The Maxima Book

1 Introduction 71.1 What is Maxima? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 A Brief History of Macsyma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Available Interfaces to Maxima 102.1 The Terminal Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 The Emacs Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.1 Installing the Maxima Emacs Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Maxima-mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.3 Enhanced Terminal Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.4 Emaxima Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Xmaxima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.4 TEXmacs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.5 Other Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 The Basics - What you need to know to operate in Maxima 293.1 The Very Beginning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.1 Our first Maxima Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.2 To Evaluate or Not to Evaluate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1.3 The Concept of Environment - Theev Command . . . . . . . . . . . . . . . . . . . . . . . . 333.1.4 Clearing values from the system - thekill command . . . . . . . . . . . . . . . . . . . . . . 383.2 Common Operators in Maxima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.1 Assignment Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 Trig through Calculus 424.1 Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2 Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.3 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3.1 The assume Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3.2 Definite Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.3.3 changevar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.3.4 Behind the Black Box - Using Specific Approaches . . . . . . . . . . . . . . . . . . . . . . . 484.3.5 Other Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

[1]  M.G.R. Degrauwe,et al.  A symbolic analysis tool for analog circuit design automation , 1988, [1988] IEEE International Conference on Computer-Aided Design (ICCAD-89) Digest of Technical Papers.

[2]  T. F. Chan.  Analysis of Self-Excited Induction Generators Using Symbolic Programming , 1992 .

[3]  Richard Pavelle,et al.  MACSYMA: Capabilities and Applications to Problems in Engineering and the Sciences , 1985, European Conference on Computer Algebra.

[4]  Barbara Heller,et al.  MACSYMA for Statisticians , 1991 .

[5]  Unmeel Mehta.  Knowledge based systems for computational aerodynamics and fluid dynamics , 1986 .

[6]  T. Y. Chang,et al.  Application of symbolic method to hybrid/mixed finite elements and computer implementation , 1990 .

[7]  William B. Retallick,et al.  Solutions in closed form for a double-spiral heat exchanger , 1992 .

[8]  Ph. Tombal,et al.  MACSYMA Computation of the Dirac-Bergmann Algorithm for Hamiltonian Systems with Constraints , 1985, J. Symb. Comput..

[9]  Abhay K. Bhushan,et al.  Using MIT-Mathlab MACSYMA from MIT-DMS Muddle , 1973, RFC.

[10]  C. T. Sun,et al.  Parallel computation using boundary elements in solid mechanics , 1990 .

[11]  J. Ph. Chancelier,et al.  MACROTeX : un générateur de code LaTeX implémenté en MACSYMA , 1989 .

[12]  Raouf A. Ibrahim,et al.  Structural modal interaction with combination internal resonance under wide-band random excitation , 1988 .

[13]  Pierre Falzon,et al.  Institut national de recherche en informatique et en automatique , 1992 .

[14]  John J. Wavrik,et al.  Computer simplification of engineering systems formulas , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[15]  Rae A. Earnshaw,et al.  Theoretical Foundations of Computer Graphics and CAD , 1988, NATO ASI Series.

[16]  James A. Fabunmi,et al.  System Parameters of Output Feedback Controlled Flexible Structures , 1992 .

[17]  Bengt Mårtensson.  Automatic \TeX Code Generation from Macsyma and CTRL-C , 1986 .

[18]  Peter Wayner.  Mainframe math on a PC , 1990 .

[19]  George C. Atallah,et al.  Non-linear oscillations with multiple forcing terms , 1987 .

[20]  Aynur Unal,et al.  An algebraic criterion for the onset of chaos in nonlinear dynamical systems , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[21]  N. K. Mani,et al.  Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing , 1993 .

[22]  Allan Reiman.  Computer-aided closure of the lie algebra associated with a nonlinear partial differential equation , 1981 .

[23]  Khalid Aziz,et al.  Use of Symbolic Computation in Petroleum Engineering , 1991 .

