43