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
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