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Rhys Ulerich
12/17/08 4:55pm


I'd like to work with symbolic linear and symmetric bilinear operators over a vector space within Mathematica. For example, for
scalars a,b
vectors u,v,w
linear operator L
bilinear operator B
I'd like to define operational rules like the following
L[a u] -> a L[u]
L[u + v] -> L[u] + L[v]
B[a u, v] -> a B[u,v]
B[u, a v] -> a B[u,v]
B[u + v, w] -> B[u,w] + B[v,w]

Does anyone have any pointers for how to define reduction rules/definitions for these types of operators?

Thank you,

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