GSoC 2014
Sage Project Proposals
OpenSourcing SageMathCloud’s Notebook
Summation and integration routines using hypergeometric and Meijer G function representations
Pattern matching based symbolic integration
Numeric class wrappers in Pynac
Advanced Symbolic Expression Manipulation
Semidefinite Programming and sums of squares of real multivariate polynomials
Point Counting on curves over finite fields (Sage/FLINT/Pari)
This is related to elliptic curves:
Better point counting code on curves over finite fields.
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 Git 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. To get a better feeling of Sage’s features, please check out the documentation, especially the thematic tutorials.
Student’s proposal template at the bottom.
Project Proposals
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 cloud.sagemath.com, 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  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:
Code: https://github.com/sagemath/sagenb In particular, check out the branch “newui” 
Mentor  Jason Grout backup: Dan Drake 
Difficulty  Easy 
Skills 

Description  Sage’s 3d plots are dynamic: the user can zoom in and out and rotate the image. By contrast, 2d plots are static: the user can see a picture, but cannot zoom in on features of interest, zoom out to obtain a more global perspective, trace along the curve, or pan the view. The goal of this project is to add features like this to 2d plots, at least in the notebook view, making the notebook more suitable for educational purposes. Make sure to check out libraries like mpld3. 
Mentor  John Perry 
Difficulty  Intermediate 
Skills 

Description  The Sage Cell Server is basically a text box, where you can enter code and it is sent to a server for evaluation. This box can be embedded in any HTML website and for example, is in use for many online textbooks. Besides basic calculations, it is able to present plots in 2D and 3D and also add html widgets for small interactive applications. The goal of this project would be to extend the existing functionality, add better modes for plotting 2D or 3D, and/or work on serverside aspects. 
Mentor  Jason Grout 
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 
Code: https://github.com/sagemath/sagenb In particular, check out the branch “newui” 
Mentor  Jason Grout, Dan Drake discussion here: sagegsoc 
Difficulty  Easy to Intermediate, project could consist of one bigger project or several small and independent subprojects. 
Skills 

Description  The “SageMathCloud” is a successor of the traditional webbased Sage Notebook. It’s an online webservice, redesigned from the ground up for scalability, reliability and faulttolerance. On top of that infrastructure, it allows to collaboratively edit (mathematical) documents like the notebook and other textbased files. It uses the “Differential Synchronization” algorithm by Neil Fraser  the same used e.g. for Google’s Drive Documents. The goal of this project is opensourcing the relevant parts for the notebook interface, and to reimplement necessary parts of the underlying infrastructure to make them work. 
Mentor  William Stein 
Difficulty  Intermediate 
Skills 

Description  Currently, Sage has several different user interfaces. There is a webbased notebook interface, various online services and the commandline. What’s missing is a native GUI. This mode of interaction with Sage has it’s own benefits, drawbacks and challenges. So far, basic ingredients like an asynchronous remote procedure call service over plain TCP have been created. We have a MVC framework for the notebook with a Python Gtk3 interface an a proofofconcept HTML/Websocket interface. The goal of this project would be to make it viable and useful. Work out a plan for implementing features and assess which features are missing and how important they are. Code: 
Mentor  Volker Braun 
Difficulty  Intermediate, and no hard mathematics involved :) 
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.
Description  The current android app for Sage is here: https://play.google.com/store/apps/details?id=org.sagemath.droid It allows to run code remotely on a dedicated server and guides and assists the user with a helpful interface. Check it out, look at the list of open issues (bugs, stack trackes, new ideas) and make sure to also learn what “interacts” are. Besides just fixing bugs, there are many ways this application can be extended, improved and enhanced. 
Mentor  Volker Braun backup: Harald Schilly 
Difficulty  Easy, and no hard mathematics involved :) 
Skills 

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

Mentor  Ivan Andrus 
Difficulty  Easy, and no hard mathematics involved :) 
Skills 

