A new metod to detect similarty of rational algebraic curves

In this thesis, a new method for determining the similarity relationship between two rational algebraic curves given in a three-dimensional real vector space is developed. The method is based on the solution of the situation that arises when the similarity relation between two curves is reduced to an equivalence between the parametrizations of these curves with the help of differential invariants. The differential invariants generated for this purpose reduce the computations from operations between rational functions in multiple unknowns to the search for the greatest common factor between polynomials in two unknowns. The method considers all similarity relations between the input curves if they are similar. The computational steps are converted into an algorithm and computerized using the computer algebra system MapleTM (2021) and the effectiveness of the method is demonstrated through extensive testing.