mai'u'ei

valsi

mai'u'ei

type

experimental cmavo

creator

krtisfranks

time entered

Tue Oct 29 01:41:59 2024  

English

Definition #73677 - Preferred

 

selma'o

VUhU3

definition

mekso unary operator: Levi-Civita symbol; for input n-tuple MATH

$(a_1, a_2,$

(a₁, a₂, ... , a_n), where n is a strictly positive integer, the output is MATH

$\varepsilon_{a_1, a_2, ..., a_n}$

<img alt="$\varepsilon_Template:a 1, a 2, ..., a n^{}$" src="/jbovlaste_export/vDiUrtORQI/img1.png" style="height: 1.96ex; vertical-align: -1.01ex; "/>, where MATH

$\varepsilon$

<img alt="$\varepsilon$" src="/jbovlaste_export/vDiUrtORQI/img2.png" style="height: 1.12ex; vertical-align: -0.12ex; "/> is the Levi-Civita symbol under the convention of mapping (1, 2, ..., n) to 1.

notes

If any at least two elements of the input tuple are mutually equal (id est: if there exists i and j which are strictly positive integers which do not exceed n such that a_i = a_j, where the input tuple is as defined supra), then the output is 0; else, the output is sgn MATH

$((a_1, a_2,$

((a₁, a₂, ... , a_n)), where the input to the sgn function there is a permutation denoted in one-line permutation notation. This format is somewhat consistent with index notation in tensor calculus, but treats the indices as ordered entries of a tuple. More generally, the Levi-Civita symbol may be defined for any function f which maps space S to S; in such case, the input could be f instead of the aforementioned tuple. Covariant and contravariant Levi-Civita tensors can also be defined. See also: "mai'u'e", "mai'u".

gloss words

• Levi-Civita symbol

created by

krtisfranks

vote information

1

time

Tue Oct 29 01:47:41 2024

Examples

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