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