Search on a Deadline with Uncertain Recall: Technical Appendix

By S. Nuray Akin and Brennan C. Platt

Introduction

This document accompanies “A Theory of Search on a Deadline with Uncertain Recall” by S. Nuray Akin and Brennan C. Platt.  It purpose is to provide the intermediate algebraic steps in the proofs and facilitate testing the effect of various parameter combinations.

Proposition 1

Bellman Equations

The Bellman equations are:

V0==d+λ a(x-R2)+λ(∫_pmin^R0)(x-q) F'[q]\[DifferentialD]q+β(1-λ)V0

V1==b+λ a(x-R2)+λ(∫_pmin^R0)(x-q) F'[q]\[DifferentialD]q+β(1-λ)V0

V2==b+λ a(x-R2)+β λ(∫_pmin^R0)((1-γ)W1[q]+γ V1) F'[q]\[DifferentialD]q+β(1-λ)V1

W0[p]==d+λ a(x-R2)+λ(∫_pmin^p)(x-q) F'[q]\[DifferentialD]q+(1-λ F[p])(x-p)

W1[p]==b+λ a(x-R2)+λ(∫_pmin^p)(x-q) F'[q]\[DifferentialD]q+(1-λ F[p])(x-p)

Note that

W0[R0]==d+λ a(x-R2)+λ(∫_pmin^R0)(x-q) F'[q]\[DifferentialD]q+(1-λ )(x-R0)==(1-β+β λ)V0+(1-λ)(x-R0)

W1[R2]==b+x-R2

The indifference conditions are:

x-R0==β((1-γ)W0[R0]+γ V0)

x-R2==β((1-γ)W1[R2]+γ V1)

For the first, we substitute for W0[R0] to get:

FullSimplify[Solve[x-R0==β((1-γ)W0[R0]+γ V0)/.W0[R0]->(1-β+β λ)V0+(1-λ)(x-R0),R0]]

For the second, we note that

V1==V0+b-d

and substitute for V1 and W1 in the indifference condition:

Collect[Solve[x-R2==β((1-γ)W1[R2]+γ V1)/.W1[R2]->b+x-R2/.V1->V0+b-d,R2],x]

We can also solve for V0 from its Bellman definition:

FullSimplify[Solve[V0==d+λ a(x-R2)+λ(∫_pmin^R0)(x-q) F'[q]\[DifferentialD]q+β(1-λ)V0,V0]]

These three equations will allow us to find R0 and R2 once F’ is known.

R0->x-V0 β

R2->x+((-b β+d β γ-V0 β γ)/(1-β+β γ))

V0->((d+a (-R2+x) λ+λ (∫_pmin^R0)(-q+x) F'[q]\[DifferentialD]q)/(1+β (-1+λ)))

Steady State conditions

The steady state conditions in the text jointly solve as follows:

FullSimplify[Solve[{h2==δ,h1==(1-λ)h2+γ λ(1-a)h2,λ h0==(1-λ)h1,g1[p]== (1-γ)λ F'[p] h2},{h0,h1,h2,g1[p]}]]

Equal Profit conditions

The profit from offering R2 is:

λ(R2-c)

The profit from offering any p between pmin and R0 is:

FullSimplify[ λ((h0+h1+(∫_p^R0)g1[q]\[DifferentialD]q+β(1-γ)(1-λ F[p])h2)/(h0+h1+(∫_pmin^R0)g1[q]\[DifferentialD]q+h2))(p-c)/.{h0->((δ (-1+λ) (-1+(1+(-1+a) γ) λ))/λ),h1->δ+(-1+γ-a γ) δ λ,h2->δ,g1[q]->-(-1+γ) δ λ F'[q]}/.F[R0]->1/.F[pmin]->a]

λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ F[p])))/(1+λ (γ+λ-γ λ) (1-a))))(p-c)

FullSimplify[λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ F[p])))/(1+λ (γ+λ-γ λ) (1-a))))(p-c)== (((c-p) λ (-1+λ (1+β (-1+γ)-λ+γ (-1+a+λ))-(1+β) (-1+γ) (λ^2) F[p]))/(1+(-1+a) (γ (-1+λ)-λ) λ))]

This must result in the same profit for all prices between pmin and R0; so we solve for the c.d.f. F[p] which ensures this will hold.

FullSimplify[Solve[λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))(R0-c)==λ(1-((λ (1-(1-γ)(β +a λ)+(1+β) (1-γ) λ F[p]))/(1+λ (γ+λ-γ λ) (1-a))))(p-c),F[p]]]

F[p]->1-(((R0-p) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((p-c)(1-γ) (λ^2) (1+β) ))

FullSimplify[1-(((R0-p) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((p-c)(1-γ) (λ^2) (1+β) ))==((p-R0-(p-R0) (1-β+(-1+a+β) γ) λ+(c-p+c β-R0 β) (-1+γ) (λ^2))/((c-p) (1+β) (-1+γ) (λ^2)))]

The p.d.f. in the continuous range is:

FullSimplify[D[F[p]->1-(((R0-p) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((p-c)(1-γ) (λ^2) (1+β) )),p]]

F'[p]->(((R0-c) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((((p-c))^2) (1-γ) (λ^2)(1+β)))

FullSimplify[(((c-R0) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ))/((((c-p))^2) (1+β) (-1+γ) (λ^2)))== (((R0-c) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((((p-c))^2) (1-γ) (λ^2)(1+β)))]

We also can compute pmin, since F[pmin] = a.

Collect[Solve[a==1-(((R0-pmin) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((pmin-c)(1-γ) (λ^2) (1+β) )),pmin],{R0,c}]

pmin->FullSimplify[(((1-λ+β λ+γ λ-a γ λ-β γ λ-β (λ^2)+β γ (λ^2)))/(1-λ+β λ+γ λ-a γ λ-β γ λ+(λ^2)-a (λ^2)-a β (λ^2)-γ (λ^2)+a γ (λ^2)+a β γ (λ^2)))]R0+FullSimplify[(( ((λ^2)-a (λ^2)+β (λ^2)-a β (λ^2)-γ (λ^2)+a γ (λ^2)-β γ (λ^2)+a β γ (λ^2)))/(1-λ+β λ+γ λ-a γ λ-β γ λ+(λ^2)-a (λ^2)-a β (λ^2)-γ (λ^2)+a γ (λ^2)+a β γ (λ^2)))]c

pmin->(((1-γ) (λ^2)(1-a) (1+β)c  + (1-a γ λ-λ(1-γ)(1-β+β λ))R0)/(1-a γ λ-λ(1-γ)(1-β-λ(1-a-a β))))

FullSimplify[(((1-γ) (λ^2)(1-a) (1+β)c  + (1-a γ λ-λ(1-γ)(1-β+β λ))R0)/(1-a γ λ-λ(1-γ)(1-β-λ(1-a-a β))))==((R0 (1-λ+β λ+γ λ-a γ λ-β γ λ-β (λ^2)+β γ (λ^2)))/(1-λ+β λ+γ λ-a γ λ-β γ λ+(λ^2)-a (λ^2)-a β (λ^2)-γ (λ^2)+a γ (λ^2)+a β γ (λ^2)))+((c ((λ^2)-a (λ^2)+β (λ^2)-a β (λ^2)-γ (λ^2)+a γ (λ^2)-β γ (λ^2)+a β γ (λ^2)))/(1-λ+β λ+γ λ-a γ λ-β γ λ+(λ^2)-a (λ^2)-a β (λ^2)-γ (λ^2)+a γ (λ^2)+a β γ (λ^2)))]

Equilibirum solution

Having obtained the necessary price distribution, we can now compute V0.

Assuming[R0>pmin>c,FullSimplify[V0->((d+a (-R2+x) λ+λ (∫_pmin^R0)(-q+x) (((R0-c) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((((q-c))^2) (1-γ) (λ^2)(1+β)))\[DifferentialD]q)/(1+β (-1+λ)))/.pmin->(((1-γ) (λ^2)(1-a) (1+β)c  + (1-a γ λ-λ(1-γ)(1-β+β λ))R0)/(1-a γ λ-λ(1-γ)(1-β-λ(1-a-a β))))]]

ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((λ^2) (1-γ)(1-a) (1+β))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]

V0->((d+λ(x-c-a(R2-c)) +(R0-c)ϕ[a])/(1-β+β λ))

FullSimplify[((d+((-1+a) c-a R2+x) λ+(((c-R0) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[((1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ)/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ) λ)))/(1+β (-1+λ)))==((d+λ(x-c-a(R2-c)) +(R0-c)ϕ[a])/(1-β+β λ))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]]

We now solve for R0 and R2:

FullSimplify[Solve[{R0==x-V0 β,R2==x+((-b β+d β γ-V0 β γ)/(1-β+β γ))}/.V0->((d+λ(x-c-a(R2-c)) +(R0-c)ϕ[a])/(1-β+β λ)),{R0,R2}]]

κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))

R0->c+κ[a]

FullSimplify[c+κ[a]==(-(x (-1+β)+d β) (1+β (-1+γ))+β (-(-1+a) c (1+β (-1+γ))+a (-b β+x (-1+β) (-1+γ)+d β γ)) λ+c β (1+β (-1+γ)) ϕ[a])/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ)+β (1+β (-1+γ)) ϕ[a])/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))]

R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ)))

FullSimplify[x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ)))==(x (-1+β) (-1+β (-1+γ) (-1+λ))-β (b (1+β (-1+λ))-d β γ (-1+λ)+(-1+a) c γ λ)+β (-b β+x (-1+β) (-1+γ)+(c+d β) γ) ϕ[a])/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ)+β (1+β (-1+γ)) ϕ[a])/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))]

We now simplify the other equilibrium objects accordingly:  The minimum price:

FullSimplify[pmin->(((1-γ) (λ^2)(1-a) (1+β)c  + (1-a γ λ-λ(1-γ)(1-β+β λ))R0)/(1-a γ λ-λ(1-γ)(1-β-λ(1-a-a β))))/.R0->c+κ[a]]

The Price Distribution:

F[p]->1-(((c+κ[a]-p) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((p-c)(1-γ) (λ^2) (1+β) ))

The profit from R2

λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))

The profit from pmin to R0

λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]

Calculation of total welfare

From the ex-ante perspective of a new buyer entering the market, several outcomes could occur with the probabilities listed below:

Grid[{{"State 2 offer","State 1 offer","Outcome Probability"},{"Accepted","-","λ a"},{"Retained","Received","(λ^2)(1-a) (1-γ)"},{"Retained","None","λ (1-λ) (1-a) (1-γ)"},{"Lost","Received","(λ^2)(1-a) γ"},{"Lost","None","λ (1-λ) (1-a) γ"},{"None","Received","(1-λ)λ"},
{"None","None","(1-λ)^2"}}]

We can use these to compute the expected total welfare.  If an offer is accepted in state 2, the total flow of added value is b+x-c.  If accepted in state 1, it is b+β(b+x-c).  If accepted in state 0, we must also account for the number of periods one remains in state 0 before receiving an offer.  Such people add b+β b, as well as (β^(2+t))(x-c)if an offer is received in the t-th period, and (∑_(s=0)^t)(β^s)d in penalties.

FullSimplify[λ a(b+x-c)+((λ^2)(1-a) (1-γ)+λ (1-λ) (1-a) (1-γ)+(λ^2)(1-a) γ+(1-λ)λ)(b+β(b+x-c))+(λ (1-λ) (1-a) γ+(((1-λ))^2))(b+β b+(β^2)(∑_(t=0)^∞)((((1-λ))^t)λ ((β^t)(x-c)+(∑_(s=0)^t)(β^s)d)))]

Calculation of V2

For the numerical illustration, we want to know ex-ante utility.  This is computed as follows.

V2==b+λ a(x-R2)+β λ(∫_pmin^R0)((1-γ)W1[q]+γ V1) F'[q]\[DifferentialD]q+β(1-λ)V1

By rearrangement:

V2==b+λ a(x-R2)+β λ(1-γ)(∫_pmin^R0)W1[q] F'[q]\[DifferentialD]q+β(1-λ+λ(1-a)γ)V1

Since

V1==V0+b-d

then:

V2==b+λ a(x-R2)+β λ(1-γ)(∫_pmin^R0)W1[q] F'[q]\[DifferentialD]q+β(1-λ+λ(1-a)γ)(V0+b-d)

We also need:

W1[p]==b+x-λ a R2-λ(∫_pmin^p)q F'[q]\[DifferentialD]q-(1-λ F[p])p

This integrates as follows:

Assuming[R0≥p>pmin>c>0,FullSimplify[W1[p]->b+x-λ a R2-λ(∫_pmin^p)q (((R0-c) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((((q-c))^2) (1-γ) (λ^2)(1+β)))\[DifferentialD]q-(1-λ(1-(((R0-p) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((p-c)(1-γ) (λ^2) (1+β) ))))p]]

And then substituted into V2, we get:

Assuming[R0>pmin>c>0,V2->b+λ a(x-R2)+β λ(1-γ)(∫_pmin^R0)(b+x-a R2 λ-q (1-λ (1+(((q-R0) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ))/((c-q) (1+β) (-1+γ) (λ^2)))))-(((c-R0) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (c ((1/(c-q))+(1/(-c+pmin)))+Log[((c-q)/(c-pmin))]))/((1+β) (-1+γ) λ))) (((R0-c) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((((q-c))^2) (1-γ) (λ^2)(1+β)))\[DifferentialD]q+β(1-λ+λ(1-a)γ)(V0+b-d)]

A little rearrangement:

V2->b+a (-R2+x) λ+(b-d+V0) β (1-λ+(1-a) γ λ)-((-c+R0) β (1-γ) (1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (FullSimplify[((2 b (c-pmin) (-pmin+R0))/(c-R0))+((2 (c-pmin) (-pmin+R0) x)/(c-R0))+((2 a (c-pmin) (pmin-R0) R2 λ)/(c-R0))-((c (-2 c pmin+(pmin^2)+2 c R0-(R0^2)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ))/((c-R0) (1+β) (-1+γ) λ))+(((pmin-R0) R0 (-2 pmin R0+c (pmin+R0)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ))/((((c-R0))^2) (1+β) (-1+γ) λ))-((2 c (pmin-R0) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)))/((1+β) (-1+γ) λ))-(1/((1+β) (-1+γ) λ))2 (c-pmin) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (-pmin+R0)+1/(c-R0)2 (c-pmin) (c (pmin-R0))+1/(c-R0)2 (c-pmin) λ (c (-pmin+R0))+((1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (c (pmin-R0) (2 (c^2)+4 pmin R0-3 c (pmin+R0))))/((((c-R0))^2) (1+β) (-1+γ) λ)]+FullSimplify[-(1/((1+β) (-1+γ) λ))2 (c-pmin) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) ((c-pmin) Log[((c-R0)/(c-pmin))])+1/(c-R0)2 (c-pmin) (-(c-pmin) (c-R0) Log[((-c+R0)/(-c+pmin))])+1/(c-R0)2 (c-pmin) λ ((c-pmin) (c-R0) Log[((-c+R0)/(-c+pmin))])+((1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (-2 (((c-pmin))^2) (((c-R0))^2) Log[((-c+R0)/(-c+pmin))]))/((((c-R0))^2) (1+β) (-1+γ) λ)]))/(2 (((c-pmin))^2) (1+β) (-1+γ) λ)

And replacement of equilibrium prices:

Simplify[V2->b+a (-R2+x) λ+(b-d+V0) β (1-λ+(1-a) γ λ)-((-c+R0) β (1-γ) (1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) ((2 (pmin-R0) (pmin ((1+β) (-1+γ) λ (b+x-a R2 λ)+2 R0 (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ))+(c^2) (2+λ (-3+β (-1+γ) (-1+λ)+λ-γ (-3+2 a+λ)))+c (-(1+β) (-1+γ) λ (b+x-a R2 λ)+R0 (-1+λ (1+(-1+a) γ+β (-1+γ+λ-γ λ)))+pmin (-3+λ (4-λ+γ (-4+3 a+λ)+2 β (-1+γ+λ-γ λ))))))/((c-R0) (1+β) (-1+γ) λ)-((2 (((c-pmin))^2) (2+λ (-3+β (-1+γ) (-1+λ)+λ-γ (-3+2 a+λ))) Log[((c-R0)/(c-pmin))])/((1+β) (-1+γ) λ))))/(2 (((c-pmin))^2) (1+β) (-1+γ) λ)/.V0->((d+λ(x-c-a(R2-c)) +(R0-c)ϕ[a])/(1-β+β λ))/.R0->c+κ[a]/.R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ)))/.pmin->(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ)))]

Monotone Property

Suppose a full equilibrium exists; that is, for a given 0 < a < 1, the following condition holds:

λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))==λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]

After substitution and simplification, this becomes:

Simplify[(x-c-((β b+γ(x-c-β d))/((1-β+β γ))))==(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a)))-(γ/((1-β+β γ))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]]

We rearrange this to solve for x:

FullSimplify[Solve[x+((-b β+(c-x+d β) γ)/(1+β (-1+γ)))==c+((-a (b-d) (β^2) λ+(x+c (-1+β)-d β-x β) (1-β (-1+γ) (-1+a λ))) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))))/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])),x]]

Collect[%,c]

x->FullSimplify[(c (((-1+β) (1+β) (1+β (-1+γ)) (-1+γ) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/((1+(-1+a) (γ (-1+λ)-λ) λ) (-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))+β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+((-1+β) β (1+β (-1+γ)) (-1+γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/(-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))+β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/((1+β (-1+γ)) (1-(γ/(1+β (-1+γ)))-((1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))+((λ (-1+β-β γ+(1-a+β) (-1+γ) λ))/(1+(-1+a) (γ (-1+λ)-λ) λ))))/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+(β (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))+((λ (-1+β-β γ+(1-a+β) (-1+γ) λ))/(1+(-1+a) (γ (-1+λ)-λ) λ))))/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))))]+FullSimplify[(b β+(a b (-1-β) (β^2) (-1+γ) (λ^2) (-1+γ+λ+(-1+γ) ((-1+a) γ (-1+λ) λ+(β^2) λ (-1+γ+λ-γ λ)-β (1+λ (-2+γ-a γ+λ)))))/((1+(-1+a) (γ (-1+λ)-λ) λ) (-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))+β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+(d (-1-β) β (1+β (-1+γ)) (-1+γ) λ (-1+λ+(-1+a) γ λ+(β^2) (-1+γ) (-1+λ) λ (1+γ (-1+a λ))+β (1+λ (-2+λ-(-1+a) (γ^2) λ (-2+a+λ)+γ (2-2 a λ+(-1+a) (λ^2))))))/((1+(-1+a) (γ (-1+λ)-λ) λ) (-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))+β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))-(d (β^2) (1+β (-1+γ)) γ (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/(-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))+β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((1+β (-1+γ)) (1-(γ/(1+β (-1+γ)))-((1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))+((λ (-1+β-β γ+(1-a+β) (-1+γ) λ))/(1+(-1+a) (γ (-1+λ)-λ) λ))))/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+(β (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))+((λ (-1+β-β γ+(1-a+β) (-1+γ) λ))/(1+(-1+a) (γ (-1+λ)-λ) λ))))/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))))]

Next, we take the derivative of the equilibrium condition w.r.t. a, then immediately substitute for x (which can be done if the derivative is evaluated at the equilibrium a*):

Simplify[D[x+((-b β+(c-x+d β) γ)/(1+β (-1+γ)))-(c+((-a (b-d) (β^2) λ+(x+c (-1+β)-d β-x β) (1-β (-1+γ) (-1+a λ))) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))))/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))),a]/.x->c+(β (-((1+β) (-1+γ) λ (-(b-d) (-1+β)+(d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)+(-1+a) b (-β+(-1+β) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))]

In fact, c entirely cancels out after simplification.  First we collect the c terms together, then simplify them.  This eliminates c.

Collect[%,c]

(c FullSimplify[(β (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ))))+(-1+β) β (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ))))-(β^2) (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ))))+((λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2)+((-1+β) (λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2)-(β (λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2)-β (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+(1-β) β (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+(β^2) (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))])/(((1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))^2)+(-a (b-d) (β^3) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ))))-d (β^2) (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ))))-(a (b-d) (β^2) (λ^3) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2)-(d β (λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2)-(-b+d) (β^2) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+d (β^2) (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+((β^2) (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ)))) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))-((β^3) (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ)))) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+(β (λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))-((β^2) (λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))-((β^2) (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+((β^3) (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))^2)

Next, we collect b and d terms.  After simplification, this allows us to factor out (b-d), which is always positive, from the expression.

To speed up the evaluation, we temporarily replace the Log terms, all of which are identical, with Z.

(-a (b-d) (β^3) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ))))-d (β^2) (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ))))-(a (b-d) (β^2) (λ^3) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2)-(d β (λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2)-(-b+d) (β^2) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+d (β^2) (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+((β^2) (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ)))) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))-((β^3) (1-β (-1+γ) (-1+a λ)) (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (-γ λ+(((1+β (-1+γ)) (-1+λ) λ (-1+β (-1+γ) λ))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))+(((1+β (-1+γ)) γ Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])/((1+β) (-1+γ)))) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+(β (λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))-((β^2) (λ^2) (1-β (-1+γ) (-1+a λ)) (β (γ^2) (((-1+λ))^2)+(-1+λ) (1+β λ)-γ (-2+β+λ-3 β λ+2 β (λ^2))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((1+(-1+a) γ (-1+λ) λ-(-1+a) (λ^2)))^2) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))-((β^2) (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))+((β^3) (1-γ) λ (1-(γ/(1+β (-1+γ)))-((λ (1-(-1+γ) (β (-1+λ)+λ-a λ)))/(1+(1-a) λ (γ+λ-γ λ)))) (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])) (-((1+β) (-1+γ) λ ((-b+d) (-1+β)+((-1+a) b (β (-1+γ)-γ)+d (1+β (2+β (-1+γ)) (-1+γ)+(-1+a) γ)) λ+(-b (1+a (-1+β)) (-1+β)+b (-1+2 β+a (1+β (-3+a+β))) γ+d β (1-β-2 a γ+(2+a) β γ-(2+β+a (-3+a+β)) (γ^2))) (λ^2)+(1+a (-1+β)) β (-1+γ) (-b+d γ) (λ^3)))/(1+(-1+a) (γ (-1+λ)-λ) λ)+β (b-d γ) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((-1+γ) (((-1+(β^2)) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2))))/(1+(-1+a) (γ (-1+λ)-λ) λ)+(-1+β) β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))/(((1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])))^2)/.Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]->Z/.Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]->Z

Together[%]

