2
votes
0answers
50 views

Taking the (pseudo)inverse of a monoid operation.

Let $M$ be a monoid with binary operation $f : M \times M \to M$. I'm interested in functions $g : M \to M\times M$ that obey the property: $$ f(g(m)) = m $$ I want to understand what all of the ...
2
votes
0answers
43 views

Inverses of two argument functions with respect to one argument

Consider a function $f : A \times B \to C$ and two inverses, each with respect to one argument; i.e. $g$ and $h$ defined such that $f(x,y)=z \iff g(y,z)=x \iff h(z,x)=y$. A simple example is addition: ...
2
votes
1answer
64 views

Monoid with inversion

Is there a name for monoid with operation $a\mapsto a^{-1}$ conforming the equations $(a^{-1})^{-1}=a$ and $(b\cdot a)^{-1} = a^{-1}\cdot b^{-1}$? (with no requirement that $a^{-1}\cdot a$ would be ...
1
vote
2answers
65 views

correct name of mathematical property

I am developing a program that transforms artifacts in one (computer) language to artifacts in another language. In my program there are certain border line situations where the result of applyin the ...
1
vote
2answers
75 views

How do I write a trig function that includes inverses in terms of another variable?

It's been awhile since I've used trig and I feel stupid asking this question lol but here goes: Given: $z = \tan(\arcsin(x))$ Question: How do I write something like that in terms of $x$? Thanks! ...
1
vote
1answer
160 views

Terminology question; inverse vs complement in Boolean algebra

This was said at a lecture I attended: $e$ is neutral element for operation $*$ if $\forall x (x*e=x \wedge e*x = x)$. So, for example 0 is n. e. for disjunction and 1 is n. e. for ...
1
vote
0answers
45 views

Looking for correct terminology

Given the functions $f\colon A\to B$ and $g\colon B\to B$, a common, useful strategy is to define a new function $h\colon A\to A$ as the composition $f^{-1}\circ g\circ f$. There seem to be many ...