Converting Subalgebra Bases with the Sagbi Walk

Details Converting Subalgebra Bases with the Sagbi Walk Converting Subalgebra Bases with the Sagbi Walk

2009-11-25

arxiv.org/abs/0911.4773v1

Mathematics

Commutative Algebra

Scientific paper

We present an algorithm which converts a given Sagbi basis of a polynomial $K$-subalgebra $\mathcal{A}$ to a Sagbi basis of $\mathcal{A}$ in a polynomial ring with respect to another term ordering, under the assumption that subalgebra $\mathcal{A}$ admits a finite Sagbi basis with respect to all term ordering. The Sagbi walk method converts a Sagbi basis by partitioning the computations following a path in the Sagbi Fan. The algorithms have been implemented as a library for the computer algebra system SINGULAR \cite{GPS1}.

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