Many thanks to Gabor Grothendieck for responding to my posting about Automatic Differentiation (invite from Shaun Forth for interaction with R developers) showing how one might use rSymPy and symbolic (rather than automatic) differentiation to get a function that computes gradients. See http://code.google.com/p/rsympy/#Automatic_Differentiation_(well,_sort_of) for a worked example on the Broyden test function. This is a big step forward. There's still a way to go before we can produce a vectorized gradient code automatically when the size of the problem is variable, but the example may serve to incite some imaginative coders to action. Thanks again Gabor. JN