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Special Options

It is possible to obtain output generated by the KANT package using the verbose printing feature of Magma, furthermore, the general style of the output can be changed. It is also possible to alter the precision used for internal real computations.

SetVerbose(s, n) : MonStgElt, RngIntElt ->
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.

SetKantPrinting(f) : BoolElt -> BoolElt
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.
SetKantPrecision(n) : RngIntElt ->
SetKantPrecision(O, n) : RngOrd, RngIntElt ->
SetKantPrecision(O, n, m) : RngOrd, RngIntElt, RngIntElt ->
SetKantPrecision(F, n) : FldAlg, RngIntElt ->
SetKantPrecision(F, n, m) : FldAlg, RngIntElt, RngIntElt ->
For internal real computations, some number field functions use real arithmetic to a fixed precision; therefore every algebraic field and every order comes equipped with some real-rings.

Initially, the precision (in decimal digits) will be the maximum of the set precision P, 20 and four times the degree of the algebraic field (order) in which calculations are performed. By default P=52.

In addition all unit computations use a second real-ring in which the default precision is always twice the ordinary precision. This ring can be set using the third argument of SetKantPrecision.

Furthermore, the computation of the zeroes of the defining polynomial of the field or order uses a third, independent, precision which initially is the maximum of 32 and the (binary) logarithm of the largest coefficient of the defining polynomial.

Note however, that several functions will work automatically with a much larger precision if necessary to guarantee P digits for the user. Generally all functions take care of the necessary precision. Only under rare circumstances will any computation fail because of precision loss.

Certain calculations that fail if the precision is too small may succeed after restarting with increased precision.

If the order O or field F is given, then the precision change will apply only in the context of that order (field).

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012