✦ LIBER ✦
A Case Where Choosing a Product Order Makes the Calculations of a Groebner Basis Much Faster
✍ Scribed by Freyja Hreinsdóttir
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 138 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
✦ Synopsis
Let (X) and (Y) be generic (n) by (n) matrices of indeterminates. Let (S=k\left[x_{1}, \ldots, x_{r}, y_{1}, \ldots, y_{r}\right]) where (k) is a field of characteristic 0 and (r=n^{2}). Let (I \subset S) be the ideal generated by the entries of the matrix (X Y-Y X). We will consider the ring (S / I) and show that it is Cohen-Macaulay for the case (n=4). In order to calculate its Groebner basis we use a product order with 3 blocks of variables and reverse lexicographic order in each block. This makes the computation much smaller and less time consuming.