Re: Mysterious Apply troubles (a bug?)

• To: mathgroup at smc.vnet.net
• Subject: [mg113684] Re: Mysterious Apply troubles (a bug?)
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Sun, 7 Nov 2010 05:13:20 -0500 (EST)

Hi Sam,

Since you do not provide ddSA and ddSa functions, it is hard to say exactly
what is
wrong. The error you quote happens when you have supplied to a pure function
less
arguments than it expects (the number of slots used). In your case, you used
two
slots #1 and #2, but apparently supplied a single argument.

Regards,
Leonid

On Sat, Nov 6, 2010 at 1:01 PM, Sam Takoy <sam.takoy at yahoo.com> wrote:

> Hi,
>
> I can't seem to produce a working self-contained example, so I'll keep
> chipping away at it, until someone spots what's wrong. I keep getting
> different behaviors depending on whether I use := or = and here's
> another manifestation. I have
>
> TP[tensors__] := Outer[Times, tensors]
> sTP[tensors__][t_, a_] :=
>  Apply[TP, Sequence[ Map[Apply[#, {t, a}] &, {tensors}]]]
>
> The idea of sTP is that if b, c, d, e are tensor functions of (t, a), I
> can say
>
> sTP[b, c, d, e][t, a] instead of TP[b[t, a], c[t, a], d[t, a], e[t, a]]
>
> Later, I have the following code (not self-contained, since I'm not
> explaining ddSa and ddSA except that sTP is called within them):
>
> f[t_, a_] := t Cos[a]
> SurfaceLaplacian[tensor_][t_, a_] := ddSA[ddSa[tensor]][t, a];
> lapF[t_, a_] := SurfaceLaplacian[f][t, a]
> Derivative[1, 0][lapF][t, a]
>
> And I get the following error:
>
> Function::slotn: Slot number 2 in #1@@{#1,#2}& cannot be filled from
> (#1@@{#1,#2}&)[SAB].
>
> I gather that #1@@{#1,#2}&  refers to Apply[#, {t, a}]& and doesn't it
> appear that # got mixed with "t" since they are both referred to as #1.
>
> Finally, I can mention that if I use
>    SurfaceLaplacian[tensor_][t_, a_] = ddSA[ddSa[tensor]][t, a]
> that is "=" in place of ":=", the error goes away.
>
> What's going on here?
>