Sitzung S. 110

g1[x_, y_] := 2 y Cos[(y^2)] Cos[2 x]  - Cos[y];
g2[x_, y_] := 
        2 Sin[(y^2)] Sin[2  x] - Sin[x];
{a, b, c, d}  =  {-3.45,  3.45,  -4, 
          3};
contourdata = 
        Map[First, 
          Cases[Graphics[
 
              ContourPlot[g1[x, y], {x, a, b}, {y, c, d}, 
                Contours -> {0}, 
                PlotPoints -> 60]], _Line, ∞]];
seeds = 
        Flatten[Map[#[[1 + 
                  Flatten[
                    Position[
                      Rest[ss = Sign[Apply[g2, #, 2]]]*
                        Rest[RotateRight[
                            ss]], -1]]]] &, 
            contourdata], 1];
roots = 
        Select[Map[{x, y} /. 
                FindRoot[{g1[x, y] == 0, 
                    g2[x, y] == 
                      0}, {x, #[[1]]}, {y, #[[2]]}] &, seeds], 
          a < #[[1]] < b ∧ 
              c < #[[2]] < 
                d &];
Length[roots]