However, the parameters ( \ lambda, \ mu ) of the Hessian form may belong to an extension field of the field of definition of the original curve.
12.
It is an extension field of "'C "', if we identify every complex number with the corresponding constant function defined on " M ".
13.
So the Arf invariant of a nonsingular quadratic form over " K " is either zero or it describes a separable quadratic extension field of " K ".
14.
In algebraic terms, two varieties over a field " k " are birational if and only if their function fields are isomorphic as extension fields of " k ".
15.
It is a known result that for finite field extensions, the general linear group of the base field is a conjugacy-closed subgroup of the general linear group over the extension field.
16.
This polynomial has a zero in Galois extension field GF ( 8 ) at the primitive element \ alpha, and all codewords satisfy \ mathcal { C } ( \ alpha ) = 0.
17.
He investigates two endomorphism of the unit group U = U _ L of the extension field, viewed as a Galois module with respect to the group G, briefly a G-module.
18.
Alabama Extension s Auburn University headquarters also was equipped with a full-service studio and live production facility so that Extension field offices would have had full access to live and recorded productions via satellite.
19.
The group \ textstyle G is the image due to the pairing of the group generated by \ textstyle P ( in the extension field of degree 2 of the finite field of order p ).
20.
If the base field is of characteristic 2, e . g . ( { \ Bbb Z } _ 2, +, \ cdot ), arithmetic over the extension field can be done very efficiently.
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