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Supplementary Material for the paper "Tikhonov-Fenichel Reductions and their Application to a Novel Modelling Approach for Mutualism"

arxiv.org/abs/2501.12069
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Tikhonov-Fenichel Reductions and Their Application to a Novel Modelling Approach for Mutualism

Johannes Apelt 2025-07-11

This Julia script demonstrates how all time scale reductions for slow-fast separations of rates can be computed for the model

$$ \begin{aligned} \dot{H} &= - \delta_1 H - \eta SH + \mu_1C\left(1-\frac{H}{K_1}\right) \\ \dot{S} &= \beta_2 S \left(1-\frac{S}{K_2}\right) - \delta_2 S - \eta S H + \mu_2 C \left(1-\frac{S}{K_2}\right) \\ \dot{C} &= \beta_3 C \left(1-\frac{C}{K_3}\right) - \delta_3 C + \eta S H \end{aligned} $$

Problem Setup

First, we need to load the packages (note that loading Oscar.jl is optional).

using Oscar
using TikhonovFenichelReductions

Then we define the state variables and parameters along with the RHS of the system. Here we want the carrying capacities to be fixed, i.e. these will not be considered as possible small parameters. Note that we also use the parameter substitutions $k_i = K_i^{-1}$ in order to have a polynomial RHS both in the state variables and parameters. Then we initialize the problem of finding all reductions for slow-fast separations of rates that yield a reduction onto a 2-dimensional system.

# state variables and parameters 
# here we substitute kᵢ := 1/Kᵢ
x = ["H","S","C"]
p = ["β₂","β₃","δ₁","δ₂","δ₃","μ₁","μ₂", "η", "k₁", "k₂", "k₃"]

# index of parameters that are used for the slow-fast separations (others are fixed)
idx_slow_fast = Bool[1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]

# Define ODE system f
function f(x, p)
  H, S, C = x
  β₂, β₃, δ₁, δ₂, δ₃, μ₁, μ₂, η, k₁, k₂, k₃ = p
  return [
    -δ₁*H - η*S*H + μ₁*C*(1-H*k₁),
    β₂*S*(1-S*k₂) - δ₂*S - η*S*H  + μ₂*C*(1-S*k₂),
    β₃*C*(1-C*k₃) - δ₃*C + η*S*H
  ]
end

# Dimension of reduced system
s = 2

# find TFPV candidates
problem = ReductionProblem(f, x, p, s; idx_slow_fast=idx_slow_fast)
ReductionProblem for dimension s = 2
 x    = [H, S, C]
 p    = [β₂, β₃, δ₁, δ₂, δ₃, μ₁, μ₂, η, k₁, k₂, k₃]
 p_sf = [β₂, β₃, δ₁, δ₂, δ₃, μ₁, μ₂, η]
 ODE system:
  dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C - η*H*S
  dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - μ₂*k₂*S*C + μ₂*C - η*H*S
  dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + η*H*S

Finding Slow-Fast Separations of Rates

We can use the method tfpvs_and_varieties to find all slow-fast separations of rates that are TFPVs and the corresponding slow manifolds. Note that the latter are given implicitly as affine varieties $\mathcal{V}(f(\cdot,\pi^\star))$ for a TFPV candidate $\pi^\star$. The function print_results shows all slow-fast separations together with the irreducible components of the varieties and their dimension. These correspond to the potential slow manifolds.

tfpvs, varieties = tfpvs_and_varieties(problem);
print_results(problem, tfpvs, varieties)
1
 π̃: [0, 0, 0, 0, 0, 0, 0, η]
 V: [S], 2
    [H], 2

2
 π̃: [0, 0, 0, 0, 0, 0, μ₂, 0]
 V: [C], 2
    [k₂*S - 1], 2

3
 π̃: [0, 0, 0, 0, 0, μ₁, 0, 0]
 V: [C], 2
    [k₁*H - 1], 2

4
 π̃: [0, 0, 0, 0, δ₃, 0, 0, 0]
 V: [C], 2

5
 π̃: [0, 0, 0, 0, δ₃, 0, μ₂, 0]
 V: [C], 2

6
 π̃: [0, 0, 0, 0, δ₃, μ₁, 0, 0]
 V: [C], 2

7
 π̃: [0, 0, 0, 0, δ₃, μ₁, μ₂, 0]
 V: [C], 2

8
 π̃: [0, 0, 0, δ₂, 0, 0, 0, 0]
 V: [S], 2

9
 π̃: [0, 0, 0, δ₂, 0, 0, 0, η]
 V: [S], 2

10
 π̃: [0, 0, 0, δ₂, 0, 0, μ₂, 0]
 V: [δ₂*S + μ₂*k₂*S*C - μ₂*C], 2

11
 π̃: [0, 0, δ₁, 0, 0, 0, 0, 0]
 V: [H], 2

12
 π̃: [0, 0, δ₁, 0, 0, 0, 0, η]
 V: [H], 2

13
 π̃: [0, 0, δ₁, 0, 0, μ₁, 0, 0]
 V: [δ₁*H + μ₁*k₁*H*C - μ₁*C], 2

14
 π̃: [0, β₃, 0, 0, 0, 0, 0, 0]
 V: [C], 2
    [k₃*C - 1], 2

15
 π̃: [0, β₃, 0, 0, 0, 0, μ₂, 0]
 V: [C], 2
    [k₃*C - 1, k₂*S - 1], 1

16
 π̃: [0, β₃, 0, 0, 0, μ₁, 0, 0]
 V: [C], 2
    [k₃*C - 1, k₁*H - 1], 1

17
 π̃: [0, β₃, 0, 0, 0, μ₁, μ₂, 0]
 V: [C], 2
    [k₃*C - 1, k₂*S - 1, k₁*H - 1], 0

18
 π̃: [0, β₃, 0, 0, δ₃, 0, 0, 0]
 V: [C], 2
    [β₃*k₃*C - β₃ + δ₃], 2

19
 π̃: [0, β₃, 0, 0, δ₃, 0, μ₂, 0]
 V: [C], 2
    [β₃*k₃*C - β₃ + δ₃, k₂*S - 1], 1

20
 π̃: [0, β₃, 0, 0, δ₃, μ₁, 0, 0]
 V: [C], 2
    [β₃*k₃*C - β₃ + δ₃, k₁*H - 1], 1

21
 π̃: [0, β₃, 0, 0, δ₃, μ₁, μ₂, 0]
 V: [C], 2
    [β₃*k₃*C - β₃ + δ₃, k₂*S - 1, k₁*H - 1], 0

22
 π̃: [β₂, 0, 0, 0, 0, 0, 0, 0]
 V: [S], 2
    [k₂*S - 1], 2

23
 π̃: [β₂, 0, 0, 0, 0, 0, 0, η]
 V: [S], 2
    [k₂*S - 1, H], 1

24
 π̃: [β₂, 0, 0, 0, 0, 0, μ₂, 0]
 V: [β₂*S + μ₂*C], 2
    [k₂*S - 1], 2

25
 π̃: [β₂, 0, 0, δ₂, 0, 0, 0, 0]
 V: [S], 2
    [β₂*k₂*S - β₂ + δ₂], 2

26
 π̃: [β₂, 0, 0, δ₂, 0, 0, 0, η]
 V: [S], 2
    [β₂*k₂*S - β₂ + δ₂, H], 1

27
 π̃: [β₂, 0, 0, δ₂, 0, 0, μ₂, 0]
 V: [β₂*k₂*S^2 - β₂*S + δ₂*S + μ₂*k₂*S*C - μ₂*C], 2

Computing Reductions

With the results above, we can find all slow manifolds with dimension 2 and compute the corresponding reductions. Here, we can use the heuristic get_explicit_manifold to compute a parameterized description of the slow manifolds from the generators of the irreducible components of each variety $\mathcal{V}(f(\cdot,\pi^\star))$.

# make variables available in Main namespace
H, S, C = system_components(problem)
β₂, β₃, δ₁, δ₂, δ₃, μ₁, μ₂, η, k₁, k₂, k₃ = system_parameters(problem)

# get all unique varieties
all_varieties = unique_varieties(problem, varieties)

# get explicit description of manifolds
M_auto = [get_explicit_manifold(problem, V) for V in all_varieties]

# make sure heuristic worked in all cases
@assert all([m[2] for m in M_auto])

# all slow manifolds with dimension s=2
manifolds = [m[1] for m in M_auto];

# choose a different parametrization for this manifold
manifolds[7] = problem._F.([H, S, δ₁*H//(μ₁*(1 - k₁*H))])

# compute all reductions
reductions, idx_M = compute_all_reductions(problem, tfpvs, varieties, manifolds; print=true);
M[1] = (H, 0, C)

Reduction 1.1
 slow: β₂, β₃, δ₁, δ₂, δ₃, μ₁, μ₂
 fast: η
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C - μ₂*C
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + μ₂*C

Reduction 8.1
 slow: β₂, β₃, δ₁, δ₃, μ₁, μ₂, η
 fast: δ₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C

Reduction 9.1
 slow: β₂, β₃, δ₁, δ₃, μ₁, μ₂
 fast: δ₂, η
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (-μ₂*η*H*C)//(δ₂ + η*H)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (μ₂*η*H*C)//(δ₂ + η*H)

Reduction 22.1
 slow: β₃, δ₁, δ₂, δ₃, μ₁, μ₂, η
 fast: β₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C

Reduction 23.1
 slow: β₃, δ₁, δ₂, δ₃, μ₁, μ₂
 fast: β₂, η
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (μ₂*η*H*C)//(β₂ - η*H)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (-μ₂*η*H*C)//(β₂ - η*H)

Reduction 25.1
 slow: β₃, δ₁, δ₃, μ₁, μ₂, η
 fast: β₂, δ₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C

Reduction 26.1
 slow: β₃, δ₁, δ₃, μ₁, μ₂
 fast: β₂, δ₂, η
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (μ₂*η*H*C)//(β₂ - δ₂ - η*H)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (-μ₂*η*H*C)//(β₂ - δ₂ - η*H)

M[2] = (0, S, C)

Reduction 1.2
 slow: β₂, β₃, δ₁, δ₂, δ₃, μ₁, μ₂
 fast: η
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - μ₁*C - μ₂*k₂*S*C + μ₂*C
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + μ₁*C

Reduction 11.1
 slow: β₂, β₃, δ₂, δ₃, μ₁, μ₂, η
 fast: δ₁
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - μ₂*k₂*S*C + μ₂*C
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C

Reduction 12.1
 slow: β₂, β₃, δ₂, δ₃, μ₁, μ₂
 fast: δ₁, η
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - μ₂*k₂*S*C + μ₂*C + (-μ₁*η*S*C)//(δ₁ + η*S)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (μ₁*η*S*C)//(δ₁ + η*S)

M[3] = (H, S, 0)

Reduction 2.1
 slow: β₂, β₃, δ₁, δ₂, δ₃, μ₁, η
 fast: μ₂

Reduction 3.1
 slow: β₂, β₃, δ₁, δ₂, δ₃, μ₂, η
 fast: μ₁

Reduction 4.1
 slow: β₂, β₃, δ₁, δ₂, μ₁, μ₂, η
 fast: δ₃
 dH/dt = -δ₁*H - η*H*S
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S

Reduction 5.1
 slow: β₂, β₃, δ₁, δ₂, μ₁, η
 fast: δ₃, μ₂
 dH/dt = -δ₁*H - η*H*S
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (-μ₂*η*k₂*H*S^2 + μ₂*η*H*S)//(δ₃)

Reduction 6.1
 slow: β₂, β₃, δ₁, δ₂, μ₂, η
 fast: δ₃, μ₁
 dH/dt = -δ₁*H - η*H*S + (-μ₁*η*k₁*H^2*S + μ₁*η*H*S)//(δ₃)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S

Reduction 7.1
 slow: β₂, β₃, δ₁, δ₂, η
 fast: δ₃, μ₁, μ₂
 dH/dt = -δ₁*H - η*H*S + (-μ₁*η*k₁*H^2*S + μ₁*η*H*S)//(δ₃)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (-μ₂*η*k₂*H*S^2 + μ₂*η*H*S)//(δ₃)

Reduction 14.1
 slow: β₂, δ₁, δ₂, δ₃, μ₁, μ₂, η
 fast: β₃
 dH/dt = -δ₁*H - η*H*S
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S

Reduction 15.1
 slow: β₂, δ₁, δ₂, δ₃, μ₁, η
 fast: β₃, μ₂
 dH/dt = -δ₁*H - η*H*S
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (μ₂*η*k₂*H*S^2 - μ₂*η*H*S)//(β₃)

Reduction 16.1
 slow: β₂, δ₁, δ₂, δ₃, μ₂, η
 fast: β₃, μ₁
 dH/dt = -δ₁*H - η*H*S + (μ₁*η*k₁*H^2*S - μ₁*η*H*S)//(β₃)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S

Reduction 17.1
 slow: β₂, δ₁, δ₂, δ₃, η
 fast: β₃, μ₁, μ₂
 dH/dt = -δ₁*H - η*H*S + (μ₁*η*k₁*H^2*S - μ₁*η*H*S)//(β₃)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (μ₂*η*k₂*H*S^2 - μ₂*η*H*S)//(β₃)

Reduction 18.1
 slow: β₂, δ₁, δ₂, μ₁, μ₂, η
 fast: β₃, δ₃
 dH/dt = -δ₁*H - η*H*S
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S

Reduction 19.1
 slow: β₂, δ₁, δ₂, μ₁, η
 fast: β₃, δ₃, μ₂
 dH/dt = -δ₁*H - η*H*S
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (μ₂*η*k₂*H*S^2 - μ₂*η*H*S)//(β₃ - δ₃)

Reduction 20.1
 slow: β₂, δ₁, δ₂, μ₂, η
 fast: β₃, δ₃, μ₁
 dH/dt = -δ₁*H - η*H*S + (μ₁*η*k₁*H^2*S - μ₁*η*H*S)//(β₃ - δ₃)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S

Reduction 21.1
 slow: β₂, δ₁, δ₂, η
 fast: β₃, δ₃, μ₁, μ₂
 dH/dt = -δ₁*H - η*H*S + (μ₁*η*k₁*H^2*S - μ₁*η*H*S)//(β₃ - δ₃)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (μ₂*η*k₂*H*S^2 - μ₂*η*H*S)//(β₃ - δ₃)

M[4] = (H, 1//k₂, C)

Reduction 2.2
 slow: β₂, β₃, δ₁, δ₂, δ₃, μ₁, η
 fast: μ₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (-η*H)//(k₂)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (η*H)//(k₂)

Reduction 22.2
 slow: β₃, δ₁, δ₂, δ₃, μ₁, μ₂, η
 fast: β₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (-η*H)//(k₂)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (η*H)//(k₂)

Reduction 24.2
 slow: β₃, δ₁, δ₂, δ₃, μ₁, η
 fast: β₂, μ₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (-η*H)//(k₂)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (η*H)//(k₂)

M[5] = (1//k₁, S, C)

Reduction 3.2
 slow: β₂, β₃, δ₁, δ₂, δ₃, μ₂, η
 fast: μ₁
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - μ₂*k₂*S*C + μ₂*C + (-η*S)//(k₁)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (η*S)//(k₁)

M[6] = (H, (μ₂*C)//(δ₂ + μ₂*k₂*C), C)

Reduction 10.1
 slow: β₂, β₃, δ₁, δ₃, μ₁, η
 fast: δ₂, μ₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (-μ₂*η*H*C)//(δ₂ + μ₂*k₂*C)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (μ₂*η*H*C)//(δ₂ + μ₂*k₂*C)

M[7] = (H, S, (-δ₁*H)//(μ₁*k₁*H - μ₁))

Reduction 13.1
 slow: β₂, β₃, δ₂, δ₃, μ₂, η
 fast: δ₁, μ₁
 dH/dt = -β₃*k₁*H^2 + β₃*H + δ₃*k₁*H^2 - δ₃*H + (-β₃*δ₁^2*k₃*H^2 + μ₁^2*η*k₁^2*H^3*S - 2*μ₁^2*η*k₁*H^2*S + μ₁^2*η*H*S)//(δ₁*μ₁)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (δ₁*μ₂*k₂*H*S - δ₁*μ₂*H)//(μ₁*k₁*H - μ₁)

M[8] = (H, S, 1//k₃)

Reduction 14.2
 slow: β₂, δ₁, δ₂, δ₃, μ₁, μ₂, η
 fast: β₃
 dH/dt = -δ₁*H - η*H*S + (-μ₁*k₁*H + μ₁)//(k₃)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (-μ₂*k₂*S + μ₂)//(k₃)

M[9] = (H, S, (β₃ - δ₃)//(β₃*k₃))

Reduction 18.2
 slow: β₂, δ₁, δ₂, μ₁, μ₂, η
 fast: β₃, δ₃
 dH/dt = -δ₁*H - η*H*S + (-β₃*μ₁*k₁*H + β₃*μ₁ + δ₃*μ₁*k₁*H - δ₃*μ₁)//(β₃*k₃)
 dS/dt = -β₂*k₂*S^2 + β₂*S - δ₂*S - η*H*S + (-β₃*μ₂*k₂*S + β₃*μ₂ + δ₃*μ₂*k₂*S - δ₃*μ₂)//(β₃*k₃)

M[10] = (H, (-μ₂*C)//β₂, C)

Reduction 24.1
 slow: β₃, δ₁, δ₂, δ₃, μ₁, η
 fast: β₂, μ₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (μ₂*η*H*C)//(β₂)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (-μ₂*η*H*C)//(β₂)

M[11] = (H, (β₂ - δ₂)//(β₂*k₂), C)

Reduction 25.2
 slow: β₃, δ₁, δ₃, μ₁, μ₂, η
 fast: β₂, δ₂
 dH/dt = -δ₁*H - μ₁*k₁*H*C + μ₁*C + (-β₂*η*H + δ₂*η*H)//(β₂*k₂)
 dC/dt = -β₃*k₃*C^2 + β₃*C - δ₃*C + (β₂*η*H - δ₂*η*H)//(β₂*k₂)

M[12] = (H, S, (-β₂*k₂*S^2 + β₂*S - δ₂*S)//(μ₂*k₂*S - μ₂))

Reduction 27.1
 slow: β₃, δ₁, δ₃, μ₁, η
 fast: β₂, δ₂, μ₂
 dH/dt = -δ₁*H - η*H*S + (β₂*μ₁*k₁*k₂*H*S^2 - β₂*μ₁*k₁*H*S - β₂*μ₁*k₂*S^2 + β₂*μ₁*S + δ₂*μ₁*k₁*H*S - δ₂*μ₁*S)//(μ₂*k₂*S - μ₂)
 dS/dt = β₃*S - δ₃*S + (β₂^2*β₃*k₂^2*k₃*S^4 - 2*β₂^2*β₃*k₂*k₃*S^3 + β₂^2*β₃*k₃*S^2 + 2*β₂*β₃*δ₂*k₂*k₃*S^3 - 2*β₂*β₃*δ₂*k₃*S^2 + β₃*δ₂^2*k₃*S^2 + β₃*δ₂*μ₂*k₂*S^2 - δ₂*δ₃*μ₂*k₂*S^2 - μ₂^2*η*k₂^2*H*S^3 + 2*μ₂^2*η*k₂*H*S^2 - μ₂^2*η*H*S)//(β₂*μ₂*k₂^2*S^2 - 2*β₂*μ₂*k₂*S + β₂*μ₂ - δ₂*μ₂)

It is also possible to print the reductions as $\LaTeX$ code.

using Latexify, LaTeXStrings, Markdown
for k in eachindex(idx_M)
  display(Markdown.parse("### Slow Manfiold $(k)"))
  display(latexstring("\$\$ \\mathcal{M}_0 = \\left(" * join(latexify.(string.(manifolds[k]); env=:raw, mult_symbol=""), ", ") * "\\right) \$\$"))
  for (i,j) in idx_M[k]
    if all(reductions[i][j].reduction_cached)
      display(Markdown.parse("Reduction $(i).$(j)"))
      io = IOBuffer()
      print_reduced_system(io, reductions[i][j]; latex=true)
      display(latexstring("\$\$" * String(take!(io)) * "\$\$"));
      close(io)
    end
  end
end

Slow Manfiold 1

$$ \mathcal{M}_0 = \left(H, 0, C\right) $$

Reduction 1.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C - \mu_2 C\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \mu_2 C\end{aligned} $$

Reduction 8.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C\end{aligned} $$

Reduction 9.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{ - \mu_2 \eta H C}{\delta_2 + \eta H}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{\mu_2 \eta H C}{\delta_2 + \eta H}\end{aligned} $$

Reduction 22.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C\end{aligned} $$

Reduction 23.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{\mu_2 \eta H C}{\beta_2 - \eta H}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{ - \mu_2 \eta H C}{\beta_2 - \eta H}\end{aligned} $$

Reduction 25.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C\end{aligned} $$

Reduction 26.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{\mu_2 \eta H C}{\beta_2 - \delta_2 - \eta H}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{ - \mu_2 \eta H C}{\beta_2 - \delta_2 - \eta H}\end{aligned} $$

Slow Manfiold 2

$$ \mathcal{M}_0 = \left(0, S, C\right) $$

Reduction 1.2

$$\begin{aligned}\frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \mu_1 C - \mu_2 k_2 S C + \mu_2 C\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \mu_1 C\end{aligned} $$

Reduction 11.1

$$\begin{aligned}\frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \mu_2 k_2 S C + \mu_2 C\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C\end{aligned} $$

Reduction 12.1

$$\begin{aligned}\frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \mu_2 k_2 S C + \mu_2 C + \frac{ - \mu_1 \eta S C}{\delta_1 + \eta S}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{\mu_1 \eta S C}{\delta_1 + \eta S}\end{aligned} $$

Slow Manfiold 3

$$ \mathcal{M}_0 = \left(H, S, 0\right) $$

Reduction 4.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S\end{aligned} $$

Reduction 5.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{ - \mu_2 \eta k_2 H S^{2} + \mu_2 \eta H S}{\delta_3}\end{aligned} $$

Reduction 6.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{ - \mu_1 \eta k_1 H^{2} S + \mu_1 \eta H S}{\delta_3}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S\end{aligned} $$

Reduction 7.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{ - \mu_1 \eta k_1 H^{2} S + \mu_1 \eta H S}{\delta_3}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{ - \mu_2 \eta k_2 H S^{2} + \mu_2 \eta H S}{\delta_3}\end{aligned} $$

Reduction 14.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S\end{aligned} $$

Reduction 15.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{\mu_2 \eta k_2 H S^{2} - \mu_2 \eta H S}{\beta_3}\end{aligned} $$

Reduction 16.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{\mu_1 \eta k_1 H^{2} S - \mu_1 \eta H S}{\beta_3}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S\end{aligned} $$

Reduction 17.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{\mu_1 \eta k_1 H^{2} S - \mu_1 \eta H S}{\beta_3}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{\mu_2 \eta k_2 H S^{2} - \mu_2 \eta H S}{\beta_3}\end{aligned} $$

Reduction 18.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S\end{aligned} $$

Reduction 19.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{\mu_2 \eta k_2 H S^{2} - \mu_2 \eta H S}{\beta_3 - \delta_3}\end{aligned} $$

Reduction 20.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{\mu_1 \eta k_1 H^{2} S - \mu_1 \eta H S}{\beta_3 - \delta_3}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S\end{aligned} $$

Reduction 21.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{\mu_1 \eta k_1 H^{2} S - \mu_1 \eta H S}{\beta_3 - \delta_3}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{\mu_2 \eta k_2 H S^{2} - \mu_2 \eta H S}{\beta_3 - \delta_3}\end{aligned} $$

Slow Manfiold 4

$$ \mathcal{M}_0 = \left(H, \frac{1}{k_2}, C\right) $$

Reduction 2.2

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{ - \eta H}{k_2}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{\eta H}{k_2}\end{aligned} $$

Reduction 22.2

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{ - \eta H}{k_2}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{\eta H}{k_2}\end{aligned} $$

Reduction 24.2

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{ - \eta H}{k_2}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{\eta H}{k_2}\end{aligned} $$

Slow Manfiold 5

$$ \mathcal{M}_0 = \left(\frac{1}{k_1}, S, C\right) $$

Reduction 3.2

$$\begin{aligned}\frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \mu_2 k_2 S C + \mu_2 C + \frac{ - \eta S}{k_1}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{\eta S}{k_1}\end{aligned} $$

Slow Manfiold 6

$$ \mathcal{M}_0 = \left(H, \frac{\mu_2 C}{\delta_2 + \mu_2 k_2 C}, C\right) $$

Reduction 10.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{ - \mu_2 \eta H C}{\delta_2 + \mu_2 k_2 C}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{\mu_2 \eta H C}{\delta_2 + \mu_2 k_2 C}\end{aligned} $$

Slow Manfiold 7

$$ \mathcal{M}_0 = \left(H, S, \frac{ - \delta_1 H}{\mu_1 k_1 H - \mu_1}\right) $$

Reduction 13.1

$$\begin{aligned}\frac{dH}{dt} &= - \beta_3 k_1 H^{2} + \beta_3 H + \delta_3 k_1 H^{2} - \delta_3 H + \frac{ - \beta_3 \delta_1^{2} k_3 H^{2} + \mu_1^{2} \eta k_1^{2} H^{3} S - 2 \mu_1^{2} \eta k_1 H^{2} S + \mu_1^{2} \eta H S}{\delta_1 \mu_1}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{\delta_1 \mu_2 k_2 H S - \delta_1 \mu_2 H}{\mu_1 k_1 H - \mu_1}\end{aligned} $$

Slow Manfiold 8

$$ \mathcal{M}_0 = \left(H, S, \frac{1}{k_3}\right) $$

Reduction 14.2

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{ - \mu_1 k_1 H + \mu_1}{k_3}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{ - \mu_2 k_2 S + \mu_2}{k_3}\end{aligned} $$

Slow Manfiold 9

$$ \mathcal{M}_0 = \left(H, S, \frac{\beta_3 - \delta_3}{\beta_3 k_3}\right) $$

Reduction 18.2

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{ - \beta_3 \mu_1 k_1 H + \beta_3 \mu_1 + \delta_3 \mu_1 k_1 H - \delta_3 \mu_1}{\beta_3 k_3}\\ \frac{dS}{dt} &= - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S - \eta H S + \frac{ - \beta_3 \mu_2 k_2 S + \beta_3 \mu_2 + \delta_3 \mu_2 k_2 S - \delta_3 \mu_2}{\beta_3 k_3}\end{aligned} $$

Slow Manfiold 10

$$ \mathcal{M}_0 = \left(H, \frac{ - \mu_2 C}{\beta_2}, C\right) $$

Reduction 24.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{\mu_2 \eta H C}{\beta_2}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{ - \mu_2 \eta H C}{\beta_2}\end{aligned} $$

Slow Manfiold 11

$$ \mathcal{M}_0 = \left(H, \frac{\beta_2 - \delta_2}{\beta_2 k_2}, C\right) $$

Reduction 25.2

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \mu_1 k_1 H C + \mu_1 C + \frac{ - \beta_2 \eta H + \delta_2 \eta H}{\beta_2 k_2}\\ \frac{dC}{dt} &= - \beta_3 k_3 C^{2} + \beta_3 C - \delta_3 C + \frac{\beta_2 \eta H - \delta_2 \eta H}{\beta_2 k_2}\end{aligned} $$

Slow Manfiold 12

$$ \mathcal{M}_0 = \left(H, S, \frac{ - \beta_2 k_2 S^{2} + \beta_2 S - \delta_2 S}{\mu_2 k_2 S - \mu_2}\right) $$

Reduction 27.1

$$\begin{aligned}\frac{dH}{dt} &= - \delta_1 H - \eta H S + \frac{\beta_2 \mu_1 k_1 k_2 H S^{2} - \beta_2 \mu_1 k_1 H S - \beta_2 \mu_1 k_2 S^{2} + \beta_2 \mu_1 S + \delta_2 \mu_1 k_1 H S - \delta_2 \mu_1 S}{\mu_2 k_2 S - \mu_2}\\ \frac{dS}{dt} &= \beta_3 S - \delta_3 S + \frac{\beta_2^{2} \beta_3 k_2^{2} k_3 S^{4} - 2 \beta_2^{2} \beta_3 k_2 k_3 S^{3} + \beta_2^{2} \beta_3 k_3 S^{2} + 2 \beta_2 \beta_3 \delta_2 k_2 k_3 S^{3} - 2 \beta_2 \beta_3 \delta_2 k_3 S^{2} + \beta_3 \delta_2^{2} k_3 S^{2} + \beta_3 \delta_2 \mu_2 k_2 S^{2} - \delta_2 \delta_3 \mu_2 k_2 S^{2} - \mu_2^{2} \eta k_2^{2} H S^{3} + 2 \mu_2^{2} \eta k_2 H S^{2} - \mu_2^{2} \eta H S}{\beta_2 \mu_2 k_2^{2} S^{2} - 2 \beta_2 \mu_2 k_2 S + \beta_2 \mu_2 - \delta_2 \mu_2}\end{aligned} $$

General TFPVs

We can use TikhonovFenichelReductions.jl to find TFPVs that are not slow-fast separations of rates. This is a computationally intensive task, because it relies on the computation of an elimination ideal based on the computation of a Gröbner basis. In this case, this is still feasible.

