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Real solutions to
systems of polynomial equations in Macaulay2
Jordy Lopez Garcia, Kelly Maluccio, Frank Sottile and Thomas Yahl |
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Vol. 14 (2024), 87–95
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Abstract |
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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. |
Keywords
Sturm theorem, Budan–Fourier theorem, trace form
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Mathematical Subject Classification
Primary: 14Q30, 14-04, 68W30
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Supplementary materialA package for symbolically exploring, counting, and locating real solutions to polynomial systems. |
Milestones
Received: 19 August 2022
Revised: 4 March 2024
Accepted: 18 March 2024
Published: 31 May 2024
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Authors |
| Jordy Lopez Garcia | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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| Kelly Maluccio | |
| Department of Mathematics Austin Community College Austin, TX United States |
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| Frank Sottile | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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| Thomas Yahl | |
| Department of Mathematics University of Wisconsin-Madison Madison, WI United States |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
