By Jakob Ablinger, Johannes Blümlein (auth.), Carsten Schneider, Johannes Blümlein (eds.)
The booklet specializes in complicated desktop algebra tools and precise features that experience amazing purposes within the context of quantum box concept. It offers the cutting-edge and new equipment for (infinite) a number of sums, a number of integrals, specifically Feynman integrals, distinction and differential equations within the structure of survey articles. The awarded concepts emerge from interdisciplinary fields: arithmetic, laptop technology and theoretical physics; the articles are written via mathematicians and physicists with the target that either teams can examine from the opposite box, together with most modern advancements. along with that, the gathering of articles additionally serves as an up to date guide of accessible algorithms/software which are primary or might actually help within the fields of arithmetic, physics or different sciences.
Read or Download Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions PDF
Best algebra books
Uncomplicated Algebra and complex Algebra systematically boost recommendations and instruments in algebra which are very important to each mathematician, no matter if natural or utilized, aspiring or demonstrated. jointly, the 2 books supply the reader a world view of algebra and its position in arithmetic as an entire. Key issues and lines of complex Algebra:*Topics construct upon the linear algebra, workforce conception, factorization of beliefs, constitution of fields, Galois concept, and straight forward thought of modules as built in uncomplicated Algebra*Chapters deal with a number of issues in commutative and noncommutative algebra, offering introductions to the speculation of associative algebras, homological algebra, algebraic quantity thought, and algebraic geometry*Sections in chapters relate the speculation to the topic of Gröbner bases, the root for dealing with platforms of polynomial equations in machine applications*Text emphasizes connections among algebra and different branches of arithmetic, relatively topology and intricate analysis*Book incorporates on well known issues routine in uncomplicated Algebra: the analogy among integers and polynomials in a single variable over a box, and the connection among quantity idea and geometry*Many examples and hundreds of thousands of difficulties are incorporated, besides tricks or entire strategies for many of the problems*The exposition proceeds from the actual to the overall, frequently supplying examples good sooner than a conception that comes with them; it contains blocks of difficulties that remove darkness from elements of the textual content and introduce extra topicsAdvanced Algebra offers its material in a forward-looking means that takes into consideration the old improvement of the topic.
- Higher-dimensional categories: an illustrated guide book
- Mathematik für Wirtschaftswissenschaftler 2: Lineare Algebra, Funktionen mehrerer Variablen
- Cohomology Operations and Applications to Homotopy Theory
- Mathematik für Wirtschaftswissenschaftler Lineare Algebra und ökonomische Anwendung
- Lectures on topics in algebraic number theory. Ghorpade
- The Computational Complexity of Groebner Bases
Additional resources for Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions
Novi Comm. Acad. Sci. Petropol. 20, 140–186 (1775). (reprinted in Opera Omnia Ser I, vol. 15, pp. 217–267. G. Teubner, Berlin (1927)) 79. Hoffman, M. : Sums of triple harmonic series. J. : A decomposition of Riemann’s zeta-function. In: Motohashi, Y. ) Analytic Number Theory, London Mathematical Society. Lecture Note Series, vol. 247, pp. 95–101. : Multiple Zeta Values. (preprint) 80. : Multiple harmonic series. Pac. J. Math. 152, 275–290 (1992) 81. : Algebraic aspects of multiple zeta values. , T.
Phys. Commun. 180, 2218–2249 (2009). 3106 [hep-ph]] 15. : A symbolic summation approach to Feynman integral calculus. J. Symb. Comput. 47, 1267–1289 (2012). SC]] 16. : A new development of the theory of the hypergeometric functions. Proc. Lond. Math. Soc. 6(2), 141 (1908); A transformation of generalized hypergeometric series. Quart. Journ. Math. : Abriß einer einheitlichen Theorie der Gamma- und der hypergeometrischen Funktionen. Math. Ann. 68, 305–337 (1910) 17. : AMBRE: a mathematica package for the construction of Mellin-Barnes representations for Feynman integrals.
Math. ) 12, 483–487 (2001) 89. : Cyclic sum of multiple zeta values. Acta Arithmetica 123, 289–295 (2006) 90. : Evaluations of K fold Euler/Zagier sums: a compendium of results for arbitrary k. [hep-th/9611004] 91. : Derivation and double shuffle relations for multiple zeta values. Compositio Math. 142, 307–338 (2006); Preprint MPIM2004-100 ´ 92. : Th´eorie des moules, vol. 3, pr´epublications math´ematiques d‘Orsay (1981, 1982, 1985); La libre g´en´eration des multicˆetas et leur d’ecomposition canonico-explicite en irr´eductibles, automne (1999); Ari/gari et la d´ecomposition des multizˆetas en irr´eductibles.