PairGroupIndex[g, x] returns the cycle index of the pair group induced by g as a polynomial in x[1], x[2], ....PairGroupIndex[ci, x] takes the cycle index ci of a group g ...

NumberFieldSignature[a] gives the signature of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

Expectation[expr, x \[Distributed] dist] gives the expectation of expr under the assumption that x follows the probability distribution dist. Expectation[expr, x ...

RootOfUnityQ[a] yields True if a is a root of unity, and yields False otherwise.

Expand[expr] expands out products and positive integer powers in expr. Expand[expr, patt] leaves unexpanded any parts of expr that are free of the pattern patt. >

$MinPrecision gives the minimum number of digits of precision to be allowed in arbitrary-precision numbers.

Many calculations involve solving systems of linear equations. In many cases, you will find it convenient to write down the equations explicitly, and then solve them using ...

A method like "Newton's" method chooses a step, but the validity of that step only goes as far as the Newton quadratic model for the function really reflects the function. ...

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

SemialgebraicComponentInstances[ineqs, {x_1, x_2, ...}] gives at least one sample point in each connected component of the semialgebraic set defined by the inequalities ineqs ...