ICM-199805-0003 - Kent State University
Contents
1. 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit SOR RRR RRR A KA Kk Select 1 11 5 Server ox mcs kent edu MAXIMA closed 5 2 Example 2 This example shows that can also handle real numbers and the constants Also it tests the supported operators sin log and sqrt HE OR OO OO KK K K KK K K KK K K KK K KK KK K KK K K K K KK K K K KK K K K OK K K KK K K FK FK KK KOK K K K K K IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit xookokoleleokotokejeedolelelekelelejoekeleleolelelelelelelelelelelelelelelelelelelejelelelolejeleketolelejeletolelejeelek Select 1 11 1 Please input your expression sin pi log e 2 sqrt 19 98 Valid input 45 special HE OO E K K K K K K K K K K K KK K K KK K K K KK K KK K K K OK KK K K K KK K K K OK K K KK K K FK OK KK K K K KK KOK IAMC Client MENU 1 Type your infix input 22. ke kk kk ke GRR kkk k kkk Select 1 11 2 Server ox mcs kent edu MAXIMA connected ke sk ok sk ok kk kk oko ok kk koe oko IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit HE OK OO E K K K RK K K K KK K KK K K KK K K K KK K KK K K K K KK K FK K KK K K K OK K K KK K K FK K KK K K K K K K K 44 Select 1 11 1 Please input your expression 19 98 241998 2 1998 1998 Valid input xookokoleleokolokeleetoleleleelelejeelelelelolelelelejelelelelelelelelelelelelelelelelelelolejelelelelelejeetelelejeelek IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit JO OR OB kk kk Select 1 11 4 d2 177481 OG KORG IAMC Client MENU
3. 1 execution produces a result which is in valid MAXIMA internal represen tation 4 The result is simplified by the function simplifya which transforms the answer and returns a valid internal representation 5 The final answer is displayed in 2 D form by displa 6 The prompt for the next C line is displayed and the cycles restarts from step 1 So when we issue the command 27 3 1 to MAXIMA after the displa func tion the output will look like C1 factor x 3 1 2 D1 X 1 X 1 The above output is useless for the IAMC Server because the structure of the output is lost The Server needs the un rendered result from MAXIMA for converting to MP data This means a slight modification to MAXIMA for the purpose of being controlled by the IAMC Server We expect a certain amount of minor modification to any existing compute engine before it can be made into a part of IAMC The following simple Lisp program newdispla 1sp does the job SowdISpIS ISD Purpose Makes maxima display prefix internal form Usage load this file into maxima 13 loadfile newdisplay lsp Author Paul 5 Wang Date 2 3 98 953 SF 93 9 3 1 9 FH 3 3 9 9 4 9 9 4 3 9 9 9 4 3 9 99 LS SF SOS SS 9 3 9 3 2 3 3 9 FH 3 99 93233 9393 in package maxima defun displa exp print BEGIN EXP 39 print exp print END EXP terpri The file newdispla ls
4. Internet 9 is the network that is changing the way people communicate interact and define community The Internet has a spirit of invention within the human community it encompasses as expressed in the tools software and hardware that are used The Internet represents a changing paradigm for human interaction It is a collaborative medium in which you can access information and data it is place for learning commerce entertainment and intensive interaction with people major purpose of the Internet is the sharing of information between universi ties companies governments nonprofit organizations and individuals At present millions of pieces of information are available on the Internet in a variety of formats but sharing of mathematical computation and data is lagging behind Some universities and organizations have mathematical computation systems ex perimental and commercial which are powerful tools for scientists engineers and educators They aim to automate mathematical computations of all sorts These tools may be general purpose such as Maple 21 MAXIMA 12 and Mathematica 32 for computer algebra or specialized such as Camal 39 for general relativity and Singular 40 for commutative algebra and algebraic geometry On the other hand almost all the powerful computation systems are only accessible directly on their host computers Usually outside users can not use these systems remotely without obtain ing
5. kkk k k IAMC Client MENU 11 Type your infix input Send MP file to Server End Session Save current exp to MP Open MP file Exit 6 8 10 New Session Send current exp to Server History Save current result to MP Help xookokoleleokolokejeetolelelekeleleleeleleleelelelelejeleleleleleleleleleleelelelelelelelolejelekelolelejeletelelejeelek Select 1 11 1 Please input your expression y 9 x 2 1 Valid input xookekolelejokololeleetolelelekeleleleelelelelelelelelelelelelelelelelelelelelelelelelelelelolelelelelolelejeelelelejeetek IAMC Client MENU 1 Type your infix input 2 New Session 3 Type your infix input Send MP file to Server 2 New Session 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 1 BER ROR OR OR aK kA sk kak a ak Select 1 11 4 d2 1 9 x72 BEC RR OR ORR A OIA IA I a AR ak ak ak a ak IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit xookokoleleokololejeetolelelekeleleleeelelejelelelelelelelelele
6. BO OR OR OR RRA KKK A k k kk Select 1 11 4 d5 1 9 x72 FOO GOR OR RR RA RK A ACK kk IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit xookokolelejokololejeetolelelekelelejeelelelejeleleleleleleleleleleeleleleleelelelelelelelolejelelelolelejelelelelejeetek Select 1 11 1 Please input your expression diff d5 x Valid input xookokolelejokelolejeetolelelekeleleleeleleleeleleleleleleleleleleeleleleleelelelelelelelolelelelelelelejeletelelejeetek IAMC Client MENU 49 11 Type your infix input 2 Send MP file to Server 4 End Session 6 Save current exp to MP 8 Open MP file 10 Exit New Session Send current exp to Server History Save current result to MP Help OR Select 1 11 4 d6 18 x 50 CHAPTER 6 Conclusion Work reported here is part of the overall IAMC effort being conducted by Wang s research group at ICM Kent This work builds an experimental client server package for a bare bones version of an IAMC system and the system does serve to prove the concept and to expose many details for furthe
7. Access to remote scientific databases Making parallel super computing accessible e Distance learning Computing via NetPC for high school or occasional users e Establishing Problem Solving Environments PSE IAMC should be convenient simple to use and easy to learn It must also leverage appropriate existing technologies to reduce R amp D and to increase the chance of wide acceptance e Internet and the Web MathML the mathematical markup language an extension to HTML e MP a binary math data encoding transfer protocol developed at ICM Kent OpenMath evolving mathematical representation and semantics specifications developed by the European Maple group and collaborators Java 10 platform independent programming system with built in network and GUI support IAMC services should be available via TCP IP 8 the Web or email The work reported here constitutes a simple proof of concept system where a simple IAMC client server pair is written in Java MP is used for mathematical data encoding and transfer and the pair provides Internet based access to the MAXIMA symbolic computation system By this experiment we hope to shed more light on the IAMC approach and to provide experience for a full blown IAMC prototype From this point on the name IAMC refers to the proof of concept system CHAPTER 2 Design of IAMC current IAMC system is bare bones version of an IAMC system and builds a
8. Proceedings 1986 Symposium on Symbolic and Algebraic Computation pp 1 6 ACM Press July 1986 MathSoft Inc MathStation Version 1 0 a computer program 201 Broad way Cambridge MA 02139 1989 Abbott J Diaz A and Sutor R S A Report on OpenMath ACM SIGSAM Bulletin pp 21 24 March 1996 Pintur D A MathEdge The Application Development Toolkit for Maple MapleTech 1 2 pp 31 38 1994 von Sydow B design of the Euromath system Euromath Bulletin 1 1 pp 39 48 1992 Diaz Kaltofen E Schmitz K Valente T Hitz M Lobo and Smyth P DSC A System for Distributed Symbolic Computation Proceedings of ISSAC 91 Bonn Germany pp 323 332 ACM Press July 1991 Dalmas 5 Ga tano and Sausse a protocol for symbolic com putation systems INRIA Technical Report 162 March 1994 3l 32 33 34 35 36 3T 38 39 40 55 Abbott J and Traverso C Specification of the POSSO External Data Rep resentation Technical report Sept 1995 Wolfram S Mathematica A System for Doing Mathematics by Computer Addison Wesley 1988 Wolfram Research Inc MathLink Reference Guide Mathematica Technical Report 1993 Bonadio A and Warren E Theorist Reference Manual Prescience Corporation 814 Castro St San Francisco CA 94114 1989 XML http www arbortext com xml SGML http www sil org sgml sgml html
9. Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit JO OR RO Select 1 11 4 kkk k k IAMC Client MENU d2 440 1 3 5 T 9 11 KEEK K K K K K K KK K K KK K K KK K K KK K KK K K FK KK K K FK K KK K K K KK K K K K K FK FKK K K FK FK KK K K K K K K Type your infix input Send MP file to Server End Session Save current exp to MP Open MP file Exit Select 1 11 1 Please input your expression sin x cos x y1 zi kk 2 integrate x 9 x 1 4 Invalid input parse stopped at sin x cos x y1 zi kk 2 integrate x 9 x 1 5 4 Example 4 6 8 10 New Session Send current exp to Server History Save current result to MP Help 47 This example is meant to show in one session how the user can do computation make variable assignment and use label representation Also it demonstrates that IAMC can do symbolic computation keep the context of one session and recognize the naming of an expression and label representation The symbolic computation operators factor integrate expand and diff will also be tested ROR IRA k kkk kk
10. Sun Micro Systems Java gained world wide acceptance with unprecedented speed It is primarily due to Java s simple yet powerful mechanisms for object oriented pro gramming OOP and network based computing two dominating trends shaping the future of the computer and information industries IAMC system chose Java as the implementing language because IAMC is based on the Internet and Java is the best networking language so far The team that designed Java was well aware that if Java was to support applications on networks it would have to support a variety of systems with a variety of CPU and operating system architectures A Java application can execute anywhere on the network or on the Internet because the compiler generates an architecture neutral object file Once a Java program is written it stays written It doesn t need to be recompiled for each different platform because Java programs are compiled into Java bytecodes that run on any computer with a Java interpreter The bytecodes are architecture and operating system independent Thus Java programs 14 can be written and compiled once and then transmitted to run anywhere Another important reason for IAMC to choose Java is that since Java is an OOP language it can be extended very easily We can add more operators and functions for the mathematical computation 2 2 IAMC Client The IAMC client acts as an interface to the user The IAMC client will read the user s input and display
11. in Stack B generate the prefix notation and push the prefix result back onto Stack B When the incoming token is push it into Stack A the special C has lowest precedence and also push it onto Stack B to mark the beginning of an expression 4 When the incoming token is all the operators before the in Stack should be popped and the associated operands in Stack B also should be popped to generate prefix notation Push the prefix result into Stack B pop up C from Stack A then look at the top operator in Stack if it is a unary operator except NEGATIVE or POSITIVE sign it will also be popped and the prefix notation is constructed 5 If the incoming token is 5 7 all the operators before the in Stack A should be popped and the associated operands in Stack B also should be popped to generate prefix notation Push the prefix result into Stack B Suppose the user inputs x 2 sin xty y z the final prefix notation will be C x 2 Csin y z 31 Figure 5 shows the steps of stack information during the prefix notation generation 2 x 2 sin x 2 sin x y sin x y i x 2 E x 2 x y sin x y z i x 2 x 2 x 2 0 sin x y y 2 Figure 5 Example of Prefix Generati
12. New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit Select 1 11 4 d2 6 469899178 5 3 Example 3 46 This example has two purposes is to show that IAMC can handle unsupported operators such as sum and get the correct answer back the other is to show how IAMC deals with user input error That is IAMC will show where it is stopped the next token is wrong in the input DE OO OO KK K K K K K K KK K K KK K KK KK K KK K K K K KK K K K KK K K K OK K K KK K K FK FK KK K K K KK K K IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit EOS OG AGORA Select 1 11 1 Please input your expression sum x 2 x x 1 10 Valid input ookekoeleokolokejeetolelelekeleleleoelelelejoleleleleleleleleleleeleleleleelelelejeleetolelelelelolelejelelelelejeetek IAMC Client MENU 1 Type your infix input 2 New Session 3
13. accounts on these machines and logging in first It is desirable to make powerful 1 mathematical and scientific computing systems accessible on the Internet as simply and easily as a Web page Some simple tools such as interactive calculators 38 exist on the Internet for limited mathematical calculation but a systematic approach for access control ex pression encoding and interoperability must be devised if complex mathematical oriented computation services are to become usable on the Internet via the client server paradigm Some existing systems such as SUI 13 can let the user connect to multiple powerful compute engines but they have the problem of platform limitation they only can be used on Unix machine The goal of Internet Accessible Mathematical Computation LAMC research is to design a system to let the user access remote mathematical computation systems based on the Internet through any computer platform machine and to let the user do numeric symbolic and other scientific computations Internet users can input their mathematical request send it to the remote mathematical computation server and get the answer back For example a user in China wants to know the factors of polynomial z 10 1 He she can use his her home PC to access the Internet by any browser and run the IAMC Client service in Kent On the IAMC Client interface the user can input the compute request and select the IAMC Server in New York which has a Mapl
14. begins with letter and followed by letter or digit Number is any digit combination including one for real numbers Some of the supported operators such as sin and factor have only one argument operand sin x y factor x 6 1 while some operators such as integrate have varied arguments operands Use the command integrate exp var to find the indefinite integral of the expression exp with respect to the variable var On the other hand integrate exp var high low will be used to find the definite integral of the expression exp with respect to the variable var from low to high 3 1 2 Recursive Descent Parsing For a given grammar there are different parsing technologies to choose from Here the IAMC Client uses Recursive Descent Parsing 14 because it is simple effective and easy to extend One approach to writing a recursive descent parser is All legal strings in the language must be derived from the start nonterminal S Hence if we can write a procedure S which matches all strings derivable from 5 24 then we are done In order to do this for each nonterminal we will construct a parsing procedure N which matches all strings derivable from N If a nonterminal N has only a single grammar rule then its parsing procedure is easy to write To match the rule we know that we need to match each grammar symbol on its right hand side RHS There are two possibilities 1 If the RHS symbol is a ter
