Question: Recognize specific algebraic forms


Wondered if anyone could help with the query below.

Consider f(x,y) defined as:
f := proc (x, y) options operator, arrow; x*y/(x+y) end proc


Then f(A, B); becomes:
(A * B )/(A + B)


now consider the polynomial:(poly2)



This polynomial is just the expansion of the polynomial below (lets call it poly1) which MAPLE does not recognize.


Here you can see that A,B on top and X,Y on the bottom are clearly of the form f(x,y).


Is there a way you can get MAPLE to recognize certain algebraic forms such that the polynomial poly2 could be written either as poly1 (already shown above) or as poly3 below:

poly3:=(f(A, B)+X)/(X+f(Y, X))


I have tried using simplify in the following form but not much luck. It doesn't seem to recognize anything other than the obvious.

simplify(poly2, {A*B/(A+B) = F1}, tdeg(A, B))


(I am still a bit new to the MAPLE syntax and procedures so apologies if I have missed something obvious function that can do this.)




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