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The simplest method, that will usually be correct, is to just use NSolve. polys = {x^2 y + 2 x y + 2, y^3 + 2 x + 1}; Length[NSolve[polys]] (* Out[421]= 7 *) Below is from code I have used for solution counting and related (it is related to code inside NSolve, to answer the question of "Why not just use NSolve?"). Some is also used in this MSE response. ...


1

The documentation is very instructive. For your particular example: gb = GroebnerBasis[{x^2 y + 2 x y + 2, y^3 + 2 x + 1}, {x, y}] Finding roots: sol = N@Solve[gb[[1]] == 0, y] =>{{y -> -1.29819}, {y -> -0.871821 - 1.29622 I}, {y -> -0.871821 + 1.29622 I}, {y -> 0.274176 - 1.20102 I}, {y -> 0.274176 + 1.20102 I}, {y -> 1.24674 - 0.331078 I}, ...



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