' MACSYMA Users'Conference Held at University of California Berkeley, California July 27-29, 1977 I TECH LIBRARY KAFB, NY NASA CP-2012 Proceedings of the 1977 MACSYMA Users’ Conference Sponsored by Massachusetts Institute of Technology, University of California at Berkeley, NASA Langley Research Center and held at Berkeley, California July 27-29, 1977 Scientific and TechnicalInformation Office 1977 NATIONALAERONAUTICS AND SPACE ADMINISTRATION NA5A Washington, D.C. FOREWORD The technical programof the 1977 MACSPMA Users' Conference, held at Berkeley,California, from July 27 to July 29, 1977, consisted of the 45 contributedpapers reported in.this publicationand of a workshop.The work- shop was designed to promote an exchange of information between implementers and users of the MACSYMA computersystem and to help guide future developments. I The response to the call for papers has well exceeded the early estimates of the conference organizers; and the high quality and broad ra.ngeof topics of thepapers submitted has been most satisfying. A bibliography of papers concerned with the MACSYMA system is included at the endof this publication. We would like to thank the members of the programcommittee, the many referees, and the secretarial and technical staffs at the University of California at Berkeley and at the Laboratory for Computer Science, Massachusetts Instituteof Technology, for shepherding the many papersthrough the submission- to-publicationprocess. We are especiallyappreciative of theburden. carried by .V. Ellen Lewis of M. I. T. for serving as expert in document preparation from computer-readableto camera-ready copy for several papers. This conference originated as the result of an organizing session called by Joel Moses of M.I.T. at the1976 ACM Symposium onSymbolic and Algebraic Comput- ation, at Yorktown Heights, New York, in August1976. It owes its successto his continuingencouragements and efforts, not to mention his intellectual and practical skills in keeping the MACSYMA project thriving. We wishto acknowledge the kind cooperation of ACM, ACM-SIGSAM, the Elec- tronics Research Laboratory and theDepartment of Electrical Engineeringand Computer Sciencesof the University of California, the Laboratory for Computer Science of M.I.T., NASA LangleyResearch Center, and the U.S. EnergyResearch andDevelopment Administration. We wish to extend our gratitude to the Scientific and Technical Information Programs Division.of the NASA Langley Research Center for publishing these proceedings. Richard J. Fateman,General Chairman Carl M. Andersen,Program Committee Chairman iii t OFFICERS OF THE 1977 MACSYMA USERS' CONFERENCE General Chairman: RichardFateman, University of California,Berkeley Program Chairman: Carl M. Andersen,The College of William andMary in Virginia ProgramCommittee: Mary EllenBrennan, Aerospace Corporation, Los Angeles Jo Ann Howell,Los Alamos Scientific Laboratory, University of California JohnKulp, Research Laboratory of Electronics andPlasma Fusion Center, MassachusettsInstitute of Technology Joel Moses, Laboratory for Computer Science, Massachusetts Institute of Technology Edward Ng, Jet Propulsion Laboratory, California Institute of Technology DavidStoutemyer, University of Hawaii Editosial Committee: Carl M. Andersen,The College of William and Mary in Virginia Jeffrey Golden,Laboratory for Computer Science, Massachusetts Institute ofTechnology John N. Shoosmith, NASA LangleyResearch Center Treasurer: Michael Genesereth, Harvard University and Massachusetts Institute of Technology Local Arrangements: RichardFateman, University of California,Berkeley iv PREFACE Symbolic and algebraic manipulation enables one to do exact, symbolic mathematical computations on a computer. To illustrate the difference between numeric and symbolic processing, consider a computer program (in FORTRAN, say) which, given the quantitiesA, B, and Cy can apply the quadratic formula to approximate the, roots of the quadratic equationA*x**2+B*&C = 0. The names A, By and Cy must of course correspond to numerical values at run-time. This is because the program has been written to provide numerical processing. If A had as its run-time value the expression,'I B "Qhad value "(-P*Q-1),It and C had value "P," the FORTRAN program wouldbe useless. Nevertheless, by applying the quadratic formula symbolically, the two roots [-(-P*Q-l)?SQRT(P**2*Q**2+2*P*Q+1-4*P*Q)]/(2*Q) can be represented. By further efforts, this expression can be reduced to the set of values1/Q). (P, This substitution (in this case, into the ,quadratic formula) and subsequent simpli- fication are but two of the necessary operationsan inalgebra system. Some of the more elaborate facilities that can be built up (and have been, in MACSYMA) include partial differentiation, indefinite