Denote by V1 and C1 the value and constraints of vc1. Similarly, denote by V2 and C2 the value and constraints of vc2.

Denote by D1 the domain of vc1 and by D2 that of vc2

Then, the command PairCompare(vc1,vc2) returns three lists of value-under-constraints objects L1, L12 and L2 so that the following five conditions hold:

any value-under-constraint object in L1 has value V1 and its domain is contained in the set theoretic difference of D1 and D2;

any value-under-constraint object in L12 has value V1 union V2 and its domain is contained in the intersection of D1 and D2;

any value-under-constraint object in L2 has value V2 and its domain is contained in the set theoretic difference of D2 and D2;

any point satisfying C1 or C2 satisfies the set of constraints of one and only one value-under-constraints objects among L1, L12 and L2;

the set of constraints of every value-under-constraints object among L1, L12 and L2 is satisfiable.

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

$\mathrm{vc1}≔\mathrm{ValueUnderConstraints}\left(\left[1\right]\,\left[a\,b\,c\,d\,e\,f\,g\,h\right]\,\left[\right]\,\left[a\,b\right]\,\left[c\,d\right]\,\left[\right]\,\left\{a\,b\,c\,d\,e\,f\,g\,h\right\}\right)$

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

$\mathrm{vc2}≔\mathrm{ValueUnderConstraints}\left(\left[2\right]\,\left[a\,b\,c\,d\,e\,f\,g\,h\right]\,\left[\right]\,\left[e\,f\right]\,\left[g\,h\right]\,\left[\right]\,\left\{a\,b\,c\,d\,e\,f\,g\,h\right\}\right)$

$\mathrm{vc2}≔⟨\text{value}\left\{2\right\}\text{when}\left[0\le e\,0\le f\,0\le g-1\,0\le h-1\right]⟩$

$\mathrm{L0}≔\mathrm{PairCompare}\left(\mathrm{vc1}\,\mathrm{vc2}\right)\:$

$\mathrm{ToPiecewise}\left(\mathrm{map}\left(\mathrm{op}\,\left[\mathrm{L0}\right]\right)\right)$

$\mathrm{ToPiecewise}\left(\left[⟨\text{value}\left\{1\right\}\text{when}\left[0\le a\,0\le b\,0\le c-1\,0\le d-1\,0\le -e-1\right]⟩\,⟨\text{value}\left\{1\right\}\text{when}\left[0\le a\,0\le b\,0\le e\,0\le c-1\,0\le d-1\,0\le -f-1\right]⟩\,⟨\text{value}\left\{1\right\}\text{when}\left[0\le a\,0\le b\,0\le e\,0\le f\,0\le -g\,0\le c-1\,0\le d-1\right]⟩\,⟨\text{value}\left\{1\right\}\text{when}\left[0\le a\,0\le b\,0\le e\,0\le f\,0\le -h\,0\le c-1\,0\le d-1\,0\le g-1\right]⟩\,⟨\text{values}\left\{1\,2\right\}\text{when}\left[0\le a\,0\le b\,0\le e\,0\le f\,0\le c-1\,0\le d-1\,0\le g-1\,0\le h-1\right]⟩\,⟨\text{value}\left\{2\right\}\text{when}\left[0\le e\,0\le f\,0\le -a-1\,0\le g-1\,0\le h-1\right]⟩\,⟨\text{value}\left\{2\right\}\text{when}\left[0\le a\,0\le e\,0\le f\,0\le -b-1\,0\le g-1\,0\le h-1\right]⟩\,⟨\text{value}\left\{2\right\}\text{when}\left[0\le a\,0\le b\,0\le e\,0\le f\,0\le -c\,0\le g-1\,0\le h-1\right]⟩\,⟨\text{value}\left\{2\right\}\text{when}\left[0\le a\,0\le b\,0\le e\,0\le f\,0\le -d\,0\le c-1\,0\le g-1\,0\le h-1\right]⟩\right]\right)$

$\mathrm{vc14}≔\mathrm{ValueUnderConstraints}\left(\left[1\right]\,\left[a\,b\,c\,d\,e\,f\,g\,h\right]\,\left[a\right]\,\left[b\right]\,\left[c\,1-b\right]\,\left[d\right]\,\varnothing \right)$

$\mathrm{vc14}≔⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;d\ne 0\&comma;0<c\&comma;0<1-b\&comma;0\le b\right]⟩$

$\mathrm{vc15}≔\mathrm{ValueUnderConstraints}\left(\left[2\right]\&comma;\left[a\&comma;b\&comma;c\&comma;d\&comma;e\&comma;f\&comma;g\&comma;h\right]\&comma;\left[e\right]\&comma;\left[f\right]\&comma;\left[g\&comma;1-f\right]\&comma;\left[h\right]\&comma;\varnothing \right)$

$\mathrm{vc15}≔⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;h\ne 0\&comma;0<g\&comma;0<1-f\&comma;0\le f\right]⟩$

$\mathrm{L1}≔\mathrm{PairCompare}\left(\mathrm{vc14}\&comma;\mathrm{vc15}\right)\&colon;$

$\mathrm{ToPiecewise}\left(\mathrm{map}\left(\mathrm{op}\&comma;\left[\mathrm{L1}\right]\right)\right)$

