"Defining Variables" discussed assignments such as x=y which set x equal to y. Here we discuss equations, which test equality. The equation x==y tests whether x is equal to ...

Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, ...

Mathematica's symbolic architecture allows it to represent any equation as a symbolic expression that can be manipulated using any of Mathematica's powerful collection of ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

When Solve cannot find solutions in terms of radicals to polynomial equations, it returns a symbolic form of the result in terms of Root objects. You can get numerical ...

Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically ...

Automatically selecting between hundreds of powerful and in many cases original algorithms, Mathematica provides both numerical and symbolic solving of differential equations ...

You can use the Mathematica function DSolve to find symbolic solutions to ordinary and partial differential equations. Solving a differential equation consists essentially in ...

PolynomialExtendedGCD[poly_1, poly_2, x] gives the extended GCD of poly_1 and poly_2 treated as univariate polynomials in x.PolynomialExtendedGCD[poly_1, poly_2, x, Modulus ...

Mathematica's handling of polynomial systems is a tour de force of algebraic computation. Building on mathematical results spanning more than a century, Mathematica for the ...