exact computations with algebraic numbers
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
sage: r = sqrt(2)
sage: a = AA(r)
sage: b = AA(1/r)
sage: c = a*b
Then I get:
sage: c
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()
to find a polynomial and .roots(QQbar)
to find the roots of that polynomial.