Since ℚ(φ) = ℚ(√5), an alternative implementation is to use numbers of the form a + b√5, where a and b are rationals. This can be a nice stepping stone, since p

Since ℚ(φ) = ℚ(√5), an alternative implementation is to use numbers of the form a + b√5, where a and b are rationals. This can be a nice stepping stone, since people are more familiar with manipulating square roots than they are with symbols which happen to obey an equation. It's also a nice exercise to try to match up these two implementations of the same number field.