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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