Gröbner basis. A new algorithm for computing the Frobenius number
Marcel Moralès, Dung Nguyen Thi · arXiv (Cornell University) · 2015
Let consider $n$ natural numbers $a_1 ,\ldots , a_{n} $. Set $A=K[t^{a_1}, \ldots , t^{a_n}]=K[{x_1}, \ldots , {x_n}]/I$. Our aim is to describe explicitly: * The \gbb of $I$ for the reverse lexicographic order to $x_n,\ldots ,x_1$, without using Buchberger's algorithm. * $\ini{I} $ for the reverse lexicographic order to $x_n,\ldots ,x_1$. * $A$ as a $K[t^{ a_1 }]$-module. * The Apery set and the Frobenius number. The implementation of this algorithm frobenius-number-mm can be downloaded in \hfill\break https://www-fourier.ujf-grenoble.fr/~morales/frobenius-number-mm