
From:  Tim Daly 
Subject:  Re: [Axiomdeveloper] unexpected behaviour of normalize(1(cos(x))^2) 
Date:  Wed, 05 Aug 2009 09:59:59 0400 
Useragent:  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 (1cos(x)^2) occurs in your expression E you can write: sinrule:=rule((1cos(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 backsubstitution 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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