Computer Algebra - Elementary Function, Automatic Differentiation, Grobner Basis, Record Linkage, Synthetic Division, Schwartz-Zippel Lemma (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 26. Chapters: Elementary function, Automatic differentiation, Grobner basis, Record linkage, Synthetic division, Schwartz-Zippel lemma, Triangular decomposition, Wu's method of characteristic set, Factorization of polynomials, Conway polynomial, Risch algorithm, Regular chain, Cantor-Zassenhaus algorithm, Pollard's kangaroo algorithm, Berlekamp's algorithm, Polynomial long division, Symbolic integration, RegularChains, Buchberger's algorithm, Gosper's algorithm, Faugere's F4 and F5 algorithms, Sum of radicals, Elimination theory, Regular semi-algebraic system, Symbolic computation, Multivariate division algorithm, Berlekamp-Zassenhaus algorithm, Symbolic-numeric computation, Landau's algorithm. Excerpt: In mathematics and computer algebra, automatic differentiation (AD), sometimes alternatively called algorithmic differentiation, is a method to numerically evaluate the derivative of a function specified by a computer program. Automatic differentiation contrasts with two classical methods of differentiation: Figure 1: How automatic differentiation relates to symbolic differentiation These classical methods run into problems: symbolic differentiation works at low speed, and faces the difficulty of converting a computer program into a single expression, while numerical differentiation can introduce round-off errors in the discretization process and cancellation. Both classical methods have problems with calculating higher derivatives, where the complexity and errors increase. Finally, both classical methods are slow at computing the partial derivatives of a function with respect to many inputs, as is needed for gradient-based optimization algorithms. Automatic differentiation solves all of these problems. AD exploits the fact that any computer program that implements a vector function y = F(x) (generally) can be decomposed into a se...