Talk:Normal forms: Difference between revisions

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The footnote criticizes IRREF for making enfactored mappings. But I originally proposed IRREF for the comma list, not the mapping. I agree that IRREF mappings are a horrible idea! From my last edit of this page: "For a monzo list, it has the advantage of limiting the appearance of the N highest primes to only one comma each (where N is the codimension), isolating each prime's effect on the pergen, but has the disadvantage that the commas tend to have high odd limits, and the comma list may have torsion." I think IRREF is valuable as a sort of secondary comma list. It would be nice if x31eq listed the IRREF comma list as well as the usual one, so that one could see all the various restrictions at a glance. It also helps compare two different temperaments to see what they have in common. For example consider (81/80 36/35) and (2048/2025 64/63), two comma lists defined by ascending prime limit, least odd limit and no enfactoring. Their IRREF forms are (81/80 64/63) and (2048/2025 64/63). The IRREFs show that they have 64/63 in common. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:55, 13 October 2021 (UTC)

: Thanks for this Kite. I'm sorry that I misrepresented your writing. I didn't do it intentionally; I think I just wasn't being careful to mind possible importance that you may have placed on distinguishing between mappings and comma lists. As far as I was concerned IRREF was no good for either mappings or comma lists, because I was concerned about enfactoring (what you refer to here as "torsion", but as Dave and I determined in our recent research, torsion is the name for a related problem which only pertains to periodicity blocks, not temperaments; I can refer to you our findings again if you like).

: I've simply removed that part of the footnote, because I realized not only did it misrepresent your writing, what it says otherwise is no longer really relevant at all.

: Okay. So I see your point that IRREF can provide a different sort of value here. And at this point I can't see any reason why it wouldn't qualify as a "normal form". So if you want, feel free to add it back to the page. Flora politely commented it out but I was brash and straight up deleted your stuff. So here it is, dug up from the change logs:

:: Another important normalized form for integral matrices is what [[Kite Giedraitis]] has dubbed the IRREF, the '''integral reduced row echelon form'''. It is the [[Wikipedia: Row echelon form|reduced row echelon form]] made integral by multiplying each row of the matrix by the least common multiple of all denominators in that row. It differs from the Hermite normal form in that each pivot is the only nonzero entry in its column. For a monzo list, it has the advantage of limiting the appearance of the ''N'' highest primes to only one comma each (where ''N'' is the codimension), isolating each prime's effect on the [[pergen]], but has the disadvantage that the commas tend to have high odd limits, and the comma list may have torsion. Sometimes the IRREF is identical to the Hermite normal form.

: I had forgotten that the name IRREF was coined by you! Well, I think Dave and I did find one or two other academic sites which came up with the same term. But I believe you did so independently :)

: Right! So, however, if you want to add it back to the page, there is a slight issue. As you can see, at the moment, HNF is up top, because it's part of every normal form presently on the page. So if you want to add IRREF back, you would have to rework the page a bit to accommodate that. I got us into this mess so I'm happy to help with that. Perhaps we could do it together next week. Let me know. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:04, 14 October 2021 (UTC)

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 The footnote criticizes IRREF for making enfactored mappings. But I originally proposed IRREF for the comma list, not the mapping. I agree that IRREF mappings are a horrible idea! From my last edit of this page: "For a monzo list, it has the advantage of limiting the appearance of the N highest primes to only one comma each (where N is the codimension), isolating each prime's effect on the pergen, but has the disadvantage that the commas tend to have high odd limits, and the comma list may have torsion." I think IRREF is valuable as a sort of secondary comma list. It would be nice if x31eq listed the IRREF comma list as well as the usual one, so that one could see all the various restrictions at a glance. It also helps compare two different temperaments to see what they have in common. For example consider (81/80 36/35) and (2048/2025 64/63), two comma lists defined by ascending prime limit, least odd limit and no enfactoring. Their IRREF forms are (81/80 64/63) and (2048/2025 64/63). The IRREFs show that they have 64/63 in common. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:55, 13 October 2021 (UTC)
+: Thanks for this Kite. I'm sorry that I misrepresented your writing. I didn't do it intentionally; I think I just wasn't being careful to mind possible importance that you may have placed on distinguishing between mappings and comma lists. As far as I was concerned IRREF was no good for either mappings or comma lists, because I was concerned about enfactoring (what you refer to here as "torsion", but as Dave and I determined in our recent research, torsion is the name for a related problem which only pertains to periodicity blocks, not temperaments; I can refer to you our findings again if you like).
+: I've simply removed that part of the footnote, because I realized not only did it misrepresent your writing, what it says otherwise is no longer really relevant at all.
+: Okay. So I see your point that IRREF can provide a different sort of value here. And at this point I can't see any reason why it wouldn't qualify as a "normal form". So if you want, feel free to add it back to the page. Flora politely commented it out but I was brash and straight up deleted your stuff. So here it is, dug up from the change logs:
+:: Another important normalized form for integral matrices is what [[Kite Giedraitis]] has dubbed the IRREF, the '''integral reduced row echelon form'''. It is the [[Wikipedia: Row echelon form|reduced row echelon form]] made integral by multiplying each row of the matrix by the least common multiple of all denominators in that row. It differs from the Hermite normal form in that each pivot is the only nonzero entry in its column. For a monzo list, it has the advantage of limiting the appearance of the ''N'' highest primes to only one comma each (where ''N'' is the codimension), isolating each prime's effect on the [[pergen]], but has the disadvantage that the commas tend to have high odd limits, and the comma list may have torsion. Sometimes the IRREF is identical to the Hermite normal form.
+: I had forgotten that the name IRREF was coined by you! Well, I think Dave and I did find one or two other academic sites which came up with the same term. But I believe you did so independently :)
+: Right! So, however, if you want to add it back to the page, there is a slight issue. As you can see, at the moment, HNF is up top, because it's part of every normal form presently on the page. So if you want to add IRREF back, you would have to rework the page a bit to accommodate that. I got us into this mess so I'm happy to help with that. Perhaps we could do it together next week. Let me know. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 01:04, 14 October 2021 (UTC)