Talk:Mathematical theory of saturation: Difference between revisions
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Cmloegcmluin (talk | contribs) →Edge case?: never mind: just needed to use MatrixRank instead of length, and the description of the algorithm works fine as it's written, because it says to use rank |
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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) | ||
: If anyone comes to this later, Dave and I managed to answer our own question. Our findings are compiled here: [[Canonical_form#defactoring_methods]] --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 06:15, 27 September 2021 (UTC) | |||
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Revision as of 06:15, 27 September 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)
- If anyone comes to this later, Dave and I managed to answer our own question. Our findings are compiled here: Canonical_form#defactoring_methods --Cmloegcmluin (talk) 06:15, 27 September 2021 (UTC)
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