PathGraph[{v_1, v_2, ...}] yields a path with vertices v_i and edges between v_i and v i +\[ThinSpace]1 .PathGraph[{e_1, e_2, ...}] yields a path with edges ...

StringSplit["string"] splits " string" into a list of substrings separated by whitespace. StringSplit["string", patt] splits into substrings separated by delimiters matching ...

Subsets[list] gives a list of all possible subsets of list. Subsets[list, n] gives all subsets containing at most n elements. Subsets[list, {n}] gives all subsets containing ...

Definitions such as f[x_]=x^2 specify values for functions. Sometimes, however, you need to specify general properties of functions, without necessarily giving explicit ...

Integration functions. Here is the integral ∫_a^bx^2 dx. This gives the multiple integral ∫_0^adx ∫_0^bd y(x^2+y^2).

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

On most computer systems, you can execute external programs or commands from within Mathematica. Often you will want to take expressions you have generated in Mathematica, ...

Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...

Mathematica provides users with access to their computer's file system (Files), interprocess communication (MathLink Mathematica Functions), evaluation of data as code ...

In a statement like x^4+x^2>0, Mathematica treats the variable x as having a definite, though unspecified, value. Sometimes, however, it is useful to be able to make ...