Basic To Poly

Overview

All of my week was mostly consumed by asking questions like “Should this throw?” and “What are it’s generators?”. My work for this week was to make a mechanism for converting arbitrary expression into polynomials. Turns out, it isn’t as trivial as it initially sounded. I will discuss my progress below. This week has been a lot more of logic involved, and thinking about how to go ahead instead of just development, so I do not have a lot to write about.

The Idea

A multivariate polynomial is made of generators. A univariate polynomial is made of a single generator. Each term in a polynomial is a monomial which is multiplication of it’s generators to a non-negative power, which also has a non-zero coefficient multiplied to it. Here are some polynomials and their generators :

x**2 + x**5          		->      x

sqrt(3) + sqrt(3)**3        ->		sqrt(3)

(1/x**2) + (1/x**5) 		-> 		(1/x)

x**2 + y**2 + x				-> 		x, y

2**x + 1					-> 		2**x

I hope you get the idea. The main task is given a Basic, we need to construct a polynomial with appropriate generator. The task is broken down into two parts. First off, we try and extract a generator from the given expression. Secondly, use the found (or user given) generator to construct the polynomial.

Ideally the API should look as follows:

RCP<Basic> UIntPoly::from_basic(Basic x);
RCP<Basic> UIntPoly::from_basic(Basic x, Basic gen);

My Progress

I have only worked on the univariate polynomial class as of now, and was to write the from_basic method just for the univariate classes for now. Although I just had to deal with the specific case of univariate integer polynomials, I haven’t successfully been able to get the job done just yet.

The work started with converting Symbol var to Basic var. Initially, the generators of the polynomial class could only be symbols, however this needed to be changed, as we’ve seen generators can be anything! This change did not take a lot of effort.

I started off with a find_gen function which given a Basic will try and find a unique generator for the polynomial to be constructed. Ideally, if no generator/ more than one generator is found it will throw a runtime error. I covered most of the cases but a few still remain.

Also, an initial implementation of the to_poly functionality has been done, complete with the required API. Some cases related to conversion still need to be handled. I do not want to go into the logic involved into each conversion as it is tedious and not very structured. All the work done till now can be seen in #998.

I hope with all the information I have gained over this week, I will wind up the Basic to UPoly conversions for both the integer coefficients as well as the general expression coefficients by the end of next week. I also intend to make the logic more concrete, so that the same API can be used in the multivariate case.

Miscellaneous Work

• I made some changes in the expand function related to polynomials. They mostly have to deal with removal of code, which has already been implemented. It is also a partial fix for #886, work is in #999.

Tata!