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

Sage是一个开源的通用数学软件系统，在过去的六年里得到了爆炸性的发展。Sage-Combinat是一个子项目，其使命是“改进Sage作为（代数）组合学计算机探索的可扩展工具箱，并促进该领域研究人员之间的代码共享”。 代数组合学的软件包有着悠久的传统。自20世纪60年代以来，这些在组合数学的发展中至关重要。 Sage-Combinat项目的独创性在于成功地解决了以下同时存在的目标。它提供了各种各样的可互操作和可扩展的工具，集成在一个通用的数学软件包中，作为日常计算机探索代数组合学的需要;它是由遍布世界各地的研究人员社区和跨机构开发的;它是开源的，只依赖于开源软件。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Sage-Combinat的强大贡献者。Hivert和Thi 'ery（巴黎南部，奥赛）是Sage Combinat的创始人和主要开发人员，他们都与这个项目密切相关。该项目涉及的一些研究领域包括对称函数，特别是任意Cartan类型及其非对称类似物的麦克唐纳多项式，晶体，操纵配置和组合R-矩阵，仿射Weyl群和Hecke代数，簇代数和偏序集。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日研讨会，并将与ICERM的第三个预定研讨会相关联。这些研讨会包括一个强大的外联部分，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，该服务器将托管在西雅图的Sage计算农场。重点将放在编写专题教程，使新用户能够使用这些代码。该提案还将资助研究生RA支持，课程开发和其他指导。

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.