User:Inthar/Style guide: Difference between revisions
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** <math>\mathsf{MOS}(5,2;6)(\mathbf{L}, \mathbf{s}) = \mathbf{LLLsLLs}</math> | ** <math>\mathsf{MOS}(5,2;6)(\mathbf{L}, \mathbf{s}) = \mathbf{LLLsLLs}</math> | ||
** Blackdye is <math>\mathsf{Fl}(\mathrm{Pyth}[5]; 10/9)</math> | ** Blackdye is <math>\mathsf{Fl}(\mathrm{Pyth}[5]; 10/9)</math> | ||
== Discrete sets == | |||
* For <math>k \in \mathbb{R}</math> and <math>n\in \mathbb{Z}_{>0},</math> <math>[n]_k</math> denotes <math>\{k, k+1, ..., k+n-1\}.</math> I may also use <math>[i:j]</math> for <math>[j-i]_i.</math> | |||
[[Category:Math]] | |||
== Words == | == Words == | ||
* Zero-indexing is used for indices. | * Zero-indexing is used for indices. | ||
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* 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''}}]. 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''}}. | ||
* 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). | * 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). | ||
== Algebraic structures == | == Algebraic structures == | ||
* <math>\mathrm{JI}\langle p_1, ..., p_r \rangle</math> is the ''p''<sub>1</sub>.[...].''p''<sub>''r''</sub> subgroup, the subgroup of <math>(\mathbb{Q}_{>0}, \cdot)</math> generated by rationals <math>p_1, ..., p_r.</math> | * <math>\mathrm{JI}\langle p_1, ..., p_r \rangle</math> is the ''p''<sub>1</sub>.[...].''p''<sub>''r''</sub> subgroup, the subgroup of <math>(\mathbb{Q}_{>0}, \cdot)</math> generated by rationals <math>p_1, ..., p_r.</math> | ||
* If ''R'' is a commutative ring with 1, <math>R^r\langle a_1, ..., a_r\rangle</math> is the rank-''r'' free ''R''-module generated by basis elements <math>a_1, ..., a_r.</math> Ordered tuples in such modules are assumed to be in the given basis. Example: <math>\mathbf{m} + 3\mathbf{s} = (0,1,3) \in \mathbb{Z}^3\langle \mathbf{L}, \mathbf{m}, \mathbf{s}\rangle</math> | * If ''R'' is a commutative ring with 1, <math>R^r\langle a_1, ..., a_r\rangle</math> is the rank-''r'' free ''R''-module generated by basis elements <math>a_1, ..., a_r.</math> Ordered tuples in such modules are assumed to be in the given basis. Example: <math>\mathbf{m} + 3\mathbf{s} = (0,1,3) \in \mathbb{Z}^3\langle \mathbf{L}, \mathbf{m}, \mathbf{s}\rangle</math> | ||
== Miscellaneous == | == Miscellaneous == | ||
* <math>\log</math> is base e. | * <math>\log</math> is base e. | ||
* Temperament names are.capitalized. | * Temperament names are.capitalized. | ||