[24]  Paul S. Wang,et al.  GI/S: A Graphical User Interface For Symbolic Computation Systems , 1987, J. Symb. Comput..

[25]  Jacques Calmet.  Computer Algebra, EUROCAM '82, European Computer Algebra Conference, Marseille, France, 5-7 April, 1982, Proceedings , 1982, EUROCAM.

[26]  Chandrajit L. Bajaj,et al.  Proving Geometric Algorithm Non-Solvability: An Application of Factoring Polynomials , 1986, J. Symb. Comput..

[27]  James Purtilo.  Polylith: An environment to support management of tool interfaces , 1985, SLIPE '85.

[28]  Bruce W. Char,et al.  ON THE DESIGN AND PERFORMANCE OF THE MAPLE SYSTEM * , 2005 .

[29]  N. E. Oussous.  Macsyma Computation of Local Minimal Realization of Dynamical Systems of which Generating Power Series are Finite , 1991, J. Symb. Comput..

[30]  Autar Kaw,et al.  Comparison of Interphase Models for a Crack in Fiber Reinforced Composite , 1992 .

[31]  Roux,et al.  Closed-form expressions for the Dirac-Coulomb radial rt integrals. , 1985, Physical review. A, General physics.

[32]  G. C. Nielsen,et al.  Use of Computer Algebra to Locate Critical Loci in Fluid Mixtures , 1990, J. Symb. Comput..

[33]  W. Hereman,et al.  Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA , 1990 .

[34]  I. Ben-Zvi,et al.  ASAP-a symbolic algebra package for accelerator design , 1991, Conference Record of the 1991 IEEE Particle Accelerator Conference.

[35]  Richard H. Rand,et al.  Topics in Nonlinear Dynamics with Computer Algebra , 1994 .

[36]  Laurent Gerbaud,et al.  On the use of Macsyma symbolic language to generate simulation softwares for the control of converter-machine drives , 2002 .

[37]  R. W. Douglass,et al.  Natural Convection Within Spherical Annuli by Symbolic Algebra , 1991 .

[38]  Patrizia Gianni.  ISSAC '88: proceedings of the international symposium on Symbolic and algebraic computation , 1988 .

[39]  Atef F. Saleeb,et al.  An efficient quadrilateral element for plate bending analysis , 1987 .

[40]  Michael R. Genesereth.  The Role of Plans in Automated Consultation , 1979, IJCAI.

[41]  D. W. Rand,et al.  ODEPAINLEVE - A MACSYMA package for painlevé analysis of ordinary differential equations , 1986 .

[42]  D. W. Pepper,et al.  Computational techniques and numerical heat transfer on PCs and workstations : presented at the Winter Annual Meeting of the American Society of Mechanical Engineers, Atlanta, Georgia, December 1-6, 1991 , 1991 .

[43]  P. Coppens,et al.  Closed‐form expressions for Fourier–Bessel transform of Slater‐type functions , 1990 .

[44]  Richard Jenks.  Scratchpad II: A computer algebra language and system , 1988 .

[45]  Erich Kaltofen,et al.  Computers and Mathematics , 1989, Springer US.

[46]  James A. Fabunmi,et al.  Feedback Gain Sensitivities of Closed-Loop Modal Parameters of Controlled Structures , 1993 .

[47]  Michael Lundh.  Using MACSYMA to Evaluate Likelihood Functions , 1986 .

[48]  Andrew M. Olson.  An object-oriented analysis model of an iconic interface to Macsyma , 1992, Proceedings Fourth International Conference on Software Engineering and Knowledge Engineering.

[49]  Clifford Goodman,et al.  American Society of Mechanical Engineers , 1988 .

[50]  Robert W. Rand.  Determinacy of degenerate equilibria with linear part x'=y, y'= 0 using ? , 1987 .

[51]  W. A. Beyer,et al.  A Steiner Tree Associated with Three Quarks , 1987, J. Symb. Comput..

