As far as I know singular does not have gcd for multivariate
polynomials over numberfields
(Martin: is this true?)
but it seems pari does. Is there a reason why this functionality is
not exported to sage (or is it)?
I did a bit of timing and it does not seem to be particularly slow.
I tried gp.gcd but I don't understand what it is supposed to do. It
seems to be undocumented (I did not look in the source yet).
sage: Q=NumberField(t^2+1,'s')
sage: s=Q.gen()
sage: K=Q['p','q']
sage: p,q=K.gens()
sage: gp.gcd((p+s*q)^3,(p+s*q)^5)
1 <== wrong!!
I don't know pari, but after some trying I think the equivalent direct
command is
sage: gp('gcd((p+Mod(s,s^2+1)*q)^5,(p+Mod(s,s^2+1)*q)^3)')
p^3 + Mod(3*q*s, s^2 + 1)*p^2 + Mod(-3*q^2, s^2 + 1)*p + Mod(-q^3*s,
s^2 + 1)
which produces slightly odd but sensible looking output (I tried to
coerce it back
into K but that didn't work :-()
Michel
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