**How do you denote the dihedral group of order n?**

This is not a question of “vim or emacs” or “tabs or spaces” sort, but still there are two notations in use. Some sources use *D _{n}* to denote a dihedral group of order

*n*, and some others – a dihedral group of order 2

*n*. Both notations are also reflected in mathematical software.

For example, in GAP `DihedralGroup(n)`

returns a group of order *n*:

and in SageMath – a group of order 2*n*:

Let us look at other systems:

- Magma online calculator

- Maple

- Mathematica

- WolframAlpha “knows” about both notations and suggest to choose one:

These examples show that one should not assume that similarly named functions have the same semantics while designing interfaces between computer algebra systems. They may differ in many things – for example, in the range of acceptable arguments, in the output type, etc. Even more, all of this may suddenly change in the next version of the system.

Here comes **OpenMath**. For example, the documentation for the OpenMath symbol for the dihedral group says:

GAP supports OpenMath through the **OpenMath** package. In the example below, it parses OpenMath code for the dihedral group of order 8 and returns the correct group:

OpenMath package provides functionality for the conversion between GAP and OpenMath. It is enhanced by the **SCSCP** package that implements the framework for remote procedure calls in which both data and instructions are encoded using OpenMath. SCSCP stands for the **Symbolic Computation Software Composability Protocol**. Using it, one could connect any SCSCP-compliant software – you may find the list at the **SCIEnce project’s website**.