Domain basis: Difference between revisions

Line 188:

Then, each resulting vector becomes a column of our desired matrix.

So, for example, 2.9/7.5 in the form of a matrix <math>F</math> ("basis matrix") looks like this. For convenience, we've labeled each column with the basis element, and each row with the prime:

So, for example, 2.9/7.5 in the form of a matrix <math>B</math> ("basis matrix") looks like this. For convenience, we've labeled each column with the basis element, and each row with the prime:

Line 227:

To make a popular culture reference, you may be starting to get an [[Wikipedia:Inception|Inception]] vibe here: we're breaking primes into deeper primes (perhaps we could call this "intervalception"?). Indeed, this might all seem dizzyingly abstract, but fortunately, we don't need to go any deeper than this. And we assure you that this matrix representation of the domain basis (again, called the "basis matrix") will be quite helpful for comparing different domain bases.

== Column Hermite normal form ==

@@ Line 188: / Line 188: @@
 Then, each resulting vector becomes a column of our desired matrix.
-So, for example, 2.9/7.5 in the form of a matrix <math>F</math> ("basis matrix") looks like this. For convenience, we've labeled each column with the basis element, and each row with the prime:
+So, for example, 2.9/7.5 in the form of a matrix <math>B</math> ("basis matrix") looks like this. For convenience, we've labeled each column with the basis element, and each row with the prime:
@@ Line 227: / Line 227: @@
 To make a popular culture reference, you may be starting to get an [[Wikipedia:Inception|Inception]] vibe here: we're breaking primes into deeper primes (perhaps we could call this "intervalception"?). Indeed, this might all seem dizzyingly abstract, but fortunately, we don't need to go any deeper than this. And we assure you that this matrix representation of the domain basis (again, called the "basis matrix") will be quite helpful for comparing different domain bases.
 == Column Hermite normal form ==