interger-ring() and maximal_order() is the same in numberfield
interger-ring() and maximal_order() is the same in numberfield,I try many times,get same rusults...
I think you must mean
ring_of_integers rather than "
interger-ring". And indeed
K.maximal_order() are the same for a number field
K. You can see this explicitly as follows:
sage: K.ring_of_integers?? Type: builtin_function_or_method String Form:<built-in method ring_of_integers of NumberField_absolute_with_category object at 0x7f85bc4dae00> Definition: K.ring_of_integers(self, *args, **kwds) Source: def ring_of_integers(self, *args, **kwds): r""" Synomym for ``self.maximal_order(...)``. EXAMPLES:: sage: K.<a> = NumberField(x^2 + 1) sage: K.ring_of_integers() Maximal Order in Number Field in a with defining polynomial x^2 + 1 """ return self.maximal_order()