GSoC Ideas - sympy/sympy GitHub Wiki

Introduction

This is the list of ideas for students wishing to apply for Google Summer of Code. For more information on how to apply, see the GSoC Student Instructions. This list is here for inspiration and to give students an idea of what directions may be good for SymPy.

If you want to pursue an idea listed here, you should contact us on our mailing list and discuss it. Be sure to always ask about these ideas to get the latest information about what is implemented and what exactly has to be done.

The list is organized as follows:

High Priority Projects
Projects that are considered important in our roadmap.
Mathematics Projects
Well developed ideas of interest for us, however they do not block the release of the next major version of SymPy. These require deep understanding of the mathematics in question.
Physics Projects
Well developed ideas of interest for us, however they do not block the release of the next major version of SymPy. A number of well developed modules dealing with classical and modern physics are being developed as part of SymPy.
Computer Science, Graphics, and Infrastructure Projects
These ideas enhance the core capabilities of SymPy.
SymEngine Projects
These ideas support the C++ based project SymEngine. SymEngine provides core symbolic capabilities at very fast speeds. It will eventually provide an optional core for SymPy to improve its computation speeds.
Idea Prompts
List in a "brainstorming" style that has many nice project ideas. Each of the above projects were born in this list. Read it carefully as the most interesting projects may come from there.

The order of ideas in this list has no bearing to the chances of an idea to be accepted. All of them are equally good and your chances depend on the quality of your application. Also do not worry if there are no mentors assigned to a given idea. If the application is good, we will find a mentor. As already said, you can very well submit your own idea not listed here.

Project length

GSoC allows three different project lengths, 90 hours, 175, hours and 350 hours. The ideas below specify which project length is the best fit.

In some cases, it may be possible to extend a smaller project into a larger one by extending the ideas of what can be done in the project. Similarly, in some cases a larger project can be shortened by only implementing part of the full idea and leaving the rest for a future project. In either case, if you want to do this, please discuss it with us first.

Submitting Your Own Idea

You can apply with something completely different if you like. The best project for you is one you are interested in, and are knowledgeable about. That way, you will be the most successful in your project and have the most fun doing it, while we will be the most confident in your commitment and your ability to complete it.

If you do want to suggest your own idea, please discuss it with us first, so we can determine if it is already been implemented, if it is enough work to constitute a summer's worth of coding, if it is not too much work, and if it is within the scope of our project.

Please use the below Idea Template to Mention Ideas:

Title

Idea

(Specify your idea with proper explanation)

Status

(What is the Status of this Idea in the Sympy Community currently, previous work done and Issues)

Involved Software

(Any other Software Involved that would be required to implement your idea)

Difficulty

(Advanced, Intermediate, or Beginner and any specific comments on the difficulty)

Prerequisite Knowledge

(Any prerequisite knowledge or approach needed)

Project Length

Whether this project is appropriate for a 175 hours or 350 hours GSoC project, or both.

Potential Mentors

If you are willing to mentor, please add yourself here. Also please register at https://summerofcode.withgoogle.com and add your email that you registered with. Finally, list your name with any projects below that you would be willing to mentor.

Table of Contents

High Priority

Polynomial GCD

Idea

Add new algorithms for computing the greatest common divisor (GCD) of polynomials in the sparse representation. This would improve the speed of many parts of sympy such as matrices, solvers, integration and so on.

The issues and potential solutions along with many references are discussed in this issue: https://github.com/sympy/sympy/issues/23131

Status

There is plenty of work that can be done in this area so this is effectively an open-ended area for improvement in sympy.

Involved Software

Difficulty

Medium to high difficulty

Prerequisite Knowledge

Python, some understanding of abstract algebra and of algorithms.

Project Length

175 or 350 hours, depending on the scope of the project.

Benchmarks and performance

Idea

Speed is important for SymPy. One issue is that it's difficult to tell what is too slow, and, more importantly, if a given change makes things faster or slower.

SymPy needs more benchmarks. It also needs an automated system to run them. That way, when someone adds some code that slows things down in an unexpected way, we will know about it.

There are already some benchmarks at https://github.com/sympy/sympy_benchmarks, and some others in the main SymPy repo. But not all benchmarks are in the sympy_benchmarks repo. Also, the repo uses asv, but the results are run and hosted ad hoc, as we don't have a dedicated machine to run the benchmarks.

This project should do the following:

  • Move benchmarks from the sympy repo to the sympy_benchmarks repo.
  • Add new benchmarks as needed.
  • Work with the community to set up a dedicated machine that can constantly run asv to warn about benchmarks. It would also be nice if this could be set up to warn for performance regressions on PRs.
  • Make improvements to SymPy to improve performance issues found throughout the project.
  • Improve the usability of the current GitHub Actions bot that adds benchmarks outputs to pull requests.

Some prior art:

Status

We currently have a benchmarking suite and run the benchmarks on GitHub Actions, but this is limited and is often buggy.

Involved Software

Difficulty

Medium to low difficulty

Prerequisite Knowledge

Python

Project Length

175 hours or 350 hours, depending on the scope of the project.

Assumptions

Idea

The project is to completely remove our old assumptions system, replacing it with the new one. The difference between the two systems is outlined in the first two sections of this blog post.

This project is challenging. It requires deep understanding of the core of SymPy, basic logical inference, excellent code organization, and attention to performance. It is also very important and of high value to the SymPy community.

Numerous related tasks are mentioned in the "Ideas" section.

Status

There has been a significant amount of merged and unmerged work on this topic. A list of detailed issues can be found at this issue. You should take a look at the work started at https://github.com/sympy/sympy/pull/2508.

This mailing list post by Aaron Meurer outlines the status of the project and some ideas of what to do. It is from 2015 but most of what is written there is still true. The main thing that is new is that the new assumptions call the old assumptions (ask(Q.real(Symbol('x', real=True)))). See also the prior GSoC projects on assumptions, including this one, which was accepted, but there may be parts of it that were not completed, and https://github.com/sympy/sympy/wiki/GSoC-2013-Application-Tom-Bachmann:-Removing-the-old-assumptions-module, which was not accepted (the student chose to do another project), but contains some good ideas.

Involved Software

None

Difficulty

Advanced

Prerequisite Knowledge

Number theory, Boolean algebra, etc.

Project Length

350 hours

Speed: Improve SymEngine - SymPy Integration

SymPy can be slow. SymEngine provides a very fast implementation of core symbolic algorithms, and SymPy should use it to gain speed.

See here for more details:

https://github.com/sympy/sympy/wiki/GSoC-Ideas#improve-sympy-integration

Potential mentor - Co-mentor: Shekhar (@Shekharrajak)

Mathematics Projects

Solvers

Idea

SymPy already has a pretty powerful solve function. But it has a lot of major issues

  1. It doesn't have a consistent output for various types of solutions It needs to return a lot of types of solutions consistently:

    • single solution : x == 1
    • Multiple solutions: x**2 == 1
    • No Solution: x**2 + 1 == 0; x is real
    • Interval of solution: floor(x) == 0
    • Infinitely many solutions: sin(x) == 0
    • Multivariate functions with point solutions x**2 + y**2 == 0
    • Multivariate functions with non point solution x**2 + y**2 == 1
    • System of equations x + y == 1 and x - y == 0
    • Relational x > 0
    • And the most important case "We don't Know"

  2. The input API is also a mess, there are a lot of parameter. Many of them are not needed and they makes it hard for the user and the developers to work on solvers.

