4 ms·
If you want to do exact computations, SAGE is handy, Free, and built on Python: sage: k.<a> = QuadraticField(7); k Number Field in a with defining poly
by hdevalence 13y ago
If you want to do exact computations, SAGE is handy, Free, and built on Python:
sage: k.<a> = QuadraticField(7); k
Number Field in a with defining polynomial x^2 - 7
sage: x = 3*a - 8
sage: x.is_integral()
True
sage: 1/x
-3*a - 8
sage: x * (1/x)
1
sage: (1/x).is_integral()
True
(Note: the is_integral() is because we define k to be QQ(sqrt(7)), not ZZ(sqrt(7)), so we want to check that our elements are really integers, i.e., lie in ZZ(sqrt(7))).