Cases[{e_1, e_2, ...}, pattern] gives a list of the e_i that match the pattern. Cases[{e_1, ...}, pattern -> rhs] gives a list of the values of rhs corresponding to the e_i ...

ExportString[expr, " format"] generates a string corresponding to expr exported in the specified format. ExportString[rules, {"format", "Rules"}] gives explicit rules for ...

Flat is an attribute that can be assigned to a symbol f to indicate that all expressions involving nested functions f should be flattened out. This property is accounted for ...

MemberQ[list, form] returns True if an element of list matches form, and False otherwise. MemberQ[list, form, levelspec] tests all parts of list specified by levelspec.

Here is one way to enter a particular expression. Here is another way to enter the same expression. With a notebook front end, you can also enter the expression directly in ...

When you make a function definition using :=, the value of the function is recomputed every time you ask for it. In some kinds of calculations, you may end up asking for the ...

Unless f is a flat function, a pattern like f[x_,y_] stands only for instances of the function with exactly two arguments. Sometimes you need to set up patterns that can ...

When you enter a piece of input such as 2+2, Mathematica first recognizes the + as an operator and constructs the expression Plus[2,2], then uses the built-in rules for Plus ...

Sometimes you may want to set up functions where certain arguments, if omitted, are given "default values". The pattern x_:v stands for an object that can be omitted, and if ...

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 ...