G = tfpvs_groebner(problem)
289-element Vector{QQMPolyRingElem}:
 β₂^2*β₃*δ₁*k₃ + β₂*β₃^2*δ₁*k₂ - 2*β₂*β₃*δ₁*δ₂*k₃ - 2*β₂*β₃*δ₁*δ₃*k₂ + β₂*β₃*δ₁*μ₂*k₂ + β₂*δ₁*δ₃^2*k₂ - β₂*δ₁*δ₃*μ₂*k₂ + β₃*δ₁*δ₂^2*k₃ + β₃*δ₁*δ₂*μ₂*k₂ - δ₁*δ₂*δ₃*μ₂*k₂ + δ₁*δ₂*μ₂^2*k₂
 3*β₂^2*β₃*δ₁*k₃ + β₂^2*β₃*μ₁*k₁ - β₂^2*δ₃*μ₁*k₁ - β₂*β₃^2*η - 6*β₂*β₃*δ₁*δ₂*k₃ + 2*β₂*β₃*δ₁*μ₂*k₂ - 2*β₂*β₃*δ₂*μ₁*k₁ + 2*β₂*β₃*δ₃*η - β₂*β₃*μ₁*η - β₂*β₃*μ₂*η - 2*β₂*δ₁*δ₃*μ₂*k₂ + 2*β₂*δ₂*δ₃*μ₁*k₁ - β₂*δ₃^2*η + β₂*δ₃*μ₁*η + β₂*δ₃*μ₂*η - β₂*μ₁*μ₂*η + β₃^2*δ₂*η + 3*β₃*δ₁*δ₂^2*k₃ + 2*β₃*δ₁*δ₂*μ₂*k₂ + β₃*δ₂^2*μ₁*k₁ - 2*β₃*δ₂*δ₃*η + β₃*δ₂*μ₁*η + β₃*δ₂*μ₂*η - 2*δ₁*δ₂*δ₃*μ₂*k₂ + 4*δ₁*δ₂*μ₂^2*k₂ - δ₂^2*δ₃*μ₁*k₁ + δ₂*δ₃^2*η - δ₂*δ₃*μ₁*η - δ₂*δ₃*μ₂*η + δ₂*μ₁*μ₂*η
 β₂*β₃^2*δ₁*η - 2*β₂*β₃*δ₁*δ₃*η + 2*β₂*β₃*δ₁*μ₁*η + β₂*δ₁*δ₃^2*η - 2*β₂*δ₁*δ₃*μ₁*η + β₂*δ₁*μ₁*μ₂*η + δ₁*δ₂*μ₁*μ₂*η - δ₁*δ₂*μ₂^2*η
 β₂*β₃^3*δ₁ - 3*β₂*β₃^2*δ₁*δ₃ + 2*β₂*β₃^2*δ₁*μ₁ + 3*β₂*β₃*δ₁*δ₃^2 - 4*β₂*β₃*δ₁*δ₃*μ₁ + β₂*β₃*δ₁*μ₁*μ₂ - β₂*δ₁*δ₃^3 + 2*β₂*δ₁*δ₃^2*μ₁ - β₂*δ₁*δ₃*μ₁*μ₂ + β₃*δ₁*δ₂*μ₁*μ₂ - β₃*δ₁*δ₂*μ₂^2 - δ₁*δ₂*δ₃*μ₁*μ₂ + δ₁*δ₂*δ₃*μ₂^2
 -β₂^2*β₃*δ₁*η*k₃ + 2*β₂*β₃*δ₁*δ₂*η*k₃ + 2*β₂*β₃*δ₁*μ₁*η*k₂ - β₂*β₃*δ₁*μ₂*η*k₂ - 2*β₂*δ₁*δ₃*μ₁*η*k₂ + β₂*δ₁*δ₃*μ₂*η*k₂ + β₂*δ₁*μ₁*μ₂*η*k₂ - β₃*δ₁*δ₂^2*η*k₃ - β₃*δ₁*δ₂*μ₂*η*k₂ + δ₁*δ₂*δ₃*μ₂*η*k₂ + δ₁*δ₂*μ₁*μ₂*η*k₂ - 2*δ₁*δ₂*μ₂^2*η*k₂
 β₂^2*β₃^2*δ₁*k₃ - β₂^2*β₃*δ₁*δ₃*k₃ + 2*β₂^2*β₃*δ₁*μ₁*k₃ - β₂^2*β₃*δ₁*μ₂*k₃ - 2*β₂*β₃^2*δ₁*δ₂*k₃ + 2*β₂*β₃*δ₁*δ₂*δ₃*k₃ - 4*β₂*β₃*δ₁*δ₂*μ₁*k₃ + 2*β₂*β₃*δ₁*δ₂*μ₂*k₃ + β₂*β₃*δ₁*μ₁*μ₂*k₂ - β₂*β₃*δ₁*μ₂^2*k₂ - β₂*δ₁*δ₃*μ₁*μ₂*k₂ + β₂*δ₁*δ₃*μ₂^2*k₂ + β₃^2*δ₁*δ₂^2*k₃ + β₃^2*δ₁*δ₂*μ₂*k₂ - β₃*δ₁*δ₂^2*δ₃*k₃ + 2*β₃*δ₁*δ₂^2*μ₁*k₃ - β₃*δ₁*δ₂^2*μ₂*k₃ - 2*β₃*δ₁*δ₂*δ₃*μ₂*k₂ + β₃*δ₁*δ₂*μ₁*μ₂*k₂ + β₃*δ₁*δ₂*μ₂^2*k₂ + δ₁*δ₂*δ₃^2*μ₂*k₂ - δ₁*δ₂*δ₃*μ₁*μ₂*k₂ - δ₁*δ₂*δ₃*μ₂^2*k₂ + 2*δ₁*δ₂*μ₁*μ₂^2*k₂ - δ₁*δ₂*μ₂^3*k₂
 β₂*β₃^2*δ₁*δ₂*μ₂ - 2*β₂*β₃*δ₁*δ₂*δ₃*μ₂ + 2*β₂*β₃*δ₁*δ₂*μ₁*μ₂ + β₂*δ₁*δ₂*δ₃^2*μ₂ - 2*β₂*δ₁*δ₂*δ₃*μ₁*μ₂ + β₂*δ₁*δ₂*μ₁*μ₂^2 + δ₁*δ₂^2*μ₁*μ₂^2 - δ₁*δ₂^2*μ₂^3
 -3*β₂^2*β₃*δ₁^2*k₃^2 + β₂^2*δ₁*δ₃*μ₁*k₁*k₃ + 6*β₂*β₃*δ₁^2*δ₂*k₃^2 + 2*β₂*β₃*δ₁*μ₁*μ₂*k₁*k₂ - 3*β₂*β₃*δ₁*μ₁*η*k₃ + 3*β₂*β₃*δ₁*μ₂*η*k₃ + 2*β₂*δ₁^2*δ₃*μ₂*k₂*k₃ - 2*β₂*δ₁*δ₂*δ₃*μ₁*k₁*k₃ - 2*β₂*δ₁*δ₃*μ₁*μ₂*k₁*k₂ + β₂*δ₁*δ₃*μ₁*η*k₃ - β₂*δ₁*δ₃*μ₂*η*k₃ - β₃^2*δ₁*δ₂*η*k₃ + β₃^2*δ₁*μ₂*η*k₂ - 3*β₃*δ₁^2*δ₂^2*k₃^2 + β₃*δ₁^2*μ₂^2*k₂^2 + 2*β₃*δ₁*δ₂*δ₃*η*k₃ + 2*β₃*δ₁*δ₂*μ₁*μ₂*k₁*k₂ + β₃*δ₁*δ₂*μ₁*η*k₃ - 3*β₃*δ₁*δ₂*μ₂*η*k₃ - 2*β₃*δ₁*δ₃*μ₂*η*k₂ + β₃*δ₁*μ₁*μ₂*η*k₂ + β₃*δ₁*μ₂^2*η*k₂ + 2*δ₁^2*δ₂*δ₃*μ₂*k₂*k₃ - 4*δ₁^2*δ₂*μ₂^2*k₂*k₃ - δ₁^2*δ₃*μ₂^2*k₂^2 + δ₁*δ₂^2*δ₃*μ₁*k₁*k₃ - δ₁*δ₂*δ₃^2*η*k₃ - 2*δ₁*δ₂*δ₃*μ₁*μ₂*k₁*k₂ + δ₁*δ₂*δ₃*μ₁*η*k₃ + δ₁*δ₂*δ₃*μ₂*η*k₃ + 4*δ₁*δ₂*μ₁*μ₂^2*k₁*k₂ - 2*δ₁*δ₂*μ₁*μ₂*η*k₃ + δ₁*δ₂*μ₂^2*η*k₃ + δ₁*δ₃^2*μ₂*η*k₂ - δ₁*δ₃*μ₁*μ₂*η*k₂ - δ₁*δ₃*μ₂^2*η*k₂ + δ₁*μ₁*μ₂^2*η*k₂
 β₂^2*β₃^2*δ₁*μ₂*k₃ - β₂^2*β₃*δ₁*δ₃*μ₂*k₃ + 2*β₂^2*β₃*δ₁*μ₁*μ₂*k₃ - β₂^2*β₃*δ₁*μ₂^2*k₃ - β₂*β₃*δ₁*δ₂*δ₃*μ₂*k₃ + β₂*β₃*δ₁*δ₂*μ₂^2*k₃ + β₂*β₃*δ₁*μ₁*μ₂^2*k₂ - β₂*β₃*δ₁*μ₂^3*k₂ + β₂*δ₁*δ₂*δ₃^2*μ₂*k₃ - 2*β₂*δ₁*δ₂*δ₃*μ₁*μ₂*k₃ + β₂*δ₁*δ₂*μ₁*μ₂^2*k₃ - β₂*δ₁*δ₃*μ₁*μ₂^2*k₂ + β₂*δ₁*δ₃*μ₂^3*k₂ + δ₁*δ₂^2*μ₁*μ₂^2*k₃ - δ₁*δ₂^2*μ₂^3*k₃ + δ₁*δ₂*μ₁*μ₂^3*k₂ - δ₁*δ₂*μ₂^4*k₂
 -β₂^2*β₃*δ₁*δ₂*μ₂*k₃ + 2*β₂*β₃*δ₁*δ₂^2*μ₂*k₃ + 2*β₂*β₃*δ₁*δ₂*μ₁*μ₂*k₂ - β₂*β₃*δ₁*δ₂*μ₂^2*k₂ - 2*β₂*δ₁*δ₂*δ₃*μ₁*μ₂*k₂ + β₂*δ₁*δ₂*δ₃*μ₂^2*k₂ + β₂*δ₁*δ₂*μ₁*μ₂^2*k₂ - β₃*δ₁*δ₂^3*μ₂*k₃ - β₃*δ₁*δ₂^2*μ₂^2*k₂ + δ₁*δ₂^2*δ₃*μ₂^2*k₂ + δ₁*δ₂^2*μ₁*μ₂^2*k₂ - 2*δ₁*δ₂^2*μ₂^3*k₂
 ⋮
 2*β₂^2*β₃*δ₁^4*δ₃*μ₁*μ₂^2*k₃^3 + β₂^2*δ₁^4*δ₃^4*μ₂*k₃^3 - 4*β₂^2*δ₁^4*δ₃^2*μ₁^2*μ₂*k₃^3 + β₂^2*δ₁^4*δ₃^2*μ₁*μ₂^2*k₃^3 + 2*β₂^2*δ₁^4*δ₃*μ₁^2*μ₂^2*k₃^3 - 8*β₂*β₃*δ₁^4*δ₂*δ₃*μ₂^3*k₃^3 + β₂*β₃*δ₁^3*δ₃^3*μ₁*μ₂*η*k₃^2 - β₂*β₃*δ₁^3*δ₃^3*μ₂^2*η*k₃^2 + 2*β₂*β₃*δ₁^3*δ₃^2*μ₁^2*μ₂*η*k₃^2 + β₂*β₃*δ₁^3*δ₃^2*μ₁*μ₂^2*η*k₃^2 - 8*β₂*β₃*δ₁^3*δ₃*μ₁^2*μ₂^2*η*k₃^2 + β₂*β₃*δ₁^3*δ₃*μ₁*μ₂^3*η*k₃^2 + 21*β₂*β₃*δ₁^3*μ₁^2*μ₂^3*η*k₃^2 - β₂*β₃*δ₁^2*δ₃^2*μ₁*μ₂^3*η*k₁*k₃ - 3*β₂*β₃*δ₁^2*δ₃*μ₁*μ₂^4*η*k₁*k₃ - 3*β₂*β₃*δ₁^2*μ₁*μ₂^5*η*k₁*k₃ - β₂*δ₁^4*δ₂*δ₃^4*μ₂*k₃^3 + 4*β₂*δ₁^4*δ₂*δ₃^2*μ₁^2*μ₂*k₃^3 + 2*β₂*δ₁^4*δ₂*δ₃^2*μ₂^3*k₃^3 - 8*β₂*δ₁^4*δ₂*δ₃*μ₁*μ₂^3*k₃^3 + 3*β₂*δ₁^4*δ₂*μ₁*μ₂^4*k₃^3 - β₂*δ₁^3*δ₃^4*μ₁*μ₂*η*k₃^2 + β₂*δ₁^3*δ₃^4*μ₂^2*η*k₃^2 - 2*β₂*δ₁^3*δ₃^3*μ₁^2*μ₂*η*k₃^2 + 9*β₂*δ₁^3*δ₃^2*μ₁^2*μ₂^2*η*k₃^2 + 4*β₂*δ₁^3*δ₃^2*μ₁*μ₂^3*η*k₃^2 - 2*β₂*δ₁^3*δ₃*μ₁^3*μ₂^2*η*k₃^2 - 18*β₂*δ₁^3*δ₃*μ₁^2*μ₂^3*η*k₃^2 + 9*β₂*δ₁^3*μ₁^2*μ₂^4*η*k₃^2 + β₂*δ₁^2*δ₃^3*μ₁*μ₂^3*η*k₁*k₃ + β₂*δ₁^2*δ₃^2*μ₁^2*μ₂^3*η*k₁*k₃ + 3*β₂*δ₁^2*δ₃^2*μ₁*μ₂^4*η*k₁*k₃ + 4*β₂*δ₁^2*δ₃*μ₁^3*μ₂^3*η*k₁*k₃ + 3*β₂*δ₁^2*μ₁^4*μ₂^3*η*k₁*k₃ + 3*β₂*δ₁^2*μ₁^3*μ₂^4*η*k₁*k₃ - 15*β₂*δ₁^2*μ₁^2*μ₂^5*η*k₁*k₃ + β₂*δ₁*δ₃*μ₁^3*μ₂^4*η*k₁^2 - β₂*δ₁*δ₃*μ₁^2*μ₂^5*η*k₁^2 + 3*β₃^5*δ₁*μ₂^3*η^2*k₁ + 6*β₃^4*δ₁^2*δ₂*μ₂^3*η*k₁*k₃ + 2*β₃^4*δ₁^2*δ₃*μ₂^2*η^2*k₃ + 3*β₃^4*δ₁^2*μ₂^4*η*k₁*k₂ - 18*β₃^4*δ₁^2*μ₂^3*η^2*k₃ - 16*β₃^4*δ₁*δ₃*μ₂^3*η^2*k₁ + 3*β₃^4*δ₁*μ₁*μ₂^3*η^2*k₁ + 6*β₃^4*δ₁*μ₂^4*η^2*k₁ + 4*β₃^3*δ₁^3*δ₂*δ₃*μ₂^2*η*k₃^2 - 33*β₃^3*δ₁^3*δ₂*μ₂^3*η*k₃^2 + 2*β₃^3*δ₁^3*δ₃*μ₂^3*η*k₂*k₃ - 18*β₃^3*δ₁^3*μ₂^4*η*k₂*k₃ - 20*β₃^3*δ₁^2*δ₂*δ₃*μ₂^3*η*k₁*k₃ - 8*β₃^3*δ₁^2*δ₃^2*μ₂^2*η^2*k₃ + 2*β₃^3*δ₁^2*δ₃*μ₁*μ₂^2*η^2*k₃ - 13*β₃^3*δ₁^2*δ₃*μ₂^4*η*k₁*k₂ + 76*β₃^3*δ₁^2*δ₃*μ₂^3*η^2*k₃ - 18*β₃^3*δ₁^2*μ₁*μ₂^3*η^2*k₃ + 3*β₃^3*δ₁^2*μ₂^5*η*k₁*k₂ - 36*β₃^3*δ₁^2*μ₂^4*η^2*k₃ + 34*β₃^3*δ₁*δ₃^2*μ₂^3*η^2*k₁ - 13*β₃^3*δ₁*δ₃*μ₁*μ₂^3*η^2*k₁ - 26*β₃^3*δ₁*δ₃*μ₂^4*η^2*k₁ + 6*β₃^3*δ₁*μ₁*μ₂^4*η^2*k₁ + 3*β₃^3*δ₁*μ₂^5*η^2*k₁ + 3*β₃^2*δ₁^4*δ₂^2*μ₂^3*k₃^3 - 8*β₃^2*δ₁^3*δ₂*δ₃^2*μ₂^2*η*k₃^2 + 6*β₃^2*δ₁^3*δ₂*δ₃*μ₁*μ₂^2*η*k₃^2 + 68*β₃^2*δ₁^3*δ₂*δ₃*μ₂^3*η*k₃^2 - 12*β₃^2*δ₁^3*δ₂*μ₁*μ₂^3*η*k₃^2 + 3*β₃^2*δ₁^3*δ₂*μ₂^4*η*k₃^2 - 6*β₃^2*δ₁^3*δ₃^2*μ₂^3*η*k₂*k₃ + 56*β₃^2*δ₁^3*δ₃*μ₂^4*η*k₂*k₃ - 18*β₃^2*δ₁^3*μ₂^5*η*k₂*k₃ + β₃^2*δ₁^2*δ₂*δ₃^2*μ₁*μ₂^2*η*k₁*k₃ + 22*β₃^2*δ₁^2*δ₂*δ₃^2*μ₂^3*η*k₁*k₃ + 4*β₃^2*δ₁^2*δ₂*δ₃*μ₁*μ₂^3*η*k₁*k₃ + 3*β₃^2*δ₁^2*δ₂*μ₁*μ₂^4*η*k₁*k₃ - 6*β₃^2*δ₁^2*δ₂*μ₂^5*η*k₁*k₃ + 12*β₃^2*δ₁^2*δ₃^3*μ₂^2*η^2*k₃ - 6*β₃^2*δ₁^2*δ₃^2*μ₁*μ₂^2*η^2*k₃ + 21*β₃^2*δ₁^2*δ₃^2*μ₂^4*η*k₁*k₂ - 120*β₃^2*δ₁^2*δ₃^2*μ₂^3*η^2*k₃ + 58*β₃^2*δ₁^2*δ₃*μ₁*μ₂^3*η^2*k₃ - 10*β₃^2*δ₁^2*δ₃*μ₂^5*η*k₁*k₂ + 110*β₃^2*δ₁^2*δ₃*μ₂^4*η^2*k₃ - 36*β₃^2*δ₁^2*μ₁*μ₂^4*η^2*k₃ - 18*β₃^2*δ₁^2*μ₂^5*η^2*k₃ - 3*β₃^2*δ₁*δ₂*μ₁*μ₂^5*η*k₁^2 - 36*β₃^2*δ₁*δ₃^3*μ₂^3*η^2*k₁ + 21*β₃^2*δ₁*δ₃^2*μ₁*μ₂^3*η^2*k₁ + 42*β₃^2*δ₁*δ₃^2*μ₂^4*η^2*k₁ - 20*β₃^2*δ₁*δ₃*μ₁*μ₂^4*η^2*k₁ - 10*β₃^2*δ₁*δ₃*μ₂^5*η^2*k₁ + 3*β₃^2*δ₁*μ₁*μ₂^5*η^2*k₁ - 2*β₃*δ₁^4*δ₂^2*δ₃*μ₁*μ₂^2*k₃^3 + 2*β₃*δ₁^4*δ₂^2*δ₃*μ₂^3*k₃^3 + 6*β₃*δ₁^4*δ₂^2*μ₁*μ₂^3*k₃^3 + 4*β₃*δ₁^3*δ₂*δ₃^3*μ₂^2*η*k₃^2 - 12*β₃*δ₁^3*δ₂*δ₃^2*μ₁*μ₂^2*η*k₃^2 - 36*β₃*δ₁^3*δ₂*δ₃^2*μ₂^3*η*k₃^2 + 6*β₃*δ₁^3*δ₂*δ₃*μ₁^2*μ₂^2*η*k₃^2 + 20*β₃*δ₁^3*δ₂*δ₃*μ₁*μ₂^3*η*k₃^2 - 5*β₃*δ₁^3*δ₂*δ₃*μ₂^4*η*k₃^2 - 9*β₃*δ₁^3*δ₂*μ₁^2*μ₂^3*η*k₃^2 - 21*β₃*δ₁^3*δ₂*μ₁*μ₂^4*η*k₃^2 + 36*β₃*δ₁^3*δ₂*μ₂^5*η*k₃^2 + 6*β₃*δ₁^3*δ₃^3*μ₂^3*η*k₂*k₃ - 58*β₃*δ₁^3*δ₃^2*μ₂^4*η*k₂*k₃ + 36*β₃*δ₁^3*δ₃*μ₂^5*η*k₂*k₃ - 2*β₃*δ₁^2*δ₂*δ₃^3*μ₁*μ₂^2*η*k₁*k₃ - 8*β₃*δ₁^2*δ₂*δ₃^3*μ₂^3*η*k₁*k₃ + β₃*δ₁^2*δ₂*δ₃^2*μ₁^2*μ₂^2*η*k₁*k₃ - 9*β₃*δ₁^2*δ₂*δ₃^2*μ₁*μ₂^3*η*k₁*k₃ - 2*β₃*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^3*η*k₁*k₃ - 5*β₃*δ₁^2*δ₂*δ₃*μ₁*μ₂^4*η*k₁*k₃ + 8*β₃*δ₁^2*δ₂*δ₃*μ₂^5*η*k₁*k₃ + 3*β₃*δ₁^2*δ₂*μ₁^2*μ₂^4*η*k₁*k₃ + 21*β₃*δ₁^2*δ₂*μ₁*μ₂^5*η*k₁*k₃ - 8*β₃*δ₁^2*δ₃^4*μ₂^2*η^2*k₃ + 6*β₃*δ₁^2*δ₃^3*μ₁*μ₂^2*η^2*k₃ - 15*β₃*δ₁^2*δ₃^3*μ₂^4*η*k₁*k₂ + 84*β₃*δ₁^2*δ₃^3*μ₂^3*η^2*k₃ - 62*β₃*δ₁^2*δ₃^2*μ₁*μ₂^3*η^2*k₃ + 11*β₃*δ₁^2*δ₃^2*μ₂^5*η*k₁*k₂ - 112*β₃*δ₁^2*δ₃^2*μ₂^4*η^2*k₃ + 74*β₃*δ₁^2*δ₃*μ₁*μ₂^4*η^2*k₃ + 36*β₃*δ₁^2*δ₃*μ₂^5*η^2*k₃ - 18*β₃*δ₁^2*μ₁*μ₂^5*η^2*k₃ - β₃*δ₁*δ₂*δ₃*μ₁^2*μ₂^4*η*k₁^2 + 7*β₃*δ₁*δ₂*δ₃*μ₁*μ₂^5*η*k₁^2 - 3*β₃*δ₁*δ₂*μ₁^2*μ₂^5*η*k₁^2 - 3*β₃*δ₁*δ₂*μ₁*μ₂^6*η*k₁^2 + 19*β₃*δ₁*δ₃^4*μ₂^3*η^2*k₁ - 15*β₃*δ₁*δ₃^3*μ₁*μ₂^3*η^2*k₁ - 30*β₃*δ₁*δ₃^3*μ₂^4*η^2*k₁ + 22*β₃*δ₁*δ₃^2*μ₁*μ₂^4*η^2*k₁ + 11*β₃*δ₁*δ₃^2*μ₂^5*η^2*k₁ - 7*β₃*δ₁*δ₃*μ₁*μ₂^5*η^2*k₁ - δ₁^4*δ₂^2*δ₃^2*μ₁*μ₂^2*k₃^3 + δ₁^4*δ₂^2*δ₃^2*μ₂^3*k₃^3 - 2*δ₁^4*δ₂^2*δ₃*μ₁^2*μ₂^2*k₃^3 + 2*δ₁^4*δ₂^2*δ₃*μ₁*μ₂^3*k₃^3 + 3*δ₁^4*δ₂^2*μ₁*μ₂^4*k₃^3 - 3*δ₁^4*δ₂^2*μ₂^5*k₃^3 + 6*δ₁^3*δ₂*δ₃^3*μ₁*μ₂^2*η*k₃^2 - 5*δ₁^3*δ₂*δ₃^2*μ₁^2*μ₂^2*η*k₃^2 - 12*δ₁^3*δ₂*δ₃^2*μ₁*μ₂^3*η*k₃^2 - δ₁^3*δ₂*δ₃^2*μ₂^4*η*k₃^2 + 2*δ₁^3*δ₂*δ₃*μ₁^3*μ₂^2*η*k₃^2 + 4*δ₁^3*δ₂*δ₃*μ₁^2*μ₂^3*η*k₃^2 + 12*δ₁^3*δ₂*δ₃*μ₁*μ₂^4*η*k₃^2 + 3*δ₁^3*δ₂*μ₁^2*μ₂^4*η*k₃^2 - 9*δ₁^3*δ₂*μ₁*μ₂^5*η*k₃^2 - 2*δ₁^3*δ₃^4*μ₂^3*η*k₂*k₃ + 20*δ₁^3*δ₃^3*μ₂^4*η*k₂*k₃ - 18*δ₁^3*δ₃^2*μ₂^5*η*k₂*k₃ + δ₁^2*δ₂*δ₃^4*μ₁*μ₂^2*η*k₁*k₃ - δ₁^2*δ₂*δ₃^3*μ₁^2*μ₂^2*η*k₁*k₃ + 5*δ₁^2*δ₂*δ₃^3*μ₁*μ₂^3*η*k₁*k₃ + 2*δ₁^2*δ₂*δ₃^2*μ₁^2*μ₂^3*η*k₁*k₃ - δ₁^2*δ₂*δ₃^2*μ₁*μ₂^4*η*k₁*k₃ - 4*δ₁^2*δ₂*δ₃*μ₁^3*μ₂^3*η*k₁*k₃ - 5*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^4*η*k₁*k₃ - 24*δ₁^2*δ₂*δ₃*μ₁*μ₂^5*η*k₁*k₃ - 3*δ₁^2*δ₂*μ₁^4*μ₂^3*η*k₁*k₃ - 3*δ₁^2*δ₂*μ₁^3*μ₂^4*η*k₁*k₃ + 18*δ₁^2*δ₂*μ₁^2*μ₂^5*η*k₁*k₃ + 15*δ₁^2*δ₂*μ₁*μ₂^6*η*k₁*k₃ + 2*δ₁^2*δ₃^5*μ₂^2*η^2*k₃ - 2*δ₁^2*δ₃^4*μ₁*μ₂^2*η^2*k₃ + 4*δ₁^2*δ₃^4*μ₂^4*η*k₁*k₂ - 22*δ₁^2*δ₃^4*μ₂^3*η^2*k₃ + 22*δ₁^2*δ₃^3*μ₁*μ₂^3*η^2*k₃ - 4*δ₁^2*δ₃^3*μ₂^5*η*k₁*k₂ + 38*δ₁^2*δ₃^3*μ₂^4*η^2*k₃ - 38*δ₁^2*δ₃^2*μ₁*μ₂^4*η^2*k₃ - 18*δ₁^2*δ₃^2*μ₂^5*η^2*k₃ + 18*δ₁^2*δ₃*μ₁*μ₂^5*η^2*k₃ + δ₁*δ₂*δ₃^2*μ₁^2*μ₂^4*η*k₁^2 - 4*δ₁*δ₂*δ₃^2*μ₁*μ₂^5*η*k₁^2 - δ₁*δ₂*δ₃*μ₁^3*μ₂^4*η*k₁^2 + 3*δ₁*δ₂*δ₃*μ₁^2*μ₂^5*η*k₁^2 + 4*δ₁*δ₂*δ₃*μ₁*μ₂^6*η*k₁^2 - 3*δ₁*δ₂*μ₁^2*μ₂^6*η*k₁^2 - 4*δ₁*δ₃^5*μ₂^3*η^2*k₁ + 4*δ₁*δ₃^4*μ₁*μ₂^3*η^2*k₁ + 8*δ₁*δ₃^4*μ₂^4*η^2*k₁ - 8*δ₁*δ₃^3*μ₁*μ₂^4*η^2*k₁ - 4*δ₁*δ₃^3*μ₂^5*η^2*k₁ + 4*δ₁*δ₃^2*μ₁*μ₂^5*η^2*k₁
 4*β₂^3*β₃*δ₁^4*δ₃*μ₁*μ₂*k₃^3 + 2*β₂^3*δ₁^4*δ₃^4*k₃^3 - 8*β₂^3*δ₁^4*δ₃^2*μ₁^2*k₃^3 + 2*β₂^3*δ₁^4*δ₃^2*μ₁*μ₂*k₃^3 + 4*β₂^3*δ₁^4*δ₃*μ₁^2*μ₂*k₃^3 - 16*β₂^2*β₃*δ₁^4*δ₂*δ₃*μ₂^2*k₃^3 - 4*β₂^2*β₃*δ₁^3*δ₃^3*μ₂*η*k₃^2 + 6*β₂^2*β₃*δ₁^3*δ₃^2*μ₂^2*η*k₃^2 - 4*β₂^2*β₃*δ₁^3*μ₁*μ₂^3*η*k₃^2 - 4*β₂^2*δ₁^4*δ₂*δ₃^4*k₃^3 + 16*β₂^2*δ₁^4*δ₂*δ₃^2*μ₁^2*k₃^3 - 4*β₂^2*δ₁^4*δ₂*δ₃^2*μ₁*μ₂*k₃^3 + 4*β₂^2*δ₁^4*δ₂*δ₃^2*μ₂^2*k₃^3 - 16*β₂^2*δ₁^4*δ₂*δ₃*μ₁*μ₂^2*k₃^3 - 2*β₂^2*δ₁^4*δ₂*μ₁^2*μ₂^2*k₃^3 + 6*β₂^2*δ₁^4*δ₂*μ₁*μ₂^3*k₃^3 + 4*β₂^2*δ₁^3*δ₃^4*μ₂*η*k₃^2 - 8*β₂^2*δ₁^3*δ₃^3*μ₂^2*η*k₃^2 + 21*β₂^2*δ₁^3*δ₃^2*μ₁*μ₂^2*η*k₃^2 - 32*β₂^2*δ₁^3*δ₃*μ₁^4*η*k₃^2 + 28*β₂^2*δ₁^3*δ₃*μ₁^3*μ₂*η*k₃^2 - 22*β₂^2*δ₁^3*δ₃*μ₁^2*μ₂^2*η*k₃^2 - 8*β₂^2*δ₁^3*δ₃*μ₁*μ₂^3*η*k₃^2 + 16*β₂^2*δ₁^3*μ₁^4*μ₂*η*k₃^2 - 12*β₂^2*δ₁^3*μ₁^3*μ₂^2*η*k₃^2 + 13*β₂^2*δ₁^3*μ₁^2*μ₂^3*η*k₃^2 - 8*β₂*β₃*δ₁^4*δ₂^2*δ₃*μ₁*μ₂*k₃^3 + 32*β₂*β₃*δ₁^4*δ₂^2*δ₃*μ₂^2*k₃^3 + 2*β₂*β₃*δ₁^3*δ₂*δ₃^3*μ₂*η*k₃^2 - 22*β₂*β₃*δ₁^3*δ₂*δ₃^2*μ₁*μ₂*η*k₃^2 - 8*β₂*β₃*δ₁^3*δ₂*δ₃^2*μ₂^2*η*k₃^2 - 22*β₂*β₃*δ₁^3*δ₂*δ₃*μ₁*μ₂^2*η*k₃^2 - 16*β₂*β₃*δ₁^3*δ₂*δ₃*μ₂^3*η*k₃^2 + 32*β₂*β₃*δ₁^3*δ₂*μ₁^4*η*k₃^2 + 76*β₂*β₃*δ₁^3*δ₂*μ₁*μ₂^3*η*k₃^2 + 6*β₂*β₃*δ₁^3*δ₂*μ₂^4*η*k₃^2 - 2*β₂*β₃*δ₁^2*δ₂*δ₃^2*μ₂^3*η*k₁*k₃ + 4*β₂*β₃*δ₁^2*δ₃^2*μ₁^3*η^2*k₃ + 28*β₂*β₃*δ₁^2*δ₃^2*μ₁^2*μ₂*η^2*k₃ - 16*β₂*β₃*δ₁^2*δ₃^2*μ₁*μ₂^2*η^2*k₃ + 2*β₂*β₃*δ₁^2*δ₃^2*μ₂^3*η^2*k₃ + 16*β₂*β₃*δ₁^2*δ₃*μ₁^4*η^2*k₃ - 100*β₂*β₃*δ₁^2*δ₃*μ₁^3*μ₂*η^2*k₃ + 49*β₂*β₃*δ₁^2*δ₃*μ₁^2*μ₂^2*η^2*k₃ + 77*β₂*β₃*δ₁^2*δ₃*μ₁*μ₂^3*η^2*k₃ - 16*β₂*β₃*δ₁^2*μ₁^4*μ₂*η^2*k₃ + 102*β₂*β₃*δ₁^2*μ₁^3*μ₂^2*η^2*k₃ - 213*β₂*β₃*δ₁^2*μ₁^2*μ₂^3*η^2*k₃ + 3*β₂*β₃*δ₁^2*μ₁*μ₂^4*η^2*k₃ + 2*β₂*δ₁^4*δ₂^2*δ₃^4*k₃^3 - 8*β₂*δ₁^4*δ₂^2*δ₃^2*μ₁^2*k₃^3 - 8*β₂*δ₁^4*δ₂^2*δ₃^2*μ₂^2*k₃^3 - 8*β₂*δ₁^4*δ₂^2*δ₃*μ₁^2*μ₂*k₃^3 + 32*β₂*δ₁^4*δ₂^2*δ₃*μ₁*μ₂^2*k₃^3 - 4*β₂*δ₁^4*δ₂^2*μ₁*μ₂^3*k₃^3 - 6*β₂*δ₁^4*δ₂^2*μ₂^4*k₃^3 - 2*β₂*δ₁^3*δ₂*δ₃^4*μ₂*η*k₃^2 + 16*β₂*δ₁^3*δ₂*δ₃^3*μ₁*μ₂*η*k₃^2 + 4*β₂*δ₁^3*δ₂*δ₃^3*μ₂^2*η*k₃^2 - 26*β₂*δ₁^3*δ₂*δ₃^2*μ₁^2*μ₂*η*k₃^2 - 31*β₂*δ₁^3*δ₂*δ₃^2*μ₁*μ₂^2*η*k₃^2 + 28*β₂*δ₁^3*δ₂*δ₃^2*μ₂^3*η*k₃^2 + 32*β₂*δ₁^3*δ₂*δ₃*μ₁^4*η*k₃^2 - 16*β₂*δ₁^3*δ₂*δ₃*μ₁^3*μ₂*η*k₃^2 + 30*β₂*δ₁^3*δ₂*δ₃*μ₁^2*μ₂^2*η*k₃^2 - 48*β₂*δ₁^3*δ₂*δ₃*μ₁*μ₂^3*η*k₃^2 + 8*β₂*δ₁^3*δ₂*δ₃*μ₂^4*η*k₃^2 - 14*β₂*δ₁^3*δ₂*μ₁^3*μ₂^2*η*k₃^2 + 19*β₂*δ₁^3*δ₂*μ₁*μ₂^4*η*k₃^2 + 2*β₂*δ₁^2*δ₂*δ₃^3*μ₂^3*η*k₁*k₃ - 4*β₂*δ₁^2*δ₃^3*μ₁^3*η^2*k₃ - 28*β₂*δ₁^2*δ₃^3*μ₁^2*μ₂*η^2*k₃ + 16*β₂*δ₁^2*δ₃^3*μ₁*μ₂^2*η^2*k₃ - 2*β₂*δ₁^2*δ₃^3*μ₂^3*η^2*k₃ - 16*β₂*δ₁^2*δ₃^2*μ₁^4*η^2*k₃ + 102*β₂*δ₁^2*δ₃^2*μ₁^3*μ₂*η^2*k₃ - 33*β₂*δ₁^2*δ₃^2*μ₁^2*μ₂^2*η^2*k₃ - 69*β₂*δ₁^2*δ₃^2*μ₁*μ₂^3*η^2*k₃ + 24*β₂*δ₁^2*δ₃*μ₁^4*μ₂*η^2*k₃ - 144*β₂*δ₁^2*δ₃*μ₁^3*μ₂^2*η^2*k₃ + 232*β₂*δ₁^2*δ₃*μ₁^2*μ₂^3*η^2*k₃ - 26*β₂*δ₁^2*δ₃*μ₁*μ₂^4*η^2*k₃ - 16*β₂*δ₁^2*μ₁^5*μ₂*η^2*k₃ + 28*β₂*δ₁^2*μ₁^4*μ₂^2*η^2*k₃ + 9*β₂*δ₁^2*μ₁^3*μ₂^3*η^2*k₃ - 73*β₂*δ₁^2*μ₁^2*μ₂^4*η^2*k₃ + 2*β₂*δ₁*δ₃*μ₁^4*μ₂^2*η^2*k₁ + 10*β₂*δ₁*δ₃*μ₁^3*μ₂^3*η^2*k₁ - 12*β₂*δ₁*δ₃*μ₁^2*μ₂^4*η^2*k₁ + 6*β₂*δ₁*μ₁^5*μ₂^2*η^2*k₁ - 6*β₂*δ₁*μ₁^4*μ₂^3*η^2*k₁ - 42*β₂*δ₁*μ₁^3*μ₂^4*η^2*k₁ + 42*β₂*δ₁*μ₁^2*μ₂^5*η^2*k₁ - 6*β₃^5*δ₁*δ₂*μ₂^2*η^2*k₁ - 8*β₃^5*δ₁*δ₃*μ₂*η^3 + 10*β₃^5*δ₁*μ₂^2*η^3 - 6*β₃^4*δ₁^2*δ₂^2*μ₂^2*η*k₁*k₃ - 20*β₃^4*δ₁^2*δ₂*δ₃*μ₂*η^2*k₃ + 50*β₃^4*δ₁^2*δ₂*μ₂^2*η^2*k₃ - 8*β₃^4*δ₁^2*δ₃*μ₂^2*η^2*k₂ + 10*β₃^4*δ₁^2*μ₂^3*η^2*k₂ + 32*β₃^4*δ₁*δ₂*δ₃*μ₂^2*η^2*k₁ - 12*β₃^4*δ₁*δ₂*μ₂^3*η^2*k₁ + 40*β₃^4*δ₁*δ₃^2*μ₂*η^3 - 8*β₃^4*δ₁*δ₃*μ₁*μ₂*η^3 - 78*β₃^4*δ₁*δ₃*μ₂^2*η^3 + 10*β₃^4*δ₁*μ₁*μ₂^2*η^3 + 66*β₃^4*δ₁*μ₂^3*η^3 - 4*β₃^3*δ₁^3*δ₂^2*δ₃*μ₂*η*k₃^2 + 24*β₃^3*δ₁^3*δ₂^2*μ₂^2*η*k₃^2 + 20*β₃^3*δ₁^2*δ₂^2*δ₃*μ₂^2*η*k₁*k₃ - 6*β₃^3*δ₁^2*δ₂^2*μ₂^3*η*k₁*k₃ + 66*β₃^3*δ₁^2*δ₂*δ₃^2*μ₂*η^2*k₃ - 54*β₃^3*δ₁^2*δ₂*δ₃*μ₁*μ₂*η^2*k₃ - 208*β₃^3*δ₁^2*δ₂*δ₃*μ₂^2*η^2*k₃ + 32*β₃^3*δ₁^2*δ₂*μ₁^3*η^2*k₃ + 56*β₃^3*δ₁^2*δ₂*μ₁*μ₂^2*η^2*k₃ + 160*β₃^3*δ₁^2*δ₂*μ₂^3*η^2*k₃ + 32*β₃^3*δ₁^2*δ₃^2*μ₂^2*η^2*k₂ - 60*β₃^3*δ₁^2*δ₃*μ₂^3*η^2*k₂ + 56*β₃^3*δ₁^2*μ₂^4*η^2*k₂ - 68*β₃^3*δ₁*δ₂*δ₃^2*μ₂^2*η^2*k₁ + 52*β₃^3*δ₁*δ₂*δ₃*μ₂^3*η^2*k₁ - 6*β₃^3*δ₁*δ₂*μ₂^4*η^2*k₁ - 80*β₃^3*δ₁*δ₃^3*μ₂*η^3 + 32*β₃^3*δ₁*δ₃^2*μ₁*μ₂*η^3 + 212*β₃^3*δ₁*δ₃^2*μ₂^2*η^3 - 68*β₃^3*δ₁*δ₃*μ₁*μ₂^2*η^3 - 296*β₃^3*δ₁*δ₃*μ₂^3*η^3 + 66*β₃^3*δ₁*μ₁*μ₂^3*η^3 + 102*β₃^3*δ₁*μ₂^4*η^3 - 6*β₃^2*δ₁^4*δ₂^3*μ₂^2*k₃^3 + 10*β₃^2*δ₁^3*δ₂^2*δ₃^2*μ₂*η*k₃^2 - 52*β₃^2*δ₁^3*δ₂^2*δ₃*μ₂^2*η*k₃^2 + 32*β₃^2*δ₁^3*δ₂^2*μ₂^3*η*k₃^2 - 22*β₃^2*δ₁^2*δ₂^2*δ₃^2*μ₂^2*η*k₁*k₃ + 14*β₃^2*δ₁^2*δ₂^2*δ₃*μ₂^3*η*k₁*k₃ + 6*β₃^2*δ₁^2*δ₂^2*μ₂^4*η*k₁*k₃ - 78*β₃^2*δ₁^2*δ₂*δ₃^3*μ₂*η^2*k₃ + 152*β₃^2*δ₁^2*δ₂*δ₃^2*μ₁*μ₂*η^2*k₃ + 306*β₃^2*δ₁^2*δ₂*δ₃^2*μ₂^2*η^2*k₃ - 96*β₃^2*δ₁^2*δ₂*δ₃*μ₁^3*η^2*k₃ - 64*β₃^2*δ₁^2*δ₂*δ₃*μ₁^2*μ₂*η^2*k₃ - 282*β₃^2*δ₁^2*δ₂*δ₃*μ₁*μ₂^2*η^2*k₃ - 384*β₃^2*δ₁^2*δ₂*δ₃*μ₂^3*η^2*k₃ + 64*β₃^2*δ₁^2*δ₂*μ₁^4*η^2*k₃ + 48*β₃^2*δ₁^2*δ₂*μ₁^3*μ₂*η^2*k₃ + 18*β₃^2*δ₁^2*δ₂*μ₁^2*μ₂^2*η^2*k₃ + 197*β₃^2*δ₁^2*δ₂*μ₁*μ₂^3*η^2*k₃ + 12*β₃^2*δ₁^2*δ₂*μ₂^4*η^2*k₃ - 48*β₃^2*δ₁^2*δ₃^3*μ₂^2*η^2*k₂ + 120*β₃^2*δ₁^2*δ₃^2*μ₂^3*η^2*k₂ - 180*β₃^2*δ₁^2*δ₃*μ₂^4*η^2*k₂ + 46*β₃^2*δ₁^2*μ₂^5*η^2*k₂ + 72*β₃^2*δ₁*δ₂*δ₃^3*μ₂^2*η^2*k₁ - 84*β₃^2*δ₁*δ₂*δ₃^2*μ₂^3*η^2*k₁ + 14*β₃^2*δ₁*δ₂*δ₃*μ₁*μ₂^3*η^2*k₁ + 20*β₃^2*δ₁*δ₂*δ₃*μ₂^4*η^2*k₁ - 35*β₃^2*δ₁*δ₂*μ₁*μ₂^4*η^2*k₁ + 80*β₃^2*δ₁*δ₃^4*μ₂*η^3 - 48*β₃^2*δ₁*δ₃^3*μ₁*μ₂*η^3 - 268*β₃^2*δ₁*δ₃^3*μ₂^2*η^3 + 144*β₃^2*δ₁*δ₃^2*μ₁*μ₂^2*η^3 + 492*β₃^2*δ₁*δ₃^2*μ₂^3*η^3 - 230*β₃^2*δ₁*δ₃*μ₁*μ₂^3*η^3 - 318*β₃^2*δ₁*δ₃*μ₂^4*η^3 + 102*β₃^2*δ₁*μ₁*μ₂^4*η^3 + 46*β₃^2*δ₁*μ₂^5*η^3 + 4*β₃*δ₁^4*δ₂^3*δ₃*μ₁*μ₂*k₃^3 - 4*β₃*δ₁^4*δ₂^3*δ₃*μ₂^2*k₃^3 - 12*β₃*δ₁^4*δ₂^3*μ₁*μ₂^2*k₃^3 - 6*β₃*δ₁^3*δ₂^2*δ₃^3*μ₂*η*k₃^2 + 18*β₃*δ₁^3*δ₂^2*δ₃^2*μ₁*μ₂*η*k₃^2 + 34*β₃*δ₁^3*δ₂^2*δ₃^2*μ₂^2*η*k₃^2 + 18*β₃*δ₁^3*δ₂^2*δ₃*μ₁^2*μ₂*η*k₃^2 + 2*β₃*δ₁^3*δ₂^2*δ₃*μ₁*μ₂^2*η*k₃^2 - 44*β₃*δ₁^3*δ₂^2*δ₃*μ₂^3*η*k₃^2 - 32*β₃*δ₁^3*δ₂^2*μ₁^4*η*k₃^2 + 2*β₃*δ₁^3*δ₂^2*μ₁^2*μ₂^2*η*k₃^2 - 8*β₃*δ₁^3*δ₂^2*μ₁*μ₂^3*η*k₃^2 - 30*β₃*δ₁^3*δ₂^2*μ₂^4*η*k₃^2 + 8*β₃*δ₁^2*δ₂^2*δ₃^3*μ₂^2*η*k₁*k₃ + 4*β₃*δ₁^2*δ₂^2*δ₃^2*μ₁*μ₂^2*η*k₁*k₃ - 8*β₃*δ₁^2*δ₂^2*δ₃^2*μ₂^3*η*k₁*k₃ + 16*β₃*δ₁^2*δ₂^2*δ₃*μ₁^2*μ₂^2*η*k₁*k₃ - 16*β₃*δ₁^2*δ₂^2*δ₃*μ₁*μ₂^3*η*k₁*k₃ - 8*β₃*δ₁^2*δ₂^2*δ₃*μ₂^4*η*k₁*k₃ + 26*β₃*δ₁^2*δ₂^2*μ₁^2*μ₂^3*η*k₁*k₃ - 26*β₃*δ₁^2*δ₂^2*μ₁*μ₂^4*η*k₁*k₃ + 6*β₃*δ₁^2*δ₂^2*μ₂^5*η*k₁*k₃ + 38*β₃*δ₁^2*δ₂*δ₃^4*μ₂*η^2*k₃ - 142*β₃*δ₁^2*δ₂*δ₃^3*μ₁*μ₂*η^2*k₃ - 188*β₃*δ₁^2*δ₂*δ₃^3*μ₂^2*η^2*k₃ + 96*β₃*δ₁^2*δ₂*δ₃^2*μ₁^3*η^2*k₃ + 122*β₃*δ₁^2*δ₂*δ₃^2*μ₁^2*μ₂*η^2*k₃ + 378*β₃*δ₁^2*δ₂*δ₃^2*μ₁*μ₂^2*η^2*k₃ + 310*β₃*δ₁^2*δ₂*δ₃^2*μ₂^3*η^2*k₃ - 128*β₃*δ₁^2*δ₂*δ₃*μ₁^4*η^2*k₃ - 126*β₃*δ₁^2*δ₂*δ₃*μ₁^3*μ₂*η^2*k₃ - 102*β₃*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^2*η^2*k₃ - 477*β₃*δ₁^2*δ₂*δ₃*μ₁*μ₂^3*η^2*k₃ - 40*β₃*δ₁^2*δ₂*δ₃*μ₂^4*η^2*k₃ + 32*β₃*δ₁^2*δ₂*μ₁^5*η^2*k₃ + 96*β₃*δ₁^2*δ₂*μ₁^4*μ₂*η^2*k₃ - 40*β₃*δ₁^2*δ₂*μ₁^3*μ₂^2*η^2*k₃ + 94*β₃*δ₁^2*δ₂*μ₁^2*μ₂^3*η^2*k₃ + 239*β₃*δ₁^2*δ₂*μ₁*μ₂^4*η^2*k₃ - 98*β₃*δ₁^2*δ₂*μ₂^5*η^2*k₃ + 32*β₃*δ₁^2*δ₃^4*μ₂^2*η^2*k₂ - 100*β₃*δ₁^2*δ₃^3*μ₂^3*η^2*k₂ + 192*β₃*δ₁^2*δ₃^2*μ₂^4*η^2*k₂ - 92*β₃*δ₁^2*δ₃*μ₂^5*η^2*k₂ - 38*β₃*δ₁*δ₂*δ₃^4*μ₂^2*η^2*k₁ + 60*β₃*δ₁*δ₂*δ₃^3*μ₂^3*η^2*k₁ - 28*β₃*δ₁*δ₂*δ₃^2*μ₁*μ₂^3*η^2*k₁ - 22*β₃*δ₁*δ₂*δ₃^2*μ₂^4*η^2*k₁ + 2*β₃*δ₁*δ₂*δ₃*μ₁^2*μ₂^3*η^2*k₁ + 96*β₃*δ₁*δ₂*δ₃*μ₁*μ₂^4*η^2*k₁ + 7*β₃*δ₁*δ₂*μ₁^2*μ₂^4*η^2*k₁ - 77*β₃*δ₁*δ₂*μ₁*μ₂^5*η^2*k₁ - 40*β₃*δ₁*δ₃^5*μ₂*η^3 + 32*β₃*δ₁*δ₃^4*μ₁*μ₂*η^3 + 162*β₃*δ₁*δ₃^4*μ₂^2*η^3 - 124*β₃*δ₁*δ₃^3*μ₁*μ₂^2*η^3 - 360*β₃*δ₁*δ₃^3*μ₂^3*η^3 + 262*β₃*δ₁*δ₃^2*μ₁*μ₂^3*η^3 + 330*β₃*δ₁*δ₃^2*μ₂^4*η^3 - 216*β₃*δ₁*δ₃*μ₁*μ₂^4*η^3 - 92*β₃*δ₁*δ₃*μ₂^5*η^3 + 46*β₃*δ₁*μ₁*μ₂^5*η^3 + 2*δ₁^4*δ₂^3*δ₃^2*μ₁*μ₂*k₃^3 - 2*δ₁^4*δ₂^3*δ₃^2*μ₂^2*k₃^3 + 4*δ₁^4*δ₂^3*δ₃*μ₁^2*μ₂*k₃^3 - 4*δ₁^4*δ₂^3*δ₃*μ₁*μ₂^2*k₃^3 + 2*δ₁^4*δ₂^3*μ₁^2*μ₂^2*k₃^3 - 14*δ₁^4*δ₂^3*μ₁*μ₂^3*k₃^3 + 12*δ₁^4*δ₂^3*μ₂^4*k₃^3 - 12*δ₁^3*δ₂^2*δ₃^3*μ₁*μ₂*η*k₃^2 + 8*δ₁^3*δ₂^2*δ₃^2*μ₁^2*μ₂*η*k₃^2 + 26*δ₁^3*δ₂^2*δ₃^2*μ₁*μ₂^2*η*k₃^2 + 2*δ₁^3*δ₂^2*δ₃^2*μ₂^3*η*k₃^2 - 12*δ₁^3*δ₂^2*δ₃*μ₁^3*μ₂*η*k₃^2 + 8*δ₁^3*δ₂^2*δ₃*μ₁^2*μ₂^2*η*k₃^2 - 28*δ₁^3*δ₂^2*δ₃*μ₁*μ₂^3*η*k₃^2 - 4*δ₁^3*δ₂^2*δ₃*μ₂^4*η*k₃^2 - 16*δ₁^3*δ₂^2*μ₁^4*μ₂*η*k₃^2 + 26*δ₁^3*δ₂^2*μ₁^3*μ₂^2*η*k₃^2 - 11*δ₁^3*δ₂^2*μ₁^2*μ₂^3*η*k₃^2 + 45*δ₁^3*δ₂^2*μ₁*μ₂^4*η*k₃^2 - 32*δ₁^3*δ₂^2*μ₂^5*η*k₃^2 - 4*δ₁^2*δ₂^2*δ₃^3*μ₁*μ₂^2*η*k₁*k₃ - 16*δ₁^2*δ₂^2*δ₃^2*μ₁^2*μ₂^2*η*k₁*k₃ + 20*δ₁^2*δ₂^2*δ₃^2*μ₁*μ₂^3*η*k₁*k₃ - 10*δ₁^2*δ₂^2*δ₃*μ₁^2*μ₂^3*η*k₁*k₃ + 10*δ₁^2*δ₂^2*δ₃*μ₁*μ₂^4*η*k₁*k₃ - 2*δ₁^2*δ₂^2*δ₃*μ₂^5*η*k₁*k₃ + 26*δ₁^2*δ₂^2*μ₁^2*μ₂^4*η*k₁*k₃ - 26*δ₁^2*δ₂^2*μ₁*μ₂^5*η*k₁*k₃ - 6*δ₁^2*δ₂*δ₃^5*μ₂*η^2*k₃ + 44*δ₁^2*δ₂*δ₃^4*μ₁*μ₂*η^2*k₃ + 40*δ₁^2*δ₂*δ₃^4*μ₂^2*η^2*k₃ - 32*δ₁^2*δ₂*δ₃^3*μ₁^3*η^2*k₃ - 58*δ₁^2*δ₂*δ₃^3*μ₁^2*μ₂*η^2*k₃ - 152*δ₁^2*δ₂*δ₃^3*μ₁*μ₂^2*η^2*k₃ - 86*δ₁^2*δ₂*δ₃^3*μ₂^3*η^2*k₃ + 64*δ₁^2*δ₂*δ₃^2*μ₁^4*η^2*k₃ + 80*δ₁^2*δ₂*δ₃^2*μ₁^3*μ₂*η^2*k₃ + 90*δ₁^2*δ₂*δ₃^2*μ₁^2*μ₂^2*η^2*k₃ + 248*δ₁^2*δ₂*δ₃^2*μ₁*μ₂^3*η^2*k₃ + 56*δ₁^2*δ₂*δ₃^2*μ₂^4*η^2*k₃ - 32*δ₁^2*δ₂*δ₃*μ₁^5*η^2*k₃ - 88*δ₁^2*δ₂*δ₃*μ₁^4*μ₂*η^2*k₃ - 48*δ₁^2*δ₂*δ₃*μ₁^3*μ₂^2*η^2*k₃ - 66*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^3*η^2*k₃ - 162*δ₁^2*δ₂*δ₃*μ₁*μ₂^4*η^2*k₃ - 2*δ₁^2*δ₂*δ₃*μ₂^5*η^2*k₃ + 48*δ₁^2*δ₂*μ₁^5*μ₂*η^2*k₃ - 12*δ₁^2*δ₂*μ₁^4*μ₂^2*η^2*k₃ + 37*δ₁^2*δ₂*μ₁^3*μ₂^3*η^2*k₃ - 64*δ₁^2*δ₂*μ₁^2*μ₂^4*η^2*k₃ + 101*δ₁^2*δ₂*μ₁*μ₂^5*η^2*k₃ - 8*δ₁^2*δ₃^5*μ₂^2*η^2*k₂ + 30*δ₁^2*δ₃^4*μ₂^3*η^2*k₂ - 68*δ₁^2*δ₃^3*μ₂^4*η^2*k₂ + 46*δ₁^2*δ₃^2*μ₂^5*η^2*k₂ + 8*δ₁*δ₂*δ₃^5*μ₂^2*η^2*k₁ - 16*δ₁*δ₂*δ₃^4*μ₂^3*η^2*k₁ + 14*δ₁*δ₂*δ₃^3*μ₁*μ₂^3*η^2*k₁ + 8*δ₁*δ₂*δ₃^3*μ₂^4*η^2*k₁ - 2*δ₁*δ₂*δ₃^2*μ₁^2*μ₂^3*η^2*k₁ - 61*δ₁*δ₂*δ₃^2*μ₁*μ₂^4*η^2*k₁ - 2*δ₁*δ₂*δ₃*μ₁^4*μ₂^2*η^2*k₁ - 10*δ₁*δ₂*δ₃*μ₁^3*μ₂^3*η^2*k₁ + 7*δ₁*δ₂*δ₃*μ₁^2*μ₂^4*η^2*k₁ + 89*δ₁*δ₂*δ₃*μ₁*μ₂^5*η^2*k₁ - 6*δ₁*δ₂*μ₁^5*μ₂^2*η^2*k₁ + 6*δ₁*δ₂*μ₁^4*μ₂^3*η^2*k₁ + 42*δ₁*δ₂*μ₁^3*μ₂^4*η^2*k₁ - 35*δ₁*δ₂*μ₁^2*μ₂^5*η^2*k₁ - 42*δ₁*δ₂*μ₁*μ₂^6*η^2*k₁ + 8*δ₁*δ₃^6*μ₂*η^3 - 8*δ₁*δ₃^5*μ₁*μ₂*η^3 - 38*δ₁*δ₃^5*μ₂^2*η^3 + 38*δ₁*δ₃^4*μ₁*μ₂^2*η^3 + 98*δ₁*δ₃^4*μ₂^3*η^3 - 98*δ₁*δ₃^3*μ₁*μ₂^3*η^3 - 114*δ₁*δ₃^3*μ₂^4*η^3 + 114*δ₁*δ₃^2*μ₁*μ₂^4*η^3 + 46*δ₁*δ₃^2*μ₂^5*η^3 - 46*δ₁*δ₃*μ₁*μ₂^5*η^3
 6*β₂^2*β₃^2*δ₁^5*δ₂*k₃^4 + 8*β₂^2*β₃*δ₁^5*δ₂*δ₃*k₃^4 - 8*β₂^2*β₃*δ₁^5*δ₂*μ₁*k₃^4 - 16*β₂^2*β₃*δ₁^4*δ₃^2*η*k₃^3 + 38*β₂^2*β₃*δ₁^4*δ₃*μ₁*η*k₃^3 - 4*β₂^2*β₃*δ₁^4*δ₃*μ₂*η*k₃^3 - 4*β₂^2*β₃*δ₁^4*μ₁*μ₂*η*k₃^3 + 8*β₂^2*β₃*δ₁^4*μ₂^2*η*k₃^3 + 4*β₂^2*β₃*δ₁^3*δ₃^2*μ₂*η*k₁*k₃^2 - 4*β₂^2*β₃*δ₁^3*δ₃*μ₂^2*η*k₁*k₃^2 + 16*β₂^2*δ₁^4*δ₃^3*η*k₃^3 - 66*β₂^2*δ₁^4*δ₃^2*μ₁*η*k₃^3 + 12*β₂^2*δ₁^4*δ₃^2*μ₂*η*k₃^3 + 68*β₂^2*δ₁^4*δ₃*μ₁^2*η*k₃^3 - 8*β₂^2*δ₁^4*δ₃*μ₁*μ₂*η*k₃^3 - 34*β₂^2*δ₁^4*μ₁^2*μ₂*η*k₃^3 + 12*β₂^2*δ₁^4*μ₁*μ₂^2*η*k₃^3 - 4*β₂^2*δ₁^3*δ₃^3*μ₂*η*k₁*k₃^2 + 4*β₂^2*δ₁^3*δ₃^2*μ₂^2*η*k₁*k₃^2 - 20*β₂^2*δ₁^3*δ₃*μ₁*μ₂^2*η*k₁*k₃^2 + 4*β₂^2*δ₁^3*μ₁*μ₂^3*η*k₁*k₃^2 - 12*β₂*β₃^2*δ₁^5*δ₂^2*k₃^4 - 16*β₂*β₃*δ₁^5*δ₂^2*δ₃*k₃^4 + 16*β₂*β₃*δ₁^5*δ₂^2*μ₁*k₃^4 + 32*β₂*β₃*δ₁^4*δ₂*δ₃^2*η*k₃^3 + 22*β₂*β₃*δ₁^4*δ₂*δ₃*μ₁*η*k₃^3 + 36*β₂*β₃*δ₁^4*δ₂*δ₃*μ₂*η*k₃^3 - 172*β₂*β₃*δ₁^4*δ₂*μ₁^2*η*k₃^3 + 10*β₂*β₃*δ₁^4*δ₂*μ₁*μ₂*η*k₃^3 - 2*β₂*β₃*δ₁^4*δ₂*μ₂^2*η*k₃^3 + 2*β₂*β₃*δ₁^3*δ₂*δ₃^2*μ₂*η*k₁*k₃^2 - 12*β₂*β₃*δ₁^3*δ₂*δ₃*μ₂^2*η*k₁*k₃^2 + 8*β₂*β₃*δ₁^3*δ₂*μ₂^3*η*k₁*k₃^2 - 10*β₂*β₃*δ₁^3*δ₃^2*μ₁*η^2*k₃^2 - 11*β₂*β₃*δ₁^3*δ₃*μ₁^2*η^2*k₃^2 - 106*β₂*β₃*δ₁^3*δ₃*μ₁*μ₂*η^2*k₃^2 - 8*β₂*β₃*δ₁^3*δ₃*μ₂^2*η^2*k₃^2 + 64*β₂*β₃*δ₁^3*μ₁^3*η^2*k₃^2 + 97*β₂*β₃*δ₁^3*μ₁^2*μ₂*η^2*k₃^2 + 15*β₂*β₃*δ₁^3*μ₁*μ₂^2*η^2*k₃^2 - 8*β₂*β₃*δ₁^3*μ₂^3*η^2*k₃^2 + 28*β₂*β₃*δ₁^2*δ₃*μ₁*μ₂^2*η^2*k₁*k₃ + 13*β₂*β₃*δ₁^2*μ₁*μ₂^3*η^2*k₁*k₃ - 8*β₂*δ₁^5*δ₂*δ₃^2*μ₂*k₂*k₃^3 - 32*β₂*δ₁^4*δ₂*δ₃^3*η*k₃^3 + 42*β₂*δ₁^4*δ₂*δ₃^2*μ₁*η*k₃^3 - 8*β₂*δ₁^4*δ₂*δ₃^2*μ₂*η*k₃^3 + 36*β₂*δ₁^4*δ₂*δ₃*μ₁^2*η*k₃^3 + 8*β₂*δ₁^4*δ₂*δ₃*μ₁*μ₂*η*k₃^3 - 16*β₂*δ₁^4*δ₂*δ₃*μ₂^2*η*k₃^3 - 56*β₂*δ₁^4*δ₂*μ₁^2*μ₂*η*k₃^3 + 38*β₂*δ₁^4*δ₂*μ₁*μ₂^2*η*k₃^3 - 12*β₂*δ₁^4*δ₂*μ₂^3*η*k₃^3 + 28*β₂*δ₁^4*μ₁*μ₂^3*η*k₂*k₃^2 - 2*β₂*δ₁^3*δ₂*δ₃^3*μ₂*η*k₁*k₃^2 + 4*β₂*δ₁^3*δ₂*δ₃^2*μ₂^2*η*k₁*k₃^2 + 4*β₂*δ₁^3*δ₂*δ₃*μ₂^3*η*k₁*k₃^2 - 4*β₂*δ₁^3*δ₂*μ₂^4*η*k₁*k₃^2 + 10*β₂*δ₁^3*δ₃^3*μ₁*η^2*k₃^2 + 8*β₂*δ₁^3*δ₃^2*μ₁^2*η^2*k₃^2 + 70*β₂*δ₁^3*δ₃^2*μ₁*μ₂*η^2*k₃^2 + 8*β₂*δ₁^3*δ₃^2*μ₂^2*η^2*k₃^2 - 64*β₂*δ₁^3*δ₃*μ₁^3*η^2*k₃^2 - 116*β₂*δ₁^3*δ₃*μ₁^2*μ₂*η^2*k₃^2 - 30*β₂*δ₁^3*δ₃*μ₁*μ₂^2*η^2*k₃^2 + 8*β₂*δ₁^3*δ₃*μ₂^3*η^2*k₃^2 + 66*β₂*δ₁^3*μ₁^3*μ₂*η^2*k₃^2 + 48*β₂*δ₁^3*μ₁^2*μ₂^2*η^2*k₃^2 + 4*β₂*δ₁^3*μ₁*μ₂^4*η*k₁*k₂*k₃ - 8*β₂*δ₁^3*μ₁*μ₂^3*η^2*k₃^2 - 28*β₂*δ₁^2*δ₃^2*μ₁*μ₂^2*η^2*k₁*k₃ - 36*β₂*δ₁^2*δ₃*μ₁^3*μ₂*η^2*k₁*k₃ + 9*β₂*δ₁^2*δ₃*μ₁^2*μ₂^2*η^2*k₁*k₃ + 4*β₂*δ₁^2*δ₃*μ₁*μ₂^3*η^2*k₁*k₃ - 16*β₂*δ₁^2*μ₁^4*μ₂*η^2*k₁*k₃ + 25*β₂*δ₁^2*μ₁^3*μ₂^2*η^2*k₁*k₃ + 42*β₂*δ₁^2*μ₁^2*μ₂^3*η^2*k₁*k₃ + 2*β₂*δ₁*μ₁^3*μ₂^3*η^2*k₁^2 - 2*β₂*δ₁*μ₁^2*μ₂^4*η^2*k₁^2 + 4*β₃^6*δ₁*η^3*k₁ + 14*β₃^5*δ₁^2*δ₂*η^2*k₁*k₃ + 4*β₃^5*δ₁^2*μ₂*η^2*k₁*k₂ - 8*β₃^5*δ₁^2*η^3*k₃ - 24*β₃^5*δ₁*δ₃*η^3*k₁ + 4*β₃^5*δ₁*μ₁*η^3*k₁ - 2*β₃^5*δ₁*μ₂*η^3*k₁ + 6*β₃^4*δ₁^3*δ₂^2*η*k₁*k₃^2 - 22*β₃^4*δ₁^3*δ₂*η^2*k₃^2 - 8*β₃^4*δ₁^3*μ₂*η^2*k₂*k₃ - 60*β₃^4*δ₁^2*δ₂*δ₃*η^2*k₁*k₃ - 16*β₃^4*δ₁^2*δ₂*μ₂*η^2*k₁*k₃ - 20*β₃^4*δ₁^2*δ₃*μ₂*η^2*k₁*k₂ + 20*β₃^4*δ₁^2*δ₃*η^3*k₃ - 8*β₃^4*δ₁^2*μ₁*η^3*k₃ - 6*β₃^4*δ₁^2*μ₂^2*η^2*k₁*k₂ + 10*β₃^4*δ₁^2*μ₂*η^3*k₃ + 60*β₃^4*δ₁*δ₃^2*η^3*k₁ - 20*β₃^4*δ₁*δ₃*μ₁*η^3*k₁ + 10*β₃^4*δ₁*δ₃*μ₂*η^3*k₁ - 2*β₃^4*δ₁*μ₁*μ₂*η^3*k₁ - 16*β₃^4*δ₁*μ₂^2*η^3*k₁ - 16*β₃^3*δ₁^3*δ₂^2*δ₃*η*k₁*k₃^2 - 2*β₃^3*δ₁^3*δ₂^2*μ₂*η*k₁*k₃^2 + 8*β₃^3*δ₁^3*δ₂*δ₃*η^2*k₃^2 - 42*β₃^3*δ₁^3*δ₂*μ₁*η^2*k₃^2 + 52*β₃^3*δ₁^3*δ₂*μ₂*η^2*k₃^2 + 12*β₃^3*δ₁^3*δ₃*μ₂*η^2*k₂*k₃ + 18*β₃^3*δ₁^3*μ₂^2*η^2*k₂*k₃ + 100*β₃^3*δ₁^2*δ₂*δ₃^2*η^2*k₁*k₃ + 40*β₃^3*δ₁^2*δ₂*δ₃*μ₂*η^2*k₁*k₃ - 2*β₃^3*δ₁^2*δ₂*μ₂^2*η^2*k₁*k₃ + 40*β₃^3*δ₁^2*δ₃^2*μ₂*η^2*k₁*k₂ + 12*β₃^3*δ₁^2*δ₃*μ₁*η^3*k₃ + 24*β₃^3*δ₁^2*δ₃*μ₂^2*η^2*k₁*k₂ - 86*β₃^3*δ₁^2*δ₃*μ₂*η^3*k₃ + 10*β₃^3*δ₁^2*μ₁*μ₂*η^3*k₃ - 10*β₃^3*δ₁^2*μ₂^3*η^2*k₁*k₂ + 48*β₃^3*δ₁^2*μ₂^2*η^3*k₃ - 80*β₃^3*δ₁*δ₃^3*η^3*k₁ + 40*β₃^3*δ₁*δ₃^2*μ₁*η^3*k₁ - 20*β₃^3*δ₁*δ₃^2*μ₂*η^3*k₁ + 8*β₃^3*δ₁*δ₃*μ₁*μ₂*η^3*k₁ + 64*β₃^3*δ₁*δ₃*μ₂^2*η^3*k₁ - 16*β₃^3*δ₁*μ₁*μ₂^2*η^3*k₁ - 8*β₃^3*δ₁*μ₂^3*η^3*k₁ + 6*β₃^2*δ₁^5*δ₂^3*k₃^4 - 16*β₃^2*δ₁^4*δ₂^2*δ₃*η*k₃^3 + 4*β₃^2*δ₁^4*δ₂^2*μ₂*η*k₃^3 + 14*β₃^2*δ₁^3*δ₂^2*δ₃^2*η*k₁*k₃^2 - 2*β₃^2*δ₁^3*δ₂^2*δ₃*μ₂*η*k₁*k₃^2 + 2*β₃^2*δ₁^3*δ₂^2*μ₂^2*η*k₁*k₃^2 + 66*β₃^2*δ₁^3*δ₂*δ₃^2*η^2*k₃^2 + 142*β₃^2*δ₁^3*δ₂*δ₃*μ₁*η^2*k₃^2 - 136*β₃^2*δ₁^3*δ₂*δ₃*μ₂*η^2*k₃^2 - 136*β₃^2*δ₁^3*δ₂*μ₁^2*η^2*k₃^2 - 72*β₃^2*δ₁^3*δ₂*μ₁*μ₂*η^2*k₃^2 + 16*β₃^2*δ₁^3*δ₂*μ₂^2*η^2*k₃^2 + 12*β₃^2*δ₁^3*δ₃^2*μ₂*η^2*k₂*k₃ - 80*β₃^2*δ₁^3*δ₃*μ₂^2*η^2*k₂*k₃ + 30*β₃^2*δ₁^3*μ₂^3*η^2*k₂*k₃ - 80*β₃^2*δ₁^2*δ₂*δ₃^3*η^2*k₁*k₃ - 24*β₃^2*δ₁^2*δ₂*δ₃^2*μ₂*η^2*k₁*k₃ - 16*β₃^2*δ₁^2*δ₂*δ₃*μ₁*μ₂*η^2*k₁*k₃ - 10*β₃^2*δ₁^2*δ₂*μ₁*μ₂^2*η^2*k₁*k₃ + 24*β₃^2*δ₁^2*δ₂*μ₂^3*η^2*k₁*k₃ - 40*β₃^2*δ₁^2*δ₃^3*μ₂*η^2*k₁*k₂ - 40*β₃^2*δ₁^2*δ₃^3*η^3*k₃ + 12*β₃^2*δ₁^2*δ₃^2*μ₁*η^3*k₃ - 36*β₃^2*δ₁^2*δ₃^2*μ₂^2*η^2*k₁*k₂ + 198*β₃^2*δ₁^2*δ₃^2*μ₂*η^3*k₃ - β₃^2*δ₁^2*δ₃*μ₁^2*η^3*k₃ - 74*β₃^2*δ₁^2*δ₃*μ₁*μ₂*η^3*k₃ + 30*β₃^2*δ₁^2*δ₃*μ₂^3*η^2*k₁*k₂ - 170*β₃^2*δ₁^2*δ₃*μ₂^2*η^3*k₃ + 5*β₃^2*δ₁^2*μ₁^2*μ₂*η^3*k₃ + 40*β₃^2*δ₁^2*μ₁*μ₂^2*η^3*k₃ + 2*β₃^2*δ₁^2*μ₂^4*η^2*k₁*k₂ + 30*β₃^2*δ₁^2*μ₂^3*η^3*k₃ + 16*β₃^2*δ₁*δ₂*μ₁*μ₂^3*η^2*k₁^2 + 60*β₃^2*δ₁*δ₃^4*η^3*k₁ - 40*β₃^2*δ₁*δ₃^3*μ₁*η^3*k₁ + 20*β₃^2*δ₁*δ₃^3*μ₂*η^3*k₁ - 12*β₃^2*δ₁*δ₃^2*μ₁*μ₂*η^3*k₁ - 96*β₃^2*δ₁*δ₃^2*μ₂^2*η^3*k₁ + 48*β₃^2*δ₁*δ₃*μ₁*μ₂^2*η^3*k₁ + 24*β₃^2*δ₁*δ₃*μ₂^3*η^3*k₁ + 5*β₃^2*δ₁*μ₁^2*μ₂^2*η^3*k₁ - 11*β₃^2*δ₁*μ₁*μ₂^3*η^3*k₁ + 2*β₃^2*δ₁*μ₂^4*η^3*k₁ + 8*β₃*δ₁^5*δ₂^3*δ₃*k₃^4 - 8*β₃*δ₁^5*δ₂^3*μ₁*k₃^4 + 8*β₃*δ₁^5*δ₂^2*μ₂^2*k₂*k₃^3 + 16*β₃*δ₁^4*δ₂^2*δ₃^2*η*k₃^3 - 44*β₃*δ₁^4*δ₂^2*δ₃*μ₁*η*k₃^3 - 40*β₃*δ₁^4*δ₂^2*δ₃*μ₂*η*k₃^3 + 76*β₃*δ₁^4*δ₂^2*μ₁^2*η*k₃^3 + 50*β₃*δ₁^4*δ₂^2*μ₁*μ₂*η*k₃^3 - 6*β₃*δ₁^4*δ₂^2*μ₂^2*η*k₃^3 - 32*β₃*δ₁^4*δ₂*δ₃*μ₂^2*η*k₂*k₃^2 - 4*β₃*δ₁^3*δ₂^2*δ₃^3*η*k₁*k₃^2 + 4*β₃*δ₁^3*δ₂^2*δ₃^2*μ₁*η*k₁*k₃^2 + 4*β₃*δ₁^3*δ₂^2*δ₃^2*μ₂*η*k₁*k₃^2 - 32*β₃*δ₁^3*δ₂^2*δ₃*μ₁^2*η*k₁*k₃^2 + 4*β₃*δ₁^3*δ₂^2*δ₃*μ₂^2*η*k₁*k₃^2 + 8*β₃*δ₁^3*δ₂^2*μ₁^2*μ₂*η*k₁*k₃^2 + 24*β₃*δ₁^3*δ₂^2*μ₁*μ₂^2*η*k₁*k₃^2 - 6*β₃*δ₁^3*δ₂^2*μ₂^3*η*k₁*k₃^2 - 68*β₃*δ₁^3*δ₂*δ₃^3*η^2*k₃^2 - 158*β₃*δ₁^3*δ₂*δ₃^2*μ₁*η^2*k₃^2 + 116*β₃*δ₁^3*δ₂*δ₃^2*μ₂*η^2*k₃^2 + 281*β₃*δ₁^3*δ₂*δ₃*μ₁^2*η^2*k₃^2 + 166*β₃*δ₁^3*δ₂*δ₃*μ₁*μ₂*η^2*k₃^2 + 4*β₃*δ₁^3*δ₂*δ₃*μ₂^2*η^2*k₃^2 - 68*β₃*δ₁^3*δ₂*μ₁^3*η^2*k₃^2 - 199*β₃*δ₁^3*δ₂*μ₁^2*μ₂*η^2*k₃^2 - 57*β₃*δ₁^3*δ₂*μ₁*μ₂^2*η^2*k₃^2 - 50*β₃*δ₁^3*δ₂*μ₂^3*η^2*k₃^2 - 28*β₃*δ₁^3*δ₃^3*μ₂*η^2*k₂*k₃ + 106*β₃*δ₁^3*δ₃^2*μ₂^2*η^2*k₂*k₃ - β₃*δ₁^3*δ₃*μ₁^2*μ₂*η^2*k₂*k₃ + 2*β₃*δ₁^3*δ₃*μ₁*μ₂^2*η^2*k₂*k₃ - 60*β₃*δ₁^3*δ₃*μ₂^3*η^2*k₂*k₃ + 5*β₃*δ₁^3*μ₁^2*μ₂^2*η^2*k₂*k₃ - 8*β₃*δ₁^3*μ₁*μ₂^3*η^2*k₂*k₃ + 30*β₃*δ₁^2*δ₂*δ₃^4*η^2*k₁*k₃ - 8*β₃*δ₁^2*δ₂*δ₃^3*μ₂*η^2*k₁*k₃ + 32*β₃*δ₁^2*δ₂*δ₃^2*μ₁*μ₂*η^2*k₁*k₃ + 6*β₃*δ₁^2*δ₂*δ₃^2*μ₂^2*η^2*k₁*k₃ + 6*β₃*δ₁^2*δ₂*δ₃*μ₁^3*η^2*k₁*k₃ + 40*β₃*δ₁^2*δ₂*δ₃*μ₁^2*μ₂*η^2*k₁*k₃ + 8*β₃*δ₁^2*δ₂*δ₃*μ₁*μ₂^2*η^2*k₁*k₃ - 24*β₃*δ₁^2*δ₂*δ₃*μ₂^3*η^2*k₁*k₃ - 10*β₃*δ₁^2*δ₂*μ₁^4*η^2*k₁*k₃ - 48*β₃*δ₁^2*δ₂*μ₁^2*μ₂^2*η^2*k₁*k₃ - 69*β₃*δ₁^2*δ₂*μ₁*μ₂^3*η^2*k₁*k₃ - 4*β₃*δ₁^2*δ₂*μ₂^4*η^2*k₁*k₃ + 20*β₃*δ₁^2*δ₃^4*μ₂*η^2*k₁*k₂ + 40*β₃*δ₁^2*δ₃^4*η^3*k₃ - 28*β₃*δ₁^2*δ₃^3*μ₁*η^3*k₃ + 24*β₃*δ₁^2*δ₃^3*μ₂^2*η^2*k₁*k₂ - 178*β₃*δ₁^2*δ₃^3*μ₂*η^3*k₃ + 2*β₃*δ₁^2*δ₃^2*μ₁^2*η^3*k₃ + 118*β₃*δ₁^2*δ₃^2*μ₁*μ₂*η^3*k₃ - 30*β₃*δ₁^2*δ₃^2*μ₂^3*η^2*k₁*k₂ + 196*β₃*δ₁^2*δ₃^2*μ₂^2*η^3*k₃ - β₃*δ₁^2*δ₃*μ₁^3*η^3*k₃ - 9*β₃*δ₁^2*δ₃*μ₁^2*μ₂*η^3*k₃ - 104*β₃*δ₁^2*δ₃*μ₁*μ₂^2*η^3*k₃ - 4*β₃*δ₁^2*δ₃*μ₂^4*η^2*k₁*k₂ - 60*β₃*δ₁^2*δ₃*μ₂^3*η^3*k₃ + 5*β₃*δ₁^2*μ₁^3*μ₂*η^3*k₃ + 5*β₃*δ₁^2*μ₁^2*μ₂^3*η^2*k₁*k₂ - 3*β₃*δ₁^2*μ₁^2*μ₂^2*η^3*k₃ - 3*β₃*δ₁^2*μ₁*μ₂^4*η^2*k₁*k₂ + 22*β₃*δ₁^2*μ₁*μ₂^3*η^3*k₃ - 32*β₃*δ₁*δ₂*δ₃*μ₁*μ₂^3*η^2*k₁^2 + 14*β₃*δ₁*δ₂*μ₁^2*μ₂^3*η^2*k₁^2 + 18*β₃*δ₁*δ₂*μ₁*μ₂^4*η^2*k₁^2 - 24*β₃*δ₁*δ₃^5*η^3*k₁ + 20*β₃*δ₁*δ₃^4*μ₁*η^3*k₁ - 10*β₃*δ₁*δ₃^4*μ₂*η^3*k₁ + 8*β₃*δ₁*δ₃^3*μ₁*μ₂*η^3*k₁ + 64*β₃*δ₁*δ₃^3*μ₂^2*η^3*k₁ - 48*β₃*δ₁*δ₃^2*μ₁*μ₂^2*η^3*k₁ - 24*β₃*δ₁*δ₃^2*μ₂^3*η^3*k₁ - 10*β₃*δ₁*δ₃*μ₁^2*μ₂^2*η^3*k₁ + 22*β₃*δ₁*δ₃*μ₁*μ₂^3*η^3*k₁ - 4*β₃*δ₁*δ₃*μ₂^4*η^3*k₁ + 5*β₃*δ₁*μ₁^3*μ₂^2*η^3*k₁ + 2*β₃*δ₁*μ₁^2*μ₂^3*η^3*k₁ - β₃*δ₁*μ₁*μ₂^4*η^3*k₁ - 8*δ₁^5*δ₂^2*δ₃^2*μ₂*k₂*k₃^3 + 16*δ₁^5*δ₂^2*δ₃*μ₂^2*k₂*k₃^3 + 2*δ₁^5*δ₂*δ₃^2*μ₂^2*k₂^2*k₃^2 + 8*δ₁^4*δ₂^2*δ₃^2*μ₁*η*k₃^3 - 8*δ₁^4*δ₂^2*δ₃*μ₁^2*η*k₃^3 - 40*δ₁^4*δ₂^2*δ₃*μ₁*μ₂*η*k₃^3 + 32*δ₁^4*δ₂^2*δ₃*μ₂^2*η*k₃^3 - 6*δ₁^4*δ₂^2*μ₁^2*μ₂*η*k₃^3 + 6*δ₁^4*δ₂^2*μ₁*μ₂^2*η*k₃^3 + 8*δ₁^4*δ₂^2*μ₂^3*η*k₃^3 + 6*δ₁^4*δ₂*δ₃^2*μ₁*μ₂*η*k₂*k₃^2 + 24*δ₁^4*δ₂*δ₃^2*μ₂^2*η*k₂*k₃^2 - 20*δ₁^4*δ₂*δ₃*μ₁*μ₂^2*η*k₂*k₃^2 - 20*δ₁^4*δ₂*δ₃*μ₂^3*η*k₂*k₃^2 - 14*δ₁^4*δ₂*μ₁*μ₂^3*η*k₂*k₃^2 - 4*δ₁^4*δ₂*μ₂^4*η*k₂*k₃^2 - 4*δ₁^3*δ₂^2*δ₃^3*μ₁*η*k₁*k₃^2 + 32*δ₁^3*δ₂^2*δ₃^2*μ₁^2*η*k₁*k₃^2 + 4*δ₁^3*δ₂^2*δ₃^2*μ₁*μ₂*η*k₁*k₃^2 - 40*δ₁^3*δ₂^2*δ₃*μ₁^2*μ₂*η*k₁*k₃^2 - 4*δ₁^3*δ₂^2*δ₃*μ₁*μ₂^2*η*k₁*k₃^2 + 2*δ₁^3*δ₂^2*δ₃*μ₂^3*η*k₁*k₃^2 + 8*δ₁^3*δ₂^2*μ₁^2*μ₂^2*η*k₁*k₃^2 + 20*δ₁^3*δ₂^2*μ₁*μ₂^3*η*k₁*k₃^2 - 4*δ₁^3*δ₂^2*μ₂^4*η*k₁*k₃^2 + 16*δ₁^3*δ₂*δ₃^4*η^2*k₃^2 + 58*δ₁^3*δ₂*δ₃^3*μ₁*η^2*k₃^2 - 32*δ₁^3*δ₂*δ₃^3*μ₂*η^2*k₃^2 - 142*δ₁^3*δ₂*δ₃^2*μ₁^2*η^2*k₃^2 - 68*δ₁^3*δ₂*δ₃^2*μ₁*μ₂*η^2*k₃^2 + 22*δ₁^3*δ₂*δ₃^2*μ₂^2*η^2*k₃^2 + 68*δ₁^3*δ₂*δ₃*μ₁^3*η^2*k₃^2 + 216*δ₁^3*δ₂*δ₃*μ₁^2*μ₂*η^2*k₃^2 - 28*δ₁^3*δ₂*δ₃*μ₁*μ₂^2*η^2*k₃^2 + 4*δ₁^3*δ₂*δ₃*μ₂^4*η*k₁*k₂*k₃ - 22*δ₁^3*δ₂*δ₃*μ₂^3*η^2*k₃^2 - 70*δ₁^3*δ₂*μ₁^3*μ₂*η^2*k₃^2 - 14*δ₁^3*δ₂*μ₁^2*μ₂^2*η^2*k₃^2 - 4*δ₁^3*δ₂*μ₁*μ₂^3*η^2*k₃^2 - 4*δ₁^3*δ₂*μ₂^5*η*k₁*k₂*k₃ + 12*δ₁^3*δ₃^4*μ₂*η^2*k₂*k₃ - 44*δ₁^3*δ₃^3*μ₂^2*η^2*k₂*k₃ + δ₁^3*δ₃^2*μ₁^2*μ₂*η^2*k₂*k₃ - 2*δ₁^3*δ₃^2*μ₁*μ₂^2*η^2*k₂*k₃ + 30*δ₁^3*δ₃^2*μ₂^3*η^2*k₂*k₃ - 5*δ₁^3*δ₃*μ₁^2*μ₂^2*η^2*k₂*k₃ + 8*δ₁^3*δ₃*μ₁*μ₂^3*η^2*k₂*k₃ - 4*δ₁^2*δ₂*δ₃^5*η^2*k₁*k₃ + 8*δ₁^2*δ₂*δ₃^4*μ₂*η^2*k₁*k₃ - 16*δ₁^2*δ₂*δ₃^3*μ₁*μ₂*η^2*k₁*k₃ - 4*δ₁^2*δ₂*δ₃^3*μ₂^2*η^2*k₁*k₃ - 6*δ₁^2*δ₂*δ₃^2*μ₁^3*η^2*k₁*k₃ - 40*δ₁^2*δ₂*δ₃^2*μ₁^2*μ₂*η^2*k₁*k₃ + 2*δ₁^2*δ₂*δ₃^2*μ₁*μ₂^2*η^2*k₁*k₃ + 10*δ₁^2*δ₂*δ₃*μ₁^4*η^2*k₁*k₃ + 42*δ₁^2*δ₂*δ₃*μ₁^3*μ₂*η^2*k₁*k₃ + 79*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^2*η^2*k₁*k₃ + 84*δ₁^2*δ₂*δ₃*μ₁*μ₂^3*η^2*k₁*k₃ + 6*δ₁^2*δ₂*μ₁^4*μ₂*η^2*k₁*k₃ - 25*δ₁^2*δ₂*μ₁^3*μ₂^2*η^2*k₁*k₃ - 90*δ₁^2*δ₂*μ₁^2*μ₂^3*η^2*k₁*k₃ - 46*δ₁^2*δ₂*μ₁*μ₂^4*η^2*k₁*k₃ - 4*δ₁^2*δ₃^5*μ₂*η^2*k₁*k₂ - 12*δ₁^2*δ₃^5*η^3*k₃ + 12*δ₁^2*δ₃^4*μ₁*η^3*k₃ - 6*δ₁^2*δ₃^4*μ₂^2*η^2*k₁*k₂ + 56*δ₁^2*δ₃^4*μ₂*η^3*k₃ - δ₁^2*δ₃^3*μ₁^2*η^3*k₃ - 54*δ₁^2*δ₃^3*μ₁*μ₂*η^3*k₃ + 10*δ₁^2*δ₃^3*μ₂^3*η^2*k₁*k₂ - 74*δ₁^2*δ₃^3*μ₂^2*η^3*k₃ + δ₁^2*δ₃^2*μ₁^3*η^3*k₃ + 4*δ₁^2*δ₃^2*μ₁^2*μ₂*η^3*k₃ + 64*δ₁^2*δ₃^2*μ₁*μ₂^2*η^3*k₃ + 2*δ₁^2*δ₃^2*μ₂^4*η^2*k₁*k₂ + 30*δ₁^2*δ₃^2*μ₂^3*η^3*k₃ - 6*δ₁^2*δ₃*μ₁^3*μ₂*η^3*k₃ - 5*δ₁^2*δ₃*μ₁^2*μ₂^3*η^2*k₁*k₂ + 5*δ₁^2*δ₃*μ₁^2*μ₂^2*η^3*k₃ + 3*δ₁^2*δ₃*μ₁*μ₂^4*η^2*k₁*k₂ - 22*δ₁^2*δ₃*μ₁*μ₂^3*η^3*k₃ + 5*δ₁^2*μ₁^3*μ₂^2*η^3*k₃ - 8*δ₁^2*μ₁^2*μ₂^3*η^3*k₃ + 16*δ₁*δ₂*δ₃^2*μ₁*μ₂^3*η^2*k₁^2 - 14*δ₁*δ₂*δ₃*μ₁^2*μ₂^3*η^2*k₁^2 - 18*δ₁*δ₂*δ₃*μ₁*μ₂^4*η^2*k₁^2 - 2*δ₁*δ₂*μ₁^3*μ₂^3*η^2*k₁^2 + 16*δ₁*δ₂*μ₁^2*μ₂^4*η^2*k₁^2 + 2*δ₁*δ₂*μ₁*μ₂^5*η^2*k₁^2 + 4*δ₁*δ₃^6*η^3*k₁ - 4*δ₁*δ₃^5*μ₁*η^3*k₁ + 2*δ₁*δ₃^5*μ₂*η^3*k₁ - 2*δ₁*δ₃^4*μ₁*μ₂*η^3*k₁ - 16*δ₁*δ₃^4*μ₂^2*η^3*k₁ + 16*δ₁*δ₃^3*μ₁*μ₂^2*η^3*k₁ + 8*δ₁*δ₃^3*μ₂^3*η^3*k₁ + 5*δ₁*δ₃^2*μ₁^2*μ₂^2*η^3*k₁ - 11*δ₁*δ₃^2*μ₁*μ₂^3*η^3*k₁ + 2*δ₁*δ₃^2*μ₂^4*η^3*k₁ - 5*δ₁*δ₃*μ₁^3*μ₂^2*η^3*k₁ - 2*δ₁*δ₃*μ₁^2*μ₂^3*η^3*k₁ + δ₁*δ₃*μ₁*μ₂^4*η^3*k₁ + 5*δ₁*μ₁^3*μ₂^3*η^3*k₁ - 3*δ₁*μ₁^2*μ₂^4*η^3*k₁
 10*β₂^3*β₃*δ₁^5*δ₂*k₃^4 - 31*β₂^3*β₃*δ₁^4*δ₃*η*k₃^3 - 15*β₂^3*β₃*δ₁^4*μ₁*η*k₃^3 - 4*β₂^3*β₃*δ₁^4*μ₂*η*k₃^3 - 4*β₂^3*β₃*δ₁^3*δ₃^2*η*k₁*k₃^2 - 2*β₂^3*δ₁^4*δ₂*δ₃*μ₁*k₁*k₃^3 + 7*β₂^3*δ₁^4*δ₃^2*η*k₃^3 - 14*β₂^3*δ₁^4*δ₃*μ₁*η*k₃^3 + 7*β₂^3*δ₁^4*μ₁*μ₂*η*k₃^3 + 4*β₂^3*δ₁^3*δ₃^3*η*k₁*k₃^2 - 22*β₂^2*β₃*δ₁^5*δ₂^2*k₃^4 - 12*β₂^2*β₃*δ₁^5*δ₂*δ₃*k₂*k₃^3 + 4*β₂^2*β₃*δ₁^5*δ₂*μ₁*k₂*k₃^3 + 10*β₂^2*β₃*δ₁^5*δ₂*μ₂*k₂*k₃^3 + 57*β₂^2*β₃*δ₁^4*δ₂*δ₃*η*k₃^3 + 27*β₂^2*β₃*δ₁^4*δ₂*μ₁*η*k₃^3 - 12*β₂^2*β₃*δ₁^4*δ₂*μ₂*η*k₃^3 + 12*β₂^2*β₃*δ₁^4*δ₃^2*η*k₂*k₃^2 + 4*β₂^2*β₃*δ₁^3*δ₂*δ₃^2*η*k₁*k₃^2 + 4*β₂^2*β₃*δ₁^3*δ₂*δ₃*μ₂*η*k₁*k₃^2 + β₂^2*β₃*δ₁^3*δ₃^2*η^2*k₃^2 - 72*β₂^2*β₃*δ₁^3*δ₃*μ₁*η^2*k₃^2 + 44*β₂^2*β₃*δ₁^3*δ₃*μ₂*η^2*k₃^2 + 28*β₂^2*β₃*δ₁^3*μ₁*μ₂*η^2*k₃^2 + 4*β₂^2*β₃*δ₁^3*μ₂^2*η^2*k₃^2 + 4*β₂^2*β₃*δ₁^2*δ₃*μ₂^2*η^2*k₁*k₃ + 4*β₂^2*δ₁^5*δ₂*δ₃^2*k₂*k₃^3 - 8*β₂^2*δ₁^5*δ₂*δ₃*μ₂*k₂*k₃^3 + 2*β₂^2*δ₁^4*δ₂^2*δ₃*μ₁*k₁*k₃^3 - 7*β₂^2*δ₁^4*δ₂*δ₃^2*η*k₃^3 + 12*β₂^2*δ₁^4*δ₂*δ₃*μ₁*η*k₃^3 + 2*β₂^2*δ₁^4*δ₂*δ₃*μ₂*η*k₃^3 - 7*β₂^2*δ₁^4*δ₂*μ₂^2*η*k₃^3 - 12*β₂^2*δ₁^4*δ₃^3*η*k₂*k₃^2 + 2*β₂^2*δ₁^4*δ₃^2*μ₁*η*k₂*k₃^2 + 4*β₂^2*δ₁^4*δ₃*μ₁^2*η*k₂*k₃^2 + 8*β₂^2*δ₁^4*δ₃*μ₂^2*η*k₂*k₃^2 + 7*β₂^2*δ₁^4*μ₁*μ₂^2*η*k₂*k₃^2 - 4*β₂^2*δ₁^3*δ₂*δ₃^3*η*k₁*k₃^2 + 4*β₂^2*δ₁^3*δ₂*δ₃^2*μ₂*η*k₁*k₃^2 - 4*β₂^2*δ₁^3*δ₂*δ₃*μ₂^2*η*k₁*k₃^2 - β₂^2*δ₁^3*δ₃^3*η^2*k₃^2 + 29*β₂^2*δ₁^3*δ₃^2*μ₁*η^2*k₃^2 - 12*β₂^2*δ₁^3*δ₃^2*μ₂*η^2*k₃^2 - 45*β₂^2*δ₁^3*δ₃*μ₁^2*η^2*k₃^2 + 10*β₂^2*δ₁^3*δ₃*μ₁*μ₂*η^2*k₃^2 + 4*β₂^2*δ₁^3*δ₃*μ₂^2*η^2*k₃^2 + 4*β₂^2*δ₁^3*μ₁^3*η^2*k₃^2 + 19*β₂^2*δ₁^3*μ₁^2*μ₂*η^2*k₃^2 - 8*β₂^2*δ₁^3*μ₁*μ₂^2*η^2*k₃^2 - 4*β₂^2*δ₁^2*δ₃^2*μ₂^2*η^2*k₁*k₃ - 8*β₂^2*δ₁^2*δ₃*μ₁*μ₂^2*η^2*k₁*k₃ - 4*β₂^2*δ₁^2*μ₁*μ₂^3*η^2*k₁*k₃ + 14*β₂*β₃*δ₁^5*δ₂^3*k₃^4 + 24*β₂*β₃*δ₁^5*δ₂^2*δ₃*k₂*k₃^3 - 8*β₂*β₃*δ₁^5*δ₂^2*μ₁*k₂*k₃^3 + 16*β₂*β₃*δ₁^5*δ₂^2*μ₂*k₂*k₃^3 - 21*β₂*β₃*δ₁^4*δ₂^2*δ₃*η*k₃^3 - 13*β₂*β₃*δ₁^4*δ₂^2*μ₁*η*k₃^3 + 36*β₂*β₃*δ₁^4*δ₂^2*μ₂*η*k₃^3 - 24*β₂*β₃*δ₁^4*δ₂*δ₃^2*η*k₂*k₃^2 + 4*β₂*β₃*δ₁^3*δ₂^2*δ₃^2*η*k₁*k₃^2 - 4*β₂*β₃*δ₁^3*δ₂^2*δ₃*μ₂*η*k₁*k₃^2 - 2*β₂*β₃*δ₁^3*δ₂*δ₃^2*η^2*k₃^2 + 170*β₂*β₃*δ₁^3*δ₂*δ₃*μ₁*η^2*k₃^2 - 24*β₂*β₃*δ₁^3*δ₂*δ₃*μ₂*η^2*k₃^2 - 56*β₂*β₃*δ₁^3*δ₂*μ₁^2*η^2*k₃^2 + β₂*β₃*δ₁^3*δ₂*μ₁*μ₂*η^2*k₃^2 + 13*β₂*β₃*δ₁^3*δ₂*μ₂^2*η^2*k₃^2 + 12*β₂*β₃*δ₁^2*δ₂*δ₃*μ₂^2*η^2*k₁*k₃ + 8*β₂*β₃*δ₁^2*δ₂*μ₂^3*η^2*k₁*k₃ - 177*β₂*β₃*δ₁^2*δ₃*μ₁^2*η^3*k₃ - 80*β₂*β₃*δ₁^2*δ₃*μ₁*μ₂*η^3*k₃ - 32*β₂*β₃*δ₁^2*δ₃*μ₂^2*η^3*k₃ + 337*β₂*β₃*δ₁^2*μ₁^3*η^3*k₃ + 92*β₂*β₃*δ₁^2*μ₁^2*μ₂*η^3*k₃ + 12*β₂*β₃*δ₁^2*μ₁*μ₂^2*η^3*k₃ + 12*β₂*β₃*δ₁*μ₁*μ₂^3*η^3*k₁ - 8*β₂*δ₁^5*δ₂^2*δ₃^2*k₂*k₃^3 - 4*β₂*δ₁^5*δ₂^2*δ₃*μ₂*k₂*k₃^3 + 12*β₂*δ₁^5*δ₂^2*μ₂^2*k₂*k₃^3 + 2*β₂*δ₁^4*δ₂^3*δ₃*μ₁*k₁*k₃^3 - 7*β₂*δ₁^4*δ₂^2*δ₃^2*η*k₃^3 + 14*β₂*δ₁^4*δ₂^2*δ₃*μ₁*η*k₃^3 - 12*β₂*δ₁^4*δ₂^2*μ₁*μ₂*η*k₃^3 + 5*β₂*δ₁^4*δ₂^2*μ₂^2*η*k₃^3 + 24*β₂*δ₁^4*δ₂*δ₃^3*η*k₂*k₃^2 - 6*β₂*δ₁^4*δ₂*δ₃^2*μ₁*η*k₂*k₃^2 - 7*β₂*δ₁^4*δ₂*δ₃^2*μ₂*η*k₂*k₃^2 - 8*β₂*δ₁^4*δ₂*δ₃*μ₁^2*η*k₂*k₃^2 + 12*β₂*δ₁^4*δ₂*δ₃*μ₂^2*η*k₂*k₃^2 - 10*β₂*δ₁^4*δ₂*μ₁*μ₂^2*η*k₂*k₃^2 - 3*β₂*δ₁^4*δ₂*μ₂^3*η*k₂*k₃^2 - 4*β₂*δ₁^3*δ₂^2*δ₃^3*η*k₁*k₃^2 - 12*β₂*δ₁^3*δ₂^2*δ₃^2*μ₂*η*k₁*k₃^2 + 8*β₂*δ₁^3*δ₂^2*δ₃*μ₁*μ₂*η*k₁*k₃^2 + 4*β₂*δ₁^3*δ₂^2*δ₃*μ₂^2*η*k₁*k₃^2 - 16*β₂*δ₁^3*δ₂^2*μ₁^2*μ₂*η*k₁*k₃^2 - 4*β₂*δ₁^3*δ₂^2*μ₂^3*η*k₁*k₃^2 + 2*β₂*δ₁^3*δ₂*δ₃^3*η^2*k₃^2 - 76*β₂*δ₁^3*δ₂*δ₃^2*μ₁*η^2*k₃^2 - 20*β₂*δ₁^3*δ₂*δ₃^2*μ₂*η^2*k₃^2 + 146*β₂*δ₁^3*δ₂*δ₃*μ₁^2*η^2*k₃^2 + 41*β₂*δ₁^3*δ₂*δ₃*μ₁*μ₂*η^2*k₃^2 - 4*β₂*δ₁^3*δ₂*δ₃*μ₂^3*η*k₁*k₂*k₃ - β₂*δ₁^3*δ₂*δ₃*μ₂^2*η^2*k₃^2 - 8*β₂*δ₁^3*δ₂*μ₁^3*η^2*k₃^2 - 44*β₂*δ₁^3*δ₂*μ₁^2*μ₂*η^2*k₃^2 - 44*β₂*δ₁^3*δ₂*μ₁*μ₂^2*η^2*k₃^2 + 4*β₂*δ₁^3*δ₂*μ₂^3*η^2*k₃^2 + 2*β₂*δ₁^3*μ₁^3*μ₂*η^2*k₂*k₃ + 4*β₂*δ₁^3*μ₁*μ₂^3*η^2*k₂*k₃ - 12*β₂*δ₁^2*δ₂*δ₃^2*μ₂^2*η^2*k₁*k₃ + 4*β₂*δ₁^2*δ₂*μ₂^4*η^2*k₁*k₃ + 177*β₂*δ₁^2*δ₃^2*μ₁^2*η^3*k₃ + 80*β₂*δ₁^2*δ₃^2*μ₁*μ₂*η^3*k₃ + 32*β₂*δ₁^2*δ₃^2*μ₂^2*η^3*k₃ - 331*β₂*δ₁^2*δ₃*μ₁^3*η^3*k₃ - 185*β₂*δ₁^2*δ₃*μ₁^2*μ₂*η^3*k₃ - 62*β₂*δ₁^2*δ₃*μ₁*μ₂^2*η^3*k₃ + 146*β₂*δ₁^2*μ₁^3*μ₂*η^3*k₃ + 143*β₂*δ₁^2*μ₁^2*μ₂^2*η^3*k₃ - 12*β₂*δ₁*δ₃*μ₁*μ₂^3*η^3*k₁ + 2*β₂*δ₁*μ₁^5*η^3*k₁ + 15*β₂*δ₁*μ₁^4*μ₂*η^3*k₁ - 13*β₂*δ₁*μ₁^3*μ₂^2*η^3*k₁ + 4*β₂*δ₁*μ₁^2*μ₂^3*η^3*k₁ + 4*β₂*δ₁*μ₁*μ₂^4*η^3*k₁ - 4*β₃^5*δ₁^2*δ₂*η^2*k₁*k₂ - 4*β₃^5*δ₁^2*η^3*k₂ + β₃^5*δ₁*δ₂*η^3*k₁ + 41*β₃^5*δ₁*η^4 - 4*β₃^4*δ₁^3*δ₂^2*η*k₁*k₂*k₃ - 4*β₃^4*δ₁^3*μ₂*η^2*k₂^2 + 9*β₃^4*δ₁^2*δ₂^2*η^2*k₁*k₃ + 20*β₃^4*δ₁^2*δ₂*δ₃*η^2*k₁*k₂ + 88*β₃^4*δ₁^2*δ₂*η^3*k₃ + 20*β₃^4*δ₁^2*δ₃*η^3*k₂ - 4*β₃^4*δ₁^2*μ₁*η^3*k₂ + 37*β₃^4*δ₁^2*μ₂*η^3*k₂ - 5*β₃^4*δ₁*δ₂*δ₃*η^3*k₁ + 16*β₃^4*δ₁*δ₂*μ₂*η^3*k₁ - 205*β₃^4*δ₁*δ₃*η^4 + 45*β₃^4*δ₁*μ₁*η^4 + 45*β₃^4*δ₁*μ₂*η^4 + 4*β₃^3*δ₁^4*δ₂^2*η*k₂*k₃^2 + 4*β₃^3*δ₁^3*δ₂^3*η*k₁*k₃^2 + 12*β₃^3*δ₁^3*δ₂^2*δ₃*η*k₁*k₂*k₃ - 19*β₃^3*δ₁^3*δ₂^2*η^2*k₃^2 + 8*β₃^3*δ₁^3*δ₂*δ₃*η^2*k₂*k₃ - 16*β₃^3*δ₁^3*δ₂*μ₁*η^2*k₂*k₃ + 16*β₃^3*δ₁^3*δ₃*μ₂*η^2*k₂^2 - 35*β₃^3*δ₁^2*δ₂^2*δ₃*η^2*k₁*k₃ + 7*β₃^3*δ₁^2*δ₂^2*μ₂*η^2*k₁*k₃ - 40*β₃^3*δ₁^2*δ₂*δ₃^2*η^2*k₁*k₂ - 258*β₃^3*δ₁^2*δ₂*δ₃*η^3*k₃ + 182*β₃^3*δ₁^2*δ₂*μ₁*η^3*k₃ - 119*β₃^3*δ₁^2*δ₂*μ₂*η^3*k₃ - 40*β₃^3*δ₁^2*δ₃^2*η^3*k₂ + 16*β₃^3*δ₁^2*δ₃*μ₁*η^3*k₂ - 148*β₃^3*δ₁^2*δ₃*μ₂*η^3*k₂ + 4*β₃^3*δ₁^2*μ₂^2*η^3*k₂ + 10*β₃^3*δ₁*δ₂*δ₃^2*η^3*k₁ - 64*β₃^3*δ₁*δ₂*δ₃*μ₂*η^3*k₁ - β₃^3*δ₁*δ₂*μ₂^2*η^3*k₁ + 410*β₃^3*δ₁*δ₃^2*η^4 - 180*β₃^3*δ₁*δ₃*μ₁*η^4 - 180*β₃^3*δ₁*δ₃*μ₂*η^4 + 4*β₃^3*δ₁*μ₁^2*η^4 + 49*β₃^3*δ₁*μ₁*μ₂*η^4 - 33*β₃^3*δ₁*μ₂^2*η^4 - 4*β₃^2*δ₁^5*δ₂^3*k₂*k₃^3 - 5*β₃^2*δ₁^4*δ₂^3*η*k₃^3 + 4*β₃^2*δ₁^4*δ₂^2*δ₃*η*k₂*k₃^2 - 12*β₃^2*δ₁^3*δ₂^3*δ₃*η*k₁*k₃^2 - 8*β₃^2*δ₁^3*δ₂^3*μ₂*η*k₁*k₃^2 - 12*β₃^2*δ₁^3*δ₂^2*δ₃^2*η*k₁*k₂*k₃ + 37*β₃^2*δ₁^3*δ₂^2*δ₃*η^2*k₃^2 - 28*β₃^2*δ₁^3*δ₂^2*μ₂*η^2*k₃^2 - 24*β₃^2*δ₁^3*δ₂*δ₃^2*η^2*k₂*k₃ + 52*β₃^2*δ₁^3*δ₂*δ₃*μ₁*η^2*k₂*k₃ - 8*β₃^2*δ₁^3*δ₂*μ₁^2*η^2*k₂*k₃ - 24*β₃^2*δ₁^3*δ₃^2*μ₂*η^2*k₂^2 + 51*β₃^2*δ₁^2*δ₂^2*δ₃^2*η^2*k₁*k₃ - 6*β₃^2*δ₁^2*δ₂^2*δ₃*μ₂*η^2*k₁*k₃ - 25*β₃^2*δ₁^2*δ₂^2*μ₂^2*η^2*k₁*k₃ + 40*β₃^2*δ₁^2*δ₂*δ₃^3*η^2*k₁*k₂ + 246*β₃^2*δ₁^2*δ₂*δ₃^2*η^3*k₃ - 425*β₃^2*δ₁^2*δ₂*δ₃*μ₁*η^3*k₃ + 266*β₃^2*δ₁^2*δ₂*δ₃*μ₂*η^3*k₃ + 216*β₃^2*δ₁^2*δ₂*μ₁^2*η^3*k₃ + 174*β₃^2*δ₁^2*δ₂*μ₁*μ₂*η^3*k₃ - 112*β₃^2*δ₁^2*δ₂*μ₂^2*η^3*k₃ + 40*β₃^2*δ₁^2*δ₃^3*η^3*k₂ - 24*β₃^2*δ₁^2*δ₃^2*μ₁*η^3*k₂ + 222*β₃^2*δ₁^2*δ₃^2*μ₂*η^3*k₂ - 12*β₃^2*δ₁^2*δ₃*μ₂^2*η^3*k₂ - 37*β₃^2*δ₁^2*μ₂^3*η^3*k₂ - 10*β₃^2*δ₁*δ₂*δ₃^3*η^3*k₁ + 96*β₃^2*δ₁*δ₂*δ₃^2*μ₂*η^3*k₁ + 3*β₃^2*δ₁*δ₂*δ₃*μ₂^2*η^3*k₁ - 26*β₃^2*δ₁*δ₂*μ₁*μ₂^2*η^3*k₁ - 24*β₃^2*δ₁*δ₂*μ₂^3*η^3*k₁ - 410*β₃^2*δ₁*δ₃^3*η^4 + 270*β₃^2*δ₁*δ₃^2*μ₁*η^4 + 270*β₃^2*δ₁*δ₃^2*μ₂*η^4 - 12*β₃^2*δ₁*δ₃*μ₁^2*η^4 - 147*β₃^2*δ₁*δ₃*μ₁*μ₂*η^4 + 99*β₃^2*δ₁*δ₃*μ₂^2*η^4 + 2*β₃^2*δ₁*μ₁^3*η^4 - 35*β₃^2*δ₁*μ₁*μ₂^2*η^4 - 37*β₃^2*δ₁*μ₂^3*η^4 - 2*β₃*δ₁^5*δ₂^4*k₃^4 - 4*β₃*δ₁^5*δ₂^3*δ₃*k₂*k₃^3 + 4*β₃*δ₁^5*δ₂^3*μ₁*k₂*k₃^3 - 2*β₃*δ₁^5*δ₂^3*μ₂*k₂*k₃^3 + 5*β₃*δ₁^4*δ₂^3*δ₃*η*k₃^3 - 9*β₃*δ₁^4*δ₂^3*μ₁*η*k₃^3 - 20*β₃*δ₁^4*δ₂^3*μ₂*η*k₃^3 - 8*β₃*δ₁^4*δ₂^2*δ₃^2*η*k₂*k₃^2 + 8*β₃*δ₁^4*δ₂^2*δ₃*μ₁*η*k₂*k₃^2 - 20*β₃*δ₁^4*δ₂^2*μ₂^2*η*k₂*k₃^2 + 8*β₃*δ₁^3*δ₂^3*δ₃^2*η*k₁*k₃^2 + 16*β₃*δ₁^3*δ₂^3*δ₃*μ₂*η*k₁*k₃^2 - 16*β₃*δ₁^3*δ₂^3*μ₁^2*η*k₁*k₃^2 - 8*β₃*δ₁^3*δ₂^3*μ₁*μ₂*η*k₁*k₃^2 - 4*β₃*δ₁^3*δ₂^3*μ₂^2*η*k₁*k₃^2 + 4*β₃*δ₁^3*δ₂^2*δ₃^3*η*k₁*k₂*k₃ - 16*β₃*δ₁^3*δ₂^2*δ₃^2*η^2*k₃^2 - 66*β₃*δ₁^3*δ₂^2*δ₃*μ₁*η^2*k₃^2 + 36*β₃*δ₁^3*δ₂^2*δ₃*μ₂*η^2*k₃^2 - 28*β₃*δ₁^3*δ₂^2*μ₁^2*η^2*k₃^2 - 39*β₃*δ₁^3*δ₂^2*μ₁*μ₂*η^2*k₃^2 + 6*β₃*δ₁^3*δ₂^2*μ₂^2*η^2*k₃^2 + 24*β₃*δ₁^3*δ₂*δ₃^3*η^2*k₂*k₃ - 56*β₃*δ₁^3*δ₂*δ₃^2*μ₁*η^2*k₂*k₃ + 24*β₃*δ₁^3*δ₂*δ₃*μ₁^2*η^2*k₂*k₃ - 2*β₃*δ₁^3*δ₂*δ₃*μ₂^2*η^2*k₂*k₃ - 4*β₃*δ₁^3*δ₂*μ₁^3*η^2*k₂*k₃ + 16*β₃*δ₁^3*δ₃^3*μ₂*η^2*k₂^2 - 33*β₃*δ₁^2*δ₂^2*δ₃^3*η^2*k₁*k₃ - 9*β₃*δ₁^2*δ₂^2*δ₃^2*μ₂*η^2*k₁*k₃ - 4*β₃*δ₁^2*δ₂^2*δ₃*μ₁^2*η^2*k₁*k₃ + 32*β₃*δ₁^2*δ₂^2*δ₃*μ₁*μ₂*η^2*k₁*k₃ + 33*β₃*δ₁^2*δ₂^2*δ₃*μ₂^2*η^2*k₁*k₃ - 28*β₃*δ₁^2*δ₂^2*μ₁^2*μ₂*η^2*k₁*k₃ - 15*β₃*δ₁^2*δ₂^2*μ₂^3*η^2*k₁*k₃ - 20*β₃*δ₁^2*δ₂*δ₃^4*η^2*k₁*k₂ - 70*β₃*δ₁^2*δ₂*δ₃^3*η^3*k₃ + 304*β₃*δ₁^2*δ₂*δ₃^2*μ₁*η^3*k₃ - 175*β₃*δ₁^2*δ₂*δ₃^2*μ₂*η^3*k₃ - 378*β₃*δ₁^2*δ₂*δ₃*μ₁^2*η^3*k₃ - 187*β₃*δ₁^2*δ₂*δ₃*μ₁*μ₂*η^3*k₃ + 134*β₃*δ₁^2*δ₂*δ₃*μ₂^2*η^3*k₃ + 4*β₃*δ₁^2*δ₂*μ₁^4*η^2*k₁*k₂ + 89*β₃*δ₁^2*δ₂*μ₁^3*η^3*k₃ + 137*β₃*δ₁^2*δ₂*μ₁^2*μ₂*η^3*k₃ - 101*β₃*δ₁^2*δ₂*μ₁*μ₂^2*η^3*k₃ + 95*β₃*δ₁^2*δ₂*μ₂^3*η^3*k₃ - 20*β₃*δ₁^2*δ₃^4*η^3*k₂ + 16*β₃*δ₁^2*δ₃^3*μ₁*η^3*k₂ - 148*β₃*δ₁^2*δ₃^3*μ₂*η^3*k₂ + 12*β₃*δ₁^2*δ₃^2*μ₂^2*η^3*k₂ + 74*β₃*δ₁^2*δ₃*μ₂^3*η^3*k₂ + 2*β₃*δ₁^2*μ₁^3*μ₂*η^3*k₂ - 4*β₃*δ₁^2*μ₁^2*μ₂^2*η^3*k₂ - 2*β₃*δ₁^2*μ₁*μ₂^3*η^3*k₂ + 5*β₃*δ₁*δ₂*δ₃^4*η^3*k₁ - 64*β₃*δ₁*δ₂*δ₃^3*μ₂*η^3*k₁ - 3*β₃*δ₁*δ₂*δ₃^2*μ₂^2*η^3*k₁ + 52*β₃*δ₁*δ₂*δ₃*μ₁*μ₂^2*η^3*k₁ + 48*β₃*δ₁*δ₂*δ₃*μ₂^3*η^3*k₁ - 3*β₃*δ₁*δ₂*μ₁^4*η^3*k₁ + 3*β₃*δ₁*δ₂*μ₁^2*μ₂^2*η^3*k₁ - 38*β₃*δ₁*δ₂*μ₁*μ₂^3*η^3*k₁ - 12*β₃*δ₁*δ₂*μ₂^4*η^3*k₁ + 205*β₃*δ₁*δ₃^4*η^4 - 180*β₃*δ₁*δ₃^3*μ₁*η^4 - 180*β₃*δ₁*δ₃^3*μ₂*η^4 + 12*β₃*δ₁*δ₃^2*μ₁^2*η^4 + 