Topics in computational algebraic number theory

return L/K, as an rnf algsplittingfield(al) split A over an extension of K algsplittingdata(al) splitting field of A as an rnf over center algsplittingfield(al) multiplication

The Hopf algebra of rooted trees associated to Butcher’s group (as well as the Hopf algebras of planar rooted trees in [MKW08, BO05]) can be seen as a particular instance of a

with integral algebraic coefficients and the argument running through the ring of rational integers. §

asymptoti theory of global elds (that is number elds or funtion elds) and v arieties over.. them are quite diverse

The characteristics for the five most repeated prokaryote genomes are pre- sented in Table 1. These short genome sequences have been extensively studied and are well known

In the next three subsections we describe how this construction works for cy- clotomic fields, for CM fields and for other more general fields. To simplify the notations, we only

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since a generic algorithm can only obtain new group elements by querying two known group elements to the generic group oracle; hence a reduction can always extract a