piecewise polynomial in one dimension

[NicoleYueqiLi]

Implement real value piecewise polynomial function over the real set. For the polynomial function, we adopted code from the polynomial ring of SageMath. For piecewise function, we adopted code by Matthias Köppe et al., at https://github.com/mkoeppe/cutgeneratingfunctionology/blob/master/cutgeneratingfunctionology/igp/fast_piecewise.py and code by David Joyner et al. at SageMath piecewise function.

This code can do general piecewise add, subtraction, multiplication, divide the real number, equal, detect pieces with discontinuity, and compute limits at certain points. we are currently working on plotting piecewise functions.

Depends on #11225

CC: @yuan-zhou

Component: geometry

Keywords: piecewise

Author: Yueqi Li

Branch/Commit: u/gh-NicoleYueqiLi/piecewise_polynomial_in_one_dimension @ e185e1d

Issue created by migration from https://trac.sagemath.org/ticket/34456

[yuan-zhou]

Branch: u/gh-NicoleYueqiLi/piecewise_polynomial_in_one_dimension

[yuan-zhou]

New commits:

d26bb5d	Implement piecewise polynomial
cca011a	recommit
604de7d	rewrite
4d9ab5e	implement piecewise_polynomial
e185e1d	implement piecewise_polynomial

[yuan-zhou]

Commit: e185e1d

[yuan-zhou]

Changed author from Yueqi Li, Yuan Zhou to Yueqi Li

[mkoeppe]

comment:3

+class Piecewise_Polynomial(ModuleElement):

This naming scheme does not follow our common usage.

It should be changed to one of these:

• PiecewisePolynomial -- following the general Python convention for naming of classes
• PiecewiseFunction_polynomial -- when the intention is that there is a public constructor PiecewiseFunction with several private implementation classes such as PiecewiseFunction_multi_polynomial, PiecewiseFunction_neural_network, ...

[mkoeppe]

comment:4

Yes, I agree that this should be a ModuleElement.
Now to which module (vector space) should it belong?

[NicoleYueqiLi]

comment:6

Replying to @mkoeppe:

Yes, I agree that this should be a ModuleElement.
Now to which module (vector space) should it belong?

This code didn't use any properties from ModuleElement. I'm wondering if you know any sample codes or if there is any way would be helpful for me to learn how to adapt the ModuleElement into the current code. Thank you so much for any suggestions!

[mkoeppe]

comment:7

Take a look at CombinatorialFreeModule (defined in sage.combinat.free_module) and the element class IndexedFreeModuleElement (defined in sage.modules.with_basis.indexed_element)

[NicoleYueqiLi]

comment:8

Replying to @mkoeppe:

Take a look at CombinatorialFreeModule (defined in sage.combinat.free_module) and the element class IndexedFreeModuleElement (defined in sage.modules.with_basis.indexed_element)

Thank you so much!

[NicoleYueqiLi]

Dependencies: #11225

[kcrisman]

It's not clear in what sense this ticket depends on #11225 so I recommend removing that.