Val: Difference between revisions

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To notate a subgroup val, we typically precede the "bra" notation with an indicator regarding the subgroup (and choice of basis). For instance, the patent val for 12 equal on the 2.3.7 subgroup is often notated "2.3.7 {{val|12 19 34}}". If the subgroup indicator isn't present, the subgroup can be inferred from context. It is very typical for a val with no explicit subgroup indicator to be interpreted as representing some prime limit, e.g. {{val| a b c }} would represent a 5-limit val.

Note that we could, for instance, use a different basis for the same subgroup - for instance, we could instead write "2.3.21 {{val| 12 19 43 }}", which is the 12 equal patent val in the "2.3.21" subgroup. Since the "2.3.21" subgroup is the same as the "2.3.7" subgroup, just written with a different basis, these two apparently "different" svals represent the same map from this subgroup to a rank-1 generator chain. (It is a matter of semantics if these are thought of as "different" svals or "the same sval" written using a different basis.)

Note that we could, for instance, use a different basis for the same subgroup - for instance, we could instead write "2.3.21 {{val| 12 19 53 }}", which is the 12 equal patent val in the "2.3.21" subgroup. Since the "2.3.21" subgroup is the same as the "2.3.7" subgroup, just written with a different basis, these two apparently "different" svals represent the same map from this subgroup to a rank-1 generator chain. (It is a matter of semantics if these are thought of as "different" svals or "the same sval" written using a different basis.)

Svals can also be written using subgroups that don't involve primes, e.g. 2.3.7.13/5 {{val| 46 73 129 63 }}.

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 To notate a subgroup val, we typically precede the "bra" notation with an indicator regarding the subgroup (and choice of basis). For instance, the patent val for 12 equal on the 2.3.7 subgroup is often notated "2.3.7 {{val|12 19 34}}". If the subgroup indicator isn't present, the subgroup can be inferred from context. It is very typical for a val with no explicit subgroup indicator to be interpreted as representing some prime limit, e.g. {{val| a b c }} would represent a 5-limit val.
-Note that we could, for instance, use a different basis for the same subgroup - for instance, we could instead write "2.3.21 {{val| 12 19 43 }}", which is the 12 equal patent val in the "2.3.21" subgroup. Since the "2.3.21" subgroup is the same as the "2.3.7" subgroup, just written with a different basis, these two apparently "different" svals represent the same map from this subgroup to a rank-1 generator chain. (It is a matter of semantics if these are thought of as "different" svals or "the same sval" written using a different basis.)
+Note that we could, for instance, use a different basis for the same subgroup - for instance, we could instead write "2.3.21 {{val| 12 19 53 }}", which is the 12 equal patent val in the "2.3.21" subgroup. Since the "2.3.21" subgroup is the same as the "2.3.7" subgroup, just written with a different basis, these two apparently "different" svals represent the same map from this subgroup to a rank-1 generator chain. (It is a matter of semantics if these are thought of as "different" svals or "the same sval" written using a different basis.)
 Svals can also be written using subgroups that don't involve primes, e.g. 2.3.7.13/5 {{val| 46 73 129 63 }}.