  3. There are cases like finding the maxima and minima of function using critical points where it is important to know if it has returned all the solutions. solve does not guarantee this.

Salient Features of solveset

  • solveset has a cleaner input and output interface: solveset returns a set object and a set object take care of all the types of the output. For cases where it doesn't "know" all the solutions a NotImplementedError is raised. For input only takes the equation and the variables for which the equations has to be solved.

  • solveset can return infinitely many solutions. For example solving for sin(x) = 0 returns {2⋅n⋅π | n ∊ ℤ} ∪ {2⋅n⋅π + π | n ∊ ℤ} Whereas solve only returns [0, π]

  • There is a clear code level and interface level separation between solvers for equations in complex domain and equations in real domain. For example solving exp(x) = 1 when x is complex returns the set of all solutions that is {2⋅n⋅ⅈ⋅π | n ∊ ℤ} . Whereas if x is a real symbol then only {0} is returned.

  • solveset returns a solution only when it can guarantee that it is returning all the solutions.

Status

GSoC 2014 Project: Harsh Gupta

During the summer of 2014 Harsh Gupta worked to improve solvers as part of his GSoC project. Instead of making changes in the current solve function a new submodule named solveset was written.

GSoC 2015 Project: Amit Kumar

In the summer of 2015 Amit Kumar worked on this project to improve solveset, implement complex sets as a part of his GSoC project.

GSoC 2016 Project: Kshitij SaraogiKshitij Saraogi | GSoC 2016 Project: Shekhar Rajak

In the summer of 2016, two projects were selected to participate in Google Summer of Code to work on the Solvers. New solver helper functions such as solve_decomposition and nonlinsolve were implemented to facilitate the porting from solve to solveset. Also, the inequality solver solve_univariate_inequality was refactored and added to solveset. Several methods related to functional analysis, such as periodicty, continuous_domain and function_range were implemented.

GSoC 2018 Project: Yathartha Joshi

In the summer of 2018, Yathartha worked on the project to implement transcendental equation solver for solveset. transolve alongwith its helper solvers was implemented as a result of it.

TODOs

  • Extending transolve: As part of the work done in the summer of 2018, transolve is fully designed and is now able to handle logarithmic and exponential equations for solveset. To make solveset fully fledged and replace solve completely we expect it to handle equations like:

    • Lambert type equations (PR #14972)
    • Handling modular equations (#13178)
    • Solving transcendental equations in complex domain.

    There may be other types of equations that transolve can be made to handle. It's still under development!! Feel free to propose any of your ideas.

  • Integrating helper solvers with solveset: Currently, solveset only solves a single equation for a single variable. In the future, we expect it to be capable of solving a system of equations and for more than one variable. linsolve: Solves a system of linear equations nonlinsolve: Solves a system of non-linear equations solve_decomposition: Solves a varied class of equations using the concept of Rewriting and Decomposition These are the helper functions that have been implemented in solveset during the past few years. We would like to have all these solvers(including transolve) to be integrating in solveset so as to increase its power.

  • Build the set infrastructure: This includes implementing functions to handle multidimensional ImageSet etc., This part must go hand in hand with the improvements in the solvers as set module can be a universe in itself. Also there can be fundamental limits on the things you can do.

  • nonlinsolve is not able to handle system having trigonometric/transcendental equations correctly all the time. Improve solveset's trigonometric solver and handle trig system of equations separately in nonlinsolve.

References There had been a lot of discussion during and before the project and you should know why we did what we did. Here are some links:

Involved Software

SymPy

Difficulty

This project is difficult because it requires a good deal of thought in the application period. You should have a clear plan of most of what you plan to do in your application: waiting until the Summer to do the designing will not work.

#10006 and #8711 can be good entry points.

Prerequisite Knowledge

Algebraic and differential equations

Potential mentor - Co-mentor: Shekhar (@Shekharrajak)

Project Length

350 hours.

Optimize floating point expressions

Idea

Optimize floating point expressions (à la https://herbie.uwplse.org/). The user will supply a SymPy expression and an optional range of "x" (and other variables) and the module would determine which symbolic simplifications make sense to make things more accurate and/or faster.

Part of this project would also be to provide faster implementations of special functions, say if it is determined that "x" in sin(x) is in the range [0, 1e-3], then there are much faster polynomial approximations that give the same accuracy (the same is possible for other finite ranges, e.g., [1.5, 1.7]).

One mode is to concentrate on accuracy (possibly with larger/slower expression). Another mode is to concentrate on speed, and this mode can have a user prescribed accuracy, say 1e-16 for machine precision, or 1e-3 for lower accuracy. For lower accuracies one can replace functions like sin(x) with a much faster polynomial approximation.

Difficulty

Intermediate, Advanced

Project Length

350 hours, although you may propose a 175 hour project with a more limited scope.

Group theory

Idea

Continue developing the group theory functionality of the combinatorics module. You should take a look at the GAP library, as this is the canonical group theory computation system right now.

Algorithms to think about implementing:

  • Computation of various subgroups of infinite finitely presented groups
  • Computation of Galois groups for a given polynomial
  • Finding kernels of homomorphisms with infinite domains
  • Extend functionalities of polycyclic groups
  • Quotient groups
  • Automorphism groups

Status

Previous projects on the topic include:

A good amount of work has been done on polycyclic groups, polycyclic presentation with the base class collector were introduced in 2019 GSoC project but still there are a lot of things to be added for e.g. polycyclic orbit stabilizer and canonical polycyclic sequence to check if two polycylic subgroups are equal or not could be implemented. In addition, few other algorithms like abelian invariants and composition series implemented in 2019 GSoC project can be extended for infinite groups.

Some major algorithms for finitely presented groups include coset enumeration (there's been work on modified Todd-Coxeter in the 2018 GSoC project: see this PR), low index subgroup search and Reidemeister-Schreier algorithm for subgroup presentation. Rewriting systems together with the Knuth-Bendix completion algorithm are available but could be made more efficient.

Additionally, the 2017 project implemented group homomorphisms and the 2018 project implemented the computation of the isomorphism between 2 groups, an automaton for word reduction and a few additional algorithms. Find the complete work done during 2018 in the project report in the link below.

See the 2016, 2017 and 2019 reports for suggestions on where the work could continue.

Quite a lot of work has been done on permutation groups, but still, some things remain (some of those mentioned in GSoC 2012 Report by Aleksandar Makelov are still relevant, e.g. subgroup intersection). Some work is already done on discrete groups. Nonetheless, there is still much that can be done both for discrete groups and for Lie groups.

