S-expression: Difference between revisions
m looks more natural when reading and in the summary i think |
m →Abstraction: same reason as before; looks better i think? |
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== Abstraction == | == Abstraction == | ||
=== The maths | === The maths === | ||
Let ''H'' be a [[Wikipedia:Abelian group|commutative group]] with generators h<sub>i</sub>, ..., h<sub>k</sub>, ..., h<sub>j</sub> (such that i ≤ k ≤ j). | Let ''H'' be a [[Wikipedia:Abelian group|commutative group]] with generators h<sub>i</sub>, ..., h<sub>k</sub>, ..., h<sub>j</sub> (such that i ≤ k ≤ j). | ||
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The meanings of these analogues are up to us to interpret, however. This brings us to applications, which we will examine next, with a focus on the musical ones: | The meanings of these analogues are up to us to interpret, however. This brings us to applications, which we will examine next, with a focus on the musical ones: | ||
=== Applications | === Applications === | ||
Unless otherwise specified, we will let ''k'' be in the positive integers (Z<sub>+</sub>) and we will let the group operation be the multiplication of rationals, but this abstraction is much more powerful than that. | Unless otherwise specified, we will let ''k'' be in the positive integers (Z<sub>+</sub>) and we will let the group operation be the multiplication of rationals, but this abstraction is much more powerful than that. | ||