[52]  N. Hemati,et al.  Automated Symbolic Derivation of Dynamic Equations of Motion for Robotic Manipulators , 1986 .

[53]  Antonio Tornambè,et al.  Dynamic modelling of flexible robot manipulators , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[54]  N. K. Mani,et al.  Analysis and Optimal Design of Spatial Mechanical Systems , 1990 .

[55]  A. Tornambe,et al.  Discrete-time modeling of flexible robots , 1990, 29th IEEE Conference on Decision and Control.

[56]  Gregory J. Reid,et al.  Reduction of systems of differential equations to standard form and their integration using directed graphs , 1991, ISSAC '91.

[57]  G. H. Gonnet.  Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC '89, Portland, Oregon, USA, July 17-19, 1989 , 1989, ISSAC.

[58]  N. E. Oussous.  Computation, on Macsyma, of the Minimal Differential Representation of Noncommutative Polynomials , 1991, Theor. Comput. Sci..

[59]  John Martin Zugel.  Prolog implementation in robot kinematics , 1985 .

[60]  Willy Hereman,et al.  Exact solitary wave solutions of coupled nonlinear evolution equations using MACSYMA , 1991 .

[61]  Bernard Mourrain,et al.  Visualization of Mathematical Surfaces: The IZIC Server Approach , 1995, J. Symb. Comput..

[62]  L. A. Skinner.  Matched asymptotic expansions of integrals , 1993 .

[63]  Mileta M. Tomovic,et al.  Computer algebra systems enhance teaching engineering technology courses , 1994, Proceedings of 1994 IEEE Frontiers in Education Conference - FIE '94.

[64]  T. C. Huang.  Machinery dynamics and element vibrations : presented at the 1991 ASME Design Technical Conferences - 13th Biennial Conference on Mechanical Vibration and Noise, September 22-25, 1991, Miami, Florida , 1991 .

[65]  Shigeki Toyama,et al.  SYMTOM: an algebraic robotic manipulator modelling program , 1990, EEE International Workshop on Intelligent Robots and Systems, Towards a New Frontier of Applications.

[66]  M. Jerosolimski,et al.  A new method for fast calculation of Jacobian matrices: automatic differentiation for power system simulation , 1993 .

[67]  Pierre Hansen,et al.  An Automated Procedure for Globally Optimal Design , 1988 .

[68]  Richard H. Rand,et al.  Computer algebra in applied mathematics: An introduction to MACSYMA , 1984 .

[69]  Yiu-Kwong Man,et al.  Computing Closed Form Solutions of First Order ODEs Using the Prelle-Singer Procedure , 1993, J. Symb. Comput..

[70]  John J. Wavrik,et al.  Computer simplification of formulas in linear systems theory , 1998, IEEE Trans. Autom. Control..

[71]  Stefan Braun,et al.  Macsyma Version 2 - systemnahe und praxisnahe Einführung mit Anwendungsbeispielen , 1995 .

[72]  Ronald E. Graham,et al.  Arrow Mode Reboost Analysis for Space Station Freedom , 1993, 1993 American Control Conference.

[73]  Stephen M. Watt.  Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, ISSAC '91, Bonn, Germany, July 15-17, 1991 , 1991, ISSAC.

[74]  Willy Hereman,et al.  The computer calculation of Lie point symmetries of large systems of differential equations , 1991 .

[75]  Structures Congress,et al.  Computer utilization in structural engineering : proceedings of the sessions related to computer utilization at Structures Congress '89, San Francisco Hilton, San Francisco, CA, May 1-5, 1989 , 1989 .

[76]  Richard J. Fateman,et al.  A Review of Macsyma , 1989, IEEE Trans. Knowl. Data Eng..

[77]  Ulf Holmberg.  Some MACSYMA Functions for Analysis of Multivariable Linear Systems , 1986 .

[78]  N. S. Rajaram.  Expert system development: current problems, future needs , 1987 .

[79]  M. Donath,et al.  The automated symbolic derivation of state equations for dynamic systems , 1988, [1988] Proceedings. The Fourth Conference on Artificial Intelligence Applications.

[80]  Stanley J. Watowich,et al.  Stability Analysis of an Optimally Controlled Light-Driven Engine , 1986, J. Symb. Comput..

[81]  O. Akhrif,et al.  Integration of symbolic and numerical processing in control engineering design , 1988, Digest of Papers. COMPCON Spring 88 Thirty-Third IEEE Computer Society International Conference.

[82]  P. W. Grant,et al.  A comparison of rule-based and algebraic approaches to the computer-aided manipulation of linear dynamic system models , 1988 .

[83]  Control Division,et al.  Sensors and controls for automated manufacturing and robotics : presented at the Winter Annual Meeting of the American Society of Mechanical Engineers, New Orleans, Louisiana, December 9-14, 1984 , 1984 .

[84]  D. Armbruster,et al.  "Perturbation Methods, Bifurcation Theory and Computer Algebra" , 1987 .

[85]  Doug Schuler.  Directions and implications of advanced computing: a report from Berkeley , 1992, SGCH.

[86]  John S. Baras,et al.  Fast error-free algorithms for polynomial matrix computations , 1990, 29th IEEE Conference on Decision and Control.

[87]  Bob Gilbert,et al.  Computer-Supported Calculus , 2002, Texts and Monographs in Symbolic Computation.

[88]  Richard J. Fateman,et al.  A MACSYMA package for the generation and manipulation of chebyshev series , 1989, ISSAC '89.

[89]  R. H. Lance.  Computer algebra and undergraduate engineering teaching , 1989, Proceedings 1989 Frontiers in Education Conference.

[90]  Robin J. Evans,et al.  Automatic control : World Congress 1993 : proceedings of the 12th Triennial World Congress of the International Federation of Automatic Control, Sydney, Australia, 18-23 July 1993 , 1994 .

[91]  Wolfram Koepf,et al.  Examples for the algorithmic calculation of formal Puisieux, Laurent and power series , 1993, SIGS.

[92]  H. Q. Tan,et al.  Optimization techniques for symbolic equation solver in engineering applications , 1990, ISSAC '90.

[93]  J. L. White.  LISP: Data is program. A tutorial in LISP , 1977 .

[94]  Jean-Philippe Chancelier,et al.  MACROTEX : a LATEX code generator in MACSYMA , 1987 .

[95]  B. Drachman,et al.  Computation of normal forms , 1990 .

[96]  Wolfram Koepf,et al.  Power Series in Computer Algebra , 1992, J. Symb. Comput..

[97]  David E. Gilsinn,et al.  Constructing Galerkin's approximations of invariant tori using MACSYMA , 1995 .

[98]  Adrian Ioinovici,et al.  Simulation of cyclically switching systems using the generalized alternor definition , 1990 .

[99]  Pete Thomas,et al.  Pitfalls and limitations of computer algebra , 1994 .

[100]  John Fitch.  Problems #3 and #4 in REDUCE and MACSYMA , 1973, SIGS.

[101]  Paul S. Wang,et al.  MACSYMA from F to G , 1985, J. Symb. Comput..

[102]  Patrick J. Roache,et al.  Using VAXIMA to Write FORTRAN Code , 1985 .

[103]  Dongming Wang.  A toolkit for manipulating indefinite summations with application to neural networks , 1991, SIGS.

[104]  Harvey Cohn,et al.  Application of symbolic manipulation to Hecke transformations of modular forms in two variables , 1987 .

[105]  N. Sreenath,et al.  DYNAMAN: A tool for manipulator design and analysis , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[106]  Michael B. Monagan,et al.  A Heuristic Irreducibility Test for Univariate Polynomials , 1992, J. Symb. Comput..

[107]  John ffitch,et al.  Symbolic computing with and without LISP , 1980, LISP Conference.

