Reduce[expr, vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers. Reduce[expr, vars, dom] does the reduction over the ...

ToRules[eqns] takes logical combinations of equations, in the form generated by Roots and Reduce, and converts them to lists of rules, of the form produced by Solve.

Mathematica ' s differential equation solving functions can be applied to many different classes of differential equations, automatically selecting the appropriate algorithms ...

Mathematica incorporates the latest algorithms for solving industrial-scale linear systems, automatically switching between optimal dense and sparse algorithms—and handling ...

InverseFunctions is an option for Solve and related functions that specifies whether inverse functions should be used.

Mathematica has a flexible system for specifying arbitrary symbolic assumptions about variables. It uses a wide range of sophisticated algorithms to infer the consequences of ...

StepMonitor is an option for iterative numerical computation functions that gives an expression to evaluate whenever a step is taken by the numerical method used.

LUDecomposition[m] generates a representation of the LU decomposition of a square matrix m.

MathieuCharacteristicA[r, q] gives the characteristic value a_r for even Mathieu functions with characteristic exponent r and parameter q.

MathieuCharacteristicB[r, q] gives the characteristic value b_r for odd Mathieu functions with characteristic exponent r and parameter q.