Hi and welcome to the Matladpi blog!

In the previous post I actually did not show every notation of the tget language. Partly due to the fact that the notations are not so convenient to use with the basic arithmetical symbols, and partly due to the fact that I forgot about them. It happens!

Well, here are the rest of those I think can be used with basic arithmetical symbols:

•= is the vertex sum equality sign, used between sum forms that have equal vertex sums. For example,

1 + 2×3 •= 1 + (1 + 3) + 2,

as both have 7 vertices in them.

~ is a graphical equality sign and is used between two sum forms that have equal graphical representations. For example, for free trees,

1 + 1×2 ~ 1 + 2.

0 is an empty branch, in other words its size is zero. By adding an empty branch to a sum form, you actually do nothing to the sum form. For example,

1 + 0 = 1 and 1 + (1 + 0) = 1 + 1

However, the concept of having a neutral element (empty branch) is actually useful, as it is of fundamental interest for an algebra to have. This language? I call it vertex edge algebra. Njäf! said.

I am Jesse Sakari Hyttinen and I will see you in the next post!