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# Edit detail for SandBox Functional Addition revision 1 of 2

 1 2 Editor: Time: 2007/11/18 18:02:32 GMT-8 Note:

changed:
-
This library code is based directly on MappingPackage3 in

\begin{axiom}
)abbrev package MAPHAC2X MapPackInternalHac2x
++ Description: Mapping hack for Addition
++ The function \spad{funcAdd(f,g,x)} is \spad{fx+gx} which is needed below
MapPackInternalHac2x(A: SetCategory, B: Ring):
with funcAdd:  (A->B, A->B, A) -> B ==
add funcAdd(g,h,x)  == ((g x) + (h x))$B \end{axiom} This package is the one that actually provides the Functional Addition operator. The overloaded symbol + also represents this type of addition. \begin{axiom} )abbrev package MAPPK2X MappingPackage2x ++ Description: Functional Addition ++ Given functions f and g, returns the function \spad{fx+gx} ++ \spad{f+g} is the function \spad{h} such that \spad{h x = f x + g x}. MappingPackage2x(A:SetCategory, B:Ring): with "+": (A->B, A->B) -> (A->B) == add MapPackInternalHac2x(A, B) fab: A -> B fab+fab == funcAdd(fab,fab,#1) \end{axiom} \begin{axiom} f := (x:INT):INT +-> 3*x g := (x:INT):INT +-> 2*x+3 (f+g)(3) \end{axiom} We should be able to generalize this to [SandBox Direct Product] From BillPage Tue Jun 28 15:52:26 -0500 2005 From: Bill Page Date: Tue, 28 Jun 2005 15:52:26 -0500 Subject: Finally got the frigg'n name right! :) Message-ID: <20050628155226-0500@page.axiom-developer.org>  This library code is based directly on MappingPackage3? in mappkg.spad.pamphlet axiom )abbrev package MAPHAC2X MapPackInternalHac2x ++ Description: Mapping hack for Addition ++ The function \spad{funcAdd(f,g,x)} is \spad{fx+gx} which is needed below MapPackInternalHac2x(A: SetCategory, B: Ring): with funcAdd: (A->B, A->B, A) -> B == add funcAdd(g,h,x) == ((g x) + (h x))$B
axiom
Compiling FriCAS source code from file
old system compiler.
MAPHAC2X abbreviates package MapPackInternalHac2x
------------------------------------------------------------------------
initializing NRLIB MAPHAC2X for MapPackInternalHac2x
compiling into NRLIB MAPHAC2X
compiling exported funcAdd : (A -> B,A -> B,A) -> B
Time: 0.04 SEC.
(time taken in buildFunctor:  0)
;;;     ***       |MapPackInternalHac2x| REDEFINED
;;;     ***       |MapPackInternalHac2x| REDEFINED
Time: 0.01 SEC.
Cumulative Statistics for Constructor MapPackInternalHac2x
Time: 0.05 seconds
finalizing NRLIB MAPHAC2X
Processing MapPackInternalHac2x for Browser database:
--->-->MapPackInternalHac2x((funcAdd (B (Mapping B A) (Mapping B A) A))): Not documented!!!!
--------constructor---------
; compiling file "/var/zope2/var/LatexWiki/MAPHAC2X.NRLIB/MAPHAC2X.lsp" (written 11 JUN 2011 08:31:02 AM):
; /var/zope2/var/LatexWiki/MAPHAC2X.NRLIB/MAPHAC2X.fasl written
; compilation finished in 0:00:00.086
------------------------------------------------------------------------
MapPackInternalHac2x is now explicitly exposed in frame initial
MapPackInternalHac2x will be automatically loaded when needed from
/var/zope2/var/LatexWiki/MAPHAC2X.NRLIB/MAPHAC2X
>> System error:
The bounding indices 163 and 162 are bad for a sequence of length 162.
The ANSI Standard, Glossary entry for "bounding index designator"
The ANSI Standard, writeup for Issue SUBSEQ-OUT-OF-BOUNDS:IS-AN-ERROR

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

axiom
)abbrev package MAPPK2X MappingPackage2x
++ 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}.
MappingPackage2x(A:SetCategory, B:Ring):
with "+":   (A->B, A->B) -> (A->B) ==
MapPackInternalHac2x(A, B)
fab:  A -> B
fab+fab == funcAdd(fab,fab,#1)
axiom
Compiling FriCAS source code from file
old system compiler.
MAPPK2X abbreviates package MappingPackage2x
------------------------------------------------------------------------
initializing NRLIB MAPPK2X for MappingPackage2x
compiling into NRLIB MAPPK2X
>> Apparent user error:
Use: import
(MapPackInternalHac2x A B)

axiom
f := (x:INT):INT +-> 3*x (1)
Type: (Integer -> Integer)
axiom
g := (x:INT):INT +-> 2*x+3 (2)
Type: (Integer -> Integer)
axiom
(f+g)(3)
There are 11 exposed and 7 unexposed library operations named +
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op +
or "\$" to specify which version of the function you need.