Defactoring: Difference between revisions
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DCF is not only for mappings. Comma-bases — the duals of mappings — may also be put into DCF, as long as they are first antitransposed<ref>See a discussion of the antitranspose here: https://en.xen.wiki/w/User:Cmloegcmluin/Sandbox#null-space</ref>, and then antitransposed again at the end, or in other words, you sandwich the defactoring and HNF operations between antitransposes. | DCF is not only for mappings. Comma-bases — the duals of mappings — may also be put into DCF, as long as they are first antitransposed<ref>See a discussion of the antitranspose here: https://en.xen.wiki/w/User:Cmloegcmluin/Sandbox#null-space</ref>, and then antitransposed again at the end, or in other words, you sandwich the defactoring and HNF operations between antitransposes. | ||
DCF is arguably even more important for comma-bases than it is for mappings, because enfactored mappings at least have clear musical meaning, while enfactored comma-bases are little but a wellspring of confusion. In other words, {{map|24 38 56}} may not be a true temperament, but it still represents a temperoid and an EDO. | DCF is arguably even more important for comma-bases than it is for mappings, because enfactored mappings at least have clear musical meaning, while enfactored comma-bases are little but a wellspring of confusion. In other words, {{map|24 38 56}} may not be a true temperament, but it still represents a temperoid and an EDO. For more detail on this idea, see the above section: https://en.xen.wiki/w/User:Cmloegcmluin/Defactored_canonical_form#deeper_dive_on_concerns_re:_contorsion_concept.3B_enfactorization_illustrated_with_lattices_to_demonstrate_pathology_of_temperoids | ||
== other stuff to report == | == other stuff to report == | ||