$\mathrm{ToPiecewise}\left(\left[⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;d\ne 0\&comma;0<c\&comma;0<1-b\&comma;0\le b\&comma;0\le -g\right]⟩\&comma;⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;d\ne 0\&comma;0<c\&comma;0<g\&comma;0<1-b\&comma;0\le b\&comma;0\le -1+f\right]⟩\&comma;⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;d\ne 0\&comma;0<c\&comma;0<g\&comma;0<-f\&comma;0<1-b\&comma;0\le b\right]⟩\&comma;⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;d\ne 0\&comma;e\ne 0\&comma;0<c\&comma;0<g\&comma;0<1-b\&comma;0<1-f\&comma;0\le b\&comma;0\le f\right]⟩\&comma;⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;e=0\&comma;h=0\&comma;d\ne 0\&comma;0<c\&comma;0<g\&comma;0<1-b\&comma;0<1-f\&comma;0\le b\&comma;0\le f\right]⟩\&comma;⟨\text{values}\left\{1\&comma;2\right\}\text{when}\left[a=0\&comma;e=0\&comma;d\ne 0\&comma;h\ne 0\&comma;0<c\&comma;0<g\&comma;0<1-b\&comma;0<1-f\&comma;0\le b\&comma;0\le f\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;h\ne 0\&comma;0<g\&comma;0<1-f\&comma;0\le f\&comma;0\le -c\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;h\ne 0\&comma;0<c\&comma;0<g\&comma;0<1-f\&comma;0\le f\&comma;0\le -1+b\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;h\ne 0\&comma;0<c\&comma;0<g\&comma;0<-b\&comma;0<1-f\&comma;0\le f\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;a\ne 0\&comma;h\ne 0\&comma;0<c\&comma;0<g\&comma;0<1-b\&comma;0<1-f\&comma;0\le b\&comma;0\le f\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[a=0\&comma;d=0\&comma;e=0\&comma;h\ne 0\&comma;0<c\&comma;0<g\&comma;0<1-b\&comma;0<1-f\&comma;0\le b\&comma;0\le f\right]⟩\right]\right)$

$\mathrm{vc14}≔\mathrm{ValueUnderConstraints}\left(\left[1\right]\&comma;\left[a\&comma;b\&comma;c\&comma;d\&comma;e\&comma;f\&comma;g\&comma;h\right]\&comma;\left[a\right]\&comma;\left[b\right]\&comma;\left[c\&comma;1-b\right]\&comma;\left[d\right]\&comma;\left\{b\&comma;f\right\}\right)$

$\mathrm{vc14}≔⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;b=0\&comma;d\ne 0\&comma;0<c\right]⟩$

$\mathrm{vc15}≔\mathrm{ValueUnderConstraints}\left(\left[2\right]\&comma;\left[a\&comma;b\&comma;c\&comma;d\&comma;e\&comma;f\&comma;g\&comma;h\right]\&comma;\left[e\right]\&comma;\left[f\right]\&comma;\left[g\&comma;1-f\right]\&comma;\left[h\right]\&comma;\left\{b\&comma;f\right\}\right)$

$\mathrm{vc15}≔⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;f=0\&comma;h\ne 0\&comma;0<g\right]⟩$

$\mathrm{L2}≔\mathrm{PairCompare}\left(\mathrm{vc14}\&comma;\mathrm{vc15}\right)\&colon;$

$\mathrm{ToPiecewise}\left(\mathrm{map}\left(\mathrm{op}\&comma;\left[\mathrm{L2}\right]\right)\right)$

$\mathrm{ToPiecewise}\left(\left[⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;b=0\&comma;d\ne 0\&comma;0<c\&comma;0\le -g\right]⟩\&comma;⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;b=0\&comma;d\ne 0\&comma;0<c\&comma;0<g\&comma;0\le -f-1\right]⟩\&comma;⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;b=0\&comma;d\ne 0\&comma;0<c\&comma;0<g\&comma;0\le -1+f\right]⟩\&comma;⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;b=0\&comma;f=0\&comma;d\ne 0\&comma;e\ne 0\&comma;0<c\&comma;0<g\right]⟩\&comma;⟨\text{value}\left\{1\right\}\text{when}\left[a=0\&comma;e=0\&comma;h=0\&comma;b=0\&comma;f=0\&comma;d\ne 0\&comma;0<c\&comma;0<g\right]⟩\&comma;⟨\text{values}\left\{1\&comma;2\right\}\text{when}\left[a=0\&comma;e=0\&comma;b=0\&comma;f=0\&comma;d\ne 0\&comma;h\ne 0\&comma;0<c\&comma;0<g\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;f=0\&comma;h\ne 0\&comma;0<g\&comma;0\le -c\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;f=0\&comma;h\ne 0\&comma;0<c\&comma;0<g\&comma;0\le -b-1\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;f=0\&comma;h\ne 0\&comma;0<c\&comma;0<g\&comma;0\le -1+b\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[e=0\&comma;b=0\&comma;f=0\&comma;a\ne 0\&comma;h\ne 0\&comma;0<c\&comma;0<g\right]⟩\&comma;⟨\text{value}\left\{2\right\}\text{when}\left[a=0\&comma;d=0\&comma;e=0\&comma;b=0\&comma;f=0\&comma;h\ne 0\&comma;0<c\&comma;0<g\right]⟩\right]\right)$

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[PairCompare] command was introduced in Maple 2025.

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