An improved term ordering for the ideal of commuting matrices

Let X and Y be generic n by n matrices of indeterminates x 1 , … , x r , y 1 , … , y r . Let S = k [ x 1 , … , x r , y 1 , … , y r ] where k is a field and r = n 2 . Let I ⊂ S be the ideal generated by the entries of the matrix X Y − Y X . We will show how an old result on a good term order for this...

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Bibliographic Details
Published inJournal of symbolic computation Vol. 41; no. 9; pp. 999 - 1003
Main Author Hreinsdóttir, Freyja
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2006
Subjects
Commuting matrices
Gröbner basis
Term ordering
Gröbner basis
Commuting matrices
Term ordering
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Summary:Let X and Y be generic n by n matrices of indeterminates x 1 , … , x r , y 1 , … , y r . Let S = k [ x 1 , … , x r , y 1 , … , y r ] where k is a field and r = n 2 . Let I ⊂ S be the ideal generated by the entries of the matrix X Y − Y X . We will show how an old result on a good term order for this ideal can be improved using elementary methods.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2006.05.002