Difficulty: Medium/Difficult

Resources: Handbook of Computational Group Theory by Derek F. Holt, Bettina Eick and Eamonn A. O'Brien

Prerequisite Knowledge: Basic knowledge of Abstract Algebra

Potential mentor - Co-mentor: Divyanshu Thakur (@divyanshu132)

Project Length

350 hours.

Risch algorithm for symbolic integration

Idea

The Risch algorithm is a complete algorithm to integrate any elementary function. Given an elementary function, it will either produce an antiderivative, or prove that none exists. The algorithm described in Bronstein's book deals with transcendental functions (functions that do not have algebraic functions, so log(x) is transcendental, but sqrt(x) and sqrt(log(x)) are not).

Status

The project is to continue where Aaron Meurer left off in his 2010 GSoC project, implementing the algorithm from Manuel Bronstein's book, Symbolic Integration I: Transcendental Functions. If you want to do this project, be sure to ask on the mailing list or our IRC channel to get the status of the current project.

The algorithm has already been partially implemented, but there is plenty of work remaining to do. Contact Aaron Meurer for more information. There was also work done in 2013, which hasn't been completely merged yet. A good place to start would be to look at finishing this work: https://github.com/sympy/sympy/pulls/cheatiiit. See https://groups.google.com/forum/#!msg/sympy/bYHtVOmKEFs/UZoyDX81eP4J for some more details on this project (nothing has changed since that email thread).

Involved Software

Difficulty

Prerequisite Knowledge

You should have at least a semester's worth of knowledge in abstract algebra. Knowing more, especially about differential algebra, will be beneficial, as you will be starting from the middle of a project. Take a look at the first chapter of Bronstein's book (you should be able to read it for free via Google Books) and see how much of that you already know. If you are unsure, discuss this with Aaron Meurer (asmeurer).

Project Length

350 hours.

Other ODE ideas

You also might want to look at Manuel Bronstein's sumit.

Status

Involved Software

Difficulty

Medium

Prerequisite Knowledge

Differential equations

Project Length

175 hours or 350 hours, depending on the project details (discuss with us).

Improving Series Expansions & Limit Computations

Idea

This includes numerous smaller subprojects and is more of a bug burn down project than implementing things from scratch. Hence we should aim at solving as many bugs and possible issues having the label series or limits on them. There are around 146 open issues with the series label & around 26 open issues with the limits label with some overlap and the proposal should have a comprehensive list of ideas to fix a significant portion of these issues.

Status

There is already a fast implementation called rs_series in SymPy. This project would extend it to work for all functions and then make it the default series expansion in SymPy.

SymPy now has support for Formal Power Series (series.formal). The algorithm is more or less complete. The module should be made faster. There are also a lot of XFAIL tests that can be made to pass.

A new algorithm for computing limits of sequences has also been added (series.limitseq). There are still XFAIL tests that can be made to pass.

Some references

  1. "Formal Power Series" by Dominik Gruntz and Wolfram Koepf
  2. "A New Algorithm Computing for Asymptotic Series" by Dominik Gruntz
  3. "Computing limits of Sequences" by Manuel Kauers
  4. "Symbolic Asymptotics: Functions of Two Variables, Implicit Functions" by Bruno Savly and John Shackell
  5. "Symbolic Asymptotics: Multiseries of Inverse Functions" by Bruno Savly and John Shackell

Involved Software

SymPy

Difficulty

Medium

Prerequisite Knowledge

Calculus

Project Length

175 hours or 350 hours, depending on the project details (discuss with us).

Cylindrical algebraic decomposition

Idea

  • Implement the Cylindrical algebraic decomposition algorithm

  • Use CAD to do quantifier elimination

  • Provide an interface for solving systems of polynomial inequalities

  • Some references:

Status

Involved Software

Difficulty

Prerequisite Knowledge

Project Length

350 hours

Efficient Groebner bases and their applications

Idea

Groebner bases computation is one of the most important tools in computer algebra, which can be used for computing multivariate polynomial LCM and GCD, solving systems of polynomial equations, symbolic integration, simplification of rational expressions, etc. Currently there is an efficient version of Buchberger algorithm implemented and of the F5B algorithm, along with naive multivariate polynomial arithmetic in monomial form. There is also the FGLM algorithm converting reduced Groebner bases of zero-dimensional ideals from one ordering to another.

Improve efficiency of Groebner basis algorithm by using better selection strategy (e.g. sugar method) and implement Faugere F4 algorithm and analyze which approach is better in what contexts. Implement the generic Groebner walk converting between Groebner basis of finite-dimensional ideals; there are efficient algorithms for it, by Tran (2000) and Fukuda et al. (2005).

Apply Groebner bases in integration of rational and transcendental functions and simplification of rational expressions modulo a polynomial ideal (e.g. trigonometric functions).

Status

There was a project last year relating to Groebner bases. Please take a look a the source and discuss things with us to see what remains to be done.

Some Groebner bases algorithms, in particular F4, require strong linear algebra. Thus, if you want to do that, you may have to first improve our matrices (see the ideas relating to this above).

Involved Software

Difficulty

Prerequisite Knowledge

Project Length

350 hours

Multivariate polynomials and factorization

Idea

Factorization of multivariate polynomials is an important tool in algebra systems, very useful by its own, also used in symbolic integration algorithms, simplification of expressions, partial fractions, etc. Currently multivariate factorization algorithm is based on Kronecker's method, which is impractical for real life problems. Undergo there is implementation of Wang's algorithm, the most widely used method for the task.

Start with implementing efficient multivariate polynomial arithmetic and GCD algorithm. You do this by improving existing code, which is based on recursive dense representation or implement new methods based on your research in the field. There are many interesting methods, like Yan's geobuckets or heap based algorithms (Monagan & Pearce). Having this, implement efficient GCD algorithm over integers, which is not a heuristic, e.g. Zippel's SPMOD, Musser's EZ-GCD, Wang's EEZ-GCD. Help with implementing Wang's EEZ factorization algorithm or implement your favorite method, e.g. Gao's partial differential equations approach. You can go further and extend all this to polynomials with coefficients in algebraic domains or implement efficient multivariate factorization over finite fields.

Status

Some work on this may already be done. Take a look at sympy/polys/factortools.py in the SymPy source code.

Involved Software

Difficulty

Advanced

Prerequisite Knowledge

Project Length

350 hours

Univariate polynomials over algebraic domains

Idea

Choose a univariate polynomial representation in which elements of algebraic domains will be efficiently encoded. By algebraic domains we mean algebraic numbers and algebraic function fields. Having a good representation, implement efficient arithmetic and GCD algorithm. You should refer to work due to Monagan, Pearce, van Hoeij et. al. Having this, implement your favorite algorithm for factorization over discussed domains. This will require algorithms for computing minimal polynomials (this can be done by using LLL or Groebner bases). You can also go ahead and do all this in multivariate case.

Status

Currently SymPy features efficient univariate polynomial arithmetic, GCD and factorization over modular rings and integers (rationals). This is, however, insufficient in solving real life problems, and has limited use for symbolic integration and simplification algorithms. For example, the support for finite fields GF(p^n) is missing.

