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An algebraic curve is said to be bicircular if the cyclic points (1, i,0) and (1, -i, 0), in the complex projective plane, are at least double points of the curve.

The necessary and sufficient condition is that the polynomial formed by the terms of highest degree n of its Cartesian equation be divisible by  and that the one formed by the terms of degree n - 1 be divisible by .

See bicircular quartic for the case of quartics.
See also multicircular.

© Robert FERRÉOL  2017