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The article presents the procedures for computing the finite Fourier transform of a complex data vector which is based on the Cooley-Tukey algorithm. An overview of the complextransform and realtransform's procedures are offered. Either the complex Fourier transform or its inverse are the procedure computed by complextransform, while realtransform computes either the Fourier coefficients of a sequence of real data points or evaluates a fourier series. The topic also includes orthogonal transformation, permutations, and spectral analysis.

The article discusses matrix transposition in place. Several algorithms have been used for solving the problem of transposing a rectangular matrix in place. A significantly speedier algorithm is described, based on a number of theoretical analysis, and experimentally compared with existing algorithms. The theory calls for the storing of a matrix in a vector in one of two ways, either rowwise or columnwise. The matrix is transposed by its conversion from one mode of storage to the other through permutation.

The article discusses four combinatorial algorithms. The different algorithms, by successive calls, produce a sequence of all combinatorial configurations belonging to the appropriate type, such as PERMU for permutations, COMBI for combinations of natural numbers, COMPOMIN for the composition of an integer, and COMPOMAX, which is the same as COMPOMIN but with maximum for each term. The four algorithms uses a single operation for producing a new configuration from the old one, in which PERMU is transformed by a single transposition of two adjacent elements, COMBI by replacing a single element x by a y, and COMPOMIN by changing the values of two adjacent terms.