The purpose of this set of commands, declare, undeclare, show, ON, OFF, is to permit a simple, compact display of functions and derivatives on the screen. The Physics CompactDisplay command is a synonym to declare so you can use it in place of declare when working with the Physics package.

Typically, one declares functions by using declare(f(x, y, z)) with the result that $f\left(x\,y\,z\right)$ is displayed as $f$ (that is, only its name) as well as occurrences of indexed $f$, say as in $f_j\left(x\,y\,z\right)$ are displayed as $f_j$. This avoids a significant part of redundant information on the screen. One can declare the prime variable and many functions at once.

This scheme also displays all differentiation variables as indices, and permits declaring a prime variable so that, for functions of one variable, derivatives with respect to that declared prime variable are displayed with a prime.

Different from macro and alias, this set of commands works with 'print/foo' routines, so it does not change the output, only its typesetting on the screen.

When declare is called with an algebraic expression, each unknown function in the expression gets "declared".

Note: you cannot declare for compact display known functions of the mathematical language (cos, sin, etc.).

Expressions involving declared functions or derivatives, that are compactly displayed on the screen, are copied and pasted as they were entered, not as they are displayed. For example declaring $f\left(x\,y\,z\right)$ makes it be displayed as $f$, but copying that $f$ from the output and pasting into an input line produces $f\left(x\,y\,z\right)$, not $f$. The same happens with derivatives displayed compactly as indexed or with primes '. However, it is sometimes convenient to copy and paste as displayed, for instance to paste formulas with format in an email, or in text in a worksheet. For that purpose, set the value of copyasdisplayed to true entering declare(copyasdisplayed = true);

If no arguments are given to declare, the values of the copyasdisplayed, prime, and declared variables are reported. If the arguments prime or copyasdisplayed - just the keywords - are given, the corresponding values are reported.

The command undeclare accepts the same types of arguments as declare does, that is, a function, a sequence of functions, or an algebraic expression. It is used to "undo" declarations previously done by using declare.

declare and undeclare by default print informative messages when they are called. By using the optional argument 'quiet' these messages are suppressed.

When declare is first called, the scheme for compact display is turned ON. However, to turn explicit the actual value of an expression being displayed compactly, you can toggle this feature OFF. Two macros ON and OFF are provided for that purpose. Also, in the ON mode, the macro show displays the last expression in OFF mode.

These functions are part of the PDEtools package, and so they can be used in the form declare(..) and undeclare(..) only after executing the command with(PDEtools). However, they can always be accessed through the long form of the command by using PDEtools[declare](..) or PDEtools[undeclare](..).

$\mathrm{with}\left(\mathrm{PDEtools}\right)\:$

$\mathrm{declare}\left(y\left(x\right)\,\mathrm{prime}=x\right)$

$y\left(x\right)\mathrm{will\; now\; be\; displayed\; as}y$

$\mathrm{derivatives\; with\; respect\; to}x\mathrm{of\; functions\; of\; one\; variable\; will\; now\; be\; displayed\; with\; \text{'}}$

$\mathrm{declare}\left(\right)$

$\mathrm{Declared\; :}$

$y\left(x\right)\mathrm{to\; be\; displayed\; as}y$

$\mathrm{derivatives\; with\; respect\; to}x\mathrm{of\; functions\; of\; one\; variable\; are\; being\; displayed\; with\; \text{'}}$

$\mathrm{Displayed\; derivatives\; and\; declared\; functions\; will\; be\; copied\; and\; pasted\; "as\; they\; were\; entered"}$

$\mathrm{declare}\left(\mathrm{prime}\right)$

$\mathrm{derivatives\; with\; respect\; to}x\mathrm{of\; functions\; of\; one\; variable\; are\; being\; displayed\; with\; \text{'}}$

$\mathrm{ode}≔\mathrm{diff}\left(\mathrm{diff}\left(y\left(x\right)\,x\right)\,x\right)\mathrm{diff}\left(y\left(x\right)\,x\right)y\left(x\right)f\left(x\right)-2{\mathrm{diff}\left(y\left(x\right)\,x\right)}^3{x}^6+2{\mathrm{diff}\left(y\left(x\right)\,x\right)}^{2}y\left(x\right)\mathrm{diff}\left(g\left(x\right)\,x\right)+{y\left(x\right)}^5$

$\mathrm{ode}≔\mathrm{y\text{'}\text{'}}\mathrm{y\text{'}}yf\left(x\right)-2{\mathrm{y\text{'}}}^3{x}^6+2{\mathrm{y\text{'}}}^{2}y\mathrm{g\text{'}}+y^5$

