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