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Re: very odd failure of Solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131658] Re: very odd failure of Solve
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Tue, 17 Sep 2013 21:33:52 -0400 (EDT)
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Am Montag, 16. September 2013 10:03:31 UTC+2 schrieb Richard Fateman:
> On 9/15/2013 4:03 AM, Alan wrote:
> 
> > Setting an irrelevant parameter to 0 baffles Solve. Why?
> 
> > Thanks,
> 
> > Alan Isaac
> 
> >
> 
> > $Assumptions =.
> 
> > ClearAll[f1]
> 
> > f1[x_] := s*x^\[Alpha] - (a + b + c)*x
> 
> > Solve[f1[x] == 0, x]  (* Solve works *)
> 
> > Solve[(f1[x] /. {b -> 0}) == 0, x]  (* Solve fails *)
> 
> <snip>
> 
> 
> 
> Running Reduce[ {%==0}, {x} ] on either equation seems to go into
> 
> an infinite loop.  That maybe be an independent bug, though.
> 
> 
> 
> I expected that somehow fiddling with the variable names would
> 
> do something, and that the ordering of a,b,c, alpha was critical.
> 
> Out of curiosity I tried a few variants to generate a better
> 
> hypothesis, but ran out of, um, curiosity.

Still a bit curious I tried

1) the number miracle

Solve[s*x^\[Alpha] - (a + b + c)*x, x] (* Solve works *)
Solve[s*x^\[Alpha] - (a + b )*x, x] (* Solve fails *)
Solve[s*x^\[Alpha] - (a )*x, x] (* Solve works *)

oops, size matters (1 and 3 is okay, 2 not)

2) the simplest case

The most simple case of this type in which Solve fails seems to be

Solve[x^E - 2*x == 0, x]

Solve::nsmet: This system cannot be solved with the methods available to Solve. >>

You can safely replace the irrational E by the algebraic Sqrt[2] or other constants apart from rationals. Solve will fail as well.

Competition is open to find the simplest case Solve can't do with.

Best regards,
Wolfgang





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