Saving time when typing relations involving inverses:NCMakeRelations

One can save time in inputting various types of starting relations easily by using the command NCMakeRelations.

In[12]:= <<NCMakeRelations.m             
In[13]:= NCMakeRelations[{Inv,y,1-y}]
Out[13]= {y ** Inv[y] == 1, Inv[y] ** y == 1, (1 - y) ** Inv[1 -
y] == 1,
    Inv[1 - y] ** (1 - y) == 1}

WARNING

It is traditional in mathematics to use only single characters for indeterminates (e.g., $x$, $y$ and $\alpha$). However, we allow these indeterminate names as well as more complicated constructs such as

$$Inv[x], Inv[y], Inv[1-x**y]$$    and $$Rt[x] .$$

In fact, we allow $f[expr]$ to be an indeterminate if $expr$ is an expression and $f$ is a Mathematica symbol which has no Mathematica code associated to it (e.g., $f= Dummy$ or $f=Joe$, but NOT $f=List$ or $f=Plus$). Also one should never use $inv[m]$ to represent $m^{-1}$ in the input of any of the commands explained within this document, because NCAlgebra has already assigned a meaning to $inv[m]$. It knows that $inv[m]**m$ is $1$ which will transform your starting set of data prematurely.

Besides $Inv$ many more functions are facilitated by NCMakeRelations, see Section 25.0.1.