On 5 nov, 21:45, andrew ewart <aewartma...@googlemail.com> wrote:
> i want to write a polynomial p of variables x and y such that
> p(x,y)=0
>
> i also have that x and y can be expressed in terms of a variable u
> such that
> 2x=2u^2+2u-1 and
> -y^2=u^4+2u^3-2u-1
>
> how to write code to eliminate u, hence finding p
You could use resultants in this case to eliminate de u.
{{{
sage: K.<x,y,u>=QQ[]
sage: f= 2*x -(2*u^2+2*u-1 )
sage: g=-y^2- (u^4+2*u^3-2*u-1)
sage: h=f.resultant(g,u); h
16*x^4 + 32*x^2*y^2 + 16*y^4 - 24*x^2 - 24*y^2 - 16*x - 3
}}}
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