If H#p contains a linear equation a*p+b where a is always nonzero, then p is identifiable.
If H#p contains a linear equation a*p+b where a may be zero, then p is generically identifiable.
If H#p contains a polynomial in p of degree d, then p is algebraically d-identifiable.
i1 : G = mixedGraph(digraph {{b,{c,d}},{c,{d}}},bigraph {{a,d}})
o1 = MixedGraph{Bigraph => Bigraph{a => set {d}} }
d => set {a}
Digraph => Digraph{b => set {c, d}}
c => set {d}
d => set {}
Graph => Graph{}
o1 : MixedGraph
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i2 : R = gaussianRing G o2 = R o2 : PolynomialRing |
i3 : H = identifyParameters(R,G)
o3 = HashTable{l => ideal (s , s , l s - s ) }
b,c a,c a,b b,c b,b b,c
2
l => ideal (s , s , l s - l s s + s s - s s )
b,d a,c a,b b,d b,c b,d b,b c,c b,d c,c b,c c,d
2
l => ideal (s , s , l s - l s s - s s + s s )
c,d a,c a,b c,d b,c c,d b,b c,c b,c b,d b,b c,d
p => ideal (s , s , p - s )
a,a a,c a,b a,a a,a
p => ideal (s , s , p - s )
a,d a,c a,b a,d a,d
p => ideal (s , s , p - s )
b,b a,c a,b b,b b,b
2
p => ideal (s , s , p s + s - s s )
c,c a,c a,b c,c b,b b,c b,b c,c
2 2 2 2
p => ideal (s , s , p s - p s s - s s + 2s s s - s s - s s + s s s )
d,d a,c a,b d,d b,c d,d b,b c,c b,d c,c b,c b,d c,d b,b c,d b,c d,d b,b c,c d,d
o3 : HashTable
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