Edit detail for SandBox Numerical Integration revision 2 of 2

On March 10, 2006 10:53 PM Donald J Bindner wrote:

I'm trying to learn a bit about compiling packages for Axiom, so I chose a small task to cut my teeth on. I want to implement for myself a simpler simpson() function that does numerical integration.

I've got a working package after browsing through numquad.spad. However the prototype for my function is:

 simpson( Float->Float, Segment Float )

So I can perform calculations like:

 simpson( x +-> 1/x, 1..2 )

However I'd like to use a syntax more similar to the way integrate() works. I'd prefer to be able to execute:

 simpson( 1/x, x=1..2 )

I've done a lot of browsing, but I can't figure out how this is done.

I've tried to distill the core of my question into a small example package. It contains two simple() functions. One works fine, but the other won't compile. Suggestions would be welcome.

(1) -> <spad>

)abbrev package DONSIMP donSimple

--
-- Exports simple() function which takes 2 args,
-- Working behavior is: simple( x+->x^2, 1..2 ) = 3.0
-- Not working but intended behavior is: 
--  simple( x^2, x=1..2 ) = 3.0
--

donSimple(): Exports == Implementation where
  F        ==> Float
  SF       ==> Segment F
  EF       ==> Expression F
  SBF      ==> SegmentBinding F

  Exports ==> with
   simple : (F->F,SF) -> F
   simple : (EF,SBF) -> EF

  Implementation ==> add
   simple(func:F->F, sf:SF ) ==
      a : F := low(sf)
      b : F := high(sf)
      func(b) - func(a)

   simple(func:EF, sbf:SBF) ==
      a : F := low(segment(sbf))
      b : F := high(segment(sbf))
      x : Symbol := variable(sbf)
      eval(func, kernel(x), b::EF) - eval(func, kernel(x), a::EF)</spad>

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1943595969622990287-25px001.spad
      using old system compiler.
   DONSIMP abbreviates package donSimple 
------------------------------------------------------------------------
   initializing NRLIB DONSIMP for donSimple 
   compiling into NRLIB DONSIMP 
   compiling exported simple : (Float -> Float,Segment Float) -> Float
Time: 0 SEC.

   compiling exported simple : (Expression Float,SegmentBinding Float) -> Expression Float
Time: 0.04 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |donSimple| REDEFINED

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

   Cumulative Statistics for Constructor donSimple
      Time: 0.05 seconds

   finalizing NRLIB DONSIMP 
   Processing donSimple for Browser database:
--->-->donSimple(constructor): Not documented!!!!
--->-->donSimple((simple ((Float) (Mapping (Float) (Float)) (Segment (Float))))): Not documented!!!!
--->-->donSimple((simple ((Expression (Float)) (Expression (Float)) (SegmentBinding (Float))))): Not documented!!!!
--->-->donSimple(): Missing Description
; compiling file "/var/aw/var/LatexWiki/DONSIMP.NRLIB/DONSIMP.lsp" (written 07 APR 2024 06:19:18 AM):

; wrote /var/aw/var/LatexWiki/DONSIMP.NRLIB/DONSIMP.fasl
; compilation finished in 0:00:00.012
------------------------------------------------------------------------
   donSimple is now explicitly exposed in frame initial 
   donSimple will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DONSIMP.NRLIB/DONSIMP

simple(1/x,x=2..3)

(1)