GSoC 2012
Sage Project Proposals
Sage Notebook on Google App Engine and Amazon EC2 (etc.)
3D Graphics via three.js JavaScript library and WebGL
Singular/Dynamic modules for Singular
Singular/Thread safe memory allocator for Groebner basis computation
Singular/Fast noncommutative multiplication and related data structures
PolyBoRi/Binary decision diagrams for Boolean polynomial rings
NTL/Univariate polynomials and factorization library
Sage is a GPLed opensource mathematical software system. It is designed to be not just a computer algebra system, but more like a complete environment for doing mathematics and related calculations. It is based on a vast collection of existing opensource software tools and libraries and ties them together via Python. This is also the primary interface language for the user and its objectoriented way of expressing concepts is used to express calculations  of course, there are also many “normal” functions :) Behind the scenes, the Sage library executes the commands and calculations by its own algorithms or by accessing appropriate routines from the included software packages. On top of that, there are various ways how users can interact with Sage, most notably a dynamic website called “Notebook”.
All projects will start with an introduction phase to learn about Sage’s internal organization and to get used to its established development process. This is documented in the documentation for developers and all students will be instructed by the mentors on how to get their hands dirty. We use Mercurial for revision control and trac for organizing development and code review. Our license is GPLv2+. Feel free to contact Mentors before you send us project proposals, contact details are at the bottom. Feel free to introduce yourself and your project idea in our mailing list.
Student’s proposal template at the bottom.
This list of possible projects is organized into categories, starting with the webbased notebook interface.
The Sage Notebook is the primary graphical interface for Sage. It consists of a Pythonbased server backend evaluating the computations and a rich interactive Ajaxbased website. It has a user management, each user has a list of worksheets and each worksheet consists of cells that are evaluated on the server and the output is sent back to the website. The following batch of notebook specific proposals outline projects for improving the notebook on different levels.
The core team behind the notebook consists of several people who very welcome new contributors. You can access a Sage Notebook at www.sagenb.org or demo.sagenb.org, which has proven to be a very successful way of enabling average users to access an advanced mathematics suite online. Their dedicated mailing list is here.
Description  This is one strategy for making http://sagenb.org scale to millions of users. Currently http://sagenb.org gets hammered (there are 84168 users and it is running on a single computer in the basement of the math building!). Rewriting the notebook for GAE+EC2 may make Sage available to a much wider range of people. This is a top priority project for me (William Stein) for AprilJuly, with some personal NSF funding (for my salary), but I could use help! 
Mentor  William Stein Backup: Jason Grout 
Difficulty  Intermediate 
Skills 

Description  Currently, Sage by default uses JMOL (http://jmol.sourceforge.net/) to display 3d graphics. This is a weak link for Sage, because Jmol is a very complicated Java applet, so on many platforms it crashes web browsers, won't run at all, is unstable, etc. For example, Jmol doesn't work at all on iPhones and iPads, and probably never will. Moreover, selecting objects and manipulating them is very hard, as is evidenced by nobody ever having succeeded in doing so for Sage, despite much demand. The future of 3d for the web is WebGL, which has some support by modern browsers and hardware. The three.js is a Javascript library that allows one to describe a 3d scene and interact with it purely from Javascript. Moreover, the scene can be rendered in any browser that supports HTML5's canvas2d, which is essentially all modern browsers, though it will render more quickly when WebGL is available. The goal of this project is to do a complete reimplementation of 3d rendering for Sage using three.js, which fully replicates all functionality that Jmol offered, so that three.js can instead be the default. 
Mentor  William Stein Backup: Jason Grout 
Difficulty  Intermediate 
Skills 

Description  In the Sage Notebook, each user opens a worksheet to interact with Sage for doing mathematics. A worksheet is a list of alternating input/output cells. To actually do computations, one has to know about the commands and basic Python in order to do any calculations. Currently, a new user has to read the tutorial to get started, which needs time and is a barrier for new users. The aim of this project is to make it easier for novice users to actually use the notebook and help them entering common calculations. This could be done via several independent enhancements:

Mentor  Jason Grout backup: Dan Drake, William Stein 
Difficulty  Easy 
Skills 

Description  Currently, the ways to include data from other sources than the notebook itself is limited to the capabilities of Python (e.g. reading a CSV file via Python’s CSV module) The goal of this project is to make it easier to import and edit data in the form of simple spreadsheets and databases from within worksheets in the notebook.

Mentor  Jason Grout backup: Mike Hansen, William Stein 
Difficulty  Intermediate 
Skills 

Apart from the ones above, other project ideas are also welcome. Here is a selected list of ideas for your inspiration. Contact the possible mentors for more details.:
Description 

Mentor  Jason Grout, Tomas Boothby, Mike Hansen, Dan Drake, William Stein 
Difficulty  Easy to Intermediate, project could consist of one bigger project or several small and independent subprojects. 
Skills 

Working with Sage is not restricted to a local machine. The webinterface can be made public to other computers over the Intranet/Internet. One very successful example is http://demo.sagenb.org  this is the site behind the Google Chrome Web app for the Sage Notebook. After a bit more than a month of availability in the Chrome Web Store it had more than 2,000 users. Another example is the main Notebook site with more than 40,000 registered users. Sage not only wants to be a comprehensive software suite for mathematics but also wants to be easily accessible.
Consequently, we have to improve the inner parts of Sage to be able to scale for a much broader audience and satisfy online Notebook users from High School and University students doing their homework up to employees of engineering companies sharing their calculations with coworkers. These proposed enhancement projects could have a truly global impact and will certainly drive Sage’s further growth.
Description  Webserver, session management and Notebook storage. This project addresses the needs for a better scaling Notebook server. There are several layers to consider, each of them could be a project:
Those are just some of the cornerstones that need to be done to make the Sage Notebook more scalable. Interested applicants are expected to contact Jason Grout, who is currently organizing a larger project dedicated solely to this task. There has already been good progress on this project. Links: Notebook design 
Mentor  Jason Grout, William Stein backup: Dan Drake 
Difficulty  Hard 
Skills 

Description  Easy Server Deployment. Setting up a Sage Notebook server “right” is complicated. Although it is easy to start one instance for personal use, it is getting more complicated if it is set up for a classroom setting or as a worldwide server. This involves questions about security, sandboxing and scalability. In conjunction with other improvements, this project aims to make it easy to deploy a server for various applications. This includes the following tasks:

Mentor  Dan Drake backup: Jason Grout, William Stein 
Difficulty  Intermediate 
Skills 

Description  GAP (http://www.gapsystem.org/) is a free open source system for computational discrete algebra, with extensive support for computational group theory. It has its own command line interpreter interface. It would be extremely valuable if GAP also had a C library interface. Volker Braun and William Stein have written a proof of concept C library interface to GAP, but it is not ready for production use, since it does not behave well when certain errors occur, is based on an old version of GAP, etc. The goal of this project would be to create a high quality complete C library interface to GAP, based on the existing work done in this direction. This would drastically speed up certain parts of Sage that currently communicate with GAP via a pseudotty interace. The C library interface would also be contributed back to the GAP project, making GAP (independent of Sage) easier to embed in C programs, which would make it much more generally useful than it currently is. (Martin Albrecht did something similar to this for Singular, and contributed it back; it is one of the most important improvements to Singular in years.) 
Mentor  William Stein Backup: Volker Braun, Martin Albrecht 
Difficulty  Intermediate 
Skills 

