Karim Belabas on Fri, 01 Feb 2008 22:50:01 +0100

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Re: idealappr()

* John Cremona [2008-02-01 22:15]:
> The documentation for idealappr(K,P) implies that in the case that P a
> prime ideal in the number  field K, the element returned will be a
> uniformizer for P and integral.


[ P.gen[2] is another "simpler" way to get a uniformizer ]

> Will it always be a generator for P when P is principal (as it might
> then be)


> If the latter, would it be relatively expensive to call
> bnfisprincipal() to ensure that we have a generator when it exists?

It's actually impossible: the argument to idealappr is an nf and
not a bnf, which would be required for bnfisprincipal (idealappr is a
rather trivial function, especially if the input is a prime ideal; it is
*much* simpler than bnfinit + bnfisprincipal !).

One could check whether the input is in fact a bnf, then test whether P
is principal, and if so compute a generator; but it would complicate a
simple function for a rather limited use.

What's wrong with calling directly bnfisprincipal ? [ it will actually
produce a "uniformizer" for any ideal, not necessarily a prime; and
bypass a useless idealappr call ]

What is your specific application ?


Karim Belabas                  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]