Oh yes, refreshing the page in my browser revealed that the computation was
in fact over. I don't get the same minimal polynomial:
Number Field in a with defining polynomial y^64 - 16*y^63 + 120*y^62 - 552*y^61
+ 1060*y^60 + 9192*y^59 - 109548*y^58 + 594136*y^57 - 1818336*y^56 +
1418016*y^55 +
Thank Vincent ! I've tried to do it your way, but it is still computing
after more than an hour (unless my SageMathCloud page needs refreshing, I'm
always confused about that...)
How long did it take for you? (you've erased the output of the %time
command, i think)
On Tuesday, November 10, 201
On 10/11/15 10:45, John Cremona wrote:
Two ideas:
(1) As in your first construction but replace each field constructed
after the forst with the corresponding absolute field.
(2) Let a = sqrt(2)+sqrt(3)+... as a real number and use LLL to find
its mimimum polynomial.
(2) is easily done in Sage
Hi,
This computation takes long time but Sage is able to do it. Doing it
step by step, you can observe the relation between the degree of the
field and the time needed to generate it.
sage: a=2
sage: b=-1
sage: c=5
sage: ra = QQbar(a).sqrt(); ra.exactify()
sage: rb = QQbar(b).sqrt(); rb.exact
>
>
> (1) As in your first construction but replace each field constructed
> after the forst with the corresponding absolute field.
>
>
I have tried this but got something like:
F0.= NumberField(x^2 - 2)
F1.= F0.extension( polygen(F0)^2 - 5 )
L= F1.absolute_field("bar")
L(foo0)
...
TypeError:
Two ideas:
(1) As in your first construction but replace each field constructed
after the forst with the corresponding absolute field.
(2) Let a = sqrt(2)+sqrt(3)+... as a real number and use LLL to find
its mimimum polynomial.
John Cremona
On 10 November 2015 at 06:35, Pierre wrote:
> Hi,
>
>
Hi,
I'm trying to construct a certain number field, of degree 64 over QQ (well,
I'd like to check that using Sage !).
It is constructed by adding a certain number of square roots. I have first
tried
F0= QQ
F1.= F0.extension( polygen(F0)^2 - 2) ## adding sqrt(2)
F2.= F1.extension( polygen(F1)^2
