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>

```

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