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MathGroup Archive 1998

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Re: Solving Polynomial Equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13379] Re: [mg13309] Solving Polynomial Equations?
  • From: BobHanlon at aol.com
  • Date: Mon, 20 Jul 1998 02:50:42 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Two examples:

eqns = {x^3 + 2*x^2*y + 3*x*y^2 - 22*y^3 == 0, 
    3*x^3 + 3*x^2*y + 5*x*y^2 - 46*y^3 == 0}; 

soln = Union[Solve[eqns, {x, y}]]

Solve::svars: 
   Equations may not give solutions for all "solve"
    variables.

{{x -> 2*y}, {x -> 0, y -> 0}}

eqns = {x^3 + 2*x^2*y + 3*x*y^2 - 22*y^3 == 0, 
    3*x^3 + 3*x^2*y + 5*x*y^2 - 46*y^3 == 0, 
    x^3 + 2*x^2 + 3*x - 22 == 0}; 

soln = Solve[eqns, {x, y}]

{{x -> 2, y -> 1}, {y -> (-2 - I*Sqrt[7])/2, 
   x -> -2 - I*Sqrt[7]}, 
  {y -> (-2 + I*Sqrt[7])/2, x -> -2 + I*Sqrt[7]}}

Select[soln, FreeQ[#1, Complex] & ]

{{x -> 2, y -> 1}}

or

Select[soln, Im[{x, y} /. #1] == {0, 0} & ]

{{x -> 2, y -> 1}}

Bob Hanlon

In a message dated 7/17/98 4:47:34 AM, engp7778 at nus.edu.sg wrote:

>Which software is effective in solving the Simultaneous Polynomial
>Equations?
>
>I am using Mathematica now, but it doesn't seem to be capable of solving
>such problems. And I don't know how can I tell Mathematica to neglect
>the complex roots which I don't need to know. Attached is a sample
>problem.


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