Re: Re: Bug in Solve?
- To: mathgroup at smc.vnet.net
- Subject: [mg103014] Re: [mg102951] Re: [mg102921] Bug in Solve?
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Thu, 3 Sep 2009 19:57:11 -0400 (EDT)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <200909020803.EAA03289@smc.vnet.net> <200909030937.FAA20743@smc.vnet.net>
- Reply-to: murray at math.umass.edu
FullSimplify (after ComplexExpand) is a bit of overkill here to get rid
of the I's: Simplify suffices.
Andrzej Kozlowski wrote:
> On 2 Sep 2009, at 10:03, tonysin wrote:
>
>> I am just trying to learn Mathematica. What am I doing wrong here?
>>
>> I have a very simple equation:
>>
>> x^3 - 15 x + 2 = 0
>>
>> When I plot it in Mathematica 7,
>>
>> ClearAll[*]
>> f[x_] := x^3 - 15 x + 2
>> Plot[f[x], {x, -5, 5}]
>>
>>
>> it gives the expected graph of a cubic, with three real roots near -4,
>> 0, and 4.
>>
>>
>> When I NSolve it,
>>
>> NSolve[f[x] == 0, x]
>>
>> it gives
>>
>> {{x -> -3.938}, {x -> 0.133492}, {x -> 3.80451}}
>>
>> which is exactly what you would expect from the graph.
>>
>> But when I Solve it
>>
>> Solve[f[x] == 0, x]
>>
>> it gives this mess
>>
>> {{x -> 5/(-1 + 2 I Sqrt[31])^(1/3) + (-1 + 2 I Sqrt[31])^(
>> 1/3)}, {x -> -((5 (1 + I Sqrt[3]))/(
>> 2 (-1 + 2 I Sqrt[31])^(1/3))) -
>> 1/2 (1 - I Sqrt[3]) (-1 + 2 I Sqrt[31])^(1/3)}, {x -> -((
>> 5 (1 - I Sqrt[3]))/(2 (-1 + 2 I Sqrt[31])^(1/3))) -
>> 1/2 (1 + I Sqrt[3]) (-1 + 2 I Sqrt[31])^(1/3)}}
>>
>>
>> I don't know how it looks in your font, but that "I" in each solution
>> is the imaginary i. Solve is saying this equation has no real roots,
>> even though the graph clearly shows that all three roots are real.
>>
>> Can someone tell me if I am doing something wrong, or am I expecting
>> something wrong, or if I just can't trust Mathematica? Thanks for any
>> help.
>>
>
> You should learn a little more mathematics. The fact that your
> expressions contain I does not mean at all that they have non-zero
> imaginary parts, only that Mathematica does not attempt by itself to
> find an expression without I automatically (this is a reasonable thing
> to do as trying to find such an expression would take, in general, a
> lot of extra time which would, in most cases, be wasted. But if you
> want a purely real expression then:
>
>
> FullSimplify[ComplexExpand[Solve[x^3 - 15*x + 2 == 0, x]]]
> {{x -> Sqrt[5]*
> (Sqrt[3]*Sin[(1/3)*ArcTan[2*Sqrt[31]]] +
> Cos[(1/3)*ArcTan[2*Sqrt[31]]])},
> {x -> -2*Sqrt[5]*Cos[(1/3)*ArcTan[2*Sqrt[31]]]},
> {x -> Sqrt[5]*(Cos[(1/3)*ArcTan[2*Sqrt[31]]] -
> Sqrt[3]*Sin[(1/3)*ArcTan[2*Sqrt[31]]])}}
>
> gives you one.
>
> Andrzej Kozlowski
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
- References:
- Bug in Solve?
- From: tonysin <a2mgoog@yahoo.com>
- Re: Bug in Solve?
- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
- Bug in Solve?