15. data encoding and decoding on the kernel side Recently Maple introduced MathEdge 27 a development toolkit which enables developers to link their applications with the Maple kernel Beginning with version 2 Mathematica communicates using MathLink 33 Math Link implements a communication protocol and provides a set of procedural interfaces that allow C programs to send and receive data or call or be called by Mathematica or allow different instances of Mathematica to communicate with each other Math Link is fully documented and library routines are provided for advanced users to write their own applications The POSSO 31 project is one of the European research projects centered on symbolic computation It includes the definition of two protocols for exchanging mathematical expressions XDR POSSO 31 and ASAP 30 XDR POSSO is de signed to exchange POSSO data structures using a binary encoding based on the XDR technology It is strongly tied to the POSSO project and does not include annotations or a general extension mechanism to support other kinds of mathemat ical objects ASAP A Simple ASCII Protocol is more oriented towards portable exchange of mathematical expressions encoded as linearized attributed trees It pro vides a basic technology relying on the user to define the semantics of the expressions exchanged and to provide more optimized encodings when appropriate Euromath 28 another EEC funded project defines a Doc
16. data and send it back to the Client Currently the IAMC Server uses the server ox mcs kent edu which is a UNIX machine in the Department of Computer Science at Kent State University It connects to the local mathematical compute engine MAXIMA so now the IAMC Server is specific for MAXIMA 2 4 Object Oriented Design One important advantage of Java is its object orientation The OO design of the IAMC Client consists of the following classes e IAMCClient manages the IAMC Client This is the main control class It can read the user input invoke other objects and communicate with the IAMC Server e Grammar performs the grammar check and generates prefix notation expres sions e Operator represents a mathematical operator used in parsing and prefix gen eration e Operand represents a mathmatical expression used in parsing and prefix gen eration e Mp performs the conversions between MP and any other format e Prefix converts any prefix string internal representation to MP format e Menu displays the main menu of IAMC Client 18 e Help provides all help information e History displays the history of user inputs e SendMP send the MP data including ending marker to server e WriteToFile stores the MP data coming from the server to an MP file ex cluding the ending marker e ArbCell ArbList ArbStack are generic container classes from Wang s Java book 7 They are excellent examples of generic
17. mathematical expressions at the application level 13 IAMC Wang s research group at the Institute for Computation Mathematics at Kent State University and collaborators including Prof Dieter Schmidt Electrical and Computer Engineering Cincinnati Prof Simon Gray Mathematics and Computer Science Ashland and Prof Norbert Kajler Ecole des Mines de Paris France are involved with the conceptualization architecture design and prototyping of Internet Accessible Mathematical Computation The goal simply put is that on the Internet a user should be able to access mathematical computation services directly It should be as simple and easy as accessing a Web page or sending email The IAMC research has these goals e To make math oriented data and services easily accessible on the Internet directly via the Web and by email allow remote compute servers usable almost like local programs enable effective and efficient communication of mathematical data over the Internet e To make it possible for heterogeneous compute servers to exchange computa tional results and perform further computation on them evolving IAMC architecture calls for an IAMC client to provide a GUI front end an IAMC server to provide or connect to a computation service and a Mathematical Computation Protocol MCP to connect the client and server IAMC applications may include e Use of remote computation services
18. reusable codes IAMC Client uses the ArbStack class for generating prefix notation The IAMC Server is relative simple It has only two classes e IAMCServer serves as the main control class to perform communications with IAMC Client and the actual compute engine e WriteToFile reuse writes the MP data coming from the client to an MP file Figure 4 shows the relation of these classes With the above described OO design it is very easy and clear to extend the existing functions For example if one wants to extend the grammar rule he she only needs to extend the Grammar class If a new operator has more information one can simply extend the Operator class 19 Grammar Check Internal Internal Representation Representation IAMC Server Figure 3 Flow of Computation Request ArbStack ArbCell WriteToFile SendMP Figure 4 IAMC Classes IAMCClient 7 JIAMCServer WriteToFile 20 CHAPTER 3 IAMC Client This chapter will show the details of how the IAMC Client part is implemented It will emphasize the input parsing part the conversion between ASCII and MP and the interface to Server also will be described 3 1 Parsing The IAMC Client receives mathematical expressions and commands from the user The input is parsed and converted to MP form by a simple recursive descent parser with a grammar that supports integer and floating numbers identifiers special mathematical constants mathemat
19. the RHS is identical to the LHS nonterminal Hence after a directly left recursive rule has been selected the first action of the corresponding parsing procedure will be to call itself immediately without consuming any of the input It should be clear that such a recursive call will never terminate Hence a recursive descent parser cannot be written for a grammar which contains such directly or indirectly left recursive rules in fact the grammar cannot be LL 1 in the presence of such rules Fortunately it is possible to transform the grammar to remove left recursive rules Consider the left recursive nonterminal A defined by the following rules alpha beta where alpha is nonempty and alpha and beta stand for any sequence of terminal and nonterminal grammar symbols Looking at the above rules it is clear that any string derived from A must ultimately start with beta After the beta the rest of the string must either be empty or consist of a sequence of one or more alpha s Using a new nonterminal A to represent the rest of the string we can represent the transformed grammar as follows 26 beta A empty alpha The above rules are not left recursive 3 1 3 IAMC Math Expression Grammar The most important issue for using recursive descent parsing technology is to remove left recursive rules In the mathematical expression rules there are many left recursive rules such as expression exp
20. the output to the user After the IAMC Client gets the user s Fortran like infix mathematical expression input it will perform a grammar check that is parse the input and tell the user whether the parse is successful or not When the user wants to send the request to the remote IAMC Server IAMC will translate the parsed data to MP format open a TCP IP socket to send the MP data to the IAMC Server according to its name and port number and wait for the answer from the IAMC Server In general the result can be mathematical expressions in MP format help information in HTML 2D or 3D plots in gif or other well defined information formats experiment here focuses on results in MP format answer returned by the server is then displayed for the user The IAMC client uses a simple MP to converter which displays the result in infix form This converter can be extended to convert MP to prefix notation MathML or even BIFX Future work can add a nice GUI front end for the IAMC client Figure 3 shows the flow of one computation request The connection between the IAMC Server and Client is session based Once the user opens a new session to an IAMC Server the IAMC Client is connected to that particular IAMC Server The user can send as many requests as he she wants to the IAMC Server After the user closes the session the connection between the IAMC 15 Client and Server is gone there is no context saved for the server af
