DOCSLIB.ORG

1 Home PDF (Letter Size) PDF (Legal Size) Computer Algebra Independent Integration Tests

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

1 home PDF (letter size) PDF (legal size) Computer Algebra Independent Integration Tests Nasser M. Abbasi September 17, 2021 Compiled on September 17, 2021 at 9:43am [public] Contents 1 FULL CAS integration tests 2 2 Specialized integration tests 3 2.1 Waldek Hebisch’s Yet another integration test . 3 2.2 Elementary Algebraic integrals . 3 2.3 Sam Blake’s IntegrateAlgebraic function Test . 4 2.4 LITE CAS integration tests . 4 3 Note on build system 5 3.1 My PC during running the tests . 5 4 my cheat sheet notes 6 4.1 Fricas . 6 4.2 sympy . 14 4.3 sagemath hints . 21 4.4 Trying rubi in sympy . 21 4.5 build logs . 23 These reports and the web pages themselves were written in LATEX using TeXLive distribution and compiled to HTML using TeX4ht. 1 FULL CAS integration tests These reports show the result of using full CAS test suite on different CAS’s at same time. This compares how one CAS perform against another. The test suite uses the full Rubi test files provided thanks to Albert Rich. 1. Summer 2021 build Completed. Started May 15, 2021, finished July 28, 2021. Uses Rubi 4.16.1 input data. Number of integrals [71,994]. With grading for all CAS systems except for Mupad. Eight CAS systems were tested : Rubi 4.16.1, Mathematica 12.3, Maple 2021.1, Maxima 5.44, Fricas 1.3.7, Sympy 1.8 under Python 3.7.9, Giac/XCAS 1.7 and Mupad/Matlab 2021a and Sagemath 9.3. 2 3 Maxima, Fricas and Giac were used from within Sagemath 9.3 interface. 2. April 2020 build Started March 9, 2020, Completed April 6, 2020. Uses Rubi 4.16.1 input data. Number of integrals [71,994]. With grading for all CAS systems. CAS systems used are : Rubi 4.16.1, Mathematica 12.1, Maple 2020, Maxima 5.43, Fricas 1.3.6, Sympy 1.5, Giac/XCAS 1.5 and Sagemath. 3. December 2018 build. Number of tests completed [28,425]. Completed December 16, 2018. CAS systems used are : Rubi 4.15.2, Mathematica 11.3, Maple 2018, Maxima 5.41, Fricas 1.3.3, Sympy 1.1.1, Giac/XCAS 1.4.9, SageMath version 8.3 and Rubi in Sympy implemetation (port of Rubi to Sympy) Sympy 1.3 was used in this test for both Sympy itself and for Rubi in Sympy. 2 Specialized integration tests 2.1 Waldek Hebisch’s Yet another integration test Completed on Sept 15, 2021 This report uses the integrals provided thanks to Waldek Hebisch taken from this sci.math.sym- bolic post The Number of integrals is [10,335]. With grading for all CAS systems except for Mupad. These CAS systems were tested : Rubi 4.16.1, Mathematica 12.3.1, Maple 2021.1, Maxima 5.45, Fricas 1.3.7, Sympy 1.8 under Python 3.7.9, Giac/XCAS 1.7 and Mupad/Matlab 2021a and Sage- math 9.4. Maxima, Fricas and Giac were used from within Sagemath 9.4 interface. 2.2 Elementary Algebraic integrals September 2021 version Number of integrals [22,622]. With grading for all CAS systems except for Mupad. Nine CAS systems were tested : Rubi 4.16.1, Mathematica 12.3.1, Maple 2021.1, Maxima 5.44, Fricas 1.3.7, Sympy 1.8 under Python 3.7.9, Giac/XCAS 1.7 and Mupad/Matlab 2021a and Sagemath 9.3 and IntegrateAlgebraic under Mathematica 12.3.1 on windows 10. Maxima, Fricas and Giac were used from within Sagemath 9.3 interface. 4 2.3 Sam Blake’s IntegrateAlgebraic function Test IntegrateAlgebraic test problems Finished August 26, 2021. This test Uses IntegrateAlgebraic test suite provided thanks to Sam Blake. Number of integrals [3,154]. With grading for all CAS systems except for Mupad. Nine CAS systems were tested : Rubi 4.16.1, Mathematica 12.3.1, Maple 2021.1, Maxima 5.44, Fricas 1.3.7, Sympy 1.8 under Python 3.7.9, Giac/XCAS 1.7 and Mupad/Matlab 2021a and Sagemath 9.3 and IntegrateAlgebraic under Mathematica 12.3.1 on windows 10. Maxima, Fricas and Giac were used from within Sagemath 9.3 interface. 2.4 LITE CAS integration tests These reports show the result of using same test suite on different versions of same CAS. Only Maple, Mathematica and Rubi are used. This is for regression testing to find how different version of the same CAS improved over the years. The test suite used is the lite version of the full CAS intergation tests. It contains smaller number of integrals compared to the full test suite used above. 1. Mathematica This zip file contains the raw input tests used which was obtained from Rubi website. 2. Rubi Uses same zip file as above for input. 