03097nmm a2200325 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002900139245013000168250001700298260004000315300003200355505040300387653003500790653002600825653004000851653002200891700002800913700002300941710003400964041001900998989003801017490002601055856007201081082001201153520160601165EB000707324EBX0100000000000000056040600000000000000.0cr|||||||||||||||||||||140122 ||| eng a97837091340611 aBuchberger, B.e[editor]00aComputer AlgebrahElektronische RessourcebSymbolic and Algebraic Computationcedited by B. Buchberger, G.E. Collins, R. Loos a1st ed. 1982 aViennabSpringer Viennac1982, 1982 aVII, 284 pbonline resource0 aA Guide to the Literature -- Real Zeros of Polynomials -- Factorization of Polynomials -- Generalized Polynomial Remainder Sequences -- Computing by Homomorphic Images -- Computing in Transcendental Extensions -- Computing in Algebraic Extensions -- Arithmetic in Basic Algebraic Domains -- Computer Algebra Systems -- Computer Algebra Applications -- Some Useful Bounds -- Author and Subject Index aComputer scienceâ€”Mathematics aMathematical Software aSymbolic and Algebraic Manipulation aComputer software1 aCollins, G.E.e[editor]1 aLoos, R.e[editor]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aComputing Supplementa uhttps://doi.org/10.1007/978-3-7091-3406-1?nosfx=yxVerlag3Volltext0 a005.131 aThe journal Computing has established a series of supplement volumes the fourth of which appears this year. Its purpose is to provide a coherent presentation of a new topic in a single volume. The previous subjects were Computer Arithmetic 1977, Fundamentals of Numerical Computation 1980, and Parallel Processes and Related Automata 1981; the topic of this 1982 Supplementum to Computing is Computer Algebra. This subject, which emerged in the early nineteen sixties, has also been referred to as "symbolic and algebraic computation" or "formula manipulation". Algebraic algorithms have been receiving increasing interest as a result of the recognition of the central role of algorithms in computer science. They can be easily specified in a formal and rigorous way and provide solutions to problems known and studied for a long time. Whereas traditional algebra is concerned with constructive methods, computer algebra is furthermore interested in efficiency, in implementation, and in hardware and software aspects of the algorithms. It develops that in deciding effectiveness and determining efficiency of algebraic methods many other tools - recursion theory, logic, analysis and combinatorics, for example - are necessary. In the beginning of the use of computers for symbolic algebra it soon became apparent that the straightforward textbook methods were often very inefficient. Instead of turning to numerical approximation methods, computer algebra studies systematically the sources of the inefficiency and searches for alternative algebraic methods to improve or even replace the algorithms