SagbiHomotopy.jl implements SAGBI-basis homotopy continuation, reducing path counts for horizontally parameterized polynomial systems compared with polyhedral homotopies.
SAGBI and Gr\"obner Bases Detection
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We introduce a detection algorithm for SAGBI basis in polynomial rings, analogous to a Gr\"obner basis detection algorithm previously proposed by Gritzmann and Sturmfels. We also present two accompanying software packages named SagbiGbDetection for Macaulay2 and Julia. Both packages allow the user to find one or more term orders for which a set of input polynomials form either Gr\"obner basis for the ideal they generate or a SAGBI basis for the subalgebra. Additionally, we investigate the computational complexity of homogeneous SAGBI detection and apply our implementation to several novel examples.
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
The SagbiHomotopy.jl package for solving polynomial systems
SagbiHomotopy.jl implements SAGBI-basis homotopy continuation, reducing path counts for horizontally parameterized polynomial systems compared with polyhedral homotopies.