A Frobenius equation is an equation of the form where a_1, …, a_n are positive integers, m is an integer, and the coordinates x_1, …, x_n of solutions are required to be ...

The numerical method of lines is a technique for solving partial differential equations by discretizing in all but one dimension, and then integrating the semi-discrete ...

Complex Polynomial Systems Real Polynomial Systems Diophantine Polynomial Systems

IsolatingInterval[a] gives a rational isolating interval for the algebraic number a.IsolatingInterval[a, dx] gives an isolating interval of width at most dx.

The simplest type of linear second-order ODE is one with constant coefficients. This linear second-order ODE has constant coefficients. Notice that the general solution is a ...

A linear ODE with constant coefficients can be easily solved once the roots of the auxiliary equation (or characteristic equation) are known. Some examples of this type ...

As with integers, operations related to division are key to many computations with polynomials. Mathematica includes not only highly optimized univariate polynomial-division ...

Mathematica handles formulas of all types, from polynomials with millions of terms to complex combinations of higher mathematical functions. It provides powerful general ...

NumberFieldDiscriminant[a] gives the discriminant of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...