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von zur gathen j gerhard j modern computer algebra 3ed 2013

Type:: E-books
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Textbook in PDF format Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated. Cyclohexane, cryptography, codes, and computer algebra Euclid Fundamental algorithms The Euclidean Algorithm Applications of the Euclidean Algorithm Modular algorithms and interpolation The resultant and gcd computation Application: decoding BCH codes Newton Fast multiplication Newton iteration Fast polynomial evaluation and interpolation Fast Euclidean Algorithm Fast linear algebra Fourier Transform and image compression Gauß Factoring polynomials over finite fields Hensel lifting and factoring polynomials Short vectors in lattices Applications of basis reduction Fermat Primality testing Factoring integers Application: public key cryptography Hilbert Gröbner bases Symbolic integration Symbolic summation Applications Appendix Fundamental concepts Sources of illustrations Sources of quotations List of algorithms List of figures and tables List of notation

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von zur gathen j gerhard j modern computer algebra 3ed 2013

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