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## [Axiom-developer] [Sanbox Functional Addition]

 From: Bill Page Subject: [Axiom-developer] [Sanbox Functional Addition] Date: Tue, 28 Jun 2005 14:43:27 -0500

```Changes
http://page.axiom-developer.org/zope/mathaction/SanboxFunctionalAddition/diff
--

??changed:
-++ Description:
-++ This package defines the function to be returned by
-++ functional operator below.
-
++ Description: Mapping hack for Addition
++ The function \spad{addit(f,g,x)} is \spad{fx+gx} which is needed below

??changed:
-  MPcat == MPdef where
-
-    MPcat == with
-        addit:  (A->B, A->B, A) -> B
-          ++\spad{comp(f,g,x)} is \spad{f(g x)}.
-
-    MPdef == add
-        addit(g,h,x)  == ((g x) + (h x))\$B
with addit:  (A->B, A->B, A) -> B ==
add addit(g,h,x)  == ((g x) + (h x))\$B

++added:
This package is the one that actually provides the Functional
Addition operator. The overloaded symbol + also represents this
type of addition.

??changed:
-++ Description: various Currying operations.
++ Description: Functional Addition
++ Given functions f and g, returns the function \spad{fx+gx}
++ \spad{f+g} is the function \spad{h} such that \spad{h x = f x + g x}.

??changed:
-  MPcat == MPdef where
-
-    MPcat ==  with
-
-        "+":   (A->B, A->B) -> (A->B)
-          ++\spad{f+g} is the function \spad{h}
-          ++ such that \spad{h x = f x + g x}.
-
-    MPdef == add
-
-
-        MapPackInternalHac2x(A, B)
-
-        fab:  A -> B
-
-        -- Functional addition
-        fab+fab == addit(fab,fab,#1)
-
with "+":   (A->B, A->B) -> (A->B) ==
add
MapPackInternalHac2x(A, B)
fab:  A -> B
fab+fab == addit(fab,fab,#1)

--
forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden

```

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