The Computer Algebra Package CRACK for Investigating PDEs

Thomas Wolf
School of Mathematical Sciences
Queen Mary and Westfield College
University of London
London E1 4NS
T.Wolf@maths.qmw.ac.uk

Andreas Brand
Institut für Informatik
Friedrich Schiller Universität Jena
07740 Jena
Germany
maa@hpux.rz.uni-jena.de

• Contents
• The purpose of CRACK
• How to apply CRACK
  • The call
  • The result
  • Flags
  • Help
• Contents of the CRACK package
  • Decoupling
  • Integrating exact PDEs
  • Direct separation of PDEs
  • Indirect separation of PDEs
  • Solving standard ODEs
• Examples
  • Investigating symmetries of ODEs/PDEs and systems of them
  • Determining integrating factors
  • Determining a Lagrangian for a given 2nd order ODE
  • A factorization ansatz for a given ODE
  • General remarks on complexity
  • Acknowledgement
• References
• About this document ...

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