Sage FAQ Release 9.4
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Sagemath and Sagemathcloud
Viviane Pons Ma^ıtrede conf´erence,Universit´eParis-Sud Orsay [email protected] { @PyViv SageMath and SageMathCloud Introduction SageMath SageMath is a free open source mathematics software I Created in 2005 by William Stein. I http://www.sagemath.org/ I Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab. Viviane Pons (U-PSud) SageMath and SageMathCloud October 19, 2016 2 / 7 SageMath Source and language I the main language of Sage is python (but there are many other source languages: cython, C, C++, fortran) I the source is distributed under the GPL licence. Viviane Pons (U-PSud) SageMath and SageMathCloud October 19, 2016 3 / 7 SageMath Sage and libraries One of the original purpose of Sage was to put together the many existent open source mathematics software programs: Atlas, GAP, GMP, Linbox, Maxima, MPFR, PARI/GP, NetworkX, NTL, Numpy/Scipy, Singular, Symmetrica,... Sage is all-inclusive: it installs all those libraries and gives you a common python-based interface to work on them. On top of it is the python / cython Sage library it-self. Viviane Pons (U-PSud) SageMath and SageMathCloud October 19, 2016 4 / 7 SageMath Sage and libraries I You can use a library explicitly: sage: n = gap(20062006) sage: type(n) <c l a s s 'sage. interfaces .gap.GapElement'> sage: n.Factors() [ 2, 17, 59, 73, 137 ] I But also, many of Sage computation are done through those libraries without necessarily telling you: sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]]) sage : G . g a p () Group( [ (3,4), (1,2,3)(4,5) ] ) Viviane Pons (U-PSud) SageMath and SageMathCloud October 19, 2016 5 / 7 SageMath Development model Development model I Sage is developed by researchers for researchers: the original philosophy is to develop what you need for your research and share it with the community. -
Alternatives to Python: Julia
Crossing Language Barriers with , SciPy, and thon Steven G. Johnson MIT Applied Mathemacs Where I’m coming from… [ google “Steven Johnson MIT” ] Computaonal soPware you may know… … mainly C/C++ libraries & soPware … Nanophotonics … oPen with Python interfaces … (& Matlab & Scheme & …) jdj.mit.edu/nlopt www.w.org jdj.mit.edu/meep erf(z) (and erfc, erfi, …) in SciPy 0.12+ & other EM simulators… jdj.mit.edu/book Confession: I’ve used Python’s internal C API more than I’ve coded in Python… A new programming language? Viral Shah Jeff Bezanson Alan Edelman julialang.org Stefan Karpinski [begun 2009, “0.1” in 2013, ~20k commits] [ 17+ developers with 100+ commits ] [ usual fate of all First reacBon: You’re doomed. new languages ] … subsequently: … probably doomed … sll might be doomed but, in the meanBme, I’m having fun with it… … and it solves a real problem with technical compuBng in high-level languages. The “Two-Language” Problem Want a high-level language that you can work with interacBvely = easy development, prototyping, exploraon ⇒ dynamically typed language Plenty to choose from: Python, Matlab / Octave, R, Scilab, … (& some of us even like Scheme / Guile) Historically, can’t write performance-criBcal code (“inner loops”) in these languages… have to switch to C/Fortran/… (stac). [ e.g. SciPy git master is ~70% C/C++/Fortran] Workable, but Python → Python+C = a huge jump in complexity. Just vectorize your code? = rely on mature external libraries, operang on large blocks of data, for performance-criBcal code Good advice! But… • Someone has to write those libraries. • Eventually that person may be you. -
Data Visualization in Python
Data visualization in python Day 2 A variety of packages and philosophies • (today) matplotlib: http://matplotlib.org/ – Gallery: http://matplotlib.org/gallery.html – Frequently used commands: http://matplotlib.org/api/pyplot_summary.html • Seaborn: http://stanford.edu/~mwaskom/software/seaborn/ • ggplot: – R version: http://docs.ggplot2.org/current/ – Python port: http://ggplot.yhathq.com/ • Bokeh (live plots in your browser) – http://bokeh.pydata.org/en/latest/ Biocomputing Bootcamp 2017 Matplotlib • Gallery: http://matplotlib.org/gallery.html • Top commands: http://matplotlib.org/api/pyplot_summary.html • Provides "pylab" API, a mimic of matlab • Many different graph types and options, some obscure Biocomputing Bootcamp 2017 Matplotlib • Resulting plots represented by python objects, from entire figure down to individual points/lines. • Large API allows any aspect to be tweaked • Lengthy coding sometimes required to make a plot "just so" Biocomputing Bootcamp 2017 Seaborn • https://stanford.edu/~mwaskom/software/seaborn/ • Implements more complex plot types – Joint points, clustergrams, fitted linear models • Uses matplotlib "under the hood" Biocomputing Bootcamp 2017 Others • ggplot: – (Original) R version: http://docs.ggplot2.org/current/ – A recent python port: http://ggplot.yhathq.com/ – Elegant syntax for compactly specifying plots – but, they can be hard to tweak – We'll discuss this on the R side tomorrow, both the basics of both work similarly. • Bokeh – Live, clickable plots in your browser! – http://bokeh.pydata.org/en/latest/ -
Tuto Documentation Release 0.1.0
