Keicher, Simon A software package to compute automorphisms of graded algebras. (English) Zbl 1404.13005 J. Softw. Algebra Geom. 8, 11-19 (2018). Summary: We present {autgradalg.lib}, a Singular library to compute automorphisms of integral, finitely generated \(\mathbb{C}\)-algebras that are graded pointedly by a finitely generated abelian group. The library implements algorithms of J. Hausen et al. [Math. Comput. 86, No. 308, 2955–2974 (2017; Zbl 1401.14200)]. We apply these to Mori dream spaces and investigate the automorphism groups of a series of Fano varieties. Cited in 1 Document MSC: 13A02 Graded rings 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 14J50 Automorphisms of surfaces and higher-dimensional varieties 14L30 Group actions on varieties or schemes (quotients) 14Q15 Computational aspects of higher-dimensional varieties 13A50 Actions of groups on commutative rings; invariant theory Keywords:graded algebras; automorphisms; symmetries; Cox rings; Mori dream spaces; computing; singular Citations:Zbl 1401.14200 Software:Gfan; autgradalg.lib; SINGULAR PDFBibTeX XMLCite \textit{S. Keicher}, J. Softw. Algebra Geom. 8, 11--19 (2018; Zbl 1404.13005) Full Text: DOI arXiv References: [1] ; Arzhantsev, Mosc. Math. J., 14, 429 (2014) [2] ; Arzhantsev, Cox rings. Cambridge Studies in Advanced Mathematics, 144 (2015) · Zbl 1360.14001 [3] 10.1093/imrn/rnv190 · Zbl 1346.14108 · doi:10.1093/imrn/rnv190 [4] 10.1090/S0894-0347-09-00649-3 · Zbl 1210.14019 · doi:10.1090/S0894-0347-09-00649-3 [5] ; Cox, J. Algebraic Geom., 4, 17 (1995) [6] 10.1112/S1461157015000212 · Zbl 1348.14002 · doi:10.1112/S1461157015000212 [7] 10.1090/mcom/3185 · Zbl 1401.14200 · doi:10.1090/mcom/3185 [8] 10.1016/j.jsc.2013.01.005 · Zbl 1277.13001 · doi:10.1016/j.jsc.2013.01.005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.