Real solutions to systems of polynomial equations in Macaulay2. (English) Zbl 07898681
Summary: 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.
MSC:
| 14Q30 | Computational real algebraic geometry |
| 14-04 | Software, source code, etc. for problems pertaining to algebraic geometry |
| 68W30 | Symbolic computation and algebraic computation |
References:
| [1] | 10.1007/3-540-33099-2 · Zbl 1102.14041 · doi:10.1007/3-540-33099-2 |
| [2] | ; Cox, David A., Stickelberger and the eigenvalue theorem, Commutative algebra, 283, 2021 · Zbl 1498.13067 |
| [3] | 10.1007/BF01446812 · JFM 26.0119.03 · doi:10.1007/BF01446812 |
| [4] | ; Sottile, Frank, From enumerative geometry to solving systems of polynomials equations, Computations in algebraic geometry with Macaulay 2. Algorithms Comput. Math., 8, 101, 2002 · Zbl 0993.14020 |
| [5] | 10.1090/ulect/057 · doi:10.1090/ulect/057 |
| [6] | 10.2307/3028551 · Zbl 0061.01806 · doi:10.2307/3028551 |
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