On 03/12/2014 08:34 PM, Charlie Paul wrote:
So, what I'm thinking is that I take the current Tensor classes,
switch them over so that they are TensorSymbol (analagous to
MatrixSymbol) and add a more concrete tensor class, and also
expression classes for those, including tensor product. This results
in things like physics vectors and dyads, GA vectors and multivectors,
and diffgeom differentials and tensor products and so on being
straight up instances of our tensor expressions, except perhaps with
different component types.
However, we would like to have other classes as well, like matrix or
geometric vectors, since they would have abilities that general
tensors would not, and it would also help with backwards
compatibility. So I can add a dispatch system like Franz Bonazzi is
suggesting to deal with that. This would also allow better interop
between the GA module and the physics module for instance, and can be
written generally enough to be used throughout sympy for other such
large groups as tensors.
On Mon, Mar 10, 2014 at 2:44 AM, F. B. <[email protected]
<mailto:[email protected]>> wrote:
On Saturday, March 8, 2014 4:23:50 AM UTC+1, Matthew wrote:
I do like the idea of dispatch. I'm not sure that I
understand the rest though. Maybe I need a more explicit
example. We'll probably have to convert back at some point.
As soon as there is multiple dispatch, an approach similar to this
one could be devised:
http://julia.readthedocs.org/en/latest/manual/conversion-and-promotion/
For me an example of shared functionality might be indexing.
Many matrix expressions can be reduced to indexed
expressions. Operations like matrix multiply could be written
more generally as contractions. These contractions might mean
something very different on a Matrix, a MatrixExpression, or a
Tensor* but we might be able to find simplifications that are
common to all.
Tensors defined in *sympy.tensor.tensor* do not define components
by default, they only store index-types, index-symmetries and
commutation symmetries of tensors. The only common feature with
n-dimensional arrays is the number of indices. I think that the
shared common feature would then be just the number of indices,
unless you're willing to create a structure with many optional
features.
I would not concentrate the efforts on a tensor core, rather a
system of easiness of conversion/promotion of types would be more
beneficial.
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Remember you cannot represent a spinor with tensors and likewise
Clifford numbers (multivectors in GA).
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