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- Executable file
r38/packages/spde/spde.tst
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 1974) [annotate] [blame] [check-ins using]
%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;