Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing and Using Minimal Polynomials   Given a zero-dimensional ideal I in a polynomial ring, many computations
start by finding univariate polynomials in I. Searching for a univariate
polynomial in I is a particular case of considering the minimal polynomial of
an element in P/I. It is well known that minimal polynomials may be computed
via elimination, therefore this is considered to be a "resolved problem". But
being the key of so many computations, it is worth investigating its meaning,
its optimization, its applications (e.g. testing if a zero-dimensional ideal is
radical, primary or maximal). We present efficient algorithms for computing the
minimal polynomial of an element of P/I. For the specific case where the
coefficients are in Q, we show how to use modular methods to obtain a
guaranteed result. We also present some applications of minimal polynomials,
namely algorithms for computing radicals and primary decompositions of
zero-dimensional ideals, and also for testing radicality and maximality.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex