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

Question

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

Opened this issue 9 years ago · 41 comments

mkoeppe commented 9 years ago

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
#34456: piecewise polynomial in one dimension

RealSets, underlying the current implementation of piecewise:

#16063: Unify the classes RealSet and UnionOfIntervals
#21249: RealSets fail their TestSuite: _test_category, _test_pickling
#21277: sage_input for RealSet and piecewise
#21243: RealSet: add methods closure, interior, boundary, is_open, is_closed
#31941: Make empty RealSet false
#31927: RealSet: Replace is_included_in by is_subset / issubset
#31930: Replace UnionOfIntervals by RealSet
#31914: RealSet.contains: Handle symbolic argument
#31877: Refine category of RealSet
#32181: RealSet: Faster operations by scan-line (merging) techniques
#31740: Meta-ticket: Families, posets, complexes of manifold subsets
#21242: Allow initializing RealSet from RealInterval or RBF elements (dup: #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.

#31748 PolyhedralComplex
#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
#26887: Implement CombinatorialPolyhedron
#27063: Transition of combinatorial computations of Polyhedron to Combinatorial Type
#31842: CombinatorialPolyhedralComplex
#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

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

Answer 1 · 2016-06-24T23:57:18.000Z

Description changed:

--- 
+++ 
@@ -1,6 +1,9 @@
 This meta-ticket will implement piecewise functions of several real variables. 
-The pieces are polyhedral complexes (not necessarily triangulations).
+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
+

Answer 2 · 2016-06-26T21:30:08.000Z

Description changed:

--- 
+++ 
@@ -4,6 +4,6 @@
 
 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
+- #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.

Answer 3 · 2016-06-27T03:40:24.000Z

Description changed:

--- 
+++ 
@@ -7,3 +7,8 @@
 - #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
+

Answer 4 · 2016-06-27T04:56:23.000Z

Description changed:

--- 
+++ 
@@ -11,4 +11,4 @@
 - #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`

Answer 5 · 2016-07-07T04:57:13.000Z

Description changed:

--- 
+++ 
@@ -6,9 +6,11 @@
 
 - #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

Answer 6 · 2016-07-07T20:20:35.000Z

Description changed:

--- 
+++ 
@@ -14,3 +14,4 @@
 - #11225: improve piecewise plotting
 - #16063: Unify the classes `RealSet` and `UnionOfIntervals`
 - #6895: Detect discontinuities when plotting the ceil function
+- #10597: Riemann sums, added trapezoid option

Answer 7 · 2016-08-05T18:31:23.000Z

Description changed:

--- 
+++ 
@@ -7,6 +7,7 @@
 - #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
+- #21151: Update TOPCOM to 0.17.7, disable outdated libsoplex support
 
 Piecewise functions of 1 variable and `RealSet`s:
 - #1773: piecewise functions and integration / arithmetic do not play well together

Answer 8 · 2016-08-10T20:26:03.000Z

Description changed:

--- 
+++ 
@@ -16,3 +16,4 @@
 - #16063: Unify the classes `RealSet` and `UnionOfIntervals`
 - #6895: Detect discontinuities when plotting the ceil function
 - #10597: Riemann sums, added trapezoid option
+- #9935: Make a symbolic mod function

Answer 9 · 2016-08-10T20:59:27.000Z

Description changed:

--- 
+++ 
@@ -17,3 +17,4 @@
 - #6895: Detect discontinuities when plotting the ceil function
 - #10597: Riemann sums, added trapezoid option
 - #9935: Make a symbolic mod function
+- #21215: Periodic piecewise functions

Answer 10 · 2016-08-12T19:18:29.000Z

Description changed:

--- 
+++ 
@@ -17,4 +17,5 @@
 - #6895: Detect discontinuities when plotting the ceil function
 - #10597: Riemann sums, added trapezoid option
 - #9935: Make a symbolic mod function
+- #21232: Fractional part function {x}
 - #21215: Periodic piecewise functions

Answer 11 · 2016-08-14T23:32:15.000Z

Description changed:

--- 
+++ 
@@ -9,11 +9,16 @@
 - #20892: package polymake 3.0
 - #21151: Update TOPCOM to 0.17.7, disable outdated libsoplex support
 
-Piecewise functions of 1 variable and `RealSet`s:
+`RealSet`s:
+- #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
+- #21243: RealSet: add closure and interior methods
+
+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
-- #16063: Unify the classes `RealSet` and `UnionOfIntervals`
 - #6895: Detect discontinuities when plotting the ceil function
 - #10597: Riemann sums, added trapezoid option
 - #9935: Make a symbolic mod function

Answer 12 · 2016-08-15T17:57:07.000Z

Description changed:

