Abstract: An input polynomial, in symbolic form, is received, classified, pre-processed, and factored. The input polynomial is classified as a constant, a univariate polynomial, or a multivariate polynomial. Various pre-processing is performed depending on the classification. After the input polynomial is pre-processed, the remaining polynomial is factored using a polynomial factoring algorithm. By pre-processing the input polynomial, the complexity of the polynomial to be factored is reduced, which reduces the computational expense of the polynomial factoring algorithm.

Abstract: A hybrid greatest common divisor (GCD) calculator analyzes characteristics of polynomials and selects a particular GCD algorithm from multiple available GCD algorithms based on a combination of characteristics of the polynomials. The selected GCD algorithm is then applied to calculate the GCD of the polynomials.

Abstract: A hybrid greatest common divisor (GCD) calculator analyzes characteristics of polynomials and selects a particular GCD algorithm from multiple available GCD algorithms based on a combination of characteristics of the polynomials. The selected GCD algorithm is then applied to calculate the GCD of the polynomials.

Abstract: An input polynomial, in symbolic form, is received, classified, pre-processed, and factored. The input polynomial is classified as a constant, a univariate polynomial, or a multivariate polynomial. Various pre-processing is performed depending on the classification. After the input polynomial is pre-processed, the remaining polynomial is factored using a polynomial factoring algorithm. By pre-processing the input polynomial, the complexity of the polynomial to be factored is reduced, which reduces the computational expense of the polynomial factoring algorithm.

Abstract: A method for performing symbolic computations on a mathematical expression. The mathematical expression may be converted to a tree structure having one or more parent nodes and one or more child nodes. Each parent node may be a mathematical operation. Each child node may be a mathematical expression on which the mathematical operation is performed in a specified order. Each child node may be in a hierarchical relationship to one of the parent nodes. The parent nodes, the child nodes or both may be manipulated to perform a first symbolic computation on the mathematical expression.

Abstract: A method for converting a polynomial expression to a data structure for symbolic computation. One or more variables in the polynomial expression may be determined. The variables may be stored in a first array. One or more terms in the polynomial expression may be determined. One or more exponents of the variables in each term may be determined. The exponents may be stored in a second array. One or more coefficients of the terms may be determined. The coefficients may be stored in a third array.