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Re: Help with Eliminate[]

• To: mathgroup at smc.vnet.net
• Subject: [mg84971] Re: [mg84962] Help with Eliminate[]
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 21 Jan 2008 06:56:47 -0500 (EST)
• References: <200801210912.EAA09638@smc.vnet.net>

On 21 Jan 2008, at 09:12, Kinjal Basu wrote:

> Hello everyone,
>
> Is there anyway but which i can eliminate t from the following two  
> equations.
>
> x=k*t - r*Cos[w*t]
> y=rSin[w*t]
>
> Using in built functions.
> I tried to use Eliminate[], But its not giving the desired answer  
> because 2 or more values of t can satisfy this.
>
> Is there any other way i cna eliminate t???
>
> Please Help,
>
> Thanking,
> Kinjal.
>


There is no single built-in function that will do it  so I think you  
have to do something like this:

equations = {x == k*t - r*Cos[w*t], y == r Sin[w*t]};

P = GroebnerBasis[
   Flatten[{equations /. Equal -> Subtract, Cos[w t]^2 + Sin[w t]^2 -  
1}], {x,k, t, t}, {Cos[w t], Sin[w t]}];


equations /. Solve[P == 0, t]

{{x == (k*x - Sqrt[k^2*r^2 - k^2*y^2])/k -
         r*Cos[(w*(k*x - Sqrt[k^2*r^2 - k^2*y^2]))/k^2],
     y == r*Sin[(w*(k*x - Sqrt[k^2*r^2 - k^2*y^2]))/
             k^2]}, {x == (k*x + Sqrt[k^2*r^2 - k^2*y^2])/
           k - r*Cos[(w*(k*x + Sqrt[k^2*r^2 - k^2*y^2]))/
               k^2],
     y == r*Sin[(w*(k*x + Sqrt[k^2*r^2 - k^2*y^2]))/
             k^2]}}

Andrzej Kozlowski

• References:
  • Help with Eliminate[]
    • From: Kinjal Basu <basukinjal@gmail.com>