4.1 Expressions

The most common class of objects a user deals with is the expression ex, representing a mathematical object like a variable, number, function, sum, product, etc… Expressions may be put together to form new expressions, passed as arguments to functions, and so on. Here is a little collection of valid expressions:

ex MyEx1 = 5;                       // simple number
ex MyEx2 = x + 2*y;                 // polynomial in x and y
ex MyEx3 = (x + 1)/(x - 1);         // rational expression
ex MyEx4 = sin(x + 2*y) + 3*z + 41; // containing a function
ex MyEx5 = MyEx4 + 1;               // similar to above

Expressions are handles to other more fundamental objects, that often contain other expressions thus creating a tree of expressions (See section Internal structures, for particular examples). Most methods on ex therefore run top-down through such an expression tree. For example, the method has() scans recursively for occurrences of something inside an expression. Thus, if you have declared MyEx4 as in the example above MyEx4.has(y) will find y inside the argument of sin and hence return true.

The next sections will outline the general picture of GiNaC's class hierarchy and describe the classes of objects that are handled by ex.