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Re: [Axiom-developer] typo in the guessing package pamphlet, was: Re: Al

From: Bill Page
Subject: Re: [Axiom-developer] typo in the guessing package pamphlet, was: Re: Algebra and literate documentation
Date: Wed, 8 Aug 2007 03:19:43 -0400

On 08 Aug 2007 06:56:46 +0200, Martin Rubey wrote:
> Gabriel Dos Reis writes:
> ...
> > More specifically:
> >
> >  * short hand for unnamed functions do not work properly, so one has
> >    to use the syntax x +-> f(x)
> Could you tell me in what places that happens, and what "do not work properly"
> means exactly?  I depend on unnamed functions quite a bit, since at a few
> points I actually construct such functions by code.  I do recall vividly that
> these functions were extremely hard to compile.

Well, just picking an example at random from your code (not
necessarily one that compiled with errors):

In mantepse.spad.pamphlet chunk <<implementation: Guess - Hermite-Pade
- Operators>>=
    diffHP(q: Symbol): (LGOPT -> HPSPEC) ==
        if displayAsGF(#1)$GOPT0 then
            partitions := FilteredPartitionStream #1
            [ADEguessStream(#1, partitions, qDiffDS(q, #1, #2), 1$UFPSF), _
             repeating([0$NNI])$Stream(NNI), _
             ADEtestStream(#1, partitions, qDiffDSF(q, #1, #2), 1$UFPSSUPF), _
             ADEEXPRRStream(#1, #2, partitions, qDiffDX(q, #1, #2,
#3), diff1X), _
             diffA, diffAF, diffAX, diffC]$HPSPEC
            error "Guess: guessADE supports only displayAsGF"


where reference is made to the following definitions:

    LGOPT ==> List GuessOption

    HPSPEC ==> Record(guessStream:  UFPSF -> Stream UFPSF,
                      degreeStream: Stream NNI,
                      testStream:   UFPSSUPF -> Stream UFPSSUPF,
                      exprStream:   (EXPRR, Symbol) -> Stream EXPRR,
                      A:  DIFFSPECA,
                      AF: DIFFSPECAF,
                      AX: DIFFSPECAX,
                      C:  DIFFSPECC)

UFPSF ==> UnivariateFormalPowerSeries F

ADEguessStream(f: UFPSF, partitions: Stream List Integer,
               DS: DIFFSPECS, D1: DIFFSPEC1): Stream UFPSF ==
    map(termAsUFPSF(f, #1, DS, D1), partitions)
       $StreamFunctions2(List Integer, UFPSF)


Why do you use macros for types like HPSPEC?

What do expect the meaning of #2 and #3 to be?

As I understand Spad syntax, if I write

   ( #1 + #2 + #3 )

this is a shorthand for the following anonymous function

  (x,y,z) +-> x + y + z

Is that correct? Perhaps not since with this definition I can not make
sense of your code.

For example, where you write above:

  [ADEguessStream(#1, partitions, qDiffDS(q, #1, #2), 1$UFPSF), ... ]

we could rewrite this as:

  (x,y,z) +-> [ADEguessStream(x, partitions, qDiffDS(q, x, y), 1$UFPSF),...]

but the first component of HPSPEC is

   guessStream:  UFPSF -> Stream UFPSF

which seems to require a function with a single argument.

Also from diffHP we were supposed to return a function


But the code apparently implies a function with 3 arguments.

Could you give an alternate explanation that makes better sense?

> ...

Bill Page.

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