The HammingDistance(s,t) command returns an integer measure of the distance between the two strings s and t.

The Hamming distance between two strings s and t, of equal length, is the number of character positions where they differ. If strings s and t have respective lengths m and n where, without loss of generality, $n<m$, then the generalized Hamming distance between s and t is defined to be (m - n) + HammingDistance( s[ 1 .. n ], t ). The HammingDistance procedure computes this generalized metric.

For a different notion of the distance between two strings, see StringTools[Levenshtein].

All of the StringTools package commands treat strings as (null-terminated) sequences of $8$-bit (ASCII) characters.  Thus, there is no support for multibyte character encodings, such as unicode encodings.

$\mathbf{use}\mathrm{StringTools}\mathbf{in}\mathrm{HammingDistance}\left(''Mathematics''\&comma;''Mathematische''\right)\mathbf{end\; use}$

$4$

$\mathrm{with}\left(\mathrm{StringTools}\right)\&colon;$

$\mathrm{HammingDistance}\left(''abc''\&comma;''abd''\right)$

$1$

$\mathrm{HammingDistance}\left(''abc''\&comma;''abcd''\right)$

$1$

$\mathrm{HammingDistance}\left(''Elisabeth''\&comma;''Elyse''\right)$

$6$

$\mathrm{HammingDistance}\left(''Connor''\&comma;''Constance''\right)$

$6$

$s≔\mathrm{Random}\left(1000\&comma;'\mathrm{lower}'\right)\&colon;$

$t≔\mathrm{Random}\left(1000\&comma;'\mathrm{lower}'\right)\&colon;$

$u≔\mathrm{Random}\left(1000\&comma;'\mathrm{lower}'\right)\&colon;$

$\mathrm{HammingDistance}\left(s\&comma;t\right)$

$955$

$\mathrm{HammingDistance}\left(s\&comma;u\right)+\mathrm{HammingDistance}\left(u\&comma;t\right)$

$1926$