#20877: Meta-ticket: Polyhedral complexes, piecewise functions of several
variables
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Reporter: mkoeppe | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-7.3
Component: geometry | Resolution:
Keywords: piecewise | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by mkoeppe:
Old description:
> 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.
>
> Discussion welcome, in particular in regard to how this code should
> interact with the existing classes for abstract complexes (CW complexes)
> and `PointConfiguration`.
>
> - #20878: `PointConfiguration`: Add `plot` method
> - #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.
>
> Piecewise functions of 1 variable and `RealSet`s:
> - #1773: piecewise functions and integration / arithmetic do not play
> well together
> - #8603: Partial sums are off for Fourier series of piecewise functions
> - #11225: improve piecewise plotting
> - #16063: Unify the classes `RealSet` and `UnionOfIntervals`
New description:
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.
Discussion welcome, in particular in regard to how this code should
interact with the existing classes for abstract complexes (CW complexes)
and `PointConfiguration`.
- #20878: `PointConfiguration`: Add `plot` method
- #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.
- #20892: package polymake 3.0
Piecewise functions of 1 variable and `RealSet`s:
- #1773: piecewise functions and integration / arithmetic do not play
well together
- #8603: Partial sums are off for Fourier series of piecewise functions
- #11225: improve piecewise plotting
- #16063: Unify the classes `RealSet` and `UnionOfIntervals`
- #6895: Detect discontinuities when plotting the ceil function
--
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Ticket URL: <https://trac.sagemath.org/ticket/20877#comment:5>
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