Von zur Gathen J., Gerhard J. Modern Computer Algebra 3ed 2013 torrent

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