21. 14 Recursive Descent Parsing http opal cs binghamton edu zdu 15 Ion and Miner Mathematical Markup Language W3C Working Draft January 6 1998 53 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 54 Aho V Sethi R and Ullman J D Compilers Principles Techniques and Tools Addison Wesley Publishing ISBN 0 201 10088 6 1985 Smith C J and Soiffer M MathScribe A User Interface for Computer AI gebra Systems Proceedings 1986 Symposium on Symbolic and Algebraic Com putation pp 7 12 ACM Press 1986 Arnon D Waldspurger McIsaac CaminoReal User Manual Version 1 0 Technical Report CSL 87 5 Xerox PARC 1987 Paracomp Inc Milo User s Guide 123 Townsend St Suite 310 San Francisco CA 94107 1988 Purtilo J M Polylith An Environment to Support Management of Tool Interfaces ACM Sigplan Notice 20 7 12 18 July 1985 Char B W Geddes O Gonnet H Leong B L Monagan M Watt S M Maple V Language Reference Manual Springer Verlag ISBN 0 387 97622 1 1991 Jenks D and Sutor the Scientific Computation System Springer Verlag 1992 Genesereth M R An Automated Consultant for MACSYMA Proceedings 1977 MACSYMA Users Conference pp 309 314 1977 Leong B Iris Design of an User Interface Program for Symbolic Algebra
22. C client on one end and controls an external compute engine on the other end The IAMC server has two parts e The part that deals with the IAMC client is generic e The part that controls the external compute engine is specific to the engine The interface to IAMC Client is generic All the IAMC Servers should have common responsibilities IAMC Server must have a specific IP address and port number and should always be listening for a connection from the IAMC Client IAMC Server should be able to access the actual mathematical compute engine not do computation itself otherwise it is just another on line calculator Because the data communication between IAMC Client and IAMC Server uses MP all the IAMC servers should support MP architecture The part which controls the external compute engine is specific to the actual engine IAMC Server acts as an adapter for the particular compute engine so the IAMC Server must be able to convert the MP data to the appropriate format as input for that particular compute engine For example for MAXIMA the request for getting the factors of polynomial 272 472 is the command factor x 2 y 2 So an IAMC Server must understand its compute engine s language and know how to start the engine how to feed the input and in what format how to get the answers 17 and how to terminate the engine Lastly after the Server obtains the answers from the compute engine it will convert it to MP
23. E ds 35 4 1 Interface to IAMC 35 4 2 The Compute 36 43 Interface to Compute 37 4 4 Server Client Communication 40 5 IAMC Usage 44 ad Bxample e seiste a se RE oe 8 ot 4 5 dete 44 MAIO PD 45 a etatis en uei 46 gA B Beene db ERE WU ed 47 51 BIBLIOGRAPHY 53 LIST FIGURES structure of AMG eeu t ea 11 Programming Contributions 12 Flow of Computation Request 19 18 101080 rc EO ene 2 20 Example of Prefix Generating 31 Java Exec Method 32 Interface to Compute 43 1 LIST OF TABLES IAMC Supported Operators vi Acknowledgements I would especially like to thank my advisor Dr Paul Wang for his direction advice and guidance on this research I would also like to thank Dr Robert Walker and Dr Hassan Peyravi for their suggestion and comments on this project Also I would like to thank Benjamin Norman for his help on editing my thesis vil CHAPTER 1 Introduction 11 Motivation
24. HTML http www w3 org TR Calculators http www sci lib uci edu HSG RefCalculators html Fitch J CAMAL User s Manual University of Cambridge Computer Labo ratory 2nd edition 1983 Greuel G M Pfister G and Sch nemann Singular Reference Manual Reports On Computer Algebra number 12 Centre for Computer Algebra Uni versity of Kaiserslautern May 1997
25. IST TABLES NM Lc vi Acknowledgements vii L ctu fom Daas eo mets we mene SB eene 1 LL Motivations oe q acies e ce ea a Exe 1 1 2 Previous Work dese Pe ok Be we Ee ee Rem 2 Js TAMO esr roe oh E el T 2 Desin of IAM Comen e ee peo ae ln ect 10 2 1 Overview of IAMC System 10 2 25 TAMO C Bent oela topte e e RES ER 14 2 3 TAMO Server n Re ROUND ds MEE 16 2 4 Object Oriented 17 By Clhent iu sg eU t a bk bI UE EU CAS 21 Sut cost ut re 21 sou drca gre ded es 21 3 1 2 Recursive Descent 23 3 1 8 IAMC Math Expression Grammar 26 Gud gegen qi o cade oet dee d 28 iii 3 1 5 Internal 28 3 1 6 Prefix Notation Generation 29 3 2 ASCII MP Conversions 7 Rh 32 3 2 1 Prefix to MP 32 3 2 2 to ASCII Conversions 33 3 3 Interface to IAMC 33 As Server T Due cR Sine Bla deere ae see ee RS heure
26. Wei Wu M S May 1998 COMPUTER SCIENCE EXPERIMENTS WITH INTERNET ACCESSIBLE MATHEMATICAL COMPUTATION 55 pp Director of Thesis Dr Paul 5 Wang The goal of Internet Accessible Mathematical Computation research is to design a system to let the user access remote mathematical computation systems based on the Internet through any computer platform machine and to let the user do numeric symbolic and other scientific computations Internet users can input their mathematical request send it to the remote mathematical computation server and get the answer back work here constitutes a simple proof of concept system where a simple IAMC client server pair is written in Java MP is used for mathematical data encoding and transfer and the pair provides Internet based access to the MAXIMA symbolic computation system By this experiment we hope to shed more light on the IAMC approach and to provide experience for a full blown IAMC prototype EXPERIMENTS WITH INTERNET ACCESSIBLE MATHEMATICAL COMPUTATION A thesis submitted to Kent State University in partial fulfillment of the requirements for the degree of Master of Science by Wei Wu May 1998 Thesis written by Wei Wu 5 Kent State University 1998 Approved by Advisor Chair Department of Mathematics and Computer Science Dean College of Arts and Sciences ii TABLE OF CONTENTS LIST OF FIGURES 6 2 a SR RO qe M H
27. conf This way the server does not have to set up its own socket but just uses standard I O instead This is because inetd will arrange a stream socket connection with the incoming client redirect standard I O to the stream socket then fork the IAMC Server 48 IAMC Client MP Expression Engine Interface MP to Engine Engine to MP Converter Converter Compute Engine Figure 7 Interface to Compute Engine CHAPTER 5 IAMC Usage Examples The IAMC system is an ASCII menu driven application The following exam ples show the actual scripts of using IAMC for several computations Each example demonstrates a different aspect of the IAMC system 5 1 Example 1 The purpose of this example is to demonstrate the menu of IAMC Client and how to connect with IAMC Server Also it shows how the operator precedence issue can be correctly recognized and the correct answer of numeric computation can be obtained from the IAMC Server DE OR OO OO K K KK KK K K KK K K KK K KK K K K KK K K FK K KK K K K KK K K K K K K RK K K FK OR KK KOK K K K K K IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit ke sk ok sk ok sk
28. e compute engine After the user inputs his her request the request will be sent to New York The answer will come back from New York and will be displayed on the China user s home PC screen 1 2 Previous Work Sharing mathematical computation and data is not a new problem for scientific computing There are different sub areas for this problem Firstly sharing mathematical computation and data requires a mathematical user interface which handles the user input parses the input and acts as a client to the computation server A well designed user interface not only makes a computing system more appealing and convenient to use but also increases the computation power provided to the user Different aspects of the user interface problem have been successfully addressed by different realizations Two dimensional editing of mathematical formulas is achieved in experimental systems such as MathScribe 17 GI S 5 or SUI 1 and in recent mathematical assistants such as Milo 19 and Theorist 34 some kinds of hypertex tual access to the documentation is provided by the graphical user interfaces of both Mathematica and Axiom 22 Also quality curve and surface plotting is performed by Axiom Maple V Mathematica and SUI important objective of improving these components is to have all these fa cilities gathered in a single software environment and to make such an environment independent of a given product or system Also few user inte
