Abyss and Game of Polynomials and Coefficients : Algebraic Cubic And
Elliptic Curves
Abstract
In this paper, an important novel study with interesting conclusions on
algebraic cubic curves and elliptic curves is being presented. Various
popular algebraic cubic curves and elliptic curves viz., Ochoa curve,
Mordell curve, projection, birational transformation, Conchoid of de
Sluze, Maltese cross curve, Semicubical Parabola, Tschirnhausen Cubic,
Right Strophoid, Strophoid, have been studied to find exhaustively which
could resemble with the same shape but with a different degree of
polynomial and coefficient. The affect of higher order polynomials and
the accuracy obtained with RMSE and interpolation has also been studied
and in total 392 plots are submitted with equations.Â
The manuscript has three novelties - different curves obtained by
changing coefficients, the solutions in both x and y are given and the
roots which are obtained from the algebraic curve equation, are again
interpolated with different degrees viz., degree 2, 4, 6 and 10, with
root mean square error.