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Inner products with dimension $n$.

asked 2022-07-28 04:54:36 +0200

Luis gravatar image

Is there a way to work with inner products with unspecified dimension in Sage? All the options that I've been able to find e.g. FreeModule have a required argument that asks for a dimension, basis or rank of some sort.

Ideally, what I need would work like:

INN = InnerProdSpace(RR); u, v = INN(u,v);

and it would be able to perform basic simplifications like: + ru) = +

I know that some modules like VectorSpace already do this and much more; but I would like to do it without needing to specify the dimension.

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answered 2022-09-02 10:41:48 +0200

Sylvain gravatar image

You may use symbolic variables and interpret the * operator as the inner poduct:

sage: u,v,r = var("u v r")
sage: (u*(v+r*u)).expand()
r*u^2 + u*v
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Asked: 2022-07-28 04:54:36 +0200

Seen: 120 times

Last updated: Sep 02 '22