Defactoring: Difference between revisions
Cmloegcmluin (talk | contribs) m Cmloegcmluin moved page User:Cmloegcmluin/Defactored canonical form to Canonical form: this page may require a little further iteration, but is definitely ready for prime time now. |
Cmloegcmluin (talk | contribs) add motivation section |
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Elsewhere, [[Normal_lists|Integer Reduced Row Echelon Form]], or IRREF, has been proposed as a normal form for mappings. It has a similar problem as HNF does, however, in that it does not always defactor matrices. Worse, even, sometimes IRREF introduces enfactoring where before there was none! For example, consider this mapping for 5-limit porcupine, {{vector|{{map|7 11 16}} {{map|22 35 51}}}}. This mapping is not enfactored, but its IRREF is {{vector|{{map|3 0 -1}} {{map|0 3 5}}}}, which is 3-enfactored. More on this later. | Elsewhere, [[Normal_lists|Integer Reduced Row Echelon Form]], or IRREF, has been proposed as a normal form for mappings. It has a similar problem as HNF does, however, in that it does not always defactor matrices. Worse, even, sometimes IRREF introduces enfactoring where before there was none! For example, consider this mapping for 5-limit porcupine, {{vector|{{map|7 11 16}} {{map|22 35 51}}}}. This mapping is not enfactored, but its IRREF is {{vector|{{map|3 0 -1}} {{map|0 3 5}}}}, which is 3-enfactored. More on this later. | ||
== motivation == | |||
A key goal of introducing this canonical form is to achieve for the linear-algebra-only school of RTT practioners a unique ID for temperaments, which previously was only available by using lists of minor determinants AKA wedge products of mapping rows. | |||
= terminology change proposal = | = terminology change proposal = | ||