I've given no thought to unifying these three areas or layering them in any obvious way. I'd be interested in any thoughts you have on the subject.
For quantum physics I'm working my way through Nielsen "Quantum Computation and Quantum Information" and Mermin "Quantum Computer Science" I want to be able to use the bra-ket notation. The underlying unitary matrix computations don't seem all that intimidating. I think this could be a separate package with operators like a Hadamard gate, etc. I've written a couple programs for IBM's online quantum computer so I think I understand some of the issues. I'm looking at quantum simulator code on github with the thought that the simulator could be embedded in the underlying lisp so quantum programs could be "run" in Axiom. I've looked at Kaku's book on Quantum Field Theory but I'm afraid that relativistic physics is a much longer climb. Renormalization leaves me with an uncomfortable feeling and I don't understand a lot of it. For classical physics I think a reasonable approach might be the "cookbook" files introduced this summer. The idea is to create "application notes" (cookbooks) that focus on working out a particular example, ala "worked out homework problems using Axiom". The cookbooks are literate programs constructed at build time. For Clifford Algebra I'm working my way through 2 books, Dorst "Geometric Algebra for Computer Science" Sommer "Geometric Computing with Clifford Algebras" I have worked in both computer vision and robotics so the chapters on vision and kinematics are things I'd like to implement. The scalar/vector/bivector/trivector representation seems to fit naturally into a record. The calculations amount to a lot of book-keeping which Axiom could easily automate. I'd also like to be able to implement the higher tensor products. I do plan to look at what you've already implemented but first I want to understand the area enough to be able to implement the code (see previous emails). Once I think I understand I'll see what you've already done. For geometry it falls under "Geometric Algebra". Sommer Chapter 4 is on "A Universal Model for Conformal Geometries of Euclidean, Spherical, and Double-Hyperbolic Spaces". I don't think geometry is a separate subject in this formulation. So the real question might be "Can I formulate my physics in matrix and tensors and shift between them". Which leads to the question "Can I easily convert between matrices and tensors?" >From what I've seen so far this should be possible, provided it is implemented properly. The CA wedge product is just the basis vectors times the determinant so you might have to specify the map between the matrix basis and the tensor basis. All of which implies I understand (and can implement) the extended tensor algebra. For that I'm working my way through the course: https://www.youtube.com/watch?v=_pKxbNyjNe8&list=PLRlVmXqzHjUQARA37r4Qw3SHPqVXgqO6c Tim
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