We have an abstract manifold M and a chart x.
A student (friend) is writing  det(\delta_1 x_p,..,\delta_n x_p)=... .
whereas the det should be a determinant and \delta_i x_p the basis vectors of T_p M induced by the chart.

I cann't see any sense in it. Maybe it is senseless. But maybe he uses some identifications (e.g. with some coefficients) or something like that.

What do you think?