3. Maple This zip file contains the raw input tests used which was obtained from Rubi website. 5 3 Note on build system The following diagram gives a high level view of the current test build system. Mathematica script Result table POST PROCESSOR PROGRAM Rubi script Result table Result table Test files from Maple script Program that Albert Rich Rubi generates the web site Python script to run sympy Result table Latex report PDF using input Latex report Sam Blake from the test file Matlab script for Mupad/Symbolic toolbox Result table result tables Waldek HTML Hebisch test Script to run IntegrateAlgebraic Result table file Giac Result table SageMath/Python Fricas Result table script to test SageMath Maxima, Fricas, Giac Maxima Result table One record (line) per one integral result. The line is CSV comma separated. This is description of each record 1. integer, the problem number. 2. integer. 0 for failed, 1 for passed, -1 for timeout, -2 for CAS specific exception. (this is not the grade field) 3. integer. Leaf size of result. 4. integer. Leaf size of the optimal antiderivative. High level overview of the CAS 5. number. CPU time used to solve this integral. 0 if failed. 6. string. The integral in Latex format independent integration test 7. string. The input used in CAS own syntax. build system 8. string. The result (antiderivative) produced by CAS in Latex format 9. string. The optimal antiderivative in Latex format. 10. integer. 0 or 1. Indicates if problem has known antiderivative or not 11. String. The result (antiderivative) in CAS own syntax. 12. String. The grade of the antiderivative. Can be “A”, “B”, “C”, or “F” Nasser M. Abbasi The following field present only in Rubi and Mathematica Tables May 11, 2021 13. integer. 1 if result was verified or 0 if not verified. The following fields present only in Rubi Tables 14. integer. Number of rules used. 15. integer. Integrand leaf size. 16. real number. Ratio of field 14 over field 15 17. integer. 1 if result was verified or 0 if not verified. 18. String of form “{n,n,..}” which is list of the rules used by Rubi 3.1 My PC during running the tests I really need a faster PC with much more RAM ! 6 This below shows example of CAS suddenly consuming all RAM in PC, and I had to terminate the process, since it did not time out as instructed, and just hanged. 4 my cheat sheet notes 4.1 Fricas Home page https://fricas.github.io/index.html To install fricas on Linux Manjaro sudo pacman -S sagemath. in case of error while installing the package, try sudo pacman -Rs sagemath and then repeat the previous command If copy paste does not work between windows and Linux VBox, try VBoxClient --clipboard To use Fricas online, go to http://fricas-wiki.math.uni.wroc.pl/SandBox Go to bottom of page, type \begin{axiom} setSimplifyDenomsFlag(true) 7 integrate(sin(x),x) \end{axiom} Then click the preview button to send email to supprt group use [email protected] To download go to https://sourceforge.net/projects/fricas To installl on Linux Manjaro, type yay -S fricas . Do not use the Manjaro GUI package manager, it always gives build error for some reason. Make sure to install yay first using GUI manager. Make sure when installing Linux on VBox, to add second CPU to configuration of VBox. i.e. do not use ONE CPU (which is default). There is a bug in fricas installation which makes it fail due to use of multi-threading if only one CPU exist. This should be fixed in future, but just in case. To install directly, see http://fricas.sourceforge.net/doc/INSTALL.txt To build directly (but I use yay now and not this any more) #install sbcl #sudo apt-get install sbcl #do not use this. bug sudo apt-get install clisp #This lisp works sudo apt-get install dvipng sudo apt-get install auctex bzip2 -dk fricas-1.3.2-full.tar.bz2 tar -xf fricas-1.3.2-full.tar Now build it make clean fricas-1.3.2>./configure --with-lisp=/usr/bin/clisp checking build system type... x86_64-linux-gnu checking host system type... x86_64-linux-gnu checking target system type... x86_64-linux-gnu checking for make... make checking for gcc... gcc checking whether the C compiler works... yes checking for C compiler default output file name... a.out checking for suffix of executables... checking whether we are cross compiling... no checking for suffix of object files... o checking whether we are using the GNU C compiler... yes checking whether gcc accepts -g... yes checking for gcc option to accept ISO C89..
Recommended publications
  • CAS (Computer Algebra System) Mathematica

