Some example programs

Some example programs

ex12.c

asks for an INTEGER and computes the cycle indices of the corresponding cyclic, dihedral, alternating and symmetric groups.

ex13.c

asks for two INTEGERS n and m, computes the cycle index of C_n and then for 1≤ i≤ m the variable x_i is replaced by 1+zⁱ.

ex14.c

asks for a VECTOR object; each entry of this object must be a PERMUTATION object (all of the same length). These are the generators of a group and the cycle index of this group is computed.

ex20.c

asks for two INTEGERS n and m, computes the cycle indices of C_n,D_n,A_n and S_n and then each x_i is replaced by ∑_j=1^m z_jⁱ.

ex30.c

asks for two INTEGERS k,q and computes the cycle index of GL_k(q), the order of GL_k(q) and the number of monic irreducible polynomials of degree k over GF(q).

ex31.c

computes the 3-dimensional cycle index of the group of all rotations of the cube. Then 3 INTEGERS n₁,n₂,n₃ must be input and the number of different colourings of the cube, where the vertices can be coloured with n₁ colons, the edges with n₂ colours and the faces with n₃ colours, is computed.

ex32.c

asks for an INTEGER n computes the cycle index of S_n and of the induced actions on the set of all 2-sets, all k-subsets and on the power-set.

ex33.c

asks for an INTEGER n computes the cycle index of S_n and of the induced actions on pairs, and k-tuples.

ex34.c

asks for an INTEGER n and computes the number of classes of linear graphs, directed graphs (with and without loops and with loops and edges distinguished), oriented graphs and tournaments and superpositions of a linear and a directed graph with n vertices.

ex35.c

asks for two INTEGER n,m computes the cycle indices of of the direct sum, the direct product, and the wreath product (acting on {1,...,n} × {1,...,m} ) of S_n and S_m.

ex36.c

asks for an INTEGER n and computes the number of classes of bijective functions on {1,...,n}, where D_n acts both on the domain and the range. Then it asks for another INTEGER m, and computes the Redfield cup and cap product of m copies of D_n.

Some example programs