polredabs suggestion

I have just spent a month applying polredabs to about 7 million polynomials
of degree up to 21, with 100% success even though some took a long time
(and I could be patient).

Each of these polynomials (monic and integral) defines an extension of Q
which I know to be unramified at primes > 500000 (these are the fields over
which the torsion of an elliptic curve in my database acquires extra
torsion, and were supplied by Enrique Gonzalez and Filip Najman), so I was
able to help the process by dividing out from the polynomial discriminant
all small primes, seeing that the quotient was a square, and taking its
square root before factoring it (to give the factors to polredabs).

But now although I have all the polredabs-ed polynomials (in about 92.5% of
the cases the original polynomial was returned, in 7.5% of cases a new
polynomial was returned), we want to add some or all of the fields to the
LMFDB which will require doing many more computations with these number
fields, starting with finding the maximal order.  It seems a pity that
polredabs() has laready computed the maximal order and the field
discriminant, but that has been discarded -- as far as I can tell there is
no option to polredabs() to return anything other than the new polynomial
and an expression giving its root in terms of the original (or vice
versa).  And the integral basis for the field -- but not the factored
discriminant.

Please can we have an option to polredabs to return more?  At least: the
output polynomial's factored discriminant.

I do see from the documentation that it can return the integral basis, from
which one can recover the field discriminant, and in may case this is easy
to factor.  But I did not think of that until after running it 7 million
times...

John

PS degree 16 was by far the worst
-- 
Prof J E Cremona
Warwick Mathematics Institute
University of Warwick
http://www2.warwick.ac.uk/fac/sci/maths/people/staff/john_cremona/