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SandBox Functional Addition

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
'mappkg.spad.pamphlet'

\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 
      /var/zope2/var/LatexWiki/1147191614234250090-25px.001.spad using 
      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.
See also:
  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) ==
      add
         MapPackInternalHac2x(A, B)
         fab:  A -> B
         fab+fab == funcAdd(fab,fab,#1)

axiom

Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/8693442026998160385-25px.002.spad using 
      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

$\label{eq1}\mbox{theMap (...)}$

(1)

Type: (Integer -> Integer)

axiom

g := (x:INT):INT +-> 2*x+3

$\label{eq2}\mbox{theMap (...)}$

(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 +
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named + 
      with argument type(s) 
                            (Integer -> Integer)
                            (Integer -> Integer)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

We should be able to generalize this to [SandBox Direct Product]?

Finally got the frigg'n name right! :) --Bill Page, Tue, 28 Jun 2005 15:52:26 -0500 reply