Sage: Unifying Mathematical Software for Scientists, Engineers, and Mathematicians
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Developing Scientific Computing Software: Current Processes And
DEVELOPING: SGIENffl&Pifli|ii^Mp| CURRENT PROCESSES" WMWiiiiia DEVELOPING SCIENTIFIC COMPUTING SOFTWARE MASTER OF APPLIED SCIENCE(2008) McMaster University COMPUTING AND SOFTWARE Hamilton, Ontario TITLE: Developing Scientific Computing Software: Current Processes and Future Directions AUTHOR: Jin Tang, M.M. (Nanjing University) SUPERVISOR: Dr. Spencer Smith NUMBER OF PAGERS: xxii, 216 n Abstract Considerable emphasis in scientific computing (SC) software development has been placed on the software qualities of performance and correctness. How ever, other software qualities have received less attention, such as the qualities of usability, maintainability, testability and reusability. Presented in this work is a survey titled "Survey on Developing Scien tific Computing Software, which is apparently the first conducted to explore the current approaches to SC software development and to determine which qualities of SC software are in most need of improvement. From the survey. we found that systematic development process is frequently not adopted in the SC software community, since 58% of respondents mentioned that their entire development process potentially consists only of coding and debugging. Moreover, semi-formal and formal specification is rarely used when developing SC software, which is suggested by the fact that 70% of respondents indicate that they only use informal specification. In terms of the problems in SC software development, which are dis covered by analyzing the survey results, a solution is proposed to improve the quality of SC software by using SE methodologies, concretely, using a modified Parnas' Rational Design Process (PRDP) and the Unified Software Development Process (USDP). A comparison of the two candidate processes is provided to help SC software practitioners determine which of the two pro cesses fits their particular situation. -
The Guide to Available Mathematical Software Problem Classification System
The Guide to Available Mathematical Software Problem Classification System Ronald F. Boisvert, Sally E. Howe and David K. Kahaner November 1990 U.S. DEPARTMENT OF COMMERCE National Institute of Standards and Technology Gaithersburg, MD 20899 100 U56 //4475 1990 C.2 NATIONAL, INSrrnJTE OF STANDARDS & TECHNOLOGY / THE GUIDE TO AVAILABLE MATHEMATICAL SOFTWARE PROBLEM CLASSIFICATION SYSTEM Ronald F. Boisvert Sally E. Howe David K. Kahaner U.S. DEPARTMENT OF COMMERCE National InstHute of Standards and Technology Center for Computing and Applied Mathematics Gaithersburg, MO 20899 November 1990 U.S. DEPARTMENT OF COMMERCE Robert A. Mosbacher, Secretary NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY John W. Lyons, Director 2 Boisvert, Howe and Kahaner own manuals or on-line documentation system. In order to determine what software is avail- able to solve a particular problem, users must search through a very large, heterogeneous collection of information. This is a tedious and error-prone process. As a result, there has been much interest in the development of automated advisory systems to help users select software. Keyword search is a popular technique used for this purpose. In such a system keywords or phrases are assigned to each piece of software to succinctly define its purpose, and the set of aU such keywords axe entered into a database. Keyword-based selection systems query users for a set of keywords and then present a fist of software modules which contain them. A major difficulty with such systems is that users often have trouble in providing the appropriate keywords for a given mathematical or statistical problem. There is such a wealth of alternate mathematical and statistical terminology that it would be a rare occurrence for two separate knowledgeable persons to assign the same set of keywords to a given software module. -
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. -
A Comparison of Six Numerical Software Packages for Educational Use in the Chemical Engineering Curriculum
SESSION 2520 A COMPARISON OF SIX NUMERICAL SOFTWARE PACKAGES FOR EDUCATIONAL USE IN THE CHEMICAL ENGINEERING CURRICULUM Mordechai Shacham Department of Chemical Engineering Ben-Gurion University of the Negev P. O. Box 653 Beer Sheva 84105, Israel Tel: (972) 7-6461481 Fax: (972) 7-6472916 E-mail: [email protected] Michael B. Cutlip Department of Chemical Engineering University of Connecticut Box U-222 Storrs, CT 06269-3222 Tel: (860)486-0321 Fax: (860)486-2959 E-mail: [email protected] INTRODUCTION Until the early 1980’s, computer use in Chemical Engineering Education involved mainly FORTRAN and less frequently CSMP programming. A typical com- puter assignment in that era would require the student to carry out the following tasks: 1.) Derive the model equations for the problem at hand, 2.) Find an appropri- ate numerical method to solve the model (mostly NLE’s or ODE’s), 3.) Write and debug a FORTRAN program to solve the problem using the selected numerical algo- rithm, and 4.) Analyze the results for validity and precision. It was soon recognized that the second and third tasks of the solution were minor contributions to the learning of the subject material in most chemical engi- neering courses, but they were actually the most time consuming and frustrating parts of computer assignments. The computer indeed enabled the students to solve realistic problems, but the time spent on technical details which were of minor rele- vance to the subject matter was much too long. In order to solve this difficulty, there was a tendency to provide the students with computer programs that could solve one particular type of a problem. -
