f(x_1 x_2 x_1) g(x_3 x_4) + f(x_1) g(x_3) + ...
Still not completely clear. As far as I understand f and g basically
serve as tags for elements of your free monoid. What kind of structure
is the above (formal) sum of products? Let's just write elements of you
free monoid with y if it appears inside g, then the above would be
something like
x_1 x_2 x_1 y_3 y_4 + x_1 y_3 + ...
Right? So this could be considered as a monoid ring element of
ZM where Z denotes integers, and M is the (disjoint) union of your given
FreeMonoid X with itself (in the second copy the elements are denoted by
y instead of x).
You want all terms where (roughly speaking) x appears in exactly power
3, right?
In fact a polynomial ring would be enough at the moment,
but I didn't even figure out how to do that yet.
Oh, it would take a bit more time for me to figure out the details, but
I am sure you are able to find yourself how to construct a monoid ring
in FriCAS, the rest basically comes for free. AND there is *no* need for
Expression!!!
But maybe you haven't told me the full story and your f,g expressions
are much more complicated.
Ralf
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