ListNecklaces[n, c, Cyclic] returns all distinct necklaces whose beads are colored by colors from c. Here c is a list of n, not necessarily distinct colors, and two colored ...

MakeDirected[g] constructs a directed graph from a given undirected graph g by replacing each undirected edge in g by two directed edges pointing in opposite directions.

NecklacePolynomial[n, c, Cyclic] returns a polynomial in the colors in c whose coefficients represent numbers of ways of coloring an n-bead necklace with colors chosen from ...

NumberOfNecklaces[n, nc, Cyclic] returns the number of distinct ways in which an n-bead necklace can be colored with nc colors, assuming that two colorings are equivalent if ...

OrbitInventory[ci, x, w] returns the value of the cycle index ci when each formal variable x[i] is replaced by w. OrbitInventory[ci, x, weights] returns the inventory of ...

ShortestPath[g, start, end] finds a shortest path between vertices start and end in graph g.

ToUnorderedPairs[g] constructs a list of unordered pairs representing the edges of graph g. Each edge, directed or undirected, results in a pair in which the smaller vertex ...

The functionality of Calculus`DSolveIntegrals` is now available in the built-in Mathematica kernel function DSolve.

RevolutionPlot3D and SphericalPlot3D have been added to the built-in Mathematica kernel. RevolutionPlot3D includes the functionality of CylindricalPlot3D.

New function FourierDCT has been added to the built-in Mathematica kernel. New function FourierDST has been added to the built-in Mathematica kernel.