Saturation, torsion, and contorsion: Difference between revisions
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These aren't "the same effect but slightly different"; some of them are utter antonyms. Otoh we should group up torsion and contorsion since they're similar |
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This is a general introduction to this concept; for a more mathematical take on this, see [[Mathematical theory of saturation]]. | This is a general introduction to this concept; for a more mathematical take on this, see [[Mathematical theory of saturation]]. | ||
== Saturation == | == Saturation == | ||
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'''''Defactoring''''' is the term used in the writings of [[Dave Keenan]] and [[Douglas Blumeyer]]<ref>a list of which can be found [[Douglas Blumeyer #Some of his work here on the wiki|here]]</ref> as a proposed replacement for ''saturation''. | '''''Defactoring''''' is the term used in the writings of [[Dave Keenan]] and [[Douglas Blumeyer]]<ref>a list of which can be found [[Douglas Blumeyer #Some of his work here on the wiki|here]]</ref> as a proposed replacement for ''saturation''. | ||
== Torsion == | == Torsion and contorsion == | ||
'''Torsion''' is the opposite of saturation, but only regarding comma bases; in other words, a comma basis is either saturated, or it ''has torsion''. | '''Torsion''' is the opposite of saturation, but only regarding comma bases; in other words, a comma basis is either saturated, or it ''has torsion''. | ||
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The term has been used since at least as early as 1932<ref>https://scholar.google.com/scholar?q=%22torsion+group%22&hl=en&as_sdt=0%2C5&as_ylo=1900&as_yhi=1940</ref><ref>https://math.stackexchange.com/questions/300586/where-does-the-word-torsion-in-algebra-come-from</ref> and came to RTT from the mathematical field of group theory. | The term has been used since at least as early as 1932<ref>https://scholar.google.com/scholar?q=%22torsion+group%22&hl=en&as_sdt=0%2C5&as_ylo=1900&as_yhi=1940</ref><ref>https://math.stackexchange.com/questions/300586/where-does-the-word-torsion-in-algebra-come-from</ref> and came to RTT from the mathematical field of group theory. | ||
'''Contorsion''' is the opposite of saturation, but only regarding mappings; in other words, a mapping is either saturated, or it ''has contorsion'' (or we can say that it ''is contorted''). The greatest factor of a mapping has been called its '''contorted order'''. | '''Contorsion''' is the opposite of saturation, but only regarding mappings; in other words, a mapping is either saturated, or it ''has contorsion'' (or we can say that it ''is contorted''). The greatest factor of a mapping has been called its '''contorted order'''. | ||