OK, I've created the following:

sage: S =  BinaryStrings()
sage: S
Free binary string monoid
sage: (x,y) = S.gens()
sage: x
'0'
sage: y
'1'
sage: x^7 * y^11 * x^17 * y^2
'0000000111111111110000000000000000011'
sage: x^61
'0000000000000000000000000000000000000000000000000000000000000'
sage: y^61
'1111111111111111111111111111111111111111111111111111111111111'

Internally it just stores bits as int's, which generalizes easily to
other numerical strings,
and should be useful for more sophisticated conversions in, e.g. the
AES, where 8-bit
strings are alternately interpreted as module elements or finite field
elements.

I haven't implemented any sophisticated string operations like
splicings, but the above
is to me already a more satisfying multiplicative notation than that of
Python str's.

--David


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