Re: [Axiom-developer] unexpected behaviour of normalize(1-(cos(x))^2)

[Tim Daly]

Michael,

Trig identity substitutions are somewhat problematic in Axiom.
See the src/input/schaum* files for examples.

If the subexpression (1-cos(x)^2) occurs in your expression E you can write:

  sinrule:=rule((1-cos(x)^2) == sin(x)^2)

and then use this rule for your expression E thus

 sinrule(E)

Axiom will not derive several of the trig identities from scratch.

In your expression we have something of the form
   (4a^2) / (a^2 + 1)^2    where a = tan(x/2)
so Axiom needs to show that
  (a^2+1)^2 != 0
  (a^2+1) != 0
  a^2 != -1
  a != i
or, by back-substitution
 tan(x/2) != i
which it does not conclude automatically, even though this
is clearly true in the domain Expression(Integer).



Michael Becker wrote:
>     Hi,
>
>
>    Is this (30)  the expected bevaviour of 'normalize' ??
>
>
> (29) -> normalize ((sin(x))^2+(cos(x))^2)
> (29) ->
>    (29)  1
>                                                      Type: Expression Integer
>
>
>
> (30) -> normalize (1-(cos(x))^2)
> (30) ->
>                      x 2
>                 4tan(-)
>                      2
>    (30)  ----------------------
>              x 4        x 2
>          tan(-)  + 2tan(-)  + 1
>              2          2
>                                                      Type: Expression Integer
>
>
>
>
>
>    
>     -- Michael
>