Author Thomas Wolf
Short description The package APPLYSYM takes as input a differential equation (DE) or a system of DEs and its point symmetries, for example computed by the program LIEPDE. It computes symmetry and similarity variables through solving single first order partial DEs (PDEs) with the procedure QUASILINPDE. This procedure formulates an equivalent characteristic non-linear system of ordinary DEs (ODEs) which is investigated by the program CRACK. Although the program CRACK is primarily made for dealing with overdetermined DE-systems, it nevertheless has good chances of solving the not overdetermined characteristic ODE-systems because CRACK has a number of different integration techniques built in and because Lie-symmetries often have a simple form which results in relatively simple characteristic ODE-systems. The program QUASILINPDE can be used independently without connection to symmetries for solving quasi-linear first order PDEs as demonstrated in applysym.tst.
Platform REDUCE, version 3.6, 3.7 and 3.8
System requirements The memory requirements depend crucially on the application. The non-trivial computations in the test file applysym.tst have been run in a 4MB session under LINUX.
Installation In a running REDUCE session either do
  in "applysym.red"$
or, in order to speed up computation, either compile it with
  on comp$
before the above command, or, generate a fast-loading compiled file once with
  faslout "applysym"$
  in "applysym.red"$
and load that file whenever you want to run APPLYSYM with
  load applysym$
In a similar way proceed with the files crack.red, liepde.red. The above commands assume all files to be in the current directory.
More information/updates There are available a manual, a test file and a log file.
The latest version is available from http://lie.math.brocku.ca/crack/src/.
Contact e-mail: Thomas Wolf