    CAS (Computer Algebra System) Mathematica

    CAS (Computer Algebra System) Mathematica- UML students can download a copy for free as part of the UML site license; see the course website for details From: Wikipedia 2/9/2014 A computer algebra system (CAS) is a software program that allows [one] to compute with mathematical expressions in a way which is similar to the traditional handwritten computations of the mathematicians and other scientists. The main ones are Axiom, Magma, Maple, Mathematica and Sage (the latter includes several computer algebras systems, such as Macsyma and SymPy). Computer algebra systems began to appear in the 1960s, and evolved out of two quite different sources—the requirements of theoretical physicists and research into artificial intelligence. A prime example for the first development was the pioneering work conducted by the later Nobel Prize laureate in physics Martin Veltman, who designed a program for symbolic mathematics, especially High Energy Physics, called Schoonschip (Dutch for "clean ship") in 1963. Using LISP as the programming basis, Carl Engelman created MATHLAB in 1964 at MITRE within an artificial intelligence research environment. Later MATHLAB was made available to users on PDP-6 and PDP-10 Systems running TOPS-10 or TENEX in universities. Today it can still be used on SIMH-Emulations of the PDP-10. MATHLAB ("mathematical laboratory") should not be confused with MATLAB ("matrix laboratory") which is a system for numerical computation built 15 years later at the University of New Mexico, accidentally named rather similarly. The first popular computer algebra systems were muMATH, Reduce, Derive (based on muMATH), and Macsyma; a popular copyleft version of Macsyma called Maxima is actively being maintained.
  • Axiom / Fricas

    Axiom / Fricas

    Axiom / FriCAS Christoph Koutschan Research Institute for Symbolic Computation Johannes Kepler Universit¨atLinz, Austria Computer Algebra Systems 15.11.2010 Master's Thesis: The ISAC project • initiative at Graz University of Technology • Institute for Software Technology • Institute for Information Systems and Computer Media • experimental software assembling open source components with as little glue code as possible • feasibility study for a novel kind of transparent single-stepping software for applied mathematics • experimenting with concepts and technologies from • computer mathematics (theorem proving, symbolic computation, model based reasoning, etc.) • e-learning (knowledge space theory, usability engineering, computer-supported collaboration, etc.) • The development employs academic expertise from several disciplines. The challenge for research is interdisciplinary cooperation. Rewriting, a basic CAS technique This technique is used in simplification, equation solving, and many other CAS functions, and it is intuitively comprehensible. This would make rewriting useful for educational systems|if one copes with the problem, that even elementary simplifications involve hundreds of rewrites. As an example see: http://www.ist.tugraz.at/projects/isac/www/content/ publications.html#DA-M02-main \Reverse rewriting" for comprehensible justification Many CAS functions can not be done by rewriting, for instance cancelling multivariate polynomials, factoring or integration. However, respective inverse problems can be done by rewriting and produce human readable derivations. As an example see: http://www.ist.tugraz.at/projects/isac/www/content/ publications.html#GGTs-von-Polynomen Equation solving made transparent Re-engineering equation solvers in \transparent single-stepping systems" leads to types of equations, arranged in a tree. ISAC's tree of equations are to be compared with what is produced by tracing facilities of Mathematica and/or Maple.
  • Using Computer Programming As an Effective Complement To