[108]  Bahattin Tiiretken.  COMPARISON OF SYMBOLIC COMPUTATION TECHNIQUES FOR PROBLEMS IN ELECTROMAGNETICS , 2000 .

[109]  Kevin Cahill.  How to use MACSYMA to write long FORTRAN codes for noncompact simulations of gauge theories , 1990 .

[110]  李幼升,et al.  Ph , 1989 .

[111]  Robert Y. Liang,et al.  Theoretical study of crack-induced eigenfrequency changes on beam structures , 1992 .

[112]  John M. Hosack.  A Guide to Computer Algebra Systems. , 1986 .

[113]  泰義 横小路,et al.  IEEE International Conference on Robotics and Automation , 1992 .

[114]  J. L. White.  LISP: Program is data. A historical perspective on MACLISP , 1977 .

[115]  Ph. Tombal,et al.  Algebraic Programming of Geometrical Calculus and Clifford Algebra , 1989, J. Symb. Comput..

[116]  L. Lizama,et al.  Conference record of the 1991 IEEE particle accelerator conference: Accelerator science and technology , 1991 .

[117]  J. A. van Hulzen,et al.  GENTRAN 90: a REDUCE package for the generation of Fortran 90 code , 1994, ISSAC '94.

[118]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[119]  Christopher I. Byrnes,et al.  Analysis and control of nonlinear systems , 1988 .

[120]  Klaus A. Hoffmann,et al.  Computation of Flowfields for Projectiles in Hypersonic Chemically Reacting Flows , 1991 .

[121]  Keller,et al.  van der Waals perturbation theory for fermion and boson ground-state matter. , 1987, Physical review. A, General physics.

[122]  Robert Hermann.  Geometric construction and properties of some families of solutions of nonlinear partial differential equations. I , 1983 .

[123]  Richard N. Fell.  Macsyma Tutorial for Calculus , 1998 .

[124]  S. Yurkovich,et al.  A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems , 1989, IEEE 1989 International Conference on Systems Engineering.

[125]  Daniel Claude,et al.  An Application of MACSYMA to Nonlinear Systems Decoupling , 1982, EUROCAM.

[126]  A. Tustin.  Automatic Control , 1951, Nature.

[127]  Sarah K. Spurgeon,et al.  Symbolic computation for dynamic sliding mode controller design , 1996 .

[128]  Karl G. Roesner,et al.  Verified solutions for parameters of an exact solution for non-Newtonian liquids using computer algebra , 1995 .

[129]  Paul S. Wang,et al.  A comparison of the Vaxima and Reduce factorization packages , 1983, SIGS.

[130]  S. Majumdar,et al.  An application of MACSYMA in solving the laminar flow of micropolar fluid in a meandering channel , 1987 .

[131]  J. L. Kulp.  Ray trajectories in a torus: An application of MACSYMA to a complex numerical computation , 1977 .

[132]  Joseph Deken.  Symbolic Computing and Statistics , 1983 .

[133]  Joel Moses,et al.  MACSYMA - the fifth year , 1974, SIGS.

[134]  Harvey Cohn,et al.  Application of Symbolic Manipulation to the Hecke Transformations of Modular Forms in Two Variables, II , 1987, J. Symb. Comput..

[135]  M. Fliess.  Nonliner control systems design 1992 : selected papers from the IFAC symposium, Bordeaux, France, 24-26 June 1992 , 1993 .

[136]  G. E. Klinzing,et al.  American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP , 1988 .

[137]  H. Benaroya,et al.  Random vibrations with MACSYMA , 1987 .

[138]  Maurice Mignotte,et al.  Inequalities about factors of integer polynomials , 1987, SIGS.

[139]  Francois LeGland,et al.  Systematic numerical experiments in nonlinear filtering with automatic fortran code generation , 1986, 1986 25th IEEE Conference on Decision and Control.

[140]  R Drew Drinkard,et al.  MACSYMA: A Program for Computer Algebraic Manipulation (Demonstrations and Analysis). , 1981 .

