Re: Reduce

*To*: mathgroup at smc.vnet.net*Subject*: [mg46899] Re: Reduce*From*: bobhanlon at aol.com (Bob Hanlon)*Date*: Sun, 14 Mar 2004 03:24:21 -0500 (EST)*References*: <c2u42q$f16$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Try using a symbol rather than "?" $Version "5.0 for Mac OS X (November 19, 2003)" form=Reduce[{ A Exp[x y]==B Cos[x y]+C Sin[x y], D Exp[-x y]==B Cos[x y]+C Sin[x y], (D[A Exp[x y],y]==D[(B Cos[x y]+C Sin[x y]),y]), (D[D Exp[-x y],y]==D[(B Cos[x y]+C Sin[x y]),y])}/. y->-a/2, {A,B,C,D}] x == 0 && A == 0 && B == 0 && D == 0 || A != 0 && x == 0 && B == A && D == A || ((a*x)/2 - Pi)/(2*Pi) \[NotElement] Integers && A == 0 && B == 0 && C == 0 && D == 0 || 0[1] \[Element] Integers && a != 0 && x == (2*(2*Pi*0[1] + Pi))/a && A == 0 && B == 0 && C == 0 && D == 0 Using D as both a constant and a function appears very risky. Likewise using C as both a plain constant and a constant of integration is causing the presence of 0[1] form=Reduce[{ A Exp[x y]==B Cos[x y]+k Sin[x y], d Exp[-x y]==B Cos[x y]+k Sin[x y], (D[A Exp[x y],y]==D[(B Cos[x y]+k Sin[x y]),y]), (D[d Exp[-x y],y]==D[(B Cos[x y]+k Sin[x y]),y])}/. y->-a/2, {A,B,k,d}] x == 0 && A == 0 && B == 0 && d == 0 || A != 0 && x == 0 && B == A && d == A || ((a*x)/2 - Pi)/(2*Pi) \[NotElement] Integers && A == 0 && B == 0 && k == 0 && d == 0 || C[1] \[Element] Integers && a != 0 && x == (2*(2*Pi*C[1] + Pi))/a && A == 0 && B == 0 && k == 0 && d == 0 Bob Hanlon In article <c2u42q$f16$1 at smc.vnet.net>, "Tony Harker" <a.harker at ucl.ac.uk> wrote: << I find Reduce in version 5 seems to have lost some functionality. In version 4 the input form = Reduce[{A Exp[? y] == B Cos[? y] + C Sin[? y] /. y -> -a/2, D Exp[-? y] == B Cos[? y] + C Sin[? y] /. y -> a/2, (D[A Exp[? y], y] == D[(B Cos[? y] + C Sin[? y]), y]) /. y -> -a/2, (D[D Exp[-? y], y] == D[(B Cos[ ? y] + C Sin[? y]), y]) /. y -> a/2}, {A, B, C, D}] produces a perfectly sensible result starting A == 0 && D == 0 || A == B && D == B && ? == 0 && ? == 0.... In version 5 the same input causes a long period of cogitation (far longer than version 4 took to produce its result), and finally emerges with a suggestion that I should look for further information on its failure which is not yet there. Mathematically, the problem is relatively straightforward: the equations reduce to M x = 0,where x={A,B,C,D}, so we just need the conditions under which the determinant of M is zero, and any other special cases. Are there new controls for Reduce in version 5 which will allow its functionality to be recovered, or is it irrevocably broken? >><BR><BR>