Right now Sage is installed on Windows machines as a VirtualBox virtual machine. This approach has some problems that makes some users desist in their intent to use Sage. We would need a simple GUI that deals with this issues. Namely, it should check the VirtualBox installation in the system, check the availability of connection ports, and handle the installed virtual machine status. In particular, it should run rhe virtual machine in headless mode if it is possible to connect from the local web browser.
See the discussion at https://groups.google.com/group/sagedevel/browse_thread/thread/a4808f2cf5b8b79f/03db2e576b21f42e?q=virtualbox&lnk=nl& about it.
Description  Write a GUI program to handle the VirtualBox VM. It should do something like the following:

Mentor  Miguel Marco, Volker Braun 
Difficulty  Medium 
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 backup: Dan Drake 
Difficulty  Hard 
Skills 

Description  We propose improving the summation and integration algorithms in Sage by introducing lookup tables and the usage of hypergeometric and Meijer G forms. The commercial computer algebra systems [1] as well as open source alternatives like Sympy [2] are also employing this technique. Because of the complexity of the formulas involved in the Meijer G case, we suggest starting with hypergeometric function representations. However, both cases share the same steps as can be seen from the two ISSAC papers [3, 4] describing the algorithms. After setting up lookup tables which contain instances of hypergeometric and Meijer G functions with known values in terms of special functions, a suitable chain of consecutive transformations will convert a generic representation to the instances found in the tables. These transformations can be forward and backward shift operators, contiguity relations or, in the Meijer G case, various integration theorems. During the last part of the project, with these mechanisms set in place, we can focus on rewriting classes of sums and integrals in terms of hypergeometric and Meijer G functions, respectively. While transforming sums into hypergeometric notation is straightforward (one has to check whether the ratio of consecutive terms is a rational function), for the integration case we will need to use for instance the convolution theorem as in the example [4]. [1] http://wwwm3.ma.tum.de/bornemann/Numerikstreifzug/Chapter9/MeijerG.pdf [2] http://docs.sympy.org/dev/modules/integrals/gfunctions.html [3] http://www.planetquantum.com/Papers/Issac96.pdf [4] http://www.cybertester.com/data/issac97.pdf 
Mentor  Flavia Stan, Burcin Erocal 
Difficulty  Intermediate 
Skills 

Description  The goal of this project is to port Rubi (http://www.apmaths.uwo.ca/~arich/) to Sage. Rubi is a collection of Mathematica rewrite rules for symbolic integration. Having a Sage version of this would be a great boost to our (yet nonexistent) integration engine, as well as a good test of the pattern matching and substitution capabilities of our symbolics backend. Sage uses the C++ library Pynac (http://pynac.org) to represent symbolic expressions and perform basic arithmetic and manipulation with them. Pynac (which a fork of GiNaC (http://www.ginac.de)) supports rewrite rules (http://www.ginac.de/tutorial/Patternmatchingandadvancedsubstitutions.html), but probably not to the extent required by Rubi. Depending on the complexity of the rules in Rubi, improvements to the pattern matching capabilities in Pynac might be necessary. 
Mentor  Burcin Erocal, Flavia Stan, ?? 
Difficulty  Intermediate / Hard 
Skills 

Description  This would be a continuation of Titus Nicolae’s GSoC 2012 project. The goal is to speed up the symbolic expression library used in Sage by avoiding unnecessary creation of Python objects. Pynac (http://pynac.org) is the C++ library that is used as the backend for symbolic expressions in Sage. In Pynac, numeric types are wrappers around Python objects. This allows using arbitrary Sage types in symbolic expressions at the cost of considerable overhead for creating Python objects around simple numerical types (arbitrary precision real numbers backed by MPFR, integers backed by MPIR, etc.). In 2012, Titus restructured the numeric class in Pynac (https://bitbucket.org/pynac/pynac/src/b7fe62bfb3a682773a7157d965deea2b85e3719c/ginac/numeric.h) to allow implementing wrappers for various numeric types in subclasses. However, he ran out of time before he could provide useful wrappers that could speed up Pynac. The task, if you chose to accept it, is to write wrappers in Pynac for

Mentor  Burcin Erocal, ?? 
Difficulty  Hard 
Skills 

Description  When working with symbolic expressions, manipulating them in a flexible way is essential. The goal of this project is to extend Sage's functionality of handling substitutions and patterns. This includes the following enhancements:

Mentor  Daniel Krenn 
Difficulty  Intermediate 
Skills 

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. In this, it overlaps with the next topic, concerning semidefinite programming solvers and interfaces for them. Specific examples of functionality which need wrapping would include GLPK’s (and other LP solvers, whenever available) abilities to warmstart the simplex algorithm. One problemspecific solver that might be added is the Skeleton implementation of the doubledescription method, though this may require some restructuring to turn into a library (though perhaps not, as much of the functionality is isolated into one filed, ddm.hpp). 
Mentor  Dmitrii Pasechnik (for some parts), John Perry (other parts) 
Difficulty  Intermediate 
Skills 

Description  Improving the integration of semidefinite programming (and, potentially, other convex conic programming, e.g. 2nd order cone programming) solvers in Sage, creating an interface similar to what we already have for linear programming, hooking up more backends (currently, only cvxopt is integrated into Sage), with an aim to have a M*free environment for polynomial sums of squares modelling, such as done e.g. by MATLABbased YALMIP (http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Main.WhatIsYALMIP). Potentially, it is a large project, as one can go quite far with developing modeling tools, adding symmetry treatment, etc. 
Mentor  Dima Pasechnik, Mehdi Ghasemi 
Difficulty  Intermediate to hard 
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 

Description  This is related to elliptic curves:Better point counting code on curves over finite fields. 
Mentor  JeanPierre Flori 
Difficulty  Hard 
Skills 

Description  Currently Sage cannot use the latest revision (aka spielwiese) of Singular due to significant changes in it (see Singular 3 vs Singular 4 and Spielwiese Singular  cutting Singular into pieces). It will be necessary to change the Singular package building inside of Sage (which is almost trivial due to Singular build system improvement) and adapt the current Cython code to the newest Singular API (wherever it relies on Singular). As an improvement one may also write Sage Fields or Rings wrappers around Singular coefficient domains, which were newly introduced as a separate structure in the new Singular. 
Mentor  Burcin Erocal, Oleksandr Motsak 
Difficulty  Intermediate to easy 
Skills 

Description  Matroids are combinatorial abstractions of a number of mathematical objects, including graphs and matrices. This project aims to improve and extend Sage’s support for matroids. Some examples, where the first needs very little matroid theory knowledge, the second group a little more, and the third group a lot.

Mentor  Stefan van Zwam comentor: Rudi Pendavingh 
Difficulty  Easy to medium (programming), easy to hard (mathematics) 
Skills 

Description  Knots and Links are mathematical objects that represent how one or several ropes are tied in the space. Currently sage has no support for them. Some goals of this project would be:
The javascript editor could be a project on its own. So a student could propose either to work on the backend or the editor (or two students could work on both lines of work). 
Mentor  Miguel Marco, Volker Braun 
Difficulty  Easy to medium. 
Skills 

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 
Mentors  
William Stein  SageMathCloud only  wstein+gsoc@gmail.com 
Dan Drake  general projects  drake@kaist.edu 
Burcin Erocal  Symbolics, lowlevel Cython  burcin@erocal.org 
Jason Grout  Notebook, Backend  jasonsage@creativetrax.com 
Martin Albrecht  lowlevel Cython, crypto stuff, linear algebra  martinralbrecht@googlemail.com 
Volker Braun  Android, Python, lowlevel Cython  vbraun.name@gmail.com 
Ivan Andrus  iOS/iPhone App  darthandrus@gmail.com 
Alexander Dreyer  PolyBoRi  alexander.dreyer@itwm.fraunhofer.de 
Raymond Toy  Maxima  toy.raymond@gmail.com 
Dmitrii Pasechnik  Optimization, semidefinite programming  dimpase@gmail.com 
Julien Puydt  Debian  julien.puydt@laposte.net 
John Palmieri  Debian  palmieri@math.washington.edu 
John Perry  Linear programming, commutative algebra, general  john.perry@usm.edu 
Miguel Marco  Algebra, Topology, PyQt,  mmarco@unizar.es 
Stefan van Zwam  Matroid theory  
Rudi Pendavingh  Matroid theory  rudi@win.tue.nl 
Flavia Stan  Symbolics  flavia.stan@gmail.com 
Oleksandr Motsak  Singular  motsak@mathematik.unikl.de 