William Stein wrote:
> 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?In this case: sage: arcsinh(1).n() - ln(1+sqrt(2)).n() 1.11022302462516e-16 So the computer doesn't quite think that they are equal. Jason --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
