The command Eval(vc,eqs) returns the value of the value-under-constraints object vc after evaluating it at the equation(s) given by eqs.

If the constraints are not satisfied, the command returns NULL. This is useful when dealing with a list of ValueUnderConstraints objects, such as might be returned by, for example, MakeCaseDiscussion: then one can evaluate all objects at a particular point, and obtain only the value that applies at the given point.

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

$\mathrm{vc1}≔\mathrm{ValueUnderConstraints}\left(\left[a+b+c+d\right]\,\left[a\,b\,c\,d\right]\,\left[a-2\right]\,\left[b\right]\,\left[c\right]\,\left[d\right]\,\varnothing \right)$

$\mathrm{vc1}≔⟨\text{value}\left\{a+b+c+d\right\}\text{when}\left[a-2=0\&comma;d\ne 0\&comma;0<c\&comma;0\le b\right]⟩$

$\mathrm{Value}\left(\mathrm{vc1}\right)\&semi;$$\mathrm{Constraints}\left(\mathrm{vc1}\right)$

$\left\{a+b+c+d\right\}$

$\left[a-2=0\&comma;d\ne 0\&comma;0<c\&comma;0\le b\right]$

$\mathrm{Simplify}\left(\mathrm{vc1}\right)$

$⟨\text{value}\left\{2+b+c+d\right\}\text{when}\left[a-2=0\&comma;d\ne 0\&comma;0<c\&comma;0\le b\right]⟩$

$\mathrm{Value}\left(\mathrm{vc1}\right)\&semi;$$\mathrm{Constraints}\left(\mathrm{vc1}\right)$

$\left\{2+b+c+d\right\}$

$\left[a-2=0\&comma;d\ne 0\&comma;0<c\&comma;0\le b\right]$

$\mathrm{Eval}\left(\mathrm{vc1}\&comma;\left[a=3\&comma;b=6\&comma;c=3\&comma;d=-2\right]\right)$

$\mathrm{Eval}\left(\mathrm{vc1}\&comma;\left[a=2\&comma;b=6\&comma;c=3\&comma;d=-2\right]\right)$

$\left\{9\right\}$

$\mathrm{vc2}≔\mathrm{ValueUnderConstraints}\left(\left[1\right]\&comma;\left[x\&comma;y\right]\&comma;\left[x^2+y^2+1\right]\&comma;\left[x\&comma;y\right]\&comma;\left[\right]\&comma;\left[x-y\right]\&comma;\varnothing \right)$

$\mathrm{vc2}≔⟨\text{value}\left\{1\right\}\text{(inconsistent)}⟩$

$\mathrm{Eval}\left(\mathrm{vc2}\&comma;\left[x=0\&comma;y=1\right]\right)$

Rui-Juan Jing, Yuzhuo Lei, Christopher F. S. Maligec, Marc Moreno Maza: "Counting the Integer Points of Parametric Polytopes: A Maple Implementation." Proceedings of Computer Algebra in Scientific Computing - 26th International Workshop (CASC) 2024: 140-160, Lecture Notes in Computer Science, vol. 14938, Springer.

The ValuesUnderConstraints[Eval] command was introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.