User:Inthar/Style guide: Difference between revisions

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* A ''(free) circular word'' is a class of based circular words equivalent under rotation: <math>\{x\mapsto s[x], x\mapsto s[x+1], ..., x\mapsto s[x+|s|-1] \}</math> for ''s'' a based circular word.

* The length of a linear, based circular, or free circular word ''s'' is denoted {{len|''s''}} or len(''s'').

* Circular words may be treated as (based) infinite words. Thus for ''m'', ''n'' integers, ''m'' < ''n'', then ''s''[''m''] denotes ''s''[''m'' mod {{len|''s''}}]~~. The~~ notation ''s''[''m'':''n''] denotes the (''n'' − ''m'')-letter word ''s''[''m'']''s''[''m''+1]...''s''[''n''−1], where all indices are taken mod {{len|''s''}}.

* Circular words may be treated as (based) infinite words. Thus for ''m'', ''n'' integers, ''m'' < ''n'', then ''s''[''m''] denotes ''s''[''m'' mod {{len|''s''}}], and the slice notation ''s''[''m'':''n''] denotes the (''n'' − ''m'')-letter word ''s''[''m'']''s''[''m''+1]...''s''[''n''−1], where all indices are taken mod {{len|''s''}}.

* Substitution: If ''w'' is a linear or based circular word in '''X''' and possibly other letters, and ''u'' is a based circular word in '''b''' and '''c''', then <math>\mathsf{subst}(w, \mathbf{X}, u)</math> denotes the word ''w'' but with the ''i''th occurrence of '''X''' replaced with ''u''[''i''] (for ''i'' ≥ 0).

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 * A ''(free) circular word'' is a class of based circular words equivalent under rotation: <math>\{x\mapsto s[x], x\mapsto s[x+1], ..., x\mapsto s[x+|s|-1] \}</math> for ''s'' a based circular word.
 * The length of a linear, based circular, or free circular word ''s'' is denoted {{len|''s''}} or len(''s'').
-* Circular words may be treated as (based) infinite words. Thus for ''m'', ''n'' integers, ''m'' < ''n'', then ''s''[''m''] denotes ''s''[''m'' mod {{len|''s''}}]. The notation ''s''[''m'':''n''] denotes the (''n'' &minus; ''m'')-letter word ''s''[''m'']''s''[''m''+1]...''s''[''n''&minus;1], where all indices are taken mod {{len|''s''}}.
+* Circular words may be treated as (based) infinite words. Thus for ''m'', ''n'' integers, ''m'' < ''n'', then ''s''[''m''] denotes ''s''[''m'' mod {{len|''s''}}], and the slice notation ''s''[''m'':''n''] denotes the (''n'' &minus; ''m'')-letter word ''s''[''m'']''s''[''m''+1]...''s''[''n''&minus;1], where all indices are taken mod {{len|''s''}}.
 * Substitution: If ''w'' is a linear or based circular word in '''X''' and possibly other letters, and ''u'' is a based circular word in '''b''' and '''c''', then <math>\mathsf{subst}(w, \mathbf{X}, u)</math> denotes the word ''w'' but with the ''i''th occurrence of '''X''' replaced with ''u''[''i''] (for ''i'' &ge; 0).