Manipulate[expr, {u, u_min, u_max}] generates a version of expr with controls added to allow interactive manipulation of the value of u. Manipulate[expr, {u, u_min, u_max, ...

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 ...

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 ...

ImageAlign[image_1, image_2] returns a version of image_2 that is aligned with image_1.

GeodesyData["name", " property"] gives the value of the specified property for a named geodetic datum or reference ellipsoid.GeodesyData[{a, b}, " property"] gives the value ...

ButterflyGraph[n] gives the order-n butterfly graph. ButterflyGraph[n, b] gives the base-b order-n butterfly graph.

CycleGraph[n] gives the cycle graph with n vertices C_n.

HypercubeGraph[n] gives the n-dimensional hypercube graph Q_n.

New functions Animate and ListAnimate have been added to the built-in Mathematica kernel. SpinShow is replaced by interactive rotation of three-dimensional graphics.