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BICIRCULAR ALGEBRAIC CURVE

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