
*** 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.

Method 1. 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 this chain map in homology 
with the "homchain" program.

Method 2. The map induced in homology can also be computed by the "homcubes" 
program directly.
