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problem solving polynomial equations

• To: mathgroup at smc.vnet.net
• Subject: [mg61306] problem solving polynomial equations
• From: wtplasar at ehu.es
• Date: Fri, 14 Oct 2005 22:22:37 -0400 (EDT)
• References: <200510140953.FAA28482@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,


I have  two equations. The first one is

eqy=(y*(3*b^2 + 12*b*y^2 + 12*y^4 + 3*b^2*z^4 + 4*b*y^2*z^4 + 
3*r*y*Sqrt[4*y^4 + 4*b*y^2*(1 + z^4) + b^2*(1 + 3*z^4) + z^2*(8*b*y^2 
+ 4*y^4 + b^2*(3 + z^4))*Sign[k]]*
    Sign[s] + z^2*Sign[k]*(6*b^2 + 16*b*y^2 + 8*y^4 + r*y*Sqrt[4*y^4 + 
4*b*y^2*(1 + z^4) + b^2*(1 + 3*z^4) + z^2*(8*b*y^2 + 4*y^4 + b^2*(3 + 
z^4))*Sign[k]]*
      Sign[s])))/(3*(3*b^2 + 8*b*y^2 + 4*y^4 + 3*b^2*z^4 + 2*b*(3*b + 
4*y^2)*z^2*Sign[k] + 
   2*r*y*Sqrt[4*y^4 + 4*b*y^2*(1 + z^4) + b^2*(1 + 3*z^4) + z^2*
(8*b*y^2 + 4*y^4 + b^2*(3 + z^4))*Sign[k]]*Sign[s]));


and the second one is

eqz=(y*z*(4*b*y + 8*y^3 + 4*b*y*z^4 + r*Sqrt[4*y^4 + 4*b*y^2*(1 + z^4) 
+ b^2*(1 + 3*z^4) + z^2*(8*b*y^2 + 4*y^4 + b^2*(3 + z^4))*Sign[k]]*Sign
[s] + 
   z^2*Sign[k]*(8*b*y + 8*y^3 + r*Sqrt[4*y^4 + 4*b*y^2*(1 + z^4) + b^2*
(1 + 3*z^4) + z^2*(8*b*y^2 + 4*y^4 + b^2*(3 + z^4))*Sign[k]]*Sign
[s])))/
 (3*(3*b^2 + 8*b*y^2 + 4*y^4 + 3*b^2*z^4 + 2*b*(3*b + 4*y^2)*z^2*Sign
[k] + 
   2*r*y*Sqrt[4*y^4 + 4*b*y^2*(1 + z^4) + b^2*(1 + 3*z^4) + z^2*
(8*b*y^2 + 4*y^4 + b^2*(3 + z^4))*Sign[k]]*Sign[s]));

Now when I do 

Solve[{eqy == 0, eqzsubs == 0}, {y, z}] /. Sign[s]^2 -> 1 

I get the result fairly quickly, but if I do 

Solve[{Numerator[eqy]== 0, Numerator[eqz] == 0}, {y, z}]/. Sign[s]^2 -
> 1 

it seems to get stuck. I may get an answer eventually, but it seemed 
to be taking too long and aborted it.

Any clues? Thanks.

Ruth 

• Follow-Ups:
  • Re: problem solving polynomial equations
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: problem solving polynomial equations
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>

• References:
  • Re: Solving Diophantine Equations
    • From: Andrzej Kozlowski <andrzej@yhc.att.ne.jp>