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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. -
A Comparative Evaluation of Matlab, Octave, R, and Julia on Maya 1 Introduction
A Comparative Evaluation of Matlab, Octave, R, and Julia on Maya Sai K. Popuri and Matthias K. Gobbert* Department of Mathematics and Statistics, University of Maryland, Baltimore County *Corresponding author: [email protected], www.umbc.edu/~gobbert Technical Report HPCF{2017{3, hpcf.umbc.edu > Publications Abstract Matlab is the most popular commercial package for numerical computations in mathematics, statistics, the sciences, engineering, and other fields. Octave is a freely available software used for numerical computing. R is a popular open source freely available software often used for statistical analysis and computing. Julia is a recent open source freely available high-level programming language with a sophisticated com- piler for high-performance numerical and statistical computing. They are all available to download on the Linux, Windows, and Mac OS X operating systems. We investigate whether the three freely available software are viable alternatives to Matlab for uses in research and teaching. We compare the results on part of the equipment of the cluster maya in the UMBC High Performance Computing Facility. The equipment has 72 nodes, each with two Intel E5-2650v2 Ivy Bridge (2.6 GHz, 20 MB cache) proces- sors with 8 cores per CPU, for a total of 16 cores per node. All nodes have 64 GB of main memory and are connected by a quad-data rate InfiniBand interconnect. The tests focused on usability lead us to conclude that Octave is the most compatible with Matlab, since it uses the same syntax and has the native capability of running m-files. R was hampered by somewhat different syntax or function names and some missing functions. -
GNU Readline Library
GNU Readline Library Edition 2.1, for Readline Library Version 2.1. March 1996 Brian Fox, Free Software Foundation Chet Ramey, Case Western Reserve University This do cument describ es the GNU Readline Library, a utility which aids in the consistency of user interface across discrete programs that need to provide a command line interface. Published by the Free Software Foundation 675 Massachusetts Avenue, Cambridge, MA 02139 USA Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this p ermission notice are preserved on all copies. Permission is granted to copy and distribute mo di ed versions of this manual under the con- ditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a p ermission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another lan- guage, under the ab ove conditions for mo di ed versions, except that this p ermission notice may b e stated in a translation approved by the Foundation. c Copyright 1989, 1991 Free Software Foundation, Inc. Chapter 1: Command Line Editing 1 1 Command Line Editing This chapter describ es the basic features of the GNU command line editing interface. 1.1 Intro duction to Line Editing The following paragraphs describ e the notation used to representkeystrokes. i h i h C-k is read as `Control-K' and describ es the character pro duced when the k The text key is pressed while the Control key is depressed. h i The text M-k is read as `Meta-K' and describ es the character pro duced when the meta h i key if you have one is depressed, and the k key is pressed. -
Version 7.8-Systemd
Linux From Scratch Version 7.8-systemd Created by Gerard Beekmans Edited by Douglas R. Reno Linux From Scratch: Version 7.8-systemd by Created by Gerard Beekmans and Edited by Douglas R. Reno Copyright © 1999-2015 Gerard Beekmans Copyright © 1999-2015, Gerard Beekmans All rights reserved. This book is licensed under a Creative Commons License. Computer instructions may be extracted from the book under the MIT License. Linux® is a registered trademark of Linus Torvalds. Linux From Scratch - Version 7.8-systemd Table of Contents Preface .......................................................................................................................................................................... vii i. Foreword ............................................................................................................................................................. vii ii. Audience ............................................................................................................................................................ vii iii. LFS Target Architectures ................................................................................................................................ viii iv. LFS and Standards ............................................................................................................................................ ix v. Rationale for Packages in the Book .................................................................................................................... x vi. Prerequisites -
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. -
Introduction to GNU Octave
