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. 1.81844645923206682348369896356070899378625394276899999999The 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.
Kant-style printing means that integers and rational numbers will be printed as integers and rational numbers. Especially in relative extensions this produces easier to read output - but it is no longer possible to paste the output back into the system again. Turns Kant-style printing on if f is true and off if f is false.