┌ Warning: Module Groebner with build ID fafbfcfd-ec24-cca2-0000-0c1711bae778 is missing from the cache.
│ This may mean Groebner [0b43b601-686d-58a3-8a1c-6623616c7cd4] does not support precompilation but is imported by a module that does.
└ @ Base loading.jl:1793
WARNING: using OrdinaryDiffEq.isconstant in module ModelingToolkit conflicts with an existing identifier.
WARNING: using OrdinaryDiffEq.islinear in module ModelingToolkit conflicts with an existing identifier.
┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "SEIR 34"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
[ Info: Summary of the model:
[ Info: State variables: A, N, S, E, I, R
[ Info: Parameters: gamma, K, epsilon, mu, r, beta
[ Info: Inputs: 
[ Info: Outputs: y1, y2, y3
[ Info: Summary of the model:
[ Info: State variables: x1, x2
[ Info: Parameters: a, b, d, c
[ Info: Inputs: 
[ Info: Outputs: y
[ Info: Computing IO-equations
┌ Info: Computed in 14.987737658 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 14.987737658
[ Info: Computing Wronskians
┌ Info: Computed in 11.66197221 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.66197221
[ Info: Dimensions of the Wronskians [1, 9, 1]
┌ Info: Ranks of the Wronskians computed in 0.03236805 seconds
│   :rank_time = :rank_time
└   rank_times = 0.03236805
┌ Warning: One of the Wronskians has corank greater than one, so the results of the algorithm will be valid only for multiexperiment identifiability. If you still  would like to assess single-experiment identifiability, we recommend using SIAN (https://github.com/alexeyovchinnikov/SIAN-Julia)
└ @ StructuralIdentifiability ~/StructuralIdentifiability.jl/src/global_identifiability.jl:111

⌜ # Computing specializations..  	 Time: 0:00:07[K
✓ # Computing specializations..  	 Time: 0:00:08[K

⌜ # Computing specializations..  	 Time: 0:00:03[K
✓ # Computing specializations..  	 Time: 0:00:03[K
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 24.
[ Info: Groebner basis computed in 9.627389029 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 2.923708229 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 4 for num. and 3 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 36.
[ Info: Groebner basis computed in 0.045599353 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.001481321 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 11 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 5 fractions 5 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 3.241482378 seconds. Result: true
[ Info: Out of 9 initial generators there are 5 indepdendent
[ Info: The ranking of the new set of generators is 1510
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 1 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 20.
[ Info: Groebner basis computed in 3.47026361 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.97035082 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 4 for num. and 4 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 40.
[ Info: Groebner basis computed in 0.019239757 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.035932435 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 15 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (12 in total): Nemo.QQMPolyRingElem[gamma, K, epsilon, mu, r, beta, A, N, S, E, I, R]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 25
┌ Info: Final cleaning and simplification of generators. 
└ Out of 31 fractions 25 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 1.610288338 seconds. Result: true
[ Info: Out of 11 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 107
[ Info: The search for identifiable functions concluded in 67.956370842 seconds
[ Info: Processing SEIR 34
┌ Info: Averaging over 1 runs.
│ Using keyword arguments:
│ NamedTuple{(:with_states, :strategy), Tuple{Bool, Tuple{Symbol, Int64}}}
│ (with_states = true, strategy = (:normalforms, 2))
└ ID: (:normalforms, 2)_with_states
[ Info: Computing IO-equations
┌ Info: Computed in 0.020701611 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.020701611
[ Info: Computing Wronskians
┌ Info: Computed in 0.013709356 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.013709356
[ Info: Dimensions of the Wronskians [1, 9, 1]
┌ Info: Ranks of the Wronskians computed in 1.6612e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 1.6612e-5
┌ Warning: One of the Wronskians has corank greater than one, so the results of the algorithm will be valid only for multiexperiment identifiability. If you still  would like to assess single-experiment identifiability, we recommend using SIAN (https://github.com/alexeyovchinnikov/SIAN-Julia)
└ @ StructuralIdentifiability ~/StructuralIdentifiability.jl/src/global_identifiability.jl:111
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 24.
[ Info: Groebner basis computed in 0.008958648 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.064345405 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 4 for num. and 3 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 36.
[ Info: Groebner basis computed in 0.014629976 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.001339273 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 11 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 5 fractions 5 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.002014983 seconds. Result: true
[ Info: Out of 9 initial generators there are 5 indepdendent
[ Info: The ranking of the new set of generators is 1510
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 1 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 20.
[ Info: Groebner basis computed in 0.0103924 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.002314676 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 4 for num. and 4 for den.
│ Maximal number of interpolated terms are: 2 for num. and 1 for den.
└ Points used: 40.
[ Info: Groebner basis computed in 0.051282058 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.002365989 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 15 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (12 in total): Nemo.QQMPolyRingElem[gamma, K, epsilon, mu, r, beta, A, N, S, E, I, R]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 25
┌ Info: Final cleaning and simplification of generators. 
└ Out of 31 fractions 25 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.010953265 seconds. Result: true
[ Info: Out of 11 initial generators there are 10 indepdendent
[ Info: The ranking of the new set of generators is 107
[ Info: The search for identifiable functions concluded in 0.388503355 seconds
┌ Info: Result is
│   result =
│    10-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     S
│     N
│     A
│     mu
│     ⋮
│     E + I
│     gamma + epsilon
└     (gamma*r*beta + epsilon*r*beta)//gamma
