Meta-ticket: Piecewise functions, polyhedral complexes, piecewise functions of several variables, periodic piecewise functions #20877
Description
This is a meta-ticket about piecewise functions.
Fractional part, modulo, ...:
- Make a symbolic mod function #9935: Make a symbolic mod function
- Fractional part function {x} #21232: Fractional part function {x}
- frac(x) immediate simplifications #21274: frac(x) immediate simplifications
- Standardize modulo operator % on real numbers (step 1) #21745: Standardize modulo operator % on real numbers (step 1)
- Standardize modulo operator % on real numbers (step 2) #21747: Standardize modulo operator % on real numbers (step 2)
- change the mod method of rationals #21748: change the mod method of rationals
Piecewise functions of 1 variable:
- piecewise functions and integration / arithmetic do not play well together #1773: piecewise functions and integration / arithmetic do not play well together
- Partial sums are off for Fourier series of piecewise functions #8603: Partial sums are off for Fourier series of piecewise functions
- improve piecewise plotting #11225: improve piecewise plotting
- Detect discontinuities when plotting the ceil function #6895: Detect discontinuities when plotting the ceil function
- Riemann sums, added trapezoid option #10597: Riemann sums, added trapezoid option
- Periodic piecewise functions #21215: Periodic piecewise functions
- Convert piecewise functions to SymPy #21412: Convert piecewise functions to SymPy
- plot in piecewise regression #21618: plot in piecewise regression (?)
- Categories for piecewise functions #21709: Categories for piecewise functions
- piecewise polynomial in one dimension #34456: piecewise polynomial in one dimension
RealSets, underlying the current implementation of piecewise:
- Unify the classes RealSet and UnionOfIntervals #16063: Unify the classes
RealSetandUnionOfIntervals - RealSets fail their TestSuite: _test_category, _test_pickling #21249:
RealSets fail theirTestSuite:_test_category,_test_pickling - sage_input for infinities and RealSet #21277:
sage_inputforRealSetandpiecewise - RealSet: add methods closure, interior, boundary, is_open, is_closed #21243:
RealSet: add methodsclosure,interior,boundary,is_open,is_closed - Make empty RealSet false #31941: Make empty
RealSetfalse - RealSet: Replace is_included_in, is_disjoint_from by is_subset, is_disjoint #31927:
RealSet: Replaceis_included_inbyis_subset/issubset - Replace UnionOfIntervals by RealSet #31930: Replace
UnionOfIntervalsbyRealSet - RealSet.contains: Handle symbolic argument #31914:
RealSet.contains: Handle symbolic argument - Refine category of RealSet #31877: Refine category of
RealSet - RealSet: Faster operations by scan-line (merging) techniques #32181:
RealSet: Faster operations by scan-line (merging) techniques - Meta-ticket: Families, posets, complexes of manifold subsets #31740: Meta-ticket: Families, posets, complexes of manifold subsets
- Allow initializing RealSet from RealInterval or RBF elements #21242: Allow initializing
RealSetfromRealIntervalorRBFelements (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 #31748
PolyhedralComplex - Piecewise linear functions of several variables #26512 Piecewise linear functions of several variables
Discussion welcome, in particular in regard to how this code should interact with the existing classes for abstract complexes (CW complexes) and PointConfiguration.
- PointConfiguration: Add plot method #20878:
PointConfiguration: Addplotmethod - Expose PPL's Not-Necessarily-Closed Polyhedra and Normaliz' Polyhedra with Open Facets using Sage Polyhedra #20879: Expose PPL's Not-Necessarily-Closed Polyhedra using Sage Polyhedra -- could play the same role as half-open intervals do in the context of the new piecewise functions.
- Meta-ticket: polymake #22710: Meta-ticket: polymake
- Interface to polymake's polyhedral complexes #24943: Interface to polymake's polyhedral complexes
- Update TOPCOM to 0.17.7, disable outdated libsoplex support #21151: Update TOPCOM to 0.17.7, disable outdated libsoplex support
- Implement the class CombinatorialPolyhedron #26887: Implement
CombinatorialPolyhedron - Transition of combinatorial computations of Polyhedron to Combinatorial Type #27063: Transition of combinatorial computations of Polyhedron to Combinatorial Type
- CombinatorialPolyhedralComplex #31842:
CombinatorialPolyhedralComplex - Add CGAL package #18197: Add CGAL package
General piecewise functions:
- Interface cases function with SymPy's piecewise #23923: Interface cases function with
SymPy's piecewise - implement SymPy Piecewise equivalent #20191: implement
SymPyPiecewiseequivalent - Convert piecewise functions to SymPy #21412: Convert piecewise functions to
SymPy
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