But that's the opponents' point -- the values of such coefficients make excellent trade secrets, but the fact that you can, for instance, invert a matrix, is poor material for a patent.
Personally, I think the limits of software patents should be to precise algorithms. This ends up protecting the fruits of laborious research which have found optimal solutions (in an engineering sense) to things like cryptography, or graphics, or video compression. The disclosure of these algorithms would indeed advance research and the useful arts, and the disclosure would be advantageous. Most software patents, though, are "a system for clicking on a button, but INNA FONE!!!" type of nonsense where disclosure does absolutely nothing, anyway. So sure, such posers ought to be able to patent the exact algorithm they use to click their button, if they want, but NOT to patent the idea of clicking a button, which is in effect what we have now.
This separation goes pretty far towards the concerns the OP wrote down, and is, I think, pretty intuitive to most programmers. It is also the closest to copyright, but without requiring the legal jangle of "well, you used the variable i, but I used j, so therefore my code is different!!!1!one!!" kind of nonsense that pure copyright might result in. Patenting a precise series of disclosed algorithmic steps is helpful, and is a bright line for the patent office, and easy to adjudicate as well. Patenting the notion that you can transmit particular kinds of data over a network, or have certain programs talk to other programs, is where the PTO went off the rails.
