The strategy known as "The Conjugacy Principle", the mathematical operation known as conjugation -- the primary determination in quantics -- perhaps began in group theory.

A group is

• a set of elements,
• an operation on each element ("multiplication", often simply concatenation),
• constraints such that
  • the set be closed under this operation (sameness of type, "All in the Family"),
  • and every element have an inverse such that their "product" is the identity of the group.

Any subset of a group compliying with these constraints constitutes a subgroup -- including (trivially) the group itself, on the one hand, and the Identity alone, on the other. Then conjugacy applies to subgroups.

Given group G, with elements d, e, ..., such that d^-1 the inverse of of d, with concatenation as group operation. And consider the result:

			ded-1 = f

If the result, f is also in the group, then e,f are said to be mutual conjugates. As an equivalence relation (with properties of reflexivity, symmetry, transitivity), conjugacy partitions a group into equivalence classes.

This can be readily graphed as

				--------f--------->
                                |                 ^
                              e |                 |
                                |                 | ded-1
                                |                 |
                                ---------de------->

The Principle of Comjugacy applies in different forms in different fields and as "bypass" (the name and notion of Canadian mathematician, Z. A. Melzak) provides perhaps the most powerful means we have for invention and information research.

Applied to matrices and vectors, it determines the eigenvalues and eignvectors of a given vector. These are "fixpoints" of the vector: conjugation applied to them results in no change. The resultant matrix has all zero entries except for the diagonal, so that the "determinant" of the matrix is easily calculated.

When the vector represents a wave function in quantics, this results in probabilities for the measures of the wave vector, providing the primary result in quantics.

Clearly, when the graph above is collapsed, it becomes an antitone.

So the primary algorithm in quantics is antitonic.