#5105: behaviour of the norm function in the p-adic ring
---------------------------+------------------------------------------------
Reporter: ljpk | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4.1
Component: number theory | Resolution:
Keywords: |
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Changes (by fwclarke):
* type: defect => enhancement
Comment:
There is a confusion of terminology here. It's the "field norm" that's
defined for p-adics. Thus
{{{
sage: Q11 = pAdicField(11, 6)
sage: F.<a> = Q11.ext(x^2 - 2)
sage: (2 + 3*a).norm()
8 + 9*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + O(11^6)
sage: (2 + 3*a)*(2 - 3*a)
8 + 9*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + O(11^6)
}}}
So
{{{
sage: Q11(22).norm()
2*11 + O(11^7)
}}}
is correct, as is
{{{
sage: QQ(-163).norm()
-163
}}}
What you're wanting is usually called the p-adic absolute value (it's a
norm in the functional analysis sense). It would be
good if one could do
{{{
sage: Q11(22).abs()
}}}
and get 1/11. This isn't currently defined, if z is an element of a padic
field, the absolute value can be obtained as
{{{
z.parent().prime()^(-z.ordp())
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5105#comment:2>
Sage <http://sagemath.org/>
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