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 ...

Packing a large number of sophisticated algorithms—many recent and original—into a powerful collection of functions, Mathematica draws on almost every major result in number ...

RootSum[f, form] represents the sum of form[x] for all x that satisfy the polynomial equation f[x] == 0.

The representation of algebraic numbers. When you enter a Root object, the polynomial that appears in it is automatically reduced to a minimal form. This extracts the pure ...

Since many functions in Mathematica give solutions in the form of rules, you need to be able to use these rules to explore and interpret your results. Although many of the ...

PrimitiveRoot[n] gives the smallest primitive root of n.

Subresultants[poly_1, poly_2, var] generates a list of the principal subresultant coefficients of the polynomials poly_1 and poly_2 with respect to the variable var.

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 ...

Mathematica has fundamental support for both explicit complex numbers and symbolic complex variables. All applicable mathematical functions support arbitrary-precision ...