Manual for the CSX-1 Computer

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryContract DA-36-039-SC-8512

Integrating Computer Algebra and Reasoning through the Type System of Aldor

A number of combinations of reasoning and computer algebra systems have been proposed; in this paper we describe another, namely a way to incorporate a logic in the computer algebra system Axiom. We examine the type system of Alder - the Axiom Library Compiler and show that with some modifications we can use the dependent types of the system to model a logic, under the Curry-Howard isomorphism. We give a number of example applications of the logic we construct and explain a prototype implementation of a modified type-checking system written in Haskell

Efficient implementation of polynomial arithmetic in a multiple-level programming environment

Abstract. The purpose of this study is to investigate implementation techniques for polynomial arithmetic in a multiple-level programming environment. Indeed, certain polynomial data types and algorithms can further take advantage of the features of lower level languages, such as their specialized data structures or direct access to machine arithmetic. Whereas, other polynomial operations, like Gröbner basis over an arbitrary field, are suitable for generic programming in a high-level language. We are interested in the integration of polynomial data type implementations realized at different language levels, such as Lisp, C and Assembly. In particular, we consider situations for which code from different levels can be combined together within the same application in order to achieve high-performance. We have developed implementation techniques in the multiple-level programming environment provided by the computer algebra system AXIOM. For a given algorithm realizing a polynomial operation, available at the user level, we combine the strengths of each language level and the features of a specific machine architecture. Our experimentations show that this allows us to improve performances of this operation in a significant manner.

On the virtues of generic programming for symbolic computation

Abstract. The purpose of this study is to measure the impact of C level code polynomial arithmetic on the performances of AXIOM highlevel algorithms, such as polynomial factorization. More precisely, given a high-level AXIOM package P parametrized by a univariate polynomial domain U, we have compared the performances of P when applied to different U’s, including an AXIOM wrapper for our C level code. Our experiments show that when P relies on U for its univariate polynomial computations, our specialized C level code can provide a significant speed-up. For instance, the improved implementation of square-free factorization in AXIOM is 7 times faster than the one in Maple and very close to the one in MAGMA. On the contrary, when P does not rely much on the operations of U and implements its private univariate polynomial operation, then P cannot benefit from our highly optimized C level code. Consequently, code which is poorly generic reduces the speed-up opportunities when applied to highly efficient and specialize

A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy

◮ A relatively traditional mathematics course, at, say first-year undergraduate level. Setting ◮ A relatively traditional mathematics course, at, say first-year undergraduate level. ◮ But Computer-Aided Assessment is in use. Setting ◮ A relatively traditional mathematics course, at, say first-year undergraduate level. ◮ But Computer-Aided Assessment is in use. ◮ One such example is WeBWorK, another is MapleTA. Setting ◮ A relatively traditional mathematics course, at, say first-year undergraduate level. ◮ But Computer-Aided Assessment is in use. ◮ One such example is WeBWorK, another is MapleTA. ◮ “Harness the power of technology to improve teaching and learning ” [AMS Notices, June 2009]. [1] Web-based Assessment and Testing System

Availability of Large Seed-Dispersers for Restoration of Degraded Tropical Forest

An estimated 63% of Southeast Asian forests are classed as disturbed and secondary as a result of human activity. Many of these forests remain important for biodiversity conservation and ecosystem services so there is much interest in their capacity for restoration. The role of larger animals as seed dispersers in natural regeneration is well-attested since they are often the only agent by which large-seeded trees can effectively disperse. This is especially important for late successional shade-tolerant species which might otherwise be excluded from disturbed sites. However, many larger animals are sensitive to habitat degradation so may be lost from the very areas that require them. We investigated the persistence of a suite of large mammals that are known seed-dispersers and are also threatened species, in a degraded site in lowland south-central Sumatra. We used camera traps and field observations to relate their distributions to prevailing vegetation conditions. Although most species were more frequently detected in the more intact areas, most were able to occupy habitats with high levels of disturbance and population densities were relatively high. It is clear that severe habitat degradation does not necessarily lead to the immediate loss of large-bodied seed dispersers, so ensuring adequate protection for these species from external threats, such as hunting, must be built into management plans for restoration concessions.<br/