Conversion of notional to frational coordinates for unit cells?

["E.L. Willighagen" <egonw &$at$& sci.kun.nl>]

 Hello all,
 I have a question about the conversion of notional coordinates of unit cells
 to fractional coordinates. I found on ccl.net [1] the mathematics (Eq. 6.1) ,
 but they seem wrong. I did a test for a unit cell (a=b=c=1,
 alpha=beta=gamma=90) and the b-vector becomes [0 1 1] instead of [0 1 0] in
 fractional coordinates.
 It seems that element (3,2) is wrong and that it should be:
 c*(sin(alpha) - SIN(beta)*SIN(gamma))/sin(gamma)
 Is this correct? (I cannot find it anywhere, and am not that much into
 crystallography...)
 Egon
 1. http://server.ccl.net/cca/documents/molecular-modeling/node4.html