User:Inthar/Style guide: Difference between revisions
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== Algebraic structures == | == Algebraic structures == | ||
* <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, <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> Example: <math>\mathbb{Z}^3\langle \mathbf{L}, \mathbf{m}, \mathbf{s}\rangle</math> | * If ''R'' is a commutative ring, <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> Example: <math>\mathbb{Z}^3\langle \mathbf{L}, \mathbf{m}, \mathbf{s}\rangle</math> | ||
Revision as of 01:45, 23 February 2024
My notation may differ from conventional xen notation, especially in more technical xen theory writings.
Variables
- Capital italicized Latin letters may denote scales written cumulatively. For example: S(n) = 100n cents
- Lowercase italicized Latin letters may denote scales written as steps or abstract scale words. For example: s(a, b, c) = abacaba
- Bolded variables denote interval sizes, especially letters of scale words. For example: 5L 2s
Algebraic structures
- [math]\displaystyle{ \mathrm{JI}\langle p_1, ..., p_r \rangle }[/math] is the p1.[...].pr subgroup, the subgroup of [math]\displaystyle{ (\mathbb{Q}_{\gt 0}, \cdot) }[/math] generated by rationals [math]\displaystyle{ p_1, ..., p_r. }[/math]
- If R is a commutative ring, [math]\displaystyle{ R^r\langle a_1, ..., a_r\rangle }[/math] is the rank-r free R-module generated by basis elements [math]\displaystyle{ a_1, ..., a_r. }[/math] Example: [math]\displaystyle{ \mathbb{Z}^3\langle \mathbf{L}, \mathbf{m}, \mathbf{s}\rangle }[/math]