We have received some e-mail messages asking about what the component
'.root' in a finite field record really is.

The component '.root' is only present if the finite field was contructed
as an extension with a primitive polynomial (i.e., one whose root is a
generator of the multiplicative group), and in this case it is one of the
roots of this polynomial.

If the finite field was constructed with an irreducible but not primitive
polynomial, the component '.root' is not present, but a root of this
polynomial is still available. Namely the base of the new field as
vector space over the ground field consists of the first <degree> powers
of a root. Thus '.generators[1]' is a root of the polynomial.

To clear up things a little bit we suggest the following name change
'.root' -> '.primitiveRoot' and plan to add a new component
'.primitiveElement'. And of course we are also going to add the above
paragraphs to the manual.

Any objections?

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,  +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany