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- 11.11.2010, 01:06. Chameleon в теме
«Maxima на Corum'е»
... maxima is the corruption of the main project name macsyma which stands for project mac s symbolic manipulation system mac itself is an acronym usually cited as meaning man and computer or machine aided cognition the laboratory for computer science at the massachusetts institute of technology was known as project mac during the initial development of macsyma the name macsyma is now trademarked by macsyma inc is a large computer program designed for the manipulation of algebraic expressions you can use maxima for manipulation of algebraic expressions involving constants variables and functions it can differentiate integrate take limits solve equations factor polynomials expand functions in power series solve differential equations in closed form and perform many other operations it also has a programming language that you can use to extend maxima s capabilities the dangers of computer algebra with all this marvelous capability however you must bear in mind the limitations inherent in any such tool those considering the use of computers to do mathematics particularly students must be warned that these systems are no substitute for hands on work with equations and struggling with concepts these systems do not build your mathematical intuition nor will they strengthen your core skills this will matter a great deal down the road especially to those of you who wish to break new ground in theoretical mathematics and science do not use a computer as a substitute for your basic education by the same token however proficiency with computers and computer based mathematics is crucial for attacking the many problems which literally cannot be solved by pencil and paper methods in many cases problems which would take years by hand can be reduced to seconds by powerful computers also in the course of a long derivation it is sometimes useful for those who have already mastered the fundamentals to do work in these systems as a guard against careless errors or a faster means than a table of deriving some particular result also in case of an error fixing the resulting error can often be much quicker and simpler courtesy of a mathematical notebook which can be reevaluated with the correct parameters in place but just as a computer can guard against human error the human must not trust the computer unquestioningly all of these systems have limits and when those limits are reached it is quite possible for bizarre errors to result or in some cases answers which are actually wrong to say nothing of the fact that the people who programmed these systems were human and make mistakes to illustrate the limits of computer algebra systems we take the following example when given the integral integrate 1 sqrt 2-2 cos x from x -pi 2 to pi 2 mathematica 4 1 gives with no warnings 2 log 4 2 log cos pi 8 2 log sin pi 8 which n evalutates numerically to give 1 00984 maxima 5 6 returns the integral unevaluated the commercial macsyma says the integral is divergent and maple 7 says infinity cite maxima email list here had the person who wished to learn the result blindly trusted most of the systems in question he might have been misled so remember to think about the results you are given the computer is not always necessarily right and even if it gives a correct answer that answer is not necessarily complete a brief history of macsyma the birthplace of macsyma where much of the original coding took place was project mac at mit in the late 1960s and earlier 1970s projectmac was an mit research unit which was folded into the current laboratory for computer science research support for macsyma included the advanced research projects agency arpa department of defense the us department of energy and other government and private sources the original idea first voiced by marvin minsky was to automate the kinds of manipulations done by mathematicians as a step toward understanding the power of computers to exhibit a kind of intelligent behavior the undertaking grew out of a previous effort at mitre corp called mathlab work of carl engelman and others plus the mit thesis work of joel moses on symbolic integration and the mit thesis work of william a martin the new effort was dubbed macsyma project mac s symbolic manipulator the original core design was done in july 1968 and coding began in july 1969 this was long before the days of personal computers and cheap memory initial development was centered around a single computer shared with the artificial intelligence laboratory a dec pdp-6 this was replaced by newer more powerful machines over the years and eventually the mathlab group acquired its own dec-pdp-10 mit-ml running the its operating system this machine became a host on the early arpanet predecessor to the internet which helped it gain a wider audience as the effort grew in scope and ability the general interest it created led to attempts to port the code that is to take the series of instructions which had been written for one machine and operating system and adapt them to run on another different system the earliest such effort was the running of macsyma in a maclisp environment on a ge honeywell multics mainframe another system at mit the multics environment provided essentially unlimited address space but for various reasons the system was not favored by programmers and the multics implementation was never popular the next effort came about when a group at mit designed and implemented a machine which was based on the notion that hardware support of lisp would make it possible to overcome problems that inhibited the solution of many interesting problems the lisp machine clearly had to support macsyma the largest lisp program of the day and the effort paid off with probably the best environment for macsyma to date although requiring something of an expert perspective lisp machines as well as other special purpose hardware tended to become slow and expensive compared to off-the-shelf machines built around merchant-semiconductor cpus and so the two companies that were spun off from mit symbolics inc and lmi both eventually disappeared texas instruments built a machine called the explorer bases on the lmi design but also stopped production around 1980 the idea of porting macsyma began to be more interesting and the unix based vaxima distribution which ran on a lisp system built at the university of california at berkeley for vax unix demonstrated that it was both possible and practical to run the software on less expensive systems this system franz lisp was implemented primarily in lisp with some parts written in c once the code stabilized the new version opened up porting possibilities ultimately producing at least six variations on the