Am Mittwoch, 5. August 2009 15:59 schrieben Sie:
> 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)
Tim,
this does not always work (see (6) and (7)) :
(1) -> )set mess auto off
(1) -> sinrule:=rule((1-cos(x)^2) == sin(x)^2)
(1) ->
2 2
(1) - cos(x) + %C + 1 == sin(x) + %C
Type: RewriteRule(Integer,Integer,Expression Integer)
(2) -> f:= 1 - cos(x)^2
(2) ->
2
(2) - cos(x) + 1
Type: Expression Integer
(3) -> sinrule(f)
(3) ->
2
(3) sin(x)
Type: Expression Integer
(4) -> sinrule(f+3)
(4) ->
2
(4) - cos(x) + 4
Type: Expression Integer
(5) -> sinrule(f+a)
(5) ->
2
(5) sin(x) + a
Type: Expression Integer
(6) -> sinrule (2*(f+a))
(6) ->
2
(6) - 2cos(x) + 2a + 2
Type: Expression Integer
(7) -> sinrule (1/(f+a))
(7) ->
1
(7) - ---------------
2
cos(x) - a - 1
Type: Expression Integer
- Michael
>
> 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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