--- 
+++ 
@@ -8,6 +8,7 @@
 - #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
 - #21151: Update TOPCOM to 0.17.7, disable outdated libsoplex support
+- #10777: Implement CombinatorialPolyhedron
 
 `RealSet`s:
 - #16063: Unify the classes `RealSet` and `UnionOfIntervals`

Answer 13 · 2016-08-18T06:32:46.000Z

Description changed:

--- 
+++ 
@@ -24,4 +24,5 @@
 - #10597: Riemann sums, added trapezoid option
 - #9935: Make a symbolic mod function
 - #21232: Fractional part function {x}
+- #21274: frac(x) immediate simplifications
 - #21215: Periodic piecewise functions

Answer 14 · 2016-08-18T07:03:52.000Z

Description changed:

--- 
+++ 
@@ -8,13 +8,14 @@
 - #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
 - #21151: Update TOPCOM to 0.17.7, disable outdated libsoplex support
-- #10777: Implement CombinatorialPolyhedron
+- #10777: Implement `CombinatorialPolyhedron`
 
 `RealSet`s:
 - #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
-- #21243: RealSet: add closure and interior methods
+- #21249: `RealSet`s fail their `TestSuite`: `_test_category`, `_test_pickling`
+- #21242: Allow initializing `RealSet` from `RealInterval` or `RBF` elements
+- #21243: `RealSet`: add `closure` and `interior` methods
+- #21277: `sage_input` for `RealSet` and `piecewise`
 
 Piecewise functions of 1 variable:
 - #1773: piecewise functions and integration / arithmetic do not play well together

Answer 15 · 2016-08-19T00:12:44.000Z

Description changed:

--- 
+++ 
@@ -13,7 +13,7 @@
 `RealSet`s:
 - #16063: Unify the classes `RealSet` and `UnionOfIntervals`
 - #21249: `RealSet`s fail their `TestSuite`: `_test_category`, `_test_pickling`
-- #21242: Allow initializing `RealSet` from `RealInterval` or `RBF` elements
+- #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`

Answer 16 · 2016-08-19T00:45:44.000Z

Description changed:

--- 
+++ 
@@ -9,6 +9,7 @@
 - #20892: package polymake 3.0
 - #21151: Update TOPCOM to 0.17.7, disable outdated libsoplex support
 - #10777: Implement `CombinatorialPolyhedron`
+- #18197: Add CGAL package
 
 `RealSet`s:
 - #16063: Unify the classes `RealSet` and `UnionOfIntervals`

Answer 17 · 2016-09-04T20:55:35.000Z

Description changed:

--- 
+++ 
@@ -28,3 +28,4 @@
 - #21232: Fractional part function {x}
 - #21274: frac(x) immediate simplifications
 - #21215: Periodic piecewise functions
+- #21412: Convert piecewise functions to SymPy

Answer 18 · 2016-10-01T21:26:19.000Z

Description changed:

--- 
+++ 
@@ -1,4 +1,26 @@
-This meta-ticket will implement piecewise functions of several real variables. 
+This is a meta-ticket about piecewise functions.
+
+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
+- #9935: Make a symbolic mod function
+- #21232: Fractional part function {x}
+- #21274: frac(x) immediate simplifications
+- #21215: Periodic piecewise functions
+- #21412: Convert piecewise functions to SymPy
+- #21618: plot in piecewise regression (?)
+
+`RealSet`s, underlying the current implementation of `piecewise`:
+- #16063: Unify the classes `RealSet` and `UnionOfIntervals`
+- #21249: `RealSet`s 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.
 
@@ -11,21 +33,4 @@
 - #10777: Implement `CombinatorialPolyhedron`
 - #18197: Add CGAL package
 
-`RealSet`s:
-- #16063: Unify the classes `RealSet` and `UnionOfIntervals`
-- #21249: `RealSet`s 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`
 
-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
-- #9935: Make a symbolic mod function
-- #21232: Fractional part function {x}
-- #21274: frac(x) immediate simplifications
-- #21215: Periodic piecewise functions
-- #21412: Convert piecewise functions to SymPy

Answer 19 · 2016-10-15T18:38:02.000Z

Description changed:

--- 
+++ 
@@ -12,6 +12,7 @@
 - #21215: Periodic piecewise functions
 - #21412: Convert piecewise functions to SymPy
 - #21618: plot in piecewise regression (?)
+- #21709: Categories for piecewise functions
 
 `RealSet`s, underlying the current implementation of `piecewise`:
 - #16063: Unify the classes `RealSet` and `UnionOfIntervals`

Answer 20 · 2016-10-24T22:48:17.000Z

Description changed:

--- 
+++ 
@@ -1,4 +1,11 @@
 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)
 
 Piecewise functions of 1 variable:
 - #1773: piecewise functions and integration / arithmetic do not play well together
@@ -6,9 +13,6 @@
 - #11225: improve piecewise plotting
 - #6895: Detect discontinuities when plotting the ceil function
 - #10597: Riemann sums, added trapezoid option
-- #9935: Make a symbolic mod function
-- #21232: Fractional part function {x}
-- #21274: frac(x) immediate simplifications
 - #21215: Periodic piecewise functions
 - #21412: Convert piecewise functions to SymPy
 - #21618: plot in piecewise regression (?)

