There are a number of verbose flags s applying to the functions
described in this chapter. The flags and their levels n are
mentioned in the descriptions of the functions which use them.
Note however, that setting the verbose levels may produce
unexpected results since the effective scope of the flags
is a little bit vague. Consider the following example:
> SetVerbose("MaximalOrder", 1);
> SetVerbose("Factor", 1);
> L := NumberField(PolynomialRing(Rationals()).1^2-10);
Factorize square-free polynomial over Z of degree 2
Deflation factor: 2
Number of deflated factors: 1
Factor inflated polynomial 0 of degree 2
Total factorization time: 0.000
Final irreducibility test factorization:
<x^2 - 10, 0>
> Regulator(L);
order_maximal_sub: called with algo_flag: 0
no algorithm selected
nothing about algebra-splitting selected
nothing about reduced-discriminant selected
nothing about dedekind-test selected
order_maximal_sub: calling order_maximal_sub_sub
order_maximal_sub_sub: called with algo_flag: 16
no algorithm selected
nothing about algebra-splitting selected
use reduced-discriminant selected
nothing about dedekind-test selected
red disc: f =x^2 - 10
r_disc = 20
Reduced discriminant: 20
Factorization of reduced discriminant:
2^2 * 5^1
calculation and factorisation of reduced discriminant: 0.01
Factorization of discriminant:
2^3 * 5^1
factors with (possibly) not maximal overorder:
2^3
-----------------------
order_max_p_sub called:
prime: 2, prime_bound: 3, algo_flag: 16
-----------------------
no algorithm selected
nothing about algebra-splitting selected
nothing about dedekind-test selected
---------------------------
order_max_p_sub_sub called:
prime: 2, prime_bound: 3, algo_flag: 89
---------------------------
round2 selected
no algebra-splitting selected
use dedekind-test selected
No split performed ...
(due to user advice or impossible) ...
standard algorithm.
----------------------------
order_max_p_rnd2_sub called:
prime: 2, prime_bound: 3, algo_flag: 89
----------------------------
use dedekind-test selected
Order is already 2-maximal.
1.81844645923206682348369896356070899378625394276899999999
The first few lines of output are generated, because
the creation of number fields involves a test of irreducibility
for the defining polynomial(s).
The next group of lines come from the computation of the
maximal order which is used for the regulator computation.
In general the amount of output generated increases with the
value supplied. Furthermore, the output corresponding to larger
values gets more and more technical.