Description  A unique feature of Sage is that it is able to communicate with essentially every other math software system out there, and some of that communication is fairly sophisticated, optimized, and debugged. However, the interfaces between Sage and the most popular commercial mathematics software systems  Mathematica, Maple, and Matlab  could all benefit from substantial additional work. They are buggy on certain platforms, don't deal well in some cases with large outputs, don't draw plots well, etc. Currently, the interfaces are all pseudotty based, but it may be possible in some cases to create alternative interfaces (with exactly the same API) that use proprietary socketbased protocols, e.g., MathLink (http://www.wolfram.com/solutions/mathlink/) for Mathematica. Now that the API of the Sage interfaces is very stable (after 7 years!), the goal of this project is to investigate and implement the best possible ways of implementing this API for each commercial math software system. 
Mentor  William Stein Backup: Mike Hansen 
Difficulty  Easy 
Skills  Very good knowledge of Python. 
Description  When people type "sage" to start Sage, it often takes a long time for Sage to startup. This is incredibly annoying. The main reason for this is that Python uses the stat system call to get basic information about files well over 50,000 times every single time Sage starts. This information is expensive to compute, and almost never changes. Thus it should be cached. Volker Braun has written a proof of concept patch that does such caching, but work remains. The goal of this project would be to finish that patch and get it included in Sage. Moreover, the project should go further and look at how to make that caching approach generic so it could be used by other projects outside Sage. This could have the potential impact of making "Python + scientific library" startup time better for millions of people. Make it so Python cache's module import locations on startup, thus greatly improving startup time for large Python modules. 
Mentor  William Stein Backup: Volker Braun 
Difficulty  Intermediate 
Skills  Very good knowledge of Python and C 
Description  The term "numeral systems" mean representing numbers (e.g. integers) by digits and a base. Standard numeral systems such as binary and decimal are well known, but there are lots of others. There is no framework available which allows to work with numeral systems. Implementing this is the first goal. Sage uses a standard doubleandadd algorithm to build multiples of a point of an elliptic curve. There are numeral systems (including windowing techniques), which can be used for fast scalarmultiplication on elliptic curves. Goal number two is to use the different numeral systems to speed up the mentioned scalarmultiplication. 
Mentor  Daniel Krenn 
Difficulty  Intermediate 
Skills 

Description  Goal is to implement a lattice class, that can be populated with lattice algorithms available. Those include algorithms for
Lattices arise in many different areas of mathematics, so it would be good to have the existing algorithms together in one place and a framework to implement new algorithms. 
Mentor  Daniel Krenn 
Difficulty  Intermediate 
Skills 

Piecewise functions are essential in approximation theory, numerical analysis, and throughout the classroom. Within a computer algebra system, they are invaluable for translating written mathematics in an understandable way to one’s domainspecific language.
Description  A full list of ideas (a work in progress) is available at the PiecewiseSymbolic SEP (Sage Enhancement Proposal)

Mentor  KarlDieter Crisman 
Difficulty  Intermediate 
Skills 

Part of a sophisticated mathematical software system is a way to represent symbolic expressions and fast methods to manipulate them.
Description  Pynac/GiNaC is designed for symbolic computations. This project is about enhancing and optimizing this crucial and important part of Sage. Pynac replaces the numeric coefficients in GiNaC with python objects. The implementation should be extended to use machine longs and doubles as well as the GMP and MPFR libraries for multi precision integers, rationals and floating point numbers. This would provide a significant speed boost since using these types directly instead of the Python wrappers available in Sage is more efficient. The stubs to use other types as numeric objects are available in the code. The task involves writing the required interfaces to machine types, GMP and MPFR, as well as profiling typical operations to see where the bottlenecks are. 
Mentor  Burcin Erocal backup: William Stein 
Difficulty  Intermediate 
Skills 

Description  Sage exposes mathematical functions to the user by wrapping lowerlevel libraries and algorithms. They occur in symbolic expressions and can be evaluated for given arguments. Some of them are not efficient, some of them could be improved and even some are not even exposed at all.

Mentor  Burcin Erocal backup: Martin Albrecht 
Difficulty  Intermediate 
Skills 

Misc maths related project ideas
Mentor: William Stein
Difficulty: Hard
Skills: Python, Cython; fairly advanced algebra.
Numerical Mathematics
Description  Sage has general purpose classes to express and solve linear and mixedlinear optimization problems. The first aim of this project is to enhance the features of those classes and add more convenience for the user. Additionally, new classes for quadratic and continuous nonlinear optimization should be created. On the backend side, those classes interface with various specific solvers. This requires code to wrap their functionality or the necessary linking to certain libraries (e.g. which already provide Pythonbindings to solvers, and may have been already present in Sage, such as cvxopt). The second part of this project aims to add more cluecode for additional solvers. 
Mentor   backup: Martin Albrecht 
Difficulty  Intermediate 
Skills 

Description  CryptoMiniSat is a SATsolver whose efficiency is witnessed by the fact that it won the SAT Race 2010. This project is about integrating CryptoMiniSat into Sage as an optional package by writing a C++/Cython wrapper. As a second step the project will use this interface to use CryptoMiniSat as a solver for various problem domains covered by Sage, such as polynomial system solving (cf. for example http://www.math.umd.edu/~bardg/bard_thesis.pdf and http://bitbucket.org/malb/algebraic_attacks/src/anf2cnf.py), the sage.sage.logic module and any other application the applicant and perhaps the Sage community can come up with. 
Mentor  Martin Albrecht backup: Burcin Erocal 
Difficulty  Intermediate 
Skills 

