This library code is based directly on MappingPackage3? in
mappkg.spad.pamphlet
fricas
(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
fricas
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 03 DEC 2024 09:05:24 AM):
; wrote /var/aw/var/LatexWiki/MAPHAC2X.NRLIB/MAPHAC2X.fasl
; compilation finished in 0:00:00.004
------------------------------------------------------------------------
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.
fricas
)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)
fricas
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 03 DEC 2024 09:05:24 AM):
; 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
fricas
f := (x:INT):INT +-> 3*x
Type: (Integer -> Integer)
fricas
g := (x:INT):INT +-> 2*x+3
Type: (Integer -> Integer)
fricas
(f+g)(3)
We should be able to generalize this to SandBox Direct Product