Pesticides Registration Manual Home Page You may need Adobe Reader to view files on this page. RepresentativeOperation( m, m1, m2 ) If m1 and m2 are matrices in m, RepresentativeOperation finds a permutation in p that conjugates the permutation corresponding to m1 to the permutation corresponding to m2. If no such permutation exists, it returns false. PermGroup( m ) This function simply returns the permutation group defined above. All group functions such as Centralizer and DerivedSeries are thus applicable to matrix groups. All set theoretic functions such as Size and Intersections are thus applicable to matrix groups.
Pesticide Registration Manual: Appendix D — Examples of Completed Forms | Pesticide Registration | US EPA Jump to main content Links providing EPA examples of completed forms about the pesticide registration process. See EPA’s About PDF page to learn more. Otherwise it takes the union of the orbits of the parent of m on the standard basis vectors). Then it works with the thus defined permutation group p, which is of course isomorphic to m, and finally translates the results back into the matrix group. Centralizer( m, u ) Normalizer( m, u ) SylowSubgroup( m, p ) ConjugacyClasses( m ) This functions all work by solving the problem in the permutation group p and translating the result back. Stabilizer( m, v ) The stabilizer of a vector v that lies in the union of the orbits of the parent of m on the standard basis vectors is computed by finding the stabilizer of the corresponding point in the permutation group p and translating this back.
This section describes how these functions are implemented for matrix groups. Otherwise it translates the permutation back to a matrix. Also computations with large matrix groups are not done very efficiently. We hope to improve this situation in the future, but currently you should be careful not to try too large matrix groups.