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Groups > comp.soft-sys.math.maple > #868

Re: sqrt(1/sin(alpha))

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On Saturday, March 1, 2014 8:49:59 AM UTC-8, William Unruh wrote:
> On 2014-03-01, G. A. Edgar <edgar@math.ohio-state.edu.invalid> wrote:
> 
> > In article <010320140625332981%edgar@math.ohio-state.edu.invalid>, G.
> 
> > A. Edgar <edgar@math.ohio-state.edu.invalid> wrote:
> 
> >
> 
> >> In article <5311ce00$0$3647$426a74cc@news.free.fr>, Jerome BENOIT
> 
> >> <g6299304p@rezozer.net> wrote:
> 
> >> 
> 
> >> > Hello List,
> 
> >> > 
> 
> >> > so far I cannot figure out how to (simplify|convert) 
> 
> >> > 
> 
> >> > sqrt(1/sin(alpha));
> 
> >> > 
> 
> >> > into
> 
> >> > 
> 
> >> > 1/sqrt(sin(alpha));
> 
> >> > 
> 
> >> > 
> 
> >> > Any idea ?
> 
> >> > 
> 
> >> > Thanks in advance,
> 
> >> > Jerome
> 
> >> 
> 
> >> Maple does not do that "simplification" because it is wrong (for
> 
> >> complex values).  If you like you can tell Maple more information:
> 
> >> 
> 
> >> u:=sqrt(1/sin(alpha));
> 
> >> simplify(u) assuming sin(alpha)>0;
> 
> >
> 
> > To see the incorrectness, do this:
> 
> >
> 
> > u:=sqrt(1/sin(alpha));
> 
> > v:=simplify(u) assuming sin(alpha)>0;
> 
> > eval(u,alpha=-Pi/2);
> 
> > eval(v,alpha=-Pi/2);
> 
> 
> 
> It is not wrong. The square root always has two possible values, with
> 
> neither being the "right" one. The choice is arbitrary. 
> 
> That maple makes different choices in the two cases is entirely to be
> 
> expected. 
> 
> 
> 
> >

Not only is it arbitrary, the "assumption" mechanism does not provide any valid insight into the choice of branch cut. 
 Maple is hardly unique in making this bogus inference.  There are two square roots of 4.  Even though 4 is positive.
Sqrt(x^2) becoming x makes sense assuming sqrt(x^2)=x.

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sqrt(1/sin(alpha)) Jerome BENOIT <g6299304p@rezozer.net> - 2014-03-01 13:09 +0100
  Re: sqrt(1/sin(alpha)) "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2014-03-01 06:25 -0700
    Re: sqrt(1/sin(alpha)) "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2014-03-01 06:34 -0700
      Re: sqrt(1/sin(alpha)) William Unruh <unruh@invalid.ca> - 2014-03-01 16:49 +0000
        Re: sqrt(1/sin(alpha)) fateman@gmail.com - 2014-03-10 07:57 -0700

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