Thanks to all. Your responses have been helpful.
Jim
On Oct 31, 2008, at 1:51 PM, John Cremona wrote:
>
> arcsinh(x) = log(1+sqrt(1+x^2)), I seem to remember. [Proof:
> exercise]
>
> John Cremona
>
> 2008/10/31 William Stein <[EMAIL PROTECTED]>:
>>
>> 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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