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The IsPrimitive(s) command returns the value true if s is primitive, and the value false otherwise. A string is primitive if it cannot be written as a proper power of another string. In other words, s is primitive if $\mathrm{Repeat}\left(t\,n\right)=s$ implies that either $s=''''$ or $s=t$ and $n=1$.

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.

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

$\mathrm{IsPrimitive}\left(''''\right)$

$\mathrm{false}$

$\mathrm{IsPrimitive}\left(''a''\right)$

$\mathrm{true}$

$\mathrm{IsPrimitive}\left(''aaa''\right)$

$\mathrm{false}$

$\mathrm{IsPrimitive}\left(''abc''\right)$

$\mathrm{true}$

$\mathrm{IsPrimitive}\left(''abcabc''\right)$

$\mathrm{false}$

$\mathrm{seq}\left(\mathrm{IsPrimitive}\left(\mathrm{ThueMorse}\left(n\right)\right)\,n=1..30\right)$

$\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{true}$

$\mathrm{andmap}\left(\mathrm{IsPrimitive}\,\mathrm{LyndonFactors}\left(\mathrm{Random}\left(1000\,'\mathrm{lower}'\right)\right)\right)$

$\mathrm{true}$