Content deleted Content added
No edit summary Tags: Visual edit Mobile edit Mobile web edit |
Fixed typo Tags: canned edit summary Mobile edit Mobile app edit iOS app edit |
||
Line 6:
Given any function ''f'' in ''n'' variables with values in an [[abelian group]], a symmetric function can be constructed by summing values of ''f'' over all permutations of the arguments. Similarly, an anti-symmetric function can be constructed 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.
==
* Consider the real function
| |||