Opened 4 years ago

Last modified 18 months ago

#20877 new task

Meta-ticket: Piecewise functions, polyhedral complexes, piecewise functions of several variables, periodic piecewise functions

Reported by: mkoeppe Owned by:
Priority: major Milestone: sage-8.5
Component: geometry Keywords: piecewise
Cc: tscrim, rws, vbraun, vdelecroix, jhpalmieri, kcrisman, paulmasson, tmonteil, moritz, jipilab Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by mkoeppe)

This is a meta-ticket about piecewise functions.

Fractional part, modulo, ...:

  • #9935: Make a symbolic mod function
  • #21232: Fractional part function {x}
  • #21274: frac(x) immediate simplifications
  • #21745: Standardize modulo operator % on real numbers (step 1)
  • #21747: Standardize modulo operator % on real numbers (step 2)
  • #21748: change the mod method of rationals

Piecewise functions of 1 variable:

  • #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
  • #6895: Detect discontinuities when plotting the ceil function
  • #10597: Riemann sums, added trapezoid option
  • #21215: Periodic piecewise functions
  • #21412: Convert piecewise functions to SymPy?
  • #21618: plot in piecewise regression (?)
  • #21709: Categories for piecewise functions

RealSets, underlying the current implementation of piecewise:

  • #16063: Unify the classes RealSet and UnionOfIntervals
  • #21249: RealSets fail their TestSuite: _test_category, _test_pickling
  • #21242: Allow initializing RealSet from RealInterval or RBF elements (dup: #17791)
  • #21243: RealSet: add closure and interior methods
  • #21277: sage_input for RealSet and piecewise

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.

  • #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.

  • #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.
  • #22710: Meta-ticket: polymake
  • #24943: Interface to polymake's polyhedral complexes
  • #21151: Update TOPCOM to 0.17.7, disable outdated libsoplex support
  • #10777: Implement CombinatorialPolyhedron
  • #18197: Add CGAL package

General piecewise functions:

  • #23923: Interface cases function with SymPy's piecewise
  • #20191: implement SymPy Piecewise equivalent
  • #21412: Convert piecewise functions to SymPy

Change History (27)

comment:1 Changed 4 years ago by mkoeppe

  • Cc tscrim added
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comment:2 Changed 4 years ago by mkoeppe

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comment:7 Changed 4 years ago by mkoeppe

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comment:8 Changed 4 years ago by mkoeppe

  • Description modified (diff)
  • Summary changed from Meta-ticket: Polyhedral complexes, piecewise functions of several variables to Meta-ticket: Polyhedral complexes, piecewise functions of several variables, periodic piecewise functions

comment:9 Changed 4 years ago by mkoeppe

  • Description modified (diff)

comment:10 Changed 4 years ago by mkoeppe

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comment:11 Changed 4 years ago by mkoeppe

  • Cc rws vbraun vdelecroix added
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  • Milestone changed from sage-7.3 to sage-7.4

comment:12 Changed 4 years ago by mkoeppe

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comment:17 Changed 4 years ago by mkoeppe

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comment:18 Changed 4 years ago by mkoeppe

  • Cc jhpalmieri added

comment:19 Changed 4 years ago by mkoeppe

  • Cc kcrisman paulmasson added

comment:20 Changed 4 years ago by mkoeppe

  • Description modified (diff)
  • Summary changed from Meta-ticket: Polyhedral complexes, piecewise functions of several variables, periodic piecewise functions to Meta-ticket: Piecewise functions, polyhedral complexes, piecewise functions of several variables, periodic piecewise functions

comment:21 Changed 3 years ago by mkoeppe

  • Description modified (diff)

comment:22 Changed 3 years ago by mkoeppe

  • Cc tmonteil added
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comment:23 Changed 3 years ago by mkoeppe

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comment:24 Changed 2 years ago by moritz

  • Cc moritz added

comment:25 Changed 2 years ago by mkoeppe

  • Cc jipilab added
  • Description modified (diff)
  • Milestone changed from sage-7.4 to sage-8.2

comment:26 Changed 2 years ago by mkoeppe

  • Description modified (diff)

comment:27 Changed 18 months ago by mkoeppe

  • Description modified (diff)
  • Milestone changed from sage-8.2 to sage-8.5
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