8 | | ''' |
9 | | Reals 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. |
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 | | |
| 9 | Apply |
| 10 | * [attachment:trac_13125_real_set.patch] |
| 11 | * [attachment:trac_13125_misc.patch] |