10 research outputs found
Towards the Formal Specification and Verification of Maple Programs
In this paper, we present our ongoing work and initial results on the formal
specification and verification of MiniMaple (a substantial subset of Maple with
slight extensions) programs. The main goal of our work is to find behavioral
errors in such programs w.r.t. their specifications by static analysis. This
task is more complex for widely used computer algebra languages like Maple as
these are fundamentally different from classical languages: they support
non-standard types of objects such as symbols, unevaluated expressions and
polynomials and require abstract computer algebraic concepts and objects such
as rings and orderings etc. As a starting point we have defined and formalized
a syntax, semantics, type system and specification language for MiniMaple
Minimal average degree aberration and the state polytope for experimental designs
For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Gröbner bases provide a systematic way of doing this. The algebraic method does not, in general, produce all estimable models but it can be shown that it yields models which have minimal average degree in a well-defined sense and in both a weighted and unweighted version. This provides an alternative measure to that based on “aberration” and moreover is applicable to any experimental design. A simple algorithm is given and bounds are derived for the criteria, which may be used to give asymptotic Nyquist-like estimability rates as model and sample sizes increase