Thread: Smooth?
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Old 2004-11-04, 16:21   #5
cheesehead's Avatar
"Richard B. Woods"
Aug 2002
Wisconsin USA

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Originally Posted by Xyzzy
Is it safe to say that you must have the absolute factorization before you can assign a "smooth" value?
You just have to know the largest prime factor.

I'm not too sure where the "b" is coming from when you mention "b-smooth"...
Bounds -- "b-smooth" would often be used in the context of discussing a factorization method such as P-1 that had one or more bounds as parameters.

Finally, what is the correct way to write out a factorization? I've seen it done several ways but I imagine there is an accepted proper way...
There's no one proper way -- it depends on the context. IMO writing out the multiplication as in "120 = 2×2×2×3×5" could be considered a fairly standard way to communicate the factor list. Since commas take less space than x-es, one could see "2,2,2,3,5", "((2,3),(3,1),(5,1))" and "(3,1,1)" whenever the context directed that multiplication or exponentiation be used in the appropriate combination.
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