The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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Any dynamical system evolution is analyzed by a mathematical model attached to physical model. A mathematical model is compound of the analytical and numerical phase of your deduction. In the paper, the possibilities of replacing the manual analytical calculation that intervene in the mechanical modeling, by an isomorphic numerical calculation which can be performed on digital computers are described. An original algorithm for performing the greatest common divisor of two polynomials with several variables to determine the analytical inverse matrix for a matrix of such polynomials used in a mathematical modeling of mechanical phenomena is précised. A new definition of the Euclidean ring is proposed and new possibilities of the theoretical algebraic research such are underlined. A possibility of applying our algorithm for performing the inverse matrix of differential polynomial operator matrix that intervene in the modeling for enlarger the analytical phase in the mathematical model deduction is also emphasized.