Thanks for the explanation. Perhaps we need to change the
implementation to be more like what Magma does, namely it gives either
2 O_K-generators or a Z_K-basis by default, but if you ever ask if an
ideal is principal then it works that out and stores the result, with
the generator if principal s
Actually, even that is not correct. It creates the ideal objects in no
time. It seems that it is when it comes to display them that it wants
to determine if they are principal, presumably so it can display them
with as simple a representation as possible.
Bill.
On 30 Dec, 11:39, Bill Hart <[EMAI
What is happening is that at a certain point it is checking to see if
ideals are principal. That requires bnfisprincipal and hence bnfinit
which requires computation of the unit and class group.
Essentially the way it is implemented is that it expresses the ideal
in hermite normal form. Then it f
But pari provides two number field structures (see page 117 of the
pari manual), nf and bnf. nfinit() creates a number field with more
"elementary" capabilities, including the ring of integers and prime
decompositions. bnfinit() works a lot harder and gives the class and
unit groups.
Hence it
The issue is that since Sage uses pari to do everything in the background,
one needs to create the pari data structures, which means that you currently
call nfinit on the number field, which computes the class group and unit
group. This should change eventually, but right now...
David
On Dec 29,
As John Cremona said at the sage.forum: "But why would Sage be
computing the class group in order to factor 2 in K?"
For me that is strange too. Since it would be easier to compute the
factorization of an ideal generate by a prime.
For example: Using the Proposition that asserts that if K is a
It presumably can't compute the class group, because of the proof=true
thing. Basically if you want a proven result, it is going to take
forever and will need more primes than Pari has precomputed.
It's not clear to me if SAGE is actually catching the error message,
or if it is just raising an ex
On Dec 29, 9:17 pm, [EMAIL PROTECTED] wrote:
> Hello:
>
> I am working at my Number Theory lectures and I have found a bug (?). This is
> the output:
>
> /// SAGE 2.9.1 ///
> sage: K.=CyclotomicField(23)
> sage: O=K.maximal_order()
> sage: (2*O).factor()
> *
