Many years ago, I got a B- in abstract algebra, and an A+ in differential geometry.
Now I know why I worry about the blue glow of an unplanned criticality excursion occuring in my brain. On 3/14/07, Dan Piponi <[EMAIL PROTECTED]> wrote:
On 3/14/07, Andrzej Jaworski <[EMAIL PROTECTED]> wrote: > I am glad you are interested Dan. > ... > I do not intend to bore anybody with differential geometry but as I was > pushed that far let me add that if Haskell was made to handle Riemannian > geometry it could be useful in next generation machine learning research > where logic, probability and geometry meet. I believe that you can probably handle (pseudo-)Riemannian geometry in the framework sketched here: http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html That only goes as far as playing with vector fields and Lie derivatives but I think that forms and tensors should fit just fine into that framework. There's a simple way to use types to represent tensor products, and that's sketched here: http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html (Forget that that's about geometric algebra, the thing I'm interested in is the tensor products.) So I'm guessing there's a way of combining these to give a framework for (pseudo-)Riemannian geometry. But it'd only be a good framework for answering certain types of questions - in particular for things like numerical simulation. The important thing is that you'd be able to read off accurate numerical values of quantities like curvatures without any need for symbolic algebra. -- Dan _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
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