Tuto Documentation Release 0.1.0 DevOps people 2020-05-09 09H16 CONTENTS 1 Documentation news 3 1.1 Documentation news 2020........................................3 1.1.1 New features of sphinx.ext.autodoc (typing) in sphinx 2.4.0 (2020-02-09)..........3 1.1.2 Hypermodern Python Chapter 5: Documentation (2020-01-29) by https://twitter.com/cjolowicz/..................................3 1.2 Documentation news 2018........................................4 1.2.1 Pratical sphinx (2018-05-12, pycon2018)...........................4 1.2.2 Markdown Descriptions on PyPI (2018-03-16)........................4 1.2.3 Bringing interactive examples to MDN.............................5 1.3 Documentation news 2017........................................5 1.3.1 Autodoc-style extraction into Sphinx for your JS project...................5 1.4 Documentation news 2016........................................5 1.4.1 La documentation linux utilise sphinx.............................5 2 Documentation Advices 7 2.1 You are what you document (Monday, May 5, 2014)..........................8 2.2 Rédaction technique...........................................8 2.2.1 Libérez vos informations de leurs silos.............................8 2.2.2 Intégrer la documentation aux processus de développement..................8 2.3 13 Things People Hate about Your Open Source Docs.........................9 2.4 Beautiful docs.............................................. 10 2.5 Designing Great API Docs (11 Jan 2012)................................ 10 2.6 Docness................................................. -
Ipython: a System for Interactive Scientific
P YTHON: B ATTERIES I NCLUDED IPython: A System for Interactive Scientific Computing Python offers basic facilities for interactive work and a comprehensive library on top of which more sophisticated systems can be built. The IPython project provides an enhanced interactive environment that includes, among other features, support for data visualization and facilities for distributed and parallel computation. he backbone of scientific computing is All these systems offer an interactive command mostly a collection of high-perfor- line in which code can be run immediately, without mance code written in Fortran, C, and having to go through the traditional edit/com- C++ that typically runs in batch mode pile/execute cycle. This flexible style matches well onT large systems, clusters, and supercomputers. the spirit of computing in a scientific context, in However, over the past decade, high-level environ- which determining what computations must be ments that integrate easy-to-use interpreted lan- performed next often requires significant work. An guages, comprehensive numerical libraries, and interactive environment lets scientists look at data, visualization facilities have become extremely popu- test new ideas, combine algorithmic approaches, lar in this field. As hardware becomes faster, the crit- and evaluate their outcome directly. This process ical bottleneck in scientific computing isn’t always the might lead to a final result, or it might clarify how computer’s processing time; the scientist’s time is also they need to build a more static, large-scale pro- a consideration. For this reason, systems that allow duction code. rapid algorithmic exploration, data analysis, and vi- As this article shows, Python (www.python.org) sualization have become a staple of daily scientific is an excellent tool for such a workflow.1 The work. -
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix Slaes
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs Milena Veneva ∗1 and Alexander Ayriyan y1 1Joint Institute for Nuclear Research, Laboratory of Information Technologies, Joliot-Curie 6, 141980 Dubna, Moscow region, Russia Abstract This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pen- tadiagonal, and tridiagonal coefficient matrices. The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity. These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes. Performance analysis of the implementations is done using the high-performance computing (HPC) platforms “HybriLIT” and “Avitohol”. The experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed. An analysis of the three algorithms is performed. 1 Introduction Systems of linear algebraic equations (SLAEs) with heptadiagonal (HD), pentadiagonal (PD) and tridiagonal (TD) coefficient matrices may arise after many different scientific and engineering prob- lems, as well as problems of the computational linear algebra where finding the solution of a SLAE is considered to be one of the most important problems. On the other hand, special matrix’s char- acteristics like diagonal dominance, positive definiteness, etc. are not always feasible. The latter two points explain why there is a need of methods for solving of SLAEs which take into account the band structure of the matrices and do not have any other special requirements to them. One possible approach to this problem is the symbolic algorithms. -
Running Sagemath (With Or Without Installation)
