@ACuriousMind Do you know of any work connecting those two ways of framing quantum mechanics in symplectic geometry: the Gromov-Witten invariants approach from string theory and the deformation of Hopf algebras approach from integrability?
@ACuriousMind What I mean by that is that both are somehow an embedding of quantum mechanics in the symplectic framework and they seem to be dual to each other, one being a covariant approach and the other, contravariant. I am curious if there are existing results on such a relation.
Anyhow, I'd be inclined to first write the replication bit using regular file copy, and get that all debugged and working. Then all you need to do is replace copying of FLAC files by the convert and copy.
@JohnRennie Nice. Taking a look at it. Apparently Boost::filesystem::last_time_write I was hoping to use to not re-sync files is only for POSIX-like systems
Oh Microsoft why couldn't you at least try to be POSIX
The single biggest advantage of Windows for the developer is that there is one, and only one, WIN32 API that is the same on all computers everywhere that run Windows.
It's because Windows has always been controlled by a single company. That has it's downsides because some of Microsoft's design decisions suck. But it does have advantages. The same applies to OSX of course.
@BernardoMeurer The thing with equations and all is really because algebraic constraints (equations) leads to an algebraic solution set which is essentially an analytic function on some open set of the surrounding space (R^4 in your case). By the inverse function theorem of analysis in R^n, we know it is locally invertible smoothly and so a diffeomorphism from (an open subset of) the manifold (the solution set) to open sets in R^m, where m is n-(# constraints).
@BernardoMeurer This can be extended to an open cover of the solution set, and thus forms a smooth atlas, proving the object is a manifold (locally R^n objects).
@BernardoMeurer In your specific case, you can just say: ''Oh z > 0 so a unique solution to the equation for z on the sphere as $z = z(x,y)$ is given... Which means I have a global chart for the manifold resulting from those two constraints.''.
@BernardoMeurer Adding x=y is just saying that you can find y as a function of x ''y(x)'' everywhere on the final solution set. Hence, again, a global chart is given by, say, the open interval on the x axis from -1 to 1. The maps are smooth and their inverse are smooth, and the global chart is thus a smooth atlas == My object (solution set) is a smooth manifold.
@BernardoMeurer Chart: An open subset U of the manifold M paired with an open subset V of $R^n$ together with a smooth map between the two such that its inverse is also smooth.
@BernardoMeurer Well, yes and no, manifolds are usually defined to be finite-dimensional, you can always try to extend definition but this little thing : $\infty$ likes to sap away at your foundations when you build definitions... a whole other can of worms.
There can only be 2 Hausdorff 1 dimensional manifolds (upto some equivalence - known as homeomorphism); the real line and the circle. There are ten million 1-dimensional manifolds if you're not Hausdorff
@BalarkaSen I know, I was just thinking as to what remains, if you remove Hausdorff from the definition of manifolds and still want a differential structure.
@Slereah I work mostly using algebra, and when the topics begins to come out of geometry and into topology I have very much less know-how until the cycle is completed through algebraic topology... but I see your point.
@JohnRennie I felt it was not justifiable to go with more than an i3 (7th gen) with this setup. Also, it came from my own money, so no way I'm buying a 350$ cpu... :)
It's been going on long enough that I don't remember who started it and in what circumstances. But I find it quite amusing so I'm not especially concerned.
@0celouvsky "Notice $M$ needs not be Hausdorff. The concept of Hausdorffness is irrelevant for much of local differential geometry. It becomes relevant in passing from a Riemannian metric to a distance function." -Hicks
I guess you can totally define a metric tensor on a non-Hausdorff manifold
"It is also customary to require a semi-Riemannian manifold to be Hausdorff; however, as far as the local differential geometry is concerned, this is irrelevant so the restriction is not enforced at this time."
Man Hicks is probably the only book to even mention this
Ah, apparently the trick is that, in general, the Riemannian metric tensor defines a pseudo-metric on the manifold
But it only becomes a metric if the manifold is Hausdorff.
On the other hand, MSE says you can't pseudometrize a non-Hausdorff manifold
Argh
Because a pseudometric on a $T_0$ space is also a metric
