Project 19: Analytic algorithms and symbolic manipulation Amsterdam 1977: =============== The Modular Analysis of Algorithms and Programs: N.N. Yanenko The paper by Professor Yanenko discussed the technological chain of modern computational mathematics. He noted that the structure of the ensuing program is conditioned by many factors. Essential factors are the structure of the algorithm; the structure of the computer; the need for the free exchange of programs; the need for co-operation, distribution of programming jobs and testing in program preparation (where each aspect can be aided by the use of structured programming); the need for flexibility and evolution as built-in features of program design; and the need for an effective program. Professor Yanenko observed that the last (but not least) item is a most important condition for the successful development of numerical (computational) mathematics. The modular structuring of algorithms and hence of programs was the basis of all effective modern programming. Several definitions of modular structure were available in the literature. He preferred that given by Dennis. Professor Yanenko took a classic problem of mathematical physics by way of example and gave an excellent detailed analysis of problem solution through use of the technological chain given above. Novosibrisk 1979: ================= Talks were given by N N Yanenko, W S Brown, V M Matrosov, and V L Rvatchov. Brown referred to Comp. Phys. Comm. 17 (1979) 207-215. Madison 1982: ============= There was some discussion as to whether the group should regard symbolic manipulation as within its scope. If not, then by TC2 requirements it should suggest that another group be formed. Einarsson remarked on its importance as an aid to numerical work and pointed out that two talks at Boulder on the topic strongly suggested that the group regarded it as within its scope. It was agreed that the present vague topic should be dropped but that the group hopes to establish more precise projects later. Como 1987: ========== In the absence of Shokin, Stetter remarked that the intention of the project continued to be important and he would not like to have it lost. With the aid of symbolic computation facilities a good number of old and new mathematical techniques could be utilized for scientific computation if they were combined with numerical analysis proper. At the same time, members of the symbolic computation community realize that a stronger impact of their work on scientific computation will depend on the development of software which also includes numerical procedures. Stetter will attend the EUROCAL meeting in Leipzig at the beginning of June. He will inform the group about aspects which may be interesting for the group. Eventually, PSE should encompass symbolic and numerical computation in a unified way. A discussion followed. It was concluded that cooperation with the symbolic computation community is needed, and that the WG 2.5 should help as much as possible where numerical work is concerned. (Gentleman, Ford, Delves, Gaffney, Reid) Stetter proposed that the project remain active, and he offered to coordinate it. This was accepted by IFIP/WG 2.5. Stanford 1988: ============== Documents: IFIP/WG 2.5 (Stanford-17) 1517, 1 page. IFIP/WG 2.5 (Stanford-32) 1532, 27 pages, (only for WG 2.5 internal use). H. Stetter submitted the report entitled "Analytic Algorithms and Symbolic Manipulation" (1517) by mail. The following is the summary of the report presented by M. Gentleman There are significant funding incentives by several U.S. agencies, especially NSF for symbolic algebra systems for teaching calculus, problem solving for scientists and engineers, etc. The interface between numerical and symbolic computation is emphasized. Commercially available systems, based on common microcomputers and workstations, have taken an aggressive step forward, and have shifted from being merely languages where the basic values are algebraic expressions to being problem solving environments complete with numerical calculation, graphical display of results, and automatic choice of algorithms. A paper written by Yu. Shokin and Z. Fedotova entitled "Review of Papers of Soviet Authors on Symbolic Manipulation" (submitted by B. Einarsson) is available as document number 1532. Beijing 1989: ============= H. Stetter summarized the work relating to project 19. He said that there had been no joint activity of the project group, but project members have been individually active. Observations: (i) Two most recent "computer math" systems (Mathematica, Wolfram Res; Derive, successor to mu-math, Soft Warehouse) have excellent user interfaces and graphics, but they are stand- alone PSE's without interfaces to other software. Symbolic facilities are not available in numerical packets. (ii) Interaction within "computer algebra" community has considerably improved. However, there is still very little (if any) serious interaction with computational mathematics. Conclusions: Main goal of the project is to further the use of analytic (symbolic) methods to enhance computational work (in floating point). This work is still in infancy, so WG 2.5 should continue working in this area. Suggested actions: Formulation of the needs (from computational point of view). Involvement from Computer Algebra and Numerics communities. In the discussion it was noted that one of the more specific aims for symbolic manipulation should be the handling of singularities, and ODE's. Kulisch said that a language for ODE's may be one solution to the problem. Rice noted that NSF recently held a workshop on symbolic computation in support of computer algebra, and that the report from that workshop is very relevant to numerical computations. Fosdick and Rice were of the opinion that we should urge the symbolic algebra package writers to put hooks into the packages so that they can be used in numerical computation applications. Currently it is not easy to use these packages except as stand-alone environments. Jerusalem 1990: =============== H. Stetter summarized the work relating to project 19. He pointed out that currently there is no standardized way of handling functions as data, and that a discussion of this problematics may make an interesting ICIAM minisymposium. Discussion developed (Feldman, Gaffney, Stetter, Rice, Kulisch) Karlsruhe 1991: =============== H. Stetter summarized the work relating to project 19. A minisymposium related to the project was held at ICIAM 91 (see below) ICIAM, 1991. ----------- Document: IFIP/WG 2.5 (Karlsruhe-17) 1817, 3 pages, The Second International Conference on Industrial and Applied Mathematics was held in Washington, D.C., between 8 and 12 July 1991. Three minisymposia were organized by the IFIP WG 2.5 members during ICIAM 1991: - J. Reid, "Fortran 90: How the New Language will Benefit Applied Mathematics." - S. Feldman and M. Vouk, "Scientific and Numerical Computing in C." - H. J. Stetter, "Use of Automatically Derivable Analytic Information in Numerical Computation." All three minisymposia were well attended and well received. Summary of the content of the minisymposia is given in document 1817. Toronto 1992: ============= H. Stetter summarized the work relating to project 19.