Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
On the efficiency of effective Nullstellensa¨tze
Computational Complexity
Basic algorithms for rational function fields
Journal of Symbolic Computation
ACM Communications in Computer Algebra
Differential invariants of a Lie group action: Syzygies on a generating set
Journal of Symbolic Computation
Reduction of algebraic parametric systems by rectification of their affine expanded lie symmetries
AB'07 Proceedings of the 2nd international conference on Algebraic biology
Algebraic invariants and their differential algebras
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Rational invariants of scalings from Hermite normal forms
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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Geometric constructions applied to a rational action of an algebraic group lead to a new algorithm for computing rational invariants. A finite generating set of invariants appears as the coefficients of a reduced Grobner basis. The algorithm comes in two variants. In the first construction the ideal of the graph of the action is considered. In the second one the ideal of a cross-section is added to the ideal of the graph. Zero-dimensionality of the resulting ideal brings a computational advantage. In both cases, reduction with respect to the computed Grobner basis allows us to express any rational invariant in terms of the generators.