separable polynomial


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separable polynomial

[′sep·rə·bəl ‚päl·i′nō·mē·əl]
(mathematics)
A polynomial with no multiple roots.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Let P [member of] Q[x] be a monic separable polynomial of degree at least 2 with at least one irrational root.
Let P [member of] Q[x] be a monic separable polynomial of degree at least 4 with at least one irrational root.
In [5, Theorem 1.3], it was shown that if for some monic separable polynomial P and any [[lambda].sub.1], ..., [[lambda].sub.k+l] [member of] Z(P), where g([[lambda].sub.k+1], ..., [[lambda].sub.k+l]) = 0, one has
Rational quotients of two linear forms in roots of a polynomial
Hence by the second condition aKv is a (simple) root of the separable polynomial fm(X)- uKv[X].
OPTIMAL APPROXIMATION IN HENSELIAN FIELDS

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