inverse binary string bit by bit

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For instance, using list comprehension:

sage: x = '0110101'
sage: R = range(len(x))
sage: def show_bit(s, exchange=False):
....:     if not exchange:
....:         return s
....:     return str(1-int(s))
....: 
sage: [ ''.join([show_bit(x[j], j <= k) for j in R]) for k in R ]

This gives the list of the path of the strings where one by one the bits are reverted:

['1110101', '1010101', '1000101', '1001101', '1001001', '1001011', '1001010']

You could just use Python string replacement: https://docs.python.org/2/library/std.... Replace every "0" with "x", then replace every "1" with "0", then replace every "x" with "1". Or use the translatemethod: https://docs.python.org/2/library/std...: create a translation table swapping 0 and 1 and then apply it. In Python 2:

sage: import string
sage: T = string.maketrans('01', '10')
sage: s = '00111'
sage: s.translate(T)
'11000'

In Python 3:

sage: T = str.maketrans({'0': '1', '1': '0'})
sage: s = '00111'
sage: s.translate(T)
'11000'

You can also use Bitset.

sage: B = Bitset('0110101')
sage: C = Bitset('0' * B.capacity())
sage: for i in range(B.capacity()):
....:     C.add(i)
....:     print(B.symmetric_difference(C))
....:     C.discard(i)
1110101
0010101
0100101
0111101
0110001
0110111
0110100