Computer Algebra: Systems and Algorithms for Algebraic Computation 论文

摘要

Part 1 How to use a computer algebra system introduction features of computer algebra systems syntax of the associated languages areas covered by existing systems computer algebra by example MACSYMA's possibilities in algebra general possibilities the division of the circle into 17 equal parts availability of MACSYMA other systems AXIOM. Part 2 The problem of data representation representations of data representation representations of integers representations of fractions, representations of polynomials polynomials in several variables representations of rational functions representations of algebraic functions representations of transcendentals representations of matrices, representations of series. Part 3 Polynomial simplification simplification of polynomial equations simplification of real polynomial systems. Part 4 Advanced algorithms modular methods p-adic methods. Part 5 Formal integration and differential equations introduction integration of rational functions the integration of more complicated functions integration of logarithmic functions integration of exponential functions, algebraic solutions of o.d.e.s. asymptotic solutions of o.d.e.s. appendix algebraic background annex REDUCE - a computer algebra system introduction syntax of REDUCE declarations commands built-in facilities manipulation of expressions substitution matrix algebra IRENA.