Tag Info

New answers tagged

3

As noted, what you want is to use a Gröbner basis to eliminate the parameter: curve = 2 {t (3 t^4 + 50 t^2 - 33), 7 t^6 - 60 t^4 + 15 t^2 + 2}/(t^2 + 1)^3; implicit = GroebnerBasis[Thread[{x, y} == curve], {x, y}, t] // First 550731776 - 41620992 x^2 + 585816 x^4 + 625 x^6 - 182250 x^4 y - 41620992 y^2 + 1171632 x^2 y^2 + 1875 x^4 y^2 + 364500 x^2 y^3 ...


4

There is an undocumented command (Mma V9). Use it at your own risk, YMMV. I found it following @Daniel's hint above: pols = {x - a, x - b y, y - k}; mvr = Internal`MultivariateResultant[pols, {x, y}] (* -a + b k *) We can test that that is effectively the condition for common roots: Solve[And @@ Thread[(pols /. First@Solve[mvr == 0]) == 0], {x, y}] (* ...



Top 50 recent answers are included