Running SageMath (with or without installation) http://www.sagemath.org/ Éric Gourgoulhon Running SageMath 9 Feb. 2017 1 / 5 Various ways to install/access SageMath 7.5.1 Install on your computer: 2 options: install a compiled binary version for Linux, MacOS X or Windows1 from http://www.sagemath.org/download.html compile from source (Linux, MacOS X): check the prerequisites (see here for Ubuntu) and run git clone git://github.com/sagemath/sage.git cd sage MAKE=’make -j8’ make Run on your computer without installation: Sage Debian Live http://sagedebianlive.metelu.net/ Bootable USB flash drive with SageMath (boosted with octave, scilab), Geogebra, LaTeX, gimp, vlc, LibreOffice,... Open a (free) account on SageMathCloud https://cloud.sagemath.com/ Run in SageMathCell Single cell mode: http://sagecell.sagemath.org/ 1requires VirtualBox; alternatively, a full Windows installer is in pre-release stage at https://github.com/embray/sage-windows/releases Éric Gourgoulhon Running SageMath 9 Feb. 2017 2 / 5 Example 1: installing on Ubuntu 16.04 1 Download the archive sage-7.5.1-Ubuntu_16.04-x86_64.tar.bz2 from one the mirrors listed at http://www.sagemath.org/download-linux.html 2 Run the following commands in a terminal: bunzip2 sage-7.5.1-Ubuntu_16.04-x86_64.tar.bz2 tar xvf sage-7.5.1-Ubuntu_16.04-x86_64.tar cd SageMath ./sage -n jupyter A Jupyter home page should then open in your browser. Click on New and select SageMath 7.5.1 to open a Jupyter notebook with a SageMath kernel. Éric Gourgoulhon Running SageMath 9 Feb. 2017 3 / 5 Example 2: using the SageMathCloud 1 Open a free account on https://cloud.sagemath.com/ 2 Create a new project 3 In the second top menu, click on New to create a new file 4 Select Jupyter Notebook for the file type 5 In the Jupyter menu, click on Kernel, then Change kernel and choose SageMath 7.5 Éric Gourgoulhon Running SageMath 9 Feb. -
SNC: a Cloud Service Platform for Symbolic-Numeric Computation Using Just-In-Time Compilation
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCC.2017.2656088, IEEE Transactions on Cloud Computing IEEE TRANSACTIONS ON CLOUD COMPUTING 1 SNC: A Cloud Service Platform for Symbolic-Numeric Computation using Just-In-Time Compilation Peng Zhang1, Member, IEEE, Yueming Liu1, and Meikang Qiu, Senior Member, IEEE and SQL. Other types of Cloud services include: Software as a Abstract— Cloud services have been widely employed in IT Service (SaaS) in which the software is licensed and hosted in industry and scientific research. By using Cloud services users can Clouds; and Database as a Service (DBaaS) in which managed move computing tasks and data away from local computers to database services are hosted in Clouds. While enjoying these remote datacenters. By accessing Internet-based services over lightweight and mobile devices, users deploy diversified Cloud great services, we must face the challenges raised up by these applications on powerful machines. The key drivers towards this unexploited opportunities within a Cloud environment. paradigm for the scientific computing field include the substantial Complex scientific computing applications are being widely computing capacity, on-demand provisioning and cross-platform interoperability. To fully harness the Cloud services for scientific studied within the emerging Cloud-based services environment computing, however, we need to design an application-specific [4-12]. Traditionally, the focus is given to the parallel scientific platform to help the users efficiently migrate their applications. In HPC (high performance computing) applications [6, 12, 13], this, we propose a Cloud service platform for symbolic-numeric where substantial effort has been given to the integration of computation– SNC. -
Linux Fundamentals (GL120) U8583S This Is a Challenging Course That Focuses on the Fundamental Tools and Concepts of Linux and Unix
Course data sheet Linux Fundamentals (GL120) U8583S This is a challenging course that focuses on the fundamental tools and concepts of Linux and Unix. Students gain HPE course number U8583S proficiency using the command line. Beginners develop a Course length 5 days solid foundation in Unix, while advanced users discover Delivery mode ILT, vILT patterns and fill in gaps in their knowledge. The course View schedule, local material is designed to provide extensive hands-on View now pricing, and register experience. Topics include basic file manipulation; basic and View related courses View now advanced filesystem features; I/O redirection and pipes; text manipulation and regular expressions; managing jobs and processes; vi, the standard Unix editor; automating tasks with Why HPE Education Services? shell scripts; managing software; secure remote • IDC MarketScape leader 5 years running for IT education and training* administration; and more. • Recognized by IDC for leading with global coverage, unmatched technical Prerequisites Supported distributions expertise, and targeted education consulting services* Students should be comfortable with • Red Hat Enterprise Linux 7 • Key partnerships with industry leaders computers. No familiarity with Linux or other OpenStack®, VMware®, Linux®, Microsoft®, • SUSE Linux Enterprise 12 ITIL, PMI, CSA, and SUSE Unix operating systems is required. • Complete continuum of training delivery • Ubuntu 16.04 LTS options—self-paced eLearning, custom education consulting, traditional classroom, video on-demand -
ARM HPC Ecosystem
