ExpandNumerator[expr] expands out products and powers that appear in the numerator of expr.

Unless f is a flat function, a pattern like f[x_,y_] stands only for instances of the function with exactly two arguments. Sometimes you need to set up patterns that can ...

Ways to get pieces of matrices. Matrices in Mathematica are represented as lists of lists. You can use all the standard Mathematica list-manipulation operations on matrices. ...

DiscreteLyapunovSolve[a, c] finds the numeric solution x of the discrete matrix equation a.x.a\[ConjugateTranspose] - x == c.DiscreteLyapunovSolve[a, b, c] solves a.x.b - x ...

Many computations are conveniently specified in terms of applying functions in parallel to many elements in a list. Mathematica provides a suite of elegant functional ...

GenerateConditions is an option for Integrate, Sum, and similar functions that specifies whether explicit conditions on parameters should be generated in the result.

PolynomialQ[expr, var] yields True if expr is a polynomial in var, and yields False otherwise. PolynomialQ[expr, {var_1, ...}] tests whether expr is a polynomial in the var_i.

TableDirections is an option for TableForm and MatrixForm which specifies whether successive dimensions should be arranged as rows or columns.

Lists are very important and general structures in Mathematica. They allow you to treat collections of all kinds of objects as a single entity. There are many ways to ...

EuclideanDistance[u, v] gives the Euclidean distance between vectors u and v.