M1RI
Description  M1RI, that's the code Tom wrote for dense linear algebra over GF(3), GF(5) andGF(7), i.e., small finite prime fields. This implementation is a collection of Sage worksheets at the moment, i.e. a proof of concept. From that we already know that this approach is very fast. Turning this into a proper library would be a hug benefit to the community. It requires C skills but most of the linear algebra business has been solved before, so the mathematics required is not that much. 
Mentor  Martin Albrecht backup: Burcin Erocal 
Difficulty  Intermediate 
Skills 

The traditional way of running Sage is via a “full” personal computer workstation. There are other form factors and devices from where Sage should be accessible, most notably tablets and smartphones. This involves running Sage on a remote server and designing a new user interface for interacting with it.
http://code.google.com/p/sageandroid/
Description  http://code.google.com/p/sageandroid/ No hard mathematics involved :) 
Mentor  Volker Braun backup: Harald Schilly 
Difficulty  Easy 
Skills 

Description  https://bitbucket.org/gvol/sageiphoneapp/

Mentor  Ivan Andrus 
Difficulty  Easy 
Skills 

Create a tool to check if there are any speed regressions between Sage releases.
Description  Sage uses the standard Python doctest framework to check for correctness. With more than 85% and increasing coverage these tests uncover many potential issues in new contributions. However, there is no equivalent mechanism to check if changes introduced to the Sage library cause speed regressions. There are standard solutions such as Codespeed to store timing information and display comparisons between different versions. This task involves:

Mentor  Burcin Erocal backup: William Stein 
Difficulty  Intermediate 
Skills 

This project is not directly related to Sage, but Maxima is an important component!
Description  Currently Maxima is exclusively meant for Symbolic computation with support lacking good Numerical facilities. The existing BLAS/LAPACK modules are based upon f2cled code in Common lisp, and hence performance is not portable (SBCL is probably 10x faster than CLisp). The goal of this project would be enhance Maxima's numerical capabilities by integrating parts of the Foreignfunctioninterface in Matlisp. One would then be able to interface with the compiled versions of BLAS/LAPACK, ODEPACK and also just about any other C/Fortran libraries. This would enhance Maxima's ability to do Numerical computation, and will open up new avenues like, implementing AutomaticDifferentiation, to be pursued later. 
Mentor  Raymond Toy 
Difficulty  Hard 
Skills 

