D5.13: Parallelise the Singular sparse polynomial multiplication algorithms and provide parallel versions of the Singular sparse polynomial division and GCD algorithms.

[minrk]

• WP5: High Performance Mathematical Computing
• Lead Institution: University of Kaiserslautern
• Due: 2019-08-31 (month 48)
• Nature: Demonstrator
• Task: T5.4 (T5.4: Singular #102)
• Proposal: p. 51
• Final report (sources)

Singular is a computer algebra system aimed at computations in algebraic geometry and is one of the key components used by SageMath. Computing with multivariate polynomials being at the core of Singular, their performance impacts the whole system.

The aim of this deliverable was to modernize Singular's sparse multivariate arithmetic by 1) updating the algorithms to the state of the art and by 2) applying thread level parallelism to achieve decent scaling on multi-core machines. The operations we focused on are multiplication, divisibility testing, and the computation of the greatest common divisor. The implementation was carried out in the C library Flint, which is used by Singular but also by independent systems. The latter thus also benefit from the improvements. Among many other applications, this tackles the long standing slowness of multivariate rational fractions in SageMath.

[IzabelaFaguet]

Hello everyone!
We are organising an ODK report writing sprint From August 24th to August 31st,
a good opportunity to finish the final reports in a pleasant and friendly environment.
Would someone like to participate?

The link to the poll: https://framadate.org/tfuHjZgcSU8pHI45

[wbhart]

Hi all, time for an update on progress. Daniel Schultz has been working extremely hard on this ticket and we now have all the parallel algorithms in Flint that we promised and performance seems to be very good.

The next step is to make this available for users, which we plan to do via Singular. Some of the functionality will be made available directly from Singular, e.g. multiplication, division and gcd. But to maximise impact to Singular users, we also need to use the new code to speed up Factory, which Singular uses internally for various operations, such as factorisation, rational functions and primary decomposition.

We expect the biggest improvements to rational functions, though we are hopeful we will be able to notice some improvement to factorisation too (it would be a very major project to rewrite all the factorisation code to benefit fully from the sdmp format we use, and this lies beyond the scope of the ODK project).

We believe that the approach we are taking will benefit the greatest number of Singular users and downstream beneficiaries. However, it is not at all trivial work to make use of our code in Factory, so we won't know if that aspect is completely successful until we implement it for at least one coefficient ring. We are going to start with Z/pZ, though the new code in Flint will happily handle Z, Q, GF(q) (with and without Conway polynomials) just fine as well.

[nthiery]

For the record: Daniel told me that he had a version of the report for review, just not yet in ODK's repo. He will be in Cernay from tomorrow to Wednesday, and I'll make a first pass of review.