Involved Software

Difficulty

Advanced

Prerequisite Knowledge

Project Length

350 hours

Concrete module: Implement Karr algorithm, a decision procedure for symbolic summation

Idea

Algorithm due to Karr is the most powerful tool in the field of symbolic summation, which you will implement in SymPy. There are strong similarities between this method and Risch algorithm for the integration problem. You will start with implementing the indefinite case and later can extend it to support definite summation (see work due to Schneider and Kauers). Possibly you will also need to work on solving difference equations.

  • Some references:
    • "A=B" by Marko Petkovsek, Herbert S. Wilf, Doron Zeilberger
    • "Symbolic Summation with Radical Expressions" by Manuel Kauers and Carsten Schneider
    • "An Implementation of Karr's Summation Algorithm in Mathematica" by Carsten Schneider
    • Manuel Kauers, webpage: http://www.risc.jku.at/home/mkauers
    • Carsten Schneider, webpage: http://www.risc.jku.at/people/cschneid
    • "Algorithmen für mehrfache Summen", by Torsten Sprenger

Status

SymPy currently features Gosper algorithm and some heuristics for computing sums of expressions. Special preference is for summations of hypergeometric type. It would be very convenient to support more classes of expressions, like (generalized) harmonic numbers etc. There is already an complete algorithm rational expression summation.

Involved Software

Difficulty

Advanced

Prerequisite Knowledge

Project Length

350 hours

Physics Projects

Symbolic Control Systems (sympy.physics.control)

Idea

A Control Systems subpackage (sympy.physics.control) was added to SymPy in the summer of 2020, by Naman Gera. This was built upon further by Akshansh Bhatt in 2021 and Anurag Bhat in 2023. It would be great to continue its development and make it more accessible to the public. Since the users are mostly students and researchers in the field of Control theory, a set of problems from a textbook can be solved in the documentation, as the development proceeds.

https://www.cds.caltech.edu/~murray/amwiki/Second_Edition.html can be used as a reference.

Status

The functionalities of the project can be viewed here:

https://docs.sympy.org/latest/modules/physics/control/lti.html#module-sympy.physics.control.lti

Future Work (can be modified after discussion):

  • Refactor the old plots - All the plots that were implemented previously namely - Pole Zero, Step Response, Impulse Response, Ramp Response, Bode Magnitude and Bode Phase plot use numpy and matplotlib. The numerical methods were used for speed but they sacrifice on precision. Sympy's symbolic methods are used in the first place to the precision they provide, hence these numerical methods should be replaced by algebraic methods.
    Davide, a fellow contributor has been revamping the plotting module. I would like to point out this roadmap, according to which SymPy will soon have it's own plot_list function after which this refactoring could be done with ease.

  • Complete newly implemented plots - The plots added in this GSoC project namely - Root Locus, Nichols and Nyquist plot are draft pull requests. The have clear ideas to follow and some comments which can be addressed once SymPy no longer depends upon matplotlib and numpy.

  • Implementations for the StateSpace class -

    1. Solve examples mentioned in #25502 and add them to the control_problems file . The required functionality is already supported in the pull request.
    2. Add a symbolic solver (and a numeric solver if required) with the help of the ODE module to solve x' = Ax + Bu form.

    Make the class more feature rich:

    1. Read about Laub's or Horner's method to evaluate system transfer function at complex frequency. This will be the equivalent of eval_frequency for Transfer Functions.
    2. Add Feedback interconnection between 2 state space LTI systems.
    3. Other features can be picked up on comparison with MATLAB and python-control.

  • Adding a Discrete time model - A Discrete-time TransferFunction and Discrete-time StateSpace model. Discussing the API and making things compatible with the current implementation is a challenging task. It has already been a component of the MATLAB CST package from the beginning. As a control module, we have to realize that all signals in practical real life use are always discrete in nature. This is my motivation for wanting this model, so that users can have extensive use of SymPy’s CST package in their projects.

It is best to follow the final report and blog to know more about the status.

Involved Software

Python, Git

Difficulty

Intermediate

Prerequisite Knowledge

Undergraduate level Control Systems knowledge will suffice. Otherwise, one can complete the project if they self-learn required topics and then contribute voraciously.

Project Length

350 hours.

Symbolic quantum mechanics (sympy.physics.quantum)

In the past, Brian Granger was the maintainer of the sympy.physics.quantum subpackage. He has stepped down from this position. Until someone takes over the maintenance of this subpackage, we will not be able to mentor any GSoC projects in this area. If you have questions about this, please contact Ondřej Čertík.

Continuum Mechanics: Create a Rich 2D Beam Solving System

Idea

Singularity functions are a popular tool for solving beam bending stress and deflection problems in mechanical design. This is traditionally done by hand calculations and can be very tedious and error prone. This process could be improved greatly by a CAS implementation of the functions and some high level abstractions for constructing beam loading profiles.

The deliverable would be a unit tested and documented sub-package for SymPy 2D and 3D beams that can solve many beam problems, add in arbitrary cross sections, plotting, be robust, and add any other relevant features.

Status

Sampad Saha implemented Singularity Functions in 2016. The 2017 and 2018 GSoC projects created the functionality shown here:

https://docs.sympy.org/dev/modules/physics/continuum_mechanics/beam_problems.html

The next steps involve making it easier to define complex cross sectional geometry via the geometry package, developing the 3D Beam into a well tested and robust class, and polishing to the plotting for 2D and 3D beams. Adding a large set of example problems that exercise the functionally.

Involved Software

Python, Git

Difficulty

Intermediate

Prerequisite Knowledge

No specific prerequisite knowledge is necessary but it would help if the student had some knowledge of beam stress/strain analysis methods.

Project Length

350 hours.

Classical Mechanics

The following project ideas are in approximate order of priority.

Classical Mechanics: Generalize the Equations of Motion System Output

Idea

We would like an ecosystem in which you can define/create your mechanical system in a general way using joints, bodies, forces, torques, etc., compute the equations of motion based on different methods like LagrangesMethod and KanesMethod, to be used in numerical purposes, like simulations and optimizations.

The above is the general picture for which a lot of work has been done over the years on the different parts. However, some parts are disjoint while other parts are still missing or should almost be entirely replaced.

Note that defining/creating the mechanical system falls into two other projects, namely:

Status

Previous work covers quite a few different parts, which can be improved and extended, but mostly require to be tied together more properly:

  • An abstract base class as an interface to the different equations of motion generation methods has been introduced in #21778.
  • Refer to the project Classical Mechanics: Constructing Systems From Bodies and Joints for the status of bodies and joints.
  • Refer to the project Classical Mechanics: Implement Specific Forces and Torques for the status of implementing specific loads.
  • In #25560 a System class was introduced as a general frontend to define a mechanical system and generate the equations of motion using either of the implemented methods, i.e. LagrangesMethod and KanesMethod.
  • In #11431 as SymbolicSystem was introduced as a data class to store all information about a system and its equations of motion in a general format.
  • In PyDy there also exists a System class, which can be used to simulate a system that was solved using KanesMethod.

