This paper extends the article of Bruns and Conca on Sagbi bases and their computation (J. Symb. Comput. 120 (2024)) in two directions. (i) We describe the extension of the Singular library sagbiNormaliz.sing to the computation of defining ideals of subalgebras of polynomial rings. (ii) We give a complete classification of the algebras of minors for which the generating set is a Sagbi basis with respect to a suitable monomial order and we identify universal Sagbi basis in three cases. The investigation is illustrated by several examples.
Sagbi bases, defining ideals and algebras of minors
Conca A.;Lembo F.
2025-01-01
Abstract
This paper extends the article of Bruns and Conca on Sagbi bases and their computation (J. Symb. Comput. 120 (2024)) in two directions. (i) We describe the extension of the Singular library sagbiNormaliz.sing to the computation of defining ideals of subalgebras of polynomial rings. (ii) We give a complete classification of the algebras of minors for which the generating set is a Sagbi basis with respect to a suitable monomial order and we identify universal Sagbi basis in three cases. The investigation is illustrated by several examples.
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