no doubt whatever ;)
However
asin(sin(1:DoubleFloat))::DoubleFloat => 1.0
complexNormalize asin(sin(z)) => z
In* efstruc.spad* (line 423): is?(op, 'asin) => atan(z / sqrt(1 - z^2))
yields:
(1) -> f(z)== atan(z / sqrt(1 - z^2))
Type:
Void
(2) -> f(sin(z))
Compiling function f with type Expression(Integer) -> Expression(
Integer)
sin(z)
(2) atan(----------------)
+-------------+
| 2
\|- sin(z) + 1
Type:
Expression(Integer)
(3) -> normalize %
(3) - z
Apparently we have:
(4) -> test(normalize atan(sin(z)/cos(z)) = normalize
atan(sin(z)/sqrt(cos(z)^2)))
(4) false
Type:
Boolean
Either sqrt gives wrong sign or it happens when converting to tan(z/2) ...
(5) -> normalize sqrt(1-sin(z)^2)^-1
z 2
tan(-) + 1
2
(5) -----------
z 2
tan(-) - 1
2
hm, really strange.
On Thursday, 25 September 2014 02:14:13 UTC+2, Bill Page wrote:
>
> normalize seems to return an anomalous result for asin(sin(r))
>
> (1) -> normalize acos(cos(r))-r
>
> (1) 0
>
> (2) -> normalize asin(sin(r))-r
>
> (2) - 2r
>
> (3) -> normalize acosh(cosh(r))-r
>
> (3) 0
>
> (4) -> normalize asinh(sinh(r))-r
>
> (4) 0
>
> (5) -> normalize atan(tan(r))-r
>
> (5) 0
>
> (6) -> normalize atanh(tanh(r))-r
>
> (6) 0
>
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