The goal of this project is to implement a class to function as a general interface of a system from which the equations of motion can be used for numerical purposes. This class would be an extension or replacement of sympy.physics.mechanics.system.SymbolicSystem. Some of the features it should offer are:

  • A general representation of the equations of motion and the algebraic constraints.
  • Methods to code generate the functions to be used in simulation purposes, like with scipy.integrate.odeint and scikits.odes.dae.
  • It should use sympy.physics.mechanics.system.System for the basic system information. It could possibly have multiple methods to be instantiated, like a normal __init__ where all equations and things need to be provided as is currently the case with SymbolicSystem, and a classmethod from_system, where it extracts most information from the System instance.

Involved Software

Python, Git

Difficulty

Advanced

Prerequisite Knowledge

This project requires basic understanding of dynamical systems and at least understanding of one method of generating the equations of motion for a multi-body system.

Project Length

350 hours.

Classical Mechanics: Implement and Benchmark Equations of Motion Methods

Idea

There are many methods to derive the equations of motion. Each method has its advantageous and disadvantageous when modeling different systems. SymPy currently contains only two methods: KanesMethod and LagrangesMethod. The idea of this project is to develop more methods to form the equations of motion and to benchmark them for different models to also give users more insight what model they should use for their application.

Status

  • An abstract base class as an interface to the different equations of motion generation methods has been introduced in #21778.

This project could roughly entail the following steps:

  • Improve the abstract base class, sympy.physics.mechanics.method._Methods of the equations of motion generation methods, e.g. KanesMethod.
  • Improve the implementation of KanesMethod and LagrangesMethod.
  • Implementing more methods to generate the equations of motion, like NetwonEulersMethod or HamiltonsMethod.
  • Develop a benchmark suite deriving the equations of motion using the different methods and measure their performance. Examples could include a 5-DoF planar kinematic chain, a four-bar linkage, and the Carvallo-Whipple bicycle model.

Involved Software

Python, Git

Difficulty

Intermediate

Prerequisite Knowledge

This project requires basic understanding of dynamical systems and at least understanding of one method of generating the equations of motion for a multi-body system.

Project Length

175 or 350 hours.

Classical Mechanics: Efficient Equations of Motion Generation

Idea

Currently we have basic equation of motion generation with automated Kane's and Lagrange's methods. These methods work well but can take many minutes to complete for hard problems. The algorithms that derive these equations of motion can be improved in both speed of computation and the resulting simplification of the equations of motion. This project would involve cleaning up the code base, profiling to find the slow functions, and digging into the SymPy codebase for trigonometric simplification and other relevant function calls to speed up the EoM generation. These modification will help speed up both the entire SymPy codebase and the Mechanics package.

Status

There is no previous work on this topic.

Involved Software

Python, Git

Difficulty

Beginner

Prerequisite Knowledge

There are no prequisites to this project.

Project Length

350 hours.

Classical Mechanics: Implement Specific Forces and Torques

Idea

Many forces and torques still have to be manually created by the user. It would be helpful if we had a set of typical and common forces and torques. Some possible examples:

  • Linear and nonlinear springs and dampers
  • Contact force models
  • Musculotendon models, like the Hill type muscle model
  • Actuator forces and torques
  • Aerodynamic forces

Some kind of force and torque objects will likely be needed as well as symbolic mathematical descriptions of the force and torque models. The forces and torques should work with SymPy's code generation to generate efficient and robust numerical codes.

Status

  • Timo Stienstra introduced a Force and Torque class, refer to #24258 and #24641.
  • Sam Brockie implemented an abstract base class to define actuators and implemented several types of actuators, like a LinearSpring and LinearDamper, refer to #25518.
  • Sam Brockie has done a lot of work on muscle forces and actuators, refer to #24240.

Some load types that could be worked on are:

  • Contact force models
  • Aerodynamic forces
  • Nonlinear springs and dampers
  • Models involving biomechanics, refer to #24240 for ideas.

Involved Software

Python, Git

Difficulty

Beginner to intermediate

Prerequisite Knowledge

This project requires basic understanding of dynamics and numerical methods.

Project Length

350 hours.

Classical Mechanics: Constructing Systems From Bodies and Joints

Idea

We'd like to be able to construct multibody systems by specifying descriptions of rigid bodies and the joints and constraints that connect them.

Status

The next steps are, in order of priority:

  • Fix any existing bugs with the joints.
  • Add many different example problems to test the robustness of the implementation.
  • Allow parsing constants as generalized coordinates to Joint, such as pi / 2 to the PinJoint, as if it is just a fixed pin.
  • Implement and test quaternion rotations.
  • Implement a Mobilizer joint or CustomJoint for describing complex motions, refer to (#23920 comment).
  • Implement an option to choose the generalized speeds efficiently, refer to #24053 comment.

Involved Software

Python, Git

Difficulty

Advanced

Prerequisite Knowledge

This project requires familiarity with multibody dynamics. At the least, one should know how to form the equations of motion of complex systems with one method.

Project Length

350 hours.

Classical Mechanics: Implement an O(N) Equations of Motion Method

Idea

Roy Featherstone, Abhi Jain, and others developed recursive methods of forming the right-hand side of the differential equations for complex multibody systems that have an evaluation time of O(N) instead of O(N^3). This project would be dedicated to implementing a symbolic O(N) method to complement the LagrangesMethod and KanesMethod classes. This project would involve implementing 6D vectors and spatial operators, as well as the recursive methods. This would give a significant speed boost in numerical evaluation for systems with bodies greater than 20 or so.

Status

Brandom Milam made significant headway in this project in 2016. See:

Involved Software

Python, Git

Difficulty

Extremely Advanced

Prerequisite Knowledge

This project requires proficiency with multibody dynamics. At the least, one should know how to form the equations of motion of complex systems with one method. The ideal candidate will have experience forming the equations of motion with the aforementioned Featherstone or Jain methods.

Project Length

350 hours.

Computer Science, Graphics, and Infrastructure Projects

Enhancing the flexibility of MatchPy

Idea

MatchPy, a Python library, provides associative-commutative pattern matching and replacement rules for expression trees. This functionality enhances the usability of computer algebra systems, simplifying the formulation of transformation rules for mathematical formulas.

In essence, MatchPy expressions can be likened to "regular expressions with an awareness of commutative and associative properties”. MatchPy also supports the simultaneous execution of multiple matches, contributing to its exceptional efficiency.

However, the current requirement for expression trees and wildcards to be subclasses of MatchPy objects presents a significant inflexibility. This constraint forces SymPy to delve into metaclass intricacies to function, limiting the ability to work with expression trees whose node type lacks identification by an object.

This proposal seeks to enhance MatchPy by restructuring its node type identification, the iteration criteria and wildcard definitions. This involves replacing type checks with custom node identification and iteration rules, fostering greater flexibility in working with various expression tree structures.

Since MatchPy is currently under a separate project and has experienced a period of inactivity, forking MatchPy becomes necessary for the progress of this project.

Additionally, if time allows it, this project also envisions exploring the possibility of a Rust implementation of MatchPy, aiming to enhance its speed and efficiency.

