Complex Polynomial Systems Real Polynomial Systems Diophantine Polynomial Systems

FindGeneratingFunction[{a_1, a_2, ...}, x] attempts to find a simple generating function in x whose n\[Null]^th series coefficient is a_n.FindGeneratingFunction[{{n_1, a_1}, ...

One of the important features of Mathematica is that it can do symbolic, as well as numerical calculations. This means that it can handle algebraic formulas as well as ...

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 ...

FullSimplify[expr] tries a wide range of transformations on expr involving elementary and special functions, and returns the simplest form it finds. FullSimplify[expr, assum] ...

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

PrincipalComponents[matrix] transforms elements of matrix into unscaled principal components.

Any combination of equations or inequalities can be thought of as implicitly defining a region in some kind of space. The fundamental function of Reduce is to turn this type ...

CylindricalDecomposition[ineqs, {x_1, x_2, ...}] finds a decomposition of the region represented by the inequalities ineqs into cylindrical parts whose directions correspond ...

DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...