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Real solutions to systems of polynomial equations in Macaulay2

Jordy Lopez Garcia, Kelly Maluccio, Frank Sottile and Thomas Yahl

Vol. 14 (2024), 87–95
DOI: 10.2140/jsag.2024.14.87

The Macaulay2 package RealRoots provides symbolic methods to study real solutions to systems of polynomial equations. It updates and expands an earlier package developed by Grayson and Sottile in 1999. We provide mathematical background and descriptions of the RealRoots package, giving examples which illustrate some of its implemented methods. We also prove a general version of Sylvester’s theorem whose statement and proof we could not find in the literature.

Sturm theorem, Budan–Fourier theorem, trace form
Mathematical Subject Classification
Primary: 14Q30, 14-04, 68W30
Supplementary material

A package for symbolically exploring, counting, and locating real solutions to polynomial systems.

Received: 19 August 2022
Revised: 4 March 2024
Accepted: 18 March 2024
Published: 31 May 2024
Jordy Lopez Garcia
Department of Mathematics
Texas A&M University
College Station, TX
United States
Kelly Maluccio
Department of Mathematics
Austin Community College
Austin, TX
United States
Frank Sottile
Department of Mathematics
Texas A&M University
College Station, TX
United States
Thomas Yahl
Department of Mathematics
University of Wisconsin-Madison
Madison, WI
United States