Re: [Maxima-discuss] foo(a, 2, 4, 1, 3) -> bar(bar(bar(bar(a, 2), 4), 1), 3) ?

[Stavros M. <mac...@al...>]

Eduardo,

I don't know what exactly your goal is with *foo1* (maybe just a test), but
a few observations:

   - You should always quote literal constants, e.g., *action='op*, even
   though *op *evaluates to *op *if it's not bound to some value.
   Otherwise, if there happens to be a variable called *op* in your
   environment, you will get surprising results.
   - I hope you're aware that *op* and *args* work on the *external* form
   of an expression, which is designed for human consumption. The internal
   form is more uniform and generally better for automatic manipulation. You
   can get the internal form by binding *inflag* or by using the
*inpart* function:
   *op(1/a)=part(1/a,0)="/" *but *inpart(1/a,0)="^" *(*1/a = a^-1)*.
   - A useful argument for *part* is *allbut*, which is perversely
   documented under *allbut*, but not under *part*: *inpart(a*b/c,allbut(2))
   => a/c* (because *a*b/c* is internally *a*b*c^-1)*.
   - Unfortunately, there is not an *in* version of *args*. Maybe we should
   define *(in)part(...,allbut(0))* to be equivalent to *args(...)*.

Hope this is helpful.

                  -s

On Sat, Jul 9, 2022 at 9:27 PM Eduardo Ochs <edu...@gm...> wrote:

> On Sat, 9 Jul 2022 at 22:15, Stavros Macrakis <mac...@al...>
> wrote:
> >
> > Use a=b to test structural equality.
> >
> > equal(a,b) is for mathematical equality, and is unknown (not false) in
> the absence of assertions (assume) about a and b.
>
> Perfect!
> Many thanks! =)
> Here is a transcript:
>
>   (%i1) foo1 : lambda([o, action],
>     if     action = op   then op(o)
>     elseif action = args then args(o)
>     else   args(o)[action]);
>   (%o1) lambda([o, action], if action = op then op(o) elseif action = args
>                                                  then args(o) else
> args(o)      )
>
> action
>   (%i2) foo(a, [b]) := xreduce(foo1, b, a);
>   (%o2)                 foo(a, [b]) := xreduce(foo1, b, a)
>   (%i3) ex1 : a+b*c;
>   (%o3)                               b c + a
>   (%i4) foo(ex1);
>   (%o4)                               b c + a
>   (%i5) foo(ex1, op);
>   (%o5)                                  +
>   (%i6) foo(ex1, args);
>   (%o6)                              [b c, a]
>   (%i7) foo(ex1, 1);
>   (%o7)                                 b c
>   (%i8) foo(ex1, 1, op);
>   (%o8)                                  *
>   (%i9) foo(ex1, 1, args);
>   (%o9)                               [b, c]
>   (%i10) foo(ex1, 1, 1);
>   (%o10)                                 b
>   (%i11) foo(ex1, 1, 2);
>   (%o11)                                 c
>   (%i12) foo(ex1, 2);
>   (%o12)                                 a
>
> Cheers =),
>   Eduardo Ochs
>   http://angg.twu.net/eev-maxima.html
>