TY - GEN A1 - Wolf, Thomas T1 - Applications of CRACK in the Classification of Integrable Systems N2 - The talk given by the author at the CRM workshop on Superintegrability in Sep.\ 2002 and this related paper report on work in two subjects. One is the collaboration with Vladimir Sokolov and Takayuki Tsuchida in an effort to classify polynomial integrable vector evolution equations. The other is the computer algebra package {\sc Crack} which did the main computations in solving large bi-linear algebraic systems. Although originally designed to solve over-determined systems of partial differential equations a number of extensions made {\sc Crack} a powerful tool for solving systems of bi-linear algebraic equations. Such systems turn up in many different classification problems some of which were investigated by other participants of this workshop. Two additional applications are outlined. In the talk on which this article is based a method to reduce the length of equations was presented which proved to be useful in solving the bi-linear algebraic systems. Due to numerous asked questions about the computer program, a more complete overview is given in the appendix. T3 - ZIB-Report - 02-48 KW - Integrability KW - evolution equations KW - quadratic Hamiltonians KW - Computer algebra KW - Bi-linear algebraic systems KW - conservation laws Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7159 ER - TY - GEN A1 - Wolf, Thomas T1 - Integrable quadratic Hamiltonians with a linear Lie-Poisson bracket N2 - Quadratic Hamiltonians with a linear Lie-Poisson bracket have a number of applications in mechanics. For example, the Lie-Poisson bracket $e(3)$ includes the Euler-Poinsot model describing motion of a rigid body around a fixed point under gravity and the Kirchhoff model describes the motion of a rigid body in ideal fluid. Advances in computer algebra algorithms, in implementations and hardware, together allow the computation of Hamiltonians with higher degree first integrals providing new results in the search for integrable models. A computer algebra module enabling related computations in a 3-dimensional vector formalism is described. T3 - ZIB-Report - 05-07 KW - Hamilton systems KW - Integrability KW - Computer algebra Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8414 ER -