"equivalence set" is a correct and usable term in written English.
It can be used in mathematics and logic to refer to two or more elements that have the same meaning in a given context, such as "the set of numbers {2, 4, 6, 8} and their equivalents {1+1, 2+2, 3+3, 4+4} being considered an equivalence set".
Each "n Choose k" (nCk) primitive, fundamentally, is able to map any k-subset of resources chosen from a specified resource equivalence set to a scalar value in R. STRL expressions are functions that map a resource superset to R, and does so in a very succinct form of algebraic expressions.
Equivalence set partitioning is done using a clustering algorithm for symmetry invariant properties.
On the other hand, equivalence set information can be used to restrict the possible symmetry elements to a point where no search is required.
The symmetry elements found in each equivalence set are then intersected so as to make sure they are present in all sets.
A permutation of a vector ({mathbf {D}}_{i*}) corresponding to an element (a_i) will produce another vector ({mathbf {D}}_{j*}) if (a_i) and (a_j) belong to the same equivalence set and the permutation is a symmetry operation.
The spanning vectors for the degenerate spaces also need to transform in corresponding fashion under the point group generators, i.e. they need to be similarly oriented [14], regardless of equivalence set or original basis functions.
Our results suggest that equivalence sets other than class labels, which are abundant in unlabeled visual experience, can be used for self-supervised learning of semantically relevant image embeddings.
Some algorithms use exhaustive search in combination with concepts such as equivalence sets [8] to narrow a search field [9].
Partitioning elements into equivalence sets can be done either prior to or after determination of the point group.
On one hand, determining the symmetry elements prior to the equivalence sets leaves little room for error as well as a simple way of defining the equivalence thresholds.
Since all equivalence sets and spherical harmonics of different angular momentum are treated separately, these bases will simply be denoted S and Y respectively.
