A Gröbner Bases Approach to the Detection of Improperly Parameterized Rational Curve

Certain finite sets of multivariate polynomials are known as Gröbner bases. Several issues in polynomial ideal theory (such as those involving algebraic geometry and non-linear computational geometry) are easily resolved after translating the polynomial sets used in the problem specification into Gröbner basis form. The idea of Gröbner bases is used in this research to offer an algorithm for identifying inappropriate parameterization of rational curves. The Gröbner bases’ ability to function in both univariate and multivariate fields with specified ordering is the advantage of the proposed approach.