Re: Bug in nfabsis/Round4

[Bill Allombert <allomber@math.u-bordeaux.fr>]

I have my own test-suite for nfgaloisconj.

It was not easy to produce suitable (i.e. Galois) polynomials, so I
computed once and for all Galois closure of polynomials determined by
Y.Eichenlaub in his thesis (see pari/AUTHORS).

This polynomials essentially tests the combinatorial parts of my
algorithm.  Precision problems are tested using bigger polynomial
computed as Hilbert class field of quadratic fields. Igor has had the
same idea.

It has appeared that this polynomials are particularly stressing for
nfbasis, so I used it to compare Round4 versus Round2 implementations.

I can mail it to you if you want , but it's too long to be included in
this mail.

I have also the original polynomials, which can be used to test
polgalois.

One problem is that lots of mathematical algorithm has the following
behaviour:

1) we are in a good case (90% of chance) -->easy
2) we are in a bad case  (10%)
2.1) We are in a no-so-hard case (9%) -->no-so-difficult
2.2) We are in a very hard case  (1%) -->very hard.

So only 1% of the entries will test the very hard case which is the
most likely to be buggy, and it can be very difficult ,
mathematically, to find entries which trigger the very hard case .

I have tested th patch of Xavier and I have not found any bugs.


Bill.