[Maxima-discuss] bad simp of acos, conjugate(acos..) was Re: sub expression with missing simp flags.

[Richard F. <fa...@gm...>]

There are a bunch of oddities in the definition of conjugate-acos.
1. say one calls   conjugate(acos(foo+bar)).
It would make sense for  conjugate-acos to be called on
acos(foo+bar),  i.e. ((%acos simp) ((mplus simp) $foo $bar))

in which case the expression -- with simp flag -- would be readily 
available.

2.
since the call to conjugate-acos  is a list   ( $x)  or in this case  
(    ((mplus simp) $foo $bar) )  always,
and it always computes (car ..) ,  then*** the call*** like 
(conjugate-acos ww)   should be
(conjugate-acos( car ww)) , and the internal car is made unnecessary.

finally, if nothing else is changed, it is simple to put the simp flag 
on,: that last
line could be

(cons '($conjugate simp)  (take '(%acos) x))

in which case the acos would still be resimplified unnecessarily once, 
but the simp flag would be on it.

I discovered.....

There is a really terrible something going on with simplification of 
acos, though.

do this
:lisp (trace simplifier)
acos(z)

you can see the simplifier being called many many times, on expressions 
like 3^(1/2)/2
expressions not involving z at all.

RJF






On 2/25/21 4:55 AM, Barton Willis via Maxima-discuss wrote:
> A simplified expression of the form conjugate(XXX) can include 
> subexpressions that are /not/ marked as simplified. That's not good.
> For example:
>
> (%i1) declare(z,complex)$
>
> (%i2) conjugate(acos(z));
> (%o2) conjugate(acos(z))
>
> (%i3) ?print(%);
> (($CONJUGATE SIMP) ((%ACOS) $Z)
>
> Maybe the missing simp flag on acos isn't terrible, but doesn't it 
> cause an inefficacy? Doing, for example, first(conjugate(acos(z)) 
> forces a
> re-simplification of acos(z).
>
> The function for the conjugate of an acosine expression is
>
> (defun conjugate-acos (x)
> (setq x (car x))
> (if (in-domain-of-asin x) (take '(%acos) (take '($conjugate) x))
>   `(($conjugate simp) ((%acos) ,x))))
>
> So the reason for the missing simp flag isn't a mystery.
>
> As I understand the conjugate code, it wouldn't be wrong for a 
> conjugate function, such as conjugate-acos, to paste in the simp flag 
> without doing a re-simplification--that's because the acos expression 
> has been simplified at a higher level. Pasting in simp flags makes me 
> uncomfortable but doing (take '(%acos) x) seems inefficient.
>
> Likely conjugate functions, such as conjugate-acos should receive the 
> entire expression acos(XXX), not just XXX. That way for a nounform 
> return, it could return `(($conjugate simp) ,XXX) and be safe.  But 
> changing this seems too error prone (conjugate functions are scattered 
> throughout src)  and I'm not pretty sure the gain in speed is not 
> worthwhile.
>
> Arguably, even doing `(($conjugate simp)  ...) is a wrong--if 
> $conjugate had a msimpind property (it doesn't), doing `(($conjugate 
> simp) would circumvent the msimpind flag. Maybe the msimpind flag is a 
> never-mind feature?
>
> Maybe all this is trifling, All advice is welcomed.
>
> --Barton
>
>
>
>
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