Computer Algebra

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.