evaluate polynomial systems over intervals (in RRi and CCi)

[antonleykin]

This was reported by @klee669 (at MAAG 2026).
Given intervals as elements of RRi (or CCi),
value works

needsPackage "SLPexpressions"
declareVariable X
declareVariable Y
C = sumGate {X+Y,Y,X}
D = productGate {X*Y,Y,C}
h = valueHashTable({X,Y},{interval 1, interval [0.1,0.2]})
v = value(D,h)
assert(v == product{value(X*Y,h),value(Y,h),value(C,h)})
value(gateMatrix{{C,D},{D,C}},h)

evaluate works for SLProgram

declareVariable X; declareVariable C;
XpC = X+C
XXC = productGate{X,X,C}
detXCCX = detGate{{X,C},{C,X}}
XoC = X/C
slp = makeInterpretedSLProgram(matrix{{C,X}},matrix{{XXC,detXCCX,XoC,XpC+2}})
inp = mutableMatrix{{interval [1.1,1.3], interval(-1)}}
out = mutableMatrix(ring inp,1,4)
evaluate(slp,inp,out)
out     

but not for PolySystem:

needsPackage "NAGtypes"
R = QQ[x,y]; S = polySystem {x^2+y^2-6, 2*x^2-y};                          
p = point {{interval 1.0,interval 2.3}};                                             
evaluate(S,p) -- error

[antonleykin]

Changing R = QQ[x,y] to R = RRi[x,y] doesn't help.

[d-torrance]

It looks like the bug is that evaluate eventually calls map, which needs a promote(List, R, S) method but one wasn't installed:

i1 : map(QQ, RRi_53)
stdio:1:3:(3):[1]: error: no method found for applying promote to:
     argument 1 :  {} (of class List)
     argument 2 :  RRi
                      53
     argument 3 :  RRi
                      53

[d-torrance]

Found a fix (e20a45e) and pushed it to #4040.