On Fri, Oct 31, 2008 at 12:57 PM, Jim Clark
<[EMAIL PROTECTED]> wrote:
>
> Hello sage gurus,
>
> Using sage to check a manually calculated integral :
>
> sage: var('r,h')
> (r, h)
> sage: integrate(r/sqrt(r^2 - sqrt(2)*h*r + h^2), r, 0, sqrt(2)
> *h).factor()
> sqrt(2)*arcsinh(1)*h
>
> My manual result (using an old table of integrals) was sqrt(2)*ln(sqrt
> (2)+1)*h
>
> So, wondering whether arcsinh(1) = ln(sqrt(2)+1), I asked:
>
> sage: bool(arcsinh(1) == ln(1+sqrt(2)))
> False
>
> but then,
>
> sage: arcsinh(1).n()
> 0.881373587019543
> sage: ln(1+sqrt(2)).n()
> 0.881373587019543
>
> They look equal to my eyes...
>
> Also,
> sage: bool(arcsinh(1).n() == ln(1+sqrt(2)).n())
> False
>
> What am I missing here?
>
> Thanks,
> Jim Clark
If expr is a symbolic expression in Sage, then
bool(expr)
evaluates to True only if expr can be proved to be True.
Otherwise it always evaluates to False.
The actual code that decides this is currently in Maxima.
-- William
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