Trying to convert a spectra into CRI

I posted this to sci.color, but got no real response. Perhaps someone here
could help me.

I am trying to figure out the algorithm to compute the color rendering index
from a spectrum (spaced 5nm intervals). I have the CIE 13.3-1995 publication,
but it is not clear what one is to do. I can compute X,Y,Z from the spectrum,
along with the X,Y,Z from the test samples (using Table 1 and Table 2 in the
publication), but I don't understand the notation that is used in Equations 5-3
through 5-6....

Trying to convert a spectra into CRI