Waldek Hebisch <[EMAIL PROTECTED]> writes:
> Try:
>
> eval(deq, y, z+->exp(-z))
>
> or
>
> eval(deq, y, z+->eval(res, [x = z]))
Oh dear, yes, I was afraid that something like that would be the reason...
Actually, I do not really understand what smprep is supposed to do. The doc
says:
-- op(arg)**m ==> func(arg)**(m quo n) * op(arg)**(m rem n)
but that's a little cryptic. I'd prefer:
-- within [EMAIL PROTECTED] replace
-- op(arg)**m with func(arg)**(m quo n) * op(arg)**(m rem n)
-- where m = ... and n = ...
smprep : (List SY, List N, List(List % -> %), MP) -> %
smprep(lop, lexp, lfunc, p) ==
but I still do not know what m and n are. Unfortunately, it seems to be
impossible to output or PRINT$Lisp p and also the result of smprep, since the
result contains cycles.
> It seems that you want "variable capture", but code for evaluating derivative
> is very careful to distinguish x contained in res from x in deq. Look at
> begining of smprep:
>
> smprep(lop, lexp, lfunc, p) ==
> (v := mainVariable p) case "failed" => p::%
> -- symbolIfCan(k := v::K) case SY => p::%
> k := v::K
> g := (op := operator k)
> (arg := [eval(a,lop,lexp,lfunc) for a in argument k]$List(%))
> q := map(eval(#1::%, lop, lexp, lfunc),
> now:
>
> (10) -> mainVariable numer deq
>
> ,
> (10) y (x)
>
> Type: Union(Kernel Expression Integer,...)
> (11) -> operator mainVariable numer deq
>
> (11) %diff
> Type: BasicOperator
> (12) -> argument mainVariable numer deq
>
> (12) [y(%%01),%%01,x]
> Type: List Expression Integer
>
> You see that derivative is usig special dummy variable, so I would
> guess that the intent it _not_ to capture any other x that just
> happens to be in the expression. Apparently this dummy is
> passed to substitution function, so it can insert the dummy inside
> replacement expression.
Hm, yes, but in this situation I think it should. At least, it seems to me
that from a user's perspective
f: EXPR INT -> EXPR INT := x +-> res
and
f: EXPR INT -> EXPR INT := x +-> exp(-x)
are equal. I'll look a little more into it.
(I thought that I understood dummies - at least in COMBF - but it seems I was
mistaken)
Martin
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