$\mathrm{OFF}$

$\mathrm{ode}$

$\left(\frac{{\ⅆ}^2}{\ⅆx^2}y\left(x\right)\right)\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)y\left(x\right)f\left(x\right)-2{\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)}^3{x}^6+2{\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)}^{2}y\left(x\right)\left(\frac{\ⅆ}{\ⅆx}g\left(x\right)\right)+{y\left(x\right)}^5$

$\mathrm{ON}$

$\mathrm{ode}$

$\mathrm{y\text{'}\text{'}}\mathrm{y\text{'}}yf\left(x\right)-2{\mathrm{y\text{'}}}^3{x}^6+2{\mathrm{y\text{'}}}^{2}y\mathrm{g\text{'}}+y^5$

$\mathrm{show}$

$\left(\frac{{\ⅆ}^{2}y}{\ⅆx^2}\right)\left(\frac{\ⅆy}{\ⅆx}\right)yf\left(x\right)-2{\left(\frac{\ⅆy}{\ⅆx}\right)}^3{x}^6+2{\left(\frac{\ⅆy}{\ⅆx}\right)}^{2}y\left(\frac{\ⅆ}{\ⅆx}g\left(x\right)\right)+y^5$

$\mathrm{ode}$

$\mathrm{y\text{'}\text{'}}\mathrm{y\text{'}}yf\left(x\right)-2{\mathrm{y\text{'}}}^3{x}^6+2{\mathrm{y\text{'}}}^{2}y\mathrm{g\text{'}}+y^5$

$\mathrm{undeclare}\left(\mathrm{prime}\right)$

$\mathrm{There\; is\; no\; more\; prime\; differentiation\; variable;\; all\; derivatives\; will\; be\; displayed\; as\; indexed\; functions}$

$\mathrm{ode}$

$y_{x,x}{y}_{x}yf\left(x\right)-2{y_x}^3{x}^6+2{y_x}^{2}y{g}_x+y^5$

$\mathrm{undeclare}\left(\mathrm{all}\right)$

$y\left(x\right)\mathrm{will\; now\; be\; displayed\; *as\; is*}$

$\mathrm{declare}\left(\right)$

$\mathrm{Nothing\; declared}$

$\mathrm{OFF}$

$\mathrm{pde}≔x\mathrm{diff}\left(f\left(x\,y\right)\,y\right)-\mathrm{diff}\left(f\left(x\,y\right)\,x\right)-\frac{{f\left(x\,y\right)}^{2}g\left(x\right)}{h\left(y\right)}$

$\mathrm{pde}≔x\left(\frac{\partial }{\partial y}f\left(x\,y\right)\right)-\frac{\partial }{\partial x}f\left(x\,y\right)-\frac{{f\left(x\,y\right)}^{2}g\left(x\right)}{h\left(y\right)}$

$\mathrm{ON}$

$\mathrm{pde}$

$x{f}_y-f_x-\frac{{f\left(x\,y\right)}^{2}g\left(x\right)}{h\left(y\right)}$

$\mathrm{declare}\left(f\left(x\,y\right)\right)$

$f\left(x\,y\right)\mathrm{will\; now\; be\; displayed\; as}f$

$\mathrm{pde}$

$x{f}_y-f_x-\frac{f^{2}g\left(x\right)}{h\left(y\right)}$

$\mathrm{declare}\left(\mathrm{pde}\right)$

$f\left(x\,y\right)\mathrm{will\; now\; be\; displayed\; as}f$

$g\left(x\right)\mathrm{will\; now\; be\; displayed\; as}g$

$h\left(y\right)\mathrm{will\; now\; be\; displayed\; as}h$

$\mathrm{pde}$

$x{f}_y-f_x-\frac{f^{2}g}{h}$

$\mathrm{undeclare}\left(g\right)$

$g\left(x\right)\mathrm{will\; now\; be\; displayed\; *as\; is*}$

$\mathrm{pde}$

$x{f}_y-f_x-\frac{f^{2}g\left(x\right)}{h}$

$\mathrm{undeclare}\left(\mathrm{all}\right)$

$f\left(x\,y\right)\mathrm{will\; now\; be\; displayed\; *as\; is*}$

$h\left(y\right)\mathrm{will\; now\; be\; displayed\; *as\; is*}$

$\mathrm{pde}$

$x{f}_y-f_x-\frac{{f\left(x\,y\right)}^{2}g\left(x\right)}{h\left(y\right)}$

$\mathrm{OFF}$

$\mathrm{pde}$

$x\left(\frac{\partial }{\partial y}f\left(x\,y\right)\right)-\frac{\partial }{\partial x}f\left(x\,y\right)-\frac{{f\left(x\,y\right)}^{2}g\left(x\right)}{h\left(y\right)}$

The PDEtools[declare] and Physics[CompactDisplay] commands were updated in Maple 18.

The copyasdisplayed = .. parameter was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.

The Physics[Vectors][CompactDisplay] command was updated in Maple 2023.