The Frobenius method is the most common method for computing a basis of linearly independent series which are the solutions to a linear ordinary differential equation at a regular singular point. When implemented, the classical formulas of the Frobenius method have significant computational shortcomings. In this paper we propose various techniques to improve the computational footprint of the Frobenius method, improving the classification of roots of the indicial polynomial, reducing output size and increasing readability, and decreasing execution time