The PrimitiveRoot(w) command computes the primitive root of the word (string) w. The primitive root of w is the string r of minimal length for which there is a positive integer e such that w = Repeat( r, e ). That is, r is the smallest root of which w is a power.

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.

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

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

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

$''abc''$

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

$''abc''$

$\mathrm{PrimitiveRoot}\left(''abcabcab''\right)$

$''abcabcab''$

$\mathrm{PrimitiveRoot}\left(''ababab''\right)$

$''ab''$

$\mathrm{PrimitiveRoot}\left(''abababa''\right)$

$''abababa''$

$L≔\mathrm{remove}\left(\mathrm{IsPrimitive}\,\mathrm{Generate}\left(4\,''abc''\right)\right)$

$L≔\left[''aaaa''\,''abab''\,''acac''\,''baba''\,''bbbb''\,''bcbc''\,''caca''\,''cbcb''\,''cccc''\right]$

$\mathrm{L2}≔\mathrm{map}\left(\mathrm{PrimitiveRoot}\,L\right)$

$\mathrm{L2}≔\left[''a''\,''ab''\,''ac''\,''ba''\,''b''\,''bc''\,''ca''\,''cb''\,''c''\right]$

$\mathrm{andmap}\left(\mathrm{IsPrimitive}\,\mathrm{L2}\right)$

$\mathrm{true}$