    Using Computer Programming As an Effective Complement To

    Using Computer Programming as an Effective Complement to Mathematics Education: Experimenting with the Standards for Mathematics Practice in a Multidisciplinary Environment for Teaching and Learning with Technology in the 21st Century By Pavel Solin1 and Eugenio Roanes-Lozano2 1University of Nevada, Reno, 1664 N Virginia St, Reno, NV 89557, USA. Founder and Director of NCLab (http://nclab.com). 2Instituto de Matemática Interdisciplinar & Departamento de Didáctica de las Ciencias Experimentales, Sociales y Matemáticas, Facultad de Educación, Universidad Complutense de Madrid, c/ Rector Royo Villanova s/n, 28040 – Madrid, Spain. [email protected], [email protected] Received: 30 September 2018 Revised: 12 February 2019 DOI: 10.1564/tme_v27.3.03 Many mathematics educators are not aware of a strong 2. KAREL THE ROBOT connection that exists between the education of computer programming and mathematics. The reason may be that they Karel the Robot is a widely used educational have not been exposed to computer programming. This programming language which was introduced by Richard E. connection is worth exploring, given the current trends of Pattis in his 1981 textbook Karel the Robot: A Gentle automation and Industry 4.0. Therefore, in this paper we Introduction to the Art of Computer Programming (Pattis, take a closer look at the Common Core's eight Mathematical 1995). Let us note that Karel the Robot constitutes an Practice Standards. We show how each one of them can be environment related to Turtle Geometry (Abbelson and reinforced through computer programming. The following diSessa, 1981), but is not yet another implementation, as will discussion is virtually independent of the choice of a be detailed below.
  • Addition and Subtraction

    Addition and Subtraction

    A Addition and Subtraction SUMMARY (475– 221 BCE), when arithmetic operations were per- formed by manipulating rods on a flat surface that was Addition and subtraction can be thought of as a pro- partitioned by vertical and horizontal lines. The num- cess of accumulation. For example, if a flock of 3 sheep bers were represented by a positional base- 10 system. is joined with a flock of 4 sheep, the combined flock Some scholars believe that this system— after moving will have 7 sheep. Thus, 7 is the sum that results from westward through India and the Islamic Empire— the addition of the numbers 3 and 4. This can be writ- became the modern system of representing numbers. ten as 3 + 4 = 7 where the sign “+” is read “plus” and The Greeks in the fifth century BCE, in addition the sign “=” is read “equals.” Both 3 and 4 are called to using a complex ciphered system for representing addends. Addition is commutative; that is, the order numbers, used a system that is very similar to Roman of the addends is irrelevant to how the sum is formed. numerals. It is possible that the Greeks performed Subtraction finds the remainder after a quantity is arithmetic operations by manipulating small stones diminished by a certain amount. If from a flock con- on a large, flat surface partitioned by lines. A simi- taining 5 sheep, 3 sheep are removed, then 2 sheep lar stone tablet was found on the island of Salamis remain. In this example, 5 is the minuend, 3 is the in the 1800s and is believed to date from the fourth subtrahend, and 2 is the remainder or difference.
  • A Simplified Introduction to Virus Propagation Using Maple's Turtle Graphics Package

    A Simplified Introduction to Virus Propagation Using Maple's Turtle Graphics Package

    E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package A simplified introduction to virus propagation using Maple's Turtle Graphics package Eugenio Roanes-Lozano Instituto de Matemática Interdisciplinar & Departamento de Didáctica de las Ciencias Experimentales, Sociales y Matemáticas Facultad de Educación, Universidad Complutense de Madrid, Spain Carmen Solano-Macías Departamento de Información y Comunicación Facultad de CC. de la Documentación y Comunicación, Universidad de Extremadura, Spain Eugenio Roanes-Macías Departamento de Álgebra, Universidad Complutense de Madrid, Spain [email protected] ; [email protected] ; [email protected] Partially funded by the research project PGC2018-096509-B-100 (Government of Spain) 1 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package 1. INTRODUCTION: TURTLE GEOMETRY AND LOGO • Logo language: developed at the end of the ‘60s • Characterized by the use of Turtle Geometry (a.k.a. as Turtle Graphics). • Oriented to introduce kids to programming (Papert, 1980). • Basic movements of the turtle (graphic cursor): FD, BK RT, LT. • It is not based on a Cartesian Coordinate system. 2 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package • Initially robots were used to plot the trail of the turtle. http://cyberneticzoo.com/cyberneticanimals/1969-the-logo-turtle-seymour-papert-marvin-minsky-et-al-american/ 3 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package • IBM Logo / LCSI Logo (’80) 4 E.
  • Using Xcas in Calculus Curricula: a Plan of Lectures and Laboratory Projects

