Algorithms in Invariant TheorySpringer-Verlag, 1993 - 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
Invariant theory of finite groups | 25 |
Bracket algebra and projective geometry | 77 |
Invariants of the general linear group | 137 |
Droits d'auteur | |
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Expressions et termes fréquents
a₁ algebraically independent algorithm atomic extensors b₁ basis G binary cubic binary forms bracket monomials bracket polynomial bracket ring C-algebra C-vector C[xij Cayley expression Cayley factorization coefficients Cohen-Macaulay consider Corollary covariants defined denote det(t diagonal elementary symmetric polynomials elements equals Example expansion 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 i₁ ideal implies init(f initial monomial Input integer invariant ring C[x invariant theory isomorphic Lemma lexicographic order linear Molien series monomial order multilinear normal form nullcone output polynomial f polynomial function polynomial of degree polynomial ring problem proof of Theorem Proposition quadric representation result Reynolds operator Schur polynomials secondary invariants Sect step straightening algorithm subgroup subring Subroutine subspace syzygy tableau unique variables vector space zero θη μη ση