Mathematical Sciences Research Equipment 1989

本项目为美国国家科学基金会数学科学部数学科学项目的科学计算研究设备项目。该计划支持购买专用于数学科学研究的专用计算设备。这些设备是几个研究项目所需要的，很难证明单独用于一个项目是合理的。国家科学基金会的支持与制造商的折扣和捐款以及提交提案的机构的大量费用分摊相结合。这个项目是学术、企业和政府合作支持数学科学基础研究的一个例子。该设备将用于支持加州大学洛杉矶分校数学系的几个研究项目：超椭圆曲线雅可比矩阵的计算、代数数的分布、有限域上的算术和线性循环序列，由David Cantor指导；有限域上二次曲线上同群的确定和椭圆曲线Witt环的确定偏差分算子的等谱变形，由David Gieseker指导向量空间对称代数上有限生成模的最小自由分辨率，Mark Green和代数数域上的伽罗瓦群，由Murray Schacher指导。

This is a grant under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences of the National Science Foundation. This program supports the purchase of special purpose computing equipment dedicated to the conduct of research in the mathematical sciences. This equipment is required for several research projects and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers and with substantial cost-sharing from the institutions submitting the proposal. This program is an example of academic, corporate, and government cooperation in the support of basic research in the mathematical sciences. This equipment will be used to support several research projects in the Department of Mathematics at the University of California, Los Angeles: Calculations in the Jacobians of Hyperelliptic Curves, Distribution of Algebraic Numbers, Arithmetic over Finite Fields, and Linear Recurrent Sequences, directed by David Cantor; Determination of Cohomology Groups Arising from Conic Curves and Determination of Witt Rings of Elliptic Curves over Finite Fields, directed by Richard Elman; Isospectral Deformations of Partial Difference Operators, directed by David Gieseker; Minimal Free Resolutions of Finitely Generated Modules over the Symmetric Algebra of a Vector Space, directed by Mark Green; and Galois Groups over Algebraic Number Fields, directed by Murray Schacher.