Edit detail for SandBox Numerical Integration revision 1 of 1

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.

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 := lo(sf) b : F := hi(sf) func(b) - func(a)
simple(func:EF, sbf:SBF) == a : F := lo(segment(sbf)) b : F := hi(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/zope2/var/LatexWiki/9089532301415255797-25px001.spad using 
      old system compiler.
   DONSIMP abbreviates package donSimple 
   processing macro definition F ==> Float 
   processing macro definition SF ==> Segment Float 
   processing macro definition EF ==> Expression Float 
   processing macro definition SBF ==> SegmentBinding Float 
   processing macro definition Exports ==> -- the constructor category 
   processing macro definition Implementation ==> -- the constructor capsule 
------------------------------------------------------------------------
   initializing NRLIB DONSIMP for donSimple 
   compiling into NRLIB DONSIMP 
   compiling exported simple : (Float -> Float,Segment Float) -> Float
Time: 0.05 SEC.

   compiling exported simple : (Expression Float,SegmentBinding Float) -> Expression Float
Time: 0.24 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |donSimple| REDEFINED

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

   Warnings: 
      [1] simple: not known that (OrderedSet) is of mode (CATEGORY package (SIGNATURE simple ((Float) (Mapping (Float) (Float)) (Segment (Float)))) (SIGNATURE simple ((Expression (Float)) (Expression (Float)) (SegmentBinding (Float)))))

   Cumulative Statistics for Constructor donSimple
      Time: 0.29 seconds

   finalizing NRLIB DONSIMP 
   Processing donSimple for Browser database:
--->-->donSimple((simple (F (Mapping F F) SF))): Not documented!!!!
--->-->donSimple((simple (EF EF SBF))): Not documented!!!!
--->-->donSimple(constructor): Not documented!!!!
--->-->donSimple(): Missing Description
------------------------------------------------------------------------
   donSimple is now explicitly exposed in frame initial 
   donSimple will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/DONSIMP.NRLIB/code

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

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