biinv, 12.08.2014.

----GENERAL NOTE----
The program can be downloaded from
www.math.uni.wroc.pl/~marcinkow/papers/biinv.tar
and it is an attachement to a paper
'Cancellation norm and distortion in biinvariant word metrics'
(M.Brandenbursky, Ś.Gal, J.Kędra, M.Marcinkowski)

biinv.c computes the biinvariant word length 
on the free group generated by {a,b}. 
You may either compile .c filie
(for UNIX user: compile with cc -o biinv biinv.c) 
or use enclosed executable file biinv.
You may run ./biinv for help.

----NOTATION----
Denote by |g| the standard word length of g and by ‖g‖ 
the biinvariant length of g.

----INPUT----
The program accepts two parameters.
Exponent: a natural number n.
Word: a cyclically reduced word w over alphabet {a,b}. 
Capitals A,B denote inverses. For example for a cummutator
[a,b] one shall type abAB. 

----OUTPUT----
Biinvariant length of w: ‖w‖
Biinvariant length of w^n: ‖w^n‖ 
Distorsion: ‖w^n‖/(n‖w‖)
Biinvariant vs. normal length: ‖w^n‖/(|w^n|) 

Example:
^^^^^^^^
./biinv 12 abABa

Biinvariant length of the Word: 3 
Biinvariant length of the Word^Exponent: 20 
Distorsion: 0.56 
Biinvariant vs. normal length: 0.33
