# Question:`evala/Minpoly` and PolynomialTools:-MinimalPolynomial: Wrong results?

## Question:`evala/Minpoly` and PolynomialTools:-MinimalPolynomial: Wrong results?

Maple 2023

Here are three algebraic numbers: (In fact, they are solutions to some equation. See the attachment below.)

`bSol := {RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) - 1133, index = real[2]), RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) - 1133, index = real[2]), RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) - 1133, index = real[2])}:`

One may check that 11_X9－47_X8＋96_X7－376_X6－370_X5－142_X4＋280_X3＋64_X2－17_X－11 is an “annihilating” polynomial of each of them (using another computer algebra system); accordingly, the degree of the minimal polynomial cannot be greater than 9. However, Maple's output indicates that the minimal polynomial is of degree 36

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