Open source computer algebra systems Riccardo Guida and Sylvain - - PowerPoint PPT Presentation

Open source computer algebra systems

Riccardo Guida and Sylvain Ribault

IPhT Saclay

Tuesday 7 May 2019

Riccardo Guida and Sylvain Ribault (IPhT) OSCAS Tuesday 7 May 2019 1 / 9

Summary

the trouble with Mathematica; a quick overview of the best Open Source Computer Algebra Systems (OSCAS) available today; a demonstration of SymPy.

Riccardo Guida and Sylvain Ribault (IPhT) OSCAS Tuesday 7 May 2019 2 / 9

The trouble with Mathematica

Mathematica is the most widespread computer algebra system in our field. However, it is expensive for non-academic researchers; it is not accessible by anyone anywhere (collaborators, readers of your articles, yourself after moving to another institute or ending your grant); availability of old versions is not guaranteed, and is subject to Wolfram’s commercial policy. IPhT-specific problems: We currently pay 25ke/year for only 10 system-wide licenses. We used to pay the same price for 200 licenses. Then a new salesperson came. We bought “perpetual” licenses for 11 users on MacOS. But these 32-bits licences will be unusable on the next version of MacOS (64-bits only). Upgrade cost: ∼ 700 e per “perpetual” license.

Riccardo Guida and Sylvain Ribault (IPhT) OSCAS Tuesday 7 May 2019 3 / 9

Open source software

Open source software solves the problems of cost and license availability. Other advantages include: Verifiability of algorithms: no need to trust a black box. Influencing development of the software by reporting bugs, writing code yourself, or giving grant money for adding a feature you need. Anyone can check, reproduce, and improve your results, if you give them your code. Mathematica is generally more complete and advanced than the OS alternatives . . . . . . but most people, most of the time, do not need the advanced features. You would not lose much by switching to open source tools, unless you are captive of a large existing body of code and/or specialized packages. (And if you are captive, you can use OSCAS for double-checking.)

Riccardo Guida and Sylvain Ribault (IPhT) OSCAS Tuesday 7 May 2019 4 / 9

IPhT Survey

Which computer algebra system(s) did you use in the last 3 years?

Mathematica Maple Matlab SymPy/NumPy/SciPy SageMath Maxima FriCAS Cadabra Open? ✗ ✗ ✗ ✓ ✓ ✓ ✓ ✓ # Users 35 7 3 10 2 4 1 1

Thanks to the 42 participants!

Riccardo Guida and Sylvain Ribault (IPhT) OSCAS Tuesday 7 May 2019 5 / 9

OSCAS overview 1

SymPy SageMath Maxima FriCAS Initial release 2007 2005 1998 2007 Non-OS base – – Macsyma 1982 Axiom 1977 Contributors1 59 63 11 3 User Language Python Python-ish Maxima SPAD Interpreter CPython, PyPy CPython Common Lisp Common Lisp Expected speed C/50 C/50 to C C/5 C/5 Notebooks Jupyter, TeXmacs Jupyter, TeXmacs wxMaxima, TeX- macs TeXmacs

1Number of contributors with more than 9 commits between 2018-03-15 and

2019-03-15.

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OSCAS overview 2

SymPy, SageMath, Maxima, Fricas: multi-platform, generalist OSCAS that have the usual basic features: limits, derivatives, Taylor series, basic integrals, linear algebra, special functions, polynomial equations, basic ODEs, replacements, arbitrary precision numerics, . . . They differ in the availability and quality of more advanced features.

Riccardo Guida and Sylvain Ribault (IPhT) OSCAS Tuesday 7 May 2019 7 / 9

OSCAS overview 3

SageMath SageMath = SageMathCore ⊕ SymPy ⊕ Maxima ⊕ · · · ⊕ FriCAS Manifolds, number theory, combinatorics Interface to other OSCAS not always transparent Maxima Easy language not so far from Mathematica Poor development of new mathematical features FriCAS Dedicated language inspired by mathematics New advanced mathematical features at each release Antiderivatives, noncommutative algebra, sparse polynomials Features such as plotting are postponed to better times

Riccardo Guida and Sylvain Ribault (IPhT) OSCAS Tuesday 7 May 2019 8 / 9

SymPy overview

SymPy Python = very easy and widespread language; Google/StackOverflow answer all questions SymPy is a Python module, can be combined with other modules such as NumPy, SciPy, etc Proactive developer community (including Google-funded interns) Generalized hypergeometrics, automatic generation and execution of code, rule-based integration tools (RUBI)

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