An exact simplification challenge - 96 (EllipticF/K/Pi)
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From: Vladimir Bondarenko on 17 Jul 2010 13:32 Hello, Mathematica: 2*(-1)^(1/6)*(-2*I*EllipticF[I*ArcSinh[(-1)^(5/6)],(-1)^(2/3)]- (-1)^(1/6)*EllipticK[-(-1)^(1/3)]+EllipticK[1-(-1)^(2/3)]+ I*EllipticPi[(-1)^(1/3),(-1)^(2/3)]+ (-1)^(1/6)*EllipticPi[-(-1)^(2/3),-(-1)^(1/3)]- 2*I*EllipticPi[(-1)^(1/3),(-I)*ArcSinh[(-1)^(5/6)],(-1)^(2/3)]) Maple: 2*(-1)^(1/6)*(2*I*EllipticF((-1)^(1/3),(-1)^(1/3))- (-1)^(1/6)*EllipticK((-(-1)^(1/3))^(1/2))+ EllipticK((1-(-1)^(2/3))^(1/2))+ I*EllipticPi((-1)^(1/3),(-1)^(1/3))+ (-1)^(1/6)*EllipticPi(-(-1)^(2/3),(-(-1)^(1/3))^(1/2))- 2*I*EllipticPi((-1)^(1/3),(-1)^(1/3),(-1)^(1/3))) [= 1.047...] = ? Cheers, Vladimir Bondarenko Co-founder, CEO, Mathematical Director http://www.cybertester.com/ Cyber Tester Ltd. ---------------------------------------------------------------- "We must understand that technologies like these are the way of the future." ---------------------------------------------------------------- ---------------------------------------------------------------- http://groups.google.com/group/sci.math/msg/9f429c3ea5649df5 "...... the challenges imply that a solution is built within the framework of the existent CAS functions & built-in definitions." ---------------------------------------------------------------- ----------------------------------------------------------------
From: Nasser M. Abbasi on 17 Jul 2010 19:37 On Jul 17, 10:32 am, Vladimir Bondarenko <v...(a)cybertester.com> wrote: > Maple: > > 2*(-1)^(1/6)*(2*I*EllipticF((-1)^(1/3),(-1)^(1/3))- > (-1)^(1/6)*EllipticK((-(-1)^(1/3))^(1/2))+ > EllipticK((1-(-1)^(2/3))^(1/2))+ > I*EllipticPi((-1)^(1/3),(-1)^(1/3))+ > (-1)^(1/6)*EllipticPi(-(-1)^(2/3),(-(-1)^(1/3))^(1/2))- > 2*I*EllipticPi((-1)^(1/3),(-1)^(1/3),(-1)^(1/3))) > > [= 1.047...] = ? > Do you think this below is a strange behavior of Maple 14? restart; r:=2*(-1)^(1/6)*(2*I*EllipticF((-1)^(1/3),(-1)^(1/3))- (-1)^(1/6)*EllipticK((-(-1)^(1/3))^(1/2))+EllipticK((1- (-1)^(2/3))^(1/2))+I*EllipticPi((-1)^(1/3),(-1)^(1/3))+ (-1)^(1/6)*EllipticPi(-(-1)^(2/3),(- (-1)^(1/3))^(1/2))-2*I*EllipticPi((-1)^(1/3),(-1)^(1/3),(-1)^(1/3))): evalf(r); -10 1.047197551 + 9.408996622 10 I evalf(simplify(r)); 7.790198973 - 2.156515648 I ? --Nasser
From: Vladimir Bondarenko on 18 Jul 2010 02:41 On Jul 18, 2:37 am, "Nasser M. Abbasi" <n...(a)12000.org> wrote: > On Jul 17, 10:32 am, Vladimir Bondarenko <v...(a)cybertester.com> wrote: > > > Maple: > > > 2*(-1)^(1/6)*(2*I*EllipticF((-1)^(1/3),(-1)^(1/3))- > > (-1)^(1/6)*EllipticK((-(-1)^(1/3))^(1/2))+ > > EllipticK((1-(-1)^(2/3))^(1/2))+ > > I*EllipticPi((-1)^(1/3),(-1)^(1/3))+ > > (-1)^(1/6)*EllipticPi(-(-1)^(2/3),(-(-1)^(1/3))^(1/2))- > > 2*I*EllipticPi((-1)^(1/3),(-1)^(1/3),(-1)^(1/3))) > > > [= 1.047...] = ? > > Do you think this below is a strange behavior of Maple 14? > > restart; > r:=2*(-1)^(1/6)*(2*I*EllipticF((-1)^(1/3),(-1)^(1/3))- > (-1)^(1/6)*EllipticK((-(-1)^(1/3))^(1/2))+EllipticK((1- > (-1)^(2/3))^(1/2))+I*EllipticPi((-1)^(1/3),(-1)^(1/3))+ > (-1)^(1/6)*EllipticPi(-(-1)^(2/3),(- > (-1)^(1/3))^(1/2))-2*I*EllipticPi((-1)^(1/3),(-1)^(1/3),(-1)^(1/3))): > > evalf(r); > > -10 > 1.047197551 + 9.408996622 10 I > > evalf(simplify(r)); > 7.790198973 - 2.156515648 I > > ? > > --Nasser Hi Nasser, This is an error in programming made years ago by Maplesoft: Maple 14/13/12/11 7.790198973 - 2.156515648*I 2006 Maple 10 7.790198973 - .2e-8*I 2004 Maple 9.5 2.250951140 - .464082264*I Best, Vladimir
From: Vladimir Bondarenko on 20 Jul 2010 14:19
On Jul 17, 8:32 pm, Vladimir Bondarenko <v...(a)cybertester.com> wrote: > Hello, > > Mathematica: > > 2*(-1)^(1/6)*(-2*I*EllipticF[I*ArcSinh[(-1)^(5/6)],(-1)^(2/3)]- > (-1)^(1/6)*EllipticK[-(-1)^(1/3)]+EllipticK[1-(-1)^(2/3)]+ > I*EllipticPi[(-1)^(1/3),(-1)^(2/3)]+ > (-1)^(1/6)*EllipticPi[-(-1)^(2/3),-(-1)^(1/3)]- > 2*I*EllipticPi[(-1)^(1/3),(-I)*ArcSinh[(-1)^(5/6)],(-1)^(2/3)]) > > Maple: > > 2*(-1)^(1/6)*(2*I*EllipticF((-1)^(1/3),(-1)^(1/3))- > (-1)^(1/6)*EllipticK((-(-1)^(1/3))^(1/2))+ > EllipticK((1-(-1)^(2/3))^(1/2))+ > I*EllipticPi((-1)^(1/3),(-1)^(1/3))+ > (-1)^(1/6)*EllipticPi(-(-1)^(2/3),(-(-1)^(1/3))^(1/2))- > 2*I*EllipticPi((-1)^(1/3),(-1)^(1/3),(-1)^(1/3))) > > [= 1.047...] = ? > > Cheers, > > Vladimir Bondarenko > > Co-founder, CEO, Mathematical Director > > http://www.cybertester.com/ Cyber Tester Ltd. > > ---------------------------------------------------------------- > > "We must understand that technologies > like these are the way of the future." > > ---------------------------------------------------------------- > ---------------------------------------------------------------- > > http://groups.google.com/group/sci.math/msg/9f429c3ea5649df5 > > "...... the challenges imply that a solution is built within the > framework of the existent CAS functions & built-in definitions." > > ---------------------------------------------------------------- > ---------------------------------------------------------------- A hint: The answer is Pi/3 :) |