Extended bra–ket notation: Difference between revisions

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When a bra and a ket are put together, the dot product is taken, and the result is a scalar (a single number). In order to be compatible in this way, the bra and ket must at least have the same number of entries, so that each of their entries will pair up for a product.

So mapping 45/32 with 7-ET would be notated as {{~~vmprod~~| 7 11 16 | -5 2 1 }} = {{nowrap|7 ~~⋅ -5~~}} + {{nowrap|11 ~~⋅~~ 2}} + {{nowrap|16 ~~⋅~~ 1}} = ~~-35~~ + 22 + 16 = 3.

So mapping 45/32 with 7-ET would be notated as {{nowrap|{{vmp| 7 11 16 | -5 2 1 }} {{=}} {{nowrap|7 ⋅ −5}} + {{nowrap|11 ⋅ 2}} + {{nowrap|16 ⋅ 1}}}} {{nowrap|{{=}} −35 + 22 + 16}} = 3.

Or mapping the GC-vector for porcupine's ~45/32 with a generator tuning map like {{bra| 1200 162.737 }} would look like {{~~vmprod~~| 1200 162.737 | 2 -11 }} = {{~~nowrap|~~1200 ~~⋅~~ 2}} + {{nowrap|~~162.737 ⋅ -11}}~~ = 2400 + ~~-1790~~.107 = 609.893.

Or mapping the GC-vector for porcupine's ~45/32 with a generator tuning map like {{bra| 1200 162.737 }} would look like {{nowrap|{{vmp| 1200 162.737 | 2 -11 }} {{=}} 1200 ⋅ 2 + 162.737 ⋅ −11}} {{nowrap|= 2400 + −1790.107}} = 609.893.

== Extensions ==

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 When a bra and a ket are put together, the dot product is taken, and the result is a scalar (a single number). In order to be compatible in this way, the bra and ket must at least have the same number of entries, so that each of their entries will pair up for a product.
-So mapping 45/32 with 7-ET would be notated as {{vmprod| 7 11 16 | -5 2 1 }} = {{nowrap|7 &#8901; -5}} + {{nowrap|11 &#8901; 2}} + {{nowrap|16 &#8901; 1}} = -35 + 22 + 16 = 3.
+So mapping 45/32 with 7-ET would be notated as {{nowrap|{{vmp| 7 11 16 | -5 2 1 }} {{=}} {{nowrap|7 ⋅ −5}} + {{nowrap|11 ⋅ 2}} + {{nowrap|16 ⋅ 1}}}} {{nowrap|{{=}} −35 + 22 + 16}} =&nbsp;3.
-Or mapping the GC-vector for porcupine's ~45/32 with a generator tuning map like {{bra| 1200 162.737 }} would look like {{vmprod| 1200 162.737 | 2 -11 }} = {{nowrap|1200 &#8901; 2}} + {{nowrap|162.737 &#8901; -11}} = 2400 + -1790.107 = 609.893.
+Or mapping the GC-vector for porcupine's ~45/32 with a generator tuning map like {{bra| 1200 162.737 }} would look like {{nowrap|{{vmp| 1200 162.737 | 2 -11 }} {{=}} 1200 ⋅ 2 + 162.737 ⋅ −11}} {{nowrap|= 2400 + −1790.107}} =&nbsp;609.893.
 == Extensions ==