Introduction to GNU Octave Hubert Selhofer, revised by Marcel Oliver updated to current Octave version by Thomas L. Scofield 2008/08/16 line 1 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 8 6 4 2 -8 -6 0 -4 -2 -2 0 -4 2 4 -6 6 8 -8 Contents 1 Basics 2 1.1 What is Octave? ........................... 2 1.2 Help! . 2 1.3 Input conventions . 3 1.4 Variables and standard operations . 3 2 Vector and matrix operations 4 2.1 Vectors . 4 2.2 Matrices . 4 1 2.3 Basic matrix arithmetic . 5 2.4 Element-wise operations . 5 2.5 Indexing and slicing . 6 2.6 Solving linear systems of equations . 7 2.7 Inverses, decompositions, eigenvalues . 7 2.8 Testing for zero elements . 8 3 Control structures 8 3.1 Functions . 8 3.2 Global variables . 9 3.3 Loops . 9 3.4 Branching . 9 3.5 Functions of functions . 10 3.6 Efficiency considerations . 10 3.7 Input and output . 11 4 Graphics 11 4.1 2D graphics . 11 4.2 3D graphics: . 12 4.3 Commands for 2D and 3D graphics . 13 5 Exercises 13 5.1 Linear algebra . 13 5.2 Timing . 14 5.3 Stability functions of BDF-integrators . 14 5.4 3D plot . 15 5.5 Hilbert matrix . 15 5.6 Least square fit of a straight line . 16 5.7 Trapezoidal rule . 16 1 Basics 1.1 What is Octave? Octave is an interactive programming language specifically suited for vectoriz- able numerical calculations. -
Xcode Package from App Store
KH Computational Physics- 2016 Introduction Setting up your computing environment Installation • MAC or Linux are the preferred operating system in this course on scientific computing. • Windows can be used, but the most important programs must be installed – python : There is a nice package ”Enthought Python Distribution” http://www.enthought.com/products/edudownload.php – C++ and Fortran compiler – BLAS&LAPACK for linear algebra – plotting program such as gnuplot Kristjan Haule, 2016 –1– KH Computational Physics- 2016 Introduction Software for this course: Essentials: • Python, and its packages in particular numpy, scipy, matplotlib • C++ compiler such as gcc • Text editor for coding (for example Emacs, Aquamacs, Enthought’s IDLE) • make to execute makefiles Highly Recommended: • Fortran compiler, such as gfortran or intel fortran • BLAS& LAPACK library for linear algebra (most likely provided by vendor) • open mp enabled fortran and C++ compiler Useful: • gnuplot for fast plotting. • gsl (Gnu scientific library) for implementation of various scientific algorithms. Kristjan Haule, 2016 –2– KH Computational Physics- 2016 Introduction Installation on MAC • Install Xcode package from App Store. • Install ‘‘Command Line Tools’’ from Apple’s software site. For Mavericks and lafter, open Xcode program, and choose from the menu Xcode -> Open Developer Tool -> More Developer Tools... You will be linked to the Apple page that allows you to access downloads for Xcode. You wil have to register as a developer (free). Search for the Xcode Command Line Tools in the search box in the upper left. Download and install the correct version of the Command Line Tools, for example for OS ”El Capitan” and Xcode 7.2, Kristjan Haule, 2016 –3– KH Computational Physics- 2016 Introduction you need Command Line Tools OS X 10.11 for Xcode 7.2 Apple’s Xcode contains many libraries and compilers for Mac systems. -
A Tutorial on Reliable Numerical Computation
A tutorial on reliable numerical computation Paul Zimmermann Dagstuhl seminar 17481, Schloß Dagstuhl, November 2017 The IEEE 754 standard First version in 1985, first revision in 2008, another revision for 2018. Standard formats: binary32, binary64, binary128, decimal64, decimal128 Standard rounding modes (attributes): roundTowardPositive, roundTowardNegative, roundTowardZero, roundTiesToEven p Correct rounding: required for +; −; ×; ÷; ·, recommended for other mathematical functions (sin; exp; log; :::) 2 Different kinds of arithmetic in various languages fixed precision arbitrary precision real double (C) GNU MPFR (C) numbers RDF (Sage) RealField(p) (Sage) MPFI (C) Boost Interval (C++) RealIntervalField(p) (Sage) real INTLAB (Matlab, Octave) RealBallField(p) (Sage) intervals RIF (Sage) libieeep1788 (C++) RBF (Sage) Octave Interval (Octave) libieeep1788 is developed by Marco Nehmeier GNU Octave Interval is developed by Oliver Heimlich 3 An example from Siegfried Rump Reference: S.M. Rump. Gleitkommaarithmetik auf dem Prüfstand [Wie werden verifiziert(e) numerische Lösungen berechnet?]. Jahresbericht der Deutschen Mathematiker-Vereinigung, 118(3):179–226, 2016. a p(a; b) = 21b2 − 2a2 + 55b4 − 10a2b2 + 2b Evaluate p at a = 77617, b = 33096. 4 Rump’s polynomial in the C language #include <stdio.h> TYPE p (TYPE a, TYPE b) { TYPE a2 = a * a; TYPE b2 = b * b; return 21.0*b2 - 2.0*a2 + 55*b2*b2 - 10*a2*b2 + a/(2.0*b); } int main() { printf ("%.16Le\n", (long double) p (77617.0, 33096.0)); } 5 Rump’s polynomial in the C language: results $ gcc -DTYPE=float rump.c && ./a.out -4.3870930862080000e+12 $ gcc -DTYPE=double rump.c && ./a.out 1.1726039400531787e+00 $ gcc -DTYPE="long double" rump.c && ./a.out 1.1726039400531786e+00 $ gcc -DTYPE=__float128 rump.c && ./a.out -8.2739605994682137e-01 6 The MPFR library A reference implementation of IEEE 754 in (binary) arbitrary precision in the C language. -
Installation Guide for the UNIX Versions
