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Re: Getting answer out of a ConditionalExpression[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132119] Re: Getting answer out of a ConditionalExpression[]
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Sat, 14 Dec 2013 04:03:19 -0500 (EST)
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  • References: <20131212062740.49ACB69EB@smc.vnet.net>

data = Table[x /. Solve[
      (1 + Exp[I*(n*Pi/6 + x)])*
        (1 + Exp[-I*(n*Pi/6 + x)]) ==
       1/((1 - Exp[I*n*Pi/6])*
          (1 - Exp[-I*n*Pi/6])), x],
    {n, 1, 11}] /. C[1] -> 0 // FullSimplify


{{0, -(Pi/3)}, {Pi/3, -Pi},
   {(1/2)*(Pi - 2*ArcCot[
              3/Sqrt[7]]),
     -((3*Pi)/2) + ArcCot[
         3/Sqrt[7]]},
   {-((7*Pi)/6) - ArcTan[
         5/Sqrt[11]], -(Pi/6) +
       ArcTan[5/Sqrt[11]]},
   {0, -((5*Pi)/3)},
   {-ArcCot[7/Sqrt[15]],
     -2*Pi + ArcCot[7/Sqrt[15]]},
   {-(Pi/3), -2*Pi},
   {-((11*Pi)/6) - ArcTan[
         5/Sqrt[11]], -((5*Pi)/6) +
       ArcTan[5/Sqrt[11]]},
   {-(Pi/2) - ArcCot[3/Sqrt[7]],
     -((5*Pi)/2) + ArcCot[
         3/Sqrt[7]]},
   {-Pi, -((7*Pi)/3)},
   {-((5*Pi)/3), -2*Pi}}


Show[ListCurvePathPlot[data],
 ListPlot[Tooltip /@ data,
  PlotStyle -> Directive[Red, AbsolutePointSize[4]]],
 Frame -> True, Axes -> False]



Bob Hanlon




On Thu, Dec 12, 2013 at 1:27 AM, Roger Bagula <roger.bagula at gmail.com>wrote:

> I'm interested in getting a plot-able array out of the following:
> Clear[x]
> Table[Solve[(1 + Exp[I*(n*Pi/6 + x)])*(1 + Exp[-I*(n*Pi/6 + x)]) ==
>    1/((1 - Exp[I*n*Pi/6])*(1 - Exp[-I*n*Pi/6])), x], {n, 1, 11}]
>
> There are two problems:
> 1) getting the answers out of the
> {x -> ConditionalExpression[
>    1/6 (-\[Pi] + 6 I (-((I \[Pi])/6) + 2 I \[Pi] C[1])),
>    C[1] \[Element] Integers]}
> and
> 2) removing the C[1] terms
>
> I'm particularly interested in plotting the phase angles with log
> expressions:
> {x -> ConditionalExpression[
>    1/2 (-\[Pi] + 2 I (2 I \[Pi] C[1] + Log[1/4 (-3 - I Sqrt[7])])),
>    C[1] \[Element] Integers]}, {x ->
>   ConditionalExpression[
>    1/2 (-\[Pi] + 2 I (2 I \[Pi] C[1] + Log[1/4 (-3 + I Sqrt[7])])),
>    C[1] \[Element] Integers]}
>
> Roger Bagula
>
>


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