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Re: Interval arithmetic bug


green tea <cetech07 at gmail.com> wrote:
> In[1]:= Limit[Sin[x], x -> Infinity]
>
> Out[1]= Interval[{-1, 1}]
>
> In[2]:= Limit[Sin[x + Pi/4], x -> Infinity]
>
> Out[2]= Interval[{-Sqrt[2], Sqrt[2]}]

Of course, we would like Out[2] to be the same as Out[1]. But I'm not sure
this behavior, shown in Out[2], should be called a bug. It's not new to
version 6, and I suppose that WR has long been aware of it.

Note that Out[2] contains Out[1] as a subinterval. Thus, containment has
not been violated.

David

> In[3]:= TrigExpand[Sin[x + Pi/4]]
>
> Out[3]= Cos[x]/Sqrt[2] + Sin[x]/Sqrt[2]
>
> In[4]:= (Limit[#1, x -> Infinity] & ) /@ {Cos[x]/Sqrt[2],
>   Sin[x]/Sqrt[2]}
>
> Out[4]= {Interval[{-(1/Sqrt[2]), 1/Sqrt[2]}],
>    Interval[{-(1/Sqrt[2]), 1/Sqrt[2]}]}
>
> In[5]:= Plus @@ %
>
> Out[5]= Interval[{-Sqrt[2], Sqrt[2]}]
>
> In[6]:= $Version
>
> Out[6]= "6.0 for Microsoft Windows (32-bit) (May 21, 2008)"
>
> oh my god..


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