General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...

Many large-scale applications of linear algebra involve matrices that have many elements, but comparatively few that are nonzero. You can represent such sparse matrices ...

Particularly when you write procedural programs in Mathematica, you will often need to modify the value of a particular variable repeatedly. You can always do this by ...

Palettes can be configured to remember their previous states across front end sessions. This is useful for palettes containing multiple expandable sections, tab views, ...

Invisible characters. In the input there is an invisible comma between the 1 and 2. Here there is an invisible space between the x and y, interpreted as multiplication.

Structural operations on polynomials. Here is a polynomial in one variable. Expand expands out products and powers, writing the polynomial as a simple sum of terms.

For ordinary polynomials, Factor and Expand give the most important forms. For rational expressions, there are many different forms that can be useful. Different kinds of ...

Constructing matrices with special shapes. This creates a matrix of 0s containing a radius 4 diamond of 1s. The result is a 9×9 matrix. The size of the matrix can be ...

Specifying output styles. The second x^2 is here shown in boldface. This shows the word text in font sizes from 10 to 20 points.

Evaluating sums. Mathematica recognizes this as the power series expansion of e^x. This sum comes out in terms of a Bessel function.