Answer 21 · 2016-10-25T17:54:51.000Z

Description changed:

--- 
+++ 
@@ -6,6 +6,7 @@
 - #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

Answer 22 · 2018-03-10T17:40:04.000Z

Description changed:

--- 
+++ 
@@ -34,7 +34,8 @@
 
 - #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
+- #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

Answer 23 · 2018-03-10T17:52:26.000Z

Description changed:

--- 
+++ 
@@ -40,4 +40,10 @@
 - #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`
+ 
 
+

Answer 24 · 2018-10-20T00:37:21.000Z

Description changed:

--- 
+++ 
@@ -30,6 +30,8 @@
 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

Answer 25 · 2020-10-26T20:11:26.000Z

Description changed:

--- 
+++ 
@@ -25,6 +25,7 @@
 - #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`
+- #30832: Connect `RealSet` to `sage.manifolds`
 
 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).

Answer 26 · 2021-02-13T20:51:01.000Z

comment:29

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

Answer 27 · 2021-04-28T14:39:19.000Z

Description changed:

--- 
+++ 
@@ -31,6 +31,7 @@
 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.
 
+- #31748 PolyhedralComplex
 - #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`.

Answer 28 · 2021-05-30T19:44:50.000Z

Description changed:

--- 
+++ 
@@ -26,6 +26,7 @@
 - #21243: `RealSet`: add `closure` and `interior` methods
 - #21277: `sage_input` for `RealSet` and `piecewise`
 - #30832: Connect `RealSet` to `sage.manifolds`
+- #31740: Meta-ticket: Families, posets, complexes of manifold subsets
 
 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).

Answer 29 · 2021-06-07T22:34:40.000Z

Description changed:

--- 
+++ 
@@ -22,17 +22,19 @@
 `RealSet`s, underlying the current implementation of `piecewise`:
 - #16063: Unify the classes `RealSet` and `UnionOfIntervals`
 - #21249: `RealSet`s fail their `TestSuite`: `_test_category`, `_test_pickling`
+- #21277: `sage_input` for `RealSet` and `piecewise`
+- #21243: `RealSet`: add methods `closure`, `interior`, `boundary`, `is_open`, `is_closed`
+- #31927: `RealSet`: Replace `is_included_in` by `is_subset` / `issubset`
+- #31914: `RealSet.contains`: Handle symbolic argument
+- #31877: Refine category of `RealSet`
+- **#31740: Meta-ticket: Families, posets, complexes of manifold subsets**
 - #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`
-- #30832: Connect `RealSet` to `sage.manifolds`
-- #31740: Meta-ticket: Families, posets, complexes of manifold subsets
 
 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.
 
-- #31748 PolyhedralComplex
+- #31748 `PolyhedralComplex`
 - #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`.

Answer 30 · 2021-06-08T01:10:34.000Z

Description changed:

--- 
+++ 
@@ -25,6 +25,7 @@
 - #21277: `sage_input` for `RealSet` and `piecewise`
 - #21243: `RealSet`: add methods `closure`, `interior`, `boundary`, `is_open`, `is_closed`
 - #31927: `RealSet`: Replace `is_included_in` by `is_subset` / `issubset`
+- #31930: Replace `UnionOfIntervals` by `RealSet`
 - #31914: `RealSet.contains`: Handle symbolic argument
 - #31877: Refine category of `RealSet`
 - **#31740: Meta-ticket: Families, posets, complexes of manifold subsets**

Answer 31 · 2021-06-09T04:15:30.000Z

Description changed:

--- 
+++ 
@@ -24,6 +24,7 @@
 - #21249: `RealSet`s fail their `TestSuite`: `_test_category`, `_test_pickling`
 - #21277: `sage_input` for `RealSet` and `piecewise`
 - #21243: `RealSet`: add methods `closure`, `interior`, `boundary`, `is_open`, `is_closed`
+- #31941: Make empty `RealSet` false
 - #31927: `RealSet`: Replace `is_included_in` by `is_subset` / `issubset`
 - #31930: Replace `UnionOfIntervals` by `RealSet`
 - #31914: `RealSet.contains`: Handle symbolic argument

Answer 32 · 2022-03-17T10:56:09.000Z

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. compose, is_bijective, inverse, is_convex, convex_hull, laplace_transform, etc.) Mostly, I'm interested in the case where the coefficients of the affine parts are in QQ but I might also want to consider the case where they are in a fixed number field.

