Denote by D1 (resp. D2) the union of the domains of the value-under-constraints objects in lvc (resp. lwd).

The command MergeTwoCaseDiscussions(lvc,lwd) returns L1, L12, L2 where L1, L12 and L2 are three lists of value-under-constraints so that:

the domain of any value-under-constraint object in L1 is contained in the set theoretic difference of D1 and D2;

the domain of any value-under-constraint object in L12 is contained in the intersection of D1 and D2;

the domain of any value-under-constraint object in L2 is contained in the set theoretic difference of D2 and D1;

each of L1, L12 and L2 is a case discussion;

the list [op(L1), op(L12), op(L2)] refines the list [op(lvc), op(lwd)].

By including the option output = piecewise, you instruct the command to return the result as a single piecewise expression instead. You can explicitly select the default output of three lists by passing the option output = lists.

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

$\mathrm{vc1}≔\mathrm{ValueUnderConstraints}\left(\left[3\right]\,\left[a\,b\,c\,d\right]\,\left[a\right]\,\left[b\right]\,\left[c\right]\,\left[d\right]\,\left\{a\,b\,c\,d\right\}\right)$

$\mathrm{vc1}≔⟨\text{value}\left\{3\right\}\text{when}\left[a=0\,d\ne 0\,0\le b\,0\le c-1\right]⟩$

$\mathrm{vc2}≔\mathrm{ValueUnderConstraints}\left(\left[4\right]\,\left[a\,b\,c\,d\right]\,\left[b\right]\,\left[c\right]\,\left[d\right]\,\left[a\right]\,\left\{a\,b\,c\,d\right\}\right)$

$\mathrm{vc2}≔⟨\text{value}\left\{4\right\}\text{when}\left[b=0\,a\ne 0\,0\le c\,0\le d-1\right]⟩$

$\mathrm{vc3}≔\mathrm{ValueUnderConstraints}\left(\left[5\right]\,\left[a\,b\,c\,d\right]\,\left[c\right]\,\left[d\right]\,\left[a\right]\,\left[b\right]\,\left\{a\,b\,c\,d\right\}\right)$

$\mathrm{vc3}≔⟨\text{value}\left\{5\right\}\text{when}\left[c=0\,b\ne 0\,0\le d\,0\le a-1\right]⟩$

$\mathrm{vc4}≔\mathrm{ValueUnderConstraints}\left(\left[6\right]\,\left[a\,b\,c\,d\right]\,\left[d\right]\,\left[a\right]\,\left[b\right]\,\left[c\right]\,\left\{a\,b\,c\,d\right\}\right)$

$\mathrm{vc4}≔⟨\text{value}\left\{6\right\}\text{when}\left[d=0\,c\ne 0\,0\le a\,0\le b-1\right]⟩$

$\mathrm{vc12}≔\mathrm{MakeCaseDiscussion}\left(\left[\mathrm{vc1}\,\mathrm{vc2}\right]\right)\:$

$\mathrm{vc34}≔\mathrm{MakeCaseDiscussion}\left(\left[\mathrm{vc3}\,\mathrm{vc4}\right]\right)\:$

$\mathrm{merged\_1}≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{MakeCaseDiscussion}\left(\left[\mathrm{op}\left(\mathrm{vc12}\right)\,\mathrm{op}\left(\mathrm{vc34}\right)\right]\right)\,':-\mathrm{iterations}'=20\right)$

memory used=9.91MiB, alloc change=96.99MiB, cpu time=191.00ms, real time=178.45ms, gc time=23.93ms

$\mathrm{merged\_1}≔\left[⟨\text{value}\left\{3\right\}\text{when}\left[a=0\,d\ne 0\,0\le b\,0\le c-1\right]⟩\,⟨\text{value}\left\{4\right\}\text{when}\left[b=0\,a\ne 0\,0\le c\,0\le d-1\right]⟩\,⟨\text{value}\left\{5\right\}\text{when}\left[c=0\,b\ne 0\,0\le d\,0\le a-1\right]⟩\,⟨\text{value}\left\{6\right\}\text{when}\left[d=0\,c\ne 0\,0\le a\,0\le b-1\right]⟩\right]$

$\mathrm{merged\_2}≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{MergeTwoCaseDiscussions}\left(\mathrm{vc12}\,\mathrm{vc34}\right)\,':-\mathrm{iterations}'=20\right)$

memory used=7.49MiB, alloc change=16.00MiB, cpu time=130.15ms, real time=121.75ms, gc time=13.99ms

$\mathrm{merged\_2}≔\left[⟨\text{value}\left\{3\right\}\text{when}\left[a=0\,d\ne 0\,0\le b\,0\le c-1\right]⟩\,⟨\text{value}\left\{4\right\}\text{when}\left[b=0\,a\ne 0\,0\le c\,0\le d-1\right]⟩\right],\left[\right],\left[⟨\text{value}\left\{5\right\}\text{when}\left[c=0\,b\ne 0\,0\le d\,0\le a-1\right]⟩\,⟨\text{value}\left\{6\right\}\text{when}\left[d=0\,c\ne 0\,0\le a\,0\le b-1\right]⟩\right]$

$\mathrm{zip}\left(\mathrm{AreEqual}\,\mathrm{merged\_1}\,\mathrm{map}\left(\mathrm{op}\,\left[\mathrm{merged\_2}\right]\right)\right)$

$\left[\mathrm{true}\,\mathrm{true}\,\mathrm{true}\,\mathrm{true}\right]$

$\mathrm{MergeTwoCaseDiscussions}\left(\mathrm{vc12}\,\mathrm{vc34}\,\mathrm{output}=\mathrm{piecewise}\right)$

$\left\{\begin{array}{cc}\left\{3\right\}& a=0\wedge d\ne 0\wedge 0\le b\wedge 0\le c-1\\ \left\{4\right\}& b=0\wedge a\ne 0\wedge 0\le c\wedge 0\le d-1\\ \left\{5\right\}& c=0\wedge b\ne 0\wedge 0\le d\wedge 0\le a-1\\ \left\{6\right\}& d=0\wedge c\ne 0\wedge 0\le a\wedge 0\le b-1\end{array}\right.$

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[MergeTwoCaseDiscussions] command was introduced in Maple 2025.

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