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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Diatribe

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.

断断续续

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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Innocence

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