Rings

MAGMA knows a lot of rings. The ring of integers, $\mathbb{Z}$, and more generally the ring of integers of any number field are predefined (Integers() and Integers(NumberField(p(x))), resp., where $p(x)$ is a polynomial), and many others can be easily constructed.

Example 2.14.4   For example, if you type R:= Integers( QuadraticField(-1));, i:=Basis(R)[2]; i^2; i in R;, and 1 in R; then MAGMA will return true to the last two commands.