The SimilarityCoefficient(s, t) command computes the similarity coefficient of two strings s and t, defined as follows.

Let N(S) denote the set of trigrams of any string S. Then $\frac{\mathrm{nops}\left(N\left(s\right)\cup N\left(t\right)\right)}{\mathrm{nops}\left(N\left(s\right)\cap N\left(t\right)\right)}$ is the similarity coefficient of s and t, with the convention that strings having no trigrams in common have similarity coefficient equal to infinity.

An optional argument n may be specified causing the similarity coefficient to be computed for n-gram similarity instead of the default trigram similarity.

In typical applications, n is taken to be either $2$ or $3$ (the default). Note that Maple computes this measure as an exact rational quantity, rather than a floating-point approximation. You can obtain a floating-point result by applying evalf to the result.

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.

$\mathrm{with}\left(\mathrm{StringTools}\right)\:$

$\mathrm{SimilarityCoefficient}\left(''Canada''\,''Canary''\right)$

$3$

$\mathrm{SimilarityCoefficient}\left(''Kline''\,''Cline''\right)$

$2$

$\mathrm{SimilarityCoefficient}\left(''mathematics''\,''mathematische''\right)$

$2$

$\mathrm{SimilarityCoefficient}\left(''Constance''\,''Connor''\,1\right)$

$3$

$\mathrm{SimilarityCoefficient}\left(''Constance''\,''Connor''\,2\right)$

$\frac{11}{2}$

$\mathrm{SimilarityCoefficient}\left(''Constance''\,''Connor''\,3\right)$

$10$

$\mathrm{SimilarityCoefficient}\left(''Constance''\,''Connor''\,4\right)$

$\mathrm{\infty }$

$\mathrm{SimilarityCoefficient}\left(''Constance''\,''Connor''\,5\right)$

$\mathrm{\infty }$