login  home  contents  what's new  discussion  bug reports     help  links  subscribe  changes  refresh  edit

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

fricas
)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: 0.01 SEC.
(time taken in buildFunctor: 0)
;;; *** |MapPackInternalHac2x| REDEFINED
;;; *** |MapPackInternalHac2x| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor MapPackInternalHac2x Time: 0.01 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 14 JUL 2013 10:46:55 AM):
; /var/aw/var/LatexWiki/MAPHAC2X.NRLIB/MAPHAC2X.fasl written ; compilation finished in 0:00:00.013 ------------------------------------------------------------------------ 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 14 JUL 2013 10:46:55 AM):
; /var/aw/var/LatexWiki/MAPPK2X.NRLIB/MAPPK2X.fasl written ; compilation finished in 0:00:00.012 ------------------------------------------------------------------------ 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

\label{eq1}\mbox{theMap (...)}(1)
Type: (Integer -> Integer)
fricas
g := (x:INT):INT +-> 2*x+3

\label{eq2}\mbox{theMap (...)}(2)
Type: (Integer -> Integer)
fricas
(f+g)(3)

\label{eq3}18(3)

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




  Subject:   Be Bold !!
  ( 13 subscribers )  
Please rate this page: