Titlebook: Mathematics for Computer Algebra; Maurice Mignotte Textbook 1992 Springer-Verlag New York, Inc. 1992 Mathematica.algorithms.computer algeb

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https://doi.org/10.1007/978-1-4613-9171-5Mathematica; algorithms; computer algebra; mathematics; set theory

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978-1-4613-9173-9Springer-Verlag New York, Inc. 1992

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Elementary Arithmetics,This chapter deals with the representation of rational integers and describes the basic algorithms of arithmetics (addition, multiplication, division,...). The study of theses examples introduces the fundamental notion of the cost of an algorithm

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Polynomials, Algebraic Study,This chapter presents definitions and general algebraic properties of polynomials over arbitrary domains.

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Polynomials with Complex Coefficients,The main topic of this chapter is the study of the zeros of polynomials with complex coefficients. This study leads to inequalities about the size of factors of polynomials. These inequalities play an important rôle in the last two chapters.

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Polynomials with Real Coefficients,In this chapter, we call . an ordered field such that the field . is algebraically closed. Usually, we consider that E is the field of real numbers and that C is the field of complex numbers. We study algorithms to separate the real roots of polynomials.

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