Re: Applying a function to all elements of a vector

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2024-08-18 04:20, Joe Slater wrote:
> This is long, but I thought I should attempt to address this with 
> respect to all operators, not just the first one to give unexpected 
> results. The user manual (p. 10) says
>
>     PARI operations are in general quite permissive. For instance
>     taking the exponential of a vector should not make sense. However,
>     it frequently happens that one wants to apply a given function to
>     all elements in a vector. This is easily done using a loop, or
>     using the apply built-in function, but in fact PARI assumes that
>     this is exactly what you want to do when you apply a scalar
>     function to a vector.
>
> [...]

An operator is not really a function, but since one can do:

  alias("pow", "_^_")

I'd expect similar.


>     > 1^vector(3) \\ /All the values of the vector get converted to
>     t_REAL for some reason. /
>     %3 = [1.000, 1.000, 1.000]
>     > 0^vector(3)
>       ***   at top-level: 0^vector(3)
>       ***                  ^----------
>       *** _^_: domain error in gpow(0,n): n <= 0
>       ***   Break loop: type 'break' to go back to GP prompt 

Surprises me as well, but appears to be as documented at the end of "??^".


Maybe hyper-operators should be made to look differently,
to prevent different behavior if dedicated support for some non-scalar 
parameter was added in the future.
(obviously implying that implicit-apply will be moved out)


For example like:

? 2 [^] [1, 2, 3]
% [2, 4, 8]   \\ exact

or like:

? 2 ^* [1, 2, 3]
% [2, 4, 8]   \\ exact

? [1, 2, 3] *^ 2
% [1, 4, 9]

or like:

? 2 ^<< [1, 2, 3]
% [2, 4, 8]   \\ exact

? [1, 2, 3] >>^ 2
% [1, 4, 9]

-- Ruud