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Estimating the Volumes of the Cones in a Gröbner Fan

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Abstract

We present a stochastic method for estimating the relative volumes of the Gröbner cones of a Gröbner fan without computing the actual fan. The method is particularly useful when the dimension of the Gröbner fan is large and/or the volumes of several or all cones need to be estimated. A Macaulay 2 implementation for uniform sampling from the Gröbner fan is provided by the author.

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  1. Clemson University, O-303 Martin Hall, Clemson, SC, 29634-0975, USA

    Elena S. Dimitrova

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  1. Elena S. Dimitrova
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Correspondence to Elena S. Dimitrova.

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Dimitrova, E.S. Estimating the Volumes of the Cones in a Gröbner Fan. Math.Comput.Sci. 3, 457–463 (2010). https://doi.org/10.1007/s11786-010-0039-0

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  • DOI: https://doi.org/10.1007/s11786-010-0039-0

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