\texttt{SubalgebraBases} in Macaulay2

DOI10.2140/jsag.2024.14.97zbMATH Open1546.13001MaRDI QIDQ6589554

Nathan Nichols, Jackson Leaman, Michael A. Burr, Unnamed Author, Oliver Clarke, Timothy Duff

Publication date: 19 August 2024

Published in: The Journal of Software for Algebra and Geometry (Search for Journal in Brave)

zbMATH Keywords

symbolic computationSAGBI basiscomputer algebraNewton-Okounkov bodyMacaulay2

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Cites Work

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• Certification for polynomial systems via square subsystems
• Sagbi bases of Cox-Nagata rings
• Numerical Schubert calculus
• Using SAGBI bases to compute invariants
• Computing toric degenerations of flag varieties
• Analogs of Gröbner bases in polynomial rings over a ring
• Straightening Euclidean invariants
• Gaussian graphical models with toric vanishing ideals
• Canonical bases for cluster algebras
• Khovanskii Bases, Higher Rank Valuations, and Tropical Geometry
• Ideals, Varieties, and Algorithms
• Visualizing properties of comprehensive SAGBI bases. -- Two examples
• Numerical homotopies from Khovanskii bases
• Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes
• Newton-Okounkov bodies of chemical reaction systems
• \textsc{Sagbi} combinatorics of maximal minors and a \textsc{Sagbi} algorithm

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