integration, inversion of matrices with symbolic coefficients, solution of polynomial equations, and manipulation of truncated power series. The rangeof capabilities can be seen in the papers in this conference. MACSYMA is a large symbolic and algebraic manipulation system which has been under development at the Laboratory for Computer Science (formerly Project MAC) of the Massachusetts Institute of Technology since1969. The system has more than quintupled in size since the first paper describing it appeared in 1971. It is, by any measure, a rather large program, and this makes it a challenging project from many points along the computer hardware-software spectrum. Some papers on the LISP system in these proceedings address this issue. During the last several years, the community of users of the MACSYMA system has grown at an increasing rate; and because of the wide geographicalof range the ARPA computer communication network of the Defense Communication Agency, there are now users from Hawaii to Cambridge, England. Another contributing factor in the growth has been the ability of Joel Moses and his staff at the Laboratory for Computer Science to make available at relatively low cost the most versatile of algebraic manipulation systems currently implemented. Another is the synergistic effectof the community itself: where the output of one person's program may be the input to the next person's, and where nearly instantaneous feedbackon features and repair of bugs are the rule rather than the exception. Many of the users of MACSYMA (including contributors to this conference) are also using or have used other systems (ALTRAN, FORMAC, REDUCE, SAC-1, and SCRATCHPAD, to name a few) with symbolic and algebraic manipulation facilities. Many of the techniques are not specific MACSYMA, to but are alge- braic manipulation contributions independent of particular system context. Thus we view this conference as a collection of persons interested in advancing the field of inquiry in l'symbolic and algebraic manipulation," and applying the fruits of this inquiry to other areas. We believe the papers bear out this view. V I Until re cently, major funding for MACSYMA developmenthas come fromthe Advanced ResearchProjects Agency,Department of Defense,under Office of Naval ResearchContract N00014-70-0362-0006. More recentadditions to the sponsors' rankshave come fromagencies whose own personnel and contractors have used MACSYMA. Theseinclude the U.S. EnergyResearch and Development Administration, theNational Aeronautics and Space Administration, and the U.S. Navy. Combining resources to provide the unique facility of the MACSYMA Consortium,these sponsorshave provided an invaluable resource. Richard J. Fateman General Chairman vi Karney ..............377 Ament ............. 87 Kulp ...............385 Andersen ............161 Laffer ty .............347 Anderson ............ 395 Lau ................395 Avgoustis ........... 21 Lewis ..............277 Bogen ........... 11. 75 Moenck ..............225 Bulnes .............461 Moses ........... 123.275 Caviness ............253 Ng ............. 151. 177 Char .............. 53 Noor ...............161 Cohen .............275 Pavelle ........... 75. 97 Cuthill ............131 Poole ..............145 Doohovskoy ........... 473 Pridor ..............253 Fateman ..........43. 327 Rothstein ............263 Fennelly ............ 97 Spear .............. 369 Geddes .............405 Steele ........... 203. 215 Genesereth ........ 291.309 Stoutemyer .......315. 425. 447 Golden ........... 1. 109 Wahlquist ............ 71 Gosper .............237 Wang .............55. 435 Griinbaum ............491 Yun ............... 65 Gupta .............151 Zippel ..............361 Ivie ..............317 . IL CONTENTS PREFACE.................................. V AUTHOR INDEX ............................... vii 1. MACSYMA'S SYMBOLIC ORDINARY DIFFERENTIAL EQUATION SOLVER ....... 1 Jeffrey P. Golden 2. A PROGRAM FOR THE SOLUTION OF INTEGRAL EQUATIONS ........... 11 Richard A. Bogen 3. SYMBOLIC LAPLACE TRANSFORMS OF SPECIAL FUNCTIONS ........... 21 Yannis Avgoustis 4. AN IMPROVED ALGORITHM FOR THE ISOLATION OF POLYNOMIAL REAL ZEROS... 43 Richard J. Fateman 5. FLOATING POINT ISOLATION OF ZEROS OF A REAL POLYNOMIAL VIA MACSYMA. 53 Bruce W. Char 6. PRESERVING SPARSENESS IN MULTIVARIATE POLYNOMIAL FACTORIZATION .... 55 Paul S. Wang 7. ON THE EQUIVALENCE OF POLYNOMIAL GCD AND SQUAREFREE FACTORIZATION PROBLEMS ............................... 65 David Y. Y. Yun 8. DIFFERFNTIAL FORM ANALYSIS USING MACSYMA ............... 71 Hugo D. Wahlquist 9. INDICIAL TENSOR MANIPULATION ON MACSYMA ................ 75 Richard A. Bogen and Richard Pavelle 10. PURE FIELD THEORIES AND MACSYMA ALGORITHMS .............. 87 William S. Ament