Talk:Mathematical theory of saturation: Difference between revisions
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Cmloegcmluin (talk | contribs) edge case? |
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I have been working on the topic of saturation off and on for months now, with the assistance of Dave Keenan. We cannot figure out how the algorithm that is used here — the one that uses the Smith Decomposition (named for Henry John Stephen Smith; no relation to Gene Ward Smith, as far as we know) — to desaturate matrices ''works''. We've tried devising our own methods that feel more straightforward, but they fail on edge cases. At this point Gene's method here feels a bit like magic. Can anyone explain how it works, or maybe at least where it came from — Gene's own ingenuity, or perhaps from the Sage math software (where we suspect he draws his name for the concept, "saturation")? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:53, 1 August 2021 (UTC) | I have been working on the topic of saturation off and on for months now, with the assistance of Dave Keenan. We cannot figure out how the algorithm that is used here — the one that uses the Smith Decomposition (named for Henry John Stephen Smith; no relation to Gene Ward Smith, as far as we know) — to desaturate matrices ''works''. We've tried devising our own methods that feel more straightforward, but they fail on edge cases. At this point Gene's method here feels a bit like magic. Can anyone explain how it works, or maybe at least where it came from — Gene's own ingenuity, or perhaps from the Sage math software (where we suspect he draws his name for the concept, "saturation")? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:53, 1 August 2021 (UTC) | ||
== Edge case? == | |||
I think that if the saturation algorithm begins with a matrix with a row of all zeroes, it fails as it is currently implemented, e.g. [⟨12 19 28] ⟨0 0 0]⟩ → [⟨12 19 28] ⟨-9 -14 -21]⟩. Probably we need to insert a step at the beginning where all-zero rows are eliminated. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 21:34, 2 August 2021 (UTC) | |||
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Revision as of 21:34, 2 August 2021
Origin of desaturating algorithm
I have been working on the topic of saturation off and on for months now, with the assistance of Dave Keenan. We cannot figure out how the algorithm that is used here — the one that uses the Smith Decomposition (named for Henry John Stephen Smith; no relation to Gene Ward Smith, as far as we know) — to desaturate matrices works. We've tried devising our own methods that feel more straightforward, but they fail on edge cases. At this point Gene's method here feels a bit like magic. Can anyone explain how it works, or maybe at least where it came from — Gene's own ingenuity, or perhaps from the Sage math software (where we suspect he draws his name for the concept, "saturation")? --Cmloegcmluin (talk) 22:53, 1 August 2021 (UTC)
Edge case?
I think that if the saturation algorithm begins with a matrix with a row of all zeroes, it fails as it is currently implemented, e.g. [⟨12 19 28] ⟨0 0 0]⟩ → [⟨12 19 28] ⟨-9 -14 -21]⟩. Probably we need to insert a step at the beginning where all-zero rows are eliminated. --Cmloegcmluin (talk) 21:34, 2 August 2021 (UTC)
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