Domain basis: Difference between revisions
Cmloegcmluin (talk | contribs) →Merging: gentle introduction |
Cmloegcmluin (talk | contribs) →Intersecting: another gentle introduction |
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# Canonicalize. | # Canonicalize. | ||
== | == But first: a gentle introduction == | ||
As with the interval basis merge, it is sometimes practical to eyeball the answer. The basic idea is just to take only formal primes that in both of the interval bases. So the intersection of 2.3.5 and 2.3.7 is plainly just 2.3. But other times the answer may not be so clear. Such as: What is the intersection of 2.5/3.9/7 and 2.9.5? Hint: It's not just 2! | |||
== Example == | == Example == | ||
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Canonicalization time. That's already in matrix form, and HNF even (yes, we use HNF again here). No all zeros columns. Converted back to a list of numbers we at first have 2.9/25. But the last step is to take the undirected value, which reciprocates 9/25 to its super form which is 25/9. So the intersection of 2.5/3 and 2.9.5 is 2.25/9. | Canonicalization time. That's already in matrix form, and HNF even (yes, we use HNF again here). No all zeros columns. Converted back to a list of numbers we at first have 2.9/25. But the last step is to take the undirected value, which reciprocates 9/25 to its super form which is 25/9. So the intersection of 2.5/3 and 2.9.5 is 2.25/9. | ||
== Notation == | |||
The notation for interval basis intersecting we'll use here is just the intersection symbol: <math>B_1∩B_2</math>. | |||
= Changing interval basis = | = Changing interval basis = | ||