SymPy Tutorial

Aaron Meurer, Ondˇrej Cert´ık,Amitˇ Kumar, Jason Moore, Sartaj Singh, Harsh Gupta

July 11, 2016

All materials for today’s tutorial are at

1 / 21 http://www.sympy.org/scipy-2016-tutorial/ Outline

SymPy Introduction

 Goal

 Features

 History

 Present

 Future

Tutorial

 Intro to SymPy and Basic features

 Solving real life problems

2 / 21 “SymPy is an open source Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python and does not require any external libraries.”

SymPy Goal

Goal Provide a symbolic manipulation library in Python.

3 / 21 SymPy Goal

Goal Provide a symbolic manipulation library in Python.

“SymPy is an open source Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python and does not require any external libraries.”

3 / 21 Why SymPy?

 Standalone

 Full featured

 BSD licensed

 Embraces Python

 Usable as a library

4 / 21 Features

 Core Capabilities  Calculus  Basic arithmetic: Support for operators such as  Limits: limx→0 x log(x) = 0 +, -, *, /, ** (power)  Differentiation  Simplification  Integration: It uses extended Risch-Norman  Expansion heuristic  Functions: trigonometric, hyperbolic,  Taylor (Laurent) series exponential, roots, logarithms, absolute value, spherical harmonics, factorials and gamma  Solving equations functions, zeta functions, polynomials, special Polynomial equations functions, . . .  Algebraic equations  Substitution  Differential equations  Numbers: arbitrary precision integers, rationals,  and floats  Difference equations Systems of equations  Noncommutative symbols   Pattern matching  Combinatorics  Polynomials  Permutations  Basic arithmetic: division, gcd, . . .  Combinations  Factorization  Partitions  Square-free decomposition  Subsets  Gr¨obnerbases  Permutation Groups: Polyhedral, Rubik,  Partial fraction decomposition Symmetric, . . .  Resultants  Prufer and Gray Codes

5 / 21 Features

 Discrete math  Plotting  Binomial coefficients  Coordinate modes  Summations  Plotting Geometric Entities  Products  2D and 3D  Number theory: generating prime numbers,  Interactive interface primality testing, integer factorization, . . .  Colors  Logic expressions  Physics Matrices   Units  Basic arithmetic  Mechanics  Eigenvalues/eigenvectors  Quantum  Determinants  Gaussian Optics  Inversion  Pauli Algebra  Solving  Abstract expressions  Statistics  Geometric Algebra  Normal distributions  Uniform distributions  Geometry  Probability points, lines, rays, segments, ellipses, circles,  Printing polygons, . . .   Intersection  Pretty printing: ASCII/Unicode pretty printing,  Tangency LaTeX  Similarity  Code generation: C, Fortran, Python

6 / 21 History

History

 Ondˇrej Cert´ıkstartedˇ the project in 2006.

 Development took off in 2007 when SymPy first participated in Google Summer of Code. We have participated in every Google Summer of Code since.

 In 2011, Aaron Meurer (who also joined from Google Summer of Code) took over as lead developer.

7 / 21 Present

Current Status

 Over 450 contributors.

 Current code base has over 400,000 lines of code and documentation.

 We have crossed the point of “sympy a toy” to “sympy a tool”

8 / 21 Future

GSoC (1/2) These are our current GSoC projects. Expect to see these features by the end of the summer.

 Group Theory, Gaurav Dhingra

 Extending solveset, Kshitij Saraogi

 Completing Solveset, Shekhar Prasad Rajak

 Implementation of Holonomic Functions, Shubham Tibra

 Implementation of Singularity Functions to solve Beam Bending problems, Sampad Kumar Saha

9 / 21 Future

GSoC (2/2) These are our current GSoC projects. Expect to see these features by the end of the summer.

 Adding to SymEngine’s Polynomial functionality and interfacing it with FLINT & Piranha Srajan Garg

 Implementing Finite Fields and Set module in SymEngine Nishant Nikhil

10 / 21 Future

Other Plans

 New assumptions

 Make things faster

 SymEngine (https://github.com/symengine)

 Implement more algorithms, so we can compute more things (and also make them faster)

 Replacing solve with solveset

 Encourage people to use SymPy for many applications

 https://github.com/sympy/sympy/wiki/gsoc-2016-ideas for full list of things we want done

11 / 21 Projects Using SymPy

 Sage: A CAS, visioned to be a viable free open source alternative to Magma, Maple, Mathematica and MATLAB. Sage includes many open source mathematical libraries, including SymPy.

