> < ^ From:

^ Subject:

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

> < [top]