%Appendix (Testfile).
%This appendix is a test file. The symmetry groups for various
%equations or systems of equations are determined. The variable
%PCLASS has the default value 0 and may be changed by the user
%before running it. The output may be compared with the results
%which are given in the references.
%The Burgers equations
deq 1:=u(1,1)+u 1*u(1,2)+u(1,2,2)$
cresys deq 1$ simpsys()$ result()$
%The Kadomtsev-Petviashvili equation
deq 1:=3*u(1,3,3)+u(1,2,2,2,2)+6*u(1,2,2)*u 1
+6*u(1,2)**2+4*u(1,1,2)$
cresys deq 1$ simpsys()$ result()$
%The modified Kadomtsev-Petviashvili equation
deq 1:=u(1,1,2)-u(1,2,2,2,2)-3*u(1,3,3)
+6*u(1,2)**2*u(1,2,2)+6*u(1,3)*u(1,2,2)$
cresys deq 1$ simpsys()$ result()$
%The real- and the imaginary part of the nonlinear Schroedinger
%equation
deq 1:= u(1,1)+u(2,2,2)+2*u 1**2*u 2+2*u 2**3$
deq 2:=-u(2,1)+u(1,2,2)+2*u 1*u 2**2+2*u 1**3$
%Because this is not a single equation the two assignments
sder 1:=u(2,2,2)$ sder 2:=u(1,2,2)$
%are necessary.
cresys()$ simpsys()$ result()$
%The symmetries of the system comprising the four equations
deq 1:=u(1,1)+u 1*u(1,2)+u(1,2,2)$
deq 2:=u(2,1)+u(2,2,2)$
deq 3:=u 1*u 2-2*u(2,2)$
deq 4:=4*u(2,1)+u 2*(u 1**2+2*u(1,2))$
sder 1:=u(1,2,2)$ sder 2:=u(2,2,2)$ sder 3:=u(2,2)$ sder 4:=u(2,1)$
%is obtained by calling
cresys()$ simpsys()$
df(c 5,x 1):=-df(c 5,x 2,2)$
df(c 5,x 2,x 1):=-df(c 5,x 2,3)$
simpsys()$ result()$
%The symmetries of the subsystem comprising equation 1 and 3 are
%obtained by
cresys(deq 1,deq 3)$ simpsys()$ result()$
%The result for all possible subsystems is discussed in detail in
%''Symmetries and Involution Systems: Some Experiments in Computer
%Algebra'', contribution to the Proceedings of the Oberwolfach
%Meeting on Nonlinear Evolution Equations, Summer 1986, to appear.
end;