# Question:Reducing the number of solutions in RootOf

## Question:Reducing the number of solutions in RootOf

Maple

Dear MaplePrimes,

I have a problem findning an explicit solution to an equation solve((P[h]-tau[h])*q[hf] = (P[f]-tau[f])*q[fh], [lambda[h]])]. Is you can see from my syntax, I have assumed a RealDomain and also that all parameters including the varialbe I'm solving for lambda[h] are positive, and also that lambda[h] is between 0 and 1. This is my syntax:

test := `assuming`([RealDomain:-solve((P[h]-tau[h])*q[hf] = (P[f]-tau[f])*q[fh], [lambda[h]])], [a::positive, n::positive, L::positive, (tau[h])::positive, (tau[f])::positive, b::positive, lambda[h] < 1, (lambda[h])::positive])

The solution is still very large:

test := [[lambda[h] = RootOf((n^2*tau[h]^2-2*n^2*tau[f]*tau[h]+n^2*tau[f]^2)*_Z^5+(-8*a*n^2*tau[h]+8*L*b*n^2*tau[h]-4*n*tau[f]*L*b+tau[h]^2*n+5*n^2*tau[f]*tau[h]+4*L*b*n*tau[h]+n^3*tau[h]^2-5*n^2*tau[f]^2+8*n^2*tau[f]*a-n^3*tau[f]^2-n*tau[f]^2-8*n^2*tau[f]*L*b)*_Z^4+(-32*a*n^2*b*L+16*n*b^2*L^2+20*n^2*tau[f]*L*b-2*n^3*tau[h]^2+tau[h]*L*b-3*tau[f]*n*a-2*tau[h]^2*n+16*n^2*b^2*L^2-12*L*b*n^2*tau[h]-4*n^2*tau[f]*tau[h]+12*n*tau[f]*L*b-16*n*b*L*a-4*L*b*n*tau[h]+tau[f]*L*b-3*a*n*tau[h]+16*a^2*n^2+7*n^2*tau[f]^2+2*n^3*tau[f]^2+10*a*n^2*tau[h]+4*b^2*L^2-3*n^2*tau[h]^2-22*n^2*tau[f]*a+2*n*tau[f]^2)*_Z^3+(-6*b^2*L^2-24*n^2*b^2*L^2-24*n*b^2*L^2-n*tau[f]^2+n^3*tau[h]^2+24*n*b*L*a+5*a*n*tau[h]-16*n^2*tau[f]*L*b-n^3*tau[f]^2-12*n*tau[f]*L*b-3*n^2*tau[f]^2-24*a^2*n^2+48*a*n^2*b*L+4*tau[f]*n*a+2*n^2*tau[h]^2+n^2*tau[f]*tau[h]-tau[h]*L*b+4*L*b*n^2*tau[h]+tau[h]^2*n+18*n^2*tau[f]*a-2*tau[f]*L*b)*_Z^2+(-tau[f]*n*a-8*n*b*L*a-16*a*n^2*b*L+tau[f]*L*b-2*a^2*n+8*a^2*n^2-2*a*n^2*tau[h]+8*n^2*b^2*L^2-2*a*n*tau[h]-4*n^2*tau[f]*a+2*b^2*L^2+8*n*b^2*L^2+4*n^2*tau[f]*L*b+4*n*tau[f]*L*b)*_Z+a^2*n)]]

When I use the allvalues command, the memory requirement explodes. Can you think of a way to further simplify the solution? THat would be great thank you.

Best wishes to all of you.

Christian

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