differentiating Products

[Luke Oeding]

Has anyone already implemented the product rule for the class Product or similar?

Here is a minimal example: 

R = QQ[x,y]
f = Product({x,y,x+y})
diff(x,f)

I'd like to have results that are sums of products, not completely expanded expressions.

[ztei...@boisestate.edu]

Will this work?

diff(RingElement,Product) := (d,p) -> sum(toList(apply(#p, k -> Product insert( k , diff(d,p#k) , toList delete(p#k,p) ))))

The business with "insert" just puts the differentiated factor back in the same position it came from. If you prefer it to be at the end (last factor in each summand) then this should work:

diff(RingElement,Product) := (d,p) -> sum toList apply(#p, k -> delete(p#k,p)*diff(d,p#k))

Zach