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Is this too similar to [[Sum and product of array]]? --[[User:Mwn3d|Mwn3d]] 22:42, 27 January 2008 (MST) :I think not. The sum-and-product task lets us see how these functions are specified, but they don't let us see them in relationship with another function. The point of sum-of-squares, it seems to me, is to let us see how basic function composition occurs. It takes more than one function to show that. --[[User:TBH|TBH]] 10:01, 28 January 2008 (MST) ::If that is the goal, perhaps a [[function composition]] task would be appropriate. --[[User:IanOsgood|IanOsgood]] 10:07, 28 January 2008 (MST) ::I don't think this counts as function composition. This is just accumulation, which is why I think it's similar to the sum and product. The capital sigma and capital pi symbols in math aren't really functions, and this task would use a capital sigma in its definition. --[[User:Mwn3d|Mwn3d]] 10:39, 28 January 2008 (MST) :::If summation-of-series and product-of-series are not going to be considered functions within this site, what should they be called instead? They easily fall within a common meaning of the word. To see how, I recommend that we take the Wikipedia page on [http://en.wikipedia.org/wiki/Function_composition_%28computer_science%29 function composition] as a starting point. --[[User:TBH|TBH]] 11:32, 28 January 2008 (MST) ::::If they are considered functions, then they are always function compositions (their arguments are always functions) and the sum and product of an array should be considered that way too. --[[User:Mwn3d|Mwn3d]] 12:54, 28 January 2008 (MST) :::::If we broaden "function composition" to include anything that produces a function, the resulting category will swallow everything. All tasks would count in that category when approached at the function level. We want categories that provide focus and containment of complexities. --[[User:TBH|TBH]] 14:48, 28 January 2008 (MST) ::Function composition may be too broad a topic for a single task. Consider the following:
g (f y) g (x f y) (f x) g (f y) fi (g (f y)) fi ((f x) g (f y)) y g (f y) x g (f y) (f y) g (h y) (x f y) g (x h y)
::In the notation used above f, g, and h are functions, fi is the function inverse to f, and data arguments are indicated as x and y.