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. >

FunctionExpand[expr] tries to expand out special and certain other functions in expr, when possible reducing compound arguments to simpler ones. FunctionExpand[expr, assum] ...

PowerExpand[expr] expands all powers of products and powers. PowerExpand[expr, {x_1, x_2, ...}] expands only with respect to the variables x_i.

Building on its broad algorithmic and mathematical capabilities, Mathematica provides a unique level of highly general and efficient support for additive number theory.

MinimalPolynomial[s, x] gives the minimal polynomial in x for which the algebraic number s is a root.

LQRegulatorGains[ss, {q, r}] gives the optimal state feedback gain matrix for the StateSpaceModel object ss and the quadratic cost function with state and control weighting ...

LQOutputRegulatorGains[ss, {q, r}] gives the optimal state feedback gain matrix for the StateSpaceModel object ss and the quadratic cost function with output and control ...

Mathematica contains some powerful primitives for making structural changes to expressions. You can use these primitives both to implement mathematical properties such as ...

DiscreteLQEstimatorGains[ss, {w, v}, \[Tau]] gives the optimal discrete-time estimator gain matrix with sampling period \[Tau] for the continuous-time StateSpaceModel object ...

NumberFieldIntegralBasis[a] gives an integral basis for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.