Re: Why can't Mathematica find this root?
- To: mathgroup at smc.vnet.net
- Subject: [mg38530] Re: Why can't Mathematica find this root?
- From: Name <mee at home.com.redline.ru>
- Date: Sun, 22 Dec 2002 04:13:58 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
GeneralizedSolve doesn't seem to work well for sine:
GeneralizedSolve[Sin[x] == a, x] /. a -> 0
Out[15]=
{{x -> 2*n*Pi}}
Try http://www.mathsource.com/Content/Enhancements/Algebraic/0209-797
For the original problem with f[x_] := Sin[x]^3*Cos[x] and f ' [x]==0:
TrigSolve[Derivative[1][f][x] == 0, x]
Out[21]=
{{x -> Pi*C[2]}, {x -> Pi/3 + Pi*C[2]}, {x -> -(Pi/3) + Pi*C[2]}}
Not perfect also, since the solution can be written simply as Pi*k/3.
Maxim Rytin
m.r at prontomail.com
>> arctrigs = {ArcSin, ArcCos, ArcCsc, ArcSec,
ArcTan, ArcCot, ArcSinh,
>> ArcCosh,
>> ArcCsch, ArcSech, ArcTanh, ArcCoth};
>>
>> periods = {2*Pi, 2*Pi, 2*Pi, 2*Pi, Pi, Pi,
2*I*Pi,
>> 2*I*Pi, 2*I*Pi, 2*I*Pi, I*Pi, I*Pi};
>>
>> (* We use n to denote an arbitrary integer
*)
>>
>> Generalize[f_[x_], n_] :=
>> f[x] + n periods[[Position[arctrigs,
f][[1, 1]]]] /;
>> MemberQ[arctrigs,
>> f]
>>
>>
Generalize[Log[x_],n_]:=Log[x]+2\[Pi]\[ImaginaryI]n
>>
>>
Generalize[ProductLog[x_],n_]:=ProductLog[n,x]
>>
>> Generalize[x___, n_] := x
>>
>> GeneralizedSolve[eqns_, vars_] :=
Generalize[#, n] & //@ Solve[eqns,
>> vars]