Changes
http://wiki.axiom-developer.org/354ComplexRIsNotNecessarilyAFieldWhenRIsAField/diff
--
Axiom believes
\begin{axiom}
Complex PF 5 has Field
\end{axiom}
but this is not true, as Waldek observed:
\begin{axiom}
(2 + %i)::COMPLEX PF 5 *(2 - %i)
\end{axiom}
In fact, we find in gaussian.spad::
if R has Field then -- this is a lie; we must know that
Field -- x**2+1 is irreducible in R
Waldek suggested: when creating 'COMPLEX F' we may try
to check if $x^2 - 1$ is irreducible over 'F'. In general this
may be hard to check, but just looking at characteristic we
can reject 'PF 5' cheaply.
I think that's better than nothing. Maybe Axiom should issue a warning when it
cannot determine whether $x^2-1$ is irreducible?
Is it really hard to check?
Martin
--
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