New techniques, both theoretical and practical, are presented for constructing a permutation representation for a matrix group. We assume that the resulting permutation degree, n, can be 10,000,000 and larger. The key idea is to build the new permutation representation using the conjugation action on a conjugacy class of subgroups of prime order. A unique signature for each group element corresponding to the conjugacy class is used in order to avoid matrix multiplication. The requirement of at least n matrix multiplications would otherwise have made the computation hopelessly impractical. Additional software optimizations are described, which reduce the CPU time by at least an additional factor of 10. Further, a special data structure is designed that serves both as a search tree and as a hash array, while requiring space of only 1.6n log2 n bits.

Programming languages have traditionally had more data types than database systems. The flexibility of abstract types could make a database system more useful in supporting application development. Abstract types allow users to think about and manipulate data in terms and structures that they are familiar with. This paper proposes that databases have a type system interface and describes a representation of a type system in terms of relations. The type system model supports a variety of programming language constructs, such as user-defined parameterized data types and user-defined generic operations. The efficiency of the type system is compared to the access time of the database system.