Yes Stefan, I think you are articulating our concerns well. And while I've
never done the rect/spherical/rect transform, just going back and forth
between rect. frames causes similar issues with trig expressions not
collapsing.

I'd like to know more about the mutability of diffgeom's CoordSystems
though. From reading the code, it looks like it is accomplished by storing
the mutable information outside of args, and having the parent patch as an
arg to the coordinate system? How robust does this end up being?


On Fri, Jun 14, 2013 at 6:59 AM, Stefan Krastanov <
krastanov.ste...@gmail.com> wrote:

> >> Also, Gilbert and I had a small question. How do you plan to implement
> >> expression of Vectors in different frames? Also, the relationships
> between
> >> the frames? Could you give an API and the basic idea of how those
> methods
> >> will work?
> >> The main concern the mechanics group has, is the modeling of
> relationships
> >> among frames themselves, and those with vectors. Clearing up this part
> would
> >> make things much clearer.
> >
> >
> > Again, I really do not see what is so confusing. I'll try to be clear
> this
> > time.
>
> Prasoon, in this case I do not think the issue is someones confusion
> with what the suggestion is. `mechanics` has a very specific goal and
> it is optimized for it - easily traversing a very deep tree of
> relations between reference systems. While indeed what you have
> suggested is sufficient to make such traversals possible, one should
> be wary of whether it will work _well_ with deep trees.
>
> One issue that you will meet very soon is that expressing
> cart->spherical->cart transformation will often fail to symplify to an
> identity transformation (a lot of information must be specified for
> stuff like cos(acos(cos(a))) to return cos or for sqrt(x)*sqrt(1/x) to
> return 1).
>
> While the above is probably not the exact concern of Gilbert and the
> others in the mechanics team I am sure they have similar worries.
>
> And do not forget that mechanics is fast at the moment. With your
> methodology it might be hard to keep up with its performance.
>
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