Lewis McCarthy writes in his e-mail message of 1994/08/27

I've been trying to factor in the polynomial ring over the Gaussian
rationals without success. Could someone explain what I'm doing wrong in
the following example ? Also, what syntax do I need to use to factor
over other finite field extensions ?

gap> x := Indeterminate(GaussianRationals);
X(GaussianRationals)
gap> x.name := "x";
"x"
gap> f := Polynomial(GaussianRationals,[7 - 2 * E(4),5,4 + E(4)]);
(4+E(4))*x^2 + 5*x + (7-2*E(4))
gap> Factors(PolynomialRing(f.baseRing),f);
Error, sorry, can not factor <r> in the ring <R> in
R.operations.Factors( R, r ) called from
Factors( PolynomialRing( f.baseRing ), f ) called from
main loop
brk> f in PolynomialRing(f.baseRing);
true

Alexander Hulpke answered this question rather thoroughly. I would just
like to make one small additional point. Whenever a GAP error messages
reads 'Error, sorry, can not' (or if it has already been corrected
'Error, sorry, cannot' ;-), it means that you have come upon a limitation
of GAP. I.e., you have asked a meaningfull question, and you have asked
it in the correct way, but GAP has no method to do what you asked for.

This ``has no method'' can mean different thing. In this particular
case, as Alexander pointed out, the code is there, but the code that
would connect this particular extension to the general case has not yet
been written. Another meaning might be ``there is a well known algorithm
for that problem, but have not yet implemented it''. A final meaning
might be ``there is no known algorithm to solve this problem'' or even
stronger ``there can be no algorithm to solve this problem'' (e.g. the
word problem in general finitely presented groups).

So if you see 'sorry', it is rather unlikely that you have done something
wrong (or you have done something very wrong, like trying to factor over
'GaussianRationals', when you really wanted to factor over the
'Rationals' ;-).

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany