Re: Inverse function warnings
- To: mathgroup at smc.vnet.net
- Subject: [mg99228] Re: Inverse function warnings
- From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
- Date: Thu, 30 Apr 2009 06:23:43 -0400 (EDT)
- References: <gt90og$l55$1@smc.vnet.net>
Well, lets look at the equation Solve[Sin[x] == 0, x] which yields the
same warning and has x->0 as the sole result.
Of course you know that this equation has an infinite number of
solutions; all multiples of Pi will do.
Mathematica arrives at its solution by using ArcSin, the inverse
function of Sin. So instead of Sin[x]==0 we now have x==ArcSin[0]
which equals 0. Since ArcSin maps the range {-Infinity,Infinity} to
{-1,1} it will never find the multiples of Pi as a solution.
Conclusion:Using inverse functions you may find a solution, but these
are not guaranteed to be all possible solutions to the original
equation. Reduce is better in this respect. In your case it find all
solutions which includes complex ones. For C[1]->0 and C[2]->0 you'll
have the ones reported by Solve.
WIth Off[Solve::ifun] you can switch off the warning. Wrapping Quiet
around your Solve will do as well.
Cheers -- Sjoerd
On Apr 29, 9:48 am, davef <davidfrick2... at yahoo.com> wrote:
> When I execute this in Mathematica 7:
>
> Solve[3^(2 x) - 12 (3^x) + 27 == 0, x]
>
> I get this:
>
> Solve::ifun: Inverse functions are being used by Solve, so some solutions=
may not be found; use Reduce for complete solution information. >>
>
> {{x->1},{x->2}}
>
> 1 amd 2 are proper solutions but is it possible to avoid the warning?
>
> If I use Reduce:
>
> Reduce[3^(2 x) - 12 (3^x) + 27 == 0, x]
>
> I get a set of 1 and 2 added to some imaginary number terms that I don't =
quite understand.
>
> I guess my question is: why would the use of inverse functions be so unre=
liable a solution as to necessitate a warning? And in the interest of cl=
ean output, can the warning be supressed other than by deleteing the cell? =
>
> Thanks