CompMath

Centre for Computation in Mathematics @ IISER Pune

Since the revolution in computational power, a lot of mathematical packages have developed where one can work with (abstract) objects in pure Mathematics. Here we are interested in the subjects of group theory, number theory and statistics. The softwares which we are interested in are SAGE, GAP, R and MAGMA. There are two aspects of these:

• Develop algorithms to supplement these packages

• Learn these packages to ease and improve one's ongoing research.

We aim to run a series of workshops/lectures towards this and educate the researchers around on how to use these softwares. The idea behind these workshops will be to show how these softwares can facilitate day-to-day research and teaching.

The schedule for the first workshop is as follows:

Workshop on SAGE - 26-27 January 2018

Speaker: Dr. K. R. Shamasundar, IISER Mohali

Organiser: Dr Anupam Singh, IISER Pune anupam@iiserpune.ac.in

Dr Anindya Goswami, IISER Pune

Schedule and time-table:

The workshop is divided into 4 lectures with duration one to one-and-half hours each. The contents of each lecture are as follows:

The participants will be provided with the lecture notes at the end of each lecture in the form of a Sage Notebook worksheet. They are

encouraged to try out the programs and attempt some of the excercises suggested within each worksheet. If possible, some additional

time and resources will be made available to facilitate a better grasp of how Sage objects are being used in a particular context. If any of the

participants are interested in understanding how to use features not covered in this workshop (groups, number theory, geometry), we will try to

help them follow any available online Sage related resources on that subject.

This is not an introduction to Python programming. The participants are not required to have prior exposure to Python language. A prior basic

programming experience with algorithm implementation is a pre-requirement.

Venue: Bhaskara Lab, Mathematics department at IISER Pune

Audience: Researchers, PhD, iPhD and UG students of IISER Pune List of Participants

Abstract: The workshop aims to provide an introduction to the SageMath (http://www.sagemath.org), a free open-source mathematics software system. This system brings together, on a single and simple-to-use platform, a number of well-respected mathematical open-source softwares with capabilities covering basic algebra, calculus, number theory, statistics, numerical computing, symbolic manipulation, group theory, combinatorics, exact linear algebra and many more. This system allows an easier access to their combined power through a common, python-based language programs or directly accessing them via well-documented interfaces or wrappers. SageMath is a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

The workshop introduces some of the basic and advanced features of SageMath through a set of 4-5 lectures and tutorials. It mainly aims to create interest, awareness and curiosity amongst workshop participants on how easily its advanced features can also be accessed. The first two lectures cover basic elements of Python programming and

how to use SageMath for a few basic scientific computing problems. The remaining lectures discuss a few simple mathematical problems and algorithms involving numbers and matrices and go on to demonstrate how advanced mathematical features making use of polynomials, rings, finite fields can be introduced into such context.

Some prior experience with algorithm development and programming is assumed; the Python language features are covered on the first day. A few exercises are provided to the participants to immediately try out the lecture materials in follow-up hands-on practical sessions. Advanced mathematics is not necessary to understand most of the lectures.