[141]  D. P. Schwartz,et al.  New analytical formulas for calculating magnetic field , 1988 .

[142]  Grant Keady.  FORTRAN subroutines produced from Computer Algebra systems: using GENTRANs from REDUCE and from Macsyma , 1992 .

[143]  Pedro Celis.  Remark: Corrections and Errors in John Ivie's Some MACSYMA Programs for Solving Recurrence Relations , 1984, TOMS.

[144]  L. Gerbaud,et al.  Modular approach to describe electromechanical systems-using Macsyma to generate global approach simulation software , 1992, PESC '92 Record. 23rd Annual IEEE Power Electronics Specialists Conference.

[145]  Parag A. Pathak,et al.  Massachusetts Institute of Technology , 1964, Nature.

[146]  TWO-WEEK Loan COpy,et al.  University of California , 1886, The American journal of dental science.

[147]  Paul D. Orkwis,et al.  Newton's method solver for high-speed viscous separated flowfields , 1992 .

[148]  Harry S. D. Mills.  Symbolically Precise Solutions to a Homogeneous Second Order Matrix Ordinary Differential Equation with Macsyma , 1993, J. Symb. Comput..

[149]  Paul S. Wang,et al.  An Improved Plotting Package for VAXIMA , 1985, European Conference on Computer Algebra.

[150]  G. A. Macala.  SYMBOD - A computer program for the automatic generation of symbolic equations of motion for systems of hinge-connected rigid bodies , 1983 .

[151]  J. Connor,et al.  The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points , 1984 .

[152]  Richard Pavelle.  Computer Algebra: Capabilities and Applications to Problems in Engineering and the Sciences , 1986 .

[153]  Patrick J. Roache,et al.  A new approach to grid generation using a variational formulation , 1985 .

[154]  N. Sreenath.  A hybrid computation environment for multibody simulation , 1992 .

[155]  Marie-Pierre Delest,et al.  Enumeration of Polyominoes Using Macsyma , 1991, Theor. Comput. Sci..

[156]  A. J. B. Anderson,et al.  Computer Science and Statistics: Proceedings of the Fifteenth Symposium on the Interface. , 1984 .

[157]  G. D. Gupta.  Computers in engineering 1986 : proceedings of the 1986 ASME International Computers in Engineering Conference and Exhibition, July 20-24, 1986, Chicago, Illinois , 1986 .

[158]  P. Rousseeuw,et al.  Wiley Series in Probability and Mathematical Statistics , 2005 .

[159]  James Lam,et al.  Recent Applications of Symbolic Computation in Control System Design , 1993 .

[160]  Stanly Steinberg,et al.  Using MACSYMA to Write FORTRAN Subroutines , 1986, J. Symb. Comput..

[161]  Robert D. Silverman,et al.  Finite field manipulations in Macsyma , 1989, SIGS.

[162]  Richard L. Brenner.  Simplifying Large Algebraic Expressions by Computer , 1985 .

[163]  Kevin A. Broughan,et al.  The risch algorithms of MACSYMA and SENAC , 1989, SIGS.

[164]  Hans Benker.  Ingenieurmathematik mit Computeralgebra-Systemen , 1998 .

[165]  Jeffrey F. Painter.  The matrix editor for symbolic Jacobians in ALPAL , 1992, ISSAC '92.

[166]  R. Rishel,et al.  An algorithm for a solution of a stochastic adaptive linear quadratic optimal control problem , 1985, 1985 24th IEEE Conference on Decision and Control.

[167]  Jerry F. Magnan.  A MACSYMA Program for the Multiple Bifurcation Analysis of Double-Diffusive Concection , 1989, J. Symb. Comput..

[168]  A. Noor,et al.  Computerized symbolic manipulation in structural mechanics—Progress and potential , 1979 .

[169]  J M Mansour,et al.  Simulation of the double limb support phase of human gait. , 1988, Journal of biomechanical engineering.

