The constraint associated with each edge is now the symmetric difference of its component constraint sets conditional on the intersection of its constraint sets.
12.
A family of sets closed under the symmetric difference operation can be described algebraically as a vector space over the two-element finite field modulo 2.
13.
Later authors changed the interpretation, commonly reading it as exclusive or, or in set theory terms symmetric difference; this step means that addition is always defined.
14.
It consists of a set of cycles that can be combined, using symmetric differences, to form every Eulerian subgraph, and that is minimal with this property.
15.
Each 6-cycle is disjoint from exactly three other 6-cycles; among these three 6-cycles, each one is the symmetric difference of the other two.
16.
Conversely, suppose that a matching M is not optimal, and let P be the symmetric difference M \ oplus M ^ * where M ^ * is an optimal matching.
17.
This is same as doing the symmetric difference ( i . e . remove edges common to previous matching and add non-common edges in augmented path in new matching ).
18.
The treedist program in the PHYLIP suite offers this function, as does the RAxML _ standard package and the DendroPy Python library ( under the name " symmetric difference metric " ).
19.
One can show that for a regular vine, the symmetric difference of the component constraint sets is always a doubleton and that each pair of variables occurs exactly once as constrained variables.
20.
Given a Boolean algebra " B ", we turn " B " into a Boolean ring by using the symmetric difference as addition and the meet operation \ land as multiplication.
