Talk:Normal forms: Difference between revisions

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= Smith normal form =

== Smith normal form ==

I noticed "Smith normal form" was added to this page as a name for the form of the normal val list. I've done a couple examples and I'm pretty sure that [https://en.wikipedia.org/wiki/Smith_normal_form Smith normal form] is not equivalent to this process; e.g. meantone's normal val list would be [⟨1 0 -4] ⟨0 1 4]] while I suppose you could say meantone's val list in Smith normal form (taking the first k rows only, as is demonstrated in the penultimate paragraph of the page on [[saturation]]) would be [⟨1 0 4] ⟨0 1 -4]]. If this is an attempt to name this other form for Gene Ward Smith, I think it's not a great idea, because of the preexistence of the linked Smith normal form which was named for Henry John Stephen Smith. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:24, 23 June 2021 (UTC)

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:: Oh, no big deal at all. Thanks for updating the page. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 15:17, 24 June 2021 (UTC)

= how best to handle the new canonical form for RTT matrices w/r/t normal form =

== how best to handle the new canonical form for RTT matrices w/r/t normal form ==

I recently published [[Canonical form|a page on the xen wiki proposing a canonical form for RTT mappings (or comma-bases)]]. This new page of mine solves a problem that this page seems to have set out to solve but not finished the job: establishing a form for RTT matrices which ''uniquely identifies them'', for a definition of uniqueness that is appropriate to the RTT domain. And so my page refers to this page in several places, mostly critiquing it.

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And as for this page itself: I am not saying that it is harmful or that there is nothing of value on it. Far from it! There's some good thinking here. But I do wonder what people here think about what the best approach should be for recognizing its relationship with the new canonical form. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:10, 27 September 2021 (UTC)

: First of all we must make clear what purposes these pages serve. Imo this page should always be kept up to date and used as the canonical reference. I'm not sure about your view of your ''canonical form'' article. To me it acts more like a development note thereof.

: Currently the form in all temp pages is the form defined in the ''normal val list'' section, and they are in canonical form already since they are not enfactored to start with. (More precisely, there is not a start but only the end and the end is correct.) So they are in canonical form and we don't need to do anything about them.

: The important part is the amendment of the definition in the ''normal val list'' section so that we'll convert the form to the canonical form, to ensure the correct end even if we start with an enfactored map. It can be a one-liner amendment, as simple as "defactor it", or rewritten to focus on the new reduction method.

: Finally, the irref form should be removed as it's almost never used. We cover it in another page i.e. ''generator size manipulation'', just like other forms. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:07, 28 September 2021 (UTC)

@@ Line 1: / Line 1: @@
 {{WSArchiveLink}}
-= Smith normal form =
+== Smith normal form ==
 I noticed "Smith normal form" was added to this page as a name for the form of the normal val list. I've done a couple examples and I'm pretty sure that [https://en.wikipedia.org/wiki/Smith_normal_form Smith normal form] is not equivalent to this process; e.g. meantone's normal val list would be [⟨1 0 -4] ⟨0 1 4]] while I suppose you could say meantone's val list in Smith normal form (taking the first k rows only, as is demonstrated in the penultimate paragraph of the page on [[saturation]]) would be [⟨1 0 4] ⟨0 1 -4]]. If this is an attempt to name this other form for Gene Ward Smith, I think it's not a great idea, because of the preexistence of the linked Smith normal form which was named for Henry John Stephen Smith. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:24, 23 June 2021 (UTC)
@@ Line 9: / Line 9: @@
 :: Oh, no big deal at all. Thanks for updating the page. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 15:17, 24 June 2021 (UTC)
-= how best to handle the new canonical form for RTT matrices w/r/t normal form =
+== how best to handle the new canonical form for RTT matrices w/r/t normal form ==
 I recently published [[Canonical form|a page on the xen wiki proposing a canonical form for RTT mappings (or comma-bases)]]. This new page of mine solves a problem that this page seems to have set out to solve but not finished the job: establishing a form for RTT matrices which ''uniquely identifies them'', for a definition of uniqueness that is appropriate to the RTT domain. And so my page refers to this page in several places, mostly critiquing it.
@@ Line 20: / Line 20: @@
 And as for this page itself: I am not saying that it is harmful or that there is nothing of value on it. Far from it! There's some good thinking here. But I do wonder what people here think about what the best approach should be for recognizing its relationship with the new canonical form. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:10, 27 September 2021 (UTC)
+: First of all we must make clear what purposes these pages serve. Imo this page should always be kept up to date and used as the canonical reference. I'm not sure about your view of your ''canonical form'' article. To me it acts more like a development note thereof.
+: Currently the form in all temp pages is the form defined in the ''normal val list'' section, and they are in canonical form already since they are not enfactored to start with. (More precisely, there is not a start but only the end and the end is correct.) So they are in canonical form and we don't need to do anything about them.
+: The important part is the amendment of the definition in the ''normal val list'' section so that we'll convert the form to the canonical form, to ensure the correct end even if we start with an enfactored map. It can be a one-liner amendment, as simple as "defactor it", or rewritten to focus on the new reduction method.
+: Finally, the irref form should be removed as it's almost never used. We cover it in another page i.e. ''generator size manipulation'', just like other forms. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:07, 28 September 2021 (UTC)