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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>
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