((1+β) (λ^2) (Collect[-b Z (β^2) γ+d Z (β^2) γ+b Z (β^3) γ-d Z (β^3) γ+b Z (β^2) (γ^2)-d Z (β^2) (γ^2)-b Z (β^3) (γ^2)+d Z (β^3) (γ^2)-b Z (β^2) λ+d Z (β^2) λ+b Z (β^3) λ-d Z (β^3) λ+4 b Z (β^2) γ λ-4 d Z (β^2) γ λ-8 b Z (β^3) γ λ+8 d Z (β^3) γ λ+3 b Z (β^4) γ λ-3 d Z (β^4) γ λ-4 b Z (β^2) (γ^2) λ+3 a b Z (β^2) (γ^2) λ+4 d Z (β^2) (γ^2) λ-3 a d Z (β^2) (γ^2) λ+11 b Z (β^3) (γ^2) λ-3 a b Z (β^3) (γ^2) λ-11 d Z (β^3) (γ^2) λ+3 a d Z (β^3) (γ^2) λ-6 b Z (β^4) (γ^2) λ+6 d Z (β^4) (γ^2) λ+3 b Z (β^2) (γ^3) λ-3 a b Z (β^2) (γ^3) λ-3 d Z (β^2) (γ^3) λ+3 a d Z (β^2) (γ^3) λ-4 b Z (β^3) (γ^3) λ+3 a b Z (β^3) (γ^3) λ+4 d Z (β^3) (γ^3) λ-3 a d Z (β^3) (γ^3) λ+3 b Z (β^4) (γ^3) λ-3 d Z (β^4) (γ^3) λ-b β (λ^2)+d β (λ^2)+2 b (β^2) (λ^2)-2 d (β^2) (λ^2)+3 b Z (β^2) (λ^2)-3 d Z (β^2) (λ^2)-6 b Z (β^3) (λ^2)+6 d Z (β^3) (λ^2)-2 b (β^4) (λ^2)+2 d (β^4) (λ^2)+3 b Z (β^4) (λ^2)-3 d Z (β^4) (λ^2)+b (β^5) (λ^2)-d (β^5) (λ^2)+3 b β γ (λ^2)-3 d β γ (λ^2)-8 b (β^2) γ (λ^2)+a b (β^2) γ (λ^2)+8 d (β^2) γ (λ^2)-a d (β^2) γ (λ^2)-10 b Z (β^2) γ (λ^2)+4 a b Z (β^2) γ (λ^2)+10 d Z (β^2) γ (λ^2)-4 a d Z (β^2) γ (λ^2)+b (β^3) γ (λ^2)-d (β^3) γ (λ^2)+27 b Z (β^3) γ (λ^2)-3 a b Z (β^3) γ (λ^2)-27 d Z (β^3) γ (λ^2)+3 a d Z (β^3) γ (λ^2)+8 b (β^4) γ (λ^2)-a b (β^4) γ (λ^2)-8 d (β^4) γ (λ^2)+a d (β^4) γ (λ^2)-20 b Z (β^4) γ (λ^2)-a b Z (β^4) γ (λ^2)+20 d Z (β^4) γ (λ^2)+a d Z (β^4) γ (λ^2)-4 b (β^5) γ (λ^2)+4 d (β^5) γ (λ^2)+3 b Z (β^5) γ (λ^2)-3 d Z (β^5) γ (λ^2)-2 b β (γ^2) (λ^2)+2 d β (γ^2) (λ^2)+10 b (β^2) (γ^2) (λ^2)-2 a b (β^2) (γ^2) (λ^2)-10 d (β^2) (γ^2) (λ^2)+2 a d (β^2) (γ^2) (λ^2)+13 b Z (β^2) (γ^2) (λ^2)-13 a b Z (β^2) (γ^2) (λ^2)-13 d Z (β^2) (γ^2) (λ^2)+13 a d Z (β^2) (γ^2) (λ^2)-4 b (β^3) (γ^2) (λ^2)+4 d (β^3) (γ^2) (λ^2)-37 b Z (β^3) (γ^2) (λ^2)+18 a b Z (β^3) (γ^2) (λ^2)+37 d Z (β^3) (γ^2) (λ^2)-18 a d Z (β^3) (γ^2) (λ^2)-10 b (β^4) (γ^2) (λ^2)+2 a b (β^4) (γ^2) (λ^2)+10 d (β^4) (γ^2) (λ^2)-2 a d (β^4) (γ^2) (λ^2)+37 b Z (β^4) (γ^2) (λ^2)-4 a b Z (β^4) (γ^2) (λ^2)-37 d Z (β^4) (γ^2) (λ^2)+4 a d Z (β^4) (γ^2) (λ^2)+6 b (β^5) (γ^2) (λ^2)-6 d (β^5) (γ^2) (λ^2)-9 b Z (β^5) (γ^2) (λ^2)+9 d Z (β^5) (γ^2) (λ^2)-4 b (β^2) (γ^3) (λ^2)+a b (β^2) (γ^3) (λ^2)+4 d (β^2) (γ^3) (λ^2)-a d (β^2) (γ^3) (λ^2)-8 b Z (β^2) (γ^3) (λ^2)+11 a b Z (β^2) (γ^3) (λ^2)-3 (a^2) b Z (β^2) (γ^3) (λ^2)+8 d Z (β^2) (γ^3) (λ^2)-11 a d Z (β^2) (γ^3) (λ^2)+3 (a^2) d Z (β^2) (γ^3) (λ^2)+4 b (β^3) (γ^3) (λ^2)-4 d (β^3) (γ^3) (λ^2)+21 b Z (β^3) (γ^3) (λ^2)-23 a b Z (β^3) (γ^3) (λ^2)+3 (a^2) b Z (β^3) (γ^3) (λ^2)-21 d Z (β^3) (γ^3) (λ^2)+23 a d Z (β^3) (γ^3) (λ^2)-3 (a^2) d Z (β^3) (γ^3) (λ^2)+4 b (β^4) (γ^3) (λ^2)-a b (β^4) (γ^3) (λ^2)-4 d (β^4) (γ^3) (λ^2)+a d (β^4) (γ^3) (λ^2)-26 b Z (β^4) (γ^3) (λ^2)+11 a b Z (β^4) (γ^3) (λ^2)+26 d Z (β^4) (γ^3) (λ^2)-11 a d Z (β^4) (γ^3) (λ^2)-4 b (β^5) (γ^3) (λ^2)+4 d (β^5) (γ^3) (λ^2)+9 b Z (β^5) (γ^3) (λ^2)-9 d Z (β^5) (γ^3) (λ^2)+3 b Z (β^2) (γ^4) (λ^2)-6 a b Z (β^2) (γ^4) (λ^2)+3 (a^2) b Z (β^2) (γ^4) (λ^2)-3 d Z (β^2) (γ^4) (λ^2)+6 a d Z (β^2) (γ^4) (λ^2)-3 (a^2) d Z (β^2) (γ^4) (λ^2)-b (β^3) (γ^4) (λ^2)+d (β^3) (γ^4) (λ^2)-5 b Z (β^3) (γ^4) (λ^2)+8 a b Z (β^3) (γ^4) (λ^2)-3 (a^2) b Z (β^3) (γ^4) (λ^2)+5 d Z (β^3) (γ^4) (λ^2)-8 a d Z (β^3) (γ^4) (λ^2)+3 (a^2) d Z (β^3) (γ^4) (λ^2)+6 b Z (β^4) (γ^4) (λ^2)-6 a b Z (β^4) (γ^4) (λ^2)-6 d Z (β^4) (γ^4) (λ^2)+6 a d Z (β^4) (γ^4) (λ^2)+b (β^5) (γ^4) (λ^2)-d (β^5) (γ^4) (λ^2)-3 b Z (β^5) (γ^4) (λ^2)+3 d Z (β^5) (γ^4) (λ^2)+2 b β (λ^3)-2 d β (λ^3)-7 b (β^2) (λ^3)+7 d (β^2) (λ^3)-4 b Z (β^2) (λ^3)+a b Z (β^2) (λ^3)+4 d Z (β^2) (λ^3)-a d Z (β^2) (λ^3)+4 b (β^3) (λ^3)+a b (β^3) (λ^3)-4 d (β^3) (λ^3)-a d (β^3) (λ^3)+12 b Z (β^3) (λ^3)-12 d Z (β^3) (λ^3)+5 b (β^4) (λ^3)-5 d (β^4) (λ^3)-11 b Z (β^4) (λ^3)-a b Z (β^4) (λ^3)+11 d Z (β^4) (λ^3)+a d Z (β^4) (λ^3)-6 b (β^5) (λ^3)-a b (β^5) (λ^3)+6 d (β^5) (λ^3)+a d (β^5) (λ^3)+3 b Z (β^5) (λ^3)-3 d Z (β^5) (λ^3)+2 b (β^6) (λ^3)-2 d (β^6) (λ^3)-6 b β γ (λ^3)+a b β γ (λ^3)+6 d β γ (λ^3)-a d β γ (λ^3)+26 b (β^2) γ (λ^3)-3 a b (β^2) γ (λ^3)-26 d (β^2) γ (λ^3)+3 a d (β^2) γ (λ^3)+14 b Z (β^2) γ (λ^3)-10 a b Z (β^2) γ (λ^3)-14 d Z (β^2) γ (λ^3)+10 a d Z (β^2) γ (λ^3)-22 b (β^3) γ (λ^3)+22 d (β^3) γ (λ^3)-49 b Z (β^3) γ (λ^3)+15 a b Z (β^3) γ (λ^3)+49 d Z (β^3) γ (λ^3)-15 a d Z (β^3) γ (λ^3)-18 b (β^4) γ (λ^3)+4 a b (β^4) γ (λ^3)+18 d (β^4) γ (λ^3)-4 a d (β^4) γ (λ^3)+55 b Z (β^4) γ (λ^3)-a b Z (β^4) γ (λ^3)-55 d Z (β^4) γ (λ^3)+a d Z (β^4) γ (λ^3)+27 b (β^5) γ (λ^3)-27 d (β^5) γ (λ^3)-20 b Z (β^5) γ (λ^3)-2 a b Z (β^5) γ (λ^3)+20 d Z (β^5) γ (λ^3)+2 a d Z (β^5) γ (λ^3)-9 b (β^6) γ (λ^3)+9 d (β^6) γ (λ^3)+b Z (β^6) γ (λ^3)-d Z (β^6) γ (λ^3)+6 b β (γ^2) (λ^3)-3 a b β (γ^2) (λ^3)-6 d β (γ^2) (λ^3)+3 a d β (γ^2) (λ^3)-35 b (β^2) (γ^2) (λ^3)+11 a b (β^2) (γ^2) (λ^3)-2 (a^2) b (β^2) (γ^2) (λ^3)+35 d (β^2) (γ^2) (λ^3)-11 a d (β^2) (γ^2) (λ^3)+2 (a^2) d (β^2) (γ^2) (λ^3)-19 b Z (β^2) (γ^2) (λ^3)+24 a b Z (β^2) (γ^2) (λ^3)-5 (a^2) b Z (β^2) (γ^2) (λ^3)+19 d Z (β^2) (γ^2) (λ^3)-24 a d Z (β^2) (γ^2) (λ^3)+5 (a^2) d Z (β^2) (γ^2) (λ^3)+42 b (β^3) (γ^2) (λ^3)-6 a b (β^3) (γ^2) (λ^3)-42 d (β^3) (γ^2) (λ^3)+6 a d (β^3) (γ^2) (λ^3)+74 b Z (β^3) (γ^2) (λ^3)-55 a b Z (β^3) (γ^2) (λ^3)+3 (a^2) b Z (β^3) (γ^2) (λ^3)-74 d Z (β^3) (γ^2) (λ^3)+55 a d Z (β^3) (γ^2) (λ^3)-3 (a^2) d Z (β^3) (γ^2) (λ^3)+21 b (β^4) (γ^2) (λ^3)-13 a b (β^4) (γ^2) (λ^3)+2 (a^2) b (β^4) (γ^2) (λ^3)-21 d (β^4) (γ^2) (λ^3)+13 a d (β^4) (γ^2) (λ^3)-2 (a^2) d (β^4) (γ^2) (λ^3)-98 b Z (β^4) (γ^2) (λ^3)+24 a b Z (β^4) (γ^2) (λ^3)+2 (a^2) b Z (β^4) (γ^2) (λ^3)+98 d Z (β^4) (γ^2) (λ^3)-24 a d Z (β^4) (γ^2) (λ^3)-2 (a^2) d Z (β^4) (γ^2) (λ^3)-46 b (β^5) (γ^2) (λ^3)+7 a b (β^5) (γ^2) (λ^3)+46 d (β^5) (γ^2) (λ^3)-7 a d (β^5) (γ^2) (λ^3)+45 b Z (β^5) (γ^2) (λ^3)+3 a b Z (β^5) (γ^2) (λ^3)-45 d Z (β^5) (γ^2) (λ^3)-3 a d Z (β^5) (γ^2) (λ^3)+16 b (β^6) (γ^2) (λ^3)-16 d (β^6) (γ^2) (λ^3)-4 b Z (β^6) (γ^2) (λ^3)+4 d Z (β^6) (γ^2) (λ^3)-2 b β (γ^3) (λ^3)+2 a b β (γ^3) (λ^3)+2 d β (γ^3) (λ^3)-2 a d β (γ^3) (λ^3)+21 b (β^2) (γ^3) (λ^3)-15 a b (β^2) (γ^3) (λ^3)+4 (a^2) b (β^2) (γ^3) (λ^3)-21 d (β^2) (γ^3) (λ^3)+15 a d (β^2) (γ^3) (λ^3)-4 (a^2) d (β^2) (γ^3) (λ^3)+16 b Z (β^2) (γ^3) (λ^3)-30 a b Z (β^2) (γ^3) (λ^3)+14 (a^2) b Z (β^2) (γ^3) (λ^3)-16 d Z (β^2) (γ^3) (λ^3)+30 a d Z (β^2) (γ^3) (λ^3)-14 (a^2) d Z (β^2) (γ^3) (λ^3)-34 b (β^3) (γ^3) (λ^3)+8 a b (β^3) (γ^3) (λ^3)+34 d (β^3) (γ^3) (λ^3)-8 a d (β^3) (γ^3) (λ^3)-50 b Z (β^3) (γ^3) (λ^3)+62 a b Z (β^3) (γ^3) (λ^3)-12 (a^2) b Z (β^3) (γ^3) (λ^3)+50 d Z (β^3) (γ^3) (λ^3)-62 a d Z (β^3) (γ^3) (λ^3)+12 (a^2) d Z (β^3) (γ^3) (λ^3)-7 b (β^4) (γ^3) (λ^3)+14 a b (β^4) (γ^3) (λ^3)-4 (a^2) b (β^4) (γ^3) (λ^3)+7 d (β^4) (γ^3) (λ^3)-14 a d (β^4) (γ^3) (λ^3)+4 (a^2) d (β^4) (γ^3) (λ^3)+78 b Z (β^4) (γ^3) (λ^3)-47 a b Z (β^4) (γ^3) (λ^3)-(a^2) b Z (β^4) (γ^3) (λ^3)-78 d Z (β^4) (γ^3) (λ^3)+47 a d Z (β^4) (γ^3) (λ^3)+(a^2) d Z (β^4) (γ^3) (λ^3)+36 b (β^5) (γ^3) (λ^3)-11 a b (β^5) (γ^3) (λ^3)-36 d (β^5) (γ^3) (λ^3)+11 a d (β^5) (γ^3) (λ^3)-45 b Z (β^5) (γ^3) (λ^3)+3 a b Z (β^5) (γ^3) (λ^3)+45 d Z (β^5) (γ^3) (λ^3)-3 a d Z (β^5) (γ^3) (λ^3)-14 b (β^6) (γ^3) (λ^3)+14 d (β^6) (γ^3) (λ^3)+6 b Z (β^6) (γ^3) (λ^3)-6 d Z (β^6) (γ^3) (λ^3)-5 b (β^2) (γ^4) (λ^3)+7 a b (β^2) (γ^4) (λ^3)-2 (a^2) b (β^2) (γ^4) (λ^3)+5 d (β^2) (γ^4) (λ^3)-7 a d (β^2) (γ^4) (λ^3)+2 (a^2) d (β^2) (γ^4) (λ^3)-8 b Z (β^2) (γ^4) (λ^3)+17 a b Z (β^2) (γ^4) (λ^3)-10 (a^2) b Z (β^2) (γ^4) (λ^3)+(a^3) b Z (β^2) (γ^4) (λ^3)+8 d Z (β^2) (γ^4) (λ^3)-17 a d Z (β^2) (γ^4) (λ^3)+10 (a^2) d Z (β^2) (γ^4) (λ^3)-(a^3) d Z (β^2) (γ^4) (λ^3)+11 b (β^3) (γ^4) (λ^3)-4 a b (β^3) (γ^4) (λ^3)-11 d (β^3) (γ^4) (λ^3)+4 a d (β^3) (γ^4) (λ^3)+15 b Z (β^3) (γ^4) (λ^3)-27 a b Z (β^3) (γ^4) (λ^3)+13 (a^2) b Z (β^3) (γ^4) (λ^3)-(a^3) b Z (β^3) (γ^4) (λ^3)-15 d Z (β^3) (γ^4) (λ^3)+27 a d Z (β^3) (γ^4) (λ^3)-13 (a^2) d Z (β^3) (γ^4) (λ^3)+(a^3) d Z (β^3) (γ^4) (λ^3)-2 b (β^4) (γ^4) (λ^3)-5 a b (β^4) (γ^4) (λ^3)+2 (a^2) b (β^4) (γ^4) (λ^3)+2 d (β^4) (γ^4) (λ^3)+5 a d (β^4) (γ^4) (λ^3)-2 (a^2) d (β^4) (γ^4) (λ^3)-27 b Z (β^4) (γ^4) (λ^3)+31 a b Z (β^4) (γ^4) (λ^3)-4 (a^2) b Z (β^4) (γ^4) (λ^3)+27 d Z (β^4) (γ^4) (λ^3)-31 a d Z (β^4) (γ^4) (λ^3)+4 (a^2) d Z (β^4) (γ^4) (λ^3)-12 b (β^5) (γ^4) (λ^3)+6 a b (β^5) (γ^4) (λ^3)+12 d (β^5) (γ^4) (λ^3)-6 a d (β^5) (γ^4) (λ^3)+20 b Z (β^5) (γ^4) (λ^3)-7 a b Z (β^5) (γ^4) (λ^3)-20 d Z (β^5) (γ^4) (λ^3)+7 a d Z (β^5) (γ^4) (λ^3)+6 b (β^6) (γ^4) (λ^3)-6 d (β^6) (γ^4) (λ^3)-4 b Z (β^6) (γ^4) (λ^3)+4 d Z (β^6) (γ^4) (λ^3)+b Z (β^2) (γ^5) (λ^3)-3 a b Z (β^2) (γ^5) (λ^3)+3 (a^2) b Z (β^2) (γ^5) (λ^3)-(a^3) b Z (β^2) (γ^5) (λ^3)-d Z (β^2) (γ^5) (λ^3)+3 a d Z (β^2) (γ^5) (λ^3)-3 (a^2) d Z (β^2) (γ^5) (λ^3)+(a^3) d Z (β^2) (γ^5) (λ^3)-b (β^3) (γ^5) (λ^3)+a b (β^3) (γ^5) (λ^3)+d (β^3) (γ^5) (λ^3)-a d (β^3) (γ^5) (λ^3)-2 b Z (β^3) (γ^5) (λ^3)+5 a b Z (β^3) (γ^5) (λ^3)-4 (a^2) b Z (β^3) (γ^5) (λ^3)+(a^3) b Z (β^3) (γ^5) (λ^3)+2 d Z (β^3) (γ^5) (λ^3)-5 a d Z (β^3) (γ^5) (λ^3)+4 (a^2) d Z (β^3) (γ^5) (λ^3)-(a^3) d Z (β^3) (γ^5) (λ^3)+b (β^4) (γ^5) (λ^3)-d (β^4) (γ^5) (λ^3)+3 b Z (β^4) (γ^5) (λ^3)-6 a b Z (β^4) (γ^5) (λ^3)+3 (a^2) b Z (β^4) (γ^5) (λ^3)-3 d Z (β^4) (γ^5) (λ^3)+6 a d Z (β^4) (γ^5) (λ^3)-3 (a^2) d Z (β^4) (γ^5) (λ^3)+b (β^5) (γ^5) (λ^3)-a b (β^5) (γ^5) (λ^3)-d (β^5) (γ^5) (λ^3)+a d (β^5) (γ^5) (λ^3)-3 b Z (β^5) (γ^5) (λ^3)+3 a b Z (β^5) (γ^5) (λ^3)+3 d Z (β^5) (γ^5) (λ^3)-3 a d Z (β^5) (γ^5) (λ^3)-b (β^6) (γ^5) (λ^3)+d (β^6) (γ^5) (λ^3)+b Z (β^6) (γ^5) (λ^3)-d Z (β^6) (γ^5) (λ^3)-2 b β (λ^4)+a b β (λ^4)+2 d β (λ^4)-a d β (λ^4)+8 b (β^2) (λ^4)-8 d (β^2) (λ^4)+3 b Z (β^2) (λ^4)-2 a b Z (β^2) (λ^4)-3 d Z (β^2) (λ^4)+2 a d Z (β^2) (λ^4)-9 b (β^3) (λ^4)-4 a b (β^3) (λ^4)+9 d (β^3) (λ^4)+4 a d (β^3) (λ^4)-12 b Z (β^3) (λ^4)+2 a b Z (β^3) (λ^4)+12 d Z (β^3) (λ^4)-2 a d Z (β^3) (λ^4)-2 b (β^4) (λ^4)+2 a b (β^4) (λ^4)+2 d (β^4) (λ^4)-2 a d (β^4) (λ^4)+16 b Z (β^4) (λ^4)+2 a b Z (β^4) (λ^4)-16 d Z (β^4) (λ^4)-2 a d Z (β^4) (λ^4)+10 b (β^5) (λ^4)+3 a b (β^5) (λ^4)-10 d (β^5) (λ^4)-3 a d (β^5) (λ^4)-8 b Z (β^5) (λ^4)-2 a b Z (β^5) (λ^4)+8 d Z (β^5) (λ^4)+2 a d Z (β^5) (λ^4)-6 b (β^6) (λ^4)-2 a b (β^6) (λ^4)+6 d (β^6) (λ^4)+2 a d (β^6) (λ^4)+b Z (β^6) (λ^4)-d Z (β^6) (λ^4)+b (β^7) (λ^4)-d (β^7) (λ^4)+7 b β γ (λ^4)-5 a b β γ (λ^4)-7 d β γ (λ^4)+5 a d β γ (λ^4)-32 b (β^2) γ (λ^4)+8 a b (β^2) γ (λ^4)-(a^2) b (β^2) γ (λ^4)+32 d (β^2) γ (λ^4)-8 a d (β^2) γ (λ^4)+(a^2) d (β^2) γ (λ^4)-11 b Z (β^2) γ (λ^4)+12 a b Z (β^2) γ (λ^4)-2 (a^2) b Z (β^2) γ (λ^4)+11 d Z (β^2) γ (λ^4)-12 a d Z (β^2) γ (λ^4)+2 (a^2) d Z (β^2) γ (λ^4)+41 b (β^3) γ (λ^4)+11 a b (β^3) γ (λ^4)-2 (a^2) b (β^3) γ (λ^4)-41 d (β^3) γ (λ^4)-11 a d (β^3) γ (λ^4)+2 (a^2) d (β^3) γ (λ^4)+50 b Z (β^3) γ (λ^4)-27 a b Z (β^3) γ (λ^4)-50 d Z (β^3) γ (λ^4)+27 a d Z (β^3) γ (λ^4)+4 b (β^4) γ (λ^4)-15 a b (β^4) γ (λ^4)+(a^2) b (β^4) γ (λ^4)-4 d (β^4) γ (λ^4)+15 a d (β^4) γ (λ^4)-(a^2) d (β^4) γ (λ^4)-75 b Z (β^4) γ (λ^4)+7 a b Z (β^4) γ (λ^4)+2 (a^2) b Z (β^4) γ (λ^4)+75 d Z (β^4) γ (λ^4)-7 a d Z (β^4) γ (λ^4)-2 (a^2) d Z (β^4) γ (λ^4)-43 b (β^5) γ (λ^4)-6 a b (β^5) γ (λ^4)+2 (a^2) b (β^5) γ (λ^4)+43 d (β^5) γ (λ^4)+6 a d (β^5) γ (λ^4)-2 (a^2) d (β^5) γ (λ^4)+43 b Z (β^5) γ (λ^4)+9 a b Z (β^5) γ (λ^4)-43 d Z (β^5) γ (λ^4)-9 a d Z (β^5) γ (λ^4)+28 b (β^6) γ (λ^4)+7 a b (β^6) γ (λ^4)-28 d (β^6) γ (λ^4)-7 a d (β^6) γ (λ^4)-7 b Z (β^6) γ (λ^4)-a b Z (β^6) γ (λ^4)+7 d Z (β^6) γ (λ^4)+a d Z (β^6) γ (λ^4)-5 b (β^7) γ (λ^4)+5 d (β^7) γ (λ^4)-8 b β (γ^2) (λ^4)+7 a b β (γ^2) (λ^4)+8 d β (γ^2) (λ^4)-7 a d β (γ^2) (λ^4)+50 b (β^2) (γ^2) (λ^4)-28 a b (β^2) (γ^2) (λ^4)+5 (a^2) b (β^2) (γ^2) (λ^4)-50 d (β^2) (γ^2) (λ^4)+28 a d (β^2) (γ^2) (λ^4)-5 (a^2) d (β^2) (γ^2) (λ^4)+18 b Z (β^2) (γ^2) (λ^4)-30 a b Z (β^2) (γ^2) (λ^4)+12 (a^2) b Z (β^2) (γ^2) (λ^4)-18 d Z (β^2) (γ^2) (λ^4)+30 a d Z (β^2) (γ^2) (λ^4)-12 (a^2) d Z (β^2) (γ^2) (λ^4)-73 b (β^3) (γ^2) (λ^4)-5 a b (β^3) (γ^2) (λ^4)+4 (a^2) b (β^3) (γ^2) (λ^4)+73 d (β^3) (γ^2) (λ^4)+5 a d (β^3) (γ^2) (λ^4)-4 (a^2) d (β^3) (γ^2) (λ^4)-78 b Z (β^3) (γ^2) (λ^4)+73 a b Z (β^3) (γ^2) (λ^4)-8 (a^2) b Z (β^3) (γ^2) (λ^4)+78 d Z (β^3) (γ^2) (λ^4)-73 a d Z (β^3) (γ^2) (λ^4)+8 (a^2) d Z (β^3) (γ^2) (λ^4)+4 b (β^4) (γ^2) (λ^4)+32 a b (β^4) (γ^2) (λ^4)-5 (a^2) b (β^4) (γ^2) (λ^4)-4 d (β^4) (γ^2) (λ^4)-32 a d (β^4) (γ^2) (λ^4)+5 (a^2) d (β^4) (γ^2) (λ^4)+135 b Z (β^4) (γ^2) (λ^4)-52 a b Z (β^4) (γ^2) (λ^4)-5 (a^2) b Z (β^4) (γ^2) (λ^4)-135 d Z (β^4) (γ^2) (λ^4)+52 a d Z (β^4) (γ^2) (λ^4)+5 (a^2) d Z (β^4) (γ^2) (λ^4)+73 b (β^5) (γ^2) (λ^4)-6 a b (β^5) (γ^2) (λ^4)-4 (a^2) b (β^5) (γ^2) (λ^4)-73 d (β^5) (γ^2) (λ^4)+6 a d (β^5) (γ^2) (λ^4)+4 (a^2) d (β^5) (γ^2) (λ^4)-89 b Z (β^5) (γ^2) (λ^4)-9 a b Z (β^5) (γ^2) (λ^4)+2 (a^2) b Z (β^5) (γ^2) (λ^4)+89 d Z (β^5) (γ^2) (λ^4)+9 a d Z (β^5) (γ^2) (λ^4)-2 (a^2) d Z (β^5) (γ^2) (λ^4)-52 b (β^6) (γ^2) (λ^4)-8 a b (β^6) (γ^2) (λ^4)+52 d (β^6) (γ^2) (λ^4)+8 a d (β^6) (γ^2) (λ^4)+18 b Z (β^6) (γ^2) (λ^4)+4 a b Z (β^6) (γ^2) (λ^4)-18 d Z (β^6) (γ^2) (λ^4)-4 a d Z (β^6) (γ^2) (λ^4)+10 b (β^7) (γ^2) (λ^4)-10 d (β^7) (γ^2) (λ^4)+3 b β (γ^3) (λ^4)-3 a b β (γ^3) (λ^4)-3 d β (γ^3) (λ^4)+3 a d β (γ^3) (λ^4)-36 b (β^2) (γ^3) (λ^4)+33 a b (β^2) (γ^3) (λ^4)-8 (a^2) b (β^2) (γ^3) (λ^4)+(a^3) b (β^2) (γ^3) (λ^4)+36 d (β^2) (γ^3) (λ^4)-33 a d (β^2) (γ^3) (λ^4)+8 (a^2) d (β^2) (γ^3) (λ^4)-(a^3) d (β^2) (γ^3) (λ^4)-17 b Z (β^2) (γ^3) (λ^4)+36 a b Z (β^2) (γ^3) (λ^4)-21 (a^2) b Z (β^2) (γ^3) (λ^4)+2 (a^3) b Z (β^2) (γ^3) (λ^4)+17 d Z (β^2) (γ^3) (λ^4)-36 a d Z (β^2) (γ^3) (λ^4)+21 (a^2) d Z (β^2) (γ^3) (λ^4)-2 (a^3) d Z (β^2) (γ^3) (λ^4)+64 b (β^3) (γ^3) (λ^4)-13 a b (β^3) (γ^3) (λ^4)-64 d (β^3) (γ^3) (λ^4)+13 a d (β^3) (γ^3) (λ^4)+58 b Z (β^3) (γ^3) (λ^4)-83 a b Z (β^3) (γ^3) (λ^4)+26 (a^2) b Z (β^3) (γ^3) (λ^4)-(a^3) b Z (β^3) (γ^3) (λ^4)-58 d Z (β^3) (γ^3) (λ^4)+83 a d Z (β^3) (γ^3) (λ^4)-26 (a^2) d Z (β^3) (γ^3) (λ^4)+(a^3) d Z (β^3) (γ^3) (λ^4)-16 b (β^4) (γ^3) (λ^4)-27 a b (β^4) (γ^3) (λ^4)+8 (a^2) b (β^4) (γ^3) (λ^4)-(a^3) b (β^4) (γ^3) (λ^4)+16 d (β^4) (γ^3) (λ^4)+27 a d (β^4) (γ^3) (λ^4)-8 (a^2) d (β^4) (γ^3) (λ^4)+(a^3) d (β^4) (γ^3) (λ^4)-116 b Z (β^4) (γ^3) (λ^4)+88 a b Z (β^4) (γ^3) (λ^4)-(a^2) b Z (β^4) (γ^3) (λ^4)-(a^3) b Z (β^4) (γ^3) (λ^4)+116 d Z (β^4) (γ^3) (λ^4)-88 a d Z (β^4) (γ^3) (λ^4)+(a^2) d Z (β^4) (γ^3) (λ^4)+(a^3) d Z (β^4) (γ^3) (λ^4)-61 b (β^5) (γ^3) (λ^4)+24 a b (β^5) (γ^3) (λ^4)+61 d (β^5) (γ^3) (λ^4)-24 a d (β^5) (γ^3) (λ^4)+89 b Z (β^5) (γ^3) (λ^4)-7 a b Z (β^5) (γ^3) (λ^4)-6 (a^2) b Z (β^5) (γ^3) (λ^4)-89 d Z (β^5) (γ^3) (λ^4)+7 a d Z (β^5) (γ^3) (λ^4)+6 (a^2) d Z (β^5) (γ^3) (λ^4)+48 b (β^6) (γ^3) (λ^4)+2 a b (β^6) (γ^3) (λ^4)-48 d (β^6) (γ^3) (λ^4)-2 a d (β^6) (γ^3) (λ^4)-22 b Z (β^6) (γ^3) (λ^4)-6 a b Z (β^6) (γ^3) (λ^4)+22 d Z (β^6) (γ^3) (λ^4)+6 a d Z (β^6) (γ^3) (λ^4)-10 b (β^7) (γ^3) (λ^4)+10 d (β^7) (γ^3) (λ^4)+11 b (β^2) (γ^4) (λ^4)-16 a b (β^2) (γ^4) (λ^4)+7 (a^2) b (β^2) (γ^4) (λ^4)-2 (a^3) b (β^2) (γ^4) (λ^4)-11 d (β^2) (γ^4) (λ^4)+16 a d (β^2) (γ^4) (λ^4)-7 (a^2) d (β^2) (γ^4) (λ^4)+2 (a^3) d (β^2) (γ^4) (λ^4)+10 b Z (β^2) (γ^4) (λ^4)-25 a b Z (β^2) (γ^4) (λ^4)+20 (a^2) b Z (β^2) (γ^4) (λ^4)-5 (a^3) b Z (β^2) (γ^4) (λ^4)-10 d Z (β^2) (γ^4) (λ^4)+25 a d Z (β^2) (γ^4) (λ^4)-20 (a^2) d Z (β^2) (γ^4) (λ^4)+5 (a^3) d Z (β^2) (γ^4) (λ^4)-27 b (β^3) (γ^4) (λ^4)+15 a b (β^3) (γ^4) (λ^4)-2 (a^2) b (β^3) (γ^4) (λ^4)+27 d (β^3) (γ^4) (λ^4)-15 a d (β^3) (γ^4) (λ^4)+2 (a^2) d (β^3) (γ^4) (λ^4)-22 b Z (β^3) (γ^4) (λ^4)+44 a b Z (β^3) (γ^4) (λ^4)-24 (a^2) b Z (β^3) (γ^4) (λ^4)+2 (a^3) b Z (β^3) (γ^4) (λ^4)+22 d Z (β^3) (γ^4) (λ^4)-44 a d Z (β^3) (γ^4) (λ^4)+24 (a^2) d Z (β^3) (γ^4) (λ^4)-2 (a^3) d Z (β^3) (γ^4) (λ^4)+14 b (β^4) (γ^4) (λ^4)+8 a b (β^4) (γ^4) (λ^4)-5 (a^2) b (β^4) (γ^4) (λ^4)+2 (a^3) b (β^4) (γ^4) (λ^4)-14 d (β^4) (γ^4) (λ^4)-8 a d (β^4) (γ^4) (λ^4)+5 (a^2) d (β^4) (γ^4) (λ^4)-2 (a^3) d (β^4) (γ^4) (λ^4)+47 b Z (β^4) (γ^4) (λ^4)-58 a b Z (β^4) (γ^4) (λ^4)+9 (a^2) b Z (β^4) (γ^4) (λ^4)+2 (a^3) b Z (β^4) (γ^4) (λ^4)-47 d Z (β^4) (γ^4) (λ^4)+58 a d Z (β^4) (γ^4) (λ^4)-9 (a^2) d Z (β^4) (γ^4) (λ^4)-2 (a^3) d Z (β^4) (γ^4) (λ^4)+25 b (β^5) (γ^4) (λ^4)-21 a b (β^5) (γ^4) (λ^4)+4 (a^2) b (β^5) (γ^4) (λ^4)-25 d (β^5) (γ^4) (λ^4)+21 a d (β^5) (γ^4) (λ^4)-4 (a^2) d (β^5) (γ^4) (λ^4)-43 b Z (β^5) (γ^4) (λ^4)+15 a b Z (β^5) (γ^4) (λ^4)+6 (a^2) b Z (β^5) (γ^4) (λ^4)+43 d Z (β^5) (γ^4) (λ^4)-15 a d Z (β^5) (γ^4) (λ^4)-6 (a^2) d Z (β^5) (γ^4) (λ^4)-22 b (β^6) (γ^4) (λ^4)+2 a b (β^6) (γ^4) (λ^4)+22 d (β^6) (γ^4) (λ^4)-2 a d (β^6) (γ^4) (λ^4)+13 b Z (β^6) (γ^4) (λ^4)+4 a b Z (β^6) (γ^4) (λ^4)-13 d Z (β^6) (γ^4) (λ^4)-4 a d Z (β^6) (γ^4) (λ^4)+5 b (β^7) (γ^4) (λ^4)-5 d (β^7) (γ^4) (λ^4)-b (β^2) (γ^5) (λ^4)+3 a b (β^2) (γ^5) (λ^4)-3 (a^2) b (β^2) (γ^5) (λ^4)+(a^3) b (β^2) (γ^5) (λ^4)+d (β^2) (γ^5) (λ^4)-3 a d (β^2) (γ^5) (λ^4)+3 (a^2) d (β^2) (γ^5) (λ^4)-(a^3) d (β^2) (γ^5) (λ^4)-3 b Z (β^2) (γ^5) (λ^4)+9 a b Z (β^2) (γ^5) (λ^4)-9 (a^2) b Z (β^2) (γ^5) (λ^4)+3 (a^3) b Z (β^2) (γ^5) (λ^4)+3 d Z (β^2) (γ^5) (λ^4)-9 a d Z (β^2) (γ^5) (λ^4)+9 (a^2) d Z (β^2) (γ^5) (λ^4)-3 (a^3) d Z (β^2) (γ^5) (λ^4)+4 b (β^3) (γ^5) (λ^4)-4 a b (β^3) (γ^5) (λ^4)-4 d (β^3) (γ^5) (λ^4)+4 a d (β^3) (γ^5) (λ^4)+4 b Z (β^3) (γ^5) (λ^4)-9 a b Z (β^3) (γ^5) (λ^4)+6 (a^2) b Z (β^3) (γ^5) (λ^4)-(a^3) b Z (β^3) (γ^5) (λ^4)-4 d Z (β^3) (γ^5) (λ^4)+9 a d Z (β^3) (γ^5) (λ^4)-6 (a^2) d Z (β^3) (γ^5) (λ^4)+(a^3) d Z (β^3) (γ^5) (λ^4)-4 b (β^4) (γ^5) (λ^4)+(a^2) b (β^4) (γ^5) (λ^4)-(a^3) b (β^4) (γ^5) (λ^4)+4 d (β^4) (γ^5) (λ^4)-(a^2) d (β^4) (γ^5) (λ^4)+(a^3) d (β^4) (γ^5) (λ^4)-7 b Z (β^4) (γ^5) (λ^4)+13 a b Z (β^4) (γ^5) (λ^4)-5 (a^2) b Z (β^4) (γ^5) (λ^4)-(a^3) b Z (β^4) (γ^5) (λ^4)+7 d Z (β^4) (γ^5) (λ^4)-13 a d Z (β^4) (γ^5) (λ^4)+5 (a^2) d Z (β^4) (γ^5) (λ^4)+(a^3) d Z (β^4) (γ^5) (λ^4)-4 b (β^5) (γ^5) (λ^4)+6 a b (β^5) (γ^5) (λ^4)-2 (a^2) b (β^5) (γ^5) (λ^4)+4 d (β^5) (γ^5) (λ^4)-6 a d (β^5) (γ^5) (λ^4)+2 (a^2) d (β^5) (γ^5) (λ^4)+8 b Z (β^5) (γ^5) (λ^4)-6 a b Z (β^5) (γ^5) (λ^4)-2 (a^2) b Z (β^5) (γ^5) (λ^4)-8 d Z (β^5) (γ^5) (λ^4)+6 a d Z (β^5) (γ^5) (λ^4)+2 (a^2) d Z (β^5) (γ^5) (λ^4)+4 b (β^6) (γ^5) (λ^4)-a b (β^6) (γ^5) (λ^4)-4 d (β^6) (γ^5) (λ^4)+a d (β^6) (γ^5) (λ^4)-3 b Z (β^6) (γ^5) (λ^4)-a b Z (β^6) (γ^5) (λ^4)+3 d Z (β^6) (γ^5) (λ^4)+a d Z (β^6) (γ^5) (λ^4)-b (β^7) (γ^5) (λ^4)+d (β^7) (γ^5) (λ^4)+b β (λ^5)-a b β (λ^5)-d β (λ^5)+a d β (λ^5)-5 b (β^2) (λ^5)+2 a b (β^2) (λ^5)+5 d (β^2) (λ^5)-2 a d (β^2) (λ^5)-b Z (β^2) (λ^5)+a b Z (β^2) (λ^5)+d Z (β^2) (λ^5)-a d Z (β^2) (λ^5)+7 b (β^3) (λ^5)+4 a b (β^3) (λ^5)-7 d (β^3) (λ^5)-4 a d (β^3) (λ^5)+7 b Z (β^3) (λ^5)-4 a b Z (β^3) (λ^5)-7 d Z (β^3) (λ^5)+4 a d Z (β^3) (λ^5)-b (β^4) (λ^5)-7 a b (β^4) (λ^5)+d (β^4) (λ^5)+7 a d (β^4) (λ^5)-12 b Z (β^4) (λ^5)+12 d Z (β^4) (λ^5)-6 b (β^5) (λ^5)-2 a b (β^5) (λ^5)+6 d (β^5) (λ^5)+2 a d (β^5) (λ^5)+8 b Z (β^5) (λ^5)+4 a b Z (β^5) (λ^5)-8 d Z (β^5) (λ^5)-4 a d Z (β^5) (λ^5)+6 b (β^6) (λ^5)+5 a b (β^6) (λ^5)-6 d (β^6) (λ^5)-5 a d (β^6) (λ^5)-2 b Z (β^6) (λ^5)-a b Z (β^6) (λ^5)+2 d Z (β^6) (λ^5)+a d Z (β^6) (λ^5)-2 b (β^7) (λ^5)-a b (β^7) (λ^5)+2 d (β^7) (λ^5)+a d (β^7) (λ^5)-3 b β γ (λ^5)+3 a b β γ (λ^5)+3 d β γ (λ^5)-3 a d β γ (λ^5)+22 b (β^2) γ (λ^5)-13 a b (β^2) γ (λ^5)-22 d (β^2) γ (λ^5)+13 a d (β^2) γ (λ^5)+4 b Z (β^2) γ (λ^5)-6 a b Z (β^2) γ (λ^5)+2 (a^2) b Z (β^2) γ (λ^5)-4 d Z (β^2) γ (λ^5)+6 a d Z (β^2) γ (λ^5)-2 (a^2) d Z (β^2) γ (λ^5)-34 b (β^3) γ (λ^5)-7 a b (β^3) γ (λ^5)+34 d (β^3) γ (λ^5)+7 a d (β^3) γ (λ^5)-29 b Z (β^3) γ (λ^5)+25 a b Z (β^3) γ (λ^5)-2 (a^2) b Z (β^3) γ (λ^5)+29 d Z (β^3) γ (λ^5)-25 a d Z (β^3) γ (λ^5)+2 (a^2) d Z (β^3) γ (λ^5)+5 b (β^4) γ (λ^5)+35 a b (β^4) γ (λ^5)-3 (a^2) b (β^4) γ (λ^5)-5 d (β^4) γ (λ^5)-35 a d (β^4) γ (λ^5)+3 (a^2) d (β^4) γ (λ^5)+56 b Z (β^4) γ (λ^5)-15 a b Z (β^4) γ (λ^5)-2 (a^2) b Z (β^4) γ (λ^5)-56 d Z (β^4) γ (λ^5)+15 a d Z (β^4) γ (λ^5)+2 (a^2) d Z (β^4) γ (λ^5)+27 b (β^5) γ (λ^5)-a b (β^5) γ (λ^5)-(a^2) b (β^5) γ (λ^5)-27 d (β^5) γ (λ^5)+a d (β^5) γ (λ^5)+(a^2) d (β^5) γ (λ^5)-41 b Z (β^5) γ (λ^5)-15 a b Z (β^5) γ (λ^5)+2 (a^2) b Z (β^5) γ (λ^5)+41 d Z (β^5) γ (λ^5)+15 a d Z (β^5) γ (λ^5)-2 (a^2) d Z (β^5) γ (λ^5)-27 b (β^6) γ (λ^5)-22 a b (β^6) γ (λ^5)+2 (a^2) b (β^6) γ (λ^5)+27 d (β^6) γ (λ^5)+22 a d (β^6) γ (λ^5)-2 (a^2) d (β^6) γ (λ^5)+11 b Z (β^6) γ (λ^5)+7 a b Z (β^6) γ (λ^5)-11 d Z (β^6) γ (λ^5)-7 a d Z (β^6) γ (λ^5)+10 b (β^7) γ (λ^5)+5 a b (β^7) γ (λ^5)-10 d (β^7) γ (λ^5)-5 a d (β^7) γ (λ^5)+3 b β (γ^2) (λ^5)-3 a b β (γ^2) (λ^5)-3 d β (γ^2) (λ^5)+3 a d β (γ^2) (λ^5)-35 b (β^2) (γ^2) (λ^5)+26 a b (β^2) (γ^2) (λ^5)-(a^2) b (β^2) (γ^2) (λ^5)+(a^3) b (β^2) (γ^2) (λ^5)+35 d (β^2) (γ^2) (λ^5)-26 a d (β^2) (γ^2) (λ^5)+(a^2) d (β^2) (γ^2) (λ^5)-(a^3) d (β^2) (γ^2) (λ^5)-7 b Z (β^2) (γ^2) (λ^5)+14 a b Z (β^2) (γ^2) (λ^5)-8 (a^2) b Z (β^2) (γ^2) (λ^5)+(a^3) b Z (β^2) (γ^2) (λ^5)+7 d Z (β^2) (γ^2) (λ^5)-14 a d Z (β^2) (γ^2) (λ^5)+8 (a^2) d Z (β^2) (γ^2) (λ^5)-(a^3) d Z (β^2) (γ^2) (λ^5)+68 b (β^3) (γ^2) (λ^5)-11 a b (β^3) (γ^2) (λ^5)+2 (a^2) b (β^3) (γ^2) (λ^5)+(a^3) b (β^3) (γ^2) (λ^5)-68 d (β^3) (γ^2) (λ^5)+11 a d (β^3) (γ^2) (λ^5)-2 (a^2) d (β^3) (γ^2) (λ^5)-(a^3) d (β^3) (γ^2) (λ^5)+47 b Z (β^3) (γ^2) (λ^5)-58 a b Z (β^3) (γ^2) (λ^5)+14 (a^2) b Z (β^3) (γ^2) (λ^5)-47 d Z (β^3) (γ^2) (λ^5)+58 a d Z (β^3) (γ^2) (λ^5)-14 (a^2) d Z (β^3) (γ^2) (λ^5)-13 b (β^4) (γ^2) (λ^5)-64 a b (β^4) (γ^2) (λ^5)+12 (a^2) b (β^4) (γ^2) (λ^5)-(a^3) b (β^4) (γ^2) (λ^5)+13 d (β^4) (γ^2) (λ^5)+64 a d (β^4) (γ^2) (λ^5)-12 (a^2) d (β^4) (γ^2) (λ^5)+(a^3) d (β^4) (γ^2) (λ^5)-102 b Z (β^4) (γ^2) (λ^5)+57 a b Z (β^4) (γ^2) (λ^5)+4 (a^2) b Z (β^4) (γ^2) (λ^5)-(a^3) b Z (β^4) (γ^2) (λ^5)+102 d Z (β^4) (γ^2) (λ^5)-57 a d Z (β^4) (γ^2) (λ^5)-4 (a^2) d Z (β^4) (γ^2) (λ^5)+(a^3) d Z (β^4) (γ^2) (λ^5)-51 b (β^5) (γ^2) (λ^5)+24 a b (β^5) (γ^2) (λ^5)+(a^2) b (β^5) (γ^2) (λ^5)-(a^3) b (β^5) (γ^2) (λ^5)+51 d (β^5) (γ^2) (λ^5)-24 a d (β^5) (γ^2) (λ^5)-(a^2) d (β^5) (γ^2) (λ^5)+(a^3) d (β^5) (γ^2) (λ^5)+83 b Z (β^5) (γ^2) (λ^5)+17 a b Z (β^5) (γ^2) (λ^5)-10 (a^2) b Z (β^5) (γ^2) (λ^5)-83 d Z (β^5) (γ^2) (λ^5)-17 a d Z (β^5) (γ^2) (λ^5)+10 (a^2) d Z (β^5) (γ^2) (λ^5)+48 b (β^6) (γ^2) (λ^5)+38 a b (β^6) (γ^2) (λ^5)-8 (a^2) b (β^6) (γ^2) (λ^5)-48 d (β^6) (γ^2) (λ^5)-38 a d (β^6) (γ^2) (λ^5)+8 (a^2) d (β^6) (γ^2) (λ^5)-24 b Z (β^6) (γ^2) (λ^5)-18 a b Z (β^6) (γ^2) (λ^5)+24 d Z (β^6) (γ^2) (λ^5)+18 a d Z (β^6) (γ^2) (λ^5)-20 b (β^7) (γ^2) (λ^5)-10 a b (β^7) (γ^2) (λ^5)+20 d (β^7) (γ^2) (λ^5)+10 a d (β^7) (γ^2) (λ^5)-b β (γ^3) (λ^5)+a b β (γ^3) (λ^5)+d β (γ^3) (λ^5)-a d β (γ^3) (λ^5)+26 b (β^2) (γ^3) (λ^5)-27 a b (β^2) (γ^3) (λ^5)+8 (a^2) b (β^2) (γ^3) (λ^5)-4 (a^3) b (β^2) (γ^3) (λ^5)-26 d (β^2) (γ^3) (λ^5)+27 a d (β^2) (γ^3) (λ^5)-8 (a^2) d (β^2) (γ^3) (λ^5)+4 (a^3) d (β^2) (γ^3) (λ^5)+9 b Z (β^2) (γ^3) (λ^5)-23 a b Z (β^2) (γ^3) (λ^5)+19 (a^2) b Z (β^2) (γ^3) (λ^5)-5 (a^3) b Z (β^2) (γ^3) (λ^5)-9 d Z (β^2) (γ^3) (λ^5)+23 a d Z (β^2) (γ^3) (λ^5)-19 (a^2) d Z (β^2) (γ^3) (λ^5)+5 (a^3) d Z (β^2) (γ^3) (λ^5)-65 b (β^3) (γ^3) (λ^5)+25 a b (β^3) (γ^3) (λ^5)+3 (a^2) b (β^3) (γ^3) (λ^5)-4 (a^3) b (β^3) (γ^3) (λ^5)+65 d (β^3) (γ^3) (λ^5)-25 a d (β^3) (γ^3) (λ^5)-3 (a^2) d (β^3) (γ^3) (λ^5)+4 (a^3) d (β^3) (γ^3) (λ^5)-37 b Z (β^3) (γ^3) (λ^5)+60 a b Z (β^3) (γ^3) (λ^5)-22 (a^2) b Z (β^3) (γ^3) (λ^5)-(a^3) b Z (β^3) (γ^3) (λ^5)+37 d Z (β^3) (γ^3) (λ^5)-60 a d Z (β^3) (γ^3) (λ^5)+22 (a^2) d Z (β^3) (γ^3) (λ^5)+(a^3) d Z (β^3) (γ^3) (λ^5)+21 b (β^4) (γ^3) (λ^5)+49 a b (β^4) (γ^3) (λ^5)-14 (a^2) b (β^4) (γ^3) (λ^5)+3 (a^3) b (β^4) (γ^3) (λ^5)-21 d (β^4) (γ^3) (λ^5)-49 a d (β^4) (γ^3) (λ^5)+14 (a^2) d (β^4) (γ^3) (λ^5)-3 (a^3) d (β^4) (γ^3) (λ^5)+90 b Z (β^4) (γ^3) (λ^5)-80 a b Z (β^4) (γ^3) (λ^5)+2 (a^2) b Z (β^4) (γ^3) (λ^5)+3 (a^3) b Z (β^4) (γ^3) (λ^5)-90 d Z (β^4) (γ^3) (λ^5)+80 a d Z (β^4) (γ^3) (λ^5)-2 (a^2) d Z (β^4) (γ^3) (λ^5)-3 (a^3) d Z (β^4) (γ^3) (λ^5)+51 b (β^5) (γ^3) (λ^5)-46 a b (β^5) (γ^3) (λ^5)+3 (a^2) b (β^5) (γ^3) (λ^5)+3 (a^3) b (β^5) (γ^3) (λ^5)-51 d (β^5) (γ^3) (λ^5)+46 a d (β^5) (γ^3) (λ^5)-3 (a^2) d (β^5) (γ^3) (λ^5)-3 (a^3) d (β^5) (γ^3) (λ^5)-83 b Z (β^5) (γ^3) (λ^5)-a b Z (β^5) (γ^3) (λ^5)+18 (a^2) b Z (β^5) (γ^3) (λ^5)+83 d Z (β^5) (γ^3) (λ^5)+a d Z (β^5) (γ^3) (λ^5)-18 (a^2) d Z (β^5) (γ^3) (λ^5)-42 b (β^6) (γ^3) (λ^5)-32 a b (β^6) (γ^3) (λ^5)+12 (a^2) b (β^6) (γ^3) (λ^5)+42 d (β^6) (γ^3) (λ^5)+32 a d (β^6) (γ^3) (λ^5)-12 (a^2) d (β^6) (γ^3) (λ^5)+26 b Z (β^6) (γ^3) (λ^5)+22 a b Z (β^6) (γ^3) (λ^5)-26 d Z (β^6) (γ^3) (λ^5)-22 a d Z (β^6) (γ^3) (λ^5)+20 b (β^7) (γ^3) (λ^5)+10 a b (β^7) (γ^3) (λ^5)-20 d (β^7) (γ^3) (λ^5)-10 a d (β^7) (γ^3) (λ^5)-10 b (β^2) (γ^4) (λ^5)+18 a b (β^2) (γ^4) (λ^5)-13 (a^2) b (β^2) (γ^4) (λ^5)+5 (a^3) b (β^2) (γ^4) (λ^5)+10 d (β^2) (γ^4) (λ^5)-18 a d (β^2) (γ^4) (λ^5)+13 (a^2) d (β^2) (γ^4) (λ^5)-5 (a^3) d (β^2) (γ^4) (λ^5)-8 b Z (β^2) (γ^4) (λ^5)+23 a b Z (β^2) (γ^4) (λ^5)-22 (a^2) b Z (β^2) (γ^4) (λ^5)+7 (a^3) b Z (β^2) (γ^4) (λ^5)+8 d Z (β^2) (γ^4) (λ^5)-23 a d Z (β^2) (γ^4) (λ^5)+22 (a^2) d Z (β^2) (γ^4) (λ^5)-7 (a^3) d Z (β^2) (γ^4) (λ^5)+27 b (β^3) (γ^4) (λ^5)-9 a b (β^3) (γ^4) (λ^5)-12 (a^2) b (β^3) (γ^4) (λ^5)+5 (a^3) b (β^3) (γ^4) (λ^5)-27 d (β^3) (γ^4) (λ^5)+9 a d (β^3) (γ^4) (λ^5)+12 (a^2) d (β^3) (γ^4) (λ^5)-5 (a^3) d (β^3) (γ^4) (λ^5)+14 b Z (β^3) (γ^4) (λ^5)-26 a b Z (β^3) (γ^4) (λ^5)+10 (a^2) b Z (β^3) (γ^4) (λ^5)+2 (a^3) b Z (β^3) (γ^4) (λ^5)-14 d Z (β^3) (γ^4) (λ^5)+26 a d Z (β^3) (γ^4) (λ^5)-10 (a^2) d Z (β^3) (γ^4) (λ^5)-2 (a^3) d Z (β^3) (γ^4) (λ^5)-18 b (β^4) (γ^4) (λ^5)-11 a b (β^4) (γ^4) (λ^5)+4 (a^2) b (β^4) (γ^4) (λ^5)-3 (a^3) b (β^4) (γ^4) (λ^5)+18 d (β^4) (γ^4) (λ^5)+11 a d (β^4) (γ^4) (λ^5)-4 (a^2) d (β^4) (γ^4) (λ^5)+3 (a^3) d (β^4) (γ^4) (λ^5)-38 b Z (β^4) (γ^4) (λ^5)+49 a b Z (β^4) (γ^4) (λ^5)-8 (a^2) b Z (β^4) (γ^4) (λ^5)-3 (a^3) b Z (β^4) (γ^4) (λ^5)+38 d Z (β^4) (γ^4) (λ^5)-49 a d Z (β^4) (γ^4) (λ^5)+8 (a^2) d Z (β^4) (γ^4) (λ^5)+3 (a^3) d Z (β^4) (γ^4) (λ^5)-27 b (β^5) (γ^4) (λ^5)+34 a b (β^5) (γ^4) (λ^5)-5 (a^2) b (β^5) (γ^4) (λ^5)-3 (a^3) b (β^5) (γ^4) (λ^5)+27 d (β^5) (γ^4) (λ^5)-34 a d (β^5) (γ^4) (λ^5)+5 (a^2) d (β^5) (γ^4) (λ^5)+3 (a^3) d (β^5) (γ^4) (λ^5)+41 b Z (β^5) (γ^4) (λ^5)-9 a b Z (β^5) (γ^4) (λ^5)-14 (a^2) b Z (β^5) (γ^4) (λ^5)-41 d Z (β^5) (γ^4) (λ^5)+9 a d Z (β^5) (γ^4) (λ^5)+14 (a^2) d Z (β^5) (γ^4) (λ^5)+18 b (β^6) (γ^4) (λ^5)+13 a b (β^6) (γ^4) (λ^5)-8 (a^2) b (β^6) (γ^4) (λ^5)-18 d (β^6) (γ^4) (λ^5)-13 a d (β^6) (γ^4) (λ^5)+8 (a^2) d (β^6) (γ^4) (λ^5)-14 b Z (β^6) (γ^4) (λ^5)-13 a b Z (β^6) (γ^4) (λ^5)+14 d Z (β^6) (γ^4) (λ^5)+13 a d Z (β^6) (γ^4) (λ^5)-10 b (β^7) (γ^4) (λ^5)-5 a b (β^7) (γ^4) (λ^5)+10 d (β^7) (γ^4) (λ^5)+5 a d (β^7) (γ^4) (λ^5)+2 b (β^2) (γ^5) (λ^5)-6 a b (β^2) (γ^5) (λ^5)+6 (a^2) b (β^2) (γ^5) (λ^5)-2 (a^3) b (β^2) (γ^5) (λ^5)-2 d (β^2) (γ^5) (λ^5)+6 a d (β^2) (γ^5) (λ^5)-6 (a^2) d (β^2) (γ^5) (λ^5)+2 (a^3) d (β^2) (γ^5) (λ^5)+3 b Z (β^2) (γ^5) (λ^5)-9 a b Z (β^2) (γ^5) (λ^5)+9 (a^2) b Z (β^2) (γ^5) (λ^5)-3 (a^3) b Z (β^2) (γ^5) (λ^5)-3 d Z (β^2) (γ^5) (λ^5)+9 a d Z (β^2) (γ^5) (λ^5)-9 (a^2) d Z (β^2) (γ^5) (λ^5)+3 (a^3) d Z (β^2) (γ^5) (λ^5)-3 b (β^3) (γ^5) (λ^5)-2 a b (β^3) (γ^5) (λ^5)+7 (a^2) b (β^3) (γ^5) (λ^5)-2 (a^3) b (β^3) (γ^5) (λ^5)+3 d (β^3) (γ^5) (λ^5)+2 a d (β^3) (γ^5) (λ^5)-7 (a^2) d (β^3) (γ^5) (λ^5)+2 (a^3) d (β^3) (γ^5) (λ^5)-2 b Z (β^3) (γ^5) (λ^5)+3 a b Z (β^3) (γ^5) (λ^5)-(a^3) b Z (β^3) (γ^5) (λ^5)+2 d Z (β^3) (γ^5) (λ^5)-3 a d Z (β^3) (γ^5) (λ^5)+(a^3) d Z (β^3) (γ^5) (λ^5)+6 b (β^4) (γ^5) (λ^5)-2 a b (β^4) (γ^5) (λ^5)+(a^2) b (β^4) (γ^5) (λ^5)+(a^3) b (β^4) (γ^5) (λ^5)-6 d (β^4) (γ^5) (λ^5)+2 a d (β^4) (γ^5) (λ^5)-(a^2) d (β^4) (γ^5) (λ^5)-(a^3) d (β^4) (γ^5) (λ^5)+6 b Z (β^4) (γ^5) (λ^5)-11 a b Z (β^4) (γ^5) (λ^5)+4 (a^2) b Z (β^4) (γ^5) (λ^5)+(a^3) b Z (β^4) (γ^5) (λ^5)-6 d Z (β^4) (γ^5) (λ^5)+11 a d Z (β^4) (γ^5) (λ^5)-4 (a^2) d Z (β^4) (γ^5) (λ^5)-(a^3) d Z (β^4) (γ^5) (λ^5)+6 b (β^5) (γ^5) (λ^5)-9 a b (β^5) (γ^5) (λ^5)+2 (a^2) b (β^5) (γ^5) (λ^5)+(a^3) b (β^5) (γ^5) (λ^5)-6 d (β^5) (γ^5) (λ^5)+9 a d (β^5) (γ^5) (λ^5)-2 (a^2) d (β^5) (γ^5) (λ^5)-(a^3) d (β^5) (γ^5) (λ^5)-8 b Z (β^5) (γ^5) (λ^5)+4 a b Z (β^5) (γ^5) (λ^5)+4 (a^2) b Z (β^5) (γ^5) (λ^5)+8 d Z (β^5) (γ^5) (λ^5)-4 a d Z (β^5) (γ^5) (λ^5)-4 (a^2) d Z (β^5) (γ^5) (λ^5)-3 b (β^6) (γ^5) (λ^5)-2 a b (β^6) (γ^5) (λ^5)+2 (a^2) b (β^6) (γ^5) (λ^5)+3 d (β^6) (γ^5) (λ^5)+2 a d (β^6) (γ^5) (λ^5)-2 (a^2) d (β^6) (γ^5) (λ^5)+3 b Z (β^6) (γ^5) (λ^5)+3 a b Z (β^6) (γ^5) (λ^5)-3 d Z (β^6) (γ^5) (λ^5)-3 a d Z (β^6) (γ^5) (λ^5)+2 b (β^7) (γ^5) (λ^5)+a b (β^7) (γ^5) (λ^5)-2 d (β^7) (γ^5) (λ^5)-a d (β^7) (γ^5) (λ^5)+2 b (β^2) (λ^6)-2 a b (β^2) (λ^6)-2 d (β^2) (λ^6)+2 a d (β^2) (λ^6)-3 b (β^3) (λ^6)+3 d (β^3) (λ^6)-2 b Z (β^3) (λ^6)+2 a b Z (β^3) (λ^6)+2 d Z (β^3) (λ^6)-2 a d Z (β^3) (λ^6)+6 a b (β^4) (λ^6)-6 a d (β^4) (λ^6)+5 b Z (β^4) (λ^6)-2 a b Z (β^4) (λ^6)-5 d Z (β^4) (λ^6)+2 a d Z (β^4) (λ^6)+2 b (β^5) (λ^6)-2 a b (β^5) (λ^6)-2 d (β^5) (λ^6)+2 a d (β^5) (λ^6)-4 b Z (β^5) (λ^6)-2 a b Z (β^5) (λ^6)+4 d Z (β^5) (λ^6)+2 a d Z (β^5) (λ^6)-2 b (β^6) (λ^6)-4 a b (β^6) (λ^6)+2 d (β^6) (λ^6)+4 a d (β^6) (λ^6)+b Z (β^6) (λ^6)+2 a b Z (β^6) (λ^6)-d Z (β^6) (λ^6)-2 a d Z (β^6) (λ^6)+b (β^7) (λ^6)+2 a b (β^7) (λ^6)-d (β^7) (λ^6)-2 a d (β^7) (λ^6)-7 b (β^2) γ (λ^6)+6 a b (β^2) γ (λ^6)+(a^2) b (β^2) γ (λ^6)+7 d (β^2) γ (λ^6)-6 a d (β^2) γ (λ^6)-(a^2) d (β^2) γ (λ^6)+17 b (β^3) γ (λ^6)-6 a b (β^3) γ (λ^6)+(a^2) b (β^3) γ (λ^6)-17 d (β^3) γ (λ^6)+6 a d (β^3) γ (λ^6)-(a^2) d (β^3) γ (λ^6)+8 b Z (β^3) γ (λ^6)-10 a b Z (β^3) γ (λ^6)+2 (a^2) b Z (β^3) γ (λ^6)-8 d Z (β^3) γ (λ^6)+10 a d Z (β^3) γ (λ^6)-2 (a^2) d Z (β^3) γ (λ^6)-b (β^4) γ (λ^6)-25 a b (β^4) γ (λ^6)+(a^2) b (β^4) γ (λ^6)+d (β^4) γ (λ^6)+25 a d (β^4) γ (λ^6)-(a^2) d (β^4) γ (λ^6)-23 b Z (β^4) γ (λ^6)+14 a b Z (β^4) γ (λ^6)+23 d Z (β^4) γ (λ^6)-14 a d Z (β^4) γ (λ^6)-12 b (β^5) γ (λ^6)+16 a b (β^5) γ (λ^6)-(a^2) b (β^5) γ (λ^6)+12 d (β^5) γ (λ^6)-16 a d (β^5) γ (λ^6)+(a^2) d (β^5) γ (λ^6)+20 b Z (β^5) γ (λ^6)+7 a b Z (β^5) γ (λ^6)-2 (a^2) b Z (β^5) γ (λ^6)-20 d Z (β^5) γ (λ^6)-7 a d Z (β^5) γ (λ^6)+2 (a^2) d Z (β^5) γ (λ^6)+8 b (β^6) γ (λ^6)+19 a b (β^6) γ (λ^6)-2 (a^2) b (β^6) γ (λ^6)-8 d (β^6) γ (λ^6)-19 a d (β^6) γ (λ^6)+2 (a^2) d (β^6) γ (λ^6)-5 b Z (β^6) γ (λ^6)-11 a b Z (β^6) γ (λ^6)+5 d Z (β^6) γ (λ^6)+11 a d Z (β^6) γ (λ^6)-5 b (β^7) γ (λ^6)-10 a b (β^7) γ (λ^6)+5 d (β^7) γ (λ^6)+10 a d (β^7) γ (λ^6)+10 b (β^2) (γ^2) (λ^6)-9 a b (β^2) (γ^2) (λ^6)-(a^3) b (β^2) (γ^2) (λ^6)-10 d (β^2) (γ^2) (λ^6)+9 a d (β^2) (γ^2) (λ^6)+(a^3) d (β^2) (γ^2) (λ^6)+b Z (β^2) (γ^2) (λ^6)-3 a b Z (β^2) (γ^2) (λ^6)+3 (a^2) b Z (β^2) (γ^2) (λ^6)-(a^3) b Z (β^2) (γ^2) (λ^6)-d Z (β^2) (γ^2) (λ^6)+3 a d Z (β^2) (γ^2) (λ^6)-3 (a^2) d Z (β^2) (γ^2) (λ^6)+(a^3) d Z (β^2) (γ^2) (λ^6)-33 b (β^3) (γ^2) (λ^6)+12 a b (β^3) (γ^2) (λ^6)+5 (a^2) b (β^3) (γ^2) (λ^6)-2 (a^3) b (β^3) (γ^2) (λ^6)+33 d (β^3) (γ^2) (λ^6)-12 a d (β^3) (γ^2) (λ^6)-5 (a^2) d (β^3) (γ^2) (λ^6)+2 (a^3) d (β^3) (γ^2) (λ^6)-12 b Z (β^3) (γ^2) (λ^6)+17 a b Z (β^3) (γ^2) (λ^6)-4 (a^2) b Z (β^3) (γ^2) (λ^6)-(a^3) b Z (β^3) (γ^2) (λ^6)+12 d Z (β^3) (γ^2) (λ^6)-17 a d Z (β^3) (γ^2) (λ^6)+4 (a^2) d Z (β^3) (γ^2) (λ^6)+(a^3) d Z (β^3) (γ^2) (λ^6)+8 b (β^4) (γ^2) (λ^6)+33 a b (β^4) (γ^2) (λ^6)+3 (a^2) b (β^4) (γ^2) (λ^6)-(a^3) b (β^4) (γ^2) (λ^6)-8 d (β^4) (γ^2) (λ^6)-33 a d (β^4) (γ^2) (λ^6)-3 (a^2) d (β^4) (γ^2) (λ^6)+(a^3) d (β^4) (γ^2) (λ^6)+41 b Z (β^4) (γ^2) (λ^6)-34 a b Z (β^4) (γ^2) (λ^6)+2 (a^2) b Z (β^4) (γ^2) (λ^6)-41 d Z (β^4) (γ^2) (λ^6)+34 a d Z (β^4) (γ^2) (λ^6)-2 (a^2) d Z (β^4) (γ^2) (λ^6)+29 b (β^5) (γ^2) (λ^6)-44 a b (β^5) (γ^2) (λ^6)+6 (a^2) b (β^5) (γ^2) (λ^6)-29 d (β^5) (γ^2) (λ^6)+44 a d (β^5) (γ^2) (λ^6)-6 (a^2) d (β^5) (γ^2) (λ^6)-40 b Z (β^5) (γ^2) (λ^6)-7 a b Z (β^5) (γ^2) (λ^6)+8 (a^2) b Z (β^5) (γ^2) (λ^6)+40 d Z (β^5) (γ^2) (λ^6)+7 a d Z (β^5) (γ^2) (λ^6)-8 (a^2) d Z (β^5) (γ^2) (λ^6)-12 b (β^6) (γ^2) (λ^6)-36 a b (β^6) (γ^2) (λ^6)+8 (a^2) b (β^6) (γ^2) (λ^6)+12 d (β^6) (γ^2) (λ^6)+36 a d (β^6) (γ^2) (λ^6)-8 (a^2) d (β^6) (γ^2) (λ^6)+10 b Z (β^6) (γ^2) (λ^6)+24 a b Z (β^6) (γ^2) (λ^6)-10 d Z (β^6) (γ^2) (λ^6)-24 a d Z (β^6) (γ^2) (λ^6)+10 b (β^7) (γ^2) (λ^6)+20 a b (β^7) (γ^2) (λ^6)-10 d (β^7) (γ^2) (λ^6)-20 a d (β^7) (γ^2) (λ^6)-8 b (β^2) (γ^3) (λ^6)+11 a b (β^2) (γ^3) (λ^6)-6 (a^2) b (β^2) (γ^3) (λ^6)+3 (a^3) b (β^2) (γ^3) (λ^6)+8 d (β^2) (γ^3) (λ^6)-11 a d (β^2) (γ^3) (λ^6)+6 (a^2) d (β^2) (γ^3) (λ^6)-3 (a^3) d (β^2) (γ^3) (λ^6)-3 b Z (β^2) (γ^3) (λ^6)+9 a b Z (β^2) (γ^3) (λ^6)-9 (a^2) b Z (β^2) (γ^3) (λ^6)+3 (a^3) b Z (β^2) (γ^3) (λ^6)+3 d Z (β^2) (γ^3) (λ^6)-9 a d Z (β^2) (γ^3) (λ^6)+9 (a^2) d Z (β^2) (γ^3) (λ^6)-3 (a^3) d Z (β^2) (γ^3) (λ^6)+27 b (β^3) (γ^3) (λ^6)-21 (a^2) b (β^3) (γ^3) (λ^6)+6 (a^3) b (β^3) (γ^3) (λ^6)-27 d (β^3) (γ^3) (λ^6)+21 (a^2) d (β^3) (γ^3) (λ^6)-6 (a^3) d (β^3) (γ^3) (λ^6)+8 b Z (β^3) (γ^3) (λ^6)-11 a b Z (β^3) (γ^3) (λ^6)+3 (a^3) b Z (β^3) (γ^3) (λ^6)-8 d Z (β^3) (γ^3) (λ^6)+11 a d Z (β^3) (γ^3) (λ^6)-3 (a^3) d Z (β^3) (γ^3) (λ^6)-18 b (β^4) (γ^3) (λ^6)-9 a b (β^4) (γ^3) (λ^6)-15 (a^2) b (β^4) (γ^3) (λ^6)+3 (a^3) b (β^4) (γ^3) (λ^6)+18 d (β^4) (γ^3) (λ^6)+9 a d (β^4) (γ^3) (λ^6)+15 (a^2) d (β^4) (γ^3) (λ^6)-3 (a^3) d (β^4) (γ^3) (λ^6)-35 b Z (β^4) (γ^3) (λ^6)+38 a b Z (β^4) (γ^3) (λ^6)-6 (a^2) b Z (β^4) (γ^3) (λ^6)+35 d Z (β^4) (γ^3) (λ^6)-38 a d Z (β^4) (γ^3) (λ^6)+6 (a^2) d Z (β^4) (γ^3) (λ^6)-35 b (β^5) (γ^3) (λ^6)+56 a b (β^5) (γ^3) (λ^6)-12 (a^2) b (β^5) (γ^3) (λ^6)+35 d (β^5) (γ^3) (λ^6)-56 a d (β^5) (γ^3) (λ^6)+12 (a^2) d (β^5) (γ^3) (λ^6)+40 b Z (β^5) (γ^3) (λ^6)-a b Z (β^5) (γ^3) (λ^6)-12 (a^2) b Z (β^5) (γ^3) (λ^6)-40 d Z (β^5) (γ^3) (λ^6)+a d Z (β^5) (γ^3) (λ^6)+12 (a^2) d Z (β^5) (γ^3) (λ^6)+8 b (β^6) (γ^3) (λ^6)+34 a b (β^6) (γ^3) (λ^6)-12 (a^2) b (β^6) (γ^3) (λ^6)-8 d (β^6) (γ^3) (λ^6)-34 a d (β^6) (γ^3) (λ^6)+12 (a^2) d (β^6) (γ^3) (λ^6)-10 b Z (β^6) (γ^3) (λ^6)-26 a b Z (β^6) (γ^3) (λ^6)+10 d Z (β^6) (γ^3) (λ^6)+26 a d Z (β^6) (γ^3) (λ^6)-10 b (β^7) (γ^3) (λ^6)-20 a b (β^7) (γ^3) (λ^6)+10 d (β^7) (γ^3) (λ^6)+20 a d (β^7) (γ^3) (λ^6)+4 b (β^2) (γ^4) (λ^6)-9 a b (β^2) (γ^4) (λ^6)+8 (a^2) b (β^2) (γ^4) (λ^6)-3 (a^3) b (β^2) (γ^4) (λ^6)-4 d (β^2) (γ^4) (λ^6)+9 a d (β^2) (γ^4) (λ^6)-8 (a^2) d (β^2) (γ^4) (λ^6)+3 (a^3) d (β^2) (γ^4) (λ^6)+3 b Z (β^2) (γ^4) (λ^6)-9 a b Z (β^2) (γ^4) (λ^6)+9 (a^2) b Z (β^2) (γ^4) (λ^6)-3 (a^3) b Z (β^2) (γ^4) (λ^6)-3 d Z (β^2) (γ^4) (λ^6)+9 a d Z (β^2) (γ^4) (λ^6)-9 (a^2) d Z (β^2) (γ^4) (λ^6)+3 (a^3) d Z (β^2) (γ^4) (λ^6)-8 b (β^3) (γ^4) (λ^6)-12 a b (β^3) (γ^4) (λ^6)+23 (a^2) b (β^3) (γ^4) (λ^6)-6 (a^3) b (β^3) (γ^4) (λ^6)+8 d (β^3) (γ^4) (λ^6)+12 a d (β^3) (γ^4) (λ^6)-23 (a^2) d (β^3) (γ^4) (λ^6)+6 (a^3) d (β^3) (γ^4) (λ^6)-2 b Z (β^3) (γ^4) (λ^6)+a b Z (β^3) (γ^4) (λ^6)+4 (a^2) b Z (β^3) (γ^4) (λ^6)-3 (a^3) b Z (β^3) (γ^4) (λ^6)+2 d Z (β^3) (γ^4) (λ^6)-a d Z (β^3) (γ^4) (λ^6)-4 (a^2) d Z (β^3) (γ^4) (λ^6)+3 (a^3) d Z (β^3) (γ^4) (λ^6)+16 b (β^4) (γ^4) (λ^6)-11 a b (β^4) (γ^4) (λ^6)+17 (a^2) b (β^4) (γ^4) (λ^6)-3 (a^3) b (β^4) (γ^4) (λ^6)-16 d (β^4) (γ^4) (λ^6)+11 a d (β^4) (γ^4) (λ^6)-17 (a^2) d (β^4) (γ^4) (λ^6)+3 (a^3) d (β^4) (γ^4) (λ^6)+14 b Z (β^4) (γ^4) (λ^6)-20 a b Z (β^4) (γ^4) (λ^6)+6 (a^2) b Z (β^4) (γ^4) (λ^6)-14 d Z (β^4) (γ^4) (λ^6)+20 a d Z (β^4) (γ^4) (λ^6)-6 (a^2) d Z (β^4) (γ^4) (λ^6)+21 b (β^5) (γ^4) (λ^6)-34 a b (β^5) (γ^4) (λ^6)+10 (a^2) b (β^5) (γ^4) (λ^6)-21 d (β^5) (γ^4) (λ^6)+34 a d (β^5) (γ^4) (λ^6)-10 (a^2) d (β^5) (γ^4) (λ^6)-20 b Z (β^5) (γ^4) (λ^6)+5 a b Z (β^5) (γ^4) (λ^6)+8 (a^2) b Z (β^5) (γ^4) (λ^6)+20 d Z (β^5) (γ^4) (λ^6)-5 a d Z (β^5) (γ^4) (λ^6)-8 (a^2) d Z (β^5) (γ^4) (λ^6)-2 b (β^6) (γ^4) (λ^6)-16 a b (β^6) (γ^4) (λ^6)+8 (a^2) b (β^6) (γ^4) (λ^6)+2 d (β^6) (γ^4) (λ^6)+16 a d (β^6) (γ^4) (λ^6)-8 (a^2) d (β^6) (γ^4) (λ^6)+5 b Z (β^6) (γ^4) (λ^6)+14 a b Z (β^6) (γ^4) (λ^6)-5 d Z (β^6) (γ^4) (λ^6)-14 a d Z (β^6) (γ^4) (λ^6)+5 b (β^7) (γ^4) (λ^6)+10 a b (β^7) (γ^4) (λ^6)-5 d (β^7) (γ^4) (λ^6)-10 a d (β^7) (γ^4) (λ^6)-b (β^2) (γ^5) (λ^6)+3 a b (β^2) (γ^5) (λ^6)-3 (a^2) b (β^2) (γ^5) (λ^6)+(a^3) b (β^2) (γ^5) (λ^6)+d (β^2) (γ^5) (λ^6)-3 a d (β^2) (γ^5) (λ^6)+3 (a^2) d (β^2) (γ^5) (λ^6)-(a^3) d (β^2) (γ^5) (λ^6)-b Z (β^2) (γ^5) (λ^6)+3 a b Z (β^2) (γ^5) (λ^6)-3 (a^2) b Z (β^2) (γ^5) (λ^6)+(a^3) b Z (β^2) (γ^5) (λ^6)+d Z (β^2) (γ^5) (λ^6)-3 a d Z (β^2) (γ^5) (λ^6)+3 (a^2) d Z (β^2) (γ^5) (λ^6)-(a^3) d Z (β^2) (γ^5) (λ^6)+6 a b (β^3) (γ^5) (λ^6)-8 (a^2) b (β^3) (γ^5) (λ^6)+2 (a^3) b (β^3) (γ^5) (λ^6)-6 a d (β^3) (γ^5) (λ^6)+8 (a^2) d (β^3) (γ^5) (λ^6)-2 (a^3) d (β^3) (γ^5) (λ^6)+a b Z (β^3) (γ^5) (λ^6)-2 (a^2) b Z (β^3) (γ^5) (λ^6)+(a^3) b Z (β^3) (γ^5) (λ^6)-a d Z (β^3) (γ^5) (λ^6)+2 (a^2) d Z (β^3) (γ^5) (λ^6)-(a^3) d Z (β^3) (γ^5) (λ^6)-5 b (β^4) (γ^5) (λ^6)+6 a b (β^4) (γ^5) (λ^6)-6 (a^2) b (β^4) (γ^5) (λ^6)+(a^3) b (β^4) (γ^5) (λ^6)+5 d (β^4) (γ^5) (λ^6)-6 a d (β^4) (γ^5) (λ^6)+6 (a^2) d (β^4) (γ^5) (λ^6)-(a^3) d (β^4) (γ^5) (λ^6)-2 b Z (β^4) (γ^5) (λ^6)+4 a b Z (β^4) (γ^5) (λ^6)-2 (a^2) b Z (β^4) (γ^5) (λ^6)+2 d Z (β^4) (γ^5) (λ^6)-4 a d Z (β^4) (γ^5) (λ^6)+2 (a^2) d Z (β^4) (γ^5) (λ^6)-5 b (β^5) (γ^5) (λ^6)+8 a b (β^5) (γ^5) (λ^6)-3 (a^2) b (β^5) (γ^5) (λ^6)+5 d (β^5) (γ^5) (λ^6)-8 a d (β^5) (γ^5) (λ^6)+3 (a^2) d (β^5) (γ^5) (λ^6)+4 b Z (β^5) (γ^5) (λ^6)-2 a b Z (β^5) (γ^5) (λ^6)-2 (a^2) b Z (β^5) (γ^5) (λ^6)-4 d Z (β^5) (γ^5) (λ^6)+2 a d Z (β^5) (γ^5) (λ^6)+2 (a^2) d Z (β^5) (γ^5) (λ^6)+3 a b (β^6) (γ^5) (λ^6)-2 (a^2) b (β^6) (γ^5) (λ^6)-3 a d (β^6) (γ^5) (λ^6)+2 (a^2) d (β^6) (γ^5) (λ^6)-b Z (β^6) (γ^5) (λ^6)-3 a b Z (β^6) (γ^5) (λ^6)+d Z (β^6) (γ^5) (λ^6)+3 a d Z (β^6) (γ^5) (λ^6)-b (β^7) (γ^5) (λ^6)-2 a b (β^7) (γ^5) (λ^6)+d (β^7) (γ^5) (λ^6)+2 a d (β^7) (γ^5) (λ^6)+b (β^3) (λ^7)-a b (β^3) (λ^7)-d (β^3) (λ^7)+a d (β^3) (λ^7)-a b (β^4) (λ^7)+a d (β^4) (λ^7)-b Z (β^4) (λ^7)+a b Z (β^4) (λ^7)+d Z (β^4) (λ^7)-a d Z (β^4) (λ^7)-b (β^5) (λ^7)+2 a b (β^5) (λ^7)+d (β^5) (λ^7)-2 a d (β^5) (λ^7)+b Z (β^5) (λ^7)-d Z (β^5) (λ^7)+a b (β^6) (λ^7)-a d (β^6) (λ^7)-a b Z (β^6) (λ^7)+a d Z (β^6) (λ^7)-a b (β^7) (λ^7)+a d (β^7) (λ^7)-4 b (β^3) γ (λ^7)+3 a b (β^3) γ (λ^7)+(a^2) b (β^3) γ (λ^7)+4 d (β^3) γ (λ^7)-3 a d (β^3) γ (λ^7)-(a^2) d (β^3) γ (λ^7)+b (β^4) γ (λ^7)+3 a b (β^4) γ (λ^7)+(a^2) b (β^4) γ (λ^7)-d (β^4) γ (λ^7)-3 a d (β^4) γ (λ^7)-(a^2) d (β^4) γ (λ^7)+4 b Z (β^4) γ (λ^7)-4 a b Z (β^4) γ (λ^7)-4 d Z (β^4) γ (λ^7)+4 a d Z (β^4) γ (λ^7)+5 b (β^5) γ (λ^7)-9 a b (β^5) γ (λ^7)-5 d (β^5) γ (λ^7)+9 a d (β^5) γ (λ^7)-5 b Z (β^5) γ (λ^7)+a b Z (β^5) γ (λ^7)+5 d Z (β^5) γ (λ^7)-a d Z (β^5) γ (λ^7)-4 a b (β^6) γ (λ^7)+4 a d (β^6) γ (λ^7)+5 a b Z (β^6) γ (λ^7)-5 a d Z (β^6) γ (λ^7)+5 a b (β^7) γ (λ^7)-5 a d (β^7) γ (λ^7)+6 b (β^3) (γ^2) (λ^7)-2 a b (β^3) (γ^2) (λ^7)-4 (a^2) b (β^3) (γ^2) (λ^7)-6 d (β^3) (γ^2) (λ^7)+2 a d (β^3) (γ^2) (λ^7)+4 (a^2) d (β^3) (γ^2) (λ^7)-4 b (β^4) (γ^2) (λ^7)-2 a b (β^4) (γ^2) (λ^7)-4 (a^2) b (β^4) (γ^2) (λ^7)+4 d (β^4) (γ^2) (λ^7)+2 a d (β^4) (γ^2) (λ^7)+4 (a^2) d (β^4) (γ^2) (λ^7)-6 b Z (β^4) (γ^2) (λ^7)+6 a b Z (β^4) (γ^2) (λ^7)+6 d Z (β^4) (γ^2) (λ^7)-6 a d Z (β^4) (γ^2) (λ^7)-10 b (β^5) (γ^2) (λ^7)+16 a b (β^5) (γ^2) (λ^7)+10 d (β^5) (γ^2) (λ^7)-16 a d (β^5) (γ^2) (λ^7)+10 b Z (β^5) (γ^2) (λ^7)-4 a b Z (β^5) (γ^2) (λ^7)-10 d Z (β^5) (γ^2) (λ^7)+4 a d Z (β^5) (γ^2) (λ^7)+6 a b (β^6) (γ^2) (λ^7)-6 a d (β^6) (γ^2) (λ^7)-10 a b Z (β^6) (γ^2) (λ^7)+10 a d Z (β^6) (γ^2) (λ^7)-10 a b (β^7) (γ^2) (λ^7)+10 a d (β^7) (γ^2) (λ^7)-4 b (β^3) (γ^3) (λ^7)-2 a b (β^3) (γ^3) (λ^7)+6 (a^2) b (β^3) (γ^3) (λ^7)+4 d (β^3) (γ^3) (λ^7)+2 a d (β^3) (γ^3) (λ^7)-6 (a^2) d (β^3) 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(λ^5)-3 (a^3) (β^5) (γ^3) (λ^5)+42 (β^6) (γ^3) (λ^5)+32 a (β^6) (γ^3) (λ^5)-12 (a^2) (β^6) (γ^3) (λ^5)-20 (β^7) (γ^3) (λ^5)-10 a (β^7) (γ^3) (λ^5)+10 (β^2) (γ^4) (λ^5)-18 a (β^2) (γ^4) (λ^5)+13 (a^2) (β^2) (γ^4) (λ^5)-5 (a^3) (β^2) (γ^4) (λ^5)-27 (β^3) (γ^4) (λ^5)+9 a (β^3) (γ^4) (λ^5)+12 (a^2) (β^3) (γ^4) (λ^5)-5 (a^3) (β^3) (γ^4) (λ^5)+18 (β^4) (γ^4) (λ^5)+11 a (β^4) (γ^4) (λ^5)-4 (a^2) (β^4) (γ^4) (λ^5)+3 (a^3) (β^4) (γ^4) (λ^5)+27 (β^5) (γ^4) (λ^5)-34 a (β^5) (γ^4) (λ^5)+5 (a^2) (β^5) (γ^4) (λ^5)+3 (a^3) (β^5) (γ^4) (λ^5)-18 (β^6) (γ^4) (λ^5)-13 a (β^6) (γ^4) (λ^5)+8 (a^2) (β^6) (γ^4) (λ^5)+10 (β^7) (γ^4) (λ^5)+5 a (β^7) (γ^4) (λ^5)-2 (β^2) (γ^5) (λ^5)+6 a (β^2) (γ^5) (λ^5)-6 (a^2) (β^2) (γ^5) (λ^5)+2 (a^3) (β^2) (γ^5) (λ^5)+3 (β^3) (γ^5) (λ^5)+2 a (β^3) (γ^5) (λ^5)-7 (a^2) (β^3) (γ^5) (λ^5)+2 (a^3) (β^3) (γ^5) (λ^5)-6 (β^4) (γ^5) (λ^5)+2 a (β^4) (γ^5) (λ^5)-(a^2) (β^4) (γ^5) (λ^5)-(a^3) (β^4) (γ^5) (λ^5)-6 (β^5) (γ^5) (λ^5)+9 a (β^5) (γ^5) (λ^5)-2 (a^2) (β^5) (γ^5) (λ^5)-(a^3) (β^5) (γ^5) (λ^5)+3 (β^6) (γ^5) (λ^5)+2 a (β^6) (γ^5) (λ^5)-2 (a^2) (β^6) (γ^5) (λ^5)-2 (β^7) (γ^5) (λ^5)-a (β^7) (γ^5) (λ^5)-2 (β^2) (λ^6)+2 a (β^2) (λ^6)+3 (β^3) (λ^6)-6 a (β^4) (λ^6)-2 (β^5) (λ^6)+2 a (β^5) (λ^6)+2 (β^6) (λ^6)+4 a (β^6) (λ^6)-(β^7) (λ^6)-2 a (β^7) (λ^6)+7 (β^2) γ (λ^6)-6 a (β^2) γ (λ^6)-(a^2) (β^2) γ (λ^6)-17 (β^3) γ (λ^6)+6 a (β^3) γ (λ^6)-(a^2) (β^3) γ (λ^6)+(β^4) γ (λ^6)+25 a (β^4) γ (λ^6)-(a^2) (β^4) γ (λ^6)+12 (β^5) γ (λ^6)-16 a (β^5) γ (λ^6)+(a^2) (β^5) γ (λ^6)-8 (β^6) γ (λ^6)-19 a (β^6) γ (λ^6)+2 (a^2) (β^6) γ (λ^6)+5 (β^7) γ (λ^6)+10 a (β^7) γ (λ^6)-10 (β^2) (γ^2) (λ^6)+9 a (β^2) (γ^2) (λ^6)+(a^3) (β^2) (γ^2) (λ^6)+33 (β^3) (γ^2) (λ^6)-12 a (β^3) (γ^2) (λ^6)-5 (a^2) (β^3) (γ^2) (λ^6)+2 (a^3) (β^3) (γ^2) (λ^6)-8 (β^4) (γ^2) (λ^6)-33 a (β^4) (γ^2) (λ^6)-3 (a^2) (β^4) (γ^2) (λ^6)+(a^3) (β^4) (γ^2) (λ^6)-29 (β^5) (γ^2) (λ^6)+44 a (β^5) (γ^2) (λ^6)-6 (a^2) (β^5) (γ^2) (λ^6)+12 (β^6) (γ^2) (λ^6)+36 a (β^6) (γ^2) (λ^6)-8 (a^2) (β^6) (γ^2) (λ^6)-10 (β^7) (γ^2) (λ^6)-20 a (β^7) (γ^2) (λ^6)+8 (β^2) (γ^3) (λ^6)-11 a (β^2) (γ^3) (λ^6)+6 (a^2) (β^2) (γ^3) (λ^6)-3 (a^3) (β^2) (γ^3) (λ^6)-27 (β^3) (γ^3) (λ^6)+21 (a^2) (β^3) (γ^3) (λ^6)-6 (a^3) (β^3) (γ^3) (λ^6)+18 (β^4) (γ^3) (λ^6)+9 a (β^4) (γ^3) (λ^6)+15 (a^2) (β^4) (γ^3) (λ^6)-3 (a^3) (β^4) (γ^3) (λ^6)+35 (β^5) (γ^3) (λ^6)-56 a (β^5) (γ^3) (λ^6)+12 (a^2) (β^5) (γ^3) (λ^6)-8 (β^6) (γ^3) (λ^6)-34 a (β^6) (γ^3) (λ^6)+12 (a^2) (β^6) (γ^3) (λ^6)+10 (β^7) (γ^3) (λ^6)+20 a (β^7) (γ^3) (λ^6)-4 (β^2) (γ^4) (λ^6)+9 a (β^2) (γ^4) (λ^6)-8 (a^2) (β^2) (γ^4) (λ^6)+3 (a^3) (β^2) (γ^4) (λ^6)+8 (β^3) (γ^4) (λ^6)+12 a (β^3) (γ^4) (λ^6)-23 (a^2) (β^3) (γ^4) (λ^6)+6 (a^3) (β^3) (γ^4) (λ^6)-16 (β^4) (γ^4) (λ^6)+11 a (β^4) (γ^4) (λ^6)-17 (a^2) (β^4) (γ^4) (λ^6)+3 (a^3) (β^4) (γ^4) (λ^6)-21 (β^5) (γ^4) (λ^6)+34 a (β^5) (γ^4) (λ^6)-10 (a^2) (β^5) (γ^4) (λ^6)+2 (β^6) (γ^4) (λ^6)+16 a (β^6) (γ^4) (λ^6)-8 (a^2) (β^6) (γ^4) (λ^6)-5 (β^7) (γ^4) (λ^6)-10 a (β^7) (γ^4) (λ^6)+(β^2) (γ^5) (λ^6)-3 a (β^2) (γ^5) (λ^6)+3 (a^2) (β^2) (γ^5) (λ^6)-(a^3) (β^2) (γ^5) (λ^6)-6 a (β^3) (γ^5) (λ^6)+8 (a^2) (β^3) (γ^5) (λ^6)-2 (a^3) (β^3) (γ^5) (λ^6)+5 (β^4) (γ^5) (λ^6)-6 a (β^4) (γ^5) (λ^6)+6 (a^2) (β^4) (γ^5) (λ^6)-(a^3) (β^4) (γ^5) (λ^6)+5 (β^5) (γ^5) (λ^6)-8 a (β^5) (γ^5) (λ^6)+3 (a^2) (β^5) (γ^5) (λ^6)-3 a (β^6) (γ^5) (λ^6)+2 (a^2) (β^6) (γ^5) (λ^6)+(β^7) (γ^5) (λ^6)+2 a (β^7) (γ^5) (λ^6)-(β^3) (λ^7)+a (β^3) (λ^7)+a (β^4) (λ^7)+(β^5) (λ^7)-2 a (β^5) (λ^7)-a (β^6) (λ^7)+a (β^7) (λ^7)+4 (β^3) γ (λ^7)-3 a (β^3) γ (λ^7)-(a^2) (β^3) γ (λ^7)-(β^4) γ (λ^7)-3 a (β^4) γ (λ^7)-(a^2) (β^4) γ (λ^7)-5 (β^5) γ (λ^7)+9 a (β^5) γ (λ^7)+4 a (β^6) γ (λ^7)-5 a (β^7) γ (λ^7)-6 (β^3) (γ^2) (λ^7)+2 a (β^3) (γ^2) (λ^7)+4 (a^2) (β^3) (γ^2) (λ^7)+4 (β^4) (γ^2) (λ^7)+2 a (β^4) (γ^2) (λ^7)+4 (a^2) (β^4) (γ^2) (λ^7)+10 (β^5) (γ^2) (λ^7)-16 a (β^5) (γ^2) (λ^7)-6 a (β^6) (γ^2) (λ^7)+10 a (β^7) (γ^2) (λ^7)+4 (β^3) (γ^3) (λ^7)+2 a (β^3) (γ^3) (λ^7)-6 (a^2) (β^3) (γ^3) (λ^7)-6 (β^4) (γ^3) (λ^7)+2 a (β^4) (γ^3) (λ^7)-6 (a^2) (β^4) (γ^3) (λ^7)-10 (β^5) (γ^3) (λ^7)+14 a (β^5) (γ^3) (λ^7)+4 a (β^6) (γ^3) (λ^7)-10 a (β^7) (γ^3) (λ^7)-(β^3) (γ^4) (λ^7)-3 a (β^3) (γ^4) (λ^7)+4 (a^2) (β^3) (γ^4) (λ^7)+4 (β^4) (γ^4) (λ^7)-3 a (β^4) (γ^4) (λ^7)+4 (a^2) (β^4) (γ^4) (λ^7)+5 (β^5) (γ^4) (λ^7)-6 a (β^5) (γ^4) (λ^7)-a (β^6) (γ^4) (λ^7)+5 a (β^7) (γ^4) (λ^7)+a (β^3) (γ^5) (λ^7)-(a^2) (β^3) (γ^5) (λ^7)-(β^4) (γ^5) (λ^7)+a (β^4) (γ^5) (λ^7)-(a^2) (β^4) (γ^5) (λ^7)-(β^5) (γ^5) (λ^7)+a (β^5) (γ^5) (λ^7)-a (β^7) (γ^5) (λ^7)]+Z (FullSimplify[(β^2) γ-(β^3) γ-(β^2) (γ^2)+(β^3) (γ^2)+(β^2) λ-(β^3) λ-4 (β^2) γ λ+8 (β^3) γ λ-3 (β^4) γ λ+4 (β^2) (γ^2) λ-3 a (β^2) (γ^2) λ-11 (β^3) (γ^2) λ+3 a (β^3) (γ^2) λ+6 (β^4) (γ^2) λ-3 (β^2) (γ^3) λ+3 a (β^2) (γ^3) λ+4 (β^3) (γ^3) λ-3 a (β^3) (γ^3) λ-3 (β^4) (γ^3) λ-3 (β^2) (λ^2)+6 (β^3) (λ^2)-3 (β^4) (λ^2)+10 (β^2) γ (λ^2)-4 a (β^2) γ (λ^2)-27 (β^3) γ (λ^2)+3 a (β^3) γ (λ^2)+20 (β^4) γ (λ^2)+a (β^4) γ (λ^2)-3 (β^5) γ (λ^2)-13 (β^2) (γ^2) (λ^2)+13 a (β^2) (γ^2) (λ^2)+37 (β^3) (γ^2) (λ^2)-18 a (β^3) (γ^2) (λ^2)-37 (β^4) (γ^2) (λ^2)+4 a (β^4) (γ^2) (λ^2)+9 (β^5) (γ^2) (λ^2)+8 (β^2) (γ^3) (λ^2)-11 a (β^2) (γ^3) (λ^2)+3 (a^2) (β^2) (γ^3) (λ^2)-21 (β^3) (γ^3) (λ^2)+23 a (β^3) (γ^3) (λ^2)-3 (a^2) (β^3) (γ^3) (λ^2)+26 (β^4) (γ^3) (λ^2)-11 a (β^4) (γ^3) (λ^2)-9 (β^5) (γ^3) (λ^2)-3 (β^2) (γ^4) (λ^2)+6 a (β^2) (γ^4) (λ^2)-3 (a^2) (β^2) (γ^4) (λ^2)+5 (β^3) (γ^4) (λ^2)-8 a (β^3) (γ^4) (λ^2)+3 (a^2) (β^3) (γ^4) (λ^2)-6 (β^4) (γ^4) (λ^2)+6 a (β^4) (γ^4) (λ^2)+3 (β^5) (γ^4) (λ^2)+4 (β^2) (λ^3)-a (β^2) (λ^3)-12 (β^3) (λ^3)+11 (β^4) (λ^3)+a (β^4) (λ^3)-3 (β^5) (λ^3)-14 (β^2) γ (λ^3)+10 a (β^2) γ (λ^3)+49 (β^3) γ (λ^3)-15 a (β^3) γ (λ^3)-55 (β^4) γ (λ^3)+a (β^4) γ (λ^3)+20 (β^5) γ (λ^3)+2 a (β^5) γ (λ^3)-(β^6) γ (λ^3)+19 (β^2) (γ^2) (λ^3)-24 a (β^2) (γ^2) (λ^3)+5 (a^2) (β^2) (γ^2) (λ^3)-74 (β^3) (γ^2) (λ^3)+55 a (β^3) (γ^2) (λ^3)-3 (a^2) (β^3) (γ^2) (λ^3)+98 (β^4) (γ^2) (λ^3)-24 a (β^4) (γ^2) (λ^3)-2 (a^2) (β^4) (γ^2) (λ^3)-45 (β^5) (γ^2) (λ^3)-3 a (β^5) (γ^2) (λ^3)+4 (β^6) (γ^2) (λ^3)-16 (β^2) (γ^3) (λ^3)+30 a (β^2) (γ^3) (λ^3)-14 (a^2) (β^2) (γ^3) (λ^3)+50 (β^3) (γ^3) (λ^3)-62 a (β^3) (γ^3) (λ^3)+12 (a^2) (β^3) (γ^3) (λ^3)-78 (β^4) (γ^3) (λ^3)+47 a (β^4) (γ^3) (λ^3)+(a^2) (β^4) (γ^3) (λ^3)+45 (β^5) (γ^3) (λ^3)-3 a (β^5) (γ^3) (λ^3)-6 (β^6) (γ^3) (λ^3)+8 (β^2) (γ^4) (λ^3)-17 a (β^2) (γ^4) (λ^3)+10 (a^2) (β^2) (γ^4) (λ^3)-(a^3) (β^2) (γ^4) (λ^3)-15 (β^3) (γ^4) (λ^3)+27 a (β^3) (γ^4) (λ^3)-13 (a^2) (β^3) (γ^4) (λ^3)+(a^3) (β^3) (γ^4) (λ^3)+27 (β^4) (γ^4) (λ^3)-31 a (β^4) (γ^4) (λ^3)+4 (a^2) (β^4) (γ^4) (λ^3)-20 (β^5) (γ^4) (λ^3)+7 a (β^5) (γ^4) (λ^3)+4 (β^6) (γ^4) (λ^3)-(β^2) (γ^5) (λ^3)+3 a (β^2) (γ^5) (λ^3)-3 (a^2) (β^2) (γ^5) (λ^3)+(a^3) (β^2) (γ^5) (λ^3)+2 (β^3) (γ^5) (λ^3)-5 a (β^3) (γ^5) (λ^3)+4 (a^2) (β^3) (γ^5) (λ^3)-(a^3) (β^3) (γ^5) (λ^3)-3 (β^4) (γ^5) (λ^3)+6 a (β^4) (γ^5) (λ^3)-3 (a^2) (β^4) (γ^5) (λ^3)+3 (β^5) (γ^5) (λ^3)-3 a (β^5) (γ^5) (λ^3)-(β^6) (γ^5) (λ^3)-3 (β^2) (λ^4)+2 a (β^2) (λ^4)+12 (β^3) (λ^4)-2 a (β^3) (λ^4)-16 (β^4) (λ^4)-2 a (β^4) (λ^4)+8 (β^5) (λ^4)+2 a (β^5) (λ^4)-(β^6) (λ^4)+11 (β^2) γ (λ^4)-12 a (β^2) γ (λ^4)+2 (a^2) (β^2) γ (λ^4)-50 (β^3) γ (λ^4)+27 a (β^3) γ (λ^4)+75 (β^4) γ (λ^4)-7 a (β^4) γ (λ^4)-2 (a^2) (β^4) γ (λ^4)-43 (β^5) γ (λ^4)-9 a (β^5) γ (λ^4)+7 (β^6) γ (λ^4)+a (β^6) γ (λ^4)-18 (β^2) (γ^2) (λ^4)+30 a (β^2) (γ^2) (λ^4)-12 (a^2) (β^2) (γ^2) (λ^4)+78 (β^3) (γ^2) (λ^4)-73 a (β^3) (γ^2) (λ^4)+8 (a^2) (β^3) (γ^2) (λ^4)-135 (β^4) (γ^2) (λ^4)+52 a (β^4) (γ^2) (λ^4)+5 (a^2) (β^4) (γ^2) (λ^4)+89 (β^5) (γ^2) (λ^4)+9 a (β^5) (γ^2) (λ^4)-2 (a^2) (β^5) (γ^2) (λ^4)-18 (β^6) (γ^2) (λ^4)-4 a (β^6) (γ^2) (λ^4)+17 (β^2) (γ^3) (λ^4)-36 a (β^2) (γ^3) (λ^4)+21 (a^2) (β^2) (γ^3) (λ^4)-2 (a^3) (β^2) (γ^3) (λ^4)-58 (β^3) (γ^3) (λ^4)+83 a (β^3) (γ^3) (λ^4)-26 (a^2) (β^3) (γ^3) (λ^4)+(a^3) (β^3) (γ^3) (λ^4)+116 (β^4) (γ^3) (λ^4)-88 a (β^4) (γ^3) (λ^4)+(a^2) (β^4) (γ^3) (λ^4)+(a^3) (β^4) (γ^3) (λ^4)-89 (β^5) (γ^3) (λ^4)+7 a (β^5) (γ^3) (λ^4)+6 (a^2) (β^5) (γ^3) (λ^4)+22 (β^6) (γ^3) (λ^4)+6 a (β^6) (γ^3) (λ^4)-10 (β^2) (γ^4) (λ^4)+25 a (β^2) (γ^4) (λ^4)-20 (a^2) (β^2) (γ^4) (λ^4)+5 (a^3) (β^2) (γ^4) (λ^4)+22 (β^3) (γ^4) (λ^4)-44 a (β^3) (γ^4) (λ^4)+24 (a^2) (β^3) (γ^4) (λ^4)-2 (a^3) (β^3) (γ^4) (λ^4)-47 (β^4) (γ^4) (λ^4)+58 a (β^4) (γ^4) (λ^4)-9 (a^2) (β^4) (γ^4) (λ^4)-2 (a^3) (β^4) (γ^4) (λ^4)+43 (β^5) (γ^4) (λ^4)-15 a (β^5) (γ^4) (λ^4)-6 (a^2) (β^5) (γ^4) (λ^4)-13 (β^6) (γ^4) (λ^4)-4 a (β^6) (γ^4) (λ^4)+3 (β^2) (γ^5) (λ^4)-9 a (β^2) (γ^5) (λ^4)+9 (a^2) (β^2) (γ^5) (λ^4)-3 (a^3) (β^2) (γ^5) (λ^4)-4 (β^3) (γ^5) (λ^4)+9 a (β^3) (γ^5) (λ^4)-6 (a^2) (β^3) (γ^5) (λ^4)+(a^3) (β^3) (γ^5) (λ^4)+7 (β^4) (γ^5) (λ^4)-13 a (β^4) (γ^5) (λ^4)+5 (a^2) (β^4) (γ^5) (λ^4)+(a^3) (β^4) (γ^5) (λ^4)-8 (β^5) (γ^5) (λ^4)+6 a (β^5) (γ^5) (λ^4)+2 (a^2) (β^5) (γ^5) (λ^4)+3 (β^6) (γ^5) (λ^4)+a (β^6) (γ^5) (λ^4)+(β^2) (λ^5)-a (β^2) (λ^5)-7 (β^3) (λ^5)+4 a (β^3) (λ^5)+12 (β^4) (λ^5)-8 (β^5) (λ^5)-4 a (β^5) (λ^5)+2 (β^6) (λ^5)+a (β^6) (λ^5)-4 (β^2) γ (λ^5)+6 a (β^2) γ (λ^5)-2 (a^2) (β^2) γ (λ^5)+29 (β^3) γ (λ^5)-25 a (β^3) γ (λ^5)+2 (a^2) (β^3) γ (λ^5)-56 (β^4) γ (λ^5)+15 a (β^4) γ (λ^5)+2 (a^2) (β^4) γ (λ^5)+41 (β^5) γ (λ^5)+15 a (β^5) γ (λ^5)-2 (a^2) (β^5) γ (λ^5)-11 (β^6) γ (λ^5)-7 a (β^6) γ (λ^5)+7 (β^2) (γ^2) (λ^5)-14 a (β^2) (γ^2) (λ^5)+8 (a^2) (β^2) (γ^2) (λ^5)-(a^3) (β^2) (γ^2) (λ^5)-47 (β^3) (γ^2) (λ^5)+58 a (β^3) (γ^2) (λ^5)-14 (a^2) (β^3) (γ^2) (λ^5)+102 (β^4) (γ^2) (λ^5)-57 a (β^4) (γ^2) (λ^5)-4 (a^2) (β^4) (γ^2) (λ^5)+(a^3) (β^4) (γ^2) (λ^5)-83 (β^5) (γ^2) (λ^5)-17 a (β^5) (γ^2) (λ^5)+10 (a^2) (β^5) (γ^2) (λ^5)+24 (β^6) (γ^2) (λ^5)+18 a (β^6) (γ^2) (λ^5)-9 (β^2) (γ^3) (λ^5)+23 a (β^2) (γ^3) (λ^5)-19 (a^2) (β^2) (γ^3) (λ^5)+5 (a^3) (β^2) (γ^3) (λ^5)+37 (β^3) (γ^3) (λ^5)-60 a (β^3) (γ^3) (λ^5)+22 (a^2) (β^3) (γ^3) (λ^5)+(a^3) (β^3) (γ^3) (λ^5)-90 (β^4) (γ^3) (λ^5)+80 a (β^4) (γ^3) (λ^5)-2 (a^2) (β^4) (γ^3) (λ^5)-3 (a^3) (β^4) (γ^3) (λ^5)+83 (β^5) (γ^3) (λ^5)+a (β^5) (γ^3) (λ^5)-18 (a^2) (β^5) (γ^3) (λ^5)-26 (β^6) (γ^3) (λ^5)-22 a (β^6) (γ^3) (λ^5)+8 (β^2) (γ^4) (λ^5)-23 a (β^2) (γ^4) (λ^5)+22 (a^2) (β^2) (γ^4) (λ^5)-7 (a^3) (β^2) (γ^4) (λ^5)-14 (β^3) (γ^4) (λ^5)+26 a (β^3) (γ^4) (λ^5)-10 (a^2) (β^3) (γ^4) (λ^5)-2 (a^3) (β^3) (γ^4) (λ^5)+38 (β^4) (γ^4) (λ^5)-49 a (β^4) (γ^4) (λ^5)+8 (a^2) (β^4) (γ^4) (λ^5)+3 (a^3) (β^4) (γ^4) (λ^5)-41 (β^5) (γ^4) (λ^5)+9 a (β^5) (γ^4) (λ^5)+14 (a^2) (β^5) (γ^4) (λ^5)+14 (β^6) (γ^4) (λ^5)+13 a (β^6) (γ^4) (λ^5)-3 (β^2) (γ^5) (λ^5)+9 a (β^2) (γ^5) (λ^5)-9 (a^2) (β^2) (γ^5) (λ^5)+3 (a^3) (β^2) (γ^5) (λ^5)+2 (β^3) (γ^5) (λ^5)-3 a (β^3) (γ^5) (λ^5)+(a^3) (β^3) (γ^5) (λ^5)-6 (β^4) (γ^5) (λ^5)+11 a (β^4) (γ^5) (λ^5)-4 (a^2) (β^4) (γ^5) (λ^5)-(a^3) (β^4) (γ^5) (λ^5)+8 (β^5) (γ^5) (λ^5)-4 a (β^5) (γ^5) (λ^5)-4 (a^2) (β^5) (γ^5) (λ^5)-3 (β^6) (γ^5) (λ^5)-3 a (β^6) (γ^5) (λ^5)+2 (β^3) (λ^6)-2 a (β^3) (λ^6)-5 (β^4) (λ^6)+2 a (β^4) (λ^6)+4 (β^5) (λ^6)+2 a (β^5) (λ^6)-(β^6) (λ^6)-2 a (β^6) (λ^6)-8 (β^3) γ (λ^6)+10 a (β^3) γ (λ^6)-2 (a^2) (β^3) γ (λ^6)+23 (β^4) γ (λ^6)-14 a (β^4) γ (λ^6)-20 (β^5) γ (λ^6)-7 a (β^5) γ (λ^6)+2 (a^2) (β^5) γ (λ^6)+5 (β^6) γ (λ^6)+11 a (β^6) γ (λ^6)-(β^2) (γ^2) (λ^6)+3 a (β^2) (γ^2) (λ^6)-3 (a^2) (β^2) (γ^2) (λ^6)+(a^3) (β^2) (γ^2) (λ^6)+12 (β^3) (γ^2) (λ^6)-17 a (β^3) (γ^2) (λ^6)+4 (a^2) (β^3) (γ^2) (λ^6)+(a^3) (β^3) (γ^2) (λ^6)-41 (β^4) (γ^2) (λ^6)+34 a (β^4) (γ^2) (λ^6)-2 (a^2) (β^4) (γ^2) (λ^6)+40 (β^5) (γ^2) (λ^6)+7 a (β^5) (γ^2) (λ^6)-8 (a^2) (β^5) (γ^2) (λ^6)-10 (β^6) (γ^2) (λ^6)-24 a (β^6) (γ^2) (λ^6)+3 (β^2) (γ^3) (λ^6)-9 a (β^2) (γ^3) (λ^6)+9 (a^2) (β^2) (γ^3) (λ^6)-3 (a^3) (β^2) (γ^3) (λ^6)-8 (β^3) (γ^3) (λ^6)+11 a (β^3) (γ^3) (λ^6)-3 (a^3) (β^3) (γ^3) (λ^6)+35 (β^4) (γ^3) (λ^6)-38 a (β^4) (γ^3) (λ^6)+6 (a^2) (β^4) (γ^3) (λ^6)-40 (β^5) (γ^3) (λ^6)+a (β^5) (γ^3) (λ^6)+12 (a^2) (β^5) (γ^3) (λ^6)+10 (β^6) (γ^3) (λ^6)+26 a (β^6) (γ^3) (λ^6)-3 (β^2) (γ^4) (λ^6)+9 a (β^2) (γ^4) (λ^6)-9 (a^2) (β^2) (γ^4) (λ^6)+3 (a^3) (β^2) (γ^4) (λ^6)+2 (β^3) (γ^4) (λ^6)-a (β^3) (γ^4) (λ^6)-4 (a^2) (β^3) (γ^4) (λ^6)+3 (a^3) (β^3) (γ^4) (λ^6)-14 (β^4) (γ^4) (λ^6)+20 a (β^4) (γ^4) (λ^6)-6 (a^2) (β^4) (γ^4) (λ^6)+20 (β^5) (γ^4) (λ^6)-5 a (β^5) (γ^4) (λ^6)-8 (a^2) (β^5) (γ^4) (λ^6)-5 (β^6) (γ^4) (λ^6)-14 a (β^6) (γ^4) (λ^6)+(β^2) (γ^5) (λ^6)-3 a (β^2) (γ^5) (λ^6)+3 (a^2) (β^2) (γ^5) (λ^6)-(a^3) (β^2) (γ^5) (λ^6)-a (β^3) (γ^5) (λ^6)+2 (a^2) (β^3) (γ^5) (λ^6)-(a^3) (β^3) (γ^5) (λ^6)+2 (β^4) (γ^5) (λ^6)-4 a (β^4) (γ^5) (λ^6)+2 (a^2) (β^4) (γ^5) (λ^6)-4 (β^5) (γ^5) (λ^6)+2 a (β^5) (γ^5) (λ^6)+2 (a^2) (β^5) (γ^5) (λ^6)+(β^6) (γ^5) (λ^6)+3 a (β^6) (γ^5) (λ^6)+(β^4) (λ^7)-a (β^4) (λ^7)-(β^5) (λ^7)+a (β^6) (λ^7)-4 (β^4) γ (λ^7)+4 a (β^4) γ (λ^7)+5 (β^5) γ (λ^7)-a (β^5) γ (λ^7)-5 a (β^6) γ (λ^7)+6 (β^4) (γ^2) (λ^7)-6 a (β^4) (γ^2) (λ^7)-10 (β^5) (γ^2) (λ^7)+4 a (β^5) (γ^2) (λ^7)+10 a (β^6) (γ^2) (λ^7)-4 (β^4) (γ^3) (λ^7)+4 a (β^4) (γ^3) (λ^7)+10 (β^5) (γ^3) (λ^7)-6 a (β^5) (γ^3) (λ^7)-10 a (β^6) (γ^3) (λ^7)+(β^4) (γ^4) (λ^7)-a (β^4) (γ^4) (λ^7)-5 (β^5) (γ^4) (λ^7)+4 a (β^5) (γ^4) (λ^7)+5 a (β^6) (γ^4) (λ^7)+(β^5) (γ^5) (λ^7)-a (β^5) (γ^5) (λ^7)-a (β^6) (γ^5) (λ^7)]))+b (FullSimplify[-β (λ^2)+2 (β^2) (λ^2)-2 (β^4) (λ^2)+(β^5) (λ^2)+3 β γ (λ^2)-8 (β^2) γ (λ^2)+a (β^2) γ (λ^2)+(β^3) γ (λ^2)+8 (β^4) γ (λ^2)-a (β^4) γ (λ^2)-4 (β^5) γ (λ^2)-2 β (γ^2) (λ^2)+10 (β^2) (γ^2) (λ^2)-2 a (β^2) (γ^2) (λ^2)-4 (β^3) (γ^2) (λ^2)-10 (β^4) (γ^2) (λ^2)+2 a (β^4) (γ^2) (λ^2)+6 (β^5) (γ^2) (λ^2)-4 (β^2) (γ^3) (λ^2)+a (β^2) (γ^3) (λ^2)+4 (β^3) (γ^3) (λ^2)+4 (β^4) (γ^3) (λ^2)-a (β^4) (γ^3) (λ^2)-4 (β^5) (γ^3) (λ^2)-(β^3) (γ^4) (λ^2)+(β^5) (γ^4) (λ^2)+2 β (λ^3)-7 (β^2) (λ^3)+4 (β^3) (λ^3)+a (β^3) (λ^3)+5 (β^4) (λ^3)-6 (β^5) (λ^3)-a (β^5) (λ^3)+2 (β^6) (λ^3)-6 β γ (λ^3)+a β γ (λ^3)+26 (β^2) γ (λ^3)-3 a (β^2) γ (λ^3)-22 (β^3) γ (λ^3)-18 (β^4) γ (λ^3)+4 a (β^4) γ (λ^3)+27 (β^5) γ (λ^3)-9 (β^6) γ (λ^3)+6 β (γ^2) (λ^3)-3 a β (γ^2) (λ^3)-35 (β^2) (γ^2) (λ^3)+11 a (β^2) (γ^2) (λ^3)-2 (a^2) (β^2) (γ^2) (λ^3)+42 (β^3) (γ^2) (λ^3)-6 a (β^3) (γ^2) (λ^3)+21 (β^4) (γ^2) (λ^3)-13 a (β^4) (γ^2) (λ^3)+2 (a^2) (β^4) (γ^2) (λ^3)-46 (β^5) (γ^2) (λ^3)+7 a (β^5) (γ^2) (λ^3)+16 (β^6) (γ^2) (λ^3)-2 β (γ^3) (λ^3)+2 a β (γ^3) (λ^3)+21 (β^2) (γ^3) (λ^3)-15 a (β^2) (γ^3) (λ^3)+4 (a^2) (β^2) (γ^3) (λ^3)-34 (β^3) (γ^3) (λ^3)+8 a (β^3) (γ^3) (λ^3)-7 (β^4) (γ^3) (λ^3)+14 a (β^4) (γ^3) (λ^3)-4 (a^2) (β^4) (γ^3) (λ^3)+36 (β^5) (γ^3) (λ^3)-11 a (β^5) (γ^3) (λ^3)-14 (β^6) (γ^3) (λ^3)-5 (β^2) (γ^4) (λ^3)+7 a (β^2) (γ^4) (λ^3)-2 (a^2) (β^2) (γ^4) (λ^3)+11 (β^3) (γ^4) (λ^3)-4 a (β^3) (γ^4) (λ^3)-2 (β^4) (γ^4) (λ^3)-5 a (β^4) (γ^4) (λ^3)+2 (a^2) (β^4) (γ^4) (λ^3)-12 (β^5) (γ^4) (λ^3)+6 a (β^5) (γ^4) (λ^3)+6 (β^6) (γ^4) (λ^3)-(β^3) (γ^5) (λ^3)+a (β^3) (γ^5) (λ^3)+(β^4) (γ^5) (λ^3)+(β^5) (γ^5) (λ^3)-a (β^5) (γ^5) (λ^3)-(β^6) (γ^5) (λ^3)-2 β (λ^4)+a β (λ^4)+8 (β^2) (λ^4)-9 (β^3) (λ^4)-4 a (β^3) (λ^4)-2 (β^4) (λ^4)+2 a (β^4) (λ^4)+10 (β^5) (λ^4)+3 a (β^5) (λ^4)-6 (β^6) (λ^4)-2 a (β^6) (λ^4)+(β^7) (λ^4)+7 β γ (λ^4)-5 a β γ (λ^4)-32 (β^2) γ (λ^4)+8 a (β^2) γ (λ^4)-(a^2) (β^2) γ (λ^4)+41 (β^3) γ (λ^4)+11 a (β^3) γ (λ^4)-2 (a^2) (β^3) γ (λ^4)+4 (β^4) γ (λ^4)-15 a (β^4) γ (λ^4)+(a^2) (β^4) γ (λ^4)-43 (β^5) γ (λ^4)-6 a (β^5) γ (λ^4)+2 (a^2) (β^5) γ (λ^4)+28 (β^6) γ (λ^4)+7 a (β^6) γ (λ^4)-5 (β^7) γ (λ^4)-8 β (γ^2) (λ^4)+7 a β (γ^2) (λ^4)+50 (β^2) (γ^2) (λ^4)-28 a (β^2) (γ^2) (λ^4)+5 (a^2) (β^2) (γ^2) (λ^4)-73 (β^3) (γ^2) (λ^4)-5 a (β^3) (γ^2) (λ^4)+4 (a^2) (β^3) (γ^2) (λ^4)+4 (β^4) (γ^2) (λ^4)+32 a (β^4) (γ^2) (λ^4)-5 (a^2) (β^4) (γ^2) (λ^4)+73 (β^5) (γ^2) (λ^4)-6 a (β^5) (γ^2) (λ^4)-4 (a^2) (β^5) (γ^2) (λ^4)-52 (β^6) (γ^2) (λ^4)-8 a (β^6) (γ^2) (λ^4)+10 (β^7) (γ^2) (λ^4)+3 β (γ^3) (λ^4)-3 a β (γ^3) (λ^4)-36 (β^2) (γ^3) (λ^4)+33 a (β^2) (γ^3) (λ^4)-8 (a^2) (β^2) (γ^3) (λ^4)+(a^3) (β^2) (γ^3) (λ^4)+64 (β^3) (γ^3) (λ^4)-13 a (β^3) (γ^3) (λ^4)-16 (β^4) (γ^3) (λ^4)-27 a (β^4) (γ^3) (λ^4)+8 (a^2) (β^4) (γ^3) (λ^4)-(a^3) (β^4) (γ^3) (λ^4)-61 (β^5) (γ^3) (λ^4)+24 a (β^5) (γ^3) (λ^4)+48 (β^6) (γ^3) (λ^4)+2 a (β^6) (γ^3) (λ^4)-10 (β^7) (γ^3) (λ^4)+11 (β^2) (γ^4) (λ^4)-16 a (β^2) (γ^4) (λ^4)+7 (a^2) (β^2) (γ^4) (λ^4)-2 (a^3) (β^2) (γ^4) (λ^4)-27 (β^3) (γ^4) (λ^4)+15 a (β^3) (γ^4) (λ^4)-2 (a^2) (β^3) (γ^4) (λ^4)+14 (β^4) (γ^4) (λ^4)+8 a (β^4) (γ^4) (λ^4)-5 (a^2) (β^4) (γ^4) (λ^4)+2 (a^3) (β^4) (γ^4) (λ^4)+25 (β^5) (γ^4) (λ^4)-21 a (β^5) (γ^4) (λ^4)+4 (a^2) (β^5) (γ^4) (λ^4)-22 (β^6) (γ^4) (λ^4)+2 a (β^6) (γ^4) (λ^4)+5 (β^7) (γ^4) (λ^4)-(β^2) (γ^5) (λ^4)+3 a (β^2) (γ^5) (λ^4)-3 (a^2) (β^2) (γ^5) (λ^4)+(a^3) (β^2) (γ^5) (λ^4)+4 (β^3) (γ^5) (λ^4)-4 a (β^3) (γ^5) (λ^4)-4 (β^4) (γ^5) (λ^4)+(a^2) (β^4) (γ^5) (λ^4)-(a^3) (β^4) (γ^5) (λ^4)-4 (β^5) (γ^5) (λ^4)+6 a (β^5) (γ^5) (λ^4)-2 (a^2) (β^5) (γ^5) (λ^4)+4 (β^6) (γ^5) (λ^4)-a (β^6) (γ^5) (λ^4)-(β^7) (γ^5) (λ^4)+β (λ^5)-a β (λ^5)-5 (β^2) (λ^5)+2 a (β^2) (λ^5)+7 (β^3) (λ^5)+4 a (β^3) (λ^5)-(β^4) (λ^5)-7 a (β^4) (λ^5)-6 (β^5) (λ^5)-2 a (β^5) (λ^5)+6 (β^6) (λ^5)+5 a (β^6) (λ^5)-2 (β^7) (λ^5)-a (β^7) (λ^5)-3 β γ (λ^5)+3 a β γ (λ^5)+22 (β^2) γ (λ^5)-13 a (β^2) γ (λ^5)-34 (β^3) γ (λ^5)-7 a (β^3) γ (λ^5)+5 (β^4) γ (λ^5)+35 a (β^4) γ (λ^5)-3 (a^2) (β^4) γ (λ^5)+27 (β^5) γ (λ^5)-a (β^5) γ (λ^5)-(a^2) (β^5) γ (λ^5)-27 (β^6) γ (λ^5)-22 a (β^6) γ (λ^5)+2 (a^2) (β^6) γ (λ^5)+10 (β^7) γ (λ^5)+5 a (β^7) γ (λ^5)+3 β (γ^2) (λ^5)-3 a β (γ^2) (λ^5)-35 (β^2) (γ^2) (λ^5)+26 a (β^2) (γ^2) (λ^5)-(a^2) (β^2) (γ^2) (λ^5)+(a^3) (β^2) (γ^2) (λ^5)+68 (β^3) (γ^2) (λ^5)-11 a (β^3) (γ^2) (λ^5)+2 (a^2) (β^3) (γ^2) (λ^5)+(a^3) (β^3) (γ^2) (λ^5)-13 (β^4) (γ^2) (λ^5)-64 a (β^4) (γ^2) (λ^5)+12 (a^2) (β^4) (γ^2) (λ^5)-(a^3) (β^4) (γ^2) (λ^5)-51 (β^5) (γ^2) (λ^5)+24 a (β^5) (γ^2) (λ^5)+(a^2) (β^5) (γ^2) (λ^5)-(a^3) (β^5) (γ^2) (λ^5)+48 (β^6) (γ^2) (λ^5)+38 a (β^6) (γ^2) (λ^5)-8 (a^2) (β^6) (γ^2) (λ^5)-20 (β^7) (γ^2) (λ^5)-10 a (β^7) (γ^2) (λ^5)-β (γ^3) (λ^5)+a β (γ^3) (λ^5)+26 (β^2) (γ^3) (λ^5)-27 a (β^2) (γ^3) (λ^5)+8 (a^2) (β^2) (γ^3) (λ^5)-4 (a^3) (β^2) (γ^3) (λ^5)-65 (β^3) (γ^3) (λ^5)+25 a (β^3) (γ^3) (λ^5)+3 (a^2) (β^3) (γ^3) (λ^5)-4 (a^3) (β^3) (γ^3) (λ^5)+21 (β^4) (γ^3) (λ^5)+49 a (β^4) (γ^3) (λ^5)-14 (a^2) (β^4) (γ^3) (λ^5)+3 (a^3) (β^4) (γ^3) (λ^5)+51 (β^5) (γ^3) (λ^5)-46 a (β^5) (γ^3) (λ^5)+3 (a^2) (β^5) (γ^3) (λ^5)+3 (a^3) (β^5) (γ^3) (λ^5)-42 (β^6) (γ^3) (λ^5)-32 a (β^6) (γ^3) (λ^5)+12 (a^2) (β^6) (γ^3) (λ^5)+20 (β^7) (γ^3) (λ^5)+10 a (β^7) (γ^3) (λ^5)-10 (β^2) (γ^4) (λ^5)+18 a (β^2) (γ^4) (λ^5)-13 (a^2) (β^2) (γ^4) (λ^5)+5 (a^3) (β^2) (γ^4) (λ^5)+27 (β^3) (γ^4) (λ^5)-9 a (β^3) (γ^4) (λ^5)-12 (a^2) (β^3) (γ^4) (λ^5)+5 (a^3) (β^3) (γ^4) (λ^5)-18 (β^4) (γ^4) (λ^5)-11 a (β^4) (γ^4) (λ^5)+4 (a^2) (β^4) (γ^4) (λ^5)-3 (a^3) (β^4) (γ^4) (λ^5)-27 (β^5) (γ^4) (λ^5)+34 a (β^5) (γ^4) (λ^5)-5 (a^2) (β^5) (γ^4) (λ^5)-3 (a^3) (β^5) (γ^4) (λ^5)+18 (β^6) (γ^4) (λ^5)+13 a (β^6) (γ^4) (λ^5)-8 (a^2) (β^6) (γ^4) (λ^5)-10 (β^7) (γ^4) (λ^5)-5 a (β^7) (γ^4) (λ^5)+2 (β^2) (γ^5) (λ^5)-6 a (β^2) (γ^5) (λ^5)+6 (a^2) (β^2) (γ^5) (λ^5)-2 (a^3) (β^2) (γ^5) (λ^5)-3 (β^3) (γ^5) (λ^5)-2 a (β^3) (γ^5) (λ^5)+7 (a^2) (β^3) (γ^5) (λ^5)-2 (a^3) (β^3) (γ^5) (λ^5)+6 (β^4) (γ^5) (λ^5)-2 a (β^4) (γ^5) (λ^5)+(a^2) (β^4) (γ^5) (λ^5)+(a^3) (β^4) (γ^5) (λ^5)+6 (β^5) (γ^5) (λ^5)-9 a (β^5) (γ^5) (λ^5)+2 (a^2) (β^5) (γ^5) (λ^5)+(a^3) (β^5) (γ^5) (λ^5)-3 (β^6) (γ^5) (λ^5)-2 a (β^6) (γ^5) (λ^5)+2 (a^2) (β^6) (γ^5) (λ^5)+2 (β^7) (γ^5) (λ^5)+a (β^7) (γ^5) (λ^5)+2 (β^2) (λ^6)-2 a (β^2) (λ^6)-3 (β^3) (λ^6)+6 a (β^4) (λ^6)+2 (β^5) (λ^6)-2 a (β^5) (λ^6)-2 (β^6) (λ^6)-4 a (β^6) (λ^6)+(β^7) (λ^6)+2 a (β^7) (λ^6)-7 (β^2) γ (λ^6)+6 a (β^2) γ (λ^6)+(a^2) (β^2) γ (λ^6)+17 (β^3) γ (λ^6)-6 a (β^3) γ (λ^6)+(a^2) (β^3) γ (λ^6)-(β^4) γ (λ^6)-25 a (β^4) γ (λ^6)+(a^2) (β^4) γ (λ^6)-12 (β^5) γ (λ^6)+16 a (β^5) γ (λ^6)-(a^2) (β^5) γ (λ^6)+8 (β^6) γ (λ^6)+19 a (β^6) γ (λ^6)-2 (a^2) (β^6) γ (λ^6)-5 (β^7) γ (λ^6)-10 a (β^7) γ (λ^6)+10 (β^2) (γ^2) (λ^6)-9 a (β^2) (γ^2) (λ^6)-(a^3) (β^2) (γ^2) (λ^6)-33 (β^3) (γ^2) (λ^6)+12 a (β^3) (γ^2) (λ^6)+5 (a^2) (β^3) (γ^2) (λ^6)-2 (a^3) (β^3) (γ^2) (λ^6)+8 (β^4) (γ^2) (λ^6)+33 a (β^4) (γ^2) (λ^6)+3 (a^2) (β^4) (γ^2) (λ^6)-(a^3) (β^4) (γ^2) (λ^6)+29 (β^5) (γ^2) (λ^6)-44 a (β^5) (γ^2) (λ^6)+6 (a^2) (β^5) (γ^2) (λ^6)-12 (β^6) (γ^2) (λ^6)-36 a (β^6) (γ^2) (λ^6)+8 (a^2) (β^6) (γ^2) (λ^6)+10 (β^7) (γ^2) (λ^6)+20 a (β^7) (γ^2) (λ^6)-8 (β^2) (γ^3) (λ^6)+11 a (β^2) (γ^3) (λ^6)-6 (a^2) (β^2) (γ^3) (λ^6)+3 (a^3) (β^2) (γ^3) (λ^6)+27 (β^3) (γ^3) (λ^6)-21 (a^2) (β^3) (γ^3) (λ^6)+6 (a^3) (β^3) (γ^3) (λ^6)-18 (β^4) (γ^3) (λ^6)-9 a (β^4) (γ^3) (λ^6)-15 (a^2) (β^4) (γ^3) (λ^6)+3 (a^3) (β^4) (γ^3) (λ^6)-35 (β^5) (γ^3) (λ^6)+56 a (β^5) (γ^3) (λ^6)-12 (a^2) (β^5) (γ^3) (λ^6)+8 (β^6) (γ^3) (λ^6)+34 a (β^6) (γ^3) (λ^6)-12 (a^2) (β^6) (γ^3) (λ^6)-10 (β^7) (γ^3) (λ^6)-20 a (β^7) (γ^3) (λ^6)+4 (β^2) (γ^4) (λ^6)-9 a (β^2) (γ^4) (λ^6)+8 (a^2) (β^2) (γ^4) (λ^6)-3 (a^3) (β^2) (γ^4) (λ^6)-8 (β^3) (γ^4) (λ^6)-12 a (β^3) (γ^4) (λ^6)+23 (a^2) (β^3) (γ^4) (λ^6)-6 (a^3) (β^3) (γ^4) (λ^6)+16 (β^4) (γ^4) (λ^6)-11 a (β^4) (γ^4) (λ^6)+17 (a^2) (β^4) (γ^4) (λ^6)-3 (a^3) (β^4) (γ^4) (λ^6)+21 (β^5) (γ^4) (λ^6)-34 a (β^5) (γ^4) (λ^6)+10 (a^2) (β^5) (γ^4) (λ^6)-2 (β^6) (γ^4) (λ^6)-16 a (β^6) (γ^4) (λ^6)+8 (a^2) (β^6) (γ^4) (λ^6)+5 (β^7) (γ^4) (λ^6)+10 a (β^7) (γ^4) (λ^6)-(β^2) (γ^5) (λ^6)+3 a (β^2) (γ^5) (λ^6)-3 (a^2) (β^2) (γ^5) (λ^6)+(a^3) (β^2) (γ^5) (λ^6)+6 a (β^3) (γ^5) (λ^6)-8 (a^2) (β^3) (γ^5) (λ^6)+2 (a^3) (β^3) (γ^5) (λ^6)-5 (β^4) (γ^5) (λ^6)+6 a (β^4) (γ^5) (λ^6)-6 (a^2) (β^4) (γ^5) (λ^6)+(a^3) (β^4) (γ^5) (λ^6)-5 (β^5) (γ^5) (λ^6)+8 a (β^5) (γ^5) (λ^6)-3 (a^2) (β^5) (γ^5) (λ^6)+3 a (β^6) (γ^5) (λ^6)-2 (a^2) (β^6) (γ^5) (λ^6)-(β^7) (γ^5) (λ^6)-2 a (β^7) (γ^5) (λ^6)+(β^3) (λ^7)-a (β^3) (λ^7)-a (β^4) (λ^7)-(β^5) (λ^7)+2 a (β^5) (λ^7)+a (β^6) (λ^7)-a (β^7) (λ^7)-4 (β^3) γ (λ^7)+3 a (β^3) γ (λ^7)+(a^2) (β^3) γ (λ^7)+(β^4) γ (λ^7)+3 a (β^4) γ (λ^7)+(a^2) (β^4) γ (λ^7)+5 (β^5) γ (λ^7)-9 a (β^5) γ (λ^7)-4 a (β^6) γ (λ^7)+5 a (β^7) γ (λ^7)+6 (β^3) (γ^2) (λ^7)-2 a (β^3) (γ^2) (λ^7)-4 (a^2) (β^3) (γ^2) (λ^7)-4 (β^4) (γ^2) (λ^7)-2 a (β^4) (γ^2) (λ^7)-4 (a^2) (β^4) (γ^2) (λ^7)-10 (β^5) (γ^2) (λ^7)+16 a (β^5) (γ^2) (λ^7)+6 a (β^6) (γ^2) (λ^7)-10 a (β^7) (γ^2) (λ^7)-4 (β^3) (γ^3) (λ^7)-2 a (β^3) (γ^3) (λ^7)+6 (a^2) (β^3) (γ^3) (λ^7)+6 (β^4) (γ^3) (λ^7)-2 a (β^4) (γ^3) (λ^7)+6 (a^2) (β^4) (γ^3) (λ^7)+10 (β^5) (γ^3) (λ^7)-14 a (β^5) (γ^3) (λ^7)-4 a (β^6) (γ^3) (λ^7)+10 a (β^7) (γ^3) (λ^7)+(β^3) (γ^4) (λ^7)+3 a (β^3) (γ^4) (λ^7)-4 (a^2) (β^3) (γ^4) (λ^7)-4 (β^4) (γ^4) (λ^7)+3 a (β^4) (γ^4) (λ^7)-4 (a^2) (β^4) (γ^4) (λ^7)-5 (β^5) (γ^4) (λ^7)+6 a (β^5) (γ^4) (λ^7)+a (β^6) (γ^4) (λ^7)-5 a (β^7) (γ^4) (λ^7)-a (β^3) (γ^5) (λ^7)+(a^2) (β^3) (γ^5) (λ^7)+(β^4) (γ^5) (λ^7)-a (β^4) (γ^5) (λ^7)+(a^2) (β^4) (γ^5) (λ^7)+(β^5) (γ^5) (λ^7)-a (β^5) (γ^5) (λ^7)+a (β^7) (γ^5) (λ^7)]+Z (FullSimplify[-(β^2) γ+(β^3) γ+(β^2) (γ^2)-(β^3) (γ^2)-(β^2) λ+(β^3) λ+4 (β^2) γ λ-8 (β^3) γ λ+3 (β^4) γ λ-4 (β^2) (γ^2) λ+3 a (β^2) (γ^2) λ+11 (β^3) (γ^2) λ-3 a (β^3) (γ^2) λ-6 (β^4) (γ^2) λ+3 (β^2) (γ^3) λ-3 a (β^2) (γ^3) λ-4 (β^3) (γ^3) λ+3 a (β^3) (γ^3) λ+3 (β^4) (γ^3) λ+3 (β^2) (λ^2)-6 (β^3) (λ^2)+3 (β^4) (λ^2)-10 (β^2) γ (λ^2)+4 a (β^2) γ (λ^2)+27 (β^3) γ (λ^2)-3 a (β^3) γ (λ^2)-20 (β^4) γ (λ^2)-a (β^4) γ (λ^2)+3 (β^5) γ (λ^2)+13 (β^2) (γ^2) (λ^2)-13 a (β^2) (γ^2) (λ^2)-37 (β^3) (γ^2) (λ^2)+18 a (β^3) (γ^2) (λ^2)+37 (β^4) (γ^2) (λ^2)-4 a (β^4) (γ^2) (λ^2)-9 (β^5) (γ^2) (λ^2)-8 (β^2) (γ^3) (λ^2)+11 a (β^2) (γ^3) (λ^2)-3 (a^2) (β^2) (γ^3) (λ^2)+21 (β^3) (γ^3) (λ^2)-23 a (β^3) (γ^3) (λ^2)+3 (a^2) (β^3) (γ^3) (λ^2)-26 (β^4) (γ^3) (λ^2)+11 a (β^4) (γ^3) (λ^2)+9 (β^5) (γ^3) (λ^2)+3 (β^2) (γ^4) (λ^2)-6 a (β^2) (γ^4) (λ^2)+3 (a^2) (β^2) (γ^4) (λ^2)-5 (β^3) (γ^4) (λ^2)+8 a (β^3) (γ^4) (λ^2)-3 (a^2) (β^3) (γ^4) (λ^2)+6 (β^4) (γ^4) (λ^2)-6 a (β^4) (γ^4) (λ^2)-3 (β^5) (γ^4) (λ^2)-4 (β^2) (λ^3)+a (β^2) (λ^3)+12 (β^3) (λ^3)-11 (β^4) (λ^3)-a (β^4) (λ^3)+3 (β^5) (λ^3)+14 (β^2) γ (λ^3)-10 a (β^2) γ (λ^3)-49 (β^3) γ (λ^3)+15 a (β^3) γ (λ^3)+55 (β^4) γ (λ^3)-a (β^4) γ (λ^3)-20 (β^5) γ (λ^3)-2 a (β^5) γ (λ^3)+(β^6) γ (λ^3)-19 (β^2) (γ^2) (λ^3)+24 a (β^2) (γ^2) (λ^3)-5 (a^2) (β^2) (γ^2) (λ^3)+74 (β^3) (γ^2) (λ^3)-55 a (β^3) (γ^2) (λ^3)+3 (a^2) (β^3) (γ^2) (λ^3)-98 (β^4) (γ^2) (λ^3)+24 a (β^4) (γ^2) (λ^3)+2 (a^2) (β^4) (γ^2) (λ^3)+45 (β^5) (γ^2) (λ^3)+3 a (β^5) (γ^2) (λ^3)-4 (β^6) (γ^2) (λ^3)+16 (β^2) (γ^3) (λ^3)-30 a (β^2) (γ^3) (λ^3)+14 (a^2) (β^2) (γ^3) (λ^3)-50 (β^3) (γ^3) (λ^3)+62 a (β^3) (γ^3) (λ^3)-12 (a^2) (β^3) (γ^3) (λ^3)+78 (β^4) (γ^3) (λ^3)-47 a (β^4) (γ^3) (λ^3)-(a^2) (β^4) (γ^3) (λ^3)-45 (β^5) (γ^3) (λ^3)+3 a (β^5) (γ^3) (λ^3)+6 (β^6) (γ^3) (λ^3)-8 (β^2) (γ^4) (λ^3)+17 a (β^2) (γ^4) (λ^3)-10 (a^2) (β^2) (γ^4) (λ^3)+(a^3) (β^2) (γ^4) (λ^3)+15 (β^3) (γ^4) (λ^3)-27 a (β^3) (γ^4) (λ^3)+13 (a^2) (β^3) (γ^4) (λ^3)-(a^3) (β^3) (γ^4) (λ^3)-27 (β^4) (γ^4) (λ^3)+31 a (β^4) (γ^4) (λ^3)-4 (a^2) (β^4) (γ^4) (λ^3)+20 (β^5) (γ^4) (λ^3)-7 a (β^5) (γ^4) (λ^3)-4 (β^6) (γ^4) (λ^3)+(β^2) (γ^5) (λ^3)-3 a (β^2) (γ^5) (λ^3)+3 (a^2) (β^2) (γ^5) (λ^3)-(a^3) (β^2) (γ^5) (λ^3)-2 (β^3) (γ^5) (λ^3)+5 a (β^3) (γ^5) (λ^3)-4 (a^2) (β^3) (γ^5) (λ^3)+(a^3) (β^3) (γ^5) (λ^3)+3 (β^4) (γ^5) (λ^3)-6 a (β^4) (γ^5) (λ^3)+3 (a^2) (β^4) (γ^5) (λ^3)-3 (β^5) (γ^5) (λ^3)+3 a (β^5) (γ^5) (λ^3)+(β^6) (γ^5) (λ^3)+3 (β^2) (λ^4)-2 a (β^2) (λ^4)-12 (β^3) (λ^4)+2 a (β^3) (λ^4)+16 (β^4) (λ^4)+2 a (β^4) (λ^4)-8 (β^5) (λ^4)-2 a (β^5) (λ^4)+(β^6) (λ^4)-11 (β^2) γ (λ^4)+12 a (β^2) γ (λ^4)-2 (a^2) (β^2) γ (λ^4)+50 (β^3) γ (λ^4)-27 a (β^3) γ (λ^4)-75 (β^4) γ (λ^4)+7 a (β^4) γ (λ^4)+2 (a^2) (β^4) γ (λ^4)+43 (β^5) γ (λ^4)+9 a (β^5) γ (λ^4)-7 (β^6) γ (λ^4)-a (β^6) γ (λ^4)+18 (β^2) (γ^2) (λ^4)-30 a (β^2) (γ^2) (λ^4)+12 (a^2) (β^2) (γ^2) (λ^4)-78 (β^3) (γ^2) (λ^4)+73 a (β^3) (γ^2) (λ^4)-8 (a^2) (β^3) (γ^2) (λ^4)+135 (β^4) (γ^2) (λ^4)-52 a (β^4) (γ^2) (λ^4)-5 (a^2) (β^4) (γ^2) (λ^4)-89 (β^5) (γ^2) (λ^4)-9 a (β^5) (γ^2) (λ^4)+2 (a^2) (β^5) (γ^2) (λ^4)+18 (β^6) (γ^2) (λ^4)+4 a (β^6) (γ^2) (λ^4)-17 (β^2) (γ^3) (λ^4)+36 a (β^2) (γ^3) (λ^4)-21 (a^2) (β^2) (γ^3) (λ^4)+2 (a^3) (β^2) (γ^3) (λ^4)+58 (β^3) (γ^3) (λ^4)-83 a (β^3) (γ^3) (λ^4)+26 (a^2) (β^3) (γ^3) (λ^4)-(a^3) (β^3) (γ^3) (λ^4)-116 (β^4) (γ^3) (λ^4)+88 a (β^4) (γ^3) (λ^4)-(a^2) (β^4) (γ^3) (λ^4)-(a^3) (β^4) (γ^3) (λ^4)+89 (β^5) (γ^3) (λ^4)-7 a (β^5) (γ^3) (λ^4)-6 (a^2) (β^5) (γ^3) (λ^4)-22 (β^6) (γ^3) (λ^4)-6 a (β^6) (γ^3) (λ^4)+10 (β^2) (γ^4) (λ^4)-25 a (β^2) (γ^4) (λ^4)+20 (a^2) (β^2) (γ^4) (λ^4)-5 (a^3) (β^2) (γ^4) (λ^4)-22 (β^3) (γ^4) (λ^4)+44 a (β^3) (γ^4) (λ^4)-24 (a^2) (β^3) (γ^4) (λ^4)+2 (a^3) (β^3) (γ^4) (λ^4)+47 (β^4) (γ^4) (λ^4)-58 a (β^4) (γ^4) (λ^4)+9 (a^2) (β^4) (γ^4) (λ^4)+2 (a^3) (β^4) (γ^4) (λ^4)-43 (β^5) (γ^4) (λ^4)+15 a (β^5) (γ^4) (λ^4)+6 (a^2) (β^5) (γ^4) (λ^4)+13 (β^6) (γ^4) (λ^4)+4 a (β^6) (γ^4) (λ^4)-3 (β^2) (γ^5) (λ^4)+9 a (β^2) (γ^5) (λ^4)-9 (a^2) (β^2) (γ^5) (λ^4)+3 (a^3) (β^2) (γ^5) (λ^4)+4 (β^3) (γ^5) (λ^4)-9 a (β^3) (γ^5) (λ^4)+6 (a^2) (β^3) (γ^5) (λ^4)-(a^3) (β^3) (γ^5) (λ^4)-7 (β^4) (γ^5) (λ^4)+13 a (β^4) (γ^5) (λ^4)-5 (a^2) (β^4) (γ^5) (λ^4)-(a^3) (β^4) (γ^5) (λ^4)+8 (β^5) (γ^5) (λ^4)-6 a (β^5) (γ^5) (λ^4)-2 (a^2) (β^5) (γ^5) (λ^4)-3 (β^6) (γ^5) (λ^4)-a (β^6) (γ^5) (λ^4)-(β^2) (λ^5)+a (β^2) (λ^5)+7 (β^3) (λ^5)-4 a (β^3) (λ^5)-12 (β^4) (λ^5)+8 (β^5) (λ^5)+4 a (β^5) (λ^5)-2 (β^6) (λ^5)-a (β^6) (λ^5)+4 (β^2) γ (λ^5)-6 a (β^2) γ (λ^5)+2 (a^2) (β^2) γ (λ^5)-29 (β^3) γ (λ^5)+25 a (β^3) γ (λ^5)-2 (a^2) (β^3) γ (λ^5)+56 (β^4) γ (λ^5)-15 a (β^4) γ (λ^5)-2 (a^2) (β^4) γ (λ^5)-41 (β^5) γ (λ^5)-15 a (β^5) γ (λ^5)+2 (a^2) (β^5) γ (λ^5)+11 (β^6) γ (λ^5)+7 a (β^6) γ (λ^5)-7 (β^2) (γ^2) (λ^5)+14 a (β^2) (γ^2) (λ^5)-8 (a^2) (β^2) (γ^2) (λ^5)+(a^3) (β^2) (γ^2) (λ^5)+47 (β^3) (γ^2) (λ^5)-58 a (β^3) (γ^2) (λ^5)+14 (a^2) (β^3) (γ^2) (λ^5)-102 (β^4) (γ^2) (λ^5)+57 a (β^4) (γ^2) (λ^5)+4 (a^2) (β^4) (γ^2) (λ^5)-(a^3) (β^4) (γ^2) (λ^5)+83 (β^5) (γ^2) (λ^5)+17 a (β^5) (γ^2) (λ^5)-10 (a^2) (β^5) (γ^2) (λ^5)-24 (β^6) (γ^2) (λ^5)-18 a (β^6) (γ^2) (λ^5)+9 (β^2) (γ^3) (λ^5)-23 a (β^2) (γ^3) (λ^5)+19 (a^2) (β^2) (γ^3) (λ^5)-5 (a^3) (β^2) (γ^3) (λ^5)-37 (β^3) (γ^3) (λ^5)+60 a (β^3) (γ^3) (λ^5)-22 (a^2) (β^3) (γ^3) (λ^5)-(a^3) (β^3) (γ^3) (λ^5)+90 (β^4) (γ^3) (λ^5)-80 a (β^4) (γ^3) (λ^5)+2 (a^2) (β^4) (γ^3) (λ^5)+3 (a^3) (β^4) (γ^3) (λ^5)-83 (β^5) (γ^3) (λ^5)-a (β^5) (γ^3) (λ^5)+18 (a^2) (β^5) (γ^3) (λ^5)+26 (β^6) (γ^3) (λ^5)+22 a (β^6) (γ^3) (λ^5)-8 (β^2) (γ^4) (λ^5)+23 a (β^2) (γ^4) (λ^5)-22 (a^2) (β^2) (γ^4) (λ^5)+7 (a^3) (β^2) (γ^4) (λ^5)+14 (β^3) (γ^4) (λ^5)-26 a (β^3) (γ^4) (λ^5)+10 (a^2) (β^3) (γ^4) (λ^5)+2 (a^3) (β^3) (γ^4) (λ^5)-38 (β^4) (γ^4) (λ^5)+49 a (β^4) (γ^4) (λ^5)-8 (a^2) (β^4) (γ^4) (λ^5)-3 (a^3) (β^4) (γ^4) (λ^5)+41 (β^5) (γ^4) (λ^5)-9 a (β^5) (γ^4) (λ^5)-14 (a^2) (β^5) (γ^4) (λ^5)-14 (β^6) (γ^4) (λ^5)-13 a (β^6) (γ^4) (λ^5)+3 (β^2) (γ^5) (λ^5)-9 a (β^2) (γ^5) (λ^5)+9 (a^2) (β^2) (γ^5) (λ^5)-3 (a^3) (β^2) (γ^5) (λ^5)-2 (β^3) (γ^5) (λ^5)+3 a (β^3) (γ^5) (λ^5)-(a^3) (β^3) (γ^5) (λ^5)+6 (β^4) (γ^5) (λ^5)-11 a (β^4) (γ^5) (λ^5)+4 (a^2) (β^4) (γ^5) (λ^5)+(a^3) (β^4) (γ^5) (λ^5)-8 (β^5) (γ^5) (λ^5)+4 a (β^5) (γ^5) (λ^5)+4 (a^2) (β^5) (γ^5) (λ^5)+3 (β^6) (γ^5) (λ^5)+3 a (β^6) (γ^5) (λ^5)-2 (β^3) (λ^6)+2 a (β^3) (λ^6)+5 (β^4) (λ^6)-2 a (β^4) (λ^6)-4 (β^5) (λ^6)-2 a (β^5) (λ^6)+(β^6) (λ^6)+2 a (β^6) (λ^6)+8 (β^3) γ (λ^6)-10 a (β^3) γ (λ^6)+2 (a^2) (β^3) γ (λ^6)-23 (β^4) γ (λ^6)+14 a (β^4) γ (λ^6)+20 (β^5) γ (λ^6)+7 a (β^5) γ (λ^6)-2 (a^2) (β^5) γ (λ^6)-5 (β^6) γ (λ^6)-11 a (β^6) γ (λ^6)+(β^2) (γ^2) (λ^6)-3 a (β^2) (γ^2) (λ^6)+3 (a^2) (β^2) (γ^2) (λ^6)-(a^3) (β^2) (γ^2) (λ^6)-12 (β^3) (γ^2) (λ^6)+17 a (β^3) (γ^2) (λ^6)-4 (a^2) (β^3) (γ^2) (λ^6)-(a^3) (β^3) (γ^2) (λ^6)+41 (β^4) (γ^2) (λ^6)-34 a (β^4) (γ^2) (λ^6)+2 (a^2) (β^4) (γ^2) (λ^6)-40 (β^5) (γ^2) (λ^6)-7 a (β^5) (γ^2) (λ^6)+8 (a^2) (β^5) (γ^2) (λ^6)+10 (β^6) (γ^2) (λ^6)+24 a (β^6) (γ^2) (λ^6)-3 (β^2) (γ^3) (λ^6)+9 a (β^2) (γ^3) (λ^6)-9 (a^2) (β^2) (γ^3) (λ^6)+3 (a^3) (β^2) (γ^3) (λ^6)+8 (β^3) (γ^3) (λ^6)-11 a (β^3) (γ^3) (λ^6)+3 (a^3) (β^3) (γ^3) (λ^6)-35 (β^4) (γ^3) (λ^6)+38 a (β^4) (γ^3) (λ^6)-6 (a^2) (β^4) (γ^3) (λ^6)+40 (β^5) (γ^3) (λ^6)-a (β^5) (γ^3) (λ^6)-12 (a^2) (β^5) (γ^3) (λ^6)-10 (β^6) (γ^3) (λ^6)-26 a (β^6) (γ^3) (λ^6)+3 (β^2) (γ^4) (λ^6)-9 a (β^2) (γ^4) (λ^6)+9 (a^2) (β^2) (γ^4) (λ^6)-3 (a^3) (β^2) (γ^4) (λ^6)-2 (β^3) (γ^4) (λ^6)+a (β^3) (γ^4) (λ^6)+4 (a^2) (β^3) (γ^4) (λ^6)-3 (a^3) (β^3) (γ^4) (λ^6)+14 (β^4) (γ^4) (λ^6)-20 a (β^4) (γ^4) (λ^6)+6 (a^2) (β^4) (γ^4) (λ^6)-20 (β^5) (γ^4) (λ^6)+5 a (β^5) (γ^4) (λ^6)+8 (a^2) (β^5) (γ^4) (λ^6)+5 (β^6) (γ^4) (λ^6)+14 a (β^6) (γ^4) (λ^6)-(β^2) (γ^5) (λ^6)+3 a (β^2) (γ^5) (λ^6)-3 (a^2) (β^2) (γ^5) (λ^6)+(a^3) (β^2) (γ^5) (λ^6)+a (β^3) (γ^5) (λ^6)-2 (a^2) (β^3) (γ^5) (λ^6)+(a^3) (β^3) (γ^5) (λ^6)-2 (β^4) (γ^5) (λ^6)+4 a (β^4) (γ^5) (λ^6)-2 (a^2) (β^4) (γ^5) (λ^6)+4 (β^5) (γ^5) (λ^6)-2 a (β^5) (γ^5) (λ^6)-2 (a^2) (β^5) (γ^5) (λ^6)-(β^6) (γ^5) (λ^6)-3 a (β^6) (γ^5) (λ^6)-(β^4) (λ^7)+a (β^4) (λ^7)+(β^5) (λ^7)-a (β^6) (λ^7)+4 (β^4) γ (λ^7)-4 a (β^4) γ (λ^7)-5 (β^5) γ (λ^7)+a (β^5) γ (λ^7)+5 a (β^6) γ (λ^7)-6 (β^4) (γ^2) (λ^7)+6 a (β^4) (γ^2) (λ^7)+10 (β^5) (γ^2) (λ^7)-4 a (β^5) (γ^2) (λ^7)-10 a (β^6) (γ^2) (λ^7)+4 (β^4) (γ^3) (λ^7)-4 a (β^4) (γ^3) (λ^7)-10 (β^5) (γ^3) (λ^7)+6 a (β^5) (γ^3) (λ^7)+10 a (β^6) (γ^3) (λ^7)-(β^4) (γ^4) (λ^7)+a (β^4) (γ^4) (λ^7)+5 (β^5) (γ^4) (λ^7)-4 a (β^5) (γ^4) (λ^7)-5 a (β^6) (γ^4) (λ^7)-(β^5) (γ^5) (λ^7)+a (β^5) (γ^5) (λ^7)+a (β^6) (γ^5) (λ^7)]))))/((1+γ λ-a γ λ+(λ^2)-a (λ^2)-γ (λ^2)+a γ (λ^2)) (1-λ+β λ+γ λ-a γ λ-β γ λ+(λ^2)-a (λ^2)-a β (λ^2)-γ (λ^2)+a γ (λ^2)+a β γ (λ^2)) (FullSimplify[λ-β λ-(β^2) λ+(β^3) λ-γ λ+2 β γ λ+(β^2) γ λ-2 (β^3) γ λ-β (γ^2) λ+(β^3) (γ^2) λ+β (λ^2)-(β^3) (λ^2)-β γ (λ^2)-a β γ (λ^2)+(β^2) γ (λ^2)-a (β^2) γ (λ^2)+2 (β^3) γ (λ^2)+a β (γ^2) (λ^2)-(β^2) (γ^2) (λ^2)+a (β^2) (γ^2) (λ^2)-(β^3) (γ^2) (λ^2)]+Z (FullSimplify[β-(β^2)+(β^2) γ-β λ+2 (β^2) λ-(β^3) λ+β γ λ-a β γ λ-3 (β^2) γ λ+a (β^2) γ λ+2 (β^3) γ λ+(β^2) (γ^2) λ-a (β^2) (γ^2) λ-(β^3) (γ^2) λ-(β^2) (λ^2)+(β^3) (λ^2)+(β^2) γ (λ^2)-2 (β^3) γ (λ^2)+(β^3) (γ^2) (λ^2)])) (FullSimplify[(λ^2)-a β (λ^2)-a (β^2) (λ^2)+(β^3) (λ^2)+β γ (λ^2)+a β γ (λ^2)-(β^2) γ (λ^2)+a (β^2) γ (λ^2)-2 (β^3) γ (λ^2)+(β^2) (γ^2) (λ^2)+(β^3) (γ^2) (λ^2)+(λ^3)-a (λ^3)+β (λ^3)+a β (λ^3)-(β^2) (λ^3)+a (β^2) (λ^3)-(β^3) (λ^3)-a (β^3) (λ^3)-γ (λ^3)+a γ (λ^3)+β γ (λ^3)-4 a β γ (λ^3)+(a^2) β γ (λ^3)+4 (β^2) γ (λ^3)-3 a (β^2) γ (λ^3)+(a^2) (β^2) γ (λ^3)+2 (β^3) γ (λ^3)+2 a (β^3) γ (λ^3)-2 β (γ^2) (λ^3)+3 a β (γ^2) (λ^3)-(a^2) β (γ^2) (λ^3)-3 (β^2) (γ^2) (λ^3)+2 a (β^2) (γ^2) (λ^3)-(a^2) (β^2) (γ^2) (λ^3)-(β^3) (γ^2) (λ^3)-a (β^3) (γ^2) (λ^3)+β (λ^4)-a β (λ^4)+(β^2) (λ^4)+a (β^3) (λ^4)-2 β γ (λ^4)+2 a β γ (λ^4)-2 (β^2) γ (λ^4)-2 a (β^3) γ (λ^4)+β (γ^2) (λ^4)-a β (γ^2) (λ^4)+(β^2) (γ^2) (λ^4)+a (β^3) (γ^2) (λ^4)]+Z (FullSimplify[β-β λ+(β^2) λ+2 β γ λ-2 a β γ λ-(β^2) γ λ+β (λ^2)-a β (λ^2)-(β^2) (λ^2)-2 β γ (λ^2)+2 a β γ (λ^2)+2 (β^2) γ (λ^2)-a (β^2) γ (λ^2)+β (γ^2) (λ^2)-2 a β (γ^2) (λ^2)+(a^2) β (γ^2) (λ^2)-(β^2) (γ^2) (λ^2)+a (β^2) (γ^2) (λ^2)-β (λ^3)+a β (λ^3)+(β^2) (λ^3)-a (β^2) (λ^3)+2 β γ (λ^3)-3 a β γ (λ^3)+(a^2) β γ (λ^3)-3 (β^2) γ (λ^3)+3 a (β^2) γ (λ^3)-β (γ^2) (λ^3)+2 a β (γ^2) (λ^3)-(a^2) β (γ^2) (λ^3)+2 (β^2) (γ^2) (λ^3)-2 a (β^2) (γ^2) (λ^3)-(β^2) (λ^4)+a (β^2) (λ^4)+2 (β^2) γ (λ^4)-2 a (β^2) γ (λ^4)-(β^2) (γ^2) (λ^4)+a (β^2) (γ^2) (λ^4)])))

Simplify[(-Z (β^2) (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) (-(-1+β) (-1+γ) γ+(-1+3 γ+(-1+γ) (-β+(5-2 β) β γ+2 (1+a (-1+β)+(-1+β) β) (γ^2))) λ+(2+(-5+2 a) γ-(β^3) (((-1+γ))^3) γ+(-1+a) (γ^2) (-6+(3+a (-1+γ)-γ) γ)-(β^2) (((-1+γ))^2) (-2+γ (7+2 (-1+a) γ))-β (-1+γ) (-4+γ (11-2 a+6 (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^2)+(-1+γ) (1+(β^3) (((-1+γ))^2) (-1+3 γ)+(β^2) (-1+γ) (-5+γ (11-2 a+4 (-1+a) γ))+(-1+a) γ (2+γ (-1+a+2 γ-2 a γ))+β (-5+γ (11-4 a-(-7+a) (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^3)-(((-1+γ))^2) (2 (((-1+β))^2) β-(-1+β) β (-2+2 a+5 β) γ-((((-1+a))^2)-2 (-1+a) (β^2)-3 (β^3)) (γ^2)) (λ^4)+(β^2) (1+β (-1+γ)) (((-1+γ))^3) (λ^5))-β (1+β) (-1+γ) (λ^2) ((β^5) (((-1+γ))^4) (((-1+λ))^2) (λ^2) (-1+a λ)+β (-3+(8+a (-1+γ)-4 γ) γ+9 λ+γ (-23+4 a+2 (9+(-5+a) a) γ+(-5+(7-2 a) a) (γ^2)) λ+(-10+a+(29+(-12+a) a) γ+(-29+(23-4 a) a) (γ^2)-(-1+a) (10+(-3+a) a) (γ^3)+(((-1+a))^3) (γ^4)) (λ^2)-(-1+γ) (6-3 a+(-13+10 a) γ-(-1+a) (6+(a^2)) (γ^2)+2 (((-1+a))^3) (γ^3)) (λ^3)+(-1+a) (((-1+γ))^2) (2-(1+a) γ+(((-1+a))^2) (γ^2)) (λ^4))+(β^2) (-1+γ) (-3-γ (-6+a+γ)+13 λ+(a-28 γ+6 a γ+(14+a (-9+2 a)) (γ^2)+(-1+a) (γ^3)) λ-(19+3 a+(-42+a (8+a)) γ+(28+a (-17+3 a)) (γ^2)+(-1+a) (5+(-2+a) a) (γ^3)) (λ^2)+(13+a+11 (-3+a) γ+(27+a (-19+3 a)) (γ^2)+(-1+a) (5+a) (γ^3)) (λ^3)+(-1+γ) (5-2 a-9 γ+6 a γ+(1+a (3+(-5+a) a)) (γ^2)) (λ^4)+(-1+a) (((-1+γ))^2) (-1+a γ) (λ^5))+(1+γ (-2+λ)-λ) (1+λ (-1+(-1+a) γ (-1+λ)+λ-a λ))-(β^4) (((-1+γ))^3) (-1+λ) λ (-(-1+λ) (2+(-3+2 a (-1+λ)) λ)+γ (-1+a λ) (1+λ (-4+2 a+λ)))+(β^3) (((-1+γ))^2) ((γ^2) λ (2-a+(-9+(7-2 a) a) λ+(11-6 a+(a^3)) (λ^2)-(6+(-3+a) a) (λ^3)+(λ^4))+(-1+λ) (1+λ (-a (((1-2 λ))^2)+(-1+λ) (7+(-3+λ) λ)))-γ (-1+λ) (1+λ (-11+(a^2) (-2+λ) λ+2 λ (7+(-4+λ) λ)+a (3+λ-(λ^2)))))))+(Z (β^2) (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) (-(-1+β) (-1+γ) γ+(-1+3 γ+(-1+γ) (-β+(5-2 β) β γ+2 (1+a (-1+β)+(-1+β) β) (γ^2))) λ+(2+(-5+2 a) γ-(β^3) (((-1+γ))^3) γ+(-1+a) (γ^2) (-6+(3+a (-1+γ)-γ) γ)-(β^2) (((-1+γ))^2) (-2+γ (7+2 (-1+a) γ))-β (-1+γ) (-4+γ (11-2 a+6 (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^2)+(-1+γ) (1+(β^3) (((-1+γ))^2) (-1+3 γ)+(β^2) (-1+γ) (-5+γ (11-2 a+4 (-1+a) γ))+(-1+a) γ (2+γ (-1+a+2 γ-2 a γ))+β (-5+γ (11-4 a-(-7+a) (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^3)-(((-1+γ))^2) (2 (((-1+β))^2) β-(-1+β) β (-2+2 a+5 β) γ-((((-1+a))^2)-2 (-1+a) (β^2)-3 (β^3)) (γ^2)) (λ^4)+(β^2) (1+β (-1+γ)) (((-1+γ))^3) (λ^5))+β (1+β) (-1+γ) (λ^2) ((β^5) (((-1+γ))^4) (((-1+λ))^2) (λ^2) (-1+a λ)+β (-3+(8+a (-1+γ)-4 γ) γ+9 λ+γ (-23+4 a+2 (9+(-5+a) a) γ+(-5+(7-2 a) a) (γ^2)) λ+(-10+a+(29+(-12+a) a) γ+(-29+(23-4 a) a) (γ^2)-(-1+a) (10+(-3+a) a) (γ^3)+(((-1+a))^3) (γ^4)) (λ^2)-(-1+γ) (6-3 a+(-13+10 a) γ-(-1+a) (6+(a^2)) (γ^2)+2 (((-1+a))^3) (γ^3)) (λ^3)+(-1+a) (((-1+γ))^2) (2-(1+a) γ+(((-1+a))^2) (γ^2)) (λ^4))+(β^2) (-1+γ) (-3-γ (-6+a+γ)+13 λ+(a-28 γ+6 a γ+(14+a (-9+2 a)) (γ^2)+(-1+a) (γ^3)) λ-(19+3 a+(-42+a (8+a)) γ+(28+a (-17+3 a)) (γ^2)+(-1+a) (5+(-2+a) a) (γ^3)) (λ^2)+(13+a+11 (-3+a) γ+(27+a (-19+3 a)) (γ^2)+(-1+a) (5+a) (γ^3)) (λ^3)+(-1+γ) (5-2 a-9 γ+6 a γ+(1+a (3+(-5+a) a)) (γ^2)) (λ^4)+(-1+a) (((-1+γ))^2) (-1+a γ) (λ^5))+(1+γ (-2+λ)-λ) (1+λ (-1+(-1+a) γ (-1+λ)+λ-a λ))-(β^4) (((-1+γ))^3) (-1+λ) λ (-(-1+λ) (2+(-3+2 a (-1+λ)) λ)+γ (-1+a λ) (1+λ (-4+2 a+λ)))+(β^3) (((-1+γ))^2) ((γ^2) λ (2-a+(-9+(7-2 a) a) λ+(11-6 a+(a^3)) (λ^2)-(6+(-3+a) a) (λ^3)+(λ^4))+(-1+λ) (1+λ (-a (((1-2 λ))^2)+(-1+λ) (7+(-3+λ) λ)))-γ (-1+λ) (1+λ (-11+(a^2) (-2+λ) λ+2 λ (7+(-4+λ) λ)+a (3+λ-(λ^2)))))))==0]

