Asymptotically fast computation of Hermite normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Dimensional analysis in computer algebra
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Calculating Generators for Invariant Fields of Linear Algebraic Groups
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Rational invariants of a group action. Construction and rewriting
Journal of Symbolic Computation
Smooth and Algebraic Invariants of a Group Action: Local and Global Constructions
Foundations of Computational Mathematics
Normal forms for general polynomial matrices
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
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
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Scalings form a class of group actions that have both theoretical and practical importance. A scaling is accurately described by an integer matrix. Tools from linear algebra are exploited to compute a minimal generating set of rational invariants, trivial rewriting and rational sections for such a group action. The primary tools used are Hermite normal forms and their unimodular multipliers. With the same line of ideas, a complete solution to the scaling symmetry reduction of a polynomial system is also presented.