For some time now I have been wondering how well the existing polynomial factorization algorithms perform on some of the more difficult multivariate polynomials. Below are ten (of the over 300) multivariate polynomials that the heuristic program (POLYFACT) with learning factored while I was working on my dissertation (a complete description of POLYFACT will soon appear in the journal <u>Artificial Intelligence)</u>. Table I gives the factorization times for POLYFACT. When any programs factor some or all of the ten polynomials, I think it would be interesting to publish the times (along with the polynomial number(s) in the SIGSAM Bulletin. Please indicate the machine on which the factorization was done. I am submitting the ten polynomials in factored form in order to conserve space; they need to be expanded and simplified prior to factorization attempts.

A data structure definition facility (DSDF) is described that provides definitions for several primitive data types, homogeneous and heterogeneous arrays, cells, stacks, queues, trees, and general lists. Each nonprimitive data structure consists of two separate entities-a head and a body. The head contains the entry point(s) to the body of the structure; by treating the head like a cell, the DSDF operations are capable of creating and manipulating very general data structures. A template structure is described that permits data structures to share templates.The primary objectives of the DSDF are: (1) to develop a definition facility that permits the programmer to explicitly define and manipulate generalized data structures in a consistent manner, (2) to detect mistakea and prevent the programmer from creating (either inadvertently or intentionally) undesirable (or illegal) data structures, (3) to provide a syntactic construction mechanism that separates the implementation of a data structure from its use in the program in which it is defined, and (4) to facilitate the development of reliable software.

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We describe a constructive approach to the specification of data types. The primary motivation for this approach, which is referred to as the Logical Structure Operation Specification (LSOS), is to highlight certain aspects of a data type, and to possibly suggest one or more implementations for the data type.A key feature of the LSOS is its flexibility, which permits a wide variety of specifications for a data type.This allows the specifier of a data type to communicate to the user any view or perspective which was taken in developing the data type.

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