theme which included macsyma maxima paramax paramacs punimax aljbar and vaxima these have followed somewhat different paths and most were destined to fade into the sunset the two which survived obscurity maxima and macsyma we will discuss below punimax was actually an offshoot of maxima some time around 1994 bruno haible author of clisp ported maxima to clisp due to the legal concerns of richard petti then the owner of the commercial macsyma the name was changed to punimax it has not seen much activity since the initial port and although it is still available the ability of the main maxima distribution to compile on clisp makes further development of punimax unlikely there is a certain surprising aspect in this multiplicity of versions and platforms given how the code seemed tied to the development environment which included a unique operating system fortunately berkeley s building a replica of the maclisp environment on the mit-ml pdp-10 using tools available in almost any unix c environment helped solve this problem complicating the matter was the eventual demise of the pdp-10 and maclisp systems as common lisp resembling lisp-machine lisp influenced by bbn lisp and researchers at stanford carnegie mellon university and xerox began to take hold it seemed sensible to re-target the code to make it compatible with what eventually became the ansi common lisp standard since almost everything needed for for macsyma can be done in ansi cl the trend toward standardization made many things simpler there are a few places where the language is not standardized in particular connecting to modules written in other languages but much of the power of the system can be expressed within ansi cl it is a trend the maxima project is planning to carry on to maintain and expand on this flexibility which has emerged with all these versions in recent history there are two which have been major players due this time more to economics than to code quality 1982 was a watershed year in many respects for macsyma it marks clearly the branching of macsyma into two distinct products and ultimately gave rise to the events which have made maxima both possible and desirable mit had decided with the gradual spread of computers throughout the academic world to put macsyma on the market commercially using as a marketing partner the firm of arthur d little inc this version was sold to the symbolics inc which depending on your perspective either turned the project into a significant marketing effort to help sell their high-priced lisp machines or was a diversionary tactic to deny their competitors lmi this program at the same time mit forced uc berkeley richard fateman to withdraw the copies from about 50 sites of the vax unix and vax vms versions of macsyma that he had distributed with mit s consent until some agreement could be reached for technology transfer symbolics hired some of the mit staff to work at symbolics in order to improve the code which was now proprietary the mit-ml pdp-10 also went off the arpanet in 1983 interestingly the closing of the mit lisp and macsyma efforts was a key reason richard stallman decided to form the free software foundation between the high prices closed source code and neglecting all platforms in favor of lisp machines pressure came to bear on mit to release another version to accommodate these needs which they did with some reluctance the new version was distributed via the national energy software center and called doe macsyma it had been re-coded in a dialect of lisp written for the vax at mit called nil there was never a complete implementation at about the same time a vax unix version vaxima was put into the same library by berkeley this ran on any of hundreds of machines running the berkeley version of vax unix and through a unix simulator on vms on any vax system the doe versions formed the basis of the subsequent non-symbolics distributions the code was made available through the national energy software center which in its attempt to recoup its costs charged a significant fee 1-2k it provided full source but in a concession to mit did not allow redistribution this prohibition seems to have been disregarded and especially so since nesc disappeared perhaps it didn t recoup its costs among all the new activity centered around doe macsyma prof william schelter began maintaining a version of the code at ut austin calling his variation maxima he refreshed the nesc version with a common-lisp compatible code version there were from the earliest days other computer algebra systems including reduce camal mathlab-68 pm and altran more serious competition however did not arrive until maple and mathematica were released maple in 1985 cite list of dates and mathematica in 1988 cite wolfram website these systems were inspired by macsyma in terms of their capabilities but they proved to be much better at the challenge of building mind-share doemacsyma because of the nature of its users and maintainers never responded to this challenge symbolics successor macsyma inc having lost market share and unable to meet its expenses was sold in the summer of 1999 after attempts to find endowment and academic buyers failed cite richard petti usenet post the purchaser withdrew macsyma from the market and the developers and maintainers of that system dispersed mathematica and maple appeared to have vanquished macsyma it was at this point maxima re-entered the game although it was not widely known in the general academic public w schelter had been maintaining and extending his copy of the code ever since 1982 he had decided to see what he could do about distributing it more widely he attempted to contact the nesc to request permission to distribute derivative works the duties of the nesc had been assumed in 1991 by the energy science and technology software center which granted him virtually unlimited license to make and distribute derivative works with some minor export related caveats it was a significant breakthrough while schelter s code had been available for downloading for years this activity became legal with the release from doe granted in oct 1998 and maxima began to attract more attention when the macsyma company abruptly vanished in 1999 with no warning or explanation it left their customer base hanging they began looking for a solution and some drifted toward maxima dr schelter maintained the maxima system until his untimely death in july 2001 it was a hard and unexpected blow but schelter s obtaining the go-ahead to release the source code saved the project and possibly even the macsyma system itself a group of users and developers...
- 06.11.2010, 22:32. Chameleon в теме
... texput 5 1 maxima encountered a lisp error error in macsyma-top-level or a callee macsyma-top-level or a callee requires more than one...