[170]  Exposition,et al.  Computers in engineering 1990 : proceedings of the 1990 ASME International Computers in Engineering Conference and Exposition, August 5-9 1990, Boston, Massachusetts , 1990 .

[171]  R. Rand,et al.  Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA , 1985 .

[172]  Anthony N. Palazotto,et al.  Comparison of eight variations of a higher-order theory for cylindrical shells , 1993 .

[173]  N. Vira,et al.  Use of symbolic computation in robotics education , 1992 .

[174]  John Ivie.  Some MACSYMA Programs for Solving Recurrence Relations , 1978, TOMS.

[175]  M. D. Abouzahra,et al.  Computer Algebra Applied to Radiation from Microstrip Discontinuities , 1990, J. Symb. Comput..

[176]  J. A. van Hulzen,et al.  Computer Algebra Systems Viewed by a Notorious User , 1982, EUROCAM.

[177]  Dongming Wang,et al.  Computer Aided Analysis and Derivation for Artificial Neural Systems , 1992, IEEE Trans. Software Eng..

[178]  Michael J. Wester,et al.  An extension to MACSYMA's concept of functional differentiation , 1983, SIGS.

[179]  Yue Kuen Kwok.  Application of MACSYMA to solutions of ordinary differential equations , 1991 .

[180]  M. L. Dudley,et al.  Computer-Aided Derivation of Spherical Harmonic Spectral Equations in Astrogeophysics , 1989, J. Symb. Comput..

[181]  Paul S. Wang.  Hacijan's Algorithm in VAXIMA: Improvements and Difficulties , 1982, EUROCAM.

[182]  R. J. Yamartino,et al.  An Application of Computer Algebra to a Problem in Stratified Fluid Flow , 1991, J. Symb. Comput..

[183]  Joseph M. Mansour,et al.  APPLICATION OF SIMULATION SENSITIVITY ANALYSIS TO FUNCTIONAL NEUROMUSCULAR STIMULATION OF GAIT. , 1987 .

[184]  W. A. Beyer,et al.  The Volume Common to Two Congruent Circular Cones whose Axes Intersect Symmetrically , 1987, J. Symb. Comput..

[185]  A. Tornambe,et al.  An Expert System for the Asymptotic Estimators , 1988, Proceedings of the 1988 IEEE International Conference on Systems, Man, and Cybernetics.

[186]  M. Clarkson.  MACSYMS's inverse Laplace transform , 1989, SIGS.

[187]  Jeffrey P. Golden.  Proceedings of the 1977 MACSYMA Users' Conference , 1977 .

[188]  H. K. Eldeib,et al.  Symbolic computing in computer-aided control system analysis and design , 1988, Proceedings of the IEEE 1988 National Aerospace and Electronics Conference.

[189]  Varol Akman,et al.  Geometry and Graphics Applied to Robotics , 1987 .

[190]  Sue Fitzgerald,et al.  Using a computer algebra system (Maple) to teach elementary queueing theory , 1995 .

[191]  Pierre Hansen,et al.  An analytical approach to global optimization , 1991, Math. Program..

[192]  James H. Davenport,et al.  Computer Algebra: Systems and Algorithms for Algebraic Computation , 1988 .

[193]  Robert P. Gilbert,et al.  The Use of MACSYMA for Solving Elliptic Boundary Value Problems , 1990 .

[194]  James M. Purtilo,et al.  Proceedings of the ACM SIGPLAN 85 symposium on Language issues in programming environments , 1985 .

[195]  H. K. Eldeib,et al.  Applications of symbolic manipulation in control system analysis and design , 1988, Proceedings IEEE International Symposium on Intelligent Control 1988.

[196]  Roman Maeder.  Solving boundary-value problems with perturbations , 1987, SIGS.

[197]  A. Bers,et al.  Symbolic computation of nonlinear wave interactions on MACSYMA , 1976 .

[198]  J. P. Golden.  An operator algebra for Macsyma , 1986, SYMSAC '86.

