2012-04-22 14:39, Duc Trung Ha skrev:
Am I missing something or is this behavior rather peculiar:
sage: bool(sin(x) == sin(x+2*pi))
True
...however:
plot(sin(x) - sin(x+2*pi))
gives out the result:
> [plot showing inaccuracies of floats]
I typed this instead, and got a nice line at 0:
plot(simplify(sin((2*pi) + x) - sin(x)),-100,100)
It seems that your plot evaluates both sin-calls numerically, and as we
use floating point numbers of a certain precision, they will differ
around the 15-th digit, which is what you see.
Perhaps the simplify-call uses the identity you mention to replace the
expression by 0, and then plots 0.
Moreover, example below isn't even recognized as an identity:
sage: bool ( sin((2*pi^2 + x)/pi) == sin(x/pi) )
False
You could use:
bool (sin(((2*pi^2 + x)/pi).expand()).full_simplify() == sin(x/pi))
Is this a bug or is it covered somewhere else?
I might consider it a bug that not every identity is used by default,
but I would add that I expect it to be an unsolvable problem:
1) We want it fast.
2) We want it to use all simplification methods.
3) We _need_ a yes/no answer.
I will let the experts tell the story in more detail.
Regards
Johan
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