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  • 1
    Electronic Resource
    Electronic Resource
    Semi-Invariants, equivariants and algorithms (1996)
    Springer
    Applicable algebra in engineering, communication and computing 7 (1996), S. 105-124 
    Details
    ISSN: 1432-0622
    Keywords: Invariant theory ; Linear representations of finite groups ; Gröbner bases ; Computation of fundamental equivariants ; Solution of systems of polynomial equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract The results from Invariant Theory and the results for semi-invariants and equivariants are summarized in a suitable way for combining with Gröbner basis computation. An algorithm for the determination of fundamental equivariants using projections and a Poincaré series is described. Secondly, an algorithm is given for the representation of an equivariant in terms of the fundamental equivariants. Several ways for the exact determination of zeros of equivariant systems are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01191379
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Semi-Invariants, Equivariants and Algorithms (1996)
    Springer
    Applicable algebra in engineering, communication and computing 7 (1996), S. 105-124 
    Details
    ISSN: 1432-0622
    Keywords: Keywords: Invariant theory ; Linear representations of finite groups ; Gröbner bases ; Computation of fundamental equivariants ; Solution of systems of polynomial equations.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract.  The results from Invariant Theory and the results for semi-invariants and equivariants are summarized in a suitable way for combining with Grobner basis computation. An algorithm for the determination of fundamental equivariants using projections and a Poincaré series is described. Secondly, an algorithm is given for the representation of an equivariant in terms of the fundamental equivariants. Several ways for the exact determination of zeros of equivariant systems are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01191379
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
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    Testing for Sn-Symmetry with a Recursive Detective (1995)
    Details
    Publication Date: 2014-02-26
    Description: In the recent years symmetric chaos has been studied intensively. One knows which symmetries are admissible as the symmetry of an attractor and which transitions are possible. The numeric has been developed using equivariant functions for detection of symmetry and augmented systems for determination of transition points. In this paper we look at this from a sophisticated group theoretic point of view and from the view of scientific computing, i.e. efficient evaluation of detectives is an important point. The constructed detectives are based on Young's seminormal form for $S_n$. An application completes the paper.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 4
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    Computer Algebra Methods for Equivariant Dynamical Systems (1999)
    Details
    Publication Date: 2014-02-27
    Description: An introductory chapter on Groebner bases is given which also includes new results on the detection of Groebner bases for sparse polynomial systems. Algorithms for the computation of invariants and equivariants for finite groups, compact Lie groups and algebraic groups are presented and efficient implementation and time comparision are discussed. This chapter also inlcudes improvements of the computation of Noether normalisation and Stanley decomposition. These results are applied in symmetric bifurcation theory and equivariant dynamics. As preparation of the investigation of the orbit space reduction three methods are compared for solving symmetric polynomial systems exactly. The method of orbit space reduction is improved by using the Cohen-Macaulayness of the invariant ring and nested Noether normalization. Finally this is applied for a case of mode interaction in the Taylor-Couette problem.
    Keywords: ddc:000
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 5
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    A family of sparse polynomial systems arising in chemical reaction systems (1999)
    Details
    Publication Date: 2014-02-26
    Description: A class of sparse polynomial systems is investigated which is defined by a weighted directed graph and a weighted bipartite graph. They arise in the model of mass action kinetics for chemical reaction systems. In this application the number of real positive solutions within a certain affine subspace is of particular interest. We show that the simplest cases are equivalent to binomial systems while in general the solution structure is highly determined by the properties of the two graphs. First we recall results by Feinberg and give rigorous proofs. Secondly, we explain how the graphs determine the Newton polytopes of the system of sparse polynomials and thus determine the solution structure. The results on positive solutions from real algebraic geometry are applied to this particular situation. Examples illustrate the theoretical results.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 6
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    Automatic classification of normal forms (1995)
    Details
    Publication Date: 2014-02-26
    Description: The aim of this paper is to demonstrate a specific application of Computer Algebra to bifurcation theory with symmetry. The classification of different bifurcation phenomena in case of several parameters is automated, based on a classification of Gröbner bases of possible tangent spaces. The computations are performed in new coordinates of fundamental invariants and fundamental equivariants, with the induced weighted ordering. In order to justify the approach the theory of intrinsic modules is applied. Results for the groups $D_3, Z_2,$ and $ Z_2\times Z_2$ demonstrate that the algorithm works independent of the group and that new results are obtained.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 7
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    Gröbner bases, invariant theory and equivariant dynamics (1996)
    Details
    Publication Date: 2014-02-26
    Description: This paper is about algorithmic invariant theory as it is required within equivariant dynamical systems. The question of generic bifurcation equations requires the knowledge of fundamental invariants and equivariants. We discuss computations which are related to this for finite groups and semisimple Lie groups. We consider questions such as the completeness of invariants and equivariants. Efficient computations are gained by the Hilbert series driven Buchberger algorithm. Applications such as orbit space reduction are presented.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
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