Status

An experimental connector to MatchPy has been successfully implemented and can be found in sympy.utilities.matchpy_connector. For a comprehensive understanding of the algorithm that drives MatchPy, refer to the paper authored by its creators, available at https://arxiv.org/abs/1710.06915. Furthermore, it's worth noting that MatchPyCpp, an integral submodule of SymEngine, features a translation of the main MatchPy algorithms into C++. However, its performance is presently constrained by the absence of support for coroutines.

Involved software

Python, MatchPy

Difficulty

Advanced.

This project very likely requires the MatchPy library to be forked.

This project necessitates proficiency in executing tree-visiting algorithms.

Project Length

350 hours.

Code Generation

Idea

There are quite a few potential projects for codegen.

The code generation system in SymPy has been overhauled to use AST nodes from sympy.codegen.ast, there are however lot of more nodes that can be added for e.g. Fortran in sympy.codegen.fnodes. It could also be useful if the code printers could output parallel code using OpenMP directives (e.g. parallel for loops for C and Fortran, including use of reduction). Most printers do not yet support the new AST nodes, it would be useful if those were extended so that they can express ASTs created e.g. by functions in sympy.codegen.algorithms.

Another idea for codegen is to add more support for directly working with matrices. For instance, matrix expressions (sympy.matrices.expressions objects) should print LAPACK calls.

Status

We have support for a number of backends and basic code gen classes in place. There is work on updating the system ongoing. Please ask on the mailing list.

You can check out the work done by Ankit Pandey to extend codegen to support matrix operations at Extending Codegen GSoC 2019

Involved Software

Fortran, C, C++, Julia, Rust, Python, LLVM, Javascript, Octave, Matlab, etc.

Difficulty

Intermediate to Advanced

Prerequisite Knowledge

Project Length

175 hours or 350 hours, depending on the project details (discuss with us).

Parsing

Idea

SymPy has the ability to generate Python, C, and Fortran code from SymPy expressions.

It would be very interesting to go the other way, to be able to parse Python, C, and Fortran code and produce SymPy expressions. This would allow SymPy to easily read in, alter, and write out computational code. This project would enable many other projects in the future. Ideally, this project would create a general framework for parsers and then use this system to implement parsers for a few of the languages listed above. See the other parsing ideas on this page, as well as Parsing.

Status

SymPy currently has a parsing module that supports parsing LaTeX and autolev using ANTLR, C, and Fortran. The parsing module also supports a Python parser, with special extensions to support things like implicit multiplication (2a -> 2*a) and implicit function application (sin x -> sin(x)), which uses the Python tokenize module.

You can check out the work done on the C and Fortran parsers at Creating a C and Fortran Parser GSoC 2019

The existing parsers could be improved by adding support for more features of the programming languages, or new parsers could be added for other languages like Julia, Octave, MATLAB, etc.

Involved Software

Fortran, C, C++, Julia, Rust, Python, LLVM, Octave, Matlab, etc.

Difficulty

Intermediate to Advanced

Prerequisite Knowledge

Project Length

175 hours or 350 hours, depending on the project details (discuss with us).

Improve the plotting module

Idea

A new plotting module sympy-plot-backends has been written, which is planned to replace the existing sympy.plot module (see https://github.com/sympy/sympy/issues/23036).

The idea is to merge this module into SymPy, also implementing substantial improvements and possibly new functionalities.

A very approximate guesstimate is given.

  • medium/hard: Refactoring of *Series classes in order to reduce code repetition and allow the implementation of new features.
  • easy/medium: Improve numerical evaluation.
  • medium/hard: implement custom theming for interactive applications and fix a behaviour affecting the current interactive module.
  • easy/medium: Implement new functionalities:
    • 2D and 3D linear operators (the effect of a matrix on a plane/3D space)
    • Phase portrait for Ordinary Differential Equations.
    • Improve plot_parametric_region to better visualize complex maps.
    • Animations.
  • easy/medium: Packaging: while the main plotting functionalities work just with sympy, numpy and matplotlib, the full plotting module relies on several other packages. It has been observed that building a conda package with the full dependencies is difficult: most of the time the build succeed but the installation fails. Debug and fix it.
  • easy/medium: Implement a intelligent routine that automatically determines the regions of interest for plotting.
  • Fix related things/bugs in SymPy

More detailed information can be found on this page.

Status

Currently, the new plotting module lives on an external repository: sympy-plot-backends

Involved Software

Python, HTML, Javascript, CSS

Difficulty

Intermediate to Advanced: working with several different packages can be overwhelming.

Prerequisite Knowledge

Project Length

350 hours.

Documentation tooling

Idea

SymPy's documentation makes use of Sphinx and several Sphinx extensions. The idea here is to improve the tooling around the docs by developing some Sphinx extensions. Some ideas here

NOTE: Google requires that any GSoC project be primarily coding. This project is not primarily about writing documentation, as such a project is not allowed. It is instead about developing tooling to improve the SymPy documentation system.

Status

Some things are already implemented, for instance, we have an extension that lets us use dollar signs for math in RST https://github.com/sympy/sphinx-math-dollar. See the above issues for the status of any specific item.

Involved Software

This would primarily involve working with Sphinx and building Sphinx extensions or modifying existing ones. If relevant, we may prefer to upstream changes to Sphinx itself (although the Sphinx developers will not be mentors on this project, so we should not rely on this happening).

Difficulty

Intermediate to advanced (working with Sphinx can often be difficult)

Prerequisite Knowledge

Prior experience with RST and using autodoc is recommended.

Project Length

A project to implement all or the majority of the above ideas would require a 350 hours project, but a 175 hours or even 90 hours project can also be done that only implements a subset of the above ideas.

Hypothesis testing

Idea

Hypothesis is a Python library for property-based testing. Hypothesis tests work by specifying properties that a function should satisfy, and automatically generating inputs to test it. There are more details of the idea of adding hypothesis to SymPy in this issue.

The idea is to explore adding hypothesis testing to SymPy. We should start small, ideally with a function that is already well tested and has relatively easy to generate inputs. From there we can expand the testing.

Experimental hypothesis support has been added to SymPy, but so far only a few functions are tested. Work on this project will involve adding tests to more functions, adding more hypothesis strategies for different kinds of inputs, and reporting and potentially fixing any SymPy bugs that you find along the way.

It's expected that throughout this process you will find many bugs in SymPy. You may end up spending a lot of time in this project debugging failures, fixing bugs, or working around bugs that are not so easily fixed.

Status

SymPy has some basic hypothesis tests, which demonstrate a proof-of-concept of using it. However, the usage could be expanded significantly, as only a handful of functions currently have hypothesis tests.

Involved Software

The hypothesis testing library.

Difficulty

Intermediate to Advanced.

Hypothesis testing is simple in principle, but using it in practice can be difficult because it will uncover many bugs in SymPy. It will also not be straightforward to use hypothesis to test symbolic expressions (there are some ideas on how to do this outlined in the issue).

Prerequisite Knowledge

Prior experience with using hypothesis would be a huge plus, but it is not a hard requirement. If you have not used hypothesis before it is recommended that you play around with it and perhaps try adding some simple tests for something (in SymPy or somewhere else) to get familiar with it.

