WOLFRAM|DEMONSTRATIONS PROJECT

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degree n
2
drag the black point…
The complex roots of the equation
n
z
+bz+1=0
are displayed as red dots. The blue dots correspond to the branching points, that is, to such values of
b
that the equation has a double root. The black dot corresponds to
b
, which you can drag to see the roots move. In particular, two roots dance around each other and interchange their positions every time
b
moves around a branching point. So, every time
b
runs in a loop without hitting any branching points, the roots are permuted. The group generated by such permutations is called the monodromy group of the equation. The parameter
b
and the branching points are displayed at a larger scale to keep them well separated from the roots. The green dot shows
b=0
.