ARM HPC Ecosystem Darren Cepulis HPC Segment Manager ARM Business Segment Group HPC Forum, Santa Fe, NM 19th April 2017 © ARM 2017 ARM Collaboration for Exascale Programs United States Japan ARM is currently a participant in Fujitsu and RIKEN announced that the two Department of Energy funded Post-K system targeted at Exascale will pre-Exascale projects: Data be based on ARMv8 with new Scalable Movement Dominates and Fast Vector Extensions. Forward 2. European Union China Through FP7 and Horizon 2020, James Lin, vice director for the Center ARM has been involved in several of HPC at Shanghai Jiao Tong University funded pre-Exascale projects claims China will build three pre- including the Mont Blanc program Exascale prototypes to select the which deployed one of the first architecture for their Exascale system. ARM prototype HPC systems. The three prototypes are based on AMD, SunWei TaihuLight, and ARMv8. 2 © ARM 2017 ARM HPC deployments starting in 2H2017 Tw o recent announcements about ARM in HPC in Europe: 3 © ARM 2017 Japan Exascale slides from Fujitsu at ISC’16 4 © ARM 2017 Foundational SW Ecosystem for HPC . Linux OS’s – RedHat, SUSE, CENTOS, UBUNTU,… Commercial . Compilers – ARM, GNU, LLVM,… . Libraries – ARM, OpenBLAS, BLIS, ATLAS, FFTW… . Parallelism – OpenMP, OpenMPI, MVAPICH2,… . Debugging – Allinea, RW Totalview, GDB,… Open-source . Analysis – ARM, Allinea, HPCToolkit, TAU,… . Job schedulers – LSF, PBS Pro, SLURM,… . Cluster mgmt – Bright, CMU, warewulf,… Predictable Baseline 5 © ARM 2017 – now on ARM Functional Supported packages / components Areas OpenHPC defines a baseline. It is a community effort to Base OS RHEL/CentOS 7.1, SLES 12 provide a common, verified set of open source packages for Administrative Conman, Ganglia, Lmod, LosF, ORCM, Nagios, pdsh, HPC deployments Tools prun ARM’s participation: Provisioning Warewulf Resource Mgmt. -
How to Access Python for Doing Scientific Computing
How to access Python for doing scientific computing1 Hans Petter Langtangen1,2 1Center for Biomedical Computing, Simula Research Laboratory 2Department of Informatics, University of Oslo Mar 23, 2015 A comprehensive eco system for scientific computing with Python used to be quite a challenge to install on a computer, especially for newcomers. This problem is more or less solved today. There are several options for getting easy access to Python and the most important packages for scientific computations, so the biggest issue for a newcomer is to make a proper choice. An overview of the possibilities together with my own recommendations appears next. Contents 1 Required software2 2 Installing software on your laptop: Mac OS X and Windows3 3 Anaconda and Spyder4 3.1 Spyder on Mac............................4 3.2 Installation of additional packages.................5 3.3 Installing SciTools on Mac......................5 3.4 Installing SciTools on Windows...................5 4 VMWare Fusion virtual machine5 4.1 Installing Ubuntu...........................6 4.2 Installing software on Ubuntu....................7 4.3 File sharing..............................7 5 Dual boot on Windows8 6 Vagrant virtual machine9 1The material in this document is taken from a chapter in the book A Primer on Scientific Programming with Python, 4th edition, by the same author, published by Springer, 2014. 7 How to write and run a Python program9 7.1 The need for a text editor......................9 7.2 Spyder................................. 10 7.3 Text editors.............................. 10 7.4 Terminal windows.......................... 11 7.5 Using a plain text editor and a terminal window......... 12 8 The SageMathCloud and Wakari web services 12 8.1 Basic intro to SageMathCloud................... -
An Introduction to Numpy and Scipy
An introduction to Numpy and Scipy Table of contents Table of contents ............................................................................................................................ 1 Overview ......................................................................................................................................... 2 Installation ...................................................................................................................................... 2 Other resources .............................................................................................................................. 2 Importing the NumPy module ........................................................................................................ 2 Arrays .............................................................................................................................................. 3 Other ways to create arrays............................................................................................................ 7 Array mathematics .......................................................................................................................... 8 Array iteration ............................................................................................................................... 10 Basic array operations .................................................................................................................. 11 Comparison operators and value testing ....................................................................................