    Using Xcas in Calculus Curricula: a Plan of Lectures and Laboratory Projects

    Computational and Applied Mathematics Journal 2015; 1(3): 131-138 Published online April 30, 2015 (http://www.aascit.org/journal/camj) Using Xcas in Calculus Curricula: a Plan of Lectures and Laboratory Projects George E. Halkos, Kyriaki D. Tsilika Laboratory of Operations Research, Department of Economics, University of Thessaly, Volos, Greece Email address [email protected] (K. D. Tsilika) Citation George E. Halkos, Kyriaki D. Tsilika. Using Xcas in Calculus Curricula: a Plan of Lectures and Keywords Laboratory Projects. Computational and Applied Mathematics Journal. Symbolic Computations, Vol. 1, No. 3, 2015, pp. 131-138. Computer-Based Education, Abstract Xcas Computer Software We introduce a topic in the intersection of symbolic mathematics and computation, concerning topics in multivariable Optimization and Dynamic Analysis. Our computational approach gives emphasis to mathematical methodology and aims at both symbolic and numerical results as implemented by a powerful digital mathematical tool, CAS software Received: March 31, 2015 Xcas. This work could be used as guidance to develop course contents in advanced Revised: April 20, 2015 calculus curricula, to conduct individual or collaborative projects for programming related Accepted: April 21, 2015 objectives, as Xcas is freely available to users and institutions. Furthermore, it could assist educators to reproduce calculus methodologies by generating automatically, in one entry, abstract calculus formulations. 1. Introduction Educational institutions are equipped with computer labs while modern teaching methods give emphasis in computer based learning, with curricula that include courses supported by the appropriate computer software. It has also been established that, software tools integrate successfully into Mathematics education and are considered essential in teaching Geometry, Statistics or Calculus (see indicatively [1], [2]).
  • Aldor Generics in Software Component Architectures

    Aldor Generics in Software Component Architectures

    Aldor Generics in Software Component Architectures (Spine title: Aldor Generics in Software Component Architectures) (Thesis Format: Monograph) by Michael Llewellyn Lloyd Graduate Program in Computer Science Submitted in partial fulfillment of the requirements for the degree of Masters Faculty of Graduate Studies The University of Western Ontario London, Ontario October, 2007 c Michael Llewellyn Lloyd 2007 THE UNIVERSITY OF WESTERN ONTARIO FACULTY OF GRADUATE STUDIES CERTIFICATE OF EXAMINATION Supervisor Examiners Dr. Stephen M. Watt Dr. David Jeffrey Supervisory Committee Dr. Hanan Lutfiyya Dr. Eric Schost The thesis by Michael Llewellyn Lloyd entitled Aldor Generics in Software Component Architectures is accepted in partial fulfillment of the requirements for the degree of Masters Date Chair of the Thesis Examination Board ii Abstract With the introduction of the Generic Interface Definition Language(GIDL), Software Component Architectures may now use Parameterized types between languages at a high level. Using GIDL, generic programming to be used between programming modules written in different programming languages. By exploiting this mechanism, GIDL creates a flexible programming environment where, each module may be coded in a language appropriate to its function. Currently the GIDL architecture has been implemented for C++ and Java, both object-oriented languages which support com- pile time binding for generic types. This thesis examines an implementation of GIDL for the Aldor language, an imperative language with some aspects of functional pro- gramming, particularly suited for representing algebraic types. In particular, we ex- periment with Aldors implementation of runtime binding for generic types, and show how GIDL allows programmers to use a rich set of generic types across language barriers.
  • New Method for Bounding the Roots of a Univariate Polynomial

