Content deleted Content added
actually the whole {{about}} is unnecessary, since the lead clearly explains and dispatches to related articles; also limited to one wikilink for each article |
→Symmetrization: complement |
||
Line 9:
== Symmetrization ==
{{main|Symmetrization}}
Given any function ''f'' in ''n'' variables with values in an abelian group, it can be made into a symmetric function by summing it over all permutations of the arguments. Similarly, it can be made into an anti-symmetric function by summing over [[even permutation]]s and subtracting the sum over [[odd permutation]]s. These operations are of course not invertible, and could well result in a function that is identically zero for nontrivial functions ''f''. The only general case where ''f'' can be recovered if both its symmetrization and anti-symmetrization are known is when ''n'' = 2 and the abelian group admits a division by 2 (inverse of doubling); then ''f'' is equal to half the sum of its symmetrization and its anti-symmetrization.
== Applications ==
| |||