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

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 ...

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 ...

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.

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

ExpandDenominator[expr] expands out products and powers that appear as denominators in expr.

Sometimes you may want to set up functions where certain arguments, if omitted, are given "default values". The pattern x_:v stands for an object that can be omitted, and if ...

RootSum[f, form] represents the sum of form[x] for all x that satisfy the polynomial equation f[x] == 0.