Accessing Algorithms in Mathematica
Whenever you use Mathematica, you are accessing the world's largest collection of computational algorithms.
Mathematica automatically chooses appropriate algorithms for each computation.
Mathematica uses state-of-the-art algorithms for factoring integers. The result is given as a list of factors and exponents.
This generates a 2D table corresponding to a matrix.
This displays the table in matrix form.
This computes the null space of the matrix.
Mathematica can solve differential equations both symbolically and numerically.
Here Mathematica solves a nonlinear differential equation numerically. The answer is an interpolating function that implicitly represents the whole solution.
Here is a parametric plot of the solution. The /. tells Mathematica to substitute the solution for x.