Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure of lexicographic Groebner bases in three variables of ideals
  of dimension zero   We generalize the structural theorem of Lazard in 1985, from 2 variables to 3
variables. We use the Gianni-Kalkbrener result to do this, which implies some
restrictions inside which lies the case of a radical ideal.

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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th