Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

Mathematica provides many functions to group terms in a polynomial, extract and sort the monomials, display them in various ways, and even process them as arbitrary ...

Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

When you give a list of equations to Solve, it assumes that you want all the equations to be satisfied simultaneously. It is also possible to give Solve more complicated ...

If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...

You can use the standard differential equation solving function, NDSolve , to numerically solve delay differential equations with constant delays. It returns an interpolation ...

Mathematica treats equations as logical statements. If you type in an equation like x^2+3x==2, Mathematica interprets this as a logical statement which asserts that x^2+3x is ...

Finding the structure of polynomials written in expanded form. Here is a polynomial in two variables. This is the polynomial in expanded form.

Mathematica normally assumes that variables which appear in equations can stand for arbitrary complex numbers. But when you use Reduce, you can explicitly tell Mathematica ...

NDSolve[eqns, y, {x, x_min, x_max}] finds a numerical solution to the ordinary differential equations eqns for the function y with the independent variable x in the range ...