>
> 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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