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POLYNOMIAL CURVE

Cartesian parametrization:
where P and Q are two polynomials with real coefficients, coprime, and such that the polynomials and are coprime (proper representation). |

A *polynomial* curve is a curve that can be parametrized by polynomial functions of R[*x*], so it is a special case of rational curve.

Therefore, any polynomial curve is an algebraic curve of degree equal to the higher degree of the above polynomials *P* and *Q* of a proper representation.

A polynomial curve cannot be bounded, nor have asymptotes, except if it is a line.

Examples:

- the lines are polynomial

- the only polynomial conic is the parabola

- the rational divergent parabolas (polynomial cubics with a symmetry axis)

- the cubical parabolas (polynomial cubics with a symmetry centre).

- a Lissajous polynomial quartic.

- the L'Hospital quintic is polynomial.

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© Robert FERRÉOL 2017