 SageMathCloud: SageMathCloud is a web-based cloud computing and course management platform for computational mathematics.

 Mathpix: An iOS App, that detects handwritten math as input, and uses SymPy Gamma to evaluate the math input and generate the relevant steps to solve the problem.

 PyDy: Multibody Dynamics with Python.

 IKFast: IKFast is a robot kinematics compiler provided by OpenRAVE. It analytically solves robot inverse kinematics equations and generates optimized C++ files. It uses SymPy for its internal symbolic mathematics. 12 / 21 Projects Using SymPy

 Octave Symbolic: The Octave-Forge Symbolic package adds symbolic calculation features to GNU Octave. These include common CAS tools such as algebraic operations, calculus, equation solving, Fourier and Laplace transforms, variable precision arithmetic, and other features.

 galgebra: Geometric algebra (previously sympy.galgebra).

 SymPy.jl: Provides a Julia interface to SymPy using PyCall.

 Mathics: Mathics is a free, general-purpose online CAS featuring Mathematica compatible syntax and functions. It is backed by highly extensible Python code, relying on SymPy for most mathematical tasks.

 SfePy: Simple finite elements in Python.

13 / 21 Projects Using SymPy

 Quameon: Quantum Monte Carlo in Python.

 Lcapy: Experimental Python package for teaching linear circuit analysis.

 Quantum Programming in Python: Quantum 1D Simple Harmonic Oscillator and Quantum Mapping Gate. A  LaTeX Expression project: Easy LTEX typesetting of algebraic expressions in symbolic form with automatic substitution and result computation.

 Symbolic statistical modeling: Adding statistical operations to complex physical models.

14 / 21 Authors

Ondˇrej Cert´ıkˇ James Aspnes Boris Timokhin Florian Mickler James Pearson Fabian Pedregosa Nimish Telang Robert Nicolas Pourcelot Matthew Brett Jurjen N.E. Bos Abderrahim Kitouni Andy R. Terrel Ben Goodrich Addison Cugini Mateusz Paprocki Pan Peng Hubert Tsang Toon Verstraelen Nicholas J.S. Kinar Marc-Etienne Friedrich Hagedorn Konrad Meyer Ronan Lamy Harold Erbin M.Leveille Elrond der Henrik Johansson James Abbatiello Thomas Dixon Brian Jorgensen Elbenfuerst Priit Laes Ryan Krauss Crist´ov˜aoSousa Jason Gedge Rizgar Mella Freddie Witherden Bill Flynn Andre de Fortier Robert Schwarz Felix Kaiser Brian E. Granger Kevin Goodsell Smit Pearu Peterson Roberto Nobrega Andrew Straw Jorn Baayen Mark Dewing Fredrik Johansson David Roberts Kaifeng Zhu Eh Tan Alexey U. Chris Wu Sebastian Kr¨amer Ted Horst Renato Coutinho Gudchenko Ulrich Hecht Vinzent Steinberg Andrew Docherty Oscar Benjamin Gary Kerr Goutham Riccardo Gori Akshay Srinivasan Øyvind Jensen Sherjil Ozair Lakshminarayan Case Van Horsen Aaron Meurer Julio Idichekop Filho Oleksandr Gituliar David Lawrence Stepan Roucka Barry Wardell Lukasz Pankowski Sean Vig Jaroslaw Tworek Ali Raza Syed Tomasz Buchert Chu-Ching Huang Prafullkumar P. Tale David Marek Stefano Maggiolo Vinay Kumar Fernando Perez Vladimir Peri´c Bernhard R. Link Robert Cimrman Johann Raffaele De Feo Tom Bachmann Andrej Tokarˇc´ık Bastian Weber Cohen-Tanugi Christian Muise Yuri Karadzhov Or Dvory Sebastian Krause Jochen Voss Matt Curry Saroj Adhikari Sebastian Kreft Luke Peterson Kazuo Thow Pauli Virtanen Dan Chris Smith Christian Schubert Robert Kern Alan Bromborsky Thomas Sidoti Jezreel Ng

15 / 21 Authors (continued)

