Algorithms for Computer AlgebraSpringer Science & Business Media, 1992. szept. 30. - 586 oldal Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields. |
Tartalomjegyzék
Algebra of Polynomials Rational Functions and Power Series | 23 |
Normal Forms and Algebraic Representations | 79 |
Arithmetic of Polynomials Rational Functions and Power Series | 110 |
Homomorphisms and Chinese Remainder Algorithms | 151 |
Newtons Iteration and the Hensel Construction | 204 |
Polynomial GCD Computation | 279 |
Polynomial Factorization | 336 |
Solving Systems of Equations | 389 |
Gröbner Bases for Polynomial Ideals | 429 |
Integration of Rational Functions | 473 |
Más kiadások - Összes megtekintése
Algorithms for Computer Algebra Keith O. Geddes,Stephen R. Czapor,George Labahn Korlátozott előnézet - 2007 |
Algorithms for Computer Algebra Keith O. Geddes,Stephen R. Czapor,George Labahn Nincs elérhető előnézet - 2013 |
Algorithms for Computer Algebra Keith O. Geddes,Stephen R. Czapor,George Labahn Nincs elérhető előnézet - 1992 |
Gyakori szavak és kifejezések
algebraic extension algebraic number Algorithm 6.1 applied arithmetic b₁ calculate canonical form Chapter Chinese remainder coefficient domain commutative ring computer algebra systems consider data structure defined Definition deg(a(x degree denominator denotes determine differential division divisor element Euclidean algorithm Euclidean domain evaluation homomorphism Example exponential expressed extended Euclidean algorithm field F GCD's given Gröbner basis hence Hensel construction homomorphic image ideal integer integral domain integrand inverse irreducible leading coefficient Lemma Let a(x linear log(x logarithmic matrix method mial mixed radix mod a(x modulo monic multiplication multiprecision integers multivariate polynomial Newton's iteration nonzero Note obtain operations p-adic P₁ polyno polynomial a(x polynomial domain power series primitive problem Proof quotient field rational function recursive reduced relatively prime representation result satisfying solution solving square-free factorization step subresultant symbolic Theorem tion transcendental unique unit normal univariate polynomial variables x₁ zero