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Re: How to Extract Conditional Expression?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127635] Re: How to Extract Conditional Expression?
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Thu, 9 Aug 2012 03:52:03 -0400 (EDT)
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  • References: <jvl43v$731$1@smc.vnet.net>

It can also handle the general case

step1 = x ->
   ConditionalExpression[(1/\[Pi]) 105 (-2 ArcTan[\[Sqrt]Root[
           1 - 4584 #1 + 525588 #1^2 - 24932888 #1^3 +
             643774850 #1^4 - 10134675448 #1^5 + 103523895748 #1^6 -
             713980114440 #1^7 + 3417573832943 #1^8 -
             11577472180368 #1^9 + 28132792718632 #1^10 -
             49450791062896 #1^11 + 63131885232924 #1^12 -
             58540019029360 #1^13 + 39271847011624 #1^14 -
             18902427543696 #1^15 + 6437818513647 #1^16 -
             1518441755144 #1^17 + 239987843524 #1^18 -
             24146287608 #1^19 + 1422915970 #1^20 - 42378776 #1^21 +
             478484 #1^22 - 1512 #1^23 + #1^24 &, 1]] + 2 \[Pi] C[1]),
     C[1] \[Element] Integers];

Assuming[{Element[C[1], Integers]},
 FullSimplify[step1] // N]

x -> -1. + 210. C[1]

% /. C[1] -> 3

x -> 629.


Bob Hanlon

On Wed, Aug 8, 2012 at 9:37 PM, djmpark <djmpark at comcast.net> wrote:
> step1 = x ->
>   ConditionalExpression[(1/\[Pi]) 105 (-2 ArcTan[\[Sqrt]Root[
>           1 - 4584 #1 + 525588 #1^2 - 24932888 #1^3 +
>             643774850 #1^4 - 10134675448 #1^5 + 103523895748 #1^6 -
>             713980114440 #1^7 + 3417573832943 #1^8 -
>             11577472180368 #1^9 + 28132792718632 #1^10 -
>             49450791062896 #1^11 + 63131885232924 #1^12 -
>             58540019029360 #1^13 + 39271847011624 #1^14 -
>             18902427543696 #1^15 + 6437818513647 #1^16 -
>             1518441755144 #1^17 + 239987843524 #1^18 -
>             24146287608 #1^19 + 1422915970 #1^20 - 42378776 #1^21 +
>             478484 #1^22 - 1512 #1^23 + #1^24 &, 1]] + 2 \[Pi] C[1]),
>    C[1] \[Element] Integers];
>
> step1 /. C[1] -> 3 // N
> x -> 629.
>
>
> David Park
> djmpark at comcast.net
> http://home.comcast.net/~djmpark/index.html
>
>
> From: Scott Guthery [mailto:sbg at acw.com]
>
> Thanks for everyone's help but I still can't seem to get the function out of
> the Conditional.  Here's the actual ConditionalExpression I'm dealing with:
>
> x -> ConditionalExpression[(1/\[Pi])
>   105 (-2 ArcTan[\[Sqrt]Root[
>          1 - 4584 #1 + 525588 #1^2 - 24932888 #1^3 + 643774850 #1^4 -
>            10134675448 #1^5 + 103523895748 #1^6 - 713980114440 #1^7 +
>            3417573832943 #1^8 - 11577472180368 #1^9 +
>            28132792718632 #1^10 - 49450791062896 #1^11 +
>            63131885232924 #1^12 - 58540019029360 #1^13 +
>            39271847011624 #1^14 - 18902427543696 #1^15 +
>            6437818513647 #1^16 - 1518441755144 #1^17 +
>            239987843524 #1^18 - 24146287608 #1^19 +
>            1422915970 #1^20 - 42378776 #1^21 + 478484 #1^22 -
>            1512 #1^23 + #1^24 &, 1]] + 2 \[Pi] C[1]),
>   C[1] \[Element] Integers]
>
> Using the various suggestions the closest I can get is the error statement
> ...
>
> Root::deg: 1-4584 x+525588 x^2-24932888 x^3+643774850 x^4-10134675448
> x^5+103523895748 x^6-713980114440 x^7+3417573832943 x^8-11577472180368
> x^9+28132792718632 x^10-49450791062896 x^11+63131885232924
> x^12-58540019029360 x^13+39271847011624 x^14-18902427543696
> x^15+6437818513647 x^16-1518441755144 x^17+239987843524 x^18-24146287608
> x^19+1422915970 x^20-42378776 x^21+478484 x^22-1512 x^23+x^24 has fewer than
> 1 root(s) as a polynomial in #1. >>
>
> followed by ...
>
> (1/\[Pi])210 (3 \[Pi] -
>    ArcTan[\[Sqrt]Root[
>       1 - 4584 x + 525588 x^2 - 24932888 x^3 + 643774850 x^4 -
>         10134675448 x^5 + 103523895748 x^6 - 713980114440 x^7 +
>         3417573832943 x^8 - 11577472180368 x^9 +
>         28132792718632 x^10 - 49450791062896 x^11 +
>         63131885232924 x^12 - 58540019029360 x^13 +
>         39271847011624 x^14 - 18902427543696 x^15 +
>         6437818513647 x^16 - 1518441755144 x^17 + 239987843524 x^18 -
>         24146287608 x^19 + 1422915970 x^20 - 42378776 x^21 +
>         478484 x^22 - 1512 x^23 + x^24 &, 1, 0]])
>
> I can't seem to get rid of the &,1,0 at the end.
>
> Thanks in advance for any additional clues.
>
> Cheers, Scott
>
>



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