((1+β) (λ^2) ((b-d) FullSimplify[(Z (β^2) (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) (-(-1+β) (-1+γ) γ+(-1+3 γ+(-1+γ) (-β+(5-2 β) β γ+2 (1+a (-1+β)+(-1+β) β) (γ^2))) λ+(2+(-5+2 a) γ-(β^3) (((-1+γ))^3) γ+(-1+a) (γ^2) (-6+(3+a (-1+γ)-γ) γ)-(β^2) (((-1+γ))^2) (-2+γ (7+2 (-1+a) γ))-β (-1+γ) (-4+γ (11-2 a+6 (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^2)+(-1+γ) (1+(β^3) (((-1+γ))^2) (-1+3 γ)+(β^2) (-1+γ) (-5+γ (11-2 a+4 (-1+a) γ))+(-1+a) γ (2+γ (-1+a+2 γ-2 a γ))+β (-5+γ (11-4 a-(-7+a) (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^3)-(((-1+γ))^2) (2 (((-1+β))^2) β-(-1+β) β (-2+2 a+5 β) γ-((((-1+a))^2)-2 (-1+a) (β^2)-3 (β^3)) (γ^2)) (λ^4)+(β^2) (1+β (-1+γ)) (((-1+γ))^3) (λ^5))+β (1+β) (-1+γ) (λ^2) ((β^5) (((-1+γ))^4) (((-1+λ))^2) (λ^2) (-1+a λ)+β (-3+(8+a (-1+γ)-4 γ) γ+9 λ+γ (-23+4 a+2 (9+(-5+a) a) γ+(-5+(7-2 a) a) (γ^2)) λ+(-10+a+(29+(-12+a) a) γ+(-29+(23-4 a) a) (γ^2)-(-1+a) (10+(-3+a) a) (γ^3)+(((-1+a))^3) (γ^4)) (λ^2)-(-1+γ) (6-3 a+(-13+10 a) γ-(-1+a) (6+(a^2)) (γ^2)+2 (((-1+a))^3) (γ^3)) (λ^3)+(-1+a) (((-1+γ))^2) (2-(1+a) γ+(((-1+a))^2) (γ^2)) (λ^4))+(β^2) (-1+γ) (-3-γ (-6+a+γ)+13 λ+(a-28 γ+6 a γ+(14+a (-9+2 a)) (γ^2)+(-1+a) (γ^3)) λ-(19+3 a+(-42+a (8+a)) γ+(28+a (-17+3 a)) (γ^2)+(-1+a) (5+(-2+a) a) (γ^3)) (λ^2)+(13+a+11 (-3+a) γ+(27+a (-19+3 a)) (γ^2)+(-1+a) (5+a) (γ^3)) (λ^3)+(-1+γ) (5-2 a-9 γ+6 a γ+(1+a (3+(-5+a) a)) (γ^2)) (λ^4)+(-1+a) (((-1+γ))^2) (-1+a γ) (λ^5))+(1+γ (-2+λ)-λ) (1+λ (-1+(-1+a) γ (-1+λ)+λ-a λ))-(β^4) (((-1+γ))^3) (-1+λ) λ (-(-1+λ) (2+(-3+2 a (-1+λ)) λ)+γ (-1+a λ) (1+λ (-4+2 a+λ)))+(β^3) (((-1+γ))^2) ((γ^2) λ (2-a+(-9+(7-2 a) a) λ+(11-6 a+(a^3)) (λ^2)-(6+(-3+a) a) (λ^3)+(λ^4))+(-1+λ) (1+λ (-a (((1-2 λ))^2)+(-1+λ) (7+(-3+λ) λ)))-γ (-1+λ) (1+λ (-11+(a^2) (-2+λ) λ+2 λ (7+(-4+λ) λ)+a (3+λ-(λ^2)))))))]))/FullSimplify[((1+γ λ-a γ λ+(λ^2)-a (λ^2)-γ (λ^2)+a γ (λ^2)) (1-λ+β λ+γ λ-a γ λ-β γ λ+(λ^2)-a (λ^2)-a β (λ^2)-γ (λ^2)+a γ (λ^2)+a β γ (λ^2)) (Z β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ)-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))) (Z β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (1+(-1+a) (γ (-1+λ)-λ) λ)+(1+β) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2)))))]