    New Method for Bounding the Roots of a Univariate Polynomial

    New method for bounding the roots of a univariate polynomial Eric Biagioli, Luis Penaranda,˜ Roberto Imbuzeiro Oliveira IMPA – Instituto de Matemtica Pura e Aplicada Rio de Janeiro, Brazil w3.impa.br/∼{eric,luisp,rimfog Abstract—We present a new algorithm for computing upper by any other method. Our method works as follows: at the bounds for the maximum positive real root of a univariate beginning, an upper bound for the positive roots of the input polynomial. The algorithm improves complexity and accuracy polynomial is computed using one existing method (for exam- of current methods. These improvements do impact in the performance of methods for root isolation, which are the first step ple the First Lambda method). During the execution of this (and most expensive, in terms of computational effort) executed (already existent) method, our method also creates the killing by current methods for computing the real roots of a univariate graph associated to the solution produced by that method. It polynomial. We also validated our method experimentally. structure allows, after the method have been run, to analyze Keywords-upper bounds, positive roots, polynomial real root the produced output and improve it. isolation, polynomial real root bounding. Moreover, the complexity of our method is O(t + log2(d)), where t is the number of monomials the input polynomial has I. INTRODUCTION and d is its degree. Since the other methods are either linear Computing the real roots of a univariate polynomial p(x) is or quadratic in t, our method does not introduce a significant a central problem in algebra, with applications in many fields complexity overhead.
  • 1. with Examples of Different Programming Languages Show How Programming Languages Are Organized Along the Given Rubrics: I

    1. with Examples of Different Programming Languages Show How Programming Languages Are Organized Along the Given Rubrics: I

    AGBOOLA ABIOLA CSC302 17/SCI01/007 COMPUTER SCIENCE ASSIGNMENT ​ 1. With examples of different programming languages show how programming languages are organized along the given rubrics: i. Unstructured, structured, modular, object oriented, aspect oriented, activity oriented and event oriented programming requirement. ii. Based on domain requirements. iii. Based on requirements i and ii above. 2. Give brief preview of the evolution of programming languages in a chronological order. 3. Vividly distinguish between modular programming paradigm and object oriented programming paradigm. Answer 1i). UNSTRUCTURED LANGUAGE DEVELOPER DATE Assembly Language 1949 FORTRAN John Backus 1957 COBOL CODASYL, ANSI, ISO 1959 JOSS Cliff Shaw, RAND 1963 BASIC John G. Kemeny, Thomas E. Kurtz 1964 TELCOMP BBN 1965 MUMPS Neil Pappalardo 1966 FOCAL Richard Merrill, DEC 1968 STRUCTURED LANGUAGE DEVELOPER DATE ALGOL 58 Friedrich L. Bauer, and co. 1958 ALGOL 60 Backus, Bauer and co. 1960 ABC CWI 1980 Ada United States Department of Defence 1980 Accent R NIS 1980 Action! Optimized Systems Software 1983 Alef Phil Winterbottom 1992 DASL Sun Micro-systems Laboratories 1999-2003 MODULAR LANGUAGE DEVELOPER DATE ALGOL W Niklaus Wirth, Tony Hoare 1966 APL Larry Breed, Dick Lathwell and co. 1966 ALGOL 68 A. Van Wijngaarden and co. 1968 AMOS BASIC FranÇois Lionet anConstantin Stiropoulos 1990 Alice ML Saarland University 2000 Agda Ulf Norell;Catarina coquand(1.0) 2007 Arc Paul Graham, Robert Morris and co. 2008 Bosque Mark Marron 2019 OBJECT-ORIENTED LANGUAGE DEVELOPER DATE C* Thinking Machine 1987 Actor Charles Duff 1988 Aldor Thomas J. Watson Research Center 1990 Amiga E Wouter van Oortmerssen 1993 Action Script Macromedia 1998 BeanShell JCP 1999 AngelScript Andreas Jönsson 2003 Boo Rodrigo B.
  • Emacs for Aider: an External Learning System

