r"""

Build two disjoint alphabets (i.e. sets) and a bijection between them from

the given data.

This is mainly used to build free groups.

EXAMPLES::

sage: build_alphabet_with_inverses('abc')

({'a', 'b', 'c'}, {'A', 'B', 'C'})

sage: build_alphabet(3, name='a')

({'a0', 'a1', 'a2'}, {'A0', 'A1', 'A2'})

TODO:

Fix conventions in order to fit with build_alphabet in

sage.combinat.words.alphabet

"""

if isinstance(data, (int,Integer)):

if name is None:

name = 'a'

if negname is None:

if name.islower():

negname = name.upper()

elif name.isupper():

negname = name.lower()

return build_alphabet([name+str(i) for i in xrange(data)]), build_alphabet([negname+str(i) for i in xrange(data)])

pos = build_alphabet(data)

if neg is None:

from sage.combinat.words.alphabet import set_of_letters

if all(letter in set_of_letters['lower'] for letter in pos):

neg = build_alphabet(''.join(pos).upper())

elif all(letter in set_of_letters['upper'] for letter in pos):

pos = build_alphabet(''.join(neg).lower())

else:

raise ValueError("not able to determine default inverse letters")

else:

neg = build_alphabet(neg)

assert pos.cardinality() == neg.cardinality()

for letter in pos:

if letter in neg:

raise ValueError("letter %s is both positive and negative"%letter)

for letter in neg:

if letter in pos:

raise ValueError("letter %s is both positive and negative"%letter)