Vol. 9, No. 2, 2019

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The TestIdeals package for Macaulay2

Alberto F. Boix, Daniel J. Hernández, Zhibek Kadyrsizova, Mordechai Katzman, Sara Malec, Marcus Robinson, Karl Schwede, Daniel Smolkin, Pedro Teixeira and Emily E. Witt

Vol. 9 (2019), 89–110
Abstract

We describe a Macaulay2 package for computations in prime characteristic commutative algebra. This includes those for Frobenius powers and roots, pe-linear and pe-linear maps, singularities defined in terms of these maps, different types of test ideals and modules, and ideals compatible with a given pe-linear map.

Keywords
Macaulay2, Test ideals, F-regular, F-rational, F-pure, F-injective, Frobenius root, compatibly split ideals
Mathematical Subject Classification 2010
Primary: 13A35, 14F18
Secondary: 14J17
Supplementary material

A package for calculations of singularities in positive characteristic

Milestones
Received: 19 October 2018
Revised: 13 June 2019
Accepted: 19 July 2019
Published: 16 October 2019
Authors
Alberto F. Boix
Department of Mathematics
Ben-Gurion University of the Negev
Beer-Sheva
Israel
Daniel J. Hernández
Department of Mathematics
University of Kansas
Lawrence, KS
United States
Zhibek Kadyrsizova
School of Science and Technology
Nazarbayev University
Astana
Kazakhstan
Mordechai Katzman
Department of Pure Mathematics
University of Sheffield
Sheffield
United Kingdom
Sara Malec
Department of Mathematics
Hood College
Frederick, MD
United States
Marcus Robinson
Department of Mathematics
University of Utah
Salt Lake City, UT
United States
Karl Schwede
Department of Mathematics
University of Utah
Salt Lake City, UT
United States
Daniel Smolkin
Department of Mathematics
University of Utah
Salt Lake City, UT
United States
Pedro Teixeira
Department of Mathematics
Knox College
Galesburg, IL
United States
Emily E. Witt
Department of Mathematics
University of Kansas
Lawrence, KS
United States