	The directory 'magnus/back_end/experiments' contains several
examples of how one can apply magnus to perform experiments which
sometimes are difficult or impossible to make running simple graphical
interface. To compile any of the programs first make sure you are in
the directory 'magnus/back_end/experiments', then type 'make
<filename>', where <filename> is the name of the program you want to
run. Then go to the directory 'test/bin' and run it. The names and
brief descriptions of implemented programs are listed below. If you
want to write a new program, you have to add it's name to the list of
tests in the Makefile (look for the string "TESTS = ' in the
Makefile). Then put your program into the 'test' directory, and run
make as described above.

	The list of experiments.

 
1. abelianOrder	
	 
 Contents: this program computes orders of all abelian groups
           satisfying the following pattern:
 
      < a,b; a^2 b^3, a^3 b^2 >,
      < a,b,c; a^2 b^3 c^4, a^3 b^4 c^2, a^4 b^2 c^3 >, etc.


2. ortest 

 Contents: 

      The program finds the shortest trivial word in an one-relator
      group. The algorithm is horrobly exponential, so if you give
      it a group with more then two generators, don't expect results
      in reasonable time.


3. primitive 

 Contents: 

      The program counts the number of primitive elements in a free
      group.


4. HNConjecture

 Contents: 
   
      An experiment which looks for a counter-example to the
      Hanna Neumann conjecture: if A and B are finitely generated
      subgroups of a free group of finite rank, and I is the
      intersection of A and B, then rk(I)-1 <= (rk(A)-1)(rk(B)-1).

