Karim BELABAS on Sun, 14 Sep 2003 16:39:07 +0200 (MEST)

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Re: qfbpowraw

On Sun, 14 Sep 2003, Bill Allombert wrote:
> ginv(Q) has a strange behaviour:
> If Q is real, it reduce its output, but not if Q is imaginary.

Assuming the input form is reduced, the output is reduced in both cases.
The difference with the real case is that it also works if the input is not

> Also qfbpowraw(Q,-1) is implemented as ginv(Q) which is not
> correct if Q is real, because of the above.


> It seems that PARI * and ^ operators allow operation on quadratic
> forms but reduce them. I would personnaly prefer it does not reduce
> them.

Coefficient explosion would occur for ^.

qfb[comp|pow]raw would be dumped then ?

I don't like it.

> Also l*Qfb(a,b,c)=Qfb(l*a,l*b,l*c) could be supported.


> Lastly, is it possible to get the SL2 matrix involved in the equivalence
> between two forms ? (I have written a GP script for that effect, but...)

Not from the current GP interface. In the real case, you have the distance
component, which is less useful, but remains small.


Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://www.parigp-home.de/  [PARI/GP]