Exponent[expr, form] gives the maximum power with which form appears in the expanded form of expr. Exponent[expr, form, h] applies h to the set of exponents with which form ...

In just one Mathematica command, you can easily specify a calculation that is far too complicated for any computer to do. For example, you could ask for ...

DensityHistogram[{{x_1, y_1}, {x_2, y_2}, ...}] plots a density histogram of the values {x_i, y_i}.DensityHistogram[{{x_1, y_1}, {x_2, y_2}, ...}, bspec] plots a density ...

Mathematica is uniquely suited for processing symbolic expressions because of its powerful pattern-matching abilities and large collection of built-in structural manipulation ...

ShortestPathSpanningTree[g, v] constructs a shortest-path spanning tree rooted at v, so that a shortest path in graph g from v to any other vertex is a path in the tree.

ButcherPlot[tree] gives a plot of tree.ButcherPlot[{tree_1, tree_2, ...}] gives an array of plots of tree_1, tree_2, ....

Mathematica offers great flexibility for adding text to graphics; you can add text interactively using the Drawing Tools palette or programmatically using various graphics ...

DeleteCases[expr, pattern] removes all elements of expr that match pattern. DeleteCases[expr, pattern, levelspec] removes all parts of expr on levels specified by levelspec ...

SymmetricReduction[f, {x_1, ..., x_n}] gives a pair of polynomials {p, q} in x_1, ..., x_n such that f == p + q, where p is the symmetric part and q is the ...

Through[p[f_1, f_2][x]] gives p[f_1[x], f_2[x]]. Through[expr, h] performs the transformation wherever h occurs in the head of expr.