Project Length

350 hours (175 hours is possible, but the longer is preferred since there will be many things to do for this project).

User Application Projects

LFortran SymPy Project Ideas

LFortran is a modern open-source (BSD licensed) interactive Fortran compiler built on top of LLVM. It can execute user's code interactively to allow exploratory work (much like Python, MATLAB or Julia) as well as compile to binaries with the goal to run user's code on modern architectures such as multi-core CPUs and GPUs.

The basic idea of LFortran is to provide the infrastructure that can be used as a foundation to do anything related to Fortran (tools that need any of: parsing, source code generation, code transformation, machine code generation, etc.)

LFortran is currently written in Python. Down the line it will get rewritten into C++ for speed and robustness, but even then it will have Python wrappers, so the Python API should not change much.

There are many potential projects regarding Fortran in general and . Please see the two ideas here first for background information:

https://github.com/sympy/sympy/wiki/GSoC-Ideas#code-generation https://github.com/sympy/sympy/wiki/GSoC-Ideas#parsing

And then read through LFortran's documentation, mainly the Developer Tutorial to understand LFortran's AST and ASR.

This page contains a few well developed ideas.

SymPy -> Fortran Code Generation and JIT

Idea

Code generation from SymPy -> ASR, and then have two options: ASR -> AST -> source code, or ASR -> LLVM -> JIT and load it from Python to test it out.

Down the road the LLVM route might even be producing better (faster) code than using SymEngine->LLVM, because one can do optimizations on the ASR itself and before it is lowered to LLVM (as part of LFortran down the road), especially if one starts using do loops and arrays, because one knows more semantic information at the Fortran level than the LLVM level. And one can at least see the high level Fortran code (for debugging), as opposed to the relatively low level LLVM IR.

Currently SymPy represents Fortran code as a SymPy AST which is a combination of sympy.codegen.ast and sympy.codegen.fnodes. The sympy.printing.fcode module then has a visitor pattern that transforms this ast/fnodes AST into Fortran source code.

As a first step, one would change fcode() to transform this SymPy AST to LFortran's ASR. That will greatly simplify the printing, as LFortran will take care of transforming ASR -> AST (adding variable definitions mostly) and AST->source code. So SymPy code will get simplified. But also this will enable to then use LFortran to just in time compile this ASR and execute it from Python, thus allowing to interactively test the generated code.

One would port all the features from fcode() into LFortran, where it makes sense. SymPy should only do things which are SymPy specific.

After this is done, one can implement more features. For example it could be useful if the code printers could output parallel code using OpenMP directives (e.g. parallel for loops for C and Fortran, including use of reduction). Most printers do not yet support the new AST nodes, it would be useful if those were extended so that they can express ASTs created e.g. by functions in sympy.codegen.algorithms.

Another idea for codegen is to add more support for directly working with matrices. For instance, matrix expressions (sympy.matrices.expressions objects) should print LAPACK calls.

Project Length

350 hours.

Parsing Fortran code to SymPy

Idea

LFortran can parse Fortran source code to AST and then convert AST to ASR. This ASR will then get inspected and Fortran expressions identified and converted to SymPy expressions. This would allow SymPy to easily read in, alter, and write out computational Fortran code. This project would enable many other projects in the future.

This would be a general framework, some applications of this (some of which can be part of this project):

  • load the right hand side expressions and generate manufactured solution
  • check that a special function (e.g., spherical harmonics) Fortran implementation has the right expressions in it

Part of this project can also be to implement a capability in LFortran to track the values of variables ("x") that go into an expression when you actually run the code on production data.

A separate project idea is to:

  • optimize floating point expressions (à la https://herbie.uwplse.org/)
  • Based on the range of "x" (and other variables), determine which symbolic simplifications make sense to make things more accurate --- and to provide faster implementations of special functions, say if it is determined that "x" in sin(x) is in the range [0, 1e-3], then there are much faster polynomial approximations that give the same accuracy (the same might be possible if the range is say [1.5, 1.7], or any other finite range).

See https://github.com/sympy/sympy/wiki/GSoC-Ideas#optimize-floating-point-expressions for the expansion of this idea, as this capability is independent of LFortran.

Project Length

350 hours.

SymEngine Projects

SymEngine is a standalone fast C++ symbolic manipulation library. Optional thin Python wrappers allow easy usage from Python and integration with SymPy.

Please contact the SymEngine list (or Ondřej Čertík) for questions about the SymEngine related topics. You can also ask on SymEngine's gitter: https://gitter.im/symengine/symengine and propose something that is not listed below.

Polynomials and the rest of SymEngine

Idea

Build on the already existing univariate/multivariate polynomial module and have seamless interop with the rest of SymEngine. Keeping in mind the eventual goal of being a fast core, this is of high importance for SymPy as well.

Status

  • Interop Proposal
  • Univariate class improvements:
  • Multivariate class improvements
    • Currently implemented as a hashmap from vector of ints (degrees of respective symbols) to the coefficient.
    • For any operations between two multivariate polynomials, the vectors of all of the entries in the map must be updated to a common format (representing the union of the two symbols sets)
    • This is slow
    • We can try and use a ordered_map/hashmap instead of a vector for storing the degree of each symbol (in a particular monomial)
    • Operations should become much faster
  • Multivariate bindings for Piranha
    • Write wrappers for the multivariate piranha class for easy use within SymEngine
  • Miscellaneous
    • Groebner basis
    • Square free decomposition
    • Factorization

Involved Software

C++, Cython, Python, Git

  • For implementing/testing as an interface one may need to kindle with SymEngine.py and SymPy as well.

Difficulty

Intermediate

Prerequisite Knowledge

One needs to go through the code of the currently existing Polynomial module in SymEngine.

Additional reading

Project Length

350 hours.

Improve SymPy integration

Idea

SymEngine can be used as the symbolic backend for all the functions in sympy.physics.mechanics instead of SymPy's core by setting a environment variable. This project is to expand it to more modules in SymPy and also implement missing features from SymPy core in SymEngine.

A good proposal should briefly outline the changes that needs to be implemented in order to get good results. Some prior work was done on this by @ShikharJ during GSoC 2017, and the tasks undertaken should build up on the prior work.

Related Issues: https://github.com/symengine/symengine/issues/912 https://github.com/symengine/symengine/issues/1324

Related Pull Requests: https://github.com/symengine/symengine/pull/1332 https://github.com/sympy/sympy/pulls/ShikharJ

Involved Software

C++, Cython, Python, Git

Difficulty

Medium

Prerequisite Knowledge

Project Length

350 hours.

Implement solvers for SymEngine

Idea

A lot of work is actively going on in SymPy as to the design of solvers. In this project, the student will be expected to implement expression solvers for SymEngine along the lines of those in SymPy. At least implement most of the robust solvers that are done right in SymPy.

Status

Solvers are not present currently in SymEngine

Involved Software

C++, CMake, Git

Difficulty

Intermediate

Prerequisite Knowledge

Project Length

350 hours.

