Re^4: Algorithm for cancelling common factors between two lists of multiplicands

Re-frame the factorial problem thus:

( 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 
* 8 * 7 * 6 * 5 * 4 * 3 * 2
* 8 * 7 * 6 * 5 * 4 * 3 * 2
* 8 * 7 * 6 * 5 * 4 * 3 * 2
* 6 * 5 * 4 * 3 * 2
* 4 * 3 * 2 )
/
( 5 * 4 * 3 * 2 
* 3 * 2
* 2)
[download]

And it reduces to

( 3 * 4 * 7 * 6 * 5 * 4 * 3 * 2 
* 4 * 7 * 6 * 5 * 4 * 3 * 2
* 4 * 7 * 6 * 5 * 4 * 3 * 2
* 2 * 7 * 6 * 5 * 4 * 3 * 2
* 3 * 4 * 3 * 2
* 4 * 3 * 2 )
/
( 1 )
[download]

Which eliminates factorials completely (and, in this case the need for division). More importantly and relevantly, it reduces the magnitude of the intermediate terms. In the FET, the scale of this reduction should be considerably more significant than in this example.

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