29. e information into the s besides the operator name There are two reasons that we chose prefix as internal representation Firstly it is very close to MP data format MP parses all data in the form of annotated parse trees All data are exchanged as linearized annotated parse trees A linearized version of the annotated tree is formed from a prefix parse of the tree Node packets are distinguished from annotation packets by their position in the stream of packets second reason we chose prefix as our internal representation is that it is very easy to implement the 2 D display the prefix representation makes it easy to separate the operator and operands 3 1 6 Prefix Notation Generation All operators have a pre assigned operator precedence 16 The operator has higher precedence than operator and operator operator and have higher precedence than operator and operator all the other operators have the highest precedence and are treated as unary operators To generate prefix notation two stacks A and B are used Stack A holds operators stack B holds operands The following action rules are used in parsing and generating prefix notation 30 1 An incoming operand is pushed onto Stack B 2 If the incoming operator has higher precedence than the top operator s prece dence on Stack A or Stack A is empty push the incoming operator onto stack A Otherwise pop the operator s in Stack A pop the associated operand s
30. e separated by token separators Space t and n are always token separators but 5 7 tee f e P y and are considered both tokens and token separators So in the expression 1 2 there are 5 tokens even there is no space in between at all The SIGN token POSITIVE or NEGATIVE should be distinguished from PLUS and MINUS since they the same representation If it is a SIGN POSITIVE or NEGATIVE it must satisfy the following conditions 1 There is no space between the SIGN and the following expression 2 The only allowed token before the SIGN is 47 or 3 Otherwise it is NOT the SIGN token 5o in the following expression x y4 2 is NEGATIVE is PLUS In yx the first and the third are NEGATIVE signs the second and the forth are MINUS tokens 3 1 5 Internal Representation For the valid infix user input which was parsed successfully AMC has an internal representation in prefix format All mathematical expressions will be kept in prefix notation and have the following format operator operand operand operandN 29 The operands operand1 operand2 operandN can be subexpressions One example is the expression factor x 2 y 2 The internal representation for the above expression will be factor C C x 2 C y 2 reason for putting operator into s is that it is easy to extract the operator also we can add mor
31. esley 1990 Kajler N CAS PI a Portable and Extensible Interface for Computer Algebra Systems Proceedings of 155 92 ACM Press 1992 Gray S and Kajler and Wang P S A Protocol for Efficient Exchange of Mathematical Expressions Proceedings of 155 794 ACM Press 1994 Kajler N and Soiffer Survey of User Interfaces for Computer Algebra Systems Journal of Symbolic Computation 11 1995 Young D A Wang P S GI S A Graphical User Interface for Symbolic Computation Systems Journal of Symbolic Computation 4 1987 Gray 5 Kajler N and Wang P S Design and Implementation of MP a Pro tocol for Efficient Exchange of Mathematical Expressions Journal of Symbolic Computation 11 1996 Wang P S Java with OOP and Web Applications Brooks Cole Publishing Co Pacific Grove CA ISBN 0 534 95206 2 1998 Wang P S An Introduction to UNIX with X and the Internet PWS Publishing Co Boston MA ISBN 053494768 9 July 1996 Sams net Publishing nternet Unleashed 2nd edition ISBN 0 672 30714 6 1995 Newman Using Java Que Publishing ISBN 0 7897 0604 0 1996 Symbolics Inc Macsyma User s Guide January 1988 Wang P S Helpful Hints to MAXIMA Programmers class handout Doleh Y Design and Implementation of a System Independent User Interface for an Integrated Scientific Computing Environment Ph D Disserta tion Kent State University May 1995
32. fferent services The IAMC Client sits at the user s site while AMC Server locates on the compute engine machine The IAMC Server should have the right to access the compute engine because it needs to invoke the mathematical compute engine and do the user requested job From the user s point of view the IAMC server is located on a remote machine which supplies such computation service The user doesn t need to know where it is he she just needs to know the IAMC Server s name like ox mcs kent edu and the port number which is used for IAMC computation Hopefully all the IAMC 13 Servers have unique port number to do such computation just like 80 for http and 70 for gopher In that case the user just inputs the server s name and the unique port number will be automatically assigned to the system IAMC uses MP as the data communication format between the IAMC Client and IAMC Server IAMC Client will translate all requests into MP format and send to the IAMC server For IAMC Server s part it should understand MP and convert the MP data to the appropriate data which is the input of the actual compute engine after the compute engine finishes the requested job the IAMC Server should collect the answer from the compute engine and translate to MP data then send the result back to the client IAMC Client and Server are implemented in Java 10 7 The Java programming system is one of the most exciting recent developments in computing Developed by
33. he prefix string to the prefix2mp program The prefix2mp function s duty is to construct an MP parsing tree according to the input The prefix2mp program uses MP defined operations such as IMP PutSint32 to perform its duty 3 2 2 MP to ASCII Conversions The result coming back from the IAMC server or from an MP file that a user opens is displayed by converting it to an ASCII format prefix or This is simply done by using an existing prototype program displaymp written in ANSI C which takes an MP input and converts it to prefix or as requested Again the Java exec mechanism is used By default results are displayed with displaymp infix Commands are provided in the IAMC client to display any given result in the other two formats 3 3 Interface to IAMC Server In the IAMC Client part the interface between IAMC Server and Client are implemented by three methods in the AMCClient class 1 beginSession simply asking for a connection to a particular IAMC Server 2 remoteCompute send compute request in MP format to the server and get the answer back in MP format 3 endSession close the connection with the server 34 Meanwhile the class WriteToFile performs the duty of writing the answer coming from the server to a temporary MP file without the ending marker ENDMP CHAPTER 4 IAMC Server The experimental IAMC Server is a Java program invoked by the inet daemon such i
34. ical expressions include Polylith 20 CaminoReal 18 SUI DSC 29 and CAS PI Realizing the importance of a mathematical data exchange protocol the Maple group initialized a series of work shops which led to the formation of the OpenMath group in order to develop and standardize such a protocol Multi Protocol MP 3 is a result of collaboration among Gray Kajler and Wang MP is a format for efficient communication of mathematical data among scientific computing systems MP is designed to support efficient communication of mathematical data between scientifically oriented software tools MP exchanges data in the form of linearized annotated syntax trees Syntax trees provide a simple flexible and tool independent way to represent and exchange data and annotations provide a powerful and generic expressive facility for transmitting additional infor mation In a layer above the data exchange portion of the protocol MP supports collections of definitions for annotations and mathematical symbols operators and symbolic constants in dictionaries Dictionaries address the problem of application heterogeneity by supplying a standardized representation and semantics for mathe matical objects They are identified within packets through a dictionary tag field Applications that communicate according to definitions provided in dictionaries do not need to have direct knowledge of each other promoting a plug and play style of interoperation of
35. ical functions and operators 3 1 1 Infix Input User input is entered in infix notation similar to Fortran For example 2 2 sin x 2 y 2 cos z Special constants include such quantities as AMC Client supports the standard operators in Table 1 since they are common operators their syntax number and order of arguments are quite standard The IAMC Client grammar wil expect the supported operators to have the exact correct number and order of arguments All the other operators not listed in Table 1 such as limit sum and prod are considered unsupported operators That means their syntax are not 21 22 Representation ADDITION n COSINE cos TANGENT tan cot asin atan acot sq exp log Factor dif integrate expand Table 1 IAMC Supported Operators standard their number and order of arguments are different according to different systems They also can get parsed successfully as long as they are input as operator argl arg2 argN where 1 arg2 argN are math expressions For example if one inputs sum x 2 x x 1 9 although the sum is not a supported operator it satisfied the rule and it will be correctly parsed while its syntax is unknown Even if one inputs xyz x 23 it will be also parsed successfully and it will be considered that the operator name is xyz and it has one argument x Variable Identifier is any string which
36. ient Server model for IAMC Client and IAMC Server communication Usually a network application will involve a server and a client A server process provides a specific service on a host machine that offers such a service Example services are remote host access telnet file transfer ftp and the World Wide Web http Each network wide service has its own unique port number that is identi cal across all hosts The port number together with the Internet address of a host identifies a particular server anywhere on the Network For example ftp has port number 21 and http 80 Currently the first 512 port numbers 0 511 are reserved for network wide applications registered by the InterNIC The next 512 ports 512 1023 12 prefix2mp ANSI C Wu Wu Wu IAMC Client IAMC Server maxima2mp Java Java ANSI C MAXIMA MP displaymp displaymp MP C Library ANSI C ANSI C C Library Gray Wang Wang Gray Figure 2 Programming Contributions are semi official and are used for such standard services as remote UNIX login at 513 and remote printing at 515 Still higher port numbers are used for local applications such as X Windows and NFS 8 IAMC uses port number 4450 for experiments A client process on a host connects with a server on another host to obtain its service Thus a client program is the agent through which a particular network service can be obtained Different agents are usually required for di
37. input output for different purposes one is from to the IAMC Client the other is from to MAXIMA program The IAMC Server gets data in MP format from IAMC Client converts it into MAXIMA input sends it to MAXIMA collects the results from MAXIMA translates them into MP format and sends them back to IAMC Client MP is the data format for IAMC Client and IAMC Server communication One of the IAMC Server s responsibilities is to act as an adapter between compute engine and MP Each different compute engine requires different treatment Thus the server to engine interface is custom for different engines When IAMC Server gets the MP data from IAMC Client it should translate such MP requests to the compute engine input format then send them to the compute engine For MAXIMA the input should be in infix ASCII format which is Fortran like syntax followed by as the command terminator For easy experimentation the IAMC Server invokes a child process displaymp infix to convert the MP request from the Client to an infix format string attaches a semicolon to it then sends the resulting ASCII string to MAXIMA as input Handling MAXIMA output is a little more complicated Normally the MAXIMA top level is a read eval print loop much like that of lisp 12 1 The next command typed by the user is read 2 command is parsed and converted to internal form 3 This internal form is evaluated by the function meval the MAXIMA evaluator 38
38. leeleleleleelelelelelelelolejelekelolelejelelelelejeelek Select 1 11 51 Please input your expression factor y Valid input xookokoelojokolokeleetolelelekeleleleelelelejeleleleleleeleleleleleleleleleleleleleleleelolelelekelolelejelelelelejeelek IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit 2K KK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK KOK KOK OK KK OK KK OK KK OK OK OK OK OK OK OK OK OK k k KOK OK KK OK OK OK KOK KOK KKK Select 1 11 4 d3 1 1 OK OK OK KOK OK OK OK OK OK OK KOK OK OK OK OK OK KOK KOK KK KK KK OK KK OK OK OK OK OK OK OK OK E KK OK KK OK KOK KOK KK KKK IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit xookokolelookolokejeetolelelekeleleleeleleleeleleleleleleleleleleelelelelelelelelelelelelolelelelelelelejeetelelejeetek Select 1 11 1 Please input your expression integ
39. minal symbol check that the current lookahead matches that terminal symbol If it does then advance the input setting the current lookahead to the next input symbol If it does not signal an error 2 For each occurrence of a nonterminal symbol on the RHS call in sequential order the corresponding parsing procedure match will consume a prefix of the input with a rule for the nonterminal If a nonterminal N has multiple grammar rules then the parsing procedure will need to decide which rule to use It can do so by looking at the current lookahead token to see which of the candidate rules can start with the lookahead If only a single rule can start with the lookahead then that rule is chosen If it is always possible to predict a unique rule for any nonterminal by looking ahead by at most one token then the grammar is said to be LL 1 Hence a parsing function N for nonterminal N will simply contain logic to pick a rule based on the current lookahead followed by code to match each individual rule Its structure will look something like the following NO 1 if lookahead can start first rule for N 1 match rule 1 for N else if lookahead can start second rule for N 1 25 match rule 2 for N else if lookahead can start n th rule for match rule n for N error Unfortunately there are some problems with this simple scheme grammar rule is said to be directly left recursive if the first symbol on
40. n experimental client server package This simple proof of concept system uses MP for mathematical data encoding and transfer implements IAMC client server pair in Java and provides Internet based access to the MAXIMA symbolic computation system 2 1 Overview of IAMC System IAMC system has two parts one is IAMC Client the other is Server Figure 1 shows the relations of the two parts connected by stream sockets 7 The programming of the work reported here includes the Java coded client and server parts i e all the classes and functions in the IAMC Client and Server as well as the ANSI C coded MP conversion programs prefix2mp and maxima2mp The prefix2mp program is used for converting prefix notation to MP format the maxima2mp program is used for converting MAXIMA output to MP format The displaymp program is written by Paul Wang and it is used to convert MP data to different formats such prefix and I3TEX MP library is written by Simon Gray as part of his MP project Figure 2 shows the overall programming contributions IAMC Client will be accessed by the user accept the user input and display the output to the user IAMC Server will connect to the local compute engine and control the compute engine to do the mathematical computation IAMC uses the 10 11 User Input Socket Connection IAMC Client IAMC Server Compute Request Compute Engine Figure 1 Structure of IAMC Cl
41. ng 32 3 22 ASCII MP Conversions MP is used for efficient exchange of data between scientifically oriented software tools Mathematical data represented in ASCII are translated to MP before trans mission MP data received also need to be converted into other formats 3 2 1 Prefix to MP Conversion The IAMC Client stores input in prefix form Before being sent to the remote IAMC Server prefix data needs to be converted to MP MP is supported by a set of C library functions Thus the ASCII to MP conversion is also written in C The IAMC Client calls the Java runtime method to invoke the prefix2mp process Prefix ASCII prefix2mp ANSI C Program Uses MP Library IAMC Client Java Program MP Binary Figure 6 Java Exec Method When the Java Virtual Machine runs an instance of the class Runtime records the status of the running system and provides operations it can perform The static method call Runtime rt Runtime getRuntime returns the current Runtime object rt It can initiate other programs on the platform from Java Create a process an instance of Process with an exec method call Process p rt exec command 33 The child process T created runs independently on the host platform The Process object allows the program to control and communicate with the child process Figure 6 shows the relation between the Java program and the C program prefix2mp IAMC Client passes t
