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Meta-ticket: Piecewise functions, polyhedral complexes, piecewise functions of several variables, periodic piecewise functions #20877
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comment:38
I'm interested in implementing piecewise affine functions in one variable with specific methods that are easier to implement in this setting (e.g. I'm wondering whether I should derive from the class |
comment:39
I have code in https://github.com/mkoeppe/cutgeneratingfunctionology/blob/master/cutgeneratingfunctionology/igp/fast_piecewise.py, based on the old Sage implementation of |
comment:42
Replying to @mkoeppe:
That's great! Do you plan to propose this code for integration in sage at some point or not? |
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comment:44
Replying to @xcaruso:
I'm familiar with the piecewise linear function code in the above github folder, and I'd love to have that integrated into sage. This has been on my wishlist for a few years, but the integration has never happened, partially because I don't have a clear view on where this new class should be derived from and what methods are useful to general users. Besides the class hierarchy, I think that the main modification concerns changing the use of close or open or half-open intervals defined in https://github.com/mkoeppe/cutgeneratingfunctionology/blob/master/cutgeneratingfunctionology/igp/intervals.py to |
comment:45
Replying to @yuan-zhou:
Yes, that's an important task. Related: #32181 |
comment:46
Right, I notice that #32181 is related, and I added it into the description of this meta-ticket in comment:43.
|
comment:47
Regarding the class hierarchy, There are many details so that it works correctly with all operations provided by the category. If this is added to Sage, it would be best to put it somewhere that's not If the scope remains piecewise linear functions (or even piecewise polynomial functions where the pieces are polyhedra such as box splines or simplex splines), then somewhere in Another connection: both |
This is a meta-ticket about piecewise functions.
Fractional part, modulo, ...:
Piecewise functions of 1 variable:
RealSet
s, underlying the current implementation ofpiecewise
:RealSet
andUnionOfIntervals
RealSet
s fail theirTestSuite
:_test_category
,_test_pickling
sage_input
forRealSet
andpiecewise
RealSet
: add methodsclosure
,interior
,boundary
,is_open
,is_closed
RealSet
falseRealSet
: Replaceis_included_in
byis_subset
/issubset
UnionOfIntervals
byRealSet
RealSet.contains
: Handle symbolic argumentRealSet
RealSet
: Faster operations by scan-line (merging) techniquesRealSet
fromRealInterval
orRBF
elements (dup: allow RealSet construction from RealInterval #17791)As a generalization, this meta-ticket will implement piecewise functions of several real variables.
The pieces are polyhedral complexes (not necessarily triangulations) or more generally polyhedral dissections (i.e., not necessarily face-to-face).
In my application, the functions will be piecewise linear, possibly discontinuous; but the implementation should be general enough for splines.
PolyhedralComplex
Discussion welcome, in particular in regard to how this code should interact with the existing classes for abstract complexes (CW complexes) and
PointConfiguration
.PointConfiguration
: Addplot
methodCombinatorialPolyhedron
CombinatorialPolyhedralComplex
General piecewise functions:
SymPy
's piecewiseSymPy
Piecewise
equivalentSymPy
CC: @tscrim @rwst @vbraun @videlec @jhpalmieri @kcrisman @paulmasson @sagetrac-tmonteil @mo271 @jplab @yuan-zhou
Component: geometry
Keywords: piecewise
Issue created by migration from https://trac.sagemath.org/ticket/20877
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