laziness, impatience, and hubris  
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The original problem, framed in terms of arrays, is to reduce a fraction. The equation above is less general. The less general problem can be restated as reduce a fraction where the numerator and denominator are both the product of factorials. An example of the original problem is to reduce
An example of the factorial problem is to reduce
Do I understand correctly, are you are interested in the factorial type of problem? In reply to Re^3: Algorithm for cancelling common factors between two lists of multiplicands
by jimX11

