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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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