147*β₃*δ₁*δ₃^2*μ₁*μ₂*η^4 - 99*β₃*δ₁*δ₃^2*μ₂^2*η^4 - 4*β₃*δ₁*δ₃*μ₁^3*η^4 + 70*β₃*δ₁*δ₃*μ₁*μ₂^2*η^4 + 74*β₃*δ₁*δ₃*μ₂^3*η^4 + 2*β₃*δ₁*μ₁^4*η^4 - 2*β₃*δ₁*μ₁^3*μ₂*η^4 - 6*β₃*δ₁*μ₁^2*μ₂^2*η^4 - 39*β₃*δ₁*μ₁*μ₂^3*η^4 + 4*δ₁^5*δ₂^3*δ₃*μ₂*k₂*k₃^3 + 4*δ₁^5*δ₂^2*δ₃^2*μ₂*k₂^2*k₃^2 - 8*δ₁^5*δ₂^2*δ₃*μ₂^2*k₂^2*k₃^2 - 2*δ₁^4*δ₂^4*δ₃*μ₁*k₁*k₃^3 + 2*δ₁^4*δ₂^3*δ₃^2*η*k₃^3 - 2*δ₁^4*δ₂^3*δ₃*μ₁*η*k₃^3 - 2*δ₁^4*δ₂^3*δ₃*μ₂*η*k₃^3 - 5*δ₁^4*δ₂^3*μ₁*μ₂*η*k₃^3 + 7*δ₁^4*δ₂^3*μ₂^2*η*k₃^3 - 4*δ₁^4*δ₂^2*δ₃^2*μ₁*η*k₂*k₃^2 - 9*δ₁^4*δ₂^2*δ₃^2*μ₂*η*k₂*k₃^2 + 4*δ₁^4*δ₂^2*δ₃*μ₁^2*η*k₂*k₃^2 + 8*δ₁^4*δ₂^2*δ₃*μ₁*μ₂*η*k₂*k₃^2 + 16*δ₁^4*δ₂^2*δ₃*μ₂^2*η*k₂*k₃^2 + 3*δ₁^4*δ₂^2*μ₁*μ₂^2*η*k₂*k₃^2 - 29*δ₁^4*δ₂^2*μ₂^3*η*k₂*k₃^2 + 16*δ₁^3*δ₂^3*δ₃*μ₁^2*η*k₁*k₃^2 + 4*δ₁^3*δ₂^3*δ₃*μ₂^2*η*k₁*k₃^2 - 8*δ₁^3*δ₂^3*μ₁*μ₂^2*η*k₁*k₃^2 + 12*δ₁^3*δ₂^3*μ₂^3*η*k₁*k₃^2 - 2*δ₁^3*δ₂^2*δ₃^3*η^2*k₃^2 + 15*δ₁^3*δ₂^2*δ₃^2*μ₁*η^2*k₃^2 + 4*δ₁^3*δ₂^2*δ₃^2*μ₂*η^2*k₃^2 - 17*δ₁^3*δ₂^2*δ₃*μ₁^2*η^2*k₃^2 - 9*δ₁^3*δ₂^2*δ₃*μ₁*μ₂*η^2*k₃^2 + 8*δ₁^3*δ₂^2*δ₃*μ₂^3*η*k₁*k₂*k₃ - 6*δ₁^3*δ₂^2*δ₃*μ₂^2*η^2*k₃^2 + 4*δ₁^3*δ₂^2*μ₁^3*η^2*k₃^2 - 59*δ₁^3*δ₂^2*μ₁^2*μ₂*η^2*k₃^2 + 42*δ₁^3*δ₂^2*μ₁*μ₂^2*η^2*k₃^2 - 4*δ₁^3*δ₂^2*μ₂^4*η*k₁*k₂*k₃ + 28*δ₁^3*δ₂^2*μ₂^3*η^2*k₃^2 - 8*δ₁^3*δ₂*δ₃^4*η^2*k₂*k₃ + 20*δ₁^3*δ₂*δ₃^3*μ₁*η^2*k₂*k₃ - 16*δ₁^3*δ₂*δ₃^2*μ₁^2*η^2*k₂*k₃ + 2*δ₁^3*δ₂*δ₃^2*μ₂^2*η^2*k₂*k₃ + 4*δ₁^3*δ₂*δ₃*μ₁^3*η^2*k₂*k₃ - 4*δ₁^3*δ₂*δ₃*μ₁^2*μ₂*η^2*k₂*k₃ + 10*δ₁^3*δ₂*δ₃*μ₂^3*η^2*k₂*k₃ - 6*δ₁^3*δ₂*μ₁^3*μ₂*η^2*k₂*k₃ + 20*δ₁^3*δ₂*μ₁^2*μ₂^2*η^2*k₂*k₃ - 24*δ₁^3*δ₂*μ₁*μ₂^3*η^2*k₂*k₃ - 4*δ₁^3*δ₂*μ₂^4*η^2*k₂*k₃ - 4*δ₁^3*δ₃^4*μ₂*η^2*k₂^2 + 8*δ₁^2*δ₂^2*δ₃^4*η^2*k₁*k₃ + 8*δ₁^2*δ₂^2*δ₃^3*μ₂*η^2*k₁*k₃ + 4*δ₁^2*δ₂^2*δ₃^2*μ₁^2*η^2*k₁*k₃ - 32*δ₁^2*δ₂^2*δ₃^2*μ₁*μ₂*η^2*k₁*k₃ - 8*δ₁^2*δ₂^2*δ₃^2*μ₂^2*η^2*k₁*k₃ + 24*δ₁^2*δ₂^2*δ₃*μ₁^2*μ₂*η^2*k₁*k₃ + 40*δ₁^2*δ₂^2*δ₃*μ₁*μ₂^2*η^2*k₁*k₃ - 8*δ₁^2*δ₂^2*δ₃*μ₂^3*η^2*k₁*k₃ - 28*δ₁^2*δ₂^2*μ₁^2*μ₂^2*η^2*k₁*k₃ + 4*δ₁^2*δ₂^2*μ₁*μ₂^3*η^2*k₁*k₃ + 12*δ₁^2*δ₂^2*μ₂^4*η^2*k₁*k₃ + 4*δ₁^2*δ₂*δ₃^5*η^2*k₁*k₂ - 6*δ₁^2*δ₂*δ₃^4*η^3*k₃ - 61*δ₁^2*δ₂*δ₃^3*μ₁*η^3*k₃ + 28*δ₁^2*δ₂*δ₃^3*μ₂*η^3*k₃ + 162*δ₁^2*δ₂*δ₃^2*μ₁^2*η^3*k₃ + 13*δ₁^2*δ₂*δ₃^2*μ₁*μ₂*η^3*k₃ - 22*δ₁^2*δ₂*δ₃^2*μ₂^2*η^3*k₃ - 4*δ₁^2*δ₂*δ₃*μ₁^4*η^2*k₁*k₂ - 95*δ₁^2*δ₂*δ₃*μ₁^3*η^3*k₃ - 167*δ₁^2*δ₂*δ₃*μ₁^2*μ₂*η^3*k₃ + 111*δ₁^2*δ₂*δ₃*μ₁*μ₂^2*η^3*k₃ - 32*δ₁^2*δ₂*δ₃*μ₂^3*η^3*k₃ + 280*δ₁^2*δ₂*μ₁^3*μ₂*η^3*k₃ - 130*δ₁^2*δ₂*μ₁^2*μ₂^2*η^3*k₃ - 81*δ₁^2*δ₂*μ₁*μ₂^3*η^3*k₃ + 4*δ₁^2*δ₃^5*η^3*k₂ - 4*δ₁^2*δ₃^4*μ₁*η^3*k₂ + 37*δ₁^2*δ₃^4*μ₂*η^3*k₂ - 4*δ₁^2*δ₃^3*μ₂^2*η^3*k₂ - 37*δ₁^2*δ₃^2*μ₂^3*η^3*k₂ - 2*δ₁^2*δ₃*μ₁^3*μ₂*η^3*k₂ + 4*δ₁^2*δ₃*μ₁^2*μ₂^2*η^3*k₂ + 2*δ₁^2*δ₃*μ₁*μ₂^3*η^3*k₂ - δ₁*δ₂*δ₃^5*η^3*k₁ + 16*δ₁*δ₂*δ₃^4*μ₂*η^3*k₁ + δ₁*δ₂*δ₃^3*μ₂^2*η^3*k₁ - 26*δ₁*δ₂*δ₃^2*μ₁*μ₂^2*η^3*k₁ - 24*δ₁*δ₂*δ₃^2*μ₂^3*η^3*k₁ + 3*δ₁*δ₂*δ₃*μ₁^4*η^3*k₁ - 3*δ₁*δ₂*δ₃*μ₁^2*μ₂^2*η^3*k₁ + 38*δ₁*δ₂*δ₃*μ₁*μ₂^3*η^3*k₁ + 12*δ₁*δ₂*δ₃*μ₂^4*η^3*k₁ - 2*δ₁*δ₂*μ₁^5*η^3*k₁ - 18*δ₁*δ₂*μ₁^4*μ₂*η^3*k₁ + 13*δ₁*δ₂*μ₁^3*μ₂^2*η^3*k₁ - δ₁*δ₂*μ₁^2*μ₂^3*η^3*k₁ - 4*δ₁*δ₂*μ₁*μ₂^4*η^3*k₁ - 4*δ₁*δ₂*μ₂^5*η^3*k₁ - 41*δ₁*δ₃^5*η^4 + 45*δ₁*δ₃^4*μ₁*η^4 + 45*δ₁*δ₃^4*μ₂*η^4 - 4*δ₁*δ₃^3*μ₁^2*η^4 - 49*δ₁*δ₃^3*μ₁*μ₂*η^4 + 33*δ₁*δ₃^3*μ₂^2*η^4 + 2*δ₁*δ₃^2*μ₁^3*η^4 - 35*δ₁*δ₃^2*μ₁*μ₂^2*η^4 - 37*δ₁*δ₃^2*μ₂^3*η^4 - 2*δ₁*δ₃*μ₁^4*η^4 + 2*δ₁*δ₃*μ₁^3*μ₂*η^4 + 6*δ₁*δ₃*μ₁^2*μ₂^2*η^4 + 39*δ₁*δ₃*μ₁*μ₂^3*η^4 + 2*δ₁*μ₁^4*μ₂*η^4 - 4*δ₁*μ₁^3*μ₂^2*η^4 - 2*δ₁*μ₁^2*μ₂^3*η^4
 -4*β₂^2*β₃*δ₁^5*μ₁*μ₂^2*k₃^4 - 2*β₂^2*δ₁^5*δ₃^3*μ₂*k₃^4 + 4*β₂^2*δ₁^5*δ₃^2*μ₁*μ₂*k₃^4 - 2*β₂^2*δ₁^5*δ₃*μ₁*μ₂^2*k₃^4 + 6*β₂*β₃*δ₁^5*δ₂*δ₃^2*μ₂*k₃^4 - 6*β₂*β₃*δ₁^5*δ₂*δ₃*μ₁*μ₂*k₃^4 + 2*β₂*β₃*δ₁^5*δ₂*δ₃*μ₂^2*k₃^4 + 2*β₂*β₃*δ₁^5*δ₂*μ₁*μ₂^2*k₃^4 - 16*β₂*β₃*δ₁^4*δ₃^2*μ₁*μ₂*η*k₃^3 + 2*β₂*β₃*δ₁^4*δ₃^2*μ₂^2*η*k₃^3 + 10*β₂*β₃*δ₁^4*δ₃*μ₁^2*μ₂*η*k₃^3 + 9*β₂*β₃*δ₁^4*δ₃*μ₁*μ₂^2*η*k₃^3 - 10*β₂*β₃*δ₁^4*μ₁^2*μ₂^2*η*k₃^3 - 5*β₂*β₃*δ₁^4*μ₁*μ₂^3*η*k₃^3 + 4*β₂*β₃*δ₁^3*δ₃^2*μ₁*μ₂^2*η*k₁*k₃^2 + 8*β₂*β₃*δ₁^3*δ₃*μ₁*μ₂^3*η*k₁*k₃^2 - β₂*β₃*δ₁^3*μ₁*μ₂^4*η*k₁*k₃^2 + 2*β₂*β₃*δ₁^2*δ₃*μ₁*μ₂^4*η*k₁^2*k₃ - β₂*β₃*δ₁^2*μ₁*μ₂^5*η*k₁^2*k₃ - 2*β₂*δ₁^5*δ₂*δ₃^2*μ₂^2*k₃^4 + 2*β₂*δ₁^5*δ₂*δ₃*μ₁*μ₂^2*k₃^4 + 2*β₂*δ₁^5*δ₂*δ₃*μ₂^3*k₃^4 - 2*β₂*δ₁^5*δ₂*μ₁*μ₂^3*k₃^4 + 8*β₂*δ₁^4*δ₃^3*μ₁*μ₂*η*k₃^3 - 2*β₂*δ₁^4*δ₃^3*μ₂^2*η*k₃^3 - 12*β₂*δ₁^4*δ₃^2*μ₁^2*μ₂*η*k₃^3 - 6*β₂*δ₁^4*δ₃^2*μ₁*μ₂^2*η*k₃^3 + 16*β₂*δ₁^4*δ₃*μ₁^2*μ₂^2*η*k₃^3 + 2*β₂*δ₁^4*δ₃*μ₁*μ₂^3*η*k₃^3 - 6*β₂*δ₁^4*μ₁^2*μ₂^3*η*k₃^3 - 4*β₂*δ₁^3*δ₃^3*μ₁*μ₂^2*η*k₁*k₃^2 - 5*β₂*δ₁^3*δ₃^2*μ₁^3*μ₂*η*k₁*k₃^2 - 4*β₂*δ₁^3*δ₃^2*μ₁^2*μ₂^2*η*k₁*k₃^2 - 2*β₂*δ₁^3*δ₃^2*μ₁*μ₂^3*η*k₁*k₃^2 - 2*β₂*δ₁^3*δ₃*μ₁^4*μ₂*η*k₁*k₃^2 + 3*β₂*δ₁^3*δ₃*μ₁^3*μ₂^2*η*k₁*k₃^2 + 11*β₂*δ₁^3*δ₃*μ₁^2*μ₂^3*η*k₁*k₃^2 - 2*β₂*δ₁^3*μ₁^4*μ₂^2*η*k₁*k₃^2 + 2*β₂*δ₁^3*μ₁^3*μ₂^3*η*k₁*k₃^2 + 3*β₂*δ₁^3*μ₁^2*μ₂^4*η*k₁*k₃^2 - 2*β₂*δ₁^2*δ₃^2*μ₁*μ₂^4*η*k₁^2*k₃ - 6*β₂*δ₁^2*δ₃*μ₁^3*μ₂^3*η*k₁^2*k₃ + 7*β₂*δ₁^2*δ₃*μ₁^2*μ₂^4*η*k₁^2*k₃ + 5*β₂*δ₁^2*μ₁^3*μ₂^4*η*k₁^2*k₃ - 4*β₂*δ₁^2*μ₁^2*μ₂^5*η*k₁^2*k₃ - 2*β₃^5*δ₁^2*δ₃*μ₂*η^2*k₁*k₃ - 2*β₃^5*δ₁^2*μ₂^2*η^2*k₁*k₃ - 4*β₃^4*δ₁^3*δ₂*δ₃*μ₂*η*k₁*k₃^2 - 4*β₃^4*δ₁^3*δ₂*μ₂^2*η*k₁*k₃^2 - 2*β₃^4*δ₁^3*δ₃*μ₂^2*η*k₁*k₂*k₃ + 6*β₃^4*δ₁^3*δ₃*μ₂*η^2*k₃^2 - 2*β₃^4*δ₁^3*μ₂^3*η*k₁*k₂*k₃ + 10*β₃^4*δ₁^3*μ₂^2*η^2*k₃^2 + 10*β₃^4*δ₁^2*δ₃^2*μ₂*η^2*k₁*k₃ - 2*β₃^4*δ₁^2*δ₃*μ₁*μ₂*η^2*k₁*k₃ + 10*β₃^4*δ₁^2*δ₃*μ₂^2*η^2*k₁*k₃ - 2*β₃^4*δ₁^2*μ₁*μ₂^2*η^2*k₁*k₃ - 6*β₃^4*δ₁^2*μ₂^3*η^2*k₁*k₃ + 10*β₃^3*δ₁^4*δ₂*δ₃*μ₂*η*k₃^3 + 18*β₃^3*δ₁^4*δ₂*μ₂^2*η*k₃^3 + 6*β₃^3*δ₁^4*δ₃*μ₂^2*η*k₂*k₃^2 + 10*β₃^3*δ₁^4*μ₂^3*η*k₂*k₃^2 + 12*β₃^3*δ₁^3*δ₂*δ₃^2*μ₂*η*k₁*k₃^2 + 20*β₃^3*δ₁^3*δ₂*δ₃*μ₂^2*η*k₁*k₃^2 - 4*β₃^3*δ₁^3*δ₂*μ₂^3*η*k₁*k₃^2 + 8*β₃^3*δ₁^3*δ₃^2*μ₂^2*η*k₁*k₂*k₃ - 23*β₃^3*δ₁^3*δ₃^2*μ₂*η^2*k₃^2 + 6*β₃^3*δ₁^3*δ₃*μ₁*μ₂*η^2*k₃^2 + 10*β₃^3*δ₁^3*δ₃*μ₂^3*η*k₁*k₂*k₃ - 30*β₃^3*δ₁^3*δ₃*μ₂^2*η^2*k₃^2 + 10*β₃^3*δ₁^3*μ₁*μ₂^2*η^2*k₃^2 - 4*β₃^3*δ₁^3*μ₂^4*η*k₁*k₂*k₃ + 21*β₃^3*δ₁^3*μ₂^3*η^2*k₃^2 - 20*β₃^3*δ₁^2*δ₃^3*μ₂*η^2*k₁*k₃ + 8*β₃^3*δ₁^2*δ₃^2*μ₁*μ₂*η^2*k₁*k₃ - 20*β₃^3*δ₁^2*δ₃^2*μ₂^2*η^2*k₁*k₃ + 8*β₃^3*δ₁^2*δ₃*μ₁*μ₂^2*η^2*k₁*k₃ + 30*β₃^3*δ₁^2*δ₃*μ₂^3*η^2*k₁*k₃ - 6*β₃^3*δ₁^2*μ₁*μ₂^3*η^2*k₁*k₃ - 6*β₃^3*δ₁^2*μ₂^4*η^2*k₁*k₃ - 2*β₃^2*δ₁^5*δ₂^2*δ₃*μ₂*k₃^4 - 2*β₃^2*δ₁^5*δ₂^2*μ₂^2*k₃^4 - 20*β₃^2*δ₁^4*δ₂*δ₃^2*μ₂*η*k₃^3 - 4*β₃^2*δ₁^4*δ₂*δ₃*μ₁*μ₂*η*k₃^3 - 40*β₃^2*δ₁^4*δ₂*δ₃*μ₂^2*η*k₃^3 + 4*β₃^2*δ₁^4*δ₂*μ₁*μ₂^2*η*k₃^3 - 2*β₃^2*δ₁^4*δ₂*μ₂^3*η*k₃^3 - 17*β₃^2*δ₁^4*δ₃^2*μ₂^2*η*k₂*k₃^2 - 26*β₃^2*δ₁^4*δ₃*μ₂^3*η*k₂*k₃^2 + 11*β₃^2*δ₁^4*μ₂^4*η*k₂*k₃^2 - 12*β₃^2*δ₁^3*δ₂*δ₃^3*μ₂*η*k₁*k₃^2 - 9*β₃^2*δ₁^3*δ₂*δ₃^2*μ₁*μ₂*η*k₁*k₃^2 - 28*β₃^2*δ₁^3*δ₂*δ₃^2*μ₂^2*η*k₁*k₃^2 + 8*β₃^2*δ₁^3*δ₂*δ₃*μ₁*μ₂^2*η*k₁*k₃^2 + 12*β₃^2*δ₁^3*δ₂*δ₃*μ₂^3*η*k₁*k₃^2 - 11*β₃^2*δ₁^3*δ₂*μ₁*μ₂^3*η*k₁*k₃^2 + 4*β₃^2*δ₁^3*δ₂*μ₂^4*η*k₁*k₃^2 - 12*β₃^2*δ₁^3*δ₃^3*μ₂^2*η*k₁*k₂*k₃ + 33*β₃^2*δ₁^3*δ₃^3*μ₂*η^2*k₃^2 - 18*β₃^2*δ₁^3*δ₃^2*μ₁*μ₂*η^2*k₃^2 - 18*β₃^2*δ₁^3*δ₃^2*μ₂^3*η*k₁*k₂*k₃ + 31*β₃^2*δ₁^3*δ₃^2*μ₂^2*η^2*k₃^2 - 18*β₃^2*δ₁^3*δ₃*μ₁*μ₂^2*η^2*k₃^2 + 16*β₃^2*δ₁^3*δ₃*μ₂^4*η*k₁*k₂*k₃ - 59*β₃^2*δ₁^3*δ₃*μ₂^3*η^2*k₃^2 + 20*β₃^2*δ₁^3*μ₁*μ₂^3*η^2*k₃^2 - 2*β₃^2*δ₁^3*μ₂^5*η*k₁*k₂*k₃ + 11*β₃^2*δ₁^3*μ₂^4*η^2*k₃^2 + 6*β₃^2*δ₁^2*δ₂*δ₃*μ₁*μ₂^3*η*k₁^2*k₃ - 2*β₃^2*δ₁^2*δ₂*μ₁*μ₂^4*η*k₁^2*k₃ + 20*β₃^2*δ₁^2*δ₃^4*μ₂*η^2*k₁*k₃ - 12*β₃^2*δ₁^2*δ₃^3*μ₁*μ₂*η^2*k₁*k₃ + 20*β₃^2*δ₁^2*δ₃^3*μ₂^2*η^2*k₁*k₃ - 12*β₃^2*δ₁^2*δ₃^2*μ₁*μ₂^2*η^2*k₁*k₃ - 54*β₃^2*δ₁^2*δ₃^2*μ₂^3*η^2*k₁*k₃ - 3*β₃^2*δ₁^2*δ₃*μ₁^2*μ₂^2*η^2*k₁*k₃ + 28*β₃^2*δ₁^2*δ₃*μ₁*μ₂^3*η^2*k₁*k₃ + 22*β₃^2*δ₁^2*δ₃*μ₂^4*η^2*k₁*k₃ + 3*β₃^2*δ₁^2*μ₁^2*μ₂^3*η^2*k₁*k₃ - 10*β₃^2*δ₁^2*μ₁*μ₂^4*η^2*k₁*k₃ - 2*β₃^2*δ₁^2*μ₂^5*η^2*k₁*k₃ + β₃^2*δ₁*μ₁^2*μ₂^4*η^2*k₁^2 - β₃^2*δ₁*μ₁*μ₂^5*η^2*k₁^2 - 2*β₃*δ₁^5*δ₂^2*δ₃^2*μ₂*k₃^4 + 2*β₃*δ₁^5*δ₂^2*δ₃*μ₁*μ₂*k₃^4 + 2*β₃*δ₁^5*δ₂^2*δ₃*μ₂^2*k₃^4 - 2*β₃*δ₁^5*δ₂^2*μ₁*μ₂^2*k₃^4 + 2*β₃*δ₁^5*δ₂*μ₂^4*k₂*k₃^3 + 10*β₃*δ₁^4*δ₂*δ₃^3*μ₂*η*k₃^3 + 14*β₃*δ₁^4*δ₂*δ₃^2*μ₁*μ₂*η*k₃^3 + 22*β₃*δ₁^4*δ₂*δ₃^2*μ₂^2*η*k₃^3 - 21*β₃*δ₁^4*δ₂*δ₃*μ₁*μ₂^2*η*k₃^3 - 10*β₃*δ₁^4*δ₂*δ₃*μ₂^3*η*k₃^3 + 4*β₃*δ₁^4*δ₂*μ₁^2*μ₂^2*η*k₃^3 + 11*β₃*δ₁^4*δ₂*μ₁*μ₂^3*η*k₃^3 - 20*β₃*δ₁^4*δ₂*μ₂^4*η*k₃^3 + 16*β₃*δ₁^4*δ₃^3*μ₂^2*η*k₂*k₃^2 - β₃*δ₁^4*δ₃^2*μ₁*μ₂^2*η*k₂*k₃^2 + 22*β₃*δ₁^4*δ₃^2*μ₂^3*η*k₂*k₃^2 + 2*β₃*δ₁^4*δ₃*μ₁*μ₂^3*η*k₂*k₃^2 - 22*β₃*δ₁^4*δ₃*μ₂^4*η*k₂*k₃^2 - β₃*δ₁^4*μ₁*μ₂^4*η*k₂*k₃^2 + 4*β₃*δ₁^3*δ₂*δ₃^4*μ₂*η*k₁*k₃^2 + 18*β₃*δ₁^3*δ₂*δ₃^3*μ₁*μ₂*η*k₁*k₃^2 + 12*β₃*δ₁^3*δ₂*δ₃^3*μ₂^2*η*k₁*k₃^2 - 2*β₃*δ₁^3*δ₂*δ₃^2*μ₁^2*μ₂*η*k₁*k₃^2 - 12*β₃*δ₁^3*δ₂*δ₃^2*μ₁*μ₂^2*η*k₁*k₃^2 - 8*β₃*δ₁^3*δ₂*δ₃^2*μ₂^3*η*k₁*k₃^2 - 2*β₃*δ₁^3*δ₂*δ₃*μ₁^2*μ₂^2*η*k₁*k₃^2 + 10*β₃*δ₁^3*δ₂*δ₃*μ₁*μ₂^3*η*k₁*k₃^2 - 12*β₃*δ₁^3*δ₂*δ₃*μ₂^4*η*k₁*k₃^2 - 10*β₃*δ₁^3*δ₂*μ₁^2*μ₂^3*η*k₁*k₃^2 - 13*β₃*δ₁^3*δ₂*μ₁*μ₂^4*η*k₁*k₃^2 + 4*β₃*δ₁^3*δ₂*μ₂^5*η*k₁*k₃^2 + 8*β₃*δ₁^3*δ₃^4*μ₂^2*η*k₁*k₂*k₃ - 21*β₃*δ₁^3*δ₃^4*μ₂*η^2*k₃^2 + 18*β₃*δ₁^3*δ₃^3*μ₁*μ₂*η^2*k₃^2 + 14*β₃*δ₁^3*δ₃^3*μ₂^3*η*k₁*k₂*k₃ - 12*β₃*δ₁^3*δ₃^3*μ₂^2*η^2*k₃^2 - β₃*δ₁^3*δ₃^2*μ₁^2*μ₂*η^2*k₃^2 + 6*β₃*δ₁^3*δ₃^2*μ₁*μ₂^2*η^2*k₃^2 - 20*β₃*δ₁^3*δ₃^2*μ₂^4*η*k₁*k₂*k₃ + 55*β₃*δ₁^3*δ₃^2*μ₂^3*η^2*k₃^2 - 3*β₃*δ₁^3*δ₃*μ₁^2*μ₂^3*η*k₁*k₂*k₃ + 2*β₃*δ₁^3*δ₃*μ₁^2*μ₂^2*η^2*k₃^2 + 4*β₃*δ₁^3*δ₃*μ₁*μ₂^4*η*k₁*k₂*k₃ - 34*β₃*δ₁^3*δ₃*μ₁*μ₂^3*η^2*k₃^2 + 4*β₃*δ₁^3*δ₃*μ₂^5*η*k₁*k₂*k₃ - 22*β₃*δ₁^3*δ₃*μ₂^4*η^2*k₃^2 + 3*β₃*δ₁^3*μ₁^2*μ₂^4*η*k₁*k₂*k₃ - β₃*δ₁^3*μ₁^2*μ₂^3*η^2*k₃^2 - 4*β₃*δ₁^3*μ₁*μ₂^5*η*k₁*k₂*k₃ + 10*β₃*δ₁^3*μ₁*μ₂^4*η^2*k₃^2 - 12*β₃*δ₁^2*δ₂*δ₃^2*μ₁*μ₂^3*η*k₁^2*k₃ + 12*β₃*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^3*η*k₁^2*k₃ + 2*β₃*δ₁^2*δ₂*δ₃*μ₁*μ₂^4*η*k₁^2*k₃ - 6*β₃*δ₁^2*δ₂*μ₁^2*μ₂^4*η*k₁^2*k₃ + 3*β₃*δ₁^2*δ₂*μ₁*μ₂^5*η*k₁^2*k₃ - 10*β₃*δ₁^2*δ₃^5*μ₂*η^2*k₁*k₃ + 8*β₃*δ₁^2*δ₃^4*μ₁*μ₂*η^2*k₁*k₃ - 10*β₃*δ₁^2*δ₃^4*μ₂^2*η^2*k₁*k₃ + 8*β₃*δ₁^2*δ₃^3*μ₁*μ₂^2*η^2*k₁*k₃ + 42*β₃*δ₁^2*δ₃^3*μ₂^3*η^2*k₁*k₃ + 6*β₃*δ₁^2*δ₃^2*μ₁^2*μ₂^2*η^2*k₁*k₃ - 38*β₃*δ₁^2*δ₃^2*μ₁*μ₂^3*η^2*k₁*k₃ - 26*β₃*δ₁^2*δ₃^2*μ₂^4*η^2*k₁*k₃ - 3*β₃*δ₁^2*δ₃*μ₁^3*μ₂^2*η^2*k₁*k₃ - 5*β₃*δ₁^2*δ₃*μ₁^2*μ₂^3*η^2*k₁*k₃ + 28*β₃*δ₁^2*δ₃*μ₁*μ₂^4*η^2*k₁*k₃ + 4*β₃*δ₁^2*δ₃*μ₂^5*η^2*k₁*k₃ + 3*β₃*δ₁^2*μ₁^3*μ₂^3*η^2*k₁*k₃ + β₃*δ₁^2*μ₁^2*μ₂^5*η*k₁^2*k₂ - β₃*δ₁^2*μ₁^2*μ₂^4*η^2*k₁*k₃ - β₃*δ₁^2*μ₁*μ₂^6*η*k₁^2*k₂ - 6*β₃*δ₁^2*μ₁*μ₂^5*η^2*k₁*k₃ - 2*β₃*δ₁*δ₃*μ₁^2*μ₂^4*η^2*k₁^2 + 2*β₃*δ₁*δ₃*μ₁*μ₂^5*η^2*k₁^2 + β₃*δ₁*μ₁^3*μ₂^4*η^2*k₁^2 - β₃*δ₁*μ₁*μ₂^6*η^2*k₁^2 - 2*δ₁^5*δ₂^2*μ₁*μ₂^3*k₃^4 + 2*δ₁^5*δ₂^2*μ₂^4*k₃^4 + 2*δ₁^5*δ₂*δ₃^3*μ₂^2*k₂*k₃^3 - 6*δ₁^5*δ₂*δ₃^2*μ₂^3*k₂*k₃^3 + 4*δ₁^5*δ₂*δ₃*μ₂^4*k₂*k₃^3 - 2*δ₁^4*δ₂*δ₃^3*μ₁*μ₂*η*k₃^3 + 2*δ₁^4*δ₂*δ₃^2*μ₁^2*μ₂*η*k₃^3 + 4*δ₁^4*δ₂*δ₃^2*μ₁*μ₂^2*η*k₃^3 - 8*δ₁^4*δ₂*δ₃*μ₁*μ₂^3*η*k₃^3 + 2*δ₁^4*δ₂*δ₃*μ₂^4*η*k₃^3 + 2*δ₁^4*δ₂*μ₁*μ₂^4*η*k₃^3 - 5*δ₁^4*δ₃^4*μ₂^2*η*k₂*k₃^2 + δ₁^4*δ₃^3*μ₁*μ₂^2*η*k₂*k₃^2 - 6*δ₁^4*δ₃^3*μ₂^3*η*k₂*k₃^2 - 2*δ₁^4*δ₃^2*μ₁*μ₂^3*η*k₂*k₃^2 + 11*δ₁^4*δ₃^2*μ₂^4*η*k₂*k₃^2 + δ₁^4*δ₃*μ₁*μ₂^4*η*k₂*k₃^2 - 9*δ₁^3*δ₂*δ₃^4*μ₁*μ₂*η*k₁*k₃^2 + 2*δ₁^3*δ₂*δ₃^3*μ₁^2*μ₂*η*k₁*k₃^2 + 4*δ₁^3*δ₂*δ₃^3*μ₁*μ₂^2*η*k₁*k₃^2 + 5*δ₁^3*δ₂*δ₃^2*μ₁^3*μ₂*η*k₁*k₃^2 + 4*δ₁^3*δ₂*δ₃^2*μ₁^2*μ₂^2*η*k₁*k₃^2 + 12*δ₁^3*δ₂*δ₃^2*μ₁*μ₂^3*η*k₁*k₃^2 + 2*δ₁^3*δ₂*δ₃*μ₁^4*μ₂*η*k₁*k₃^2 - 3*δ₁^3*δ₂*δ₃*μ₁^3*μ₂^2*η*k₁*k₃^2 - 3*δ₁^3*δ₂*δ₃*μ₁^2*μ₂^3*η*k₁*k₃^2 + 2*δ₁^3*δ₂*δ₃*μ₁*μ₂^4*η*k₁*k₃^2 + 2*δ₁^3*δ₂*μ₁^4*μ₂^2*η*k₁*k₃^2 - 2*δ₁^3*δ₂*μ₁^3*μ₂^3*η*k₁*k₃^2 - 13*δ₁^3*δ₂*μ₁^2*μ₂^4*η*k₁*k₃^2 - 3*δ₁^3*δ₂*μ₁*μ₂^5*η*k₁*k₃^2 - 2*δ₁^3*δ₃^5*μ₂^2*η*k₁*k₂*k₃ + 5*δ₁^3*δ₃^5*μ₂*η^2*k₃^2 - 6*δ₁^3*δ₃^4*μ₁*μ₂*η^2*k₃^2 - 4*δ₁^3*δ₃^4*μ₂^3*η*k₁*k₂*k₃ + δ₁^3*δ₃^4*μ₂^2*η^2*k₃^2 + δ₁^3*δ₃^3*μ₁^2*μ₂*η^2*k₃^2 + 2*δ₁^3*δ₃^3*μ₁*μ₂^2*η^2*k₃^2 + 8*δ₁^3*δ₃^3*μ₂^4*η*k₁*k₂*k₃ - 17*δ₁^3*δ₃^3*μ₂^3*η^2*k₃^2 + 3*δ₁^3*δ₃^2*μ₁^2*μ₂^3*η*k₁*k₂*k₃ - 3*δ₁^3*δ₃^2*μ₁^2*μ₂^2*η^2*k₃^2 - 4*δ₁^3*δ₃^2*μ₁*μ₂^4*η*k₁*k₂*k₃ + 14*δ₁^3*δ₃^2*μ₁*μ₂^3*η^2*k₃^2 - 2*δ₁^3*δ₃^2*μ₂^5*η*k₁*k₂*k₃ + 11*δ₁^3*δ₃^2*μ₂^4*η^2*k₃^2 - 3*δ₁^3*δ₃*μ₁^2*μ₂^4*η*k₁*k₂*k₃ + 3*δ₁^3*δ₃*μ₁^2*μ₂^3*η^2*k₃^2 + 4*δ₁^3*δ₃*μ₁*μ₂^5*η*k₁*k₂*k₃ - 10*δ₁^3*δ₃*μ₁*μ₂^4*η^2*k₃^2 - δ₁^3*μ₁^2*μ₂^4*η^2*k₃^2 + 6*δ₁^2*δ₂*δ₃^3*μ₁*μ₂^3*η*k₁^2*k₃ - 12*δ₁^2*δ₂*δ₃^2*μ₁^2*μ₂^3*η*k₁^2*k₃ + 6*δ₁^2*δ₂*δ₃*μ₁^3*μ₂^3*η*k₁^2*k₃ + 11*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^4*η*k₁^2*k₃ - 8*δ₁^2*δ₂*δ₃*μ₁*μ₂^5*η*k₁^2*k₃ - 5*δ₁^2*δ₂*μ₁^3*μ₂^4*η*k₁^2*k₃ - 2*δ₁^2*δ₂*μ₁^2*μ₂^5*η*k₁^2*k₃ + 4*δ₁^2*δ₂*μ₁*μ₂^6*η*k₁^2*k₃ + 2*δ₁^2*δ₃^6*μ₂*η^2*k₁*k₃ - 2*δ₁^2*δ₃^5*μ₁*μ₂*η^2*k₁*k₃ + 2*δ₁^2*δ₃^5*μ₂^2*η^2*k₁*k₃ - 2*δ₁^2*δ₃^4*μ₁*μ₂^2*η^2*k₁*k₃ - 12*δ₁^2*δ₃^4*μ₂^3*η^2*k₁*k₃ - 3*δ₁^2*δ₃^3*μ₁^2*μ₂^2*η^2*k₁*k₃ + 16*δ₁^2*δ₃^3*μ₁*μ₂^3*η^2*k₁*k₃ + 10*δ₁^2*δ₃^3*μ₂^4*η^2*k₁*k₃ + 3*δ₁^2*δ₃^2*μ₁^3*μ₂^2*η^2*k₁*k₃ + 2*δ₁^2*δ₃^2*μ₁^2*μ₂^3*η^2*k₁*k₃ - 18*δ₁^2*δ₃^2*μ₁*μ₂^4*η^2*k₁*k₃ - 2*δ₁^2*δ₃^2*μ₂^5*η^2*k₁*k₃ - 6*δ₁^2*δ₃*μ₁^3*μ₂^3*η^2*k₁*k₃ - δ₁^2*δ₃*μ₁^2*μ₂^5*η*k₁^2*k₂ + 5*δ₁^2*δ₃*μ₁^2*μ₂^4*η^2*k₁*k₃ + δ₁^2*δ₃*μ₁*μ₂^6*η*k₁^2*k₂ + 6*δ₁^2*δ₃*μ₁*μ₂^5*η^2*k₁*k₃ + 3*δ₁^2*μ₁^3*μ₂^4*η^2*k₁*k₃ - 4*δ₁^2*μ₁^2*μ₂^5*η^2*k₁*k₃ + δ₁*δ₃^2*μ₁^2*μ₂^4*η^2*k₁^2 - δ₁*δ₃^2*μ₁*μ₂^5*η^2*k₁^2 - δ₁*δ₃*μ₁^3*μ₂^4*η^2*k₁^2 + δ₁*δ₃*μ₁*μ₂^6*η^2*k₁^2 + δ₁*μ₁^3*μ₂^5*η^2*k₁^2 - δ₁*μ₁^2*μ₂^6*η^2*k₁^2
 4*β₂^3*β₃*δ₁^5*δ₃*μ₁*k₃^4 - 4*β₂^2*β₃^2*δ₁^5*δ₂*δ₃*k₃^4 - 4*β₂^2*β₃*δ₁^5*δ₂*δ₃^2*k₃^4 - 4*β₂^2*β₃*δ₁^5*δ₂*δ₃*μ₁*k₃^4 - 4*β₂^2*β₃*δ₁^5*δ₂*δ₃*μ₂*k₃^4 - 2*β₂^2*β₃*δ₁^4*δ₃*μ₂^2*η*k₃^3 - 18*β₂^2*β₃*δ₁^4*μ₁*μ₂^2*η*k₃^3 + 4*β₂^2*β₃*δ₁^4*μ₂^3*η*k₃^3 + 2*β₂^2*β₃*δ₁^3*δ₃^2*μ₂^2*η*k₁*k₃^2 - 2*β₂^2*β₃*δ₁^3*δ₃*μ₂^3*η*k₁*k₃^2 + 4*β₂^2*δ₁^5*δ₂*δ₃^2*μ₂*k₃^4 - 8*β₂^2*δ₁^5*δ₂*δ₃*μ₁*μ₂*k₃^4 + 4*β₂^2*δ₁^5*δ₂*μ₁*μ₂^2*k₃^4 - 4*β₂^2*δ₁^4*δ₃^4*η*k₃^3 + 18*β₂^2*δ₁^4*δ₃^3*μ₁*η*k₃^3 - 4*β₂^2*δ₁^4*δ₃^3*μ₂*η*k₃^3 + 68*β₂^2*δ₁^4*δ₃^2*μ₁^2*η*k₃^3 + 3*β₂^2*δ₁^4*δ₃^2*μ₁*μ₂*η*k₃^3 + 6*β₂^2*δ₁^4*δ₃^2*μ₂^2*η*k₃^3 - 184*β₂^2*δ₁^4*δ₃*μ₁^3*η*k₃^3 + 24*β₂^2*δ₁^4*δ₃*μ₁^2*μ₂*η*k₃^3 - 20*β₂^2*δ₁^4*δ₃*μ₁*μ₂^2*η*k₃^3 + 92*β₂^2*δ₁^4*μ₁^3*μ₂*η*k₃^3 - 5*β₂^2*δ₁^4*μ₁^2*μ₂^2*η*k₃^3 + 6*β₂^2*δ₁^4*μ₁*μ₂^3*η*k₃^3 - 2*β₂^2*δ₁^3*δ₃^3*μ₂^2*η*k₁*k₃^2 + 2*β₂^2*δ₁^3*δ₃^2*μ₂^3*η*k₁*k₃^2 - 10*β₂^2*δ₁^3*δ₃*μ₁*μ₂^3*η*k₁*k₃^2 + 2*β₂^2*δ₁^3*μ₁*μ₂^4*η*k₁*k₃^2 + 8*β₂*β₃^2*δ₁^5*δ₂^2*δ₃*k₃^4 + 8*β₂*β₃*δ₁^5*δ₂^2*δ₃^2*k₃^4 - 4*β₂*β₃*δ₁^5*δ₂^2*δ₃*μ₁*k₃^4 + 8*β₂*β₃*δ₁^5*δ₂^2*δ₃*μ₂*k₃^4 - 48*β₂*β₃*δ₁^4*δ₂*δ₃^2*μ₁*η*k₃^3 + 60*β₂*β₃*δ₁^4*δ₂*δ₃^2*μ₂*η*k₃^3 - 120*β₂*β₃*δ₁^4*δ₂*δ₃*μ₁*μ₂*η*k₃^3 + 38*β₂*β₃*δ₁^4*δ₂*δ₃*μ₂^2*η*k₃^3 + 184*β₂*β₃*δ₁^4*δ₂*μ₁^3*η*k₃^3 + 6*β₂*β₃*δ₁^4*δ₂*μ₁*μ₂^2*η*k₃^3 + 2*β₂*β₃*δ₁^4*δ₂*μ₂^3*η*k₃^3 + 2*β₂*β₃*δ₁^3*δ₂*δ₃^2*μ₂^2*η*k₁*k₃^2 - 6*β₂*β₃*δ₁^3*δ₂*δ₃*μ₂^3*η*k₁*k₃^2 + 4*β₂*β₃*δ₁^3*δ₂*μ₂^4*η*k₁*k₃^2 - 4*β₂*β₃*δ₁^3*δ₃^3*μ₁*η^2*k₃^2 + 4*β₂*β₃*δ₁^3*δ₃^3*μ₂*η^2*k₃^2 + 26*β₂*β₃*δ₁^3*δ₃^2*μ₁^2*η^2*k₃^2 - 20*β₂*β₃*δ₁^3*δ₃^2*μ₁*μ₂*η^2*k₃^2 + 4*β₂*β₃*δ₁^3*δ₃^2*μ₂^2*η^2*k₃^2 + 56*β₂*β₃*δ₁^3*δ₃*μ₁^3*η^2*k₃^2 - 88*β₂*β₃*δ₁^3*δ₃*μ₁^2*μ₂*η^2*k₃^2 + 16*β₂*β₃*δ₁^3*δ₃*μ₁*μ₂^2*η^2*k₃^2 - 4*β₂*β₃*δ₁^3*δ₃*μ₂^3*η^2*k₃^2 - 48*β₂*β₃*δ₁^3*μ₁^3*μ₂*η^2*k₃^2 - 110*β₂*β₃*δ₁^3*μ₁^2*μ₂^2*η^2*k₃^2 - 57*β₂*β₃*δ₁^3*μ₁*μ₂^3*η^2*k₃^2 - 4*β₂*β₃*δ₁^3*μ₂^4*η^2*k₃^2 + 12*β₂*β₃*δ₁^2*δ₃*μ₁*μ₂^3*η^2*k₁*k₃ + 23*β₂*β₃*δ₁^2*μ₁*μ₂^4*η^2*k₁*k₃ - 8*β₂*δ₁^5*δ₂^2*δ₃^2*μ₂*k₃^4 + 16*β₂*δ₁^5*δ₂^2*δ₃*μ₁*μ₂*k₃^4 - 4*β₂*δ₁^5*δ₂^2*μ₁*μ₂^2*k₃^4 - 4*β₂*δ₁^5*δ₂^2*μ₂^3*k₃^4 + 8*β₂*δ₁^4*δ₂*δ₃^4*η*k₃^3 + 10*β₂*δ₁^4*δ₂*δ₃^3*μ₁*η*k₃^3 - 36*β₂*δ₁^4*δ₂*δ₃^3*μ₂*η*k₃^3 - 136*β₂*δ₁^4*δ₂*δ₃^2*μ₁^2*η*k₃^3 + 101*β₂*δ₁^4*δ₂*δ₃^2*μ₁*μ₂*η*k₃^3 - 2*β₂*δ₁^4*δ₂*δ₃^2*μ₂^2*η*k₃^3 + 184*β₂*δ₁^4*δ₂*δ₃*μ₁^3*η*k₃^3 - 34*β₂*δ₁^4*δ₂*δ₃*μ₁^2*μ₂*η*k₃^3 - 34*β₂*δ₁^4*δ₂*δ₃*μ₁*μ₂^2*η*k₃^3 + 4*β₂*δ₁^4*δ₂*δ₃*μ₂^3*η*k₃^3 - 68*β₂*δ₁^4*δ₂*μ₁^2*μ₂^2*η*k₃^3 + 9*β₂*δ₁^4*δ₂*μ₁*μ₂^3*η*k₃^3 - 6*β₂*δ₁^4*δ₂*μ₂^4*η*k₃^3 + 14*β₂*δ₁^4*μ₁*μ₂^4*η*k₂*k₃^2 - 2*β₂*δ₁^3*δ₂*δ₃^3*μ₂^2*η*k₁*k₃^2 + 2*β₂*δ₁^3*δ₂*δ₃^2*μ₂^3*η*k₁*k₃^2 + 2*β₂*δ₁^3*δ₂*δ₃*μ₂^4*η*k₁*k₃^2 - 2*β₂*δ₁^3*δ₂*μ₂^5*η*k₁*k₃^2 + 4*β₂*δ₁^3*δ₃^4*μ₁*η^2*k₃^2 - 4*β₂*δ₁^3*δ₃^4*μ₂*η^2*k₃^2 - 26*β₂*δ₁^3*δ₃^3*μ₁^2*η^2*k₃^2 + 16*β₂*δ₁^3*δ₃^3*μ₁*μ₂*η^2*k₃^2 - 4*β₂*δ₁^3*δ₃^3*μ₂^2*η^2*k₃^2 - 56*β₂*δ₁^3*δ₃^2*μ₁^3*η^2*k₃^2 + 105*β₂*δ₁^3*δ₃^2*μ₁^2*μ₂*η^2*k₃^2 - 107*β₂*δ₁^3*δ₃^2*μ₁*μ₂^2*η^2*k₃^2 + 4*β₂*δ₁^3*δ₃^2*μ₂^3*η^2*k₃^2 + 130*β₂*δ₁^3*δ₃*μ₁^3*μ₂*η^2*k₃^2 + 44*β₂*δ₁^3*δ₃*μ₁^2*μ₂^2*η^2*k₃^2 - 28*β₂*δ₁^3*δ₃*μ₁*μ₂^3*η^2*k₃^2 + 4*β₂*δ₁^3*δ₃*μ₂^4*η^2*k₃^2 - 92*β₂*δ₁^3*μ₁^4*μ₂*η^2*k₃^2 + 109*β₂*δ₁^3*μ₁^3*μ₂^2*η^2*k₃^2 - 95*β₂*δ₁^3*μ₁^2*μ₂^3*η^2*k₃^2 + 2*β₂*δ₁^3*μ₁*μ₂^5*η*k₁*k₂*k₃ - 4*β₂*δ₁^3*μ₁*μ₂^4*η^2*k₃^2 + 8*β₂*δ₁^2*δ₃^2*μ₁^2*μ₂^2*η^2*k₁*k₃ - 12*β₂*δ₁^2*δ₃^2*μ₁*μ₂^3*η^2*k₁*k₃ - 8*β₂*δ₁^2*δ₃*μ₁^4*μ₂*η^2*k₁*k₃ - 61*β₂*δ₁^2*δ₃*μ₁^3*μ₂^2*η^2*k₁*k₃ + 66*β₂*δ₁^2*δ₃*μ₁^2*μ₂^3*η^2*k₁*k₃ + 2*β₂*δ₁^2*δ₃*μ₁*μ₂^4*η^2*k₁*k₃ + 20*β₂*δ₁^2*μ₁^5*μ₂*η^2*k₁*k₃ - 8*β₂*δ₁^2*μ₁^4*μ₂^2*η^2*k₁*k₃ - 121*β₂*δ₁^2*μ₁^3*μ₂^3*η^2*k₁*k₃ + 114*β₂*δ₁^2*μ₁^2*μ₂^4*η^2*k₁*k₃ + 15*β₂*δ₁*μ₁^3*μ₂^4*η^2*k₁^2 - 15*β₂*δ₁*μ₁^2*μ₂^5*η^2*k₁^2 - 4*β₃^6*δ₁*δ₃*η^3*k₁ - 16*β₃^6*δ₁*μ₂*η^3*k₁ - 12*β₃^5*δ₁^2*δ₂*δ₃*η^2*k₁*k₃ - 36*β₃^5*δ₁^2*δ₂*μ₂*η^2*k₁*k₃ - 4*β₃^5*δ₁^2*δ₃*μ₂*η^2*k₁*k₂ + 12*β₃^5*δ₁^2*δ₃*η^3*k₃ - 16*β₃^5*δ₁^2*μ₂^2*η^2*k₁*k₂ + 72*β₃^5*δ₁^2*μ₂*η^3*k₃ + 24*β₃^5*δ₁*δ₃^2*η^3*k₁ - 4*β₃^5*δ₁*δ₃*μ₁*η^3*k₁ + 88*β₃^5*δ₁*δ₃*μ₂*η^3*k₁ - 16*β₃^5*δ₁*μ₁*μ₂*η^3*k₁ - 52*β₃^5*δ₁*μ₂^2*η^3*k₁ - 4*β₃^4*δ₁^3*δ₂^2*δ₃*η*k₁*k₃^2 - 4*β₃^4*δ₁^3*δ₂^2*μ₂*η*k₁*k₃^2 + 28*β₃^4*δ₁^3*δ₂*δ₃*η^2*k₃^2 + 148*β₃^4*δ₁^3*δ₂*μ₂*η^2*k₃^2 + 12*β₃^4*δ₁^3*δ₃*μ₂*η^2*k₂*k₃ + 72*β₃^4*δ₁^3*μ₂^2*η^2*k₂*k₃ + 52*β₃^4*δ₁^2*δ₂*δ₃^2*η^2*k₁*k₃ + 148*β₃^4*δ₁^2*δ₂*δ₃*μ₂*η^2*k₁*k₃ - 48*β₃^4*δ₁^2*δ₂*μ₂^2*η^2*k₁*k₃ + 20*β₃^4*δ₁^2*δ₃^2*μ₂*η^2*k₁*k₂ - 44*β₃^4*δ₁^2*δ₃^2*η^3*k₃ + 12*β₃^4*δ₁^2*δ₃*μ₁*η^3*k₃ + 76*β₃^4*δ₁^2*δ₃*μ₂^2*η^2*k₁*k₂ - 276*β₃^4*δ₁^2*δ₃*μ₂*η^3*k₃ + 72*β₃^4*δ₁^2*μ₁*μ₂*η^3*k₃ - 36*β₃^4*δ₁^2*μ₂^3*η^2*k₁*k₂ + 268*β₃^4*δ₁^2*μ₂^2*η^3*k₃ - 60*β₃^4*δ₁*δ₃^3*η^3*k₁ + 20*β₃^4*δ₁*δ₃^2*μ₁*η^3*k₁ - 200*β₃^4*δ₁*δ₃^2*μ₂*η^3*k₁ + 72*β₃^4*δ₁*δ₃*μ₁*μ₂*η^3*k₁ + 256*β₃^4*δ₁*δ₃*μ₂^2*η^3*k₁ - 52*β₃^4*δ₁*μ₁*μ₂^2*η^3*k₁ - 70*β₃^4*δ₁*μ₂^3*η^3*k₁ + 12*β₃^3*δ₁^3*δ₂^2*δ₃^2*η*k₁*k₃^2 + 16*β₃^3*δ₁^3*δ₂^2*δ₃*μ₂*η*k₁*k₃^2 - 4*β₃^3*δ₁^3*δ₂^2*μ₂^2*η*k₁*k₃^2 - 48*β₃^3*δ₁^3*δ₂*δ₃^2*η^2*k₃^2 - 80*β₃^3*δ₁^3*δ₂*δ₃*μ₁*η^2*k₃^2 - 364*β₃^3*δ₁^3*δ₂*δ₃*μ₂*η^2*k₃^2 + 184*β₃^3*δ₁^3*δ₂*μ₁^2*η^2*k₃^2 - 20*β₃^3*δ₁^3*δ₂*μ₁*μ₂*η^2*k₃^2 + 256*β₃^3*δ₁^3*δ₂*μ₂^2*η^2*k₃^2 - 32*β₃^3*δ₁^3*δ₃^2*μ₂*η^2*k₂*k₃ - 216*β₃^3*δ₁^3*δ₃*μ₂^2*η^2*k₂*k₃ + 196*β₃^3*δ₁^3*μ₂^3*η^2*k₂*k₃ - 88*β₃^3*δ₁^2*δ₂*δ₃^3*η^2*k₁*k₃ - 232*β₃^3*δ₁^2*δ₂*δ₃^2*μ₂*η^2*k₁*k₃ + 160*β₃^3*δ₁^2*δ₂*δ₃*μ₂^2*η^2*k₁*k₃ + 4*β₃^3*δ₁^2*δ₂*μ₂^3*η^2*k₁*k₃ - 40*β₃^3*δ₁^2*δ₃^3*μ₂*η^2*k₁*k₂ + 56*β₃^3*δ₁^2*δ₃^3*η^3*k₃ - 32*β₃^3*δ₁^2*δ₃^2*μ₁*η^3*k₃ - 144*β₃^3*δ₁^2*δ₃^2*μ₂^2*η^2*k₁*k₂ + 416*β₃^3*δ₁^2*δ₃^2*μ₂*η^3*k₃ - 204*β₃^3*δ₁^2*δ₃*μ₁*μ₂*η^3*k₃ + 144*β₃^3*δ₁^2*δ₃*μ₂^3*η^2*k₁*k₂ - 943*β₃^3*δ₁^2*δ₃*μ₂^2*η^3*k₃ + 268*β₃^3*δ₁^2*μ₁*μ₂^2*η^3*k₃ - 34*β₃^3*δ₁^2*μ₂^4*η^2*k₁*k₂ + 322*β₃^3*δ₁^2*μ₂^3*η^3*k₃ + 80*β₃^3*δ₁*δ₃^4*η^3*k₁ - 40*β₃^3*δ₁*δ₃^3*μ₁*η^3*k₁ + 240*β₃^3*δ₁*δ₃^3*μ₂*η^3*k₁ - 128*β₃^3*δ₁*δ₃^2*μ₁*μ₂*η^3*k₁ - 504*β₃^3*δ₁*δ₃^2*μ₂^2*η^3*k₁ + 204*β₃^3*δ₁*δ₃*μ₁*μ₂^2*η^3*k₁ + 280*β₃^3*δ₁*δ₃*μ₂^3*η^3*k₁ - 70*β₃^3*δ₁*μ₁*μ₂^3*η^3*k₁ - 47*β₃^3*δ₁*μ₂^4*η^3*k₁ - 4*β₃^2*δ₁^5*δ₂^3*δ₃*k₃^4 - 4*β₃^2*δ₁^5*δ₂^3*μ₂*k₃^4 + 4*β₃^2*δ₁^4*δ₂^2*δ₃^2*η*k₃^3 - 40*β₃^2*δ₁^4*δ₂^2*δ₃*μ₂*η*k₃^3 - 12*β₃^2*δ₁^3*δ₂^2*δ₃^3*η*k₁*k₃^2 - 20*β₃^2*δ₁^3*δ₂^2*δ₃^2*μ₂*η*k₁*k₃^2 + 8*β₃^2*δ₁^3*δ₂^2*δ₃*μ₂^2*η*k₁*k₃^2 + 8*β₃^2*δ₁^3*δ₂^2*μ₂^3*η*k₁*k₃^2 + 4*β₃^2*δ₁^3*δ₂*δ₃^3*η^2*k₃^2 + 228*β₃^2*δ₁^3*δ₂*δ₃^2*μ₁*η^2*k₃^2 + 308*β₃^2*δ₁^3*δ₂*δ₃^2*μ₂*η^2*k₃^2 - 684*β₃^2*δ₁^3*δ₂*δ₃*μ₁^2*η^2*k₃^2 - 30*β₃^2*δ₁^3*δ₂*δ₃*μ₁*μ₂*η^2*k₃^2 - 618*β₃^2*δ₁^3*δ₂*δ₃*μ₂^2*η^2*k₃^2 + 368*β₃^2*δ₁^3*δ₂*μ₁^3*η^2*k₃^2 + 204*β₃^2*δ₁^3*δ₂*μ₁^2*μ₂*η^2*k₃^2 - 29*β₃^2*δ₁^3*δ₂*μ₁*μ₂^2*η^2*k₃^2 - 146*β₃^2*δ₁^3*δ₂*μ₂^3*η^2*k₃^2 + 24*β₃^2*δ₁^3*δ₃^3*μ₂*η^2*k₂*k₃ + 232*β₃^2*δ₁^3*δ₃^2*μ₂^2*η^2*k₂*k₃ - 531*β₃^2*δ₁^3*δ₃*μ₂^3*η^2*k₂*k₃ + 126*β₃^2*δ₁^3*μ₂^4*η^2*k₂*k₃ + 72*β₃^2*δ₁^2*δ₂*δ₃^4*η^2*k₁*k₃ + 168*β₃^2*δ₁^2*δ₂*δ₃^3*μ₂*η^2*k₁*k₃ - 8*β₃^2*δ₁^2*δ₂*δ₃^2*μ₁*μ₂*η^2*k₁*k₃ - 184*β₃^2*δ₁^2*δ₂*δ₃^2*μ₂^2*η^2*k₁*k₃ - 89*β₃^2*δ₁^2*δ₂*δ₃*μ₁*μ₂^2*η^2*k₁*k₃ - 8*β₃^2*δ₁^2*δ₂*δ₃*μ₂^3*η^2*k₁*k₃ - 95*β₃^2*δ₁^2*δ₂*μ₁*μ₂^3*η^2*k₁*k₃ + 42*β₃^2*δ₁^2*δ₂*μ₂^4*η^2*k₁*k₃ + 40*β₃^2*δ₁^2*δ₃^4*μ₂*η^2*k₁*k₂ - 24*β₃^2*δ₁^2*δ₃^4*η^3*k₃ + 24*β₃^2*δ₁^2*δ₃^3*μ₁*η^3*k₃ + 136*β₃^2*δ₁^2*δ₃^3*μ₂^2*η^2*k₁*k₂ - 312*β₃^2*δ₁^2*δ₃^3*μ₂*η^3*k₃ + 212*β₃^2*δ₁^2*δ₃^2*μ₁*μ₂*η^3*k₃ - 216*β₃^2*δ₁^2*δ₃^2*μ₂^3*η^2*k₁*k₂ + 1237*β₃^2*δ₁^2*δ₃^2*μ₂^2*η^3*k₃ + β₃^2*δ₁^2*δ₃*μ₁^2*μ₂*η^3*k₃ - 677*β₃^2*δ₁^2*δ₃*μ₁*μ₂^2*η^3*k₃ + 102*β₃^2*δ₁^2*δ₃*μ₂^4*η^2*k₁*k₂ - 909*β₃^2*δ₁^2*δ₃*μ₂^3*η^3*k₃ + β₃^2*δ₁^2*μ₁^2*μ₂^2*η^3*k₃ + 321*β₃^2*δ₁^2*μ₁*μ₂^3*η^3*k₃ - 13*β₃^2*δ₁^2*μ₂^5*η^2*k₁*k₂ + 126*β₃^2*δ₁^2*μ₂^4*η^3*k₃ + 23*β₃^2*δ₁*δ₂*μ₁*μ₂^4*η^2*k₁^2 - 60*β₃^2*δ₁*δ₃^5*η^3*k₁ + 40*β₃^2*δ₁*δ₃^4*μ₁*η^3*k₁ - 160*β₃^2*δ₁*δ₃^4*μ₂*η^3*k₁ + 112*β₃^2*δ₁*δ₃^3*μ₁*μ₂*η^3*k₁ + 496*β₃^2*δ₁*δ₃^3*μ₂^2*η^3*k₁ - 300*β₃^2*δ₁*δ₃^2*μ₁*μ₂^2*η^3*k₁ - 420*β₃^2*δ₁*δ₃^2*μ₂^3*η^3*k₁ + 210*β₃^2*δ₁*δ₃*μ₁*μ₂^3*η^3*k₁ + 141*β₃^2*δ₁*δ₃*μ₂^4*η^3*k₁ + β₃^2*δ₁*μ₁^2*μ₂^3*η^3*k₁ - 47*β₃^2*δ₁*μ₁*μ₂^4*η^3*k₁ - 13*β₃^2*δ₁*μ₂^5*η^3*k₁ - 4*β₃*δ₁^5*δ₂^3*δ₃^2*k₃^4 + 4*β₃*δ₁^5*δ₂^3*δ₃*μ₁*k₃^4 + 4*β₃*δ₁^5*δ₂^3*δ₃*μ₂*k₃^4 - 8*β₃*δ₁^5*δ₂^3*μ₁*μ₂*k₃^4 - 8*β₃*δ₁^4*δ₂^2*δ₃^3*η*k₃^3 + 24*β₃*δ₁^4*δ₂^2*δ₃^2*μ₁*η*k₃^3 + 20*β₃*δ₁^4*δ₂^2*δ₃^2*μ₂*η*k₃^3 + 64*β₃*δ₁^4*δ₂^2*δ₃*μ₁^2*η*k₃^3 - 24*β₃*δ₁^4*δ₂^2*δ₃*μ₁*μ₂*η*k₃^3 - 36*β₃*δ₁^4*δ₂^2*δ₃*μ₂^2*η*k₃^3 - 184*β₃*δ₁^4*δ₂^2*μ₁^3*η*k₃^3 + 64*β₃*δ₁^4*δ₂^2*μ₁^2*μ₂*η*k₃^3 - 20*β₃*δ₁^4*δ₂^2*μ₁*μ₂^2*η*k₃^3 - 6*β₃*δ₁^4*δ₂^2*μ₂^3*η*k₃^3 + 4*β₃*δ₁^3*δ₂^2*δ₃^4*η*k₁*k₃^2 + 8*β₃*δ₁^3*δ₂^2*δ₃^3*μ₂*η*k₁*k₃^2 + 16*β₃*δ₁^3*δ₂^2*δ₃^2*μ₁^2*η*k₁*k₃^2 - 4*β₃*δ₁^3*δ₂^2*δ₃^2*μ₂^2*η*k₁*k₃^2 - 24*β₃*δ₁^3*δ₂^2*δ₃*μ₁*μ₂^2*η*k₁*k₃^2 - 8*β₃*δ₁^3*δ₂^2*δ₃*μ₂^3*η*k₁*k₃^2 + 16*β₃*δ₁^3*δ₂^2*μ₁^2*μ₂^2*η*k₁*k₃^2 - 8*β₃*δ₁^3*δ₂^2*μ₁*μ₂^3*η*k₁*k₃^2 + 24*β₃*δ₁^3*δ₂*δ₃^4*η^2*k₃^2 - 216*β₃*δ₁^3*δ₂*δ₃^3*μ₁*η^2*k₃^2 - 120*β₃*δ₁^3*δ₂*δ₃^3*μ₂*η^2*k₃^2 + 812*β₃*δ₁^3*δ₂*δ₃^2*μ₁^2*η^2*k₃^2 + 90*β₃*δ₁^3*δ₂*δ₃^2*μ₁*μ₂*η^2*k₃^2 + 386*β₃*δ₁^3*δ₂*δ₃^2*μ₂^2*η^2*k₃^2 - 804*β₃*δ₁^3*δ₂*δ₃*μ₁^3*η^2*k₃^2 - 583*β₃*δ₁^3*δ₂*δ₃*μ₁^2*μ₂*η^2*k₃^2 + 228*β₃*δ₁^3*δ₂*δ₃*μ₁*μ₂^2*η^2*k₃^2 - 8*β₃*δ₁^3*δ₂*δ₃*μ₂^3*η^2*k₃^2 + 184*β₃*δ₁^3*δ₂*μ₁^4*η^2*k₃^2 + 476*β₃*δ₁^3*δ₂*μ₁^3*μ₂*η^2*k₃^2 - 157*β₃*δ₁^3*δ₂*μ₁^2*μ₂^2*η^2*k₃^2 + 167*β₃*δ₁^3*δ₂*μ₁*μ₂^3*η^2*k₃^2 - 250*β₃*δ₁^3*δ₂*μ₂^4*η^2*k₃^2 - 104*β₃*δ₁^3*δ₃^3*μ₂^2*η^2*k₂*k₃ + 474*β₃*δ₁^3*δ₃^2*μ₂^3*η^2*k₂*k₃ + β₃*δ₁^3*δ₃*μ₁^2*μ₂^2*η^2*k₂*k₃ - 2*β₃*δ₁^3*δ₃*μ₁*μ₂^3*η^2*k₂*k₃ - 252*β₃*δ₁^3*δ₃*μ₂^4*η^2*k₂*k₃ + β₃*δ₁^3*μ₁^2*μ₂^3*η^2*k₂*k₃ - β₃*δ₁^3*μ₁*μ₂^4*η^2*k₂*k₃ - 28*β₃*δ₁^2*δ₂*δ₃^5*η^2*k₁*k₃ - 52*β₃*δ₁^2*δ₂*δ₃^4*μ₂*η^2*k₁*k₃ + 16*β₃*δ₁^2*δ₂*δ₃^3*μ₁*μ₂*η^2*k₁*k₃ + 80*β₃*δ₁^2*δ₂*δ₃^3*μ₂^2*η^2*k₁*k₃ - 4*β₃*δ₁^2*δ₂*δ₃^2*μ₁^3*η^2*k₁*k₃ - 12*β₃*δ₁^2*δ₂*δ₃^2*μ₁^2*μ₂*η^2*k₁*k₃ + 162*β₃*δ₁^2*δ₂*δ₃^2*μ₁*μ₂^2*η^2*k₁*k₃ + 4*β₃*δ₁^2*δ₂*δ₃^2*μ₂^3*η^2*k₁*k₃ + 8*β₃*δ₁^2*δ₂*δ₃*μ₁^4*η^2*k₁*k₃ - 20*β₃*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^2*η^2*k₁*k₃ + 44*β₃*δ₁^2*δ₂*δ₃*μ₁*μ₂^3*η^2*k₁*k₃ - 42*β₃*δ₁^2*δ₂*δ₃*μ₂^4*η^2*k₁*k₃ + 17*β₃*δ₁^2*δ₂*μ₁^2*μ₂^3*η^2*k₁*k₃ - 234*β₃*δ₁^2*δ₂*μ₁*μ₂^4*η^2*k₁*k₃ + 26*β₃*δ₁^2*δ₂*μ₂^5*η^2*k₁*k₃ - 20*β₃*δ₁^2*δ₃^5*μ₂*η^2*k₁*k₂ - 4*β₃*δ₁^2*δ₃^5*η^3*k₃ - 64*β₃*δ₁^2*δ₃^4*μ₂^2*η^2*k₁*k₂ + 120*β₃*δ₁^2*δ₃^4*μ₂*η^3*k₃ - 100*β₃*δ₁^2*δ₃^3*μ₁*μ₂*η^3*k₃ + 144*β₃*δ₁^2*δ₃^3*μ₂^3*η^2*k₁*k₂ - 717*β₃*δ₁^2*δ₃^3*μ₂^2*η^3*k₃ - 2*β₃*δ₁^2*δ₃^2*μ₁^2*μ₂*η^3*k₃ + 566*β₃*δ₁^2*δ₃^2*μ₁*μ₂^2*η^3*k₃ - 102*β₃*δ₁^2*δ₃^2*μ₂^4*η^2*k₁*k₂ + 852*β₃*δ₁^2*δ₃^2*μ₂^3*η^3*k₃ + β₃*δ₁^2*δ₃*μ₁^3*μ₂*η^3*k₃ - 3*β₃*δ₁^2*δ₃*μ₁^2*μ₂^2*η^3*k₃ - 587*β₃*δ₁^2*δ₃*μ₁*μ₂^3*η^3*k₃ + 26*β₃*δ₁^2*δ₃*μ₂^5*η^2*k₁*k₂ - 252*β₃*δ₁^2*δ₃*μ₂^4*η^3*k₃ + β₃*δ₁^2*μ₁^3*μ₂^2*η^3*k₃ + β₃*δ₁^2*μ₁^2*μ₂^4*η^2*k₁*k₂ + 125*β₃*δ₁^2*μ₁*μ₂^4*η^3*k₃ - 46*β₃*δ₁*δ₂*δ₃*μ₁*μ₂^4*η^2*k₁^2 + 8*β₃*δ₁*δ₂*μ₁^2*μ₂^4*η^2*k₁^2 + 38*β₃*δ₁*δ₂*μ₁*μ₂^5*η^2*k₁^2 + 24*β₃*δ₁*δ₃^6*η^3*k₁ - 20*β₃*δ₁*δ₃^5*μ₁*η^3*k₁ + 56*β₃*δ₁*δ₃^5*μ₂*η^3*k₁ - 48*β₃*δ₁*δ₃^4*μ₁*μ₂*η^3*k₁ - 244*β₃*δ₁*δ₃^4*μ₂^2*η^3*k₁ + 196*β₃*δ₁*δ₃^3*μ₁*μ₂^2*η^3*k₁ + 280*β₃*δ₁*δ₃^3*μ₂^3*η^3*k₁ - 210*β₃*δ₁*δ₃^2*μ₁*μ₂^3*η^3*k₁ - 141*β₃*δ₁*δ₃^2*μ₂^4*η^3*k₁ - 2*β₃*δ₁*δ₃*μ₁^2*μ₂^3*η^3*k₁ + 94*β₃*δ₁*δ₃*μ₁*μ₂^4*η^3*k₁ + 26*β₃*δ₁*δ₃*μ₂^5*η^3*k₁ + β₃*δ₁*μ₁^3*μ₂^3*η^3*k₁ + β₃*δ₁*μ₁^2*μ₂^4*η^3*k₁ - 13*β₃*δ₁*μ₁*μ₂^5*η^3*k₁ - 8*δ₁^5*δ₂^3*μ₁*μ₂^2*k₃^4 + 8*δ₁^5*δ₂^3*μ₂^3*k₃^4 + 4*δ₁^5*δ₂^2*δ₃^3*μ₂*k₂*k₃^3 - 12*δ₁^5*δ₂^2*δ₃^2*μ₂^2*k₂*k₃^3 + 12*δ₁^5*δ₂^2*δ₃*μ₂^3*k₂*k₃^3 - 4*δ₁^5*δ₂^2*μ₂^4*k₂*k₃^3 - 4*δ₁^4*δ₂^2*δ₃^3*μ₁*η*k₃^3 + 4*δ₁^4*δ₂^2*δ₃^2*μ₁^2*η*k₃^3 + 16*δ₁^4*δ₂^2*δ₃^2*μ₁*μ₂*η*k₃^3 - 8*δ₁^4*δ₂^2*δ₃^2*μ₂^2*η*k₃^3 + 10*δ₁^4*δ₂^2*δ₃*μ₁^2*μ₂*η*k₃^3 - 58*δ₁^4*δ₂^2*δ₃*μ₁*μ₂^2*η*k₃^3 + 36*δ₁^4*δ₂^2*δ₃*μ₂^3*η*k₃^3 - 92*δ₁^4*δ₂^2*μ₁^3*μ₂*η*k₃^3 + 137*δ₁^4*δ₂^2*μ₁^2*μ₂^2*η*k₃^3 - 47*δ₁^4*δ₂^2*μ₁*μ₂^3*η*k₃^3 + 6*δ₁^4*δ₂^2*μ₂^4*η*k₃^3 - 4*δ₁^4*δ₂*δ₃^2*μ₂^3*η*k₂*k₃^2 - 4*δ₁^4*δ₂*δ₃*μ₁*μ₂^3*η*k₂*k₃^2 + 6*δ₁^4*δ₂*δ₃*μ₂^4*η*k₂*k₃^2 - 10*δ₁^4*δ₂*μ₁*μ₂^4*η*k₂*k₃^2 - 2*δ₁^4*δ₂*μ₂^5*η*k₂*k₃^2 - 16*δ₁^3*δ₂^2*δ₃^3*μ₁^2*η*k₁*k₃^2 + 16*δ₁^3*δ₂^2*δ₃^2*μ₁^2*μ₂*η*k₁*k₃^2 + 24*δ₁^3*δ₂^2*δ₃^2*μ₁*μ₂^2*η*k₁*k₃^2 - 16*δ₁^3*δ₂^2*δ₃*μ₁^2*μ₂^2*η*k₁*k₃^2 - 6*δ₁^3*δ₂^2*δ₃*μ₁*μ₂^3*η*k₁*k₃^2 + 2*δ₁^3*δ₂^2*δ₃*μ₂^4*η*k₁*k₃^2 + 16*δ₁^3*δ₂^2*μ₁^2*μ₂^3*η*k₁*k₃^2 - 10*δ₁^3*δ₂^2*μ₁*μ₂^4*η*k₁*k₃^2 - 2*δ₁^3*δ₂^2*μ₂^5*η*k₁*k₃^2 - 8*δ₁^3*δ₂*δ₃^5*η^2*k₃^2 + 68*δ₁^3*δ₂*δ₃^4*μ₁*η^2*k₃^2 + 28*δ₁^3*δ₂*δ₃^4*μ₂*η^2*k₃^2 - 312*δ₁^3*δ₂*δ₃^3*μ₁^2*η^2*k₃^2 - 40*δ₁^3*δ₂*δ₃^3*μ₁*μ₂*η^2*k₃^2 - 52*δ₁^3*δ₂*δ₃^3*μ₂^2*η^2*k₃^2 + 436*δ₁^3*δ₂*δ₃^2*μ₁^3*η^2*k₃^2 + 384*δ₁^3*δ₂*δ₃^2*μ₁^2*μ₂*η^2*k₃^2 - 146*δ₁^3*δ₂*δ₃^2*μ₁*μ₂^2*η^2*k₃^2 + 36*δ₁^3*δ₂*δ₃^2*μ₂^3*η^2*k₃^2 - 184*δ₁^3*δ₂*δ₃*μ₁^4*η^2*k₃^2 - 570*δ₁^3*δ₂*δ₃*μ₁^3*μ₂*η^2*k₃^2 + 92*δ₁^3*δ₂*δ₃*μ₁^2*μ₂^2*η^2*k₃^2 + 114*δ₁^3*δ₂*δ₃*μ₁*μ₂^3*η^2*k₃^2 + 2*δ₁^3*δ₂*δ₃*μ₂^5*η*k₁*k₂*k₃ - 4*δ₁^3*δ₂*δ₃*μ₂^4*η^2*k₃^2 + 276*δ₁^3*δ₂*μ₁^4*μ₂*η^2*k₃^2 - 49*δ₁^3*δ₂*μ₁^3*μ₂^2*η^2*k₃^2 - 192*δ₁^3*δ₂*μ₁^2*μ₂^3*η^2*k₃^2 + 123*δ₁^3*δ₂*μ₁*μ₂^4*η^2*k₃^2 - 2*δ₁^3*δ₂*μ₂^6*η*k₁*k₂*k₃ - 4*δ₁^3*δ₃^5*μ₂*η^2*k₂*k₃ + 16*δ₁^3*δ₃^4*μ₂^2*η^2*k₂*k₃ - 139*δ₁^3*δ₃^3*μ₂^3*η^2*k₂*k₃ - δ₁^3*δ₃^2*μ₁^2*μ₂^2*η^2*k₂*k₃ + 2*δ₁^3*δ₃^2*μ₁*μ₂^3*η^2*k₂*k₃ + 126*δ₁^3*δ₃^2*μ₂^4*η^2*k₂*k₃ - δ₁^3*δ₃*μ₁^2*μ₂^3*η^2*k₂*k₃ + δ₁^3*δ₃*μ₁*μ₂^4*η^2*k₂*k₃ + 4*δ₁^2*δ₂*δ₃^6*η^2*k₁*k₃ + 4*δ₁^2*δ₂*δ₃^5*μ₂*η^2*k₁*k₃ - 8*δ₁^2*δ₂*δ₃^4*μ₁*μ₂*η^2*k₁*k₃ - 8*δ₁^2*δ₂*δ₃^4*μ₂^2*η^2*k₁*k₃ + 4*δ₁^2*δ₂*δ₃^3*μ₁^3*η^2*k₁*k₃ + 12*δ₁^2*δ₂*δ₃^3*μ₁^2*μ₂*η^2*k₁*k₃ - 73*δ₁^2*δ₂*δ₃^3*μ₁*μ₂^2*η^2*k₁*k₃ - 8*δ₁^2*δ₂*δ₃^2*μ₁^4*η^2*k₁*k₃ - 4*δ₁^2*δ₂*δ₃^2*μ₁^3*μ₂*η^2*k₁*k₃ + 43*δ₁^2*δ₂*δ₃^2*μ₁*μ₂^3*η^2*k₁*k₃ + 16*δ₁^2*δ₂*δ₃*μ₁^4*μ₂*η^2*k₁*k₃ + 61*δ₁^2*δ₂*δ₃*μ₁^3*μ₂^2*η^2*k₁*k₃ - 103*δ₁^2*δ₂*δ₃*μ₁^2*μ₂^3*η^2*k₁*k₃ + 164*δ₁^2*δ₂*δ₃*μ₁*μ₂^4*η^2*k₁*k₃ - 20*δ₁^2*δ₂*μ₁^5*μ₂*η^2*k₁*k₃ + 8*δ₁^2*δ₂*μ₁^4*μ₂^2*η^2*k₁*k₃ + 121*δ₁^2*δ₂*μ₁^3*μ₂^3*η^2*k₁*k₃ - 97*δ₁^2*δ₂*μ₁^2*μ₂^4*η^2*k₁*k₃ - 116*δ₁^2*δ₂*μ₁*μ₂^5*η^2*k₁*k₃ + 4*δ₁^2*δ₃^6*μ₂*η^2*k₁*k₂ + 4*δ₁^2*δ₃^6*η^3*k₃ - 4*δ₁^2*δ₃^5*μ₁*η^3*k₃ + 12*δ₁^2*δ₃^5*μ₂^2*η^2*k₁*k₂ - 20*δ₁^2*δ₃^5*μ₂*η^3*k₃ + 20*δ₁^2*δ₃^4*μ₁*μ₂*η^3*k₃ - 36*δ₁^2*δ₃^4*μ₂^3*η^2*k₁*k₂ + 155*δ₁^2*δ₃^4*μ₂^2*η^3*k₃ + δ₁^2*δ₃^3*μ₁^2*μ₂*η^3*k₃ - 157*δ₁^2*δ₃^3*μ₁*μ₂^2*η^3*k₃ + 34*δ₁^2*δ₃^3*μ₂^4*η^2*k₁*k₂ - 265*δ₁^2*δ₃^3*μ₂^3*η^3*k₃ - δ₁^2*δ₃^2*μ₁^3*μ₂*η^3*k₃ + 2*δ₁^2*δ₃^2*μ₁^2*μ₂^2*η^3*k₃ + 266*δ₁^2*δ₃^2*μ₁*μ₂^3*η^3*k₃ - 13*δ₁^2*δ₃^2*μ₂^5*η^2*k₁*k₂ + 126*δ₁^2*δ₃^2*μ₂^4*η^3*k₃ - δ₁^2*δ₃*μ₁^2*μ₂^4*η^2*k₁*k₂ - 2*δ₁^2*δ₃*μ₁^2*μ₂^3*η^3*k₃ - 125*δ₁^2*δ₃*μ₁*μ₂^4*η^3*k₃ + δ₁^2*μ₁^3*μ₂^3*η^3*k₃ - δ₁^2*μ₁^2*μ₂^4*η^3*k₃ + 23*δ₁*δ₂*δ₃^2*μ₁*μ₂^4*η^2*k₁^2 - 8*δ₁*δ₂*δ₃*μ₁^2*μ₂^4*η^2*k₁^2 - 38*δ₁*δ₂*δ₃*μ₁*μ₂^5*η^2*k₁^2 - 15*δ₁*δ₂*μ₁^3*μ₂^4*η^2*k₁^2 + 23*δ₁*δ₂*μ₁^2*μ₂^5*η^2*k₁^2 + 15*δ₁*δ₂*μ₁*μ₂^6*η^2*k₁^2 - 4*δ₁*δ₃^7*η^3*k₁ + 4*δ₁*δ₃^6*μ₁*η^3*k₁ - 8*δ₁*δ₃^6*μ₂*η^3*k₁ + 8*δ₁*δ₃^5*μ₁*μ₂*η^3*k₁ + 48*δ₁*δ₃^5*μ₂^2*η^3*k₁ - 48*δ₁*δ₃^4*μ₁*μ₂^2*η^3*k₁ - 70*δ₁*δ₃^4*μ₂^3*η^3*k₁ + 70*δ₁*δ₃^3*μ₁*μ₂^3*η^3*k₁ + 47*δ₁*δ₃^3*μ₂^4*η^3*k₁ + δ₁*δ₃^2*μ₁^2*μ₂^3*η^3*k₁ - 47*δ₁*δ₃^2*μ₁*μ₂^4*η^3*k₁ - 13*δ₁*δ₃^2*μ₂^5*η^3*k₁ - δ₁*δ₃*μ₁^3*μ₂^3*η^3*k₁ - δ₁*δ₃*μ₁^2*μ₂^4*η^3*k₁ + 13*δ₁*δ₃*μ₁*μ₂^5*η^3*k₁ + δ₁*μ₁^3*μ₂^4*η^3*k₁