Software for Numerical Computation
Purdue University Purdue e-Pubs Department of Computer Science Technical Reports Department of Computer Science 1977 Software for Numerical Computation John R. Rice Purdue University, [email protected] Report Number: 77-214 Rice, John R., "Software for Numerical Computation" (1977). Department of Computer Science Technical Reports. Paper 154. https://docs.lib.purdue.edu/cstech/154 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Department of Computer Sciences Purdue University West Lafayette, IN 47907 CSD TR #214 January 1977 SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Mathematical Sciences Purdue University CSD-TR 214 January 12, 1977 Article to appear in the book: Research Directions in Software Technology. SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Mathematical Sciences Purdue University INTRODUCTION AND MOTIVATING PROBLEMS. The purpose of this article is to examine the research developments in software for numerical computation. Research and development of numerical methods is not intended to be discussed for two reasons. First, a reasonable survey of the research in numerical methods would require a book. The COSERS report [Rice et al, 1977] on Numerical Computation does such a survey in about 100 printed pages and even so the discussion of many important fields (never mind topics) is limited to a few paragraphs. Second, the present book is focused on software and thus it is natural to attempt to separate software research from numerical computation research. This, of course, is not easy as the two are intimately intertwined. -
RESOURCES in NUMERICAL ANALYSIS Kendall E
RESOURCES IN NUMERICAL ANALYSIS Kendall E. Atkinson University of Iowa Introduction I. General Numerical Analysis A. Introductory Sources B. Advanced Introductory Texts with Broad Coverage C. Books With a Sampling of Introductory Topics D. Major Journals and Serial Publications 1. General Surveys 2. Leading journals with a general coverage in numerical analysis. 3. Other journals with a general coverage in numerical analysis. E. Other Printed Resources F. Online Resources II. Numerical Linear Algebra, Nonlinear Algebra, and Optimization A. Numerical Linear Algebra 1. General references 2. Eigenvalue problems 3. Iterative methods 4. Applications on parallel and vector computers 5. Over-determined linear systems. B. Numerical Solution of Nonlinear Systems 1. Single equations 2. Multivariate problems C. Optimization III. Approximation Theory A. Approximation of Functions 1. General references 2. Algorithms and software 3. Special topics 4. Multivariate approximation theory 5. Wavelets B. Interpolation Theory 1. Multivariable interpolation 2. Spline functions C. Numerical Integration and Differentiation 1. General references 2. Multivariate numerical integration IV. Solving Differential and Integral Equations A. Ordinary Differential Equations B. Partial Differential Equations C. Integral Equations V. Miscellaneous Important References VI. History of Numerical Analysis INTRODUCTION Numerical analysis is the area of mathematics and computer science that creates, analyzes, and implements algorithms for solving numerically the problems of continuous mathematics. Such problems originate generally from real-world applications of algebra, geometry, and calculus, and they involve variables that vary continuously; these problems occur throughout the natural sciences, social sciences, engineering, medicine, and business. During the second half of the twentieth century and continuing up to the present day, digital computers have grown in power and availability. -
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. -
Course Description for Computer Science.Pdf
COURSE DESCRIPTIONS FOR COMPUTER SCIENCE The Department of Mathematics and Computer Science requires that, prior to enrolling in any departmental course, students should earn a grade of “C” or better in all course prerequisites. CSDP 100 Computer Science Orientation Credit 1 This course is a survey of Computer Science with special emphasis on topics of importance to computer scientists. It also provides an exploration of skills required and resources available to students majoring Computer Science. Topics include nature of problems, hardware, human factors, security, social, ethical and legal issues, familiarization of various aspects of computing and networks. This course must be taken by all Computer Science major and minor students. CSDP 120 Introduction to Computing Credit 3 This course is for students new to Computer Science. The goal is to introduce students to different general computing aspects of the computer systems. Course topics include overview of the history of computing machines, computing codes and ethics, computing algorithms, programming languages, and mathematical software packages. Prerequisite: High school mathematics. CSDP 120 does not satisfy the General Education Area III Requirement. CSDP 121 Microcomputer Applications Credit 3 This course is designed for non-technical majors in different applications of modern computing systems. The course surveys computing hardware and software systems and introduces students to the present state-of-the-art word processing, spreadsheet, and database software. Applications to other disciplines, such as medicine, administration, accounting, social sciences and humanities, will be considered. Prerequisite: High School Mathematics. CSDP 121 does not satisfy the General Education Area III Requirement. CSDP 150 Office Automation Workshop Credit 1 This course is an introduction to current progress in word processing and/or office automation. -
