When you open Maple, prime notation represents differentiation. So, when you input $A\'$ it means the derivative of $A\left(x\right)$ with respect to $x$. It is a handy shortcut to typing $\mathrm{diff}\left(A\left(x\right)\,x\right)$. This meaning of prime notation as differentiation is the useprime setting of the Typesetting package.
There is also another frequent meaning, not differentiation, for prime notation: primed variables, typically used when relating variables in different coordinate systems, e.g. $x$ and $x\'$ in two reference systems K and K', or variables that are related in some way (e.g. when working with Green functions), set complement, the dual of a vector space, etc.. New in Maple 2023, by entering $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{useprime}\=\mathrm{false}\right)$, instead of receiving an error message when you input - say - $x\'$, you can now work with $x\'$ as a primed variable. Also new, when you load the Physics package, where transformation of coordinates are the most frequent use of the prime notation, the Typesetting $\mathrm{useprime}$ keyword is automatically set to $\mathrm{false}\.$
For example, this is the default behavior
$A\'$
$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{A}{}\left({x}\right)$
| (6.1) |
New: you can work with primed variables
$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{useprime}=\mathrm{false}\right)$
$A\'$
${\mathrm{A\text{'}}}$
| (6.3) |
Turn again ON prime notation to represent differentiation
$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{useprime}\=\mathrm{true}\right)\:$
$A\'$
$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{A}{}\left({x}\right)$
| (6.4) |
Load the Physics package or its Physics:-Vectors subpackage
$\mathrm{with}\left(\mathrm{Physics}\right)\:$
$A\'$
${\mathrm{A\text{'}}}$
| (6.5) |
Query about the status of the $\mathrm{useprime}$ setting
$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{useprime}\right)$
You can also change this status directly from the $\mathrm{Physics}:-\mathrm{Setup}$ command using a keyword complementary to the one of $\mathrm{Typesetting}$; query, then change it
$\mathrm{Setup}\left(\mathrm{prime}\right)$
$\left[{\mathrm{primedvariables}}{=}{\mathrm{true}}\right]$
| (6.7) |
$\mathrm{Setup}\left(\mathrm{primedvariables}equals;\mathrm{false}\right)$
$\left[{\mathrm{primedvariables}}{=}{\mathrm{false}}\right]$
| (6.8) |
$A\'$
$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{A}{}\left({x}\right)$
| (6.9) |
${}$