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