A Case Where Choosing a Product Order Makes the Calculations of a Groebner Basis Much Faster
Let X and Y be generic n by n matrices of indeterminates. Let S = k[x1,…, xr , y1,…, yr] where k is a field of characteristic 0 and r = n2 . Let I ⊂ S be the ideal generated by the entries of the matrix XY - YX. We will consider the ring S/I and show that it is Cohen-Macaulay for the case n = 4. In...
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| Published in | Journal of symbolic computation Vol. 18; no. 4; pp. 373 - 378 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.10.1994
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| Online Access | Get full text |
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| Summary: | Let X and Y be generic n by n matrices of indeterminates. Let S = k[x1,…, xr , y1,…, yr] where k is a field of characteristic 0 and r = n2 . Let I ⊂ S be the ideal generated by the entries of the matrix XY - YX. 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. |
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| ISSN: | 0747-7171 1095-855X |
| DOI: | 10.1006/jsco.1994.1053 |