Scaling Invariants and Symmetry Reduction of Dynamical Systems

Hubert, Evelyne; Labahn, George

doi:10.1007/s10208-013-9165-9

Cited by 20 publications

(25 citation statements)

References 26 publications

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“…For instance, sections of degree one can be obtained for any scaling, i.e. diagonal representation of tori [13,14]. As shown in the previous example, this is no longer true for cross-sections.…”

Section: Section Quasi-section Cross-section Partial Sectionmentioning

confidence: 95%

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Invariant algebraic sets and symmetrization of polynomial systems

Hubert

2019

Journal of Symbolic Computation

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Assuming the variety of a polynomial set is invariant under a group action, we construct a set of invariants that define the same variety. Our construction can be seen as a generalization of the previously known construction for finite groups. The result though has to be understood outside an invariant variety which is independent of the polynomial set considered. We introduce the symmetrizations of a polynomial that are polynomials in a generating set of rational invariants. The generating set of rational invariants and the symmetrizations are constructed w.r.t. a section to the orbits of the group action.

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Section: Section Quasi-section Cross-section Partial Sectionmentioning

confidence: 95%

“…This generalizes for scalings in any dimension, i.e. diagonal linear actions of the algebraic torus (K * ) d : we can compute the (binomial) equations of a section of degree one with linear algebra over the integers [13,14].…”

Section: Sections To the Orbitsmentioning

confidence: 99%

Invariant algebraic sets and symmetrization of polynomial systems

Hubert

2019

Journal of Symbolic Computation

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“…Symmetry based approaches [2,3,4,5,6] reduce the number of parameters and as a consequence usually help the analysis of parametric systems. On the contrary, our approach keeps the number of parameters (in the same spirit as [2,Algorithm SemiRectifySteadyPoints]) and makes the systems sparsest (in the sense of Algorithms getSparsestFraction and getSparsestSumOfFractions given later).…”

Section: Introductionmentioning

confidence: 99%

Computing Sparse Representations of Systems of Rational Fractions

Lemaire

Temperville

2016

Computer Algebra in Scientific Computing

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International audienceWe present new algorithms for computing sparse representations of systems of parametric rational fractions by means of change of coordinates. Our algorithms are based on computing sparse matrices encoding the degrees of the parameters occurring in the fractions. Our methods facilitate further qualitative analysis of systems involving rational fractions. Contrary to symmetry based approaches which reduce the number of parameters, our methods only increase the sparsity, and are thus complementary. Previously hand made computations can now be fully automated by our methods

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“…They are deduced from a unimodular multiplier providing the Hermite form of the integer matrix of powers describing the scaling. Those results are extended in [HL13] to address the parameter reduction in models of mathematical biology. In this section we give a foretaste for some scalings in the plane.…”

Section: Scalingsmentioning

confidence: 99%

“…In the case above, for instance, all the needed information is read from We refer to [HL12,HL13] for the general case.…”

Section: Scalingsmentioning

confidence: 99%