 15*β₂^4*δ₁^2*δ₂*μ₁*η^2*k₁^3*k₂ - 9*β₂^4*δ₁^2*μ₁*η^3*k₁^2*k₂ + 13*β₂^4*δ₁*δ₂*μ₁*η^3*k₁^3 - 11*β₂^4*δ₁*μ₁*η^4*k₁^2 - 12*β₂^3*β₃*δ₁^4*δ₂*η*k₁^2*k₂^3 - 3*β₂^3*β₃*δ₁^4*η^2*k₁*k₂^3 - 46*β₂^3*β₃*δ₁^3*δ₂*η^2*k₁^2*k₂^2 + 7*β₂^3*β₃*δ₁^3*η^3*k₁*k₂^2 - 32*β₂^3*β₃*δ₁^2*δ₂^2*η^2*k₁^3*k₂ - 87*β₂^3*β₃*δ₁^2*δ₂*η^3*k₁^2*k₂ + 10*β₂^3*β₃*δ₁^2*η^4*k₁*k₂ - 44*β₂^3*β₃*δ₁*δ₂^2*η^3*k₁^3 - 91*β₂^3*β₃*δ₁*δ₂*η^4*k₁^2 - 6*β₂^3*δ₁^5*μ₁*η*k₁*k₂^4 + 12*β₂^3*δ₁^4*δ₂*δ₃*η*k₁^2*k₂^3 + 3*β₂^3*δ₁^4*δ₃*η^2*k₁*k₂^3 + 12*β₂^3*δ₁^4*μ₁*η^2*k₁*k₂^3 + 46*β₂^3*δ₁^3*δ₂*δ₃*η^2*k₁^2*k₂^2 + 25*β₂^3*δ₁^3*δ₂*μ₁*η^2*k₁^2*k₂^2 - 27*β₂^3*δ₁^3*δ₂*μ₂*η^2*k₁^2*k₂^2 - 7*β₂^3*δ₁^3*δ₃*η^3*k₁*k₂^2 + 27*β₂^3*δ₁^3*μ₁*η^3*k₁*k₂^2 + 32*β₂^3*δ₁^2*δ₂^2*δ₃*η^2*k₁^3*k₂ - 124*β₂^3*δ₁^2*δ₂^2*μ₁*η^2*k₁^3*k₂ + 12*β₂^3*δ₁^2*δ₂^2*μ₂*η^2*k₁^3*k₂ + 87*β₂^3*δ₁^2*δ₂*δ₃*η^3*k₁^2*k₂ - 16*β₂^3*δ₁^2*δ₂*μ₁*η^3*k₁^2*k₂ - 16*β₂^3*δ₁^2*δ₂*μ₂*η^3*k₁^2*k₂ - 10*β₂^3*δ₁^2*δ₃*η^4*k₁*k₂ - 5*β₂^3*δ₁^2*μ₁*η^4*k₁*k₂ + 44*β₂^3*δ₁*δ₂^2*δ₃*η^3*k₁^3 - 156*β₂^3*δ₁*δ₂^2*μ₁*η^3*k₁^3 + 12*β₂^3*δ₁*δ₂^2*μ₂*η^3*k₁^3 + 91*β₂^3*δ₁*δ₂*δ₃*η^4*k₁^2 - 124*β₂^3*δ₁*δ₂*μ₁*η^4*k₁^2 + 11*β₂^3*δ₁*δ₂*μ₂*η^4*k₁^2 + 24*β₂^2*β₃*δ₁^4*δ₂^2*η*k₁^2*k₂^3 + 10*β₂^2*β₃*δ₁^4*δ₂*η^2*k₁*k₂^3 - 4*β₂^2*β₃*δ₁^4*η^3*k₂^3 + 88*β₂^2*β₃*δ₁^3*δ₂^2*η^2*k₁^2*k₂^2 + 3*β₂^2*β₃*δ₁^3*δ₂*η^3*k₁*k₂^2 - 4*β₂^2*β₃*δ₁^3*η^4*k₂^2 + 64*β₂^2*β₃*δ₁^2*δ₂^3*η^2*k₁^3*k₂ + 181*β₂^2*β₃*δ₁^2*δ₂^2*η^3*k₁^2*k₂ + 25*β₂^2*β₃*δ₁^2*δ₂*η^4*k₁*k₂ + 68*β₂^2*β₃*δ₁*δ₂^3*η^3*k₁^3 + 141*β₂^2*β₃*δ₁*δ₂^2*η^4*k₁^2 + 10*β₂^2*δ₁^5*δ₂*μ₁*η*k₁*k₂^4 + 4*β₂^2*δ₁^5*δ₂*μ₂*η*k₁*k₂^4 - 24*β₂^2*δ₁^4*δ₂^2*δ₃*η*k₁^2*k₂^3 - 4*β₂^2*δ₁^4*δ₂^2*μ₂*η*k₁^2*k₂^3 - 10*β₂^2*δ₁^4*δ₂*δ₃*η^2*k₁*k₂^3 - 4*β₂^2*δ₁^4*δ₂*μ₁*η^2*k₁*k₂^3 - β₂^2*δ₁^4*δ₂*μ₂*η^2*k₁*k₂^3 + 4*β₂^2*δ₁^4*δ₃*η^3*k₂^3 - 6*β₂^2*δ₁^4*μ₁*η^3*k₂^3 - 88*β₂^2*δ₁^3*δ₂^2*δ₃*η^2*k₁^2*k₂^2 - 85*β₂^2*δ₁^3*δ₂^2*μ₁*η^2*k₁^2*k₂^2 + 47*β₂^2*δ₁^3*δ₂^2*μ₂*η^2*k₁^2*k₂^2 - 3*β₂^2*δ₁^3*δ₂*δ₃*η^3*k₁*k₂^2 + β₂^2*δ₁^3*δ₂*μ₁*η^3*k₁*k₂^2 - 43*β₂^2*δ₁^3*δ₂*μ₂*η^3*k₁*k₂^2 + 4*β₂^2*δ₁^3*δ₃*η^4*k₂^2 - 8*β₂^2*δ₁^3*μ₁*η^4*k₂^2 - 64*β₂^2*δ₁^2*δ₂^3*δ₃*η^2*k₁^3*k₂ + 202*β₂^2*δ₁^2*δ₂^3*μ₁*η^2*k₁^3*k₂ - 4*β₂^2*δ₁^2*δ₂^3*μ₂*η^2*k₁^3*k₂ - 181*β₂^2*δ₁^2*δ₂^2*δ₃*η^3*k₁^2*k₂ - 50*β₂^2*δ₁^2*δ₂^2*μ₁*η^3*k₁^2*k₂ + 92*β₂^2*δ₁^2*δ₂^2*μ₂*η^3*k₁^2*k₂ - 25*β₂^2*δ₁^2*δ₂*δ₃*η^4*k₁*k₂ + 55*β₂^2*δ₁^2*δ₂*μ₁*η^4*k₁*k₂ - 51*β₂^2*δ₁^2*δ₂*μ₂*η^4*k₁*k₂ - 68*β₂^2*δ₁*δ₂^3*δ₃*η^3*k₁^3 + 262*β₂^2*δ₁*δ₂^3*μ₁*η^3*k₁^3 + 28*β₂^2*δ₁*δ₂^3*μ₂*η^3*k₁^3 - 141*β₂^2*δ₁*δ₂^2*δ₃*η^4*k₁^2 + 174*β₂^2*δ₁*δ₂^2*μ₁*η^4*k₁^2 + 99*β₂^2*δ₁*δ₂^2*μ₂*η^4*k₁^2 - 12*β₂*β₃*δ₁^4*δ₂^3*η*k₁^2*k₂^3 - 11*β₂*β₃*δ₁^4*δ₂^2*η^2*k₁*k₂^3 + 8*β₂*β₃*δ₁^4*δ₂*η^3*k₂^3 - 38*β₂*β₃*δ₁^3*δ₂^3*η^2*k₁^2*k₂^2 - 27*β₂*β₃*δ₁^3*δ₂^2*η^3*k₁*k₂^2 + 8*β₂*β₃*δ₁^3*δ₂*η^4*k₂^2 - 32*β₂*β₃*δ₁^2*δ₂^4*η^2*k₁^3*k₂ - 101*β₂*β₃*δ₁^2*δ₂^3*η^3*k₁^2*k₂ - 80*β₂*β₃*δ₁^2*δ₂^2*η^4*k₁*k₂ - 4*β₂*β₃*δ₁*δ₂^4*η^3*k₁^3 - 9*β₂*β₃*δ₁*δ₂^3*η^4*k₁^2 + 4*β₂*δ₁^6*δ₂^2*μ₂*k₁*k₂^5 - 4*β₂*δ₁^5*δ₂^2*μ₁*η*k₁*k₂^4 - 16*β₂*δ₁^5*δ₂^2*μ₂*η*k₁*k₂^4 + 12*β₂*δ₁^4*δ₂^3*δ₃*η*k₁^2*k₂^3 + 32*β₂*δ₁^4*δ₂^3*μ₂*η*k₁^2*k₂^3 + 11*β₂*δ₁^4*δ₂^2*δ₃*η^2*k₁*k₂^3 - 20*β₂*δ₁^4*δ₂^2*μ₁*η^2*k₁*k₂^3 - 22*β₂*δ₁^4*δ₂^2*μ₂*η^2*k₁*k₂^3 - 8*β₂*δ₁^4*δ₂*δ₃*η^3*k₂^3 + 10*β₂*δ₁^4*δ₂*μ₁*η^3*k₂^3 + 38*β₂*δ₁^3*δ₂^3*δ₃*η^2*k₁^2*k₂^2 + 79*β₂*δ₁^3*δ₂^3*μ₁*η^2*k₁^2*k₂^2 + 35*β₂*δ₁^3*δ₂^3*μ₂*η^2*k₁^2*k₂^2 + 27*β₂*δ₁^3*δ₂^2*δ₃*η^3*k₁*k₂^2 - 59*β₂*δ₁^3*δ₂^2*μ₁*η^3*k₁*k₂^2 + 70*β₂*δ₁^3*δ₂^2*μ₂*η^3*k₁*k₂^2 - 8*β₂*δ₁^3*δ₂*δ₃*η^4*k₂^2 + 12*β₂*δ₁^3*δ₂*μ₁*η^4*k₂^2 + 4*β₂*δ₁^3*δ₂*μ₂*η^4*k₂^2 + 32*β₂*δ₁^2*δ₂^4*δ₃*η^2*k₁^3*k₂ - 92*β₂*δ₁^2*δ₂^4*μ₁*η^2*k₁^3*k₂ - 28*β₂*δ₁^2*δ₂^4*μ₂*η^2*k₁^3*k₂ + 101*β₂*δ₁^2*δ₂^3*δ₃*η^3*k₁^2*k₂ + 152*β₂*δ₁^2*δ₂^3*μ₁*η^3*k₁^2*k₂ - 104*β₂*δ₁^2*δ₂^3*μ₂*η^3*k₁^2*k₂ + 80*β₂*δ₁^2*δ₂^2*δ₃*η^4*k₁*k₂ - 95*β₂*δ₁^2*δ₂^2*μ₁*η^4*k₁*k₂ + 102*β₂*δ₁^2*δ₂^2*μ₂*η^4*k₁*k₂ + 4*β₂*δ₁*δ₂^4*δ₃*η^3*k₁^3 - 108*β₂*δ₁*δ₂^4*μ₁*η^3*k₁^3 - 92*β₂*δ₁*δ₂^4*μ₂*η^3*k₁^3 + 9*β₂*δ₁*δ₂^3*δ₃*η^4*k₁^2 + 68*β₂*δ₁*δ₂^3*μ₁*η^4*k₁^2 - 231*β₂*δ₁*δ₂^3*μ₂*η^4*k₁^2 + 4*β₃*δ₁^4*δ₂^3*η^2*k₁*k₂^3 - 4*β₃*δ₁^4*δ₂^2*η^3*k₂^3 - 4*β₃*δ₁^3*δ₂^4*η^2*k₁^2*k₂^2 + 17*β₃*δ₁^3*δ₂^3*η^3*k₁*k₂^2 - 4*β₃*δ₁^3*δ₂^2*η^4*k₂^2 + 7*β₃*δ₁^2*δ₂^4*η^3*k₁^2*k₂ + 45*β₃*δ₁^2*δ₂^3*η^4*k₁*k₂ - 20*β₃*δ₁*δ₂^5*η^3*k₁^3 - 41*β₃*δ₁*δ₂^4*η^4*k₁^2 - 4*δ₁^5*δ₂^3*μ₂*η*k₁*k₂^4 + 4*δ₁^5*δ₂^2*μ₂*η^2*k₂^4 + 4*δ₁^4*δ₂^4*μ₂*η*k₁^2*k₂^3 - 4*δ₁^4*δ₂^3*δ₃*η^2*k₁*k₂^3 + 12*δ₁^4*δ₂^3*μ₁*η^2*k₁*k₂^3 - 25*δ₁^4*δ₂^3*μ₂*η^2*k₁*k₂^3 + 4*δ₁^4*δ₂^2*δ₃*η^3*k₂^3 - 4*δ₁^4*δ₂^2*μ₁*η^3*k₂^3 + 8*δ₁^4*δ₂^2*μ₂*η^3*k₂^3 + 4*δ₁^3*δ₂^4*δ₃*η^2*k₁^2*k₂^2 - 19*δ₁^3*δ₂^4*μ₁*η^2*k₁^2*k₂^2 + 9*δ₁^3*δ₂^4*μ₂*η^2*k₁^2*k₂^2 - 17*δ₁^3*δ₂^3*δ₃*η^3*k₁*k₂^2 + 31*δ₁^3*δ₂^3*μ₁*η^3*k₁*k₂^2 - 27*δ₁^3*δ₂^3*μ₂*η^3*k₁*k₂^2 + 4*δ₁^3*δ₂^2*δ₃*η^4*k₂^2 - 4*δ₁^3*δ₂^2*μ₁*η^4*k₂^2 - 4*δ₁^3*δ₂^2*μ₂*η^4*k₂^2 - δ₁^2*δ₂^5*μ₁*η^2*k₁^3*k₂ + 20*δ₁^2*δ₂^5*μ₂*η^2*k₁^3*k₂ - 7*δ₁^2*δ₂^4*δ₃*η^3*k₁^2*k₂ - 77*δ₁^2*δ₂^4*μ₁*η^3*k₁^2*k₂ + 28*δ₁^2*δ₂^4*μ₂*η^3*k₁^2*k₂ - 45*δ₁^2*δ₂^3*δ₃*η^4*k₁*k₂ + 45*δ₁^2*δ₂^3*μ₁*η^4*k₁*k₂ - 51*δ₁^2*δ₂^3*μ₂*η^4*k₁*k₂ + 20*δ₁*δ₂^5*δ₃*η^3*k₁^3 - 11*δ₁*δ₂^5*μ₁*η^3*k₁^3 + 52*δ₁*δ₂^5*μ₂*η^3*k₁^3 + 41*δ₁*δ₂^4*δ₃*η^4*k₁^2 - 107*δ₁*δ₂^4*μ₁*η^4*k₁^2 + 121*δ₁*δ₂^4*μ₂*η^4*k₁^2
 -β₂^4*δ₁^2*δ₂*μ₁*η^2*k₁^3*k₂ - β₂^4*δ₁^2*μ₁*η^3*k₁^2*k₂ - 3*β₂^4*δ₁*δ₂*μ₁*η^3*k₁^3 - 3*β₂^4*δ₁*μ₁*η^4*k₁^2 + β₂^3*β₃*δ₁^4*η^2*k₁*k₂^3 - 2*β₂^3*β₃*δ₁^3*δ₂*η^2*k₁^2*k₂^2 - β₂^3*β₃*δ₁^3*η^3*k₁*k₂^2 - 7*β₂^3*β₃*δ₁^2*δ₂*η^3*k₁^2*k₂ - 2*β₂^3*β₃*δ₁^2*η^4*k₁*k₂ + 4*β₂^3*β₃*δ₁*δ₂^2*η^3*k₁^3 - 3*β₂^3*β₃*δ₁*δ₂*η^4*k₁^2 - 2*β₂^3*δ₁^5*μ₁*η*k₁*k₂^4 - β₂^3*δ₁^4*δ₃*η^2*k₁*k₂^3 + 4*β₂^3*δ₁^4*μ₁*η^2*k₁*k₂^3 + 2*β₂^3*δ₁^3*δ₂*δ₃*η^2*k₁^2*k₂^2 + 5*β₂^3*δ₁^3*δ₂*μ₁*η^2*k₁^2*k₂^2 + 5*β₂^3*δ₁^3*δ₂*μ₂*η^2*k₁^2*k₂^2 + β₂^3*δ₁^3*δ₃*η^3*k₁*k₂^2 + 11*β₂^3*δ₁^3*μ₁*η^3*k₁*k₂^2 - 12*β₂^3*δ₁^2*δ₂^2*μ₁*η^2*k₁^3*k₂ - 4*β₂^3*δ₁^2*δ₂^2*μ₂*η^2*k₁^3*k₂ + 7*β₂^3*δ₁^2*δ₂*δ₃*η^3*k₁^2*k₂ - 16*β₂^3*δ₁^2*δ₂*μ₁*η^3*k₁^2*k₂ + 8*β₂^3*δ₁^2*δ₂*μ₂*η^3*k₁^2*k₂ + 2*β₂^3*δ₁^2*δ₃*η^4*k₁*k₂ - 9*β₂^3*δ₁^2*μ₁*η^4*k₁*k₂ - 4*β₂^3*δ₁*δ₂^2*δ₃*η^3*k₁^3 + 4*β₂^3*δ₁*δ₂^2*μ₁*η^3*k₁^3 - 4*β₂^3*δ₁*δ₂^2*μ₂*η^3*k₁^3 + 3*β₂^3*δ₁*δ₂*δ₃*η^4*k₁^2 + 4*β₂^3*δ₁*δ₂*μ₁*η^4*k₁^2 + 3*β₂^3*δ₁*δ₂*μ₂*η^4*k₁^2 - 2*β₂^2*β₃*δ₁^4*δ₂*η^2*k₁*k₂^3 + 4*β₂^2*β₃*δ₁^3*δ₂^2*η^2*k₁^2*k₂^2 - β₂^2*β₃*δ₁^3*δ₂*η^3*k₁*k₂^2 + 21*β₂^2*β₃*δ₁^2*δ₂^2*η^3*k₁^2*k₂ + 5*β₂^2*β₃*δ₁^2*δ₂*η^4*k₁*k₂ - 12*β₂^2*β₃*δ₁*δ₂^3*η^3*k₁^3 + 5*β₂^2*β₃*δ₁*δ₂^2*η^4*k₁^2 + 4*β₂^2*δ₁^6*δ₂*μ₂*k₁*k₂^5 + 2*β₂^2*δ₁^5*δ₂*μ₁*η*k₁*k₂^4 - 8*β₂^2*δ₁^5*δ₂*μ₂*η*k₁*k₂^4 + 24*β₂^2*δ₁^4*δ₂^2*μ₂*η*k₁^2*k₂^3 + 2*β₂^2*δ₁^4*δ₂*δ₃*η^2*k₁*k₂^3 - 21*β₂^2*δ₁^4*δ₂*μ₂*η^2*k₁*k₂^3 - 2*β₂^2*δ₁^4*μ₁*η^3*k₂^3 - 4*β₂^2*δ₁^3*δ₂^2*δ₃*η^2*k₁^2*k₂^2 - 25*β₂^2*δ₁^3*δ₂^2*μ₁*η^2*k₁^2*k₂^2 + 31*β₂^2*δ₁^3*δ₂^2*μ₂*η^2*k₁^2*k₂^2 + β₂^2*δ₁^3*δ₂*δ₃*η^3*k₁*k₂^2 + β₂^2*δ₁^3*δ₂*μ₁*η^3*k₁*k₂^2 - 7*β₂^2*δ₁^3*δ₂*μ₂*η^3*k₁*k₂^2 - 4*β₂^2*δ₁^3*μ₁*η^4*k₂^2 + 26*β₂^2*δ₁^2*δ₂^3*μ₁*η^2*k₁^3*k₂ + 12*β₂^2*δ₁^2*δ₂^3*μ₂*η^2*k₁^3*k₂ - 21*β₂^2*δ₁^2*δ₂^2*δ₃*η^3*k₁^2*k₂ - 2*β₂^2*δ₁^2*δ₂^2*μ₁*η^3*k₁^2*k₂ + 4*β₂^2*δ₁^2*δ₂^2*μ₂*η^3*k₁^2*k₂ - 5*β₂^2*δ₁^2*δ₂*δ₃*η^4*k₁*k₂ + 19*β₂^2*δ₁^2*δ₂*μ₁*η^4*k₁*k₂ + 5*β₂^2*δ₁^2*δ₂*μ₂*η^4*k₁*k₂ + 12*β₂^2*δ₁*δ₂^3*δ₃*η^3*k₁^3 + 6*β₂^2*δ₁*δ₂^3*μ₁*η^3*k₁^3 + 12*β₂^2*δ₁*δ₂^3*μ₂*η^3*k₁^3 - 5*β₂^2*δ₁*δ₂^2*δ₃*η^4*k₁^2 - 2*β₂^2*δ₁*δ₂^2*μ₁*η^4*k₁^2 - 5*β₂^2*δ₁*δ₂^2*μ₂*η^4*k₁^2 + β₂*β₃*δ₁^4*δ₂^2*η^2*k₁*k₂^3 - 2*β₂*β₃*δ₁^3*δ₂^3*η^2*k₁^2*k₂^2 + 5*β₂*β₃*δ₁^3*δ₂^2*η^3*k₁*k₂^2 - 21*β₂*β₃*δ₁^2*δ₂^3*η^3*k₁^2*k₂ - 4*β₂*β₃*δ₁^2*δ₂^2*η^4*k₁*k₂ + 12*β₂*β₃*δ₁*δ₂^4*η^3*k₁^3 - β₂*β₃*δ₁*δ₂^3*η^4*k₁^2 - 8*β₂*δ₁^5*δ₂^2*μ₂*η*k₁*k₂^4 + 4*β₂*δ₁^5*δ₂*μ₂*η^2*k₂^4 + 8*β₂*δ₁^4*δ₂^3*μ₂*η*k₁^2*k₂^3 - β₂*δ₁^4*δ₂^2*δ₃*η^2*k₁*k₂^3 - 4*β₂*δ₁^4*δ₂^2*μ₁*η^2*k₁*k₂^3 - 30*β₂*δ₁^4*δ₂^2*μ₂*η^2*k₁*k₂^3 + 2*β₂*δ₁^4*δ₂*μ₁*η^3*k₂^3 + 8*β₂*δ₁^4*δ₂*μ₂*η^3*k₂^3 + 2*β₂*δ₁^3*δ₂^3*δ₃*η^2*k₁^2*k₂^2 + 19*β₂*δ₁^3*δ₂^3*μ₁*η^2*k₁^2*k₂^2 + 35*β₂*δ₁^3*δ₂^3*μ₂*η^2*k₁^2*k₂^2 - 5*β₂*δ₁^3*δ₂^2*δ₃*η^3*k₁*k₂^2 - 11*β₂*δ₁^3*δ₂^2*μ₁*η^3*k₁*k₂^2 - 2*β₂*δ₁^3*δ₂^2*μ₂*η^3*k₁*k₂^2 + 4*β₂*δ₁^3*δ₂*μ₁*η^4*k₂^2 + 4*β₂*δ₁^3*δ₂*μ₂*η^4*k₂^2 - 12*β₂*δ₁^2*δ₂^4*μ₁*η^2*k₁^3*k₂ - 12*β₂*δ₁^2*δ₂^4*μ₂*η^2*k₁^3*k₂ + 21*β₂*δ₁^2*δ₂^3*δ₃*η^3*k₁^2*k₂ + 24*β₂*δ₁^2*δ₂^3*μ₁*η^3*k₁^2*k₂ + 4*β₂*δ₁^2*δ₂^2*δ₃*η^4*k₁*k₂ - 11*β₂*δ₁^2*δ₂^2*μ₁*η^4*k₁*k₂ - 10*β₂*δ₁^2*δ₂^2*μ₂*η^4*k₁*k₂ - 12*β₂*δ₁*δ₂^4*δ₃*η^3*k₁^3 - 12*β₂*δ₁*δ₂^4*μ₁*η^3*k₁^3 - 12*β₂*δ₁*δ₂^4*μ₂*η^3*k₁^3 + β₂*δ₁*δ₂^3*δ₃*η^4*k₁^2 + 4*β₂*δ₁*δ₂^3*μ₁*η^4*k₁^2 + β₂*δ₁*δ₂^3*μ₂*η^4*k₁^2 - 3*β₃*δ₁^3*δ₂^3*η^3*k₁*k₂^2 + 7*β₃*δ₁^2*δ₂^4*η^3*k₁^2*k₂ + β₃*δ₁^2*δ₂^3*η^4*k₁*k₂ - 4*β₃*δ₁*δ₂^5*η^3*k₁^3 - β₃*δ₁*δ₂^4*η^4*k₁^2 + 3*δ₁^4*δ₂^3*μ₂*η^2*k₁*k₂^3 + δ₁^3*δ₂^4*μ₁*η^2*k₁^2*k₂^2 - 7*δ₁^3*δ₂^4*μ₂*η^2*k₁^2*k₂^2 + 3*δ₁^3*δ₂^3*δ₃*η^3*k₁*k₂^2 - δ₁^3*δ₂^3*μ₁*η^3*k₁*k₂^2 + 9*δ₁^3*δ₂^3*μ₂*η^3*k₁*k₂^2 - 4*δ₁^3*δ₂^2*μ₂*η^4*k₂^2 - δ₁^2*δ₂^5*μ₁*η^2*k₁^3*k₂ + 4*δ₁^2*δ₂^5*μ₂*η^2*k₁^3*k₂ - 7*δ₁^2*δ₂^4*δ₃*η^3*k₁^2*k₂ - 5*δ₁^2*δ₂^4*μ₁*η^3*k₁^2*k₂ - 12*δ₁^2*δ₂^4*μ₂*η^3*k₁^2*k₂ - δ₁^2*δ₂^3*δ₃*η^4*k₁*k₂ + δ₁^2*δ₂^3*μ₁*η^4*k₁*k₂ + 5*δ₁^2*δ₂^3*μ₂*η^4*k₁*k₂ + 4*δ₁*δ₂^5*δ₃*η^3*k₁^3 + 5*δ₁*δ₂^5*μ₁*η^3*k₁^3 + 4*δ₁*δ₂^5*μ₂*η^3*k₁^3 + δ₁*δ₂^4*δ₃*η^4*k₁^2 - 3*δ₁*δ₂^4*μ₁*η^4*k₁^2 + δ₁*δ₂^4*μ₂*η^4*k₁^2
 β₂^6*δ₁^4*δ₂*η^2*k₁^2*k₂^3 - β₂^6*δ₁^3*δ₂^2*η^2*k₁^3*k₂^2 + 2*β₂^6*δ₁^3*δ₂*η^3*k₁^2*k₂^2 - 2*β₂^6*δ₁^2*δ₂^2*η^3*k₁^3*k₂ + β₂^6*δ₁^2*δ₂*η^4*k₁^2*k₂ - β₂^6*δ₁*δ₂^2*η^4*k₁^3 + β₂^5*δ₁^7*δ₂*k₁*k₂^6 - 2*β₂^5*δ₁^6*δ₂*η*k₁*k₂^5 + 6*β₂^5*δ₁^5*δ₂^2*η*k₁^2*k₂^4 - 5*β₂^5*δ₁^5*δ₂*η^2*k₁*k₂^4 + 6*β₂^5*δ₁^4*δ₂^2*η^2*k₁^2*k₂^3 + 5*β₂^5*δ₁^3*δ₂^3*η^2*k₁^3*k₂^2 - 6*β₂^5*δ₁^3*δ₂^2*η^3*k₁^2*k₂^2 + 2*β₂^5*δ₁^3*δ₂*η^4*k₁*k₂^2 + 10*β₂^5*δ₁^2*δ₂^3*η^3*k₁^3*k₂ - 7*β₂^5*δ₁^2*δ₂^2*η^4*k₁^2*k₂ + 6*β₂^5*δ₁*δ₂^3*η^4*k₁^3 - 2*β₂^4*δ₁^7*δ₂^2*k₁*k₂^6 + 2*β₂^4*δ₁^6*δ₂^2*η*k₁*k₂^5 + β₂^4*δ₁^6*δ₂*η^2*k₂^5 - 10*β₂^4*δ₁^5*δ₂^3*η*k₁^2*k₂^4 + 2*β₂^4*δ₁^5*δ₂^2*η^2*k₁*k₂^4 + 2*β₂^4*δ₁^5*δ₂*η^3*k₂^4 - 6*β₂^4*δ₁^4*δ₂^3*η^2*k₁^2*k₂^3 - 4*β₂^4*δ₁^4*δ₂^2*η^3*k₁*k₂^3 + β₂^4*δ₁^4*δ₂*η^4*k₂^3 - 10*β₂^4*δ₁^3*δ₂^4*η^2*k₁^3*k₂^2 + 12*β₂^4*δ₁^3*δ₂^3*η^3*k₁^2*k₂^2 - 9*β₂^4*δ₁^3*δ₂^2*η^4*k₁*k₂^2 - 20*β₂^4*δ₁^2*δ₂^4*η^3*k₁^3*k₂ + 20*β₂^4*δ₁^2*δ₂^3*η^4*k₁^2*k₂ - 15*β₂^4*δ₁*δ₂^4*η^4*k₁^3 + β₂^3*δ₁^7*δ₂^3*k₁*k₂^6 + 2*β₂^3*δ₁^6*δ₂^3*η*k₁*k₂^5 - 2*β₂^3*δ₁^6*δ₂^2*η^2*k₂^5 + 2*β₂^3*δ₁^5*δ₂^4*η*k₁^2*k₂^4 + 12*β₂^3*δ₁^5*δ₂^3*η^2*k₁*k₂^4 - 4*β₂^3*δ₁^5*δ₂^2*η^3*k₂^4 - 12*β₂^3*δ₁^4*δ₂^4*η^2*k₁^2*k₂^3 + 12*β₂^3*δ₁^4*δ₂^3*η^3*k₁*k₂^3 - 3*β₂^3*δ₁^4*δ₂^2*η^4*k₂^3 + 10*β₂^3*δ₁^3*δ₂^5*η^2*k₁^3*k₂^2 - 20*β₂^3*δ₁^3*δ₂^4*η^3*k₁^2*k₂^2 + 16*β₂^3*δ₁^3*δ₂^3*η^4*k₁*k₂^2 + 20*β₂^3*δ₁^2*δ₂^5*η^3*k₁^3*k₂ - 30*β₂^3*δ₁^2*δ₂^4*η^4*k₁^2*k₂ + 20*β₂^3*δ₁*δ₂^5*η^4*k₁^3 - 2*β₂^2*δ₁^6*δ₂^4*η*k₁*k₂^5 + β₂^2*δ₁^6*δ₂^3*η^2*k₂^5 + 2*β₂^2*δ₁^5*δ₂^5*η*k₁^2*k₂^4 - 10*β₂^2*δ₁^5*δ₂^4*η^2*k₁*k₂^4 + 2*β₂^2*δ₁^5*δ₂^3*η^3*k₂^4 + 13*β₂^2*δ₁^4*δ₂^5*η^2*k₁^2*k₂^3 - 12*β₂^2*δ₁^4*δ₂^4*η^3*k₁*k₂^3 + 3*β₂^2*δ₁^4*δ₂^3*η^4*k₂^3 - 5*β₂^2*δ₁^3*δ₂^6*η^2*k₁^3*k₂^2 + 18*β₂^2*δ₁^3*δ₂^5*η^3*k₁^2*k₂^2 - 14*β₂^2*δ₁^3*δ₂^4*η^4*k₁*k₂^2 - 10*β₂^2*δ₁^2*δ₂^6*η^3*k₁^3*k₂ + 25*β₂^2*δ₁^2*δ₂^5*η^4*k₁^2*k₂ - 15*β₂^2*δ₁*δ₂^6*η^4*k₁^3 + β₂*δ₁^5*δ₂^5*η^2*k₁*k₂^4 - 2*β₂*δ₁^4*δ₂^6*η^2*k₁^2*k₂^3 + 4*β₂*δ₁^4*δ₂^5*η^3*k₁*k₂^3 - β₂*δ₁^4*δ₂^4*η^4*k₂^3 + β₂*δ₁^3*δ₂^7*η^2*k₁^3*k₂^2 - 6*β₂*δ₁^3*δ₂^6*η^3*k₁^2*k₂^2 + 6*β₂*δ₁^3*δ₂^5*η^4*k₁*k₂^2 + 2*β₂*δ₁^2*δ₂^7*η^3*k₁^3*k₂ - 11*β₂*δ₁^2*δ₂^6*η^4*k₁^2*k₂ + 6*β₂*δ₁*δ₂^7*η^4*k₁^3 - δ₁^3*δ₂^6*η^4*k₁*k₂^2 + 2*δ₁^2*δ₂^7*η^4*k₁^2*k₂ - δ₁*δ₂^8*η^4*k₁^3

