I'm trying to do exact computations with algebraic numbers. In particular, I know to expect integer answers like 1, 0, and 3 at the end of my computations, but I'm getting something slightly off.
I noticed that if I run this
a=AA(sqrt(2));
b=AA(1/sqrt(2));
c=a*b;
print(c)
, Sage prints c as "1.000000000000000?".
Is this being handled in the computer as exactly 1? Otherwise, how can I do exact computations with algebraic numbers in Sage? I obtain the algebraic numbers I'm working with using algdep() and .roots(QQbar).