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?
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
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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