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

[Raymond T. <toy...@gm...>]

>>>>> "Richard" == Richard Fateman <fa...@gm...> writes:

    >> 
    >> Perhaps because simp-%acos looks for special args?
    >> acos(sqrt(3)/2) is a something that we'd want to be simplified to
    >> %pi/6.
    Richard> it should not have to re-simplify sqrt(3)/2 ..

Yeah.  When I do (trace simplifya alike1), we get a trace like:

    1: (SIMPLIFYA ((MEXPT) 3 ((RAT SIMP) 1 2)) NIL)
      2: (SIMPLIFYA 3 NIL)
      2: SIMPLIFYA returned 3
      2: (SIMPLIFYA ((RAT SIMP) 1 2) NIL)
      2: SIMPLIFYA returned ((RAT SIMP) 1 2)
      2: (SIMPLIFYA ((MTIMES) ((MEXPT) 3 1)) NIL)
        3: (SIMPLIFYA ((MEXPT) 3 1) NIL)
          4: (SIMPLIFYA 3 NIL)
          4: SIMPLIFYA returned 3
          4: (SIMPLIFYA 1 NIL)
          4: SIMPLIFYA returned 1
        3: SIMPLIFYA returned 3
      2: SIMPLIFYA returned 3
      2: (ALIKE1 3 $%I)
      2: ALIKE1 returned NIL
      2: (SIMPLIFYA ((MEXPT) 3 ((RAT) 1 2)) NIL)
        3: (SIMPLIFYA 3 NIL)
        3: SIMPLIFYA returned 3
        3: (SIMPLIFYA ((RAT) 1 2) NIL)
        3: SIMPLIFYA returned ((RAT SIMP) 1 2)
      2: SIMPLIFYA returned ((MEXPT SIMP) 3 ((RAT SIMP) 1 2))
      2: (SIMPLIFYA ((MTIMES) ((MEXPT SIMP) 3 ((RAT SIMP) 1 2)) 1) NIL)
        3: (SIMPLIFYA ((MEXPT SIMP) 3 ((RAT SIMP) 1 2)) NIL)
        3: SIMPLIFYA returned ((MEXPT SIMP) 3 ((RAT SIMP) 1 2))
        3: (ALIKE1 3 3)
        3: ALIKE1 returned T
        3: (ALIKE1 ((RAT SIMP) 1 2) ((RAT SIMP) 1 2))
        3: ALIKE1 returned T
        3: (SIMPLIFYA 1 NIL)
        3: SIMPLIFYA returned 1
        3: (ALIKE1 1 3)
        3: ALIKE1 returned NIL
      2: SIMPLIFYA returned ((MEXPT SIMP) 3 ((RAT SIMP) 1 2))

I think that all comes from (alike1 y (div (power* 3 1//2) 2)) in
simp-%acos.  I guess this happens because we compute sqrt(3)/2 at
runtime.  Perhaps it would be worthwhile not to do that at runtime.
After all We have the symbol '1//2 that is equal to ((rat simp) 1 2).

    >> 
    >> Maybe the code for this should check to see if the arg is an atom
    >> (and not +/-1) and bypass all the tests for special args?  That
    >> would slightly speed up things like acos(z).
    Richard> That would be a simple check..

I think so.