I'm wondering whether I should derive from the class sage.functions.piecewise.PiecewiseFunction (which is mostly concerned with symbolic expressions) or if it is okay if I rewrite my own class from scratch.

Answer 33 · 2022-03-17T17:53:57.000Z

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 piecewise, which may be a starting point. It is not tied to symbolics and uses the parent-element framework

Answer 34 · 2022-03-17T17:56:08.000Z

comment:40

Also https://github.com/mkoeppe/cutgeneratingfunctionology/blob/master/cutgeneratingfunctionology/igp/move_semigroup.py

Answer 35 · 2022-03-23T07:24:44.000Z

comment:42

Replying to @mkoeppe:

I have code in https://github.com/mkoeppe/cutgeneratingfunctionology/blob/master/cutgeneratingfunctionology/igp/fast_piecewise.py, based on the old Sage implementation of piecewise, which may be a starting point. It is not tied to symbolics and uses the parent-element framework

That's great! Do you plan to propose this code for integration in sage at some point or not?

Answer 36 · 2022-03-23T08:20:09.000Z

Description changed:

--- 
+++ 
@@ -29,6 +29,7 @@
 - #31930: Replace `UnionOfIntervals` by `RealSet`
 - #31914: `RealSet.contains`: Handle symbolic argument
 - #31877: Refine category of `RealSet`
+- #32181: `RealSet`: Faster operations by scan-line (merging) techniques
 - **#31740: Meta-ticket: Families, posets, complexes of manifold subsets**
 - #21242: Allow initializing `RealSet` from `RealInterval` or `RBF` elements (dup: #17791)
 
@@ -46,7 +47,9 @@
 - #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`
+- #26887: Implement `CombinatorialPolyhedron`
+- #27063: Transition of combinatorial computations of Polyhedron to Combinatorial Type
+- #31842: `CombinatorialPolyhedralComplex`
 - #18197: Add CGAL package
 
 General piecewise functions:

Answer 37 · 2022-03-23T08:56:32.000Z

comment:44

Replying to @xcaruso:

Replying to @mkoeppe:

I have code in https://github.com/mkoeppe/cutgeneratingfunctionology/blob/master/cutgeneratingfunctionology/igp/fast_piecewise.py, based on the old Sage implementation of piecewise, which may be a starting point. It is not tied to symbolics and uses the parent-element framework

That's great! Do you plan to propose this code for integration in sage at some point or not?

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 RealSet.

Answer 38 · 2022-03-23T19:00:39.000Z

comment:45

Replying to @yuan-zhou:

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 RealSet.

Yes, that's an important task. Related: #32181

Answer 39 · 2022-03-23T19:25:42.000Z

comment:46

Right, I notice that #32181 is related, and I added it into the description of this meta-ticket in comment:43.
Replying to @mkoeppe:

Replying to @yuan-zhou:

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 RealSet.

Yes, that's an important task. Related: #32181

Answer 40 · 2022-03-23T19:37:28.000Z

comment:47

Regarding the class hierarchy, class PiecewiseLinearFunction_1d (ModuleElement) https://github.com/mkoeppe/cutgeneratingfunctionology/blob/master/cutgeneratingfunctionology/igp/fast_piecewise.py#L17 for the element is already good, I think. The corresponding parent is https://github.com/mkoeppe/cutgeneratingfunctionology/blob/master/cutgeneratingfunctionology/igp/fast_piecewise.py#L1221

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 sage.functions because this package concerns symbolic functions.

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 sage.geometry would make sense because of its close ties to https://doc.sagemath.org/html/en/reference/discrete_geometry/sage/geometry/polyhedral_complex.html

Another connection: both indicator_function and convex_indicator_function (proposed to add in #32201) of polyhedra are, of course, piecewise linear functions.

Answer 41 · 2022-08-31T04:51:29.000Z

Description changed:

--- 
+++ 
@@ -18,6 +18,8 @@
 - #21412: Convert piecewise functions to SymPy
 - #21618: plot in piecewise regression (?)
 - #21709: Categories for piecewise functions
+- #34456: piecewise polynomial in one dimension
+
 
 `RealSet`s, underlying the current implementation of `piecewise`:
 - #16063: Unify the classes `RealSet` and `UnionOfIntervals`