This project is not directly related to Sage, but Singular is an important component!
The Singular computer algebra system allows users to extend it two ways (without recompiling Singular):
Most recent feature additions to the Singular kernel and Singular interpreter are essentially extensions needed by very few projects. Dynamic Modules were developed in order to prevent these from bloating the core. Unfortunately the Singular approach to dynamic loading does not work under MSWindows due to its limitations concerning DLL linking/loading. It is possible to solve this problem as described on edll.sourceforge.net.
The task is to evaluate the proposed approaches and implement a dynamic loading mechanism which would work on Windows as well as on Unix'es.
skills/prerequisites: C/C++, experience with development under Windows, understanding of libraries and dynamic loading
mentors: Oleksandr Motsak, Hans Schoenemann
contact: libsingulardevel@googlegroups.com, sagegsoc discussion group
This project is not directly related to Sage, but Singular is an important component!
The Singular computer algebra system uses a specialized memory allocation library named omalloc to boost its performance. This library contains optimized code to allocate/deallocate blocks of memory with a predefined size (monomials) and discards pages containing these blocks at once, without the need to deallocate each separately. Unfortunately, omalloc is not thread safe and thread safe malloc libraries such as TCMalloc cannot match its performance. See this presentation for some more info.
The task here is to either add functionality to an existing memory allocation library to support this special use case or to improve omalloc so that it is thread safe.
skills/prerequisites: real good understanding of C/C++, memory allocation, debugging
mentors: Christian Eder, Hans Schoenemann
contact: libsingulardevel@googlegroups.com, sagegsoc discussion group
This project is not directly related to Sage, but Singular is an important component!
The Singular computer algebra system contains a subsystem named Plural which implements a class of noncommutative algebras, which appear often in various applied problems. Its basic (and principal) feature is the noncommutative multiplication. Unfortunately it is not always fast enough. The existing implementation can be improved in many ways, including for instance:
The Plural internals are partially described by V. Levandovskyy and O. Motsak.
The task here is to evaluate existing multiplication implementations and either to implement DFFT or to improve existing designs (possibly by redesigning them).
skills/prerequisites: C/C++ (only basic Math. knowledge)
mentors: Oleksandr Motsak, Hans Schoenemann
contact: libsingulardevel@googlegroups.com, sagegsoc discussion group
This project is not directly related to Sage, but PolyBoRi is an important component!
PolyBoRi uses (zerosuppressed) binary decision diagrams (ZDDs) to store Boolean polynomial data. Up to now it uses CUDD which is is not especially tuned for this application area.
The task is to construct a pure C++ class for the diagrams as well as a class for a decision diagram manager. The latter should handle pool allocation of diagram nodes and operation caching.
skills/prerequisites: C and C++, basic understanding of binary decision diagrams
mentors: Alexander Dreyer, Burcin Erocal
contact: polyboridiscuss@lists.sourceforge.net, sagegsoc discussion group
This project is not directly related to Sage, but NTL is an important component!
With its speed and wide ranging functionality, the Number Theory Library (NTL) written by Victor Shoup served as the standard for univariate polynomial algorithms for a long time, similar to the way GNU Multiprecision Library (GMP) defines the standard for integer and rational arithmetic now. NTL has not been maintained since 2009. In the meantime, FLINT surpassed its speed and set a new standard in this area. However, FLINT only provides a C interface and does not support all the functionality provided by NTL such as polynomials over where .
Many mathematical software packages rely on NTL for univariate polynomials and factorization. With its speed and C focus, FLINT is unlikely to support all functionality of NTL any time soon. This project proposes to build a module in FLINT and implement the missing functionality from NTL.
The algorithms implemented in NTL can be found in these papers. (Understanding these is not a requirement for the student, that's what the mentor is for. ):
skills/prerequisites: C/C++, basic understanding of univariate polynomial factorization algorithms (as described in Modern Computer Algebra )
mentors: Martin Lee, Fredrik Johansson
contact: libsingulardevel@googlegroups.com, sagegsoc discussion group
We recommend you to join our sagegsoc mailing list and introduce yourself and ask to help you for your submission.
We suggest you to introduce yourself and discuss your project idea in our mailing list. Only contact the possible mentors below if you have really specific questions!
Name  Topics  
Harald Schilly (Oversight)  general questions  harald+gsoc@schil.ly 
William Stein  Notebook, Backend 

Mentors  
Dan Drake  general projects  drake@kaist.edu 
Burcin Erocal  Symbolics, lowlevel Cython  burcin@erocal.org 
Jason Grout  Notebook, Backend  jasonsage@creativetrax.com 
KarlDieter Crisman  kcrisman@gmail.com  
Martin Albrecht  lowlevel Cython, crypto stuff, linear algebra  martinralbrecht@googlemail.com 
Thomas Boothby  Notebook, Backend  tomas.boothby@gmail.com 
Mike Hansen  Notebook, general projects  mhansen@gmail.com 
Volker Braun  Android, Python, lowlevel Cython  vbraun.name@gmail.com 
Daniel Krenn  Numeral Systems, Lattices  krenn@aon.at 
Volker Ziegler  Lattices  ziegler@math.tugraz.at 
Manfred Madritsch  Numeral Systems  madritsch@math.tugraz.at 
Daniel Smertnig  Lattices  daniel.smertnig@unigraz.at 
Ivan Andrus  iOS/iPhone App  darthandrus@gmail.com 
Oleksandr Motsak  Singular  
Christian Eder  Singular  
Hans Schoenemann  Singular  
Alexander Dreyer  PolyBoRi  alexander.dreyer@itwm.fraunhofer.de 
Raymond Toy  Maxima  toy.raymond@gmail.com 
Martin Lee  NTL  
Fredrik Johansson  NTL  fredrik.johansson@gmail.com 