There is some work in progress to create a DotProduct for matrix
expressions, which should do what you want here
https://github.com/sympy/sympy/pull/10252.

Aaron Meurer

On Fri, Jan 15, 2016 at 11:04 AM, Alexander Lindsay <[email protected]> wrote:
> Hi all,
>
> I'm pretty new to sympy. I'm wondering whether it's possible to manipulate
> expressions with vector dot products without sympy trying to actually
> evaluate the dot product. Let's say A and B are vectors; I want the
> expression A * B to simply be A * B, not a1*b1 + a2*b2 + a3*b3. I can't
> simply use:
>
> A, B = symbols('A B')
>
> and carry them around in expressions that way because I want to avoid
> simplifications like (C is another vector): A * B / (A * C) = B / C
>
> My full expressions contain many scalars as well as dot products; I want to
> allow scalar simplification, e.g. I want x*y / x*z = y / z, while avoiding
> incorrect vector simplifications like the possibility above.
>
> I hope that this is not too strange or stupid of a question!
>
> Alex
>
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