#5893: Norm Form for Number Fields and Orders
---------------------------+------------------------------------------------
Reporter: roed | Owner: roed
Type: enhancement | Status: new
Priority: major | Milestone: sage-feature
Component: number theory | Keywords:
---------------------------+------------------------------------------------
Often if one is doing computations with number fields and orders by hand,
it's useful to have the norm form with respect to a given basis. For
example:
{{{
sage: K.<sqrt2> = NumberField(x^2 - 2); T.<a, b> = QQ[]
sage: K.power_basis()
[1, sqrt2]
sage: K.norm_form([a, b])
a^2 - 2*b^2
sage: K.norm_form([1, b])
1 - 2*b^2
sage: OK = NumberField(x^2-5, names='sqrt5').maximal_order(); T.<a, b> =
ZZ[]
sage: OK.basis()
[1/2*sqrt5 + 1/2, sqrt5]
sage: OK.norm_form([a, b])
-a^2 - 5*a*b - 5*b^2
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5893>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
