admcycles swMATH ID: 36730 Software Authors: Delecroix, Vincent; Schmitt, Johannes; van Zelm, Jason Description: admcycles - a Sage package for calculations in the tautological ring of the moduli space of stable curves. The tautological ring of the moduli space of stable curves has been studied extensively in the last decades. We present a SageMath implementation of many core features of this ring. This includes lists of generators and their products, intersection numbers and verification of tautological relations. Maps between tautological rings induced by functoriality, that is pushforwards and pullbacks under gluing and forgetful maps, are implemented. Furthermore, many interesting cycle classes, such as the double ramification cycles, strata of k-differentials and hyperelliptic or bielliptic cycles are available. In this paper we show how to apply the package, including concrete example computations. Homepage: https://www.math.uni-bonn.de/people/schmitt/admcycles Source Code: https://gitlab.com/jo314schmitt/admcycles Dependencies: SageMath Keywords: Algebraic Geometry; arXiv_math.AG; Sage package; tautological ring; moduli space; stable curves; SageMath Related Software: SageMath; diffstrata; GitHub; mgn; CoCalc; MathOverflow; Macaulay2; HyperInt; KoszulDivisorOnPic14M8; GAP; LMFDB; SINGULAR; SageMathCell Cited in: 24 Documents Standard Articles 2 Publications describing the Software, including 1 Publication in zbMATH Year admcycles – a Sage package for calculations in the tautological ring of the moduli space of stable curves. Zbl 1485.14046Delecroix, Vincent; Schmitt, Johannes; van Zelm, Jason 2021 admcycles - a Sage package for calculations in the tautological ring of the moduli space of stable curves arXiv Vincent Delecroix, Johannes Schmitt, Jason van Zelm 2020 all top 5 Cited by 38 Authors 6 Lewanski, Danilo 4 Schmitt, Johannes 3 Borot, Gaëtan 3 Möller, Martin 2 Canning, Samir 2 Costantini, Matteo 2 Do, Norman 2 Eberhardt, Lorenz 2 Karev, Maksim V. 2 Larson, Hannah K. 2 van Zelm, Jason 2 Wulkenhaar, Raimar 2 Zachhuber, Jonathan 1 Bae, Younghan 1 Brandt, Madeline 1 Castorena, Abel 1 Chan, Melody 1 Chen, Dawei 1 Collier, Scott 1 Delecroix, Vincent 1 Eynard, Bertrand 1 Gendron, Quentin 1 Giacchetto, Alessandro 1 Grosse, Harald 1 Hock, Alexander 1 Kannan, Siddarth 1 Kedlaya, Kiran Sridhara 1 Kumaran, Ajith Urundolil 1 Lian, Carl 1 Molcho, Samouil 1 Moskovsky, Ellena 1 Mühlmann, Beatrix J. 1 Norbury, Paul T. 1 Pandharipande, Rahul 1 Payne, Sam 1 Ranganathan, Dhruv 1 Rodriguez, Victor A. 1 Sauvaget, Adrien all top 5 Cited in 18 Serials 2 Communications in Mathematical Physics 2 Journal für die Reine und Angewandte Mathematik 2 Selecta Mathematica. New Series 2 Forum of Mathematics, Pi 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Journal of Geometry and Physics 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Mathematische Annalen 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Experimental Mathematics 1 Journal of Algebraic Geometry 1 Geometry & Topology 1 The Journal of Software for Algebra and Geometry 1 Forum of Mathematics, Sigma 1 SciPost Physics all top 5 Cited in 12 Fields 21 Algebraic geometry (14-XX) 6 Quantum theory (81-XX) 5 Combinatorics (05-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Functions of a complex variable (30-XX) 2 Relativity and gravitational theory (83-XX) 1 Number theory (11-XX) 1 Associative rings and algebras (16-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) Citations by Year