Trace form of a number field
= Trace form of a number field
{title2=$B(x,y)=\operatorname{Tr}_{K/\mathbb Q}(xy)$}
The trace form of a number field $K$ is the symmetric bilinear form
$$
B(x,y)=\operatorname{Tr}_{K/\mathbb Q}(xy).
$$
The pairing uses the <field trace> of the product, rather than taking a trace of each factor separately.