ChineseRemainder[{r_1, r_2, ...}, {m_1, m_2, ...}] gives the smallest non-negative x that satisfies all the integer congruences x mod m_i = r_i mod m_i.

WaveletPsi[wave, x] gives the wavelet function \[Psi](x) for the symbolic wavelet wave evaluated at x.WaveletPsi[wave] gives the wavelet function as a pure function.

Complex Polynomial Systems Real Polynomial Systems Diophantine Polynomial Systems

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

Orthogonal polynomials. Legendre polynomials LegendreP[n,x] arise in studies of systems with three-dimensional spherical symmetry. They satisfy the differential equation ...

Building on its core symbolic architecture, Mathematica gives immediate access to the latest in industrial-strength Boolean computation. With highly general symbolic ...

WeierstrassP[u, {g_2, g_3}] gives the Weierstrass elliptic function \[WeierstrassP](u; g_2, g_3).

Building on Mathematica's unique base of visualization and graphics capabilities, Mathematica 7 adds several important new areas. Emphasizing integration and automation, ...

First[expr] gives the first element in expr.

When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...