Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Algorithms in invariant theory
Algorithms in invariant theory
Calculating invariant rings of finite groups over arbitrary fields
Journal of Symbolic Computation
Deciding linear disjointness of finitely generated fields
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Rational invariants of scalings from Hermite normal forms
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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We present an algorithm to calculate generators for the invariant field k(x)G of a linear algebraic group G from the defining equations of G. This work was motivated by an algorithm of Derksen which allows the computation of the invariant ring of a reductive group using ideal theoretic techniques and the Reynolds operator. The method presented here does not use the Reynolds operator and hence applies to all linear algebraic groups. Like Derksen's algorithm we start with computing the ideal vanishing on all vectors (ξ, ζ) for which ξ and ζ are on the same orbit. But then we establish a connection of this ideal to the ideal of syzygies the generators of the field k(x) have over the invariant field. From this ideal we can calculate the generators of the invariant field exploiting a field-ideal-correspondence which has been applied to the decomposition of rational mappings before.