There is a diagram on wikipedia that is part of the article on the opponent process. I assume practical equations have been developed, at least reasonable approximations, but they appear to be missing from the diagram.
There is a quanitity C1 that comes from the L and M cones, and is supposed to represent red minus green. There is a quantity C2 - C3 that comes from all three cone types. If C1 is positive it is a red hue, otherwise green. If C2-C3 is positive it is a yellow hue, otherwise blue.
However actual equations for C1 in terms of cone responses, or for C2-C3 in terms of cone responses, or for A (Brightness) in terms of all three cones and the rod responses are completely missing.
As a related question, that should possibly be separated (let me know if it needs to be a new question):
While RGB defined color can vary with the display device, it would be very useful to have a rough approximation that turns an typical 3 byte RGB triple into a triple of approximate cone and rod responses along with a model of cone and rod saturation (i.e. as you stare at a point how does the cone response change over time). I am sure this has been done and is well known in the right places. Could you point me to it?