MathAction SandBox Functional Addition

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SandBox Direct Product

This library code is based directly on MappingPackage3? in mappkg.spad.pamphlet

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(1) -> )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

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Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/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 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MapPackInternalHac2x| REDEFINED

;;;     ***       |MapPackInternalHac2x| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor MapPackInternalHac2x
      Time: 0 seconds

   finalizing NRLIB MAPHAC2X 
   Processing MapPackInternalHac2x for Browser database:
--------constructor---------
--->-->MapPackInternalHac2x((funcAdd (B (Mapping B A) (Mapping B A) A))): Not documented!!!!
; compiling file "/var/aw/var/LatexWiki/MAPHAC2X.NRLIB/MAPHAC2X.lsp" (written 06 OCT 2024 08:55:08 PM):

; wrote /var/aw/var/LatexWiki/MAPHAC2X.NRLIB/MAPHAC2X.fasl
; compilation finished in 0:00:00.016
------------------------------------------------------------------------
   MapPackInternalHac2x is now explicitly exposed in frame initial 
   MapPackInternalHac2x will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MAPHAC2X.NRLIB/MAPHAC2X

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

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)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
         import MapPackInternalHac2x(A, B)
         fab:  A -> B
         fab1 + fab2 == (xx:A) : B +-> funcAdd(fab1, fab2, xx)

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Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2049699721911340732-25px.002.spad
      using old system compiler.
   MAPPK2X abbreviates package MappingPackage2x 
------------------------------------------------------------------------
   initializing NRLIB MAPPK2X for MappingPackage2x 
   compiling into NRLIB MAPPK2X 
   importing MapPackInternalHac2x(A,B)
   compiling exported + : (A -> B,A -> B) -> A -> B
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MappingPackage2x| REDEFINED

;;;     ***       |MappingPackage2x| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor MappingPackage2x
      Time: 0 seconds

   finalizing NRLIB MAPPK2X 
   Processing MappingPackage2x for Browser database:
--------constructor---------
--->-->MappingPackage2x((+ ((Mapping B A) (Mapping B A) (Mapping B A)))): Not documented!!!!
; compiling file "/var/aw/var/LatexWiki/MAPPK2X.NRLIB/MAPPK2X.lsp" (written 06 OCT 2024 08:55:08 PM):

; wrote /var/aw/var/LatexWiki/MAPPK2X.NRLIB/MAPPK2X.fasl
; compilation finished in 0:00:00.008
------------------------------------------------------------------------
   MappingPackage2x is now explicitly exposed in frame initial 
   MappingPackage2x will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MAPPK2X.NRLIB/MAPPK2X

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