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Base field of Residue field

asked 5 years ago

Abhishek gravatar image

Let K be a number field, OK be its ring of integers, p prime ideal in Z and p be a prime ideal above p. I am trying to construct the Z/pZ vector space OK/p, and a Z/pZ subspace spanned by certain images of elements of OK.

For constructing the prime, I am able to use Q=K.primes_above(p)[0], but I do not know how to view the residue field F=K.residue_field(Q) as the vector space over Z/pZ.

The command V,fr,to=F.vector_space() indicates ValueError: too many values to unpack. Here K= Q(ζ11) and p=3. Can someone suggest me alternative commands for the same.

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answered 5 years ago

rburing gravatar image

You forgot to pass map=True to get the maps.

K.<a> = CyclotomicField(11)
Q = K.primes_above(3)[0]
KQ = K.residue_field(Q)
VQ, fr, to = KQ.vector_space(map=True)

Then:

sage: to(a)
(0, 1, 0, 0, 0)
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Asked: 5 years ago

Seen: 808 times

Last updated: Jul 22 '19