A Computer Implementation of Whitehead's Algorithm

2.2 minwd (”Minimum Word”)
minwd 4 takes two arguments, a word wd in the free group F (a, b, c) with the
convention that X denotes the inverse of x for all x in {a, b, c}, and an empty
list [ ]. To avoid complications with Maple ”evaluating” the word it is given,
it is best to enclose the argument in a pair of single quotation marks ’and’. It
returns a word that is Whitehead equivalent to wd and is of minimal length,
and the list of Whitehead automorphisms needed to get the minimal word.
It uses all three of the lemmas to reduce computation time.
oldminwd takes one argument, a word wd in F (a, b, c). To avoid complications
with Maple ”evaluating” the word it is given, it is best to enclose the
argument in a pair of single quotation marks ’and’. It returns a word that is
Whitehead equivalent to wd and is of minimal length.
Whitehead sets
aset
> aset:=combinat[powerset]({’b’,’c’,’B’,’C’}):
> aset:=aset minus {{}};
Aset
> Aset:=combinat[powerset]({’b’,’c’,’B’,’C’}):
> Aset:=Aset minus {{}};
bset
> bset:=combinat[powerset]({’a’,’c’,’A’,’C’}):
> bset:=bset minus {{}};
Bset
> Bset:=combinat[powerset]({’a’,’c’,’A’,’C’}):
> Bset:=Bset minus {{}};
cset
> cset:=combinat[powerset]({’b’,’a’,’B’,’A’}):
4 The idea and code for using “Whitehead sets” to improve the efficiency of minwd (via
Lemma 2.2) was supplied by Professor Garity.
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