Titlebook: Computer Algebra; An Algorithm-Oriente Wolfram Koepf Textbook 2021 Springer Nature Switzerland AG 2021 Computer algebra textbook.Computer a

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Eugenio Brusa,Ambra Calà,Davide FerrettoSince a rather simple (although not very efficient) algorithm exists for them we would first like to discuss bivariate sums of a specific form.

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Introduction to Computer Algebra,Before we discuss mathematical algorithms and their programming, we want to show the capabilities of a general computer algebra system such as . (The same questions can be also treated with the systems . and .,and the corresponding worksheets can be downloaded from .).

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Modular Arithmetic,The integers with their operations addition and multiplication . form a commutative ring with unity 1. Now, we would like to translate this algebraic structure to finite subsets of .. This is done by identification of certain elements in . that lie in common arithmetic progressions.

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Coding Theory and Cryptography,Coding Theory deals with the secure transfer of messages. We assume that the sender (source) of the message sends the message via a . to the recipient. The type of coding depends on the practical situation, hence the communication channel might also be disturbed.

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Polynomial Arithmetic,In the sequel (if not stated otherwise), we assume that . is a zero-divisor-free ring with unity 1. Such a ring is called an integral domain.

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Factorization in Polynomial Rings,The aim of this chapter is the development of efficient algorithms for factorization in ?[.]. For this purpose, efficient factorization algorithms for ?.[.] are used which, of course, are interesting by themselves.