Mueller-Quade, Steinwandt. Basic algorithms for rational function fields (JSC1999)(T)(28s).djvu: eKnigu

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Mueller-Quade, Steinwandt. Basic algorithms for rational function fields (JSC1999)(T)(28s).djvu

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Date Dec 19, 2004

As the implementation of the
individual steps is straightforward we omit giving an explicit algorithm, and restrict
ourselves to stating
Theorem 2.4...
By specializing some of the A^ in advance we can force a "particular
structure" of the polynomial...
Proof, (i) A consequence of (Eisenbud, 1995, Exercise Al.l)
(ii) A consequence of (Eisenbud, 1995, Exercise A1.2 a)D
By means of this lemma we can derive
Lemma 4.2...
From Jl • K(x)[Z] = f]i=1 Qi we can conclude (ii), as the reduced Grobner bases of Jl
and Jl • K(x)[Z] coincide...