Rational invariants of a group action. Construction and rewriting

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 Gr¨obner 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 Gr¨obner basis allows to express any rational invariant in terms of the generators. Key words: rational invariants, algebraic group actions, cross-section, Gr¨obner basis, differential invariants, moving frame 1991 MSC: 13A50, 13P10, 14L24, 14Q99, 53A55 .

• Type: Journal
• Year: 2007
• Where: JSC
• Authors: Evelyne Hubert, Irina A. Kogan
• Keywords: Algebraic Group, Gr¨obner Basis, JSC 2007, Rational Invariants