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interger-ring() and maximal_order() is the same in numberfield

asked 2013-12-10 21:31:03 -0500

cjsh gravatar image

interger-ring() and maximal_order() is the same in numberfield,I try many times,get same rusults...

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answered 2013-12-10 21:46:46 -0500

Francis Clarke gravatar image

I think you must mean ring_of_integers rather than "interger-ring". And indeed K.ring_of_integers() and 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)
    def ring_of_integers(self, *args, **kwds):
        Synomym for ``self.maximal_order(...)``.


            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()
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thank you very much! integer closed, integer elenment....make me mad long time

cjsh gravatar imagecjsh ( 2013-12-11 19:40:49 -0500 )edit

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Asked: 2013-12-10 21:31:03 -0500

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Last updated: Dec 11 '13