AlgebraicNumber[\[Theta], {c_0, c_1, ..., c_n}] represents the algebraic number in the field \[DoubleStruckCapitalQ][\[Theta]] given by c_0 + c_1 \[Theta] + ... + c_n ...

Function[body] or body & is a pure function. The formal parameters are # (or #1), #2, etc. Function[x, body] is a pure function with a single formal parameter x. ...

InverseFourier[list] finds the discrete inverse Fourier transform of a list of complex numbers.

LyapunovSolve[a, c] finds a solution x of the matrix Lyapunov equation a.x + x.a\[ConjugateTranspose] == c.LyapunovSolve[a, b, c] solves a.x + x.b == c.LyapunovSolve[{a, d}, ...

Simplify[expr] performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. Simplify[expr, assum] does simplification using ...

Combinatorial functions. The factorial function n! gives the number of ways of ordering n objects. For non-integer n, the numerical value of n! is obtained from the gamma ...

Finding the date and time. This gives the current date and time. The Mathematica DateList function returns whatever your computer system gives as the current date and time. ...

This is a simple homogeneous DAE with constant coefficients. This finds the general solution. It has only one arbitrary constant because the second equation in the system ...

Patterns stand for classes of expressions. They contain pattern objects that represent sets of possible expressions. Pattern objects. When several pattern objects with the ...

Mathematica provides a general mechanism for specifying constraints on patterns. All you need to do is to put /;condition at the end of a pattern to signify that it applies ...