Algorithms in Invariant TheorySpringer Science & Business Media, 17 juin 2008 - 197 pages J. Kung and G.-C. Rota, in their 1984 paper, write: “Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics”. The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this “classical and new” area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems. |
Table des matières
| 1 | |
Invariant theory of finite groups 25 | 24 |
Bracket algebra and projective geometry | 77 |
Invariants of the general linear group 137 | 136 |
References | 191 |
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Expressions et termes fréquents
algebraically independent atomic extensors basis G binary cubic binary forms Bn,d bracket monomials bracket polynomial bracket ring C-algebra C-vector C[xij Cayley expression Cayley factorization coefficients Cohen-Macaulay consider Corollary d-form defined denote det(t diagonal elementary symmetric polynomials elements equals equations Example expansion finite groups finite matrix group formal character fundamental invariants geometric GL(C Grassmann-Cayley algebra Gröbner basis hence Hilbert basis Hilbert series Hironaka decomposition homogeneous invariants homogeneous polynomial ideal implies initial monomial Input integer invariant ring C[x invariant theory isomorphic Lemma lexicographic order linear mial Molien series monomial order multilinear nonzero normal form nullcone orbit variety output polynomial f polynomial function polynomial ring problem proof of Theorem Proposition quadric representation result Reynolds operator Schur polynomials secondary invariants Sect step straightening algorithm subgroup subring Subroutine subspace symmetric group syzygy tableau unique variables vector space zero θη μη
Fréquemment cités
Page 1 - Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics." The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become...