0 the quality of having parts that match each other, especially in a way that is attractive, or similarity of shape or contents: --
1 the quality of having parts on either side or half that match each other, esp. in an attractive way, or are the same size or shape --
The par t rotational symmetries are measured with respect to the par t inser tion axis and an axis perpendicular to the inser tion axis.
The other 40 matrices, which involve nontrivial permutations of the a(1) subalgebras, do not generate symmetries of the system.
Examples of such features are symplecticity, volume preservation, integrals, symmetries, and many more.
Furthermore, rules representing symmetries can be automatically detected using the modified algorithm.
Correspondingly, these symmetries imply the conservation laws of momentum and angular momentum.
We first describe the computational results and then discuss the symmetries of the numerical solutions in order to establish the underlying bifurcation structure.
We turn now to continuous translation symmetries, which do not have analogues in crystal structure.
Nonlinearizable holomorphic dynamics having an uncountable number of symmetries.