|
From: | Tim Daly |
Subject: | Re: [Axiom-developer] unexpected behaviour of normalize(1-(cos(x))^2) |
Date: | Wed, 05 Aug 2009 09:59:59 -0400 |
User-agent: | Thunderbird 2.0.0.21 (Windows/20090302) |
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
[Prev in Thread] | Current Thread | [Next in Thread] |