Domain basis: Difference between revisions

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Given an interval, comma basis, or mapping — anything that has an associated interval basis — it is possible to change it from one interval basis to another. We can accomplish this using an '''interval rebase''', an object that works like a two-way bridge between two interval bases.

Elsewhere, these have been called [[subgroup basis matrices]], but that terminology will not be used here, for the same reasons as are described in the last section of this article (here: [[User:Cmloegcmluin/Interval basis#Terminology]]) as well as the additional reason that such a name can easily be conflated with the interval basis itself.

Elsewhere, these have been called [[subgroup basis matrices]], but that terminology will not be used here, for the same reasons as are described in the last section of this article (here: [[User:Cmloegcmluin/Interval basis#Terminology: interval basis vs. subgroup]]) as well as the additional reason that such a name can easily be conflated with the interval basis itself.

As discussed earlier, only certain interval basis changes are possible: (here: [[User:Cmloegcmluin/Interval basis#Application: determining whether it is possible to change the interval subspace]]). To quickly recap here, it is only possible to change between interval subspaces where one is a subspace of the other. So when we say a given interval rebase works like a two-way bridge, there's a more specific way to say what we mean: an interval rebase allows us to change either ''from the subspace to the superspace'', or ''from the superspace to the subspace''. Which direction we go just depends on which side we enter the bridge from: the right side or the left side.

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 Given an interval, comma basis, or mapping — anything that has an associated interval basis — it is possible to change it from one interval basis to another. We can accomplish this using an '''interval rebase''', an object that works like a two-way bridge between two interval bases.
-Elsewhere, these have been called [[subgroup basis matrices]], but that terminology will not be used here, for the same reasons as are described in the last section of this article (here: [[User:Cmloegcmluin/Interval basis#Terminology]]) as well as the additional reason that such a name can easily be conflated with the interval basis itself.
+Elsewhere, these have been called [[subgroup basis matrices]], but that terminology will not be used here, for the same reasons as are described in the last section of this article (here: [[User:Cmloegcmluin/Interval basis#Terminology: interval basis vs. subgroup]]) as well as the additional reason that such a name can easily be conflated with the interval basis itself.
 As discussed earlier, only certain interval basis changes are possible: (here: [[User:Cmloegcmluin/Interval basis#Application: determining whether it is possible to change the interval subspace]]). To quickly recap here, it is only possible to change between interval subspaces where one is a subspace of the other. So when we say a given interval rebase works like a two-way bridge, there's a more specific way to say what we mean: an interval rebase allows us to change either ''from the subspace to the superspace'', or ''from the superspace to the subspace''. Which direction we go just depends on which side we enter the bridge from: the right side or the left side.