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Interpretation of Reduce results

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3833] Interpretation of Reduce results
  • From: sherod at boussinesq.Colorado.EDU (Scott Herod)
  • Date: Mon, 29 Apr 1996 00:30:44 -0400
  • Organization: University of Colorado at Boulder
  • Sender: owner-wri-mathgroup at wolfram.com

I guess that I am a little surprised by the following output of Reduce.

In[15]:=
test = {z^2*p[1] + z*p[2] + p[4],
    y + z^2*q[1] + z*q[2] + q[4]}

Out[15]=
  2                            2
{z  p[1] + z p[2] + p[4], y + z  q[1] + z q[2] + q[4]}

In[16]:=
Reduce[test == 0, {y}, {p[1],q[1]}]

Out[16]=
p[4] == -(z p[2]) && y == -q[4] && z == 0 || 
 
  p[4] == -(z p[2]) && y == -q[4] && z == 0 || z != 0


In particular I was worried that with the final case in Out[16], z != 0,
more was not said.  Certainly arbitrary values of z, y, p's and q's won't
satisfy the original equations even if z != 0.

Can someone comment?

Scott Herod

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