I actually do believe that a core for expressions with indices is possible
here. But I don't have as much experience as Kasper, so I could be wrong.
On Wed, Mar 5, 2014 at 11:23 AM, Kasper Peeters <kasper.peet...@gmail.com>wrote:
> So how do you propose Cadabra would work with SymPy or CSymPy? Would
>> there be some core in Cadabra, that works well with SymPy, that people
>> can use to
>> build useful things upon it, or just use it for calculations?
>
>
> The way this will work is that there are 'cadabra.Ex' objects which
> represent cadabra
> tensor expressions. These can be manipulated with cadabra algorithms. For
> example,
>
> from cadabra import *
>
> Indices( Ex('{m,n,p,q,a,b}') )
> ex =Ex( 'A_{m n} ( C^{n p} + D^{n p} )' )
> rule=Ex( 'C^{a b} -> M_{m} D^{m a b}' )
>
> substitute(ex, rule)
> print(ex)
>
> would give
>
> A_{m n} ( M_{q} D^{q n p} + D^{n p} )
>
> You can then assign scalar expressions to the components of tensors in
> tensor expressions (again using a cadabra notation as above). And then you
> can extract components of tensors as sympy expressions. To expand on the
> above,
>
> Symbol( 'x, y' )
> assign:=Ex(' A_{0 1} = 3 x, A_{0 2} = y**2, D^{0 1 2} = x y, ...' )
> Extract( ex, assign, 'm=1, p=2' )
>
> would give you a Sympy expression for the m=1, p=2 component of the
> composite
> tensor defined earlier (the notation in this last bit is not yet set in
> stone, I am
> experimenting with different options).
>
> So essentially all tensor computation happens within Cadabra, with its own
> symbolic
> tree for tensor expressions which is independent of Sympy), and if you
> want to
> do component computations you have a way to extract components from tensors
> in the form of Sympy expressions.
>
> Hope that makes it a little bit more clear.
>
> Cheers,
> Kasper
>
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