My thought was actually is that if it doesn't work for all complex roots, then I am not going to bother with it, as it seems too subtle :) I was encouraged by $n=2$ though.

It's all good :)

I have an argument now that avoids the contour integration tricks (but does use an analytic continuation). I will type it up and send to Patrizio shortly.

Sorry, posted a comment by mistake -- have no idea how to touch this.

You may want to ask Noriko Yui if anybody looked at infinite order automorphisms of rigid CY threefolds. She probably knows as many of these rigid CYs as anyone.

I assume you mean CY threefolds. Why do you think they would only have a finite automorphism group?

Of course, $X_6$ is a cubic in $\mathbb P^3$. If you allow weighted projective spaces, then $X_7$ is a degree $4$ hypersurface in $\mathbb P(1,1,1,2)$. I can't think of other constructions off the top of my head.

"Order" means "order of vanishing at the origin". "Cone" means stable under linear maps $(X_i\to\lambda X_i)$.

I am not an expert on optimization, but what are your goals here? How important is accuracy (e.g. is it OK if you only get 98% of points?) How serious are the time/memory constraints? What can be said about the determinant, and perhaps the eigenvalues of A? What size of d are we talking about? How many points do you expect in the answer (10, 100, 1000, 10^10)?

@bananastack I am looking for something really simple, maybe half a page or so. Perhaps this is just too much to hope for.

Are you referring to arxiv.org/pdf/1101.5834.pdf ?

No, I haven't, will try to make sense of it. Is there a place there that I should be specifically focusing on?