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MULTICIRCULAR ALGEBRAIC CURVE

Cartesian equation: |

A *p*-circular curve is an algebraic plane curve that has the cyclic points (of the complex projective completion of the plane)
and as singular points of order at least *p*.

This translates into the Cartesian equation of a curve of degree *n* (), by the fact that divides the homogeneous part of *P* of degree
(for ).

It is a Euclidian notion (i.e. invariant by change of orthonormal frame).

For examples, see circular curve (*p* = 1) and bicircular quartic;

the Watt curve and the Cayley sextic are examples of tricircular sextics.

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© Robert FERRÉOL
2017