On 6/4/07, Sarah Reznikoff <> wrote:
> Maybe you remember me from Berkeley.
Yep!!
> Anyway, I am trying to use your
> online SAGE worksheet to do a few calculations. If you have a minute,
> maybe you can set me straight here. It will probably be easy, since I am
> not too savvy with these things and am most likely doing something
> obviously wrong.
>
> To get started I want to reproduce a calculation that Jack Wagoner did
> using PARI, which is mentioned in his paper "Strong Shift Equivalence
> Theory". He has a square matrix A with irreducible characteristic
> polynomial, and finds a set of generators for the number field Q(A) by
> using the PARI command "buchgenfu()". Buchgenfu does not seem to be
> available through SAGE, but it looks like bnfclassunit should work.
> However, it doesn't give me the information Wagoner gets, and indeed it
> only returns a vector of length 9, which is curious.
>
> Here's what I'm typing:
> v=pari("[1,0,0,-6,-5,-6,-3,1]")
> f=v.Pol()
> h=pari("bnfclassunit(f)")
> h
>
> to which it returns [f; [1,0]; [1,1]; [1]; [1,[],[]]; 1; 1; [2,-1];[]]
Just use GP instead. It's an interface to the GP interpreter instead
of the PARI C library itself.
sage: v = gp("[1,0,0,-6,-5,-6,-3,1]")
sage: f = v.Pol()
sage: f.bnfclassunit()
[x^7 - 6*x^4 - 5*x^3 - 6*x^2 - 3*x + 1; [3, 2]; [6028199129, 1]; [1,
x, x^6 - 6*x^3 - 5*x^2 - 6*x - 3, x^2, x^3 - x^2 - 3, x^4 - x^3 - 4*x,
x^5 - x^3 - 6*x^2 - 4*x - 2]; [1, [], []];
458.1702498816480192794551962; 1; [2, -1]; [x, x^6 - x^5 + x^4 - 6*x^3
+ x^2 - 5*x + 2, 2*x^5 - 5*x^3 - 6*x^2 - 9*x - 5, 2*x^6 - 4*x^4 -
14*x^3 - 11*x^2 + 2*x + 2]]
Also, if you type
sage: f.bnfclassunit?
for help.
William
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