The Invar tensor package: Differential invariants of Riemann

Abstract The long standing problem of the relations among the scalar invariants of the Riemann tensor is computationally solved for all 6 ṡ 10 ^(23)objects with up to 12 derivatives of the metric. This covers cases ranging from products of up to 6 undifferentiated Riemann tensors to cases with up to 10 covariant derivatives of a single Riemann. We extend our computer algebra system Invar to produce within seconds a canonical form for any of those objects in terms of a basis.... Title of program: Invar Tensor Package v2.0 Catalogue Id: ADZK_v2_0 Nature of problem Manipulation and simplification of scalar polynomial expressions formed from the Riemann tensor and its covariant derivatives. Versions of this program held in the CPC repository in Mendeley Data ADZK_v1_0; Invar Tensor Package; 10.1016/j.cpc.2007.05.015 ADZK_v2_0; Invar Tensor Package v2.0; 10.1016/j.cpc.2008.04.018 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 长期以来关于黎曼张量（Riemann tensor）标量不变量之间关系的问题，已针对所有含至多12阶度规（metric）导数的6×10²³个对象完成计算求解。该覆盖范围包含从至多6个未求导黎曼张量的乘积，到单个黎曼张量的至多10阶协变导数（covariant derivative）的各类场景。我们拓展了自身的计算机代数系统（computer algebra system）Invar，使其可在数秒内基于一组基为上述任意对象生成标准型（canonical form）。 程序名称：Invar张量包v2.0（Invar Tensor Package v2.0） 目录编号：ADZK_v2_0 问题本质：对由黎曼张量及其协变导数构成的标量多项式表达式进行处理与化简。 Mendeley数据的CPC程序库存储版本： ADZK_v1_0；Invar张量包；10.1016/j.cpc.2007.05.015 ADZK_v2_0；Invar张量包v2.0；10.1016/j.cpc.2008.04.018 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019年）