Re: Re: Transforming a polynomial into a trigonometric format tia sal2

*To*: mathgroup at smc.vnet.net*Subject*: [mg88336] Re: [mg88299] Re: Transforming a polynomial into a trigonometric format tia sal2*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 2 May 2008 03:42:44 -0400 (EDT)*References*: <fv42j9$5ui$1@smc.vnet.net> <200805010719.DAA26032@smc.vnet.net> <E3479FDF-B47F-4F2E-BB1B-98BEF7B973F6@mimuw.edu.pl>

It is slightly better to localize the symbol a: Chebyshev[f_, x_] := Module[{a, n = Exponent[f, x]}, Sum[a[i]*Cos[i ArcCos[x]], {i, 0, n}] /. SolveAlways[f == Sum[a[i]*ChebyshevT[i, x], {i, 0, n}], x][[1]]] Andrzej Kozlowski On 1 May 2008, at 22:19, Andrzej Kozlowski wrote: > I think what you want is this function: > > > Chebyshev[f_, x_] := > With[{n = Exponent[f, x]}, > Sum[a[i]*Cos[i ArcCos[x]], {i, 0, n}] /. > SolveAlways[f == Sum[a[i]*ChebyshevT[i, x], {i, 0, n}], x][[1]]] > > So now, for example: > > Chebyshev[21 - 10*x + x^2, x] > -10*x + (1/2)*Cos[2*ArcCos[x]] + 43/2 > > TrigExpand[%] > x^2 - 10*x + 21 > > Chebyshev[21 - 10*x + x^2 + 3*x^3, x] > -((31*x)/4) + (1/2)*Cos[2*ArcCos[x]] + (3/4)*Cos[3*ArcCos[x]] + 43/2 > > > and so on. > > Andrzej Kozlowski > > > On 1 May 2008, at 16:19, ratullochjk2 at gmail.com wrote: > >> I'm sorry if I didn't explain myself better I hope this clarifies it >> better >> >> when I test for x =3 x= 7 for equation: >> 21 - 10 x + x^2 I get zero for both answers >> >> I used another math program using the ChebyshevT command and I >> got this >> 1/2 Cos[2 ArcCos[x]] + 43/2 - 10 x I tested with x=3 and x=7 and I >> also got zero for both >> >> but when I do a TrigReduce >> >> In[148] := 21 - 10 x + x^2 /. x -> Cos[y] // TrigReduce >> >> I get >> >> Out[149]:= 1/2 (43 - 20 Cos[x] + Cos[2 x]) >> x=3 gives me 31.88 >> x=7 gives me 14.0293 >> >> I would like to use the ChebyshevT in mathematica 6 because I prefer >> that software but I'm not sure >> how to get the 1/2 Cos[2 ArcCos[x]] + 43/2 - 10 x answer in >> mathematica 6 >> >> Am I doing something wrong with the TrigReduce function or leaving a >> part out why are the answers not even close? >> >> tia sal2 >> >> On Apr 27, 10:41 pm, ratulloch... at gmail.com wrote: >>> Transforming a polynomial into a trigonometric format tiasal2 >>> >>> Greetings All >>> >>> I'm using mathematica 6 and I have a polynomial and would like to >>> convert it into >>> a Trigonometric format. Is this possible? >>> >>> Example: >>> I have a polynomial >>> 0.00154991- 4.01371 x + 1.81197 x^2 + 8.00183 x^3 - 9.3462 x^4 >>> >>> How can I transform this into a trigonometric format >>> Example: >>> 0.00596679 Cos[6.98132 x] + 0.00358397 Cos[7.21403 x] + >>> 2.25013 Sin[0.232711 x] - 4.51511 Sin[0.465421 x] >>> >>> Note: these aren't correct answers I just wanted to include and >>> example >>> >>> tiasa >> >

**References**:**Re: Transforming a polynomial into a trigonometric format tia sal2***From:*ratullochjk2@gmail.com