Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Each year since 1996 the universities of Bergen, Oslo and Trondheim have organized summer schools in Nordfjordeid in various topics in algebra and related ?elds. Nordfjordeid is the birthplace of Sophus Lie, and is a village on the western coast of Norway situated among fjords and mountains, with sp- tacularscenerywhereveryougo. AssuchitisawelcomeplaceforbothNor- gian and international participants and lecturers. The theme for the summer school in 2003 was Algebraic Combinatorics. The organizing committee c- sisted of Gunnar Fløystad and Stein Arild Strømme (Bergen), Geir Ellingsrud and Kristian Ranestad (Oslo), and Alexej Rudakov and Sverre Smalø (Tro- heim). The summer school was partly ?nanced by NorFa-Nordisk Forsker- danningsakademi. With combinatorics reaching into and playing an important part of ever more areas in mathematics, in particular algebra, algebraic combinatorics was a timely theme. The ?st lecture series Hyperplane arrangements  was given by Peter Orlik. He came as a refugee to Norway, eighteen years old, after the insurrection in Hungary in 1956. Despite now having lived more than four decades in the United States, he impressed us by speaking ?uent Norwegian without a trace of accent. The second lecture series Discrete Morse theory and free resolutions  was given by Volkmar Welker. These two topics ori- nate back in the second half of the nineteenth century with simple problems on arrangements of lines in the plane and Hilberts syzygy theorem.

Combinatorial geometry. --- Free resolutions (Algebra) --- Combinatorics. --- Algebra. --- Geometry. --- Mathematics --- Euclid's Elements --- Mathematical analysis --- Combinatorics --- Algebra --- Combinatorial analysis.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.

superposition --- SU(2) --- pseudo-remainder --- interval methods --- sparse polynomials --- element order --- Henneberg-type minimal surface --- timelike axis --- combinatorial decompositions --- sparse data structures --- mutually unbiased bases --- invariant surfaces --- projective special unitary group --- Minkowski 4-space --- free resolutions --- Dini-type helicoidal hypersurface --- linearity --- integrability --- Galois rings --- minimum point --- entanglement --- degree --- pseudo-division --- computational algebra --- polynomial arithmetic --- projective special linear group --- normal form --- Galois fields --- Gauss map --- implicit equation --- number of elements of the same order --- Weierstrass representation --- Lotka–Volterra system --- isolated zeros --- polynomial modules --- over-determined polynomial system --- simple Kn-group --- sum of squares --- four-dimensional space