An improved term ordering for the ideal of commuting matrices

Freyja Hreinsdóttir

doi:10.1016/j.jsc.2006.05.002

An improved term ordering for the ideal of commuting matrices

Freyja Hreinsdóttir

Faculty of Subject Teacher Education

University of Iceland

Research output: Contribution to journal › Article › peer-review

Abstract

Let X and Y be generic n by n matrices of indeterminates x₁, ..., x_r, y₁, ..., y_r. Let S = k [x₁, ..., x_r, y₁, ..., y_r] where k is a field and r = n². 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.

Original language	English
Pages (from-to)	999-1003
Number of pages	5
Journal	Journal of Symbolic Computation
Volume	41
Issue number	9
DOIs	https://doi.org/10.1016/j.jsc.2006.05.002
Publication status	Published - Sept 2006

Other keywords

Commuting matrices
Gröbner basis
Term ordering

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10.1016/j.jsc.2006.05.002

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title = "An improved term ordering for the ideal of commuting matrices",

abstract = "Let X and Y be generic n by n matrices of indeterminates x1, ..., xr, y1, ..., yr. Let S = k [x1, ..., xr, y1, ..., yr] where k is a field and r = n2. 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.",

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author = "Freyja Hreinsd{\'o}ttir",

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AB - Let X and Y be generic n by n matrices of indeterminates x1, ..., xr, y1, ..., yr. Let S = k [x1, ..., xr, y1, ..., yr] where k is a field and r = n2. 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.

KW - Commuting matrices

KW - Gröbner basis

KW - Term ordering

UR - https://www.scopus.com/pages/publications/33746870462

U2 - 10.1016/j.jsc.2006.05.002

DO - 10.1016/j.jsc.2006.05.002

M3 - Article

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VL - 41

SP - 999

EP - 1003

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

IS - 9

ER -

An improved term ordering for the ideal of commuting matrices

Abstract

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