((b-d) β (1+β) (λ^2) (Z β (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) (-(-1+β) (-1+γ) γ+(-1+3 γ+(-1+γ) (-β+(5-2 β) β γ+2 (1+a (-1+β)+(-1+β) β) (γ^2))) λ+(2+(-5+2 a) γ-(β^3) (((-1+γ))^3) γ+(-1+a) (γ^2) (-6+(3+a (-1+γ)-γ) γ)-(β^2) (((-1+γ))^2) (-2+γ (7+2 (-1+a) γ))-β (-1+γ) (-4+γ (11-2 a+6 (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^2)+(-1+γ) (1+(β^3) (((-1+γ))^2) (-1+3 γ)+(β^2) (-1+γ) (-5+γ (11-2 a+4 (-1+a) γ))+(-1+a) γ (2+γ (-1+a+2 γ-2 a γ))+β (-5+γ (11-4 a-(-7+a) (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^3)-(((-1+γ))^2) (2 (((-1+β))^2) β-(-1+β) β (-2+2 a+5 β) γ-((((-1+a))^2)-2 (-1+a) (β^2)-3 (β^3)) (γ^2)) (λ^4)+(β^2) (1+β (-1+γ)) (((-1+γ))^3) (λ^5))+(1+β) (-1+γ) (λ^2) ((β^5) (((-1+γ))^4) (((-1+λ))^2) (λ^2) (-1+a λ)+β (-3+(8+a (-1+γ)-4 γ) γ+9 λ+γ (-23+4 a+2 (9+(-5+a) a) γ+(-5+(7-2 a) a) (γ^2)) λ+(-10+a+(29+(-12+a) a) γ+(-29+(23-4 a) a) (γ^2)-(-1+a) (10+(-3+a) a) (γ^3)+(((-1+a))^3) (γ^4)) (λ^2)-(-1+γ) (6-3 a+(-13+10 a) γ-(-1+a) (6+(a^2)) (γ^2)+2 (((-1+a))^3) (γ^3)) (λ^3)+(-1+a) (((-1+γ))^2) (2-(1+a) γ+(((-1+a))^2) (γ^2)) (λ^4))+(β^2) (-1+γ) (-3-γ (-6+a+γ)+13 λ+(a-28 γ+6 a γ+(14+a (-9+2 a)) (γ^2)+(-1+a) (γ^3)) λ-(19+3 a+(-42+a (8+a)) γ+(28+a (-17+3 a)) (γ^2)+(-1+a) (5+(-2+a) a) (γ^3)) (λ^2)+(13+a+11 (-3+a) γ+(27+a (-19+3 a)) (γ^2)+(-1+a) (5+a) (γ^3)) (λ^3)+(-1+γ) (5-2 a-9 γ+6 a γ+(1+a (3+(-5+a) a)) (γ^2)) (λ^4)+(-1+a) (((-1+γ))^2) (-1+a γ) (λ^5))+(1+γ (-2+λ)-λ) (1+λ (-1+(-1+a) γ (-1+λ)+λ-a λ))-(β^4) (((-1+γ))^3) (-1+λ) λ (-(-1+λ) (2+(-3+2 a (-1+λ)) λ)+γ (-1+a λ) (1+λ (-4+2 a+λ)))+(β^3) (((-1+γ))^2) ((γ^2) λ (2-a+(-9+(7-2 a) a) λ+(11-6 a+(a^3)) (λ^2)-(6+(-3+a) a) (λ^3)+(λ^4))+(-1+λ) (1+λ (-a (((1-2 λ))^2)+(-1+λ) (7+(-3+λ) λ)))-γ (-1+λ) (1+λ (-11+(a^2) (-2+λ) λ+2 λ (7+(-4+λ) λ)+a (3+λ-(λ^2))))))))/((1+(-1+a) (γ (-1+λ)-λ) λ) (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) (Z β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ)-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))) (Z β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (1+(-1+a) (γ (-1+λ)-λ) λ)+(1+β) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2)))))/.Z->Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]