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix Slaes
EPJ Web of Conferences 214, 05004 (2019) https://doi.org/10.1051/epjconf/201921405004 CHEP 2018 Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs 1, 1, Milena Veneva ∗ and Alexander Ayriyan ∗∗ 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 imple- mentations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, 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 engi- neering problems, 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 characteristics 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. -
Ginac 1.8.1 an Open Framework for Symbolic Computation Within the C++ Programming Language 8 August 2021
GiNaC 1.8.1 An open framework for symbolic computation within the C++ programming language 8 August 2021 https://www.ginac.de Copyright c 1999-2021 Johannes Gutenberg University Mainz, Germany Permission is granted to make and distribute verbatim copies of this manual provided the copy- right notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the condi- tions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. i Table of Contents GiNaC :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 1 1 Introduction :::::::::::::::::::::::::::::::::::::::::::::::::::: 2 1.1 License :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 2 2 A Tour of GiNaC::::::::::::::::::::::::::::::::::::::::::::::: 3 2.1 How to use it from within C++ :::::::::::::::::::::::::::::::::::::::::::::::::::: 3 2.2 What it can do for you::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 4 3 Installation:::::::::::::::::::::::::::::::::::::::::::::::::::::: 8 3.1 Prerequisites ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 8 3.2 Configuration :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 8 3.3 Building GiNaC ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 9 3.4 Installing GiNaC::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 9 4 Basic concepts::::::::::::::::::::::::::::::::::::::::::::::::: -
Introduction to the Ginac Framework for Symbolic Computation Within the C++ Programming Language
J. Symbolic Computation (2002) 33, 1–12 doi:10.1006/jsco.2001.0494 Available online at http://www.idealibrary.com on Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language CHRISTIAN BAUER, ALEXANDER FRINK AND RICHARD KRECKEL Institute of Physics, Johannes-Gutenberg-University, Mainz, Germany The traditional split into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system that deliberately denies the need for such a distinction. It is entirely written in C++ and the user can interact with it directly in that language. It was designed to provide efficient handling of multivariate polynomials, algebras and special functions that are needed for loop calculations in theoretical quantum field theory. It also bears some potential to become a more general purpose symbolic package. c 2002 Academic Press 1. Introduction Historically, in the design and implementation of symbolic computation engines, the focus has always been rather on algebraic capabilities than on language design. The need for efficient computation in all fields of science has led to the development of powerful algorithms. Thus, the border line between inexact numerical and exact analytical com- putation has moved, such that more computation may be done exactly before resorting to numerical methods. This development has had great influence on the working practice in such fields as engineering (e.g. robotics), computer science (e.g. networks), physics (e.g. high energy physics) and even mathematics (from group theory to automatic theo- rem proving in geometry). -
Sage & Algebraic Techniques for the Lazy Symmetric Cryptographer
Sage & Algebraic Techniques for the Lazy Symmetric Cryptographer Martin R. Albrecht @martinralbrecht Crypto Group, DTU Compute, Denmark IceBreak, Reykjavik, Iceland kicebreak Outline Sage Introduction Highlevel Features Fields & Areas Algebraic Techniques Introduction Equations Solvers ...for the Lazy Cryptographer Outline Sage Introduction Highlevel Features Fields & Areas Algebraic Techniques Introduction Equations Solvers ...for the Lazy Cryptographer Blurb Sage open-source mathematical soware system “Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.” Sage is a free open-source mathematics soware system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface. First release óþþ¢ Latest version ¢.É released óþÕì-þ¢-þì > ìþþ releases Shell, webbrowser (GUI), library > Õþ developers ∼ Õþþ components > óþþ papers cite Sage > óÕþþ subscribers [sage-support] > Õþþ,þþþ web visitors/month > ä, ¢þþ downloads/month How to use it Sage can be used via the command line, as a webapp hosted on your local computer and via the Internet, or embedded on any website. Check out: http://aleph.sagemath.org and https://cloud.sagemath.com/ “How do I do ...in Sage?” ...It’s easy: implement it and send us a patch. Sage is a largely volunteer-driven eort, this means that ▸ developers work on whatever suits their needs best; ▸ the quality of code in Sage varies: ▸ is a generic or a specialised, optimised implementation used, ▸ how much attention is paid to details, ▸ is your application an untested “corner case”, ▸ how extensive are the tests, the documentation, or ▸ is the version of a particular package up to date.