# Category:ApCoCoA-1:Package gbmr

Package gbmr is designed to compute Groebner bases in monoid rings.

For the field of rationals ${\displaystyle \mathbb {Q} }$ and a monoid ${\displaystyle {\mathcal {M}}}$ presented by a string rewriting system, let ${\displaystyle \mathbb {Q} [{\mathcal {M}}]}$ denote the ring of all finite formal sums (called polynomials) ${\displaystyle \sum _{i=1}^{n}a_{i}\cdot w_{i}}$ with coefficients ${\displaystyle a_{i}\in \mathbb {Q} \setminus \{0\}}$ and terms ${\displaystyle w_{i}\in {\mathcal {M}}}$. This ring is called the monoid ring of ${\displaystyle {\mathcal {M}}}$ over ${\displaystyle {\mathcal {Q}}}$ .

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.