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MathGroup Archive 2001

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Re: Who can help me?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26880] Re: [mg26778] Who can help me?
  • From: Roberto Brambilla <rlbrambilla at cesi.it>
  • Date: Fri, 26 Jan 2001 01:27:25 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Subject: [mg26880] Re: [mg26778] Who can help me?
At 03.10 22/01/01 -0500, Jacqueline wrote:

>>I'm working on this polynomial linked to the truncated icosahedron:
>>
>>        -17808196677858180 x +
>>        138982864440593250 x^2 - 527304830550920588 x^3 +
>>        1301702220253454898 x^4 - 2358155595920193382 x^5 +
>>        3347791850698681436 x^6 - 3878279506351645237 x^7 +
>>        3764566420106299695 x^8 - 3117324712750504866 x^9 +
>>        2229873533973727384 x^10 - 1390372935143028255 x^11 +
>>        760794705528035032 x^12 - 367240961907017721 x^13 +
>>        157018216115380477 x^14 - 59650776196609992 x^15 +
>>        20179153653354540 x^16 - 6086251542996201 x^17 +
>>        1637007669992780 x^18 - 392300104078670 x^19 +
>>        83589038962550 x^20 - 15782712151030 x^21 +
>>        2628070696678 x^22 - 383466859804 x^23 + 48618908986 x^24 -
>>        5298021900 x^25 + 489095520 x^26 - 37516324 x^27 +
>>        2327268 x^28 - 112200 x^29 + 3945 x^30 - 90 x^31 + x^32;
>>
>>I'm interested at its value for x-> 2 + 2 Cos [2 [Pi] / 7].
>>Taking N [] gives  3.2628184 10^7
>>
>>But if I simplify  first and then take N[] it gives -0.0390625 +
>>0.0195313 [ImaginaryI]
>>
>>As it is a polynomial with integer coefficients, and 2 + 2 Cos [2 pi /
>>7] is real too, the result should be real.  So I prefer the 1st
>>solution,  but for another reason, I'm not so sure of this result.
>>
>>A Plot between 3 and 3.5, does not help me  neither to check if the
>>value 3.2628184  is good and If I do : polynomial /. x -> 3.2628184
>>10^7, it gives 2.7225238332205106`^240
>>
>>How could I check the result 3.2628184 10^7 ?
>>
>>Thanks
>>
>>Jacqueline
>>
>>
>
I put p[x_]:= <Jacqueline polinomial> then I approximate 
only p[x0] with different precision: 

Table[N[p[N[2 + 2 Cos [2 Pi / 7]] ],10*s],{s,1,8}]    
{3.2628184*10^7,3.2628184*10^7,3.2628184*10^7,
 3.2628184*10^7,3.2628184*10^7,3.2628184*10^7,
 3.2628184*10^7,3.2628184*10^7}

nothing happens!
Now I approximate only x0 with different precision:        
 
Table[N[p[N[2 + 2 Cos [2 Pi / 7],10*s] ]],{s,1,8}]  
{3.2628184*10^7, 0., 0.00108056072351914167, 
 0.00108056072343889031, 0.00108056072343889031, 
 0.00108056072343889031, 0.00108056072343889031,  .00108056072343889031}
    
Approximating both p[x] and x0 :
Table[N[p[N[2 + 2 Cos [2 Pi/7],10*s]],10*s],{s,1,8}]    
{3.26281840000000045*^7,
 0.3167-7.0688, 
 0.00108056072352,
 0.00108056072343889043623, 
 0.001080560723438890436215553236448920,
 0.00108056072343889043621555323644333824364337,
 0.00108056072343889043621555323644333824364333803921298, 
 0.0010805607234388904362155532364433382436433380392129926065104314}

I suppose this the right value.
Bye Rob.

Roberto Brambilla
CESI
Via Rubattino 54
20134 Milano
tel +39.2.2125.5875
fax +39.2.2125.610
rlbrambilla at cesi.it



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