# ABOUT K.ring_of_integers()

in William Stein book PAGE 31Algebraic Number Theory,a Computational Approach

## there can run out the *module basis* derectly,but I try in sagenb online,there no *module basis*,why?

*module basis*

*module basis*

```
sage: K.<a> = QuadraticField(5)
sage: OK = K.ring_of_integers(); OK
Order with ***module basis 1/2*a + 1/2***, a in Number Field
in a with defining polynomial x^2 - 5
sage: Frac(OK)
Number Field in a with defining polynomial x^2 - 5
----------------------------------
K.<a> = QuadraticField(5);K;OK = K.ring_of_integers(); OK
Number Field in a with defining polynomial x^2 - 5
Maximal Order in Number Field in a with defining polynomial x^2 - 5
```