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something (not) funny!


CAS (Mathematica 5.2 in particular) can be funny sometimes!

[Seriously now, I understand the difficulties and the problems
that appeared possibly in the following examples and more or less
I can figure what goes wrong.

Note that one of this examples appeared in a recent post
of someone leading him to wonder about the reliability of Mathematica.

That's why we should trust but verify results from CASs...

Anyway, since for someone-not me!- it is vacation period
it is needed some fun!]

Version->5.2

Example 1

In[1]:=
Timing[FourierTransform[Sech[x*a], x, s]]

Out[1]=
{58.359*Second, (Sqrt[Pi/2]*Sech[(Pi*s)/(2*a)])/a}

However,

In[2]:=
TimeConstrained[FourierTransform[Sech[x*Log[2]], x, s], 300]

Out[2]=
$Aborted

Example 2

In[4]:=
TrigToExp[Sech[x*a]]
FourierTransform[%, x, s]

Out[4]=
2/(E^((-a)*x) + E^(a*x))

Out[4]=
(Sqrt[Pi/2]*Sech[(Pi*s)/(2*a)])/a

In[5]:=
TrigToExp[Sech[x*Log[2]]]
FourierTransform[%, x, s]

Out[5]=
2/(2^(-x) + 2^x)

Out[5]=
FourierTransform[2/(2^(-x) + 2^x), x, s]

Dimitris



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