info ginac

4.4 The class hierarchy

GiNaC's class hierarchy consists of several classes representing mathematical objects, all of which (except for ex and some helpers) are internally derived from one abstract base class called basic. You do not have to deal with objects of class basic, instead you'll be dealing with symbols, numbers, containers of expressions and so on.

To get an idea about what kinds of symbolic composites may be built we have a look at the most important classes in the class hierarchy and some of the relations among the classes:

classhierarchy

The abstract classes shown here (the ones without drop-shadow) are of no interest for the user. They are used internally in order to avoid code duplication if two or more classes derived from them share certain features. An example is expairseq, a container for a sequence of pairs each consisting of one expression and a number (numeric). What is visible to the user are the derived classes add and mul, representing sums and products. See section Internal structures, where these two classes are described in more detail. The following table shortly summarizes what kinds of mathematical objects are stored in the different classes:

`symbol`	Algebraic symbols a, x, y…
`constant`	Constants like Pi
`numeric`	All kinds of numbers, 42, 7/3I, 3.14159*…
`add`	Sums like x+y or a-(2b)+3*
`mul`	Products like xy* or 2a^2(x+y+z)/b
`ncmul`	Products of non-commutative objects
`power`	Exponentials such as x^2, a^b, `sqrt(`2`)` …
`pseries`	Power Series, e.g. x-1/6x^3+1/120x^5+O(x^7)
`function`	A symbolic function like sin(2x)*
`lst`	Lists of expressions {x, 2y, 3+z*}
`matrix`	mxn matrices of expressions
`relational`	A relation like the identity x`==`y
`indexed`	Indexed object like A_ij
`tensor`	Special tensor like the delta and metric tensors
`idx`	Index of an indexed object
`varidx`	Index with variance
`spinidx`	Index with variance and dot (used in Weyl-van-der-Waerden spinor formalism)
`wildcard`	Wildcard for pattern matching
`structure`	Template for user-defined classes

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