TY - GEN

T1 - Bifurcation theory and computer algebra

T2 - European Conference on Computer Algebra, EUROCAL 1985

AU - Armbruster, D.

N1 - Funding Information:
I am grateful to H. Kredel, who overcame all difficulties in implementing the Buch-berger Algorithm System in T~bingen. He was also responsible for extending this algorithm to modules. G. Dangelmayr reminded me of the difference between E n and K\[Xl..Xn\,] which is crucial in Sect. 2. I thank W. GHttinger for his comments and the stiftung Volkswagenwerk for financial support.
Publisher Copyright:
© 1985, Springer-Verlag.

PY - 1985

Y1 - 1985

N2 - Bifurcation theory studies the behavior of multiple solutions of nonlinear (differential) equations when parameters in these equations are varied, and describes how the number and type of these solutions change. It is a domain of applied mathematics which uses concepts from such diverse fields as functional analysis, group representations, ideal theory and many others. For real, e.g. physically motivated problems, the calculations necessary to determine even the simplest bifurcations become excessively complicated. Therefore, a project to build a package “bifurcation and singularity theory” in computer algebra is presented. Specifically, Gröbner bases are used to determine the codimension of a singularity, thereby extending the Buchberger Algorithm to modules. Also, a program in SMP is described, which permits determining whether a given function g is contact equivalent to a polynomial normal form h for one dimensional bifurcation problems up to codimension three.

AB - Bifurcation theory studies the behavior of multiple solutions of nonlinear (differential) equations when parameters in these equations are varied, and describes how the number and type of these solutions change. It is a domain of applied mathematics which uses concepts from such diverse fields as functional analysis, group representations, ideal theory and many others. For real, e.g. physically motivated problems, the calculations necessary to determine even the simplest bifurcations become excessively complicated. Therefore, a project to build a package “bifurcation and singularity theory” in computer algebra is presented. Specifically, Gröbner bases are used to determine the codimension of a singularity, thereby extending the Buchberger Algorithm to modules. Also, a program in SMP is described, which permits determining whether a given function g is contact equivalent to a polynomial normal form h for one dimensional bifurcation problems up to codimension three.

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U2 - 10.1007/3-540-15984-3_245

DO - 10.1007/3-540-15984-3_245

M3 - Conference contribution

AN - SCOPUS:85025493253

SN - 9783540159841

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 126

EP - 137

BT - EUROCAL 1985 - European Conference on Computer Algebra, Proceedings

A2 - Caviness, Bob F.

PB - Springer Verlag

Y2 - 1 April 1985 through 3 April 1985

ER -