So the lexicographic ordering induced by codepoint value sorts strings in an unambiguous canonical order, but it does not necessarily alphabetize them in the conventional sense.
Weak orders have also been used in computer science, in partition refinement based algorithms for lexicographic breadth-first search and lexicographic topological ordering.
In this order monomials are compared first by total degree, with ties broken by taking the smallest monomial with respect to lexicographic ordering with the variables reversed.
This involves various lexicographic analyses: user research, dictionary typology, and a clear structure for presenting and linking the information in the dictionary.
Now one proves by induction on the leading monomial in lexicographic order, that any nonzero homogeneous symmetric polynomial of degree can be written as polynomial in the elementary symmetric polynomials.