Generator preimage: Difference between revisions
Cmloegcmluin (talk | contribs) link linearly independent, fix typo |
Cmloegcmluin (talk | contribs) GCF back to GCD, for better distention from "greatest factor", and it's more popular anyway |
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=Definition= | =Definition= | ||
Given a reduced list of [[Harmonic_Limit|p-limit]] vals V, we may define a set of transversal generators for V as a set of p-limit intervals q such that one of the vals of V maps q to 1 and the rest map it to 0. By ''reduced'' is meant that the | Given a reduced list of [[Harmonic_Limit|p-limit]] vals V, we may define a set of transversal generators for V as a set of p-limit intervals q such that one of the vals of V maps q to 1 and the rest map it to 0. By ''reduced'' is meant that the GCD of the elements of each of the vals is 1--or in other words, none of the vals are [[contorted]]--and that they are [[linearly independent]], so that if there are r vals, the rank of V as a matrix is r. | ||
If v1, v2, ... vr are the vals of V and t1, t2, ... tr are the corresponding transversal generators, then for any p-limit q we have, modulo the regular temperament defined by V | If v1, v2, ... vr are the vals of V and t1, t2, ... tr are the corresponding transversal generators, then for any p-limit q we have, modulo the regular temperament defined by V | ||