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Re: very odd failure of Solve


On Monday, September 16, 2013 3:03:31 AM UTC-5, Richard Fateman wrote:
> 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.

It does seem to involve ordering. If instead of "a+c" one has "y+c" then Solve handles it. The underlying issue is some simplifying that produces, or not, a "nice" form of intermediate expression. This was also recently reported in the Mathematica stackexchange forum.

http://mathematica.stackexchange.com/questions/25182/variable-naming-changes-everything

I hope to find time to investigate further, some day.

Daniel Lichtblau
Wolfram Research




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