COMPUTER ALGEBRA, Algorithms, Systems and Applications

COMPUTER ALGEBRA Algorithms Systems and Applications Richard Liska Ladislav Drska Jiri Limp ouch Milan Sinor Michael Wester Franz Winkler February Contents Intro duction What are algebraic calculations Why do algebraic calculations History Chronology of computer algebra systems Algorithms for algebraic computation Algebraic structures Numb er domains Algebraic expression domains Representation of algebraic structures Representation of integers Representation of p olynomials Representation of Expressions Arithmetic Numeric vs symb olic arithmetic Arithmetic of integers Arithmetic of p olynomials Simplication Canonical simplication on algebraic domains Complexity of expressions Greatest common divisor GCD of integers GCD of p olynomials with rational co ecients GCD of p olynomials with integer co ecients Resultant Solving p olynomial equations Dierentiation Summation Simple example Gosp er algorithm Examples using the Gosp er algorithm Integration Integration of rational functions Integration of elementary transcendental functions Integration examples Ordinary dierential equations Polynomial factorization Quantier elimination Integrated mathematical systems Computer algebra systems Peculiarities of programming in computer algebra systems Expression Swell An Example of Expression Swell An Example of Intermediate Expression Swell Expression Size Another Example of Intermediate Expression Swell Expression Swell Analysis Basic p ossibilities of integrated mathematical systems Axiom Numb er domains Polynomials Rational functions Solving equations Analytical op erations Matrices Graphics Derive Numb er domains Polynomials Rational functions Solving equations Analytical op erations Matrices Graphics Macsyma Numb er domains Polynomials Rational functions Solving equations Analytical op erations Matrices Co de generation Graphics Graphical presentation of formulas Maple Numb er domains Polynomials Rational functions Solving equations Analytical op erations Matrices Graphics .

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Nonlinear Evolution Equations and Solving Algebraic Systems: the Importance of Computer Algebra
- Y'M?S </#i/ ИНСТИТУТ ядерных исследований дубна Е5-89-62Ц V.P.Gerdt, N.A.Kostov, A.Yu.Zharkov* NONLINEAR EVOLUTION EQUATIONS AND SOLVING ALGEBRAIC SYSTEMS: THE IMPORTANCE OF COMPUTER ALGEBRA Submitted to International Conference "Solitons and its Applications", Dubna, August 25-27, 1989 * Saratov State University, USSR 1989 1.INTRODUCTION A wide-spread problem in the theory of nonlinear evolution equations (NEE) is to find the exact solutions of complicated algebraic systems. For example, let us consider the following evolution systems U - AU + F(U,U , ..U ), U=U(x,t)-(U1, . ,UH) , U=D1(U), D=d/dx IN 1 N-1 I /ii F«(F\ . -FH) , A==diag(A , . .A) , A *0, A *A , (i*j). The general symmetry approach to checking up the integrability and classification of integrable NEE (see the reviews [1,2] and references therein) allows to obtain the integrability conditions which are related to existence of higher order symmetries and conservation laws in a fully algorithmic way. The implementation of these algorithms in a form of FORMAC program FORMINT have been given for scalar equations (M=l in (1)) in [3 j and for the general case (M>1) in [4]. Using this program one can automatically obtain the equations in right hand side of (l) which follow from the necessary integrability conditions. The integrabiiity conditions for the right hand side with arbitrary functions have the form of systems of differential equations, the procedure of solving these equations is not generally algorithmic. But in the important particular cases when the right hand side F are polynomials and the integrability conditions are reduced to a system of nonlinear algebraic equations in coefficients of the polynomials.
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NASA Technical Memorandum 10 1578, Part One WORKSHOP on COMPUTATIONAL ASPECTS in the CONTROL of FLEXIBLE SYSTEMS Held at the Royce Hotel in WiIIiamsburg, Virginia (\!~?~-~*-lolj?d-pt-l) P&~C~L~IN~Y-F THE <UL (; 8.; t\jo~-l?~Su ~~KY,~+~JDfl~CnHPUTATIONAL ASPFCTI IY TcF --T )~uI)-- ~f'4T1.1L dC Ei'XfrLt. >Y>TtU,, f'AQT i (.\A>A- r\eu-lP>CL L an-1-y Rps~arihCentnr) 492 p C5CL 2LR UnLl ~s 55 3 G;/i3 J,'i74qA Sponsored by the NASA Langley Research Center Proceedings Compiled by Larry Taylor Table of Contents Page Introduction Computational Aspects Workshop Call for Papers 1 Workshop Organizing Committee 5 Attendance List 7 --------___-----__-------------------------------------- Needs for Advanced CSI Software NASA's Control/Structures Interaction (CSI) Program Brantley R. Hanks, NASA Langley Research Center 21-, Computational Controls for Aerospace Systems Guy Man, Robert A. Laskin and A. Fernando Tolivar Jet Propulsion Laboratory 33. Additional Software Developments Wanted for Modeling and Control of Flexible Systems Jiguan G. Lin, Control Research Corporation 4 9 Survey of Available Software Flexible Structure Control Experiments Using a Real-Time Workstation for Computer-Aided Control Engineering Michael E. Steiber, Communications Research Centre 6 7 CONSOLE: A CAD Tandem for Optimizationl-Based Design Interacting with User-Supplied Simulators Michael K.H. Fan, Li-Shen Wang, Jan Koninckx and Andre L. Tits,University of Maryland, College Park 8 9 mLPAGE IS QUALfTY ORIGINAL PAGE IS OF POOR QUALITY The Application of TSIM Software to ACT Design and Analysis of Flexible Aircraft Ian W. Kaynes, Royal Aerospace Establishment, Farnborouth 109 - Control/Structure Interaction Methods for Space Statian Power Systems Paul Blelloch, Structural Dynamics Research Corporation 121L, Flexible Missile Autopilot Design Studies with PC-MATLAB386 Michael J.
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' MACSYMA Users' Conference
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Comparative Programming Languages CM20253
We have briefly covered many aspects of language design And there are many more factors we could talk about in making choices of language The End There are many languages out there, both general purpose and specialist And there are many more factors we could talk about in making choices of language The End There are many languages out there, both general purpose and specialist We have briefly covered many aspects of language design The End There are many languages out there, both general purpose and specialist We have briefly covered many aspects of language design And there are many more factors we could talk about in making choices of language Often a single project can use several languages, each suited to its part of the project And then the interopability of languages becomes important For example, can you easily join together code written in Java and C? The End Or languages And then the interopability of languages becomes important For example, can you easily join together code written in Java and C? The End Or languages Often a single project can use several languages, each suited to its part of the project For example, can you easily join together code written in Java and C? The End Or languages Often a single project can use several languages, each suited to its part of the project And then the interopability of languages becomes important The End Or languages Often a single project can use several languages, each suited to its part of the project And then the interopability of languages becomes important For example, can you easily
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