The remaining expression involves β, λ, γ, and a, all of which must lie between 0 and 1.  At any given parameter values (β, λ, γ), we can then numerically evaluate this expression for all 0 ≤ a ≤ 1 to verify that its sign is negative.

We provide two tools to facilitate such computations.  One plots the derivative’s value for each a, given the other parameters; the other does the same for (a, γ) pairs, given β and λ.  In the latter, the graph truncates values above 0, which would show up as a dark blue plateau.

Manipulate[Plot[If[γ==1,((β λ (1-β (1+λ)))/((-1+β) (-1+(-1+a) λ))),( β (1+β) (λ^2) ((1+β) (-1+γ) (λ^2) ((β^5) (((-1+γ))^4) (((-1+λ))^2) (λ^2) (-1+a λ)+β (-3+(8+a (-1+γ)-4 γ) γ+9 λ+γ (-23+4 a+2 (9+(-5+a) a) γ+(-5+(7-2 a) a) (γ^2)) λ+(-10+a+(29+(-12+a) a) γ+(-29+(23-4 a) a) (γ^2)-(-1+a) (10+(-3+a) a) (γ^3)+(((-1+a))^3) (γ^4)) (λ^2)-(-1+γ) (6-3 a+(-13+10 a) γ-(-1+a) (6+(a^2)) (γ^2)+2 (((-1+a))^3) (γ^3)) (λ^3)+(-1+a) (((-1+γ))^2) (2-(1+a) γ+(((-1+a))^2) (γ^2)) (λ^4))+(β^2) (-1+γ) (-3-γ (-6+a+γ)+13 λ+(a-28 γ+6 a γ+(14+a (-9+2 a)) (γ^2)+(-1+a) (γ^3)) λ-(19+3 a+(-42+a (8+a)) γ+(28+a (-17+3 a)) (γ^2)+(-1+a) (5+(-2+a) a) (γ^3)) (λ^2)+(13+a+11 (-3+a) γ+(27+a (-19+3 a)) (γ^2)+(-1+a) (5+a) (γ^3)) (λ^3)+(-1+γ) (5-2 a-9 γ+6 a γ+(1+a (3+(-5+a) a)) (γ^2)) (λ^4)+(-1+a) (((-1+γ))^2) (-1+a γ) (λ^5))+(1+γ (-2+λ)-λ) (1+λ (-1+(-1+a) γ (-1+λ)+λ-a λ))-(β^4) (((-1+γ))^3) (-1+λ) λ ((1-λ) (2+(-3+2 a (-1+λ)) λ)+γ (-1+a λ) (1+λ (-4+2 a+λ)))+(β^3) (((-1+γ))^2) ((γ^2) λ (2-a+(-9+(7-2 a) a) λ+(11-6 a+(a^3)) (λ^2)-(6+(-3+a) a) (λ^3)+(λ^4))+(-1+λ) (1+λ (-a (((1-2 λ))^2)+(-1+λ) (7+(-3+λ) λ)))-γ (-1+λ) (1+λ (-11+(a^2) (-2+λ) λ+2 λ (7+(-4+λ) λ)+a (3+λ-(λ^2))))))+β (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) ((1-β) (-1+γ) γ+(-1+3 γ+(-1+γ) (-β+(5-2 β) β γ+2 (1+a (-1+β)+(-1+β) β) (γ^2))) λ+(2+(-5+2 a) γ-(β^3) (((-1+γ))^3) γ+(-1+a) (γ^2) (-6+(3+a (-1+γ)-γ) γ)-(β^2) (((-1+γ))^2) (-2+γ (7+2 (-1+a) γ))-β (-1+γ) (-4+γ (11-2 a+6 (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^2)+(-1+γ) (1+(β^3) (((-1+γ))^2) (-1+3 γ)+(β^2) (-1+γ) (-5+γ (11-2 a+4 (-1+a) γ))+(-1+a) γ (2+γ (-1+a+2 γ-2 a γ))+β (-5+γ (11-4 a-(-7+a) (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^3)-(((-1+γ))^2) (2 (((-1+β))^2) β-(-1+β) β (-2+2 a+5 β) γ-((((-1+a))^2)-2 (-1+a) (β^2)-3 (β^3)) (γ^2)) (λ^4)+(β^2) (1+β (-1+γ)) (((-1+γ))^3) (λ^5)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((1+(-1+a) (γ (-1+λ)-λ) λ) (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) (-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))+β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]) ((1+β) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2)))+β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (1+(-1+a) (γ (-1+λ)-λ) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))],{a,0,1},PlotRange->Full,AxesLabel->{"a","dD/da"}],{{λ,2/3},1/8,1},{{γ,1/2},1/12,1},{{β,0.99},8/9,0.9999999}]

Manipulate[Plot3D[( β (1+β) (λ^2) ((1+β) (-1+γ) (λ^2) ((β^5) (((-1+γ))^4) (((-1+λ))^2) (λ^2) (-1+a λ)+β (-3+(8+a (-1+γ)-4 γ) γ+9 λ+γ (-23+4 a+2 (9+(-5+a) a) γ+(-5+(7-2 a) a) (γ^2)) λ+(-10+a+(29+(-12+a) a) γ+(-29+(23-4 a) a) (γ^2)-(-1+a) (10+(-3+a) a) (γ^3)+(((-1+a))^3) (γ^4)) (λ^2)-(-1+γ) (6-3 a+(-13+10 a) γ-(-1+a) (6+(a^2)) (γ^2)+2 (((-1+a))^3) (γ^3)) (λ^3)+(-1+a) (((-1+γ))^2) (2-(1+a) γ+(((-1+a))^2) (γ^2)) (λ^4))+(β^2) (-1+γ) (-3-γ (-6+a+γ)+13 λ+(a-28 γ+6 a γ+(14+a (-9+2 a)) (γ^2)+(-1+a) (γ^3)) λ-(19+3 a+(-42+a (8+a)) γ+(28+a (-17+3 a)) (γ^2)+(-1+a) (5+(-2+a) a) (γ^3)) (λ^2)+(13+a+11 (-3+a) γ+(27+a (-19+3 a)) (γ^2)+(-1+a) (5+a) (γ^3)) (λ^3)+(-1+γ) (5-2 a-9 γ+6 a γ+(1+a (3+(-5+a) a)) (γ^2)) (λ^4)+(-1+a) (((-1+γ))^2) (-1+a γ) (λ^5))+(1+γ (-2+λ)-λ) (1+λ (-1+(-1+a) γ (-1+λ)+λ-a λ))-(β^4) (((-1+γ))^3) (-1+λ) λ ((1-λ) (2+(-3+2 a (-1+λ)) λ)+γ (-1+a λ) (1+λ (-4+2 a+λ)))+(β^3) (((-1+γ))^2) ((γ^2) λ (2-a+(-9+(7-2 a) a) λ+(11-6 a+(a^3)) (λ^2)-(6+(-3+a) a) (λ^3)+(λ^4))+(-1+λ) (1+λ (-a (((1-2 λ))^2)+(-1+λ) (7+(-3+λ) λ)))-γ (-1+λ) (1+λ (-11+(a^2) (-2+λ) λ+2 λ (7+(-4+λ) λ)+a (3+λ-(λ^2))))))+β (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) ((1-β) (-1+γ) γ+(-1+3 γ+(-1+γ) (-β+(5-2 β) β γ+2 (1+a (-1+β)+(-1+β) β) (γ^2))) λ+(2+(-5+2 a) γ-(β^3) (((-1+γ))^3) γ+(-1+a) (γ^2) (-6+(3+a (-1+γ)-γ) γ)-(β^2) (((-1+γ))^2) (-2+γ (7+2 (-1+a) γ))-β (-1+γ) (-4+γ (11-2 a+6 (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^2)+(-1+γ) (1+(β^3) (((-1+γ))^2) (-1+3 γ)+(β^2) (-1+γ) (-5+γ (11-2 a+4 (-1+a) γ))+(-1+a) γ (2+γ (-1+a+2 γ-2 a γ))+β (-5+γ (11-4 a-(-7+a) (-1+a) γ+(((-1+a))^2) (γ^2)))) (λ^3)-(((-1+γ))^2) (2 (((-1+β))^2) β-(-1+β) β (-2+2 a+5 β) γ-((((-1+a))^2)-2 (-1+a) (β^2)-3 (β^3)) (γ^2)) (λ^4)+(β^2) (1+β (-1+γ)) (((-1+γ))^3) (λ^5)) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]))/((1+(-1+a) (γ (-1+λ)-λ) λ) (1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)) (-(1+β) (-1+γ) λ (1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ))+β (1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))]) ((1+β) (λ^2) (1+(-1+a) (-1+γ) λ+(β^2) (((-1+γ))^2) (-1+λ) (-1+a λ)-β (-1+γ) (-1-a+(2 a+(-2+a) (-1+a) γ) λ+(-1+a) (-1+γ) (λ^2)))+β (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (1+(-1+a) (γ (-1+λ)-λ) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])),{a,0,1},{γ,1/12,1},AxesLabel->{"a","γ","dD/da"},PlotRange->{All,0}],{{λ,2/3},1/8,1},{{β,0.99},8/9,0.999999}]

No Recall

Solution

The prior solution is applicable just by taking the limit as γ approaches 1.  The same solution is obtained if one sets γ = 1 in the original Bellman and steady state equations.

Limit[((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],γ->1]

Simplify[κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/. ϕ[a]->(-1+a) λ/.γ->1]

κ[a]->x-c-((β (d+a b β λ-a d β λ))/(1-β))

FullSimplify[{R0->c+κ[a],pmin->(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),Π0->λ(1-((λ (1-(1-γ)(β +a λ+(1+β) λ)))/(1+λ (γ+λ-γ λ) (1-a))))κ[a],Π2-> λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))}/.κ[a]->x-c-((β (d+a b β λ-a d β λ))/(1-β))/.γ->1]

{R0->x-((β (d+a β λ(b-d)))/(1-β)),pmin->x-((β (d+a β λ(b-d)))/(1-β)),R2->x-((β (b-β(b-d)(1-a λ)))/(1-β)),Π0->λ (1+(λ/(-1+(-1+a) λ))) (x-c-((β (d+a β λ(b-d)))/(1-β))),Π2->λ (x-c-((β (d+(1-β+a β λ)(b-d)))/(1-β)))}

The comparison of profits simplifies as follows:

FullSimplify[λ (x-c-((β (d+(1-β+a β λ)(b-d)))/(1-β)))>λ (1+(λ/(-1+(-1+a) λ))) (x-c-((β (d+a β λ(b-d)))/(1-β)))]

(c-x) (1-β) λ-d β (-1+a λ) (-1+β+β λ)+b β (1+λ-a λ+β (1+λ) (-1+a λ))<0

(x-c) (1-β) λ>λ b β +FullSimplify[-d β (-1+a λ) (-1+β+β λ)+b β (1-a λ+β (1+λ) (-1+a λ))]

x-c>(β/((1-β) λ))(b λ-(β λ+β-1)(1-a λ)(b-d))

And in a full equilibrium, a must make the comparison hold with equality, so

FullSimplify[Solve[x-c==(β/((1-β) λ))(b λ-(β λ+β-1)(1-a λ)(b-d)),a]]

In which case:

FullSimplify[{R0->x-((β (d+a β λ(b-d)))/(1-β)),R2->x-((β (b-β(b-d)(1-a λ)))/(1-β))}/.a->(1/λ)+((x+c (-1+β)-(b+x) β)/((b-d) β (-1+β+β λ)))]

Guaranteed Sampling

Solution

The prior solution is applicable by setting λ = β = 1.  The same solution is obtained if one sets γ = 1 in the original Bellman and steady state equations.

Simplify[((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.λ->1/.β->1]

Simplify[κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/. ϕ[a]->(((-1+a) γ Log[-(γ/(-2+γ))])/(2 (-1+γ)))/.λ->1/.β->1]

κ[a]->-((2 (1-γ) (d γ+a (b-d γ)))/((1-a) γ (2-2 γ+γ Log[-(γ/(-2+γ))])))

FullSimplify[{R0->c+κ[a],pmin->(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),F[p]->1-(((c+κ[a]-p) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((p-c)(1-γ) (λ^2) (1+β) )),Π0->λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a],Π2-> λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))}/.λ->1/.β->1]

F[p]->1-(((1-a) γ )/(2 (1-γ)))(((κ[a])/(p-c))-1)

The comparison of profits simplifies as follows.  Π2 > Π0 iff:

d-(b/γ)+κ[a]>(((1-a) γ κ[a])/(2-a))

γ d-b>γ((((1-a) γ-2+a)/(2-a))) κ[a]

γ d-b>-((2 (1-γ) (d γ+a (b-d γ)))/((1-a) γ (2-2 γ+γ Log[-(γ/(-2+γ))])))γ((((1-a) γ-2+a)/(2-a)))

γ d-b>((2 (1-γ) (2-a-(1-a) γ)(d γ+a (b-d γ)))/((1-a)(2-a) (2(1-γ)+γ Log[(γ/(2-γ))])))

Proposition 3

Suppose profits are equated for 0 < a < 1.  Then we solve the equal profit condition for b:

FullSimplify[Solve[γ d-b==((2 (1-γ) (2-a-(1-a) γ)(d γ+a (b-d γ)))/((1-a)(2-a) (2(1-γ)+γ Log[(γ/(2-γ))]))),b]]

b->(((1-a) d (γ^2) (2 (1-a) (1-γ)+(2-a) Log[(γ/(2-γ))]))/(2 (1-γ) (2-a-(1-a) a γ)+(2-a) (1-a) γ Log[(γ/(2-γ))]))

FullSimplify[D[(γ d-b)-((2 (1-γ) (2-a-(1-a) γ)(d γ+a (b-d γ)))/((1-a)(2-a) (2(1-γ)+γ Log[(γ/(2-γ))]))),a]/.b->(((-1+a) d (γ^2) (2 (-1+a) (-1+γ)-(-2+a) Log[-(γ/(-2+γ))]))/(2 (-1+γ) (2-a+(-1+a) a γ)-(-2+a) (-1+a) γ Log[-(γ/(-2+γ))]))]

(2 d (1-γ) (γ^2) (2 (1-a) (3-a (1-γ)-γ) (1-γ)-((((1-a))^2) γ-(((2-a))^2)) Log[(γ/(2-γ))]))/((2-a) (1-a) (2(1-γ)+γ Log[(γ/(2-γ))]) (2 (1-γ) ((1-a) a γ-2+a)-(2-a) (1-a) γ Log[(γ/(2-γ))]))

We show below that the numerator is positive, and the denominator is negative.

Numerator

By assumption, 2 d (1-γ) (γ^2) is negative.  The remaining term is strictly increasing in γ:

FullSimplify[D[2 (1-a) (3-a (1-γ)-γ) (1-γ)-((((1-a))^2) γ-(((2-a))^2)) Log[(γ/(2-γ))],γ]]

(1/((2-γ) γ))(2 (((2-a))^2)-2 (1-a) (9-5 a) γ+4 (1-a) (4-3 a) (γ^2)-4 (((1-a))^2) (γ^3)-(((1-a))^2) (2-γ) γ Log[(γ/(2-γ))])

The operand of the integral is always less than 1; thus, the last term is strictly positive.  The preceeding terms can be rearranged to :

FullSimplify[2 (((2-a))^2)-2 (1-a) (9-5 a) γ+4 (1-a) (4-3 a) (γ^2)-4 (((1-a))^2) (γ^3)==2 (a^2)+(8-18 γ+12 (γ^2))(1-a)+2 a (1-a)(5-4 γ) γ+4 (γ^3)(1-2a+(a^2))(1-γ)+4 (((1-a))^2) (((1-γ))^2) (γ^2)]

2 (a^2)+(8-18 γ+12 (γ^2))(1-a)+2 a (1-a)(5-4 γ) γ+4 (γ^3)(1-2a+(a^2))(1-γ)+4 (((1-a))^2) (((1-γ))^2) (γ^2)

Each term above is positive in its own right.  (The only one that is not obvious is γ, which reaches a minimum of 1 at γ = 3/4)

Plot[8-18 γ+12 (γ^2),{γ,0,1}]

Thus, the last term in the numerator is always increasing in γ, reaching a maximum of 0 when γ = 1.  Thus the term is negative, and since this multiplied by d, the numerator is positive.

2 (1-a) (3-a (1-γ)-γ) (1-γ)-((((1-a))^2) γ-(((2-a))^2)) Log[(γ/(2-γ))]/.γ->1

Denominator, part 1

(2-a) (1-a) is always positive.  Next consider 2(1-γ)+γ Log[(γ/(2-γ))].  Its derivative w.r.t. γ is negative:

FullSimplify[D[2(1-γ)+γ Log[(γ/(2-γ))],γ]]

-((2(1-γ))/(2-γ))+Log[(1/(2-γ))]+Log[γ]

Note that the two log terms operate on a term less than 1, and are hence negative.  Thus, since this derivative is negative, then 2(1-γ)+γ Log[(γ/(2-γ))] is smallest at γ = 1, where it is 0.

Denominator, part 2

Last, we consider 2 (1-γ) ((1-a) a γ-2+a)-(2-a) (1-a) γ Log[(γ/(2-γ))].  This is strictly increasing in γ:

FullSimplify[D[2 (1-γ) ((1-a) a γ-2+a)-(2-a) (1-a) γ Log[(γ/(2-γ))],γ]]

which simplifies to:

((4(1-γ))/(2-γ))+((2 a (3-γ-(3-2 γ)(γ(1-a)+a)))/(2-γ))-(2-a) (1-a) Log[(γ/(2-γ))]

FullSimplify[((2 (2 (-1+γ)+a (-3-2 (-2+γ) γ+a (-1+γ) (-3+2 γ)))-(-2+a) (-1+a) (-2+γ) Log[(γ/(2-γ))])/(-2+γ))==((4(1-γ))/(2-γ))+((2 a (3-γ-(3-2 γ)(γ(1-a)+a)))/(2-γ))-(2-a) (1-a) Log[(γ/(2-γ))]]

The first term is clearly positive.  The second also is, as

3-γ-(3-2 γ)(γ(1-a)+a)>3-γ-(3-2 γ)==γ≥0

The operand of the Log term is always less than 1, and hence negative, making the last term positive.

Thus, 2 (1-γ) ((1-a) a γ-2+a)-(2-a) (1-a) γ Log[(γ/(2-γ))] is maximized when γ = 1, attaining a value of 0.

2 (1-γ) ((1-a) a γ-2+a)-(2-a) (1-a) γ Log[(γ/(2-γ))]/.γ->1

Hence, this term is negative.

Numerical Illustration

Computed Full Equilibrium

Before computing any particular equilibrium values, we must evaluate the following line so that V2 can be easily computed:

V2=b+((a λ (b β-γ (c-x+d β+κ[a])))/(1+β (-1+γ)))-(β (1-γ) (1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (-(2+(-3+β+3 γ-2 a γ-β γ) λ+(-1+β) (-1+γ) (λ^2)) (((1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)))^2) Log[((1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2))/(1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)))] ((κ[a])^2)+(-1+a) (1+β) (-1+γ) (λ^2) (1+(-1+β+γ-a γ-β γ) λ+(-1+a+a β) (-1+γ) (λ^2)) ((c^2) (2+λ (-3+β (-1+γ) (-1+λ)+λ-γ (-3+2 a+λ)))+c ((-1+λ (1+(-1+a) γ+β (-1+γ+λ-γ λ))) (c+κ[a])+((-3+λ (4-λ+γ (-4+3 a+λ)+2 β (-1+γ+λ-γ λ))) ((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a])))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))+(-1-β) (-1+γ) λ (b+x-((a λ (-b β+x (-1+β) (-1+γ)+c γ+d β γ+γ κ[a]))/(1+β (-1+γ)))))+(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a])) (2 (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) (c+κ[a])+(1+β) (-1+γ) λ (b+x-((a λ (-b β+x (-1+β) (-1+γ)+c γ+d β γ+γ κ[a]))/(1+β (-1+γ))))))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ)))))/((((1+β))^2) (((-1+γ))^2) (λ^2) (((1+(-1+β+γ-a γ-β γ) λ+β (-1+γ) (λ^2)))^2) κ[a])+β (1+(-1+γ-a γ) λ) (b-d+((d+λ (-c+x-a (-c+x+((-b β+(c-x+d β) γ+γ κ[a])/(1+β (-1+γ)))))+κ[a] ϕ[a])/(1+β (-1+λ))))/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))];

For the following evaluations, we fix the parameter values as specified in the text.  To clear these values, evaluate the following line:

Clear[x,c,b,d,λ,γ,β]

First, we compute the equilibrium a* associated with these parameters.

x=1500;c=1000;d=-100;b=100;λ=2/3;γ=1/2;β=0.99;FindRoot[λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))-λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],{a,0.1,0,1}]

Next, we compute the equilibrium prices, and expected firm profit:

{R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),pmin->(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),R0->c+κ[a]/.R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ)))}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.%

Plot[If[p<x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),0,If[p<(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),a,If[p>c+κ[a],1,1-(((c+κ[a]-p) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((p-c)(1-γ) (λ^2) (1+β) ))]]]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.%%,{p,1250,1600},AxesLabel->{"p","F(p)"},PlotStyle->Thick,PlotRange->{0,1}]

The steady state distribution is:

{h0->((δ (-1+λ) (-1+(1+(-1+a) γ) λ))/λ),h1->δ+(-1+γ-a γ) δ λ,h2->δ,g1[q]->-(-1+γ) δ λ F'[q]}/.%%%

The ex-ante probability of each outcome is:

N[Grid[{{"State 2 offer","State 1 offer","Outcome Probability","Example"},{"Accepted","-","λ a",λ a},{"Retained","Received","(λ^2)(1-a) (1-γ)",(λ^2)(1-a) (1-γ)},{"Retained","None","λ (1-λ) (1-a) (1-γ)",λ (1-λ) (1-a) (1-γ)},{"Lost","Received","(λ^2)(1-a) γ",(λ^2)(1-a) γ},{"Lost","None","λ (1-λ) (1-a) γ",λ (1-λ) (1-a) γ},{"None","Received","(1-λ)λ",(1-λ)λ },
{"None","None","(1-λ)^2",(((1-λ))^2)}}]]/.%%%%

Ex-ante utility is:

V2/.%%%%%

Full Equilibrium with Perfect Recall

First, we compute the equilibrium a* associated with these parameters.

x=1500;c=1000;d=-100;b=10/3;λ=2/3;γ=0;β=0.99;FindRoot[λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))-λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],{a,0.1,0,1}]

Next, we compute the equilibrium prices, and expected firm profit:

{R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),pmin->(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),R0->c+κ[a],EΠ->((-c λ+R2 λ)/(1-β+β λ))/.R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ)))}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.%

Plot[If[p<x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),0,If[p<(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),a,If[p>c+κ[a],1,1-(((c+κ[a]-p) (1-λ a γ-λ(1-γ)(1-β+β λ)))/((p-c)(1-γ) (λ^2) (1+β) ))]]]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.%%,{p,1150,1400},AxesLabel->{"p","F(p)"},PlotStyle->Thick,PlotRange->{0,1}]

The steady state distribution is:

{h0->((δ (-1+λ) (-1+(1+(-1+a) γ) λ))/λ),h1->δ+(-1+γ-a γ) δ λ,h2->δ,g1[q]->-(-1+γ) δ λ F'[q]}/.%%%

The ex-ante probability of each outcome is:

N[Grid[{{"State 2 offer","State 1 offer","Outcome Probability","Example"},{"Accepted","-","λ a",λ a},{"Retained","Received","(λ^2)(1-a) (1-γ)",(λ^2)(1-a) (1-γ)},{"Retained","None","λ (1-λ) (1-a) (1-γ)",λ (1-λ) (1-a) (1-γ)},{"Lost","Received","(λ^2)(1-a) γ",(λ^2)(1-a) γ},{"Lost","None","λ (1-λ) (1-a) γ",λ (1-λ) (1-a) γ},{"None","Received","(1-λ)λ",(1-λ)λ },
{"None","None","(1-λ)^2",(((1-λ))^2)}}]]/.%%%%

Ex-ante utility is:

V2/.%%%%%

Grid[{{"Scenario","Total Surplus"},{"Model",V2+((-c λ+R2 λ)/(1-β+β λ))/.R2->x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ)))},{"Take First chance",((-b (-1+(β^2) (((-1+λ))^2))+d (β^2) (((-1+λ))^2)+(-c+x) λ)/(1+β (-1+λ)))},{"Always get offer in state 1",(1+β)b+β (x-c)}}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.%%%%%%]

Other Parameters

To allow the user to experiment with various parameter values, we provide the following interactive tool.  This repeats the prior computations for whichever paramater values are set with the sliders.

To do this, one should first clear the parameters used in prior sections.  We also normalize c = 1000.

Clear[x,c,b,d,λ,γ,β];
c=1000;

Manipulate[Grid[{{"Equilibrium","a","R2","pmin","R0","TW"},If[ -c+x+((-b β+γ (c-x+d β+κ[1]))/(1+β (-1+γ)))<(-1+λ)(-1+β (-1+γ) λ) κ[1],{"Early","∅"},{"Early",1,x-((β b+γ(x-c-β d-κ[1]))/((1-β+β γ))),c+κ[1],c+κ[1],((d (β^2) (((-1+λ))^2)+(-c+x) λ)/(1+β (-1+λ)))+b (1+β-β λ)}]/.κ[1]->(((-b+d) (β^2) λ+(x+c (-1+β)-(d+x) β) (1+β (-1+γ+λ-γ λ)))/((-1+β) (-1+β (-1+γ) (-1+λ)))),If[ 0<a<1,{"Full",a,x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),c+κ[a],b (1+β-a β λ)+(1/(1+β (-1+λ)))(a (-c+x) λ+β (-(-1+a) (c-x) λ (-2+γ+β (-1+γ) (-1+λ)+λ-γ λ)+d β (-1+λ) (-1+(1+(-1+a) γ) λ)))},{"Full","∅"}]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((λ^2) (1-γ)(1-a) (1+β))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.Quiet[FindRoot[-c+x-((b β+(-c+x-d β) γ)/(1-β+β γ))-((1-(γ/(1+β (-1+γ)))+((λ (-1+β-β γ+(1-a+β) (-1+γ) λ))/(1+(-1+a) (γ (-1+λ)-λ) λ))) (a (-b+d) (β^2) λ+(x+c (-1+β)-(d+x) β) (1-β (-1+γ) (-1+a λ))))/(1+β (-2+γ+β (-1+γ) (-1+λ)+λ-a γ λ-1/((1+β) (-1+γ) λ)(1+β (-1+γ)) (1+(-1+γ-a γ+β (-1+γ) (-1+λ)) λ) Log[1-(((-1+a) (1+β) (-1+γ) (λ^2))/(1+(-1+β-(-1+a+β) γ) λ+(-1+a+a β) (-1+γ) (λ^2)))])),{a,0.5,0,1}]],If[-c+x+(((1+(-1+γ) (1+β (-1+λ)) λ) κ[0])/(-1+γ (-1+λ) λ-(λ^2)))+((-b β+γ (c-x+d β+κ[0]))/(1+β (-1+γ)))>0,{"Late","∅"},{"Late",0,x-((β b+γ(x-c-β d-κ[0]))/((1-β+β γ))),((-c (1+β) (-1+γ) (λ^2)+(1+(-1+γ) (1+β (-1+λ)) λ) (c+κ[0]))/(1-(-1+γ) λ (-1+β+λ))),c+κ[0],b (1+β)+((β (-d β (-1+λ) (1+(-1+γ) λ)-(-c+x) λ (-2+β+γ-β γ+(-1+β) (-1+γ) λ)))/(1+β (-1+λ)))}]/.κ[0]->((x+c (-1+β)-(d+x) β)/(1+β (-1+λ)-((β (1+(-1+γ) (1+β (-1+λ)) λ) Log[((-1+(-1+γ) λ (-1+β-β λ))/(-1+(-1+γ) λ (-1+β+λ)))])/((1+β) (-1+γ) λ))))}],{{x,1500},1000,2000},{{d,-100},-500,0},{{b,100},0,500},{{γ,1/2},0,0.999},{{λ,2/3},0.01,1},{{β,0.99},.8,.99}]

Comparative Statics

We compute comparative statics relative to the baseline parameterization.  Thus, we first compute and store the equilibrium values for a* and the equilibrium prices.

Clear[x,c,b,d,λ,γ,β]

x=1500;c=1000;d=-100;b=100;λ=2/3;γ=1/2;β=0.99;

Equil={a,x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),c+κ[a],V2,b (1+β-a β λ)+(1/(1+β (-1+λ)))(a (-c+x) λ+β (-(-1+a) (c-x) λ (-2+γ+β (-1+γ) (-1+λ)+λ-γ λ)+d β (-1+λ) (-1+(1+(-1+a) γ) λ)))}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.FindRoot[λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))-λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],{a,0.1,0,1}]

d / dx

x=x+1;Equilx={a,x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),c+κ[a],V2,b (1+β-a β λ)+(1/(1+β (-1+λ)))(a (-c+x) λ+β (-(-1+a) (c-x) λ (-2+γ+β (-1+γ) (-1+λ)+λ-γ λ)+d β (-1+λ) (-1+(1+(-1+a) γ) λ)))}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.FindRoot[λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))-λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],{a,0.1,0,1}]
x=x-1;

Equilx-Equil

d / db

b=b+1;Equilb={a,x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),c+κ[a],V2,b (1+β-a β λ)+(1/(1+β (-1+λ)))(a (-c+x) λ+β (-(-1+a) (c-x) λ (-2+γ+β (-1+γ) (-1+λ)+λ-γ λ)+d β (-1+λ) (-1+(1+(-1+a) γ) λ)))}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.FindRoot[λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))-λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],{a,0.1,0,1}]
b=b-1;

Equilb-Equil

d / dd

d=d+1;Equild={a,x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),c+κ[a],V2,b (1+β-a β λ)+(1/(1+β (-1+λ)))(a (-c+x) λ+β (-(-1+a) (c-x) λ (-2+γ+β (-1+γ) (-1+λ)+λ-γ λ)+d β (-1+λ) (-1+(1+(-1+a) γ) λ)))}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.FindRoot[λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))-λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],{a,0.1,0,1}]
d=d-1;

Equild-Equil

d / dγ

γ=γ+0.01;Equilγ={a,x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),c+κ[a],V2,b (1+β-a β λ)+(1/(1+β (-1+λ)))(a (-c+x) λ+β (-(-1+a) (c-x) λ (-2+γ+β (-1+γ) (-1+λ)+λ-γ λ)+d β (-1+λ) (-1+(1+(-1+a) γ) λ)))}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.FindRoot[λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))-λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],{a,0.1,0,1}]
γ=γ-0.01;

Equilγ-Equil

d / dλ

λ=λ+0.01;Equilλ={a,x-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))),(((-1+a) c (1+β) (-1+γ) (λ^2)+(1-a γ λ+(-1+γ) (1+β (-1+λ)) λ) (c+κ[a]))/(1-a γ λ+(-1+γ) λ (1-β+(-1+a+a β) λ))),c+κ[a],V2,b (1+β-a β λ)+(1/(1+β (-1+λ)))(a (-c+x) λ+β (-(-1+a) (c-x) λ (-2+γ+β (-1+γ) (-1+λ)+λ-γ λ)+d β (-1+λ) (-1+(1+(-1+a) γ) λ)))}/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))]/.FindRoot[λ(x-c-((β b+γ(x-c-β d-κ[a]))/((1-β+β γ))))-λ(1-((λ (1-(1-γ)(β +a λ-(1+β) λ )))/(1+λ (γ+λ-γ λ) (1-a))))κ[a]/.κ[a]->(((1-β)(x-c)-β d)(1-β+β γ+a β λ(1-γ))-(β^2) λ a(b-d))/(1+β (γ+λ-2-a γ λ+β (1-γ) (1-λ)+(1-β+β γ) ϕ[a]))/.ϕ[a]->((1-a γ λ-λ(1-γ)(1-β+β λ))/( (1-γ) λ(1+β))) Log[1-(((1-a) (1+β) (1-γ) (λ^2))/(1-a γ λ-λ(1-γ)(1-β-(1-a-a β) λ)))],{a,0.1,0,1}]
λ=λ-0.01;

Equilλ-Equil

Combined Table

Each of the preceeding comparative statics must be first executed to produce this table.

NumberForm[Grid[Transpose[{{"-","a","R2","pmin","R0","V2","TW"},Prepend[Equilx-Equil,"x"],Prepend[Equilb-Equil,"b"],Prepend[Equild-Equil,"d"],Prepend[Equilγ-Equil,"γ"],Prepend[Equilλ-Equil,"λ"]}]],3]