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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

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