User:Inthar/Style guide: Difference between revisions

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** Blackdye is <math>\mathsf{Fl}(\mathrm{Pyth}[5]; 10/9)</math>

== Words ==

* Zero-indexing is used for indices.

* A ''(linear) word'' is a function <math>w : [n]_0 \to \mathcal{A}</math> where <math>\mathcal{A}</math> is a set of letters and <math>n \in \mathbb{Z}_{>0}.</math> ''n'' is called the ''length'' of ''s''.

* A ''based circular word'' is a function <math> s: \mathbb{Z}/n \to \mathcal{A}.</math> A ''period'' of a circular word is the minimal <math>p \in [|s|]_1</math> such that for all ''i'', <math>s[i+p]=s[i].</math> If the period of ''s'' is equal to the length of ''s'', then ''s'' is called primitive.

* 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''}}.

* For substitution: If ''w'' is a linear or based circular word in '''a''' and '''X''', 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''].

== Algebraic structures ==

@@ Line 12: / Line 12: @@
 ** Blackdye is <math>\mathsf{Fl}(\mathrm{Pyth}[5]; 10/9)</math>
 == Words ==
+* Zero-indexing is used for indices.
+* A ''(linear) word'' is a function <math>w : [n]_0 \to \mathcal{A}</math> where <math>\mathcal{A}</math> is a set of letters and <math>n \in \mathbb{Z}_{>0}.</math> ''n'' is called the ''length'' of ''s''.
+* A ''based circular word'' is a function <math> s: \mathbb{Z}/n \to \mathcal{A}.</math> A ''period'' of a circular word is the minimal <math>p \in [|s|]_1</math> such that for all ''i'', <math>s[i+p]=s[i].</math> If the period of ''s'' is equal to the length of ''s'', then ''s'' is called primitive.
+* 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''}}.
+* For substitution: If ''w'' is a linear or based circular word in '''a''' and '''X''', 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''].
 == Algebraic structures ==