42. object in Internet communi cation which uses the TCP protocol TCP is a reliable stream network connection The Socket class provides methods for stream I O which make reading from and 41 writing to a socket easy ServerSocket is an object used for Internet server grams that listen to client requests ServerSocket does not actually perform the service instead it creates a socket object on behalf of the client The communication is performed through that object Sockets are based on a client server model One program the server provides the service at a particular IP address and port The server listens for service requests Any program client that wants to be serviced needs to know the IP address and port to communicate with the server 7 advantage of the socket model over other forms of data communication is that the server doesn t care where the client requests come from As long as the client is sending requests according to the TCP IP protocol the requests will reach the server provided the server is up and the Internet isn t too busy This also means that the client can be any type of computer No longer are we restricted to UNIX Macintosh DOS or Windows platforms Any computer that supports TCP IP can talk to any other computer that supports it through this socket model This is a potentially revolutionary development in computing Instead of maintaining armies of programmers to port a system from one platform to an
43. other we write it once in Java Any computer with a Java virtual machine can run it The current IAMC server is on host ox mcs kent edu and uses port 4450 for experiments The IAMC Server first creates a server side stream socket with Serversocket listen new ServerSocket port on ox at the port number 4450 The socket is used to listen and wait for incoming connections Socket s soc listen accept 42 new Socket object is returned when an incoming connection is made that is when an IAMC Client requests connection After the connection is made the Client and Server will communicate with each other The Client will send the MP data to the Server and attach a string marker ENDMP to each MP request to indicate that one MP request is completed When the Server receives the ENDMP marker it knows that is the end of this MP data Then the Server can send such MP data excluding ENDMP to the displaymp program for conversion When the server gets the answer from the MAXIMA and converts it to MP it will send the data back to the Client Also it will attach the same marker to the end to let the Client know where the MP data ends Finally when the IAMC Client decides to end such a computation session it will close the I O and the socket IAMC Server side will then automatically end this connection better way to manage the server is to register it with inetd inet daemon in the configuration file inetd
44. p should be loaded into MAXIMA first to redefine the displa function The modification causes MAXIMA to return the internal prefix representation as final output for any computation The above example now becomes C2 factor x 3 1 BEGIN EXP MLABLE D2 MTIMES SIMP FACTORED MPLUS SIMP IRREDUCIBLE 1 X MPLUS SIMP IRREDUCIBLE 1 X MEXPT SIMP RATSIMP X 2 END EXP Now the IAMC Server to MAXIMA interface can convert this data format into MP A C program maxima2mp is written for this purpose The maxima2mp program is similar to prefix2mp The only difference is maxima2mp needs to convert the internal MAXIMA representation for operators and identifiers to the regular ASCII form Basically it strips the sign and converts operators and identifiers appropriately For example MTIMES becomes and X is X D2 is an identifier that labels the whole expression Subsequent user commands can use D2 to recall the expression Thus the above MAXIMA output should be converted to the following prefix ASCII expression representation assign D2 a 1 x 1x C x 2 Such modified prefix data can then be translated to MP data using the same tech niques as prefix2mp Figure 7 shows the structure of the interface to the external engine 40 Another duty of the interface is to convert the commands from MP form to the cor responding form for the compute engine For example in MAXIMA the INTEGRATE operator has
45. r investigation Programming work reported here includes the Java coded client and server parts i e all the classes and functions in the IAMC Client and Server as well as the ANSI C coded MP conversion programs prefix2mp and maxima2mp Alos Gray s MP library and Wang s displaymp are used on the client and server parts It is hoped that the programming here can provide a starting point for modification improvements and further development of IAMC Also the current system does not take full advantage of MP Not all MP supported data formats can be converted yet This is just a matter of extending the program to handle all cases Future work on IAMC includes GUI on the Client side full specification of MCP Java coded MCP classes to be used on the Client and the Server sides mak ing IAMC compatible and accessible via the Web and via email supporting multiple mathematical encoding formats handling graphing plotting providing help and doc umentation information for the user aborting computations and applying MCP in problem solving environments 51 52 It is the hope of the author that this work has provided some ground work for future research in the area of Internet Accessible Mathematical Computation BIBLIOGRAPHY 1 Doleh Y and Wang P S SUI A System Independent User Interface for 10 11 12 13 and Integrated Scientific Computing Environment Proceedings of ISSAC 90 Addison W
46. rate d3 x 1 4 Valid input xookokoleleookololeleetoleleleeleleleeelelejolelelelejeleleleleleleleleleleleleleleleleelolejeleletolelejeletelelejeelek IAMC Client MENU 1 Type your infix input 2 New Session 48 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit FOC OR ORO OR OR OR OR OR OR OR RR I OK a Select 1 11 4 d4 186 SOAS OG CRAG KR aK TAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit xookokolelejokololeleketoleleleeleleleeleleleleelelelejeleleleleleeleleleleelelelelelelelolejelelelolelejelelelelejeelek Select 1 11 1 Please input your expression expand d3 Valid input BOAO OA ABA RAR AR kk kkk k IAMC Client MENU 1 Type your infix input 2 New Session 3 Send MP file to Server 4 Send current exp to Server 5 End Session 6 History T Save current exp to MP 8 Save current result to MP 9 Open MP file 10 Help 11 Exit
47. ression expression After removing the left recursive rules according the above technology we define the following rules which are currently supported by IAMC Client Grammar Simple IAMC Math Expression Grammar IAMC Math Grammar VAR 2 7 math expression math expression math expression SIGN math expression VAR exprRest NUM exprRest math expression 7 exprRest OPS math expression P exprRest factor 9 9 poly hy exprRest expand poly 22 exprRest giff C math expression VAR diffRest exprRest integrate math expression VAR intRest exprRest Unknown OP Q math expression argRest 2 exprRest OSP 28107 cos tan cot asin acos atan 2 log Unknown OP VAR argRest EMPTY 3 math expression argRest exprRest math expression 252 math expression math expression math expression d math expression EMPTY poly SIGN poly VAR polyRest INT polyRest gt poly polyRest polyRest 247 poly gt poly 2 poly INT polyRest EMPTY diffRest 2 d NUM intRest 23 5 NUM sy NUM SIGN gt NUM INT REAL 7 31 VAR letter varRest varRest letter varRest digit varRest EMPTY End of Grammar 27 28 3 1 4 Tokens Tokens ar
