Re: bug ?
- To: mathgroup at smc.vnet.net
- Subject: [mg122341] Re: bug ?
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Wed, 26 Oct 2011 17:36:26 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201110251016.GAA05769@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
That's odd!
If f is continuous, all eight outputs should represent the same number,
but N gives 4 distinct results:
Clear[f, s]
f[s_] = -(((s (4 s - 5)^2 - (5 + 3 Sqrt[17])/
8 (4 s + 1)) ((4 s - 5)^2 -
4 (5 + 3 Sqrt[17])/8 (4 s - 7)))/(16 s^2 - 32 s - 1)^2);
rp = 1/4 (4 + Sqrt[17]);
four = {Limit[f@s, s -> rp], f@rp, Simplify@f@rp, f@N@rp};
Grid@{four, N@four}
(output suppressed)
four//Column
1/544 (331-19 Sqrt[17])
-((((-1+Sqrt[17])^2-1/2 (-3+Sqrt[17]) (5+3 Sqrt[17])) (1/4 (-1+Sqrt[17])^2
(4+Sqrt[17])-1/8 (5+Sqrt[17]) (5+3 Sqrt[17])))/(-1-8
(4+Sqrt[17])+(4+Sqrt[17])^2)^2)
1/16 (1+2 Sqrt[17])
0.09375
N@four//Column
0.46445
0.
0.577888
0.09375
Bobby
On Tue, 25 Oct 2011 05:16:06 -0500, swiss <gregoire.nicollier at hevs.ch>
wrote:
> Following rational function has a double pole matched by a double root
> at (4+\sqrt{17})/4. The first result is correct, the other ones are
> false, but come without warning. Can somebody explain this to me?
>
> In[50]:= Limit[-(((s (4 s - 5)^2 - (5 + 3 Sqrt[17])/
> 8 (4 s + 1)) ((4 s - 5)^2 -
> 4 (5 + 3 Sqrt[17])/8 (4 s - 7)))/(16 s^2 - 32 s - 1)^2),
> s -> 1/4 (4 + Sqrt[17])]
>
> Out[50]= 1/544 (331 - 19 Sqrt[17])
>
> In[51]:= 1/544 (331 - 19 Sqrt[17]) // N
>
> Out[51]= 0.46445
>
> In[52]:= -(((s (4 s - 5)^2 - (5 + 3 Sqrt[17])/
> 8 (4 s + 1)) ((4 s - 5)^2 -
> 4 (5 + 3 Sqrt[17])/8 (4 s - 7)))/(16 s^2 - 32 s - 1)^2) /.
> s -> 1/4 (4 + Sqrt[17]) // Simplify
>
> Out[52]= 1/16 (1 + 2 Sqrt[17])
>
> In[53]:= 1/16 (1 + 2 Sqrt[17]) // N
>
> Out[53]= 0.577888
>
> In[54]:= -(((s (4 s - 5)^2 - (5 + 3 Sqrt[17])/
> 8 (4 s + 1)) ((4 s - 5)^2 -
> 4 (5 + 3 Sqrt[17])/8 (4 s - 7)))/(16 s^2 - 32 s - 1)^2) /.
> s -> 1/4 (4 + Sqrt[17.])
>
> Out[54]= 0.09375
>
--
DrMajorBob at yahoo.com
- References:
- bug ?
- From: swiss <gregoire.nicollier@hevs.ch>
- bug ?