
*** circle ***

In this example a map of a circle onto itself with double winding 
is defined. The map in homology thus maps the 1-dimensional generator 
onto itself with the coefficient of 2. The map is given as a cubical 
multivalued map.

Old Method. We first use the program "chkperf" in order to verify that the
map is "almost perfect", i.e., that it satisfies assumptions required by an
algorithm by Madjid Allili and Tomasz Kaczynski for creating a chain map
for homology computation. Then we run the program "chmap" written by Jacek
Szybowski and Marcin Mazur, and we obtain a chain map in a geometrical format.
We convert this chain map to purely algebraic data with the use of the program
"cnvchmap". At this point we are ready to compute the homomorphism
induced by this chain map in homology with the "homchain" program.

New Method. The map induced in homology can be computed directly
by the program "homcubes". The geometric approach is different,
and relies on the construction of the graph of the map and computing
the homomorphisms induced by the projections.
