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https://issues.apache.org/jira/browse/MATH-313?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12771672#action_12771672
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Jake Mannix commented on MATH-313:
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Of course, the easy alternative, if we really want to keep this interface the 
way it is, is to extend it with an interface like 
"AlgebraicallyComposableUnivariateRealFunction" (with a better name), which 
does have an abstract implementation (although we really don't want 
AbstractAlgebraicallyComposalbeUnivariateRealFunction as a class name!!!), and 
people can have both choices, and in fact, a concrete impl - 
DelegatingAlgebraicallyComposableUnivariateRealFunction - could be implemented 
by taking a UnivariateRealFunction as a constructor arg, and delegates value() 
to the delegate, and this way you can easily transition between using Functions 
as genuine objects, and as an interface on your more complex object as well, 
and you have the best of both worlds.

> Functions could be more object-oriented without losing any power.
> -----------------------------------------------------------------
>
>                 Key: MATH-313
>                 URL: https://issues.apache.org/jira/browse/MATH-313
>             Project: Commons Math
>          Issue Type: New Feature
>    Affects Versions: 2.0
>         Environment: all
>            Reporter: Jake Mannix
>             Fix For: 2.1
>
>
> UnivariateRealFunction, for example, is a map from R to R.  The set of such 
> functions has tons and tons of structure: in addition to being an algebra, 
> equipped with +,-,*, and scaling by constants, it maps the same space into 
> itself, so it is composable, both pre and post.
> I'd propose we add:
> {code}
>   UnivariateRealFunction plus(UnivariateRealFunction other);
>   UnivariateRealFunction minus(UnivariateRealFunction other);
>   UnivariateRealFunction times(UnivariateRealFunction other);
>   UnivariateRealFunction times(double scale);
>   UnivariateRealFunction preCompose(UnivariateRealFunction other);
>   UnivariateRealFunction postCompose(UnivariateRealFunction other);
> {code}
> to the interface, and then implement them in an 
> AbstractUnivariateRealFunction base class.  No implementer would need to 
> notice, other than switching to extend this class rather than implement 
> UnivariateRealFunction.
> Many people don't need or use this, but... it makes for some powerfully easy 
> code:
> {code}UnivariateRealFunction gaussian = 
> Exp.preCompose(Negate.preCompose(Pow2));{code}
> which is even nicer when done anonymously passing into a map/collect method 
> (a la MATH-312).

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