Saturation, torsion, and contorsion: Difference between revisions

Line 12:

Saturation algorithms correct for this problem, ensuring our ability to most simply — and thereby uniquely — identify temperaments using only matrices. This need can otherwise be satisfied using [[wedgie]]s. The simplest and fastest algorithm for saturating matrices is called [[column Hermite defactoring]]. For more information on such algorithms, see [[Saturation algorithms]].

The term saturation was coined by Nicolas Bourbaki in 1972<ref>https://pdfcoffee.com/commutative-algebra-bourbaki-pdf-free.html</ref>, working in the field of commutative algebra. It came to RTT via [[Gene Ward Smith]] and [[Graham Breed]]'s observations of the work of the mathematician William Stein and his Sage software<ref>It may also have come through PARI/GT.</ref>.

The term saturation was coined by Nicolas Bourbaki in 1972<ref>https://pdfcoffee.com/commutative-algebra-bourbaki-pdf-free.html</ref>, working in the field of commutative algebra. It came to RTT via [[Gene Ward Smith]] and [[Graham Breed]]'s observations of the work of the mathematician William Stein and his Sage software<ref>It may also have come through PARI/GT.</ref>. The earliest identified terminology for this concept was in 1861 by H. J. S. Smith<ref>H. J. S. Smith is the creator of the Smith Normal Form used in Gene Ward Smith's saturation algorithm.</ref> who called saturated matrices "prime matrices"<ref>See "On Systems of Linear Indeterminate Equations and Congruences", which can be accessed here: https://www.jstor.org/stable/pdf/108738.pdf, where Smith also describes the GCD of a matrix's minor determinants as its "greatest divisor" (though neither of this term nor "prime matrix" seems to have caught on).</ref>.

== Torsion ==

@@ Line 12: / Line 12: @@
 Saturation algorithms correct for this problem, ensuring our ability to most simply — and thereby uniquely — identify temperaments using only matrices. This need can otherwise be satisfied using [[wedgie]]s. The simplest and fastest algorithm for saturating matrices is called [[column Hermite defactoring]]. For more information on such algorithms, see [[Saturation algorithms]].
-The term saturation was coined by Nicolas Bourbaki in 1972<ref>https://pdfcoffee.com/commutative-algebra-bourbaki-pdf-free.html</ref>, working in the field of commutative algebra. It came to RTT via [[Gene Ward Smith]] and [[Graham Breed]]'s observations of the work of the mathematician William Stein and his Sage software<ref>It may also have come through PARI/GT.</ref>.
+The term saturation was coined by Nicolas Bourbaki in 1972<ref>https://pdfcoffee.com/commutative-algebra-bourbaki-pdf-free.html</ref>, working in the field of commutative algebra. It came to RTT via [[Gene Ward Smith]] and [[Graham Breed]]'s observations of the work of the mathematician William Stein and his Sage software<ref>It may also have come through PARI/GT.</ref>. The earliest identified terminology for this concept was in 1861 by H. J. S. Smith<ref>H. J. S. Smith is the creator of the Smith Normal Form used in Gene Ward Smith's saturation algorithm.</ref> who called saturated matrices "prime matrices"<ref>See "On Systems of Linear Indeterminate Equations and Congruences", which can be accessed here: https://www.jstor.org/stable/pdf/108738.pdf, where Smith also describes the GCD of a matrix's minor determinants as its "greatest divisor" (though neither of this term nor "prime matrix" seems to have caught on).</ref>.
 == Torsion ==