lemonhope comments on lemonhope’s Shortform

[lemonhope]

I was working on this cute math notation the other day. Curious if anybody knows a better way or if I am overcomplicating this.

Say you have $z:=c\ast x^2\ast y$. And you want $m:=dz/dx=2\ast c\ast x\ast y$ to be some particular value.

Sometimes you can control $x$, sometimes you can control $y$, and you can always easily measure $z$. So you might use these forms of the equation:

$$m=2\ast c\ast x\ast y=2\ast z/x=2\ast \sqrt{c\ast y\ast z}$$

It’s kind of confusing that $m$ seems proportional to both $z$ and $\sqrt{z}$. So here’s where the notation comes in. Can write above like

$$m(x=x,y=y,z=?)=2\ast c\ast x\ast y$$ $$m(x=x,y=?,z=z)=2\ast z/x$$ $$m(x=?,y=y,z=z)=2\ast \sqrt{c\ast y\ast z}$$

Which seems a lot clearer to me.

And you could shorten it to $m(x,y,?)$, $m(x,?,z)$, and $m(?,y,z)$.