Vladimir Lagunov Min Ragan-Kelley Imran Ahmed Swapnil Agarwal Prateek Papriwal Matthew Rocklin Emma Hogan Manzoor Kendhia Arpit Goyal Saptarshi Mandal Nikhil Sarda LjubiˇsaMo´ci´c jerryma1121 Angadh Nanjangud Gilbert Gede Julien Rioux Piotr Korgul Joachim Durchholz Comer Duncan Anatolii Koval Roberto Colistete, Jim Zhang Martin Poviˇser Jens H. Nielsen Tomo Lazovich Jr. Sam Sleight Siddhant Jain Joseph Dougherty Pavel Fedotov Raoul Bourquin tsmars15 Kevin Hunter marshall2389 Jack McCaffery Gert-Ludwig Ingold Chancellor Arkantos Michael Mayorov Guru Devanla Jeremias Yehdegho Srinivas Vasudevan Stepan Simsa Nathan Alison George Waksman Kibeom Kim Jason Moore Tobias Lenz Christian B¨uhler Alexandr Popov Gregory Ksionda Miha Marolt Siddhanathan Carsten Knoll Tarun Gaba Tom´aˇsBambas Tim Lahey Shanmugam Bharath M R Takafumi Arakaki Raymond Wong Luis Garcia Tiffany Zhu Matthias Toews Saurabh Jha Luca Weihs Matt Rajca Tristan Hume Sergiu Ivanov Rom le Clair Shai ’Deshe’ David Li Alexey Subach Jorge E. Cardona Angus Griffith Wyborski Alexandr Gudulin Joan Creus Sanket Agarwal Timothy Reluga Thomas Wiecki Bilal Akhtar Geoffry Song Manoj Babu K. Brian Stephanik Oscar´ N´ajera Grzegorz Swirski´ Puneeth Chaganti Sai Nikhil Alexander Mario Pernici Matt Habel Marcin Kostrzewa Aleksandar Makelov Ebersp¨acher Benjamin McDonald David Ju Natalia Nawara Sachin Irukula Sachin Joglekar Sam Magura Nichita Utiu vishal Raphael Michel Tyler Pirtle Stefan Krastanov Nikolay Lazarov Shruti Mangipudi Ashwini Oruganti Vasily Povalyaev Bradley Froehle Steve Anton Davy Mao Andreas Kloeckner Colleen Lee

16 / 21 Authors (continued)

Matthew Hoff Bj¨ornDahlgren Chris Conley James Goppert Ben Lucato Niklas Th¨orne Christophe Tim Swast rathmann Kunal Arora Huijun Mai Saint-Jean Dmitry Batkovich Avichal Dayal Henry Gebhardt Marek Suppaˇ Demian Wassermann Francesco Bonazzi Paul Scott Dammina Ramana Venkata Khagesh Patel Yuriy Demidov Shipra Banga Sahabandu Prasoon Shukla Stephen Loo Rick Muller Pramod Ch Shukla Stefen Yin hm Manish Gill Akshay Ralph Bean Thomas Hisch Patrick Poitras Markus M¨uller Buck Shlegeris richierichrawr Madeleine Ball Katja Sophie Hotz Amit Saha Jonathan Miller John Connor Case Van Horsen Varun Joshi Jeremy Edward Schembor Juan Luis Cano Mary Clark Chetna Gupta QuaBoo Rajath Shashidhara Rodr´ıguez Rishabh Dixit Thilina Rathnayake Stefan van der Walt Zamrath Nizam Sahil Shekhawat Manoj Kumar Max Hutchinson David Joyner Aditya Shah Kundan Kumar Akshit Agarwal Shravas K Rao Lars Buitinck Rajat Aggarwal Stas Kelvich CJ Carey Matthew Tadd Alkiviadis G. Akritas Sambuddha Basu sevaader Patrick Lacasse Alexander Hirzel Vinit Ravishankar Zeel Shah Dhruvesh Vijay Ananya H Randy Heydon Mike Boyle Abhinav Chanda Parikh Tarang Patel Oliver Lee Heiner Kirchhoffer Jim Crist Venkatesh Halli Christopher Dembia Seshagiri Prabhu Pablo Puente Sudhanshu Mishra Lennart Fricke Benjamin Fishbein Pradyumna James Fiedler Anurag Sharma Vlad Seghete Sean Ge Erik Welch Harsh Gupta Soumya Dipta Shashank Agarwal Amit Jamadagni Eric Nelson Tuomas Airaksinen Biswas carstimon Ankit Agrawal Roland Puntaier Paul Strickland Sushant Hiray Pierre Haessig

17 / 21 Authors (continued)

