Google Summer of Code 2008

Sage did not get selected as a mentoring organization.

Sage: Open Source Mathematical Software

Important Dates

Check http://code.google.com/soc/2008/faqs.html#0.1_timeline for important dates.

GSoC Sage Projects

All #numbers below refer to trac tickets.

Cython

Cython is both a Python compiler and a very nice way to write extensions to Python. It can be viewed as the successor to Pyrex. Our goal is to get Cython into Python and along the way to vastly improve the functionality, speed, and ease of use of Cython. Some specific goals for GSoC projects include:

Notebook

The Sage notebook is an AJAX application similar to Google Documents that provides functionality for all mathematical software somewhat like Mathematica notebooks. It was written from scratch (in Javascript and Python) by the Sage development team, and has been used daily by thousands of people over the last year. It's one of the main killer features of Sage. This project is about improving the notebook. No special mathematical knowledge is required. Knowledge of Javascript, jQuery, Python, and general AJAX techniques is needed.

Graph Automorphism Computation; Improve Permutation Groups

This project is to improve the world's *only* open source implementation of a general graph automorphism computation algorithm, and improve Sage's ability to compute with permutations and permutation groups.

Drawing Graphs on Surfaces with Genus greater than 0 - (Student: Emily Kirkman)

Extend the recent improvements of planar graph drawing in Sage to draw graphs of larger minimal genus. This requires an exploration of available algorithms, time improvements of the graph genus code (possibly through Mohar's algorithm for embedding graphs in a fixed surface), and combining ideas gained from several embedding algorithms. Brainstorming sessions at Sage Days 7 set a goal of drawing a graph around a platonic solid, which would be an opportunity for the student to work with the developers improving Sage's 3-D interactive graphics.

Calculus Improvements - (Student: Gary Furnish)

Currently support of symbolics is slow at best and uses maxima through a pexpect interface for almost all calculations. Furthermore it does not support integrals over differential forms or other higher dimensional integrals. There is a possible new symbolics framework that has been designed. Built in Cython and using native c libraries, it is significantly faster then anything built in python. General speed improvements for this would still be useful, especially in adding special algorithms for larger and special cases of symbolic arithmetic. It would also be a good idea to implement a very simple integration algorithm for at least polynomials to improve speed so that it is not necessary to call maxima for simple cases. Based on the material discussed at Sage Days 8, Numpy arrays would be an ideal base to work over to build support for tensors with basis (as opposed to abstract tensors) because they natively support multidimensional operations. The new symbolic framework supports defining operations other then the regular scalar ones, so it is possible to define operations (such as index contraction, wedge product, etc) over abstract tensors. This would be useful for physicists in general relativity and would help Sage become more useful in applied mathematics. Using Numpy would also require better integration with Cython and changes to the Cython code generator to ensure that tensor multiplication is fast enough to be useful for scientific computation. Although not the primary goal, these Cython would benefit a significant number of other developers because most applications of Numpy are speed dependent.

Projects include:

Combinatorial Species / Decomposable Objects (student: Mike Hansen)

Many combinatorial objects can be systematically built up from other ones. For example, a rooted trees consist of a root attached to a (possibly empty) set of of rooted trees. Combinatorial species provide a category-theoretical framework for generating and counting these types of objects which is amenable to a computer implementation. In the species framework, rooted trees can be recursively defined through the equation A = X \cdot E(A) where A is the species of rooted trees, X is the singleton species, and E is the species of sets. From this equation, one can "automatically" obtain the generating function for the number of labeled and unlabeled rooted trees as well as a procedure for generating the actual trees. This type of functionality can be found in the Aldor-combinat project as well as to an extent the MuPAD-Combinat project. The goal of this project would be to provide an implementation of combinatorial species within Sage.

Commutative Algebra (Mentor: Martin Albrecht)

Commutative algebra is an area of mathematics that is very important to cryptography, number theory, and algebraic geometry. Sage has extensive support for computations in commutative algebra, but substantial additional work remains. For this project, one should likely have at least a first year graduate school background in mathematics.

Free abelian groups and integer lattices

Integer lattices (free abelian groups endowed with a bilinear, integer-valued form) are important objects in geometry and combinatorics. The best available mathematical software for lattice computations is the (expensive and proprietary) program Magma. However, Magma can only compute with lattices that have a positive definite bilinear form. Many of the most interesting geometric applications involve negative definite or indefinite forms; furthermore, many uniqueness and classification results apply only to indefinite lattices. The first step toward expanding Sage's integer lattice capability is to expand Sage's capability for working with free abelian groups; this would have even wider and more fundamental applications.

Distributed Computing with dsage

DSage is a simple but powerful framework in included with Sage for doing distributed parallel task farming in Sage. It is meant to be ridiculously easy for end users to use and get up to speed with, by avoiding complexity. But it is also quite robust and secure. DSage has been under development for over a year, and is used regularly by several people. This project involves greatly increasing the *quality* of DSage. Projects include:

Algorithmic Number Theory Examples in Sage and Software for Web Publishing (Mentor: Dan Shumow)

This project is to write examples of number theoretic algorithms in SAGE, and evaluate and/or develop software to publish these examples on the web. The first part of the project is to learn about some number theory algorithms and write instructive examples in SAGE. The purpose of this is to showcase how SAGE can be an excellent tool for students to learn number theory algorithms. The second part of this project is to publish these examples in an extensible way. This will allow users to add their own SAGE examples and discuss examples. Specifically, the student should evaluate using open source web based source version control software in conjunction with open source message board software to allow internet users to discuss and modify SAGE examples.

Potential Mentors

GSoC/2008 (last edited 2012-03-17 19:40:27 by schilly)