Every TFPV $\pi^\star$ lies in $\mathcal{V}(G)$. As $G$ is a relatively large generating set without simple polynomials, characterising general TFPVs is not trivial for this model.

We can check whether $\langle G \rangle$ contains any monomial, which is the case if and only if

$$ \langle G \rangle : \langle \pi_1 \dots \pi_m \rangle ^\infty = \mathbb{R}[\pi_1, \cdots, \pi_m]. $$

To do so, we have to consider $\langle G \rangle$ in the ring $\mathbb{R}[\pi_1,\dots,\pi_m]$.

# get polynomial ring ℝ[x,π]
R = parent(β₂)
# construct ℝ[π] and a ring homomorphism
S, v = polynomial_ring(QQ, "_" .* p)
h = hom(S, R, system_parameters(problem))
Ring homomorphism
  from multivariate polynomial ring in 11 variables over QQ
  to multivariate polynomial ring in 14 variables over QQ
defined by
  _β₂ -> β₂
  _β₃ -> β₃
  _δ₁ -> δ₁
  _δ₂ -> δ₂
  _δ₃ -> δ₃
  _μ₁ -> μ₁
  _μ₂ -> μ₂
  _η -> η
  _k₁ -> k₁
  _k₂ -> k₂
  _k₃ -> k₃

# the ideal generated by G in the ring S
I = preimage(h, ideal(G))
# compute the saturation I:⟨π₁⋯πₘ⟩^∞
I_sat = saturation(I, ideal(prod(v)))
# check if I_sat = ℝ[π] = ⟨1⟩
is_one(I_sat)
false

Thus, $G$ does not contain any monomials.

But we find for instance that $\tilde\pi=(\varepsilon\beta_2, \beta_3, \varepsilon\delta_1, \varepsilon\delta_2, \delta_3, \mu_1, \varepsilon(\mu_1-\mu_2), \varepsilon\eta)$ is a critical parameter. However, this is just a special case of reduction 21.1 with $\mu_1=\mu_2$.

# critical parameter
p̃ = R.([0, β₃, 0, 0, δ₃, μ₁, μ₁, 0])
# check if all g∈G vanish for π = p̃
all([evaluate(g, problem.p_sf, p̃) for g in G] .== 0)
true

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Supplementary Material for the paper "Tikhonov-Fenichel Reductions and their Application to a Novel Modelling Approach for Mutualism"

arxiv.org/abs/2501.12069

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