The IsPeriod(w,p) command tests whether the positive integer p is a period of the string w. A positive integer p is said to be a period of a string s if, for all integers i with $1<=i<=\mathrm{length}\left(s\right)-p$, one has $s_i=s_{i+p}$. If p is a period of w, then the value true is returned; otherwise, false is returned.

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.

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

$\mathrm{IsPeriod}\left(''abc''\&comma;1\right)$

$\mathrm{false}$

$\mathrm{IsPeriod}\left(''abc''\&comma;2\right)$

$\mathrm{false}$

$\mathrm{IsPeriod}\left(''abc''\&comma;3\right)$

$\mathrm{true}$

$\mathrm{IsPeriod}\left(''abababa''\&comma;1\right)$

$\mathrm{false}$

$\mathrm{IsPeriod}\left(''abababa''\&comma;2\right)$

$\mathrm{true}$

$\mathrm{IsPeriod}\left(''abababa''\&comma;3\right)$

$\mathrm{false}$

$\mathrm{IsPeriod}\left(''abababa''\&comma;4\right)$

$\mathrm{true}$

$\mathrm{IsPeriod}\left(''abababa''\&comma;5\right)$

$\mathrm{false}$

$\mathrm{IsPeriod}\left(''abababa''\&comma;6\right)$

$\mathrm{true}$

$\mathrm{IsPeriod}\left(''abababa''\&comma;7\right)$

$\mathrm{true}$

$\mathrm{select}\left(\mathrm{curry}\left(\mathrm{IsPeriod}\&comma;''babbababbabbababbabbabab''\right)\&comma;\left\{\mathrm{`\$`}\left(1..24\right)\right\}\right)$

$\left\{8\&comma;16\&comma;21\&comma;23\&comma;24\right\}$