    Emacs for Aider: an External Learning System

    Emacs For Aider: An External Learning System Jeremy (Ya-Yu) Hsieh B.Sc., University Of Northern British Columbia, 2003 Thesis Submitted In Partial Fulfillment Of The Requirements For The Degree Of Master of Science in Mathematical, Computer, And Physical Sciences (Computer Science) The University Of Northern British Columbia May 2006 © Jeremy (Ya-Yu) Hsieh, 2006 Library and Bibliothèque et 1^1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de l'édition 395 Wellington Street 395, rue Wellington Ottawa ON K1A 0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre référence ISBN: 978-0-494-28361-5 Our file Notre référence ISBN: 978-0-494-28361-5 NOTICE: AVIS: The author has granted a non­ L'auteur a accordé une licence non exclusive exclusive license allowing Library permettant à la Bibliothèque et Archives and Archives Canada to reproduce,Canada de reproduire, publier, archiver, publish, archive, preserve, conserve,sauvegarder, conserver, transmettre au public communicate to the public by par télécommunication ou par l'Internet, prêter, telecommunication or on the Internet,distribuer et vendre des thèses partout dans loan, distribute and sell theses le monde, à des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, électronique commercial purposes, in microform,et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriété du droit d'auteur ownership and moral rights in et des droits moraux qui protège cette thèse. this thesis. Neither the thesis Ni la thèse ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent être imprimés ou autrement may be printed or otherwise reproduits sans son autorisation.
  • An Introduction to the Xcas Interface

    An Introduction to the Xcas Interface

    An introduction to the Xcas interface Bernard Parisse, University of Grenoble I c 2007, Bernard Parisse. Released under the Free Documentation License, as published by the Free Software Fundation. Abstract This paper describes the Xcas software, an interface to do computer algebra coupled with dynamic geometry and spreadsheet. It will explain how to organize your work. It does not explain in details the functions and syntax of the Xcas computer algebra system (see the relevant documentation). 1 A first session To run xcas , • under Windows you must select the xcasen program in the Xcas program group • under Linux type xcas in the commandline • Mac OS X.3 click on the xcas icon in Applications You should see a new window with a menubar on the top (the main menubar), a session menubar just below, a large space for this session, and at the bottom the status line, and a few buttons. The cursor should be in what we call the first level of the session, that is in the white space at the right of the number 1 just below the session menubar (otherwise click in this white space). Type for example 30! then hit the return key. You should see the answer and a new white space (with a number 2 at the left) ready for another entry. Try a few more operations, e.g. type 1/3+1/6 and hit return, plot(sin(x)), etc. You should now have a session with a few numbered pairs of input/answers, each pair is named a level. The levels created so far are all commandlines (a commandline is where you type a command following the computer algebra system syntax).
  • The Aldor-- Language

    The Aldor-- Language

    The Aldor-- language Simon Thompson and Leonid Timochouk Computing Laboratory, University of Kent Canterbury, CT2 7NF, UK ׺ºØÓÑÔ×ÓҸк ºØ ÑÓÓÙÙº ºÙ Abstract This paper introduces the Aldor-- language, which is a functional programming language with dependent types and a powerful, type-based, overloading mechanism. The language is built on a subset of Aldor, the ‘library compiler’ language for the Axiom computer algebra system. Aldor-- is designed with the intention of incorporating logical reasoning into computer algebra computations. The paper contains a formal account of the semantics and type system of Aldor--; a general discus- sion of overloading and how the overloading in Aldor-- fits into the general scheme; examples of logic within Aldor-- and notes on the implementation of the system. 1 Introduction Aldor-- is a dependently-typed functional programming language, which is based on a subset of Aldor [16]. Aldor is a programming language designed to support program development for symbolic mathe- matics, and was used as the library compiler for the Axiom computer algebra system [8]. Aldor-- embodies an approach to integrating computer algebra and logical reasoning which rests on the formulas-as-types principle, sometimes called the Curry-Howard isomorphism [14], under which logical formulas are represented as types in a system of dependent types. Aldor and Axiom have dependent types but, as was argued in earlier papers [11, 15], because there is no evaluation within the type-checker it is not possible to see the Aldor types as providing a faithful representation of logical assertions. A number of other implementations of dependently-typed systems already exist, including Coq [13], Alfa [1] and the Lego proof assistant [10].