Manipulating expressions with vectors

[Alexander Lindsay]

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

[Aaron Meurer]

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

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[Alex Lindsay]

Neat. I'll be monitoring to see when the PR is merged!

[brombo]

You may want to look at my geometric algebra module that uses sympy (github.com/brombo/galgebra) and see if it does what you want it to.  I have attached the manual (galgebra.pdf) for you to look at.

[Francesco Bonazzi]

On Friday, 15 January 2016 17:04:20 UTC+1, Alexander Lindsay wrote:

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

This is a trick: declare A, B, C as non commutative variables:

 

In [1]: A, B, C = symbols('A B C', commutative=False)

In [2]: A * B / (A * C)
Out[2]:
         -1
A*B*(A*C)  

[Alex Lindsay]

Looks neat. I will have to delve into it more. Thanks!

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[Alex Lindsay]

I like that :-) That's probably actually all I need for this case

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