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Converting subalgebra bases with the Sagbi walk. (English) Zbl 1282.13049

Summary: We present an algorithm which converts a given Sagbi basis of a polynomial \(K\)-subalgebra \(\mathcal A\) with respect to one monomial ordering to the Sagbi basis of \(\mathcal A\) with respect to another monomial ordering, under the assumption that the subalgebra \(\mathcal A\) admits a finite Sagbi basis with respect to all monomial orderings. The Sagbi walk method converts a Sagbi basis by partitioning the computations following a path in the Sagbi fan.

MSC:

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

Software:

SINGULAR; swalk.lib
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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