Collaborative Research: SI2-SSE: Sage-Combinat: Developing and Sharing Open Source Software for Algebraic Combinatorics

合作研究：SI2-SSE：Sage-Combinat：开发和共享代数组合开源软件

• 批准号: 1147463
• 负责人: Daniel Bump
• 金额: $ 14.37万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1147463&HistoricalAwards=false
• 关键词: Collaborative; Research; SI2; SSE; Sage

Sage is an open source general purpose mathematical software system that has developed explosively within the last six years. Sage-Combinat is a subproject whose mission is "to improve Sage as an extensible toolbox for computer exploration in (algebraic) combinatorics, and foster code sharing between researchers in this area". There is a long tradition of software packages for algebraic combinatorics. These have been crucial in the development of combinatorics since the 1960s. The originality of the Sage-Combinat project lies in successfully addressing the following simultaneous objectives. It offers a wide variety of interoperable and extensible tools, integrated in a general purpose mathematical software package, as needed for daily computer exploration in algebraic combinatorics; it is developed by a community of researchers spread around the world and across institutions; and it is open source and depends only on open source software. Among the proposers, Stein is founder and lead developer of Sage while Bump, Musiker, and Schilling are strong contributors to Sage-Combinat. Hivert and Thi´ery (Paris-Sud, Orsay), founders and lead developers of Sage-Combinat, are both strongly affiliated with this project. Some of the research areas addressed in this project include symmetric functions, in particular Macdonald polynomials for arbitrary Cartan types and their nonsymmetric analogues, crystals, rigged configurations and combinatorial R-matrices, affine Weyl groups and Hecke algebras, cluster algebras, and posets. The project will develop Sage-Combinat in areas relevant to the ongoing research of the participants, together with relevant underlying infrastructure. The project will include three Sage Days workshops, and will be affiliated with a third scheduled workshop at ICERM. These workshops include a strong outreach component and have been a potent tool for connecting researchers and recruiting Sage users and developers. The grant will also fund a dedicated software development and computation server for Sage-Combinat, to be hosted in the Sage computation farm in Seattle. Emphasis will be placed on the development of thematic tutorials that will make the code accessible to new users. The proposal will also fund graduate student RA support, curriculum development, and other mentoring.

Sage 是一个开源通用数学软件系统，在过去六年中得到了爆炸性的发展。Sage-Combinat 是一个子项目，其使命是“将 Sage 改进为（代数）组合学的计算机探索的可扩展工具箱，并促进代码共享。 “该领域的研究人员之间” 代数组合软件包有着悠久的传统，自 20 世纪 60 年代以来，这些软件包对于组合数学的发展至关重要。 Sage-Combinat 项目成功地实现了以下同时目标：它提供了多种可互操作和可扩展的工具，集成在通用数学软件包中，以满足日常计算机探索代数组合学的需要；研究人员遍布世界各地和各个机构；并且它是开源的，并且仅依赖于开源软件。在提议者中，Stein 是 Sage 的创始人和首席开发人员，而 Bump、Musiker 和 Schilling 是其强有力的贡献者。 Sage-Combinat。Hivert 和 Thi´ery（巴黎南部，奥赛）是 Sage-Combinat 的创始人和首席开发人员，他们都与该项目密切相关，该项目涉及的一些研究领域包括对称函数，特别是 Macdonald。任意 Cartan 类型的多项式及其非对称类似物、晶体、操纵配置和组合 R 矩阵、仿射 Weyl 群和 Hecke 代数、簇该项目将在与参与者正在进行的研究相关的领域开发 Sage-Combinat，以及相关的基础设施。该项目将包括三个 Sage Days 研讨会，并将附属于 ICERM 的第三个预定研讨会。这些研讨会包括强大的外展部分，并且是连接研究人员和招募 Sage 用户和开发人员的有力工具。这笔赠款还将资助 Sage-Combinat 的专用软件开发和计算服务器，该服务器将托管在 Sage 计算农场中。该提案还将重点关注主题教程的开发，以使新用户能够访问代码。该提案还将资助研究生 RA 支持、课程开发和其他指导。