When Maple has two functions of the same name where one begins with a capital letter and one with lower case, the capitalized function is frequently an inert representation of the lower case function. More generally, any function whose name starts with the % character, as in %F, is an inert representation for the function F. This feature provides inert representations for any Maple or user-defined function.

During computations, inert functions remain unevaluated (the operations they represent remain unperformed). The value command maps these inert functions, such as Int or %exp, into the corresponding active functions int and exp. Note that, irrespective of the value command, while computing with inert functions, the differentiation, expansion, and printing properties of the active functions they represent (when defined using extension mechanisms, such as routines like `diff/F`) are automatically taken into account by the system.

The value function can also be extended to evaluate any function call, say F, even if there is no active version of it, by defining a procedure named `value/F` which takes the same arguments as F (for example, F(x)) and returns the desired evaluation.

$\mathrm{int}\left(x,x\right)$

$\frac{x^2}{2}$

$F≔\mathrm{Int}\left(x\,x\right)$

$F≔\int x\ⅆx$

$\mathrm{value}\left(F\right)$

$\frac{x^2}{2}$

$G≔\mathrm{Limit}\left(\frac{\sin \left(x\right)}{x}\,x=0\right)$

$G≔\underset{x\to 0}{lim}\frac{\sin \left(x\right)}{x}$

$\mathrm{value}\left(G\right)$

$1$

$\mathrm{value}\left(\left(\mathrm{Sum}\left(i\,i=1..n\right)\right)+5\right)$

$\frac{{\left(n+1\right)}^2}{2}-\frac{n}{2}+\frac{9}{2}$

$\mathrm{`value/B`}≔\left(a\,b\right)\mapsto \mathrm{binomial}\left(a\,b\right)$

$\mathrm{value/B}≔\left(a\,b\right)\mapsto \left(\genfrac{}{}{0ex}{}{a}{b}\right)$

$\mathrm{value}\left(B\left(10\,5\right)\right)$

$252$

$F≔x\mapsto x^2+1$

$F≔x\mapsto x^2+1$

$\mathrm{\%F}\left(a\right)$

$F\left(a\right)$

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

$a^2+1$

$\mathrm{\%GAMMA}\left(\frac{1}{2}\right)$

$\mathrm{\Gamma }\left(\frac{1}{2}\right)$

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

$\sqrt{\mathrm{\pi }}$

$\mathrm{intg}≔\mathrm{\%intat}\left(\exp \left(x\right)+1\,x=H\left(x\right)\right)$

$\mathrm{intg}≔{\int }_{\phantom{\mathrm{`\; `}}}^{H\left(x\right)}\left({\ⅇ}^x+1\right)\ⅆx$

$\mathrm{value}\left(\mathrm{intg}\right)$

$H\left(x\right)+{\ⅇ}^{H\left(x\right)}$

$\mathrm{diff}\left(\mathrm{\%GAMMA}\left(x\right)\,x\right)$

$\mathrm{\Psi }\left(x\right)\mathrm{\Gamma }\left(x\right)$

$\mathrm{\%diff}\left(\mathrm{\Gamma }\left(x\right)\,x\right)$

$\frac{\ⅆ}{\ⅆx}\mathrm{\Gamma }\left(x\right)$

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

$\mathrm{\Psi }\left(x\right)\mathrm{\Gamma }\left(x\right)$

$\mathrm{\%eval}\left(\mathrm{\%diff}\left(\mathrm{\%exp}\left(x\right)\,x\right)\,x=0\right)$

$\genfrac{}{}{0ex}{}{\left(\frac{\ⅆ}{\ⅆx}{\ⅇ}^x\right)}{\phantom{x=0}}|\genfrac{}{}{0ex}{}{\phantom{\left(\frac{\ⅆ}{\ⅆx}{\ⅇ}^x\right)}}{x=0}$

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

$1$

$\mathrm{with}\left(\mathrm{LinearAlgebra}\,\mathrm{Transpose}\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[a\,b\right]\,\left[c\,d\right]\right]\right)$

$A≔\left[\right]$

$\mathrm{\%Transpose}\left(A\right)$

${\left[\right]}^{+}$

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

$\mathrm{with}\left(\mathrm{Physics}\,\mathrm{KroneckerDelta}\right)$

$\left[\mathrm{KroneckerDelta}\right]$

$\mathrm{\%KroneckerDelta}\left[a,a\right]$

${\mathrm{\delta }}_{a,a}$

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

$1$