In two decades of intense algorithmic development, Mathematica has established a new level of numerical computation. Particularly notable are its many original highly ...

RandomComplex[] gives a pseudorandom complex number with real and imaginary parts in the range 0 to 1.RandomComplex[{z_min, z_max}] gives a pseudorandom complex number in the ...

Mathematica 's functions for solving differential equations can be applied to many different classes of differential equations, including ordinary differential equations ...

Solve[expr, vars] attempts to solve the system expr of equations or inequalities for the variables vars. Solve[expr, vars, dom] solves over the domain dom. Common choices of ...

ChampernowneNumber[b] gives the base-b Champernowne number C_b.ChampernowneNumber[] gives the base-10 Champernowne number.

Mathematica has a wide coverage of named functions defined by sums and recurrence relations. Often using original algorithms developed at Wolfram Research, Mathematica ...

SingularValueList[m] gives a list of the nonzero singular values of a matrix m. SingularValueList[{m, a}] gives the generalized singular values of m with respect to a. ...

If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...

GenericCylindricalDecomposition[ineqs, {x_1, x_2, ...}] finds the full-dimensional part of the decomposition of the region represented by the inequalities ineqs into ...

Simplifying expressions. Mathematica does not automatically simplify an algebraic expression like this. Simplify performs the simplification.