[199]  Patrick R. Palmer,et al.  24th European Conference on Power Electronics and Applications , 2021, IEEE Power Electronics Magazine.

[200]  Dongming Wang.  Differentiation and Integration of Indefinite Summations with Respect to Indexed Variables - Some Rules and Applications , 1994, J. Symb. Comput..

[201]  B. Schurmann,et al.  Computer aided investigations of artificial neural systems , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[202]  Willy Hereman,et al.  MACSYMA Program for the Painleve Test of Nonlinear Ordinary and Partial Differential Equations. , 1987 .

[203]  John Fitch,et al.  Design and Implementation of Symbolic Computation Systems , 1993, Lecture Notes in Computer Science.

[204]  Jeffrey P. Golden.  Differentiation of unknown functions in MACSYMA , 1985, SIGS.

[205]  Jesse Ira Deutsch.  Identities Arising From Hecke Transformations of Modular Forms Over Q(\surd2) and Q(\surd3) , 1993, J. Symb. Comput..

[206]  Alkesh Punjabi,et al.  Solutions of some problems in applied mathematics using MACSYMA , 1987 .

[207]  F. A. Murzia.  Syntactic properties of the refal language , 1985 .

[208]  Yvon Siret,et al.  Calcul formel : systemes et algorithmes de manipulations algebriques , 1986 .

[209]  Richard J. Fateman.  TEX output from MACSYMA-like systems , 1987, SIGS.

[210]  Toshiaki Hata,et al.  Transient Analysis of Stress Wave Penetration in a Plate Subjected to a Stress Pulse. Application of Symbolic Manipulation System to Ray Theory. , 1994 .

[211]  Anette Kolmos.  Frontiers in Education , 1990 .

[212]  Bernie Mulgrew,et al.  IEEE International Joint Conference on Neural Networks , 1999 .

[213]  Guoting Chen,et al.  The implementation of an algorithm in Macsyma: computing the formal solutions of differential systems in the neighborhood of regular singular point , 1990, ISSAC '90.

[214]  Michael Zeitz,et al.  Rule-Based Selection of Nonlinear Observer Design Methods , 1992 .

[215]  Nancy Martin,et al.  Knowledge-Based Problem Solving , 1986, IEEE Expert.

[216]  Willy Hereman,et al.  MACSYMA at CMS. Version 309.3. , 1987 .

[217]  F. A. Chedid-Helou,et al.  Mathematical modeling of wave propagation in anisotropic media , 1991 .

[218]  Joseph M. Mansour,et al.  COMPARATIVE STUDIES OF FORMULATING THE DYNAMICS OF RIGID-BODY SYSTEMS USING MACSYMA - A CASE STUDY. , 1985 .

[219]  Xinsong Jiang.  Proceedings of the 1988 IEEE International Conference on Systems, Man, and Cybernetics, August 8-12, 1988, Beijing and Shenyang, China , 1989 .

[220]  Nick Roussopoulos,et al.  Interoperability of multiple autonomous databases , 1990, CSUR.

[221]  John W. Wilkinson,et al.  Computer Science and Statistics : proceedings of the 14th Symposium on the Interface , 1983 .

[222]  Edward Tunstel,et al.  Application of Symbolic Computation in Robot Pose Error Modeling , 1990, J. Symb. Comput..

[223]  Richard J. Fateman,et al.  Characterization of VAX Macsyma , 1981, SYMSAC '81.

[224]  Carla Limongelli,et al.  Design and Implementation of Symbolic Computation Systems , 1991, Lecture Notes in Computer Science.

[225]  Antonio Tornambè,et al.  Approximate modeling of robots having elastic links , 1988, IEEE Trans. Syst. Man Cybern..

[226]  James K. Nelson,et al.  Analysis of the Non-Planar Response of a Cantilever, with the Aid of Computerized Symbolic Manipulation , 1988 .

[227]  Anthony Tzes,et al.  A symbolic manipulation package for modeling of rigid or flexible manipulators , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.