Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...

Numerical sums, products and integrals. Here is a numerical approximation to ∑_(i=1)^∞((1)/(i^3)). NIntegrate can handle singularities in the integration region.

Mathematica provides various options for labeling three-dimensional graphics. Some of these options are directly analogous to those for two-dimensional graphics, discussed in ...

Ways to label two-dimensional plots. Here is a plot, using the default Axes->True. Setting Frame->True generates a frame with axes, and removes tick marks from the ordinary ...

Ways to construct nested lists. This generates a table corresponding to a 2×3 nested list. This generates an array corresponding to the same nested list.

Testing for numeric quantities. Pi is a symbol, so Pi+3 is not explicitly a number. It does however have a numerical value.

In some cases you may need to specify pattern sequences that are more intricate than things like x__ or x..; for such situations you can use PatternSequence[p_1,p_2,…]. ...

Permutations are basic elements in algebra. They have a natural non-commutative product (as matrices do as well), and hence can encode highly nontrivial structures in a ...

Mathematica can work with polynomials whose coefficients are in the finite field Z_p of integers modulo a prime p. Functions for manipulating polynomials over finite fields. ...

Mathematica usually works by taking whatever input you give, and then processing it. Sometimes, however, you may want to have a program you write explicitly request more ...