Hi!

On 22 Sep., 20:08, Shing Hing Man <mat...@yahoo.com> wrote:
> Thanks for the  reply!
> Just one more question.
> In general, if k is a finite field, what is k(i), where i is an
> integer, suppose to be ?

Apart from the <TAB> autocompletion, another useful way to get
information is to look into the documentation. This is possible by
putting "?" after an interesting object and hit the return key:
  sage: k.<a>=GF(9)
  sage: k?

This will tell you:
"""
...
            EXAMPLES:

                FiniteField_givaroElement are accepted where the
parent
                is either self, equals self or is the prime subfield

                sage: k = GF(2**8, 'a')
                sage: k.gen() == k(k.gen())
                True


                Floats, ints, longs, Integer are interpreted modulo
characteristic

                sage: k(2)
                0
...
"""

So, the integers are interpreted modulo the characteristic of the
field, certainly not modulo the size of the field.

Best regards
Simon

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