Tuesday, 23 June 2015

Week 4

Hope you have been taking good care of yourself! As mentioned in the previous post, the first thing I did last week was to resolve the bug in the function implementing step one of the pipeline, listream_coefs. So, now all the functions related to factorization via the Newton method work as expected. Hence, I added documentation for them.
I also wrote an initial version of the factor_riccati and the factor_op functions along with their helpers: substitute, ramification_of and iram_of. The factor_riccati function requires us to find the zero of a polynomial that is irreducible in F, the domain of coefficients. Two approaches for this task were mentioned on the mailing list - one was to use the domain SimpleAlgebraicExtension, but this approach had a problem with return values. Thus, I went with the second approach which is also used by the integrator viz. use Expression R (usually Integer) as the base domain.
This week, I plan to modify the factor_* routines according to the comments received and implement the coprime index > 1 algorithm. This will be followed by the global factorization methods. For further updates, stay tuned!

Wednesday, 17 June 2015

Week 3

This week I fixed a small problem in the lifting code regarding how I was initializing the start_D variable. Also, it was mentioned on the mailing list that the lifting step should be done in a lazy way (i.e. on demand). So, I changed the lift_newton function to an incremental version and added routines to proceed according to the following pipeline mentioned by Waldek:

stream of [l_extra, r_extra] --> list of streams of coefficients
  --> list of Laurent series --> operator

The last two steps of the pipeline were quite easy to implement. The main work involved was in the first step. There is still an issue remaining for step 1 regarding how to handle zero series and I'm working on resolving that at the moment. The next task for me is to add documentation for all the undocumented functions relating to factorization via the Newton method. This week, I look forward to really starting to write code for the Riccati solution based functions. Take care.

Tuesday, 9 June 2015

Week 2

In the second week, I implemented the lift_newton function that is used to lift coprime index 1 factorizations. plug_delta, coeffx, coefs_operator and coefs_poly were the helper functions used in the process. coefs_operator takes a polynomial and returns an operator with the given valuation, while coefs_poly takes an operator and returns a polynomial after extracting its relevant part. plug_delta simply converts a polynomial to a differential operator by substituting δ = xD in place of x. coeffx(f, e) returns the coefficient of x^e in f while simultaneously substituting x in the place of δ. The initial version of lift_newton that I implemented was buggy, but thanks to the review on the mailing list, I was able to correct it. The plan now is to tie up any loose ends in the functions finished so far which all deal with factorization using the Newton method. If there are no more problems with them, then I'll go on to implement the functions related to factorization using a Riccati solution : factor_riccati and ramification_of. That's all from me. Good-bye, until next time.

Tuesday, 2 June 2015

GSoC 2015 - Week 1

My proposal "Factorization of LODOs in FriCAS - the van Hoeij algorithm" has been accepted for Google Summer of Code 2015. So, I'll again be working under lmonade this summer (and I'm glad to be working under the same umbrella organization). My mentors for this project are Waldek Hebisch and Ralf Hemmecke. The official coding period began last week (May 25) and so I have started to code. The source code can be found here.

I've finished the implementation of the newtonpolygon function that returns the extreme points of the Newton polygon, the associated slopes and Newton polynomials of an operator.
Further, I also implemented the factor_newton function that performs coprime index 1 factorizations for which the op_with_slope function was a helper. However, the lifting step of the algorithm is still to be done and that is what I'm working on at present. So, the plan for this week is to finish the algorithm for coprime index 1 factorizations by implementing lift_newton and coefs_operator. I was a little stuck about how to actually implement the lifting algorithm, but Waldek clarified my doubts to a large extent on the fricas-devel mailing list. I'm still not completely confident but am able to work on the functions, so I guess I'll finish the implementation first and then modify it according to the comments received. Okay, that's it for now. See you next week!