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MathGroup Archive 2001

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Re: Who can help me?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26851] Re: [mg26778] Who can help me?
  • From: Ranko Bojanic <bojanic at math.ohio-state.edu>
  • Date: Thu, 25 Jan 2001 01:13:28 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com



Jacqueline Zizi 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 xÆ2+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/.xÆ3.2628184
>10^7,it gives 2.7225238332205106`^240
>
>How could I check the result 3.2628184 10^7?
>
>Thanks
>Jacqueline

Jacqueline:

What you have here is a severe loss of precision of computations.
Let f[x] be the polynomial from the message. Following a Ted Ersek's 
recommendation,  here is what you have to do in such cases:
Define

g[x_] := Module[{ t }, f[t] /.t ->  SetPrecision[x , 60]]

You will have then no problems drawing the graph of g on 
any interval you like  and you will see that 

g[2+2 Cos[2 Pi / 7]] = 0.001080560723438890436215553236443

Regards,
Ranko



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