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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 ...


5

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}] (* ...


3

Okay, sometimes you get so involved in an idea that you don't realize how foolish it is. I was fooled or seduced by the simplicity of the Chebyshev expansion. Basically, my original answer was a complicated way to do this: cosEq = 64 x^7 - 112 x^5 - 8 x^4 + 56 x^3 + 8 x^2 - 7 x - 1 /. x -> Cos[Pi t] //TrigToExp; t /. Solve[cosEq == 0 && 0 <= ...


5

You're after the Swinnerton-Dyer Polynomials. Take a look and compare with OEIS (which, BTW cites our friend Roman E. Maeder. Programming in Mathematica, Addison-Wesley, 1990, page 105): MinimalPolynomial[Sum[Sqrt[Prime[i]], {i, #}], x] & /@ Range@5 gives the same results shown in the OEIS page, but MinimalPolynomial can't calculate sixth term within ...


4

Not precisely what you asked for, but I usually do something like this and interpret the results: a =.; DeleteDuplicates@Cases[ eqn, s_Symbol /; Context[s] === "Global`", Infinity, Heads -> True] (* {x, s, a, b} *) a = 2; DeleteDuplicates@Cases[ eqn, s_Symbol /; Context[s] === "Global`", Infinity, Heads -> True] (* {x, s, b} *)



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