The proposed methodology is based on a combination of different techniques: algebraic specification through modular approach and completion algorithms, approximated and exact algebraic computing methods, object-oriented programming paradigm, automated theorem proving through methods à la Hilbert and methods of natural deduction.

State of the art and motivations.- Mathematica: doing mathematics by computer?.- An overview of the TASSO project.- Mathematical objects.- The uniform representation of mathematical objects by truncated power series.- p-adic arithmetic: a tool for error-free computations.- Exact solution of computational problems via parallel truncated p-adic arithmetic.- A canonical form guide to symbolic summation.- Indexes in sums and series: from formal definition to object-oriented implementation.- Programming methodologies.- Equational specifications: design, implementation, and reasoning.- On the algebraic specification of classes and inheritance in object-oriented programming.- On subtyping in languages for symbolic computation systems.- Enhanced strict inheritance in TASSO-L.- Reasoning capabilities.- Deduction and abduction using a sequent calculus.- A sequent calculus machine for symbolic computation systems.- Automated deduction by connection method in an object-oriented environment.- A general reasoning apparatus for intelligent tutoring systems in mathematics.

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