Appendix A: Installation Guide for the UNIX Versions 1. Required tools. Compiling PARI requires an ANSI C or a C++ compiler. If you do not have one, we suggest that you obtain the gcc/g++ compiler. As for all GNU software mentioned afterwards, you can find the most convenient site to fetch gcc at the address http://www.gnu.org/order/ftp.html (On Mac OS X, this is also provided in the Xcode tool suite.) You can certainly compile PARI with a different compiler, but the PARI kernel takes advantage of optimizations provided by gcc. This results in at least 20% speedup on most architectures. Optional packages. The following programs and libraries are useful in conjunction with gp, but not mandatory. In any case, get them before proceeding if you want the functionalities they provide. All of them are free. • GNU MP library. This provides an alternative multiprecision kernel, which is faster than PARI's native one, but unfortunately binary incompatible. To enable detection of GMP, use Con- figure --with-gmp. You should really do this if you only intend to use GP, and probably also if you will use libpari unless you have backwards compatibility requirements. • GNU readline library. This provides line editing under GP, an automatic context-dependent completion, and an editable history of commands. Note that it is incompatible with SUN com- mandtools (yet another reason to dump Suntools for X Windows). • GNU gzip/gunzip/gzcat package enables GP to read compressed data. • GNU emacs. GP can be run in an Emacs buffer, with all the obvious advantages if you are familiar with this editor. -
GNU Scientific Library – Reference Manual
GNU Scientific Library – Reference Manual: Top http://www.gnu.org/software/gsl/manual/html_node/ GNU Scientific Library – Reference Manual Next: Introduction, Previous: (dir), Up: (dir) [Index] GSL This file documents the GNU Scientific Library (GSL), a collection of numerical routines for scientific computing. It corresponds to release 1.16+ of the library. Please report any errors in this manual to [email protected]. More information about GSL can be found at the project homepage, http://www.gnu.org/software/gsl/. Printed copies of this manual can be purchased from Network Theory Ltd at http://www.network-theory.co.uk /gsl/manual/. The money raised from sales of the manual helps support the development of GSL. A Japanese translation of this manual is available from the GSL project homepage thanks to Daisuke Tominaga. Copyright © 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 The GSL Team. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections and no cover texts. A copy of the license is included in the section entitled “GNU Free Documentation License”. • Introduction: • Using the library: • Error Handling: • Mathematical Functions: • Complex Numbers: • Polynomials: • Special Functions: • Vectors and Matrices: • Permutations: • Combinations: • Multisets: • Sorting: • BLAS Support: • Linear Algebra: • Eigensystems: -
$SPAD/Lsp Makefile
$SPAD/lsp Makefile The Axiom Team December 3, 2016 Abstract 1 Contents 1 The Makefile 3 2 Gnu Common Lisp 2.6.7 3 3 Gnu Common Lisp 2.6.7pre 3 3.1 run-process patch . 3 4 Gnu Common Lisp 2.6.6 3 4.1 run-process patch . 3 5 Gnu Common Lisp 2.6.5w 4 5.1 mingw.defs . 4 5.2 alloc.c . 4 5.3 mingfile.c . 4 5.4 unixfsys.c . 4 6 Gnu Common Lisp 2.6.5 5 6.1 gmp wrappers patch . 5 7 Gnu Common Lisp 2.5.2 5 7.0.1 socket patch . 5 7.0.2 read.d patch . 9 7.0.3 fortran patch . 9 7.0.4 libspad patch . 10 7.0.5 toploop patch . 12 7.0.6 object to float patch . 14 7.0.7 in-package patch . 15 7.0.8 EXIT and MAX STACK SIZE patchs . 15 7.0.9 tail-recursive patch . 16 7.0.10 collectfn fix . 17 7.1 The GCL-2.5.2 stanza . 21 7.1.1 Configure and Make GCL . 21 7.2 The GCL-2.6.1 stanza . 23 7.3 The GCL-2.6.2 stanza . 24 7.4 Directory move . 25 7.5 The GCL-2.6.2a stanza . 25 7.6 Directory move . 26 7.7 The GCL-2.6.3 stanza . 26 7.8 The GCL-2.6.5 stanza . 27 7.9 The GCL-2.6.5w stanza . 28 7.10 The GCL-2.6.6 stanza . -
Gretl User's Guide
Gretl User’s Guide Gnu Regression, Econometrics and Time-series Allin Cottrell Department of Economics Wake Forest university Riccardo “Jack” Lucchetti Dipartimento di Economia Università di Ancona November, 2005 Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation (see http://www.gnu.org/licenses/fdl.html). Contents 1 Introduction 1 1.1 Features at a glance ......................................... 1 1.2 Acknowledgements ......................................... 1 1.3 Installing the programs ....................................... 2 2 Getting started 4 2.1 Let’s run a regression ........................................ 4 2.2 Estimation output .......................................... 6 2.3 The main window menus ...................................... 7 2.4 The gretl toolbar ........................................... 10 3 Modes of working 12 3.1 Command scripts ........................................... 12 3.2 Saving script objects ......................................... 13 3.3 The gretl console ........................................... 14 3.4 The Session concept ......................................... 14 4 Data files 17 4.1 Native format ............................................. 17 4.2 Other data file formats ....................................... 17 4.3 Binary databases ........................................... 17 4.4 Creating a data file from scratch ................................