48. rfaces support con current use of different computer algebra systems faced with conversion problems configuration management and communication protocols Pioneering work on these improvements was done by James Purtilo with Polyith 20 and Denis Arnon with CaminoReal 18 More recent results include MathStation 25 SUI and CAS PI 2 Secondly mathematical computation needs an efficient and standard encoding for mat for data exchange and communication Traditionally computer algebra systems are monolithic stand alone programs designed to communicate with a user through a specific command language They do not address interoperability issues such as the exchange of mathematical expressions with other independent programs More recently scientific computation systems have adopted the component approach and devised various schemes for inter component communication Since version V Maple has been composed of a kernel and a set of devices including a user interface Iris 24 and a plotting engine The kernel and devices can run on different computers communicating with a proprietary protocol Data can be passed in one of two ways either as string suitable to be used as Maple input or as Directed Acyclic Graphs DAGs using Maple s internal data representations DAGs have two clear advantages first they reduce the average amount of data transmitted by sharing common subexpressions second using Maple s internal data representation eases
49. t communicates with the AMC Client through standard input and standard output The evolving IAMC design calls for MCP the Mathematical Computation Protocol as the sever client protocol The MCP specification is on going and promises to support multiple mathematical encoding schemes among other features However the experiment here simply assumes each message between the server and the client to be MP encoded design of the IMAC Server consists of two major parts 1 client interface 2 external compute engine control These two parts will be described separately Modifications to the compute engine for connecting to the IAMC Server are also described 4 1 Interface to IAMC Client IAMCServer class controls the interface to the IAMC Client When IAMC Server is invoked it starts the background compute engine then waits for compute requests from the client via standard input The WriteToFile class will be re used here When the server reads data from client WriteToFile will write such data into a temporary MP file and delete the ending marker ENDMP The method getans 35 36 of IAMCServer will collect the compute answer from compute engine convert it to MP data then send it back to client When IAMC Client closes its socket the Server will get the end of file indication 4 2 Compute Engine The IAMC Server controls a MAXIMA 12 system running under UNIX MAX IMA is a version of MACSYMA 23 a comp
50. ter the user opens another session the IAMC will not remember the previous session s context such as variable assignments It is possible for the IAMC client to save a sequence of user input commands in a file which can be batched to a server This feature allows a user to create command files or to save a session to be continued later This feature is not currently implemented The IAMC Client also has the responsibility to translate between the infix and MP save the MP formatted data to an mp file for future use and send an exiting MP file to the server Another duty for the IAMC Client is remembering the user s input history and redisplaying it in order for the user to easily re issue the earlier input Finally the IAMC Client provides help facilities to help the user understand the supported operators input format remote server s information etc We can summarize the functions that the experimental IAMC Client supports e Get User Input read user s input e Grammar Check parse the input e Open MP File convert and display MP data e Save MP File convert to MP formatted data e New Session open the connection to IAMC Server e Send Computation Request send one MP file to Server e Close Session close the current connection with IAMC Server e History display user s input history 16 e Help display help information e Exit exit System 2 3 IAMC Server The IAMC Server connects to the IAM
51. the name integrate while in Maple the name is int An IAMC Server for Maple should convert integrate to int before sending it to Maple 4 4 Server Client Communication IAMC Client and IAMC Server use stream socket for communications socket is a software mechanism representing a communication s entry point on the Internet Since IAMC Client and IAMC Server are running on different host computers inde pendent processes must be able to initiate and or accept communication requests in an asynchronous manner A Client process uses its own socket to communicate with another socket belonging to a server process Each host computer on the Internet creates its own sockets to communicate with other sockets on the Internet A socket address consists of the numerical IP address of the host computer and an integer port number Different types of sockets support different protocols Communication takes place between sockets of the same type Two important types are Stream socket and Datagram socket 8 IAMC uses the stream socket With a stream socket a process can dial another stream socket s address and make a connection pair of con nected stream sockets supports bidirectional reliable sequenced and unduplicated flow of data without record boundaries Stream sockets use the Transmission Control Protocol TCP IP The Java Socket and ServerSocket classes provide the client and server side stream socket mechanisms In Java a socket is the basic
52. ument Type Definition the Euromath DTD for SGML 36 which formally specifies the structure of the mathematical objects to be exchanged and provides the GRIF 28 editor for editing them Mathematical Markup Language MathML 15 is the official HTML 37 exten sion sponsored by the W3 World Wide Web consortium MathML is an XML 35 application for describing mathematical notation and capturing both its structure and content The goal of MathML is to enable mathematics to be served received and processed on the Web just as HTML has enabled this functionality for text MathML also pays particular attention to compatibility with other mathematical software and in particular with computer algebra systems Many of the presentation elements of MathML are derived in part from the mechanism of typesetting boxes The MathML content elements are heavily indebted to the OpenMath 26 project The OpenMath project has close ties to both the SGML 36 and computer algebra communities and has laid a foundation for an SGML based means of communication between math ematical software packages among other things The feasibility of both generating and interpreting MathML in computer algebra systems has been demonstrated by prototype software Several other works related to the exchange of mathematical data between sci entific applications are reported in 4 Notable implementations of distributed ar chitectures that provide some exchange of mathemat
53. uter algebra system originally developed by the MATH Lab Group at MIT The MAXIMA used is in Common Lisp CL with enhancements from the University of Texas at Austin and Kent State University MAXIMA offers a wide range of capabilities including differentiating and integrating expressions factoring polynomials plotting expressions solving equations manipu lation of matrices and computing Taylor series MAXIMA is also a programming environment in which the user can define mathematical procedures tailored to his or her own needs It can work with symbols polynomial expressions equations and numbers It allows the widespread use of many mathematical operations with vari ous data types such as integer rational various sizes of floating points and complex numbers It also supports the use of irrational numbers such as pi Many higher level data types and operations are also available including polynomials and matrices MAXIMA is written in AKCL LISP This allows users to develop their own high level MAXIMA functions that call other high level MAXIMA functions MAXIMA data types or LISP level functions Any MAXIMA level function can be accessed at LISP level and functions written at LISP level can be accessed at the MAXIMA level 37 4 3 Interface to Compute Engine Since MAXIMA is a local program the IAMC Server just calls the Java Runtime method to execute the MAXIMA program in the background The IAMC Server maintains two sets of
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