Improve Ruby wrappers

Idea

The motivation for SymEngine is to develop the Computer Algebra System once in C++ and then use it from other languages rather than doing the same thing all over again for each language that it is required in. Not all the SymEngine classes present are wrapped in Ruby, student can dive right in and look as to what else needs to be done. Few things that the project involves are:

  • Extending the C interface of SymEngine library.
  • Wrapping up the C interface for Ruby using Ruby C API, including error handling.
  • Designing the Ruby interface.
  • Integrating IRuby with symengine gem for better printing and preparing new IRuby notebooks.
  • Integrating the gem with existing gems like gmp, mpfr and mpc.
  • Making the installation of symengine gem easier.

SciRuby organisation may also accept the student working in this project.

Status

The ruby wrappers, symengine.rb, are a result of Abinash's GSoC. Have a look at the blog post. Improve them by wrapping the rest of SymEngine.

Involved Software

Ruby, C++, CMake, Git

Difficulty

Beginner

Prerequisite Knowledge

The Beginner Contributor Guide - Ruby Extensions and the resources mentioned there contain everything the student needs to know to get started.

Project Length

350 hours.

Idea Prompts

  • Linear algebra

    • Improve the matrices module documentation
    • Refactor the MatrixBase class.
    • Add more special matrices to the matrix expressions module, and migrate some special matrices from the quantum physics module.
    • Add more matrix decomposition methods: Schur Decomposition, Polar Decomposition, Hermite Decomposition, ...
    • Make the matrices use the specialized data types (Modular Integers, Gaussian Rationals, Polynomial Ring, ...) from the polys module.

  • improve the integration algorithm

    • integration of functions on domains of maximum extent, etc.
    • Interesting idea: "SYMBOLIC COMPUTATION OF INTEGRALS BY RECURRENCE" by MICHAEL P. BARNETT
    • A Simple Method for Computing Some Pseudo-Elliptic Integrals in Terms of Elementary Functions, https://arxiv.org/pdf/2004.04910.pdf

  • definite integration & integration on complex plane using residues. Note that we already have a strong algorithm that uses Meijer G-Functions implemented. So we need to first determine if such an algorithm would be worthwhile, or if it would be better to extend the current algorithm. Note that there are many integrals that are easy to compute using residues that cannot be computed by the current engine. Other possibilities: the ability to closed path integrals in the complex plane, which is not possible with the Meijer G algorithm.

  • Groebner bases and their applications in geometry, simplification and integration

    • improve Buchberger's algorithm and implement Faugere F4 (compare their speed) Note: This has already been implemented by a previous GSoC student. Please check with us to see the current state of Groebner bases in SymPy

  • improve polynomial algorithms (gcd, factorization) by allowing coefficients in algebraic extensions of the ground domain

  • implement efficient multivariate polynomials (arithmetic, gcd, factorization)

    • Implement a sparse representation for polynomials (see the dummy files in sympy/polys/ starting with "sparse" in the SymPy source code for a start to this project).
    • Figure out which representations to use where (sparse vs. dense).
    • implement efficient arithmetic (e.g. using geobuckets (Yan) or heaps (Monagan & Pearce))

  • improve SymPy's pattern matching abilities (efficiency and generality)

    • implement similarity measure between expression trees
    • expression complexity measures (e.g. Kolmogorov's complexity)
    • implement expressions signatures and heuristic equivalence testing
    • implement semantic matching (e.g. expression: cos(x), pattern: sin(a*x) + b)
      • e.g by using power series for this purpose (improve series speed)
    • Expand the capabilities of Wild() and match() to support regular expression-like quantifiers.

  • improve simplification and term rewriting algorithms

    • add (improve) verbatim and semi-verbatim modes (more control on expression rewriting)
    • implement more expression rewrite functions (to an exact form that user specifies). This may involve rewriting the rewrite framework to be more expressive. For example, should cos(x).rewrite(sin) return sqrt(1 - sin(x)**2) or sin(pi/2 - x)?
    • maybe put transformation rules in an external database (e.g. prolog), what about speed?
    • improve context (e.g. input) depended simplification steps in different algorithms
      • e.g. the integrator needs different sets of rules to return "better" output for different input
      • but there are more: recurrences, summations, solvers, polynomials with arbitrary coefficients
    • what about information carried by expressions?
      • what is simpler: chebyshevt(1, x) or x ?
      • what is simpler: chebyshevt(1000, x) or (...) ?
    • improve trigonometric simplification. See for example the paper by fu et. al.

  • implement symbolic (formal) logic and set theory

    • implement predicate (e.g. first-order), modal, temporal, description logic
    • implement multivalued logic; fuzzy and uncertain logic and variables
    • implement rewriting, minimization, normalization (e.g. Skolem) of expressions
    • implement set theory, cardinal numbers, relations etc.
    • This task is heavily tied to the assumptions system.

  • implement symbolic global optimization (value, argument) with/without constraints, use assumptions

  • continue work on objects with indices (tensors)

    • include the index simplification algorithms used in xAct and cadabra.

  • generalized functions - Dirac delta, P(1/x), etc... Convolution, Fourier and Laplace transforms

    • Fourier and Laplace transforms are implemented but we can not do many cases involving distributions Is this enough alone for a project though? -Aaron

  • vector calculus, differential fields, maybe Lie algebras & groups

  • parametric integrals asymptotic expansion (integral series)

  • Integral equations. See for example the work started at http://code.google.com/p/sympy/issues/detail?id=2344. This could be part of a project on ODEs, for example.

  • partial differential equations. Currently, SymPy can't solve any PDEs, though a few tools related to separation of variables are implemented. The PDE module should be structured similarly to the ODE module (see the source code of sympy/solvers/ode.py).

  • improve SymPy's Common Subexpression Elimination (CSE) abilities.

  • Singular analysis and test continuous.

    • find singularities of the function and classify them.
    • test the function whether it is continuous at some point or not. And in the interval. Note: Please discuss this idea with us if you are interested, as as it currently presented, it is somewhat vague.

  • Control theory. systems for Maple and Mathematica might provide insight here. http://www.mcs.anl.gov/~wozniak/papers/wozniak_mmath.pdf might be useful.

  • Diophantine Equations: SymPy does have substantial support for solving these, nevertheless there is more work possible to improve the solver.

Other Related Projects

PyDy

The classical mechanics package is tightly coupled with the PyDy project which enhances the mechanics package with numeric and visualization capabilities. All of the ideas for sympy.physics.vector and sympy.physics.mechanics are listed on the PyDy wiki in addition to other projects that are not in the SymPy code base but related. See https://github.com/pydy/pydy/wiki/GSoC-2016-Ideas.

Non-Ideas

Every year, people ask about implementing various things that we have already decided do not belong in SymPy. Among these are:

  • Graph theory. The NetworkX package already does a great job of graph theory in Python. If you are interested in working in graph theory, you should contact them.
  • Numerical solvers. SymPy is a symbolic library, so the code should focus on solving things symbolically. There are already many libraries for solving problems numerically (NumPy, SciPy, ...).
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