On Tue, Sep 23, 2008 at 9:34 AM, pong <[EMAIL PROTECTED]> wrote:
>
>
> I tried
>
> sage: A=matrix([[1,1],[2,3]])
> sage: A.eigenvalues()
> [0.2679491924311228?, 3.732050807568878?]
>
> My question is why the last digit before ? in 0.2679491924311228? is
> '8'? Shouldn't it be "7" according to

? means the digit before the ? is unknown.

This is an algebraic number printed as an element of QQbar.
You can always get it to higher precision.

sage: RealField(100)(A.eigenvalues()[0])
0.26794919243112270647255365849


William

>
> sage: ch=characteristic_polynomial(A)
> sage: solve(ch(x)==0,x)
> [x == 2 - sqrt(3), x == sqrt(3) + 2]
> sage: N(2-sqrt(3), digits=18)
> 0.267949192431122706
>
>
>
>
> >
>



-- 
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org

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