Maciej Baranski Leonid Blouvshtein Guillaume Gay Lucas Jones Michael Zingale Benjamin Gudehus Peleg Michaeli Ray Cathcart Gregory Ashton Chak-Pong Chung Faisal Anees ck Lux Mihir Wadwekar Jennifer White David T Mark Shoulson zsc347 Tuan Manh Lai Renato Orsino Phil Ruffwind Robert Johansson Hamish Dickson Asish Panda Michael Boyle Sebastian Koslowski Kalevi Suominen Michael Gallaspy Darshan Chaudhary Alistair Lynn Kumar Krishna Kaushik Varanasi Roman Inflianskas Alec Kalinin Govind Sahai Agrawal Fawaz Alazemi Duane Nykamp Ralf Stephan Adam Bloomston Dustin Gadal Ambar Mehrotra Ted Dokos Aaditya Nair Kyle McDaniel operte David P. Sanders Sunny Aggarwal Jayesh Lahori Nguyen Truong Duy Yu Kobayashi Peter Brady Victor Brebenar Harshil Goel Alex Lindsay Shashank Kumar John V. Siratt Akshat Jain Luv Agarwal Mathew Chong Timothy Cyrus Sarwar Chahal Shivam Vats Jason Ly Jason Siefken Devyani Kota Nathan Woods Longqi Wang Lokesh Sharma Gaurav Dhingra Keval Shah Colin B. Macdonald Juan Felipe Osorio Sartaj Singh Gao, Xiang Dzhelil Rufat Marcus N¨aslund GitRay Chris Swierczewski Kevin Ventullo Pastafarianist Clemens Novak Lukas Zorich Konstantin Togoi mao8 Sourav Singh Mridul Seth Eric Miller Param Singh Isuru Fernando Jacob Garber Craig A. Stoudt Venkata Ramana Sumith Shivam Tyagi Vinay Raj Cody Herbst Juha Remes Richard Otis Mihai A. Ionescu Nishith Shah Philippe Bouafia Rich LaSota immerrr AMiT Kumar Peter Schmidt dustyrockpyle Chai Wah Wu Yury G. Kudryashov Jiaxing Liang Anton Akhmerov

18 / 21 Authors (continued)

GolimarOurHero Madhyastha Guillaume Jacquenot Sanya Khurana Nathan Musoke Prashant Tyagi Tanu Hari Dixit Bhautik Mavani Aman Deep Abhishek Garg Matthew Davis Shekhar Prasad Michal Radwa´nski Aravind Reddy Dana Jacobsen Tschijnmo TSCHAU Rajak Jerry Li Abhishek Verma Vasiliy Dommes Alexander Bentkamp Aqnouch Pablo Zubieta Matthew Parnell Phillip Berndt Moo VI Mohammed Curious72 Thomas Hickman Haimo Zhang Jack Kemp Arafat Dad Khan Chaitanya Sai Akshay Siramdas Subham Tibra Kshitij Saraogi Boris Atamanovskiy Alaparthi YiDing Jiang Anthony Scopatz Thomas Baruchel Sam Tygier arihant parsoya Jatin Yadav bluebrook Nicol´as Jai Luthra Ruslan Pisarev Matthew Thomas Normal Human Guar´ın-Zapata Guo Xingjian Akash Trehan Rehas Sachdeva Josh Burkart Jens Jørgen Sandeep Veethu Nishant Nikhil Michael Mueller Dimitra Konomi Mortensen Archit Verma Vladimir Poluhsin Srajan Garg ChristinaZografou Sampad Kumar Saha Shubham Tibra Akshay Nagar Prabhjot Singh FiachAntaw Eva Charlotte Mayer Ashutosh Saboo James Brandon Haruki Moriguchi Langston Barrett Laura Domine Michael S. Hansen Milam Tom Gijselinck Krit Karan Justin Blythe Anish Shah Abhinav Agarwal Nitin Chaudhary G. D. McBain Meghana Harshil Goel Rishabh Daal Alex Argunov Prempal Singh

19 / 21 Here at SciPy

Talks

 Jason Moore, Simulating Robot, Vehicle, Spacecraft, and Animal Motion with Python (Advanced) (Tutorial). Monday 1:30 PM - 5:30 PM - Room 103

 Aaron Meurer, Anthony Scopatz SymPy Code Generation. Thursday 11:30 PM - 12:00 PM - Room 204

 Ondˇrej Cert´ık,Isuruˇ Fernando, Thilina Rathnayake, Abhinav Agarwal SymEngine: A Fast Symbolic Manipulation Library. Friday 3:30 - 4:00 - Room 204

20 / 21 Let’s begin!

21 / 21