Raymond Hettinger <raymond.hettin...@gmail.com> added the comment:

I don't like the name overlap with itertools.product().  Currently, math and 
itertools have no overlapping names.  Also, I expect that like sum(), the 
prod() function will be used with generator comprehensions and should best be 
kept short and not dominating the rest of the expression.

It's true that factorial is spelled-out, but that was probably a mistake -- it 
has been somewhat awkward in expressions that contain factorial terms.  
Ideally, we would have comb, perm, fact, and prod.

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<https://bugs.python.org/issue35606>
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