sursumCorda

Ask a Question

Create a Post

15 Badges

Member for: 2 years, 243 days

Contact sursumCorda

MaplePrimes Activity

These are questions asked by sursumCorda

`evala/Minpoly` and PolynomialTools:-Min...

Asked: sursumCorda 1244 Product: Maple 2023

April 21 2023

2 2

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!

restart;

alias(`~`[`=`](alpha__ || (1 .. 3), ` $`, 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, .2246 .. .2266), 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), 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)))

>	$({PDETools:-Solve})({`~`[`>=`](a, b, ` $`, 0), a^5b+4a^4b^2+4a^3b^3-7a^4b-6a^2b^3-7ab^4+b^5-6a^3b+12a^2b^2+4b^4+4a^3-6ab^2+4b^3+4a^2-7a*b+a = 0, a <> b})$

evalf[2*Digits](`~`[eval](11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11, `~`[`=`](_X, bSol)))

${RootOf(1216*_Z^4+(264*alpha__1^8+408*alpha__1^7-1580*alpha__1^6-6832*alpha__1^5+3508*alpha__1^4+9944*alpha__1^3+9948*alpha__1^2-10752*alpha__1+5204)*_Z^3+(891*alpha__1^8+1652*alpha__1^7-4748*alpha__1^6-24076*alpha__1^5+5354*alpha__1^4+35356*alpha__1^3+29668*alpha__1^2-196*alpha__1+3971)*_Z^2+(506*alpha__1^8+980*alpha__1^7-2264*alpha__1^6-12420*alpha__1^5+3676*alpha__1^4+11596*alpha__1^3+33800*alpha__1^2-7772*alpha__1+1210)*_Z-473*alpha__1^8-720*alpha__1^7+2560*alpha__1^6+10960*alpha__1^5-8034*alpha__1^4-13840*alpha__1^3-9304*alpha__1^2+1104*alpha__1-1133, index = real[2]), RootOf(1216*_Z^4+(264*alpha__2^8+408*alpha__2^7-1580*alpha__2^6-6832*alpha__2^5+3508*alpha__2^4+9944*alpha__2^3+9948*alpha__2^2-10752*alpha__2+5204)*_Z^3+(891*alpha__2^8+1652*alpha__2^7-4748*alpha__2^6-24076*alpha__2^5+5354*alpha__2^4+35356*alpha__2^3+29668*alpha__2^2-196*alpha__2+3971)*_Z^2+(506*alpha__2^8+980*alpha__2^7-2264*alpha__2^6-12420*alpha__2^5+3676*alpha__2^4+11596*alpha__2^3+33800*alpha__2^2-7772*alpha__2+1210)*_Z-473*alpha__2^8-720*alpha__2^7+2560*alpha__2^6+10960*alpha__2^5-8034*alpha__2^4-13840*alpha__2^3-9304*alpha__2^2+1104*alpha__2-1133, index = real[2]), RootOf(1216*_Z^4+(264*alpha__3^8+408*alpha__3^7-1580*alpha__3^6-6832*alpha__3^5+3508*alpha__3^4+9944*alpha__3^3+9948*alpha__3^2-10752*alpha__3+5204)*_Z^3+(891*alpha__3^8+1652*alpha__3^7-4748*alpha__3^6-24076*alpha__3^5+5354*alpha__3^4+35356*alpha__3^3+29668*alpha__3^2-196*alpha__3+3971)*_Z^2+(506*alpha__3^8+980*alpha__3^7-2264*alpha__3^6-12420*alpha__3^5+3676*alpha__3^4+11596*alpha__3^3+33800*alpha__3^2-7772*alpha__3+1210)*_Z-473*alpha__3^8-720*alpha__3^7+2560*alpha__3^6+10960*alpha__3^5-8034*alpha__3^4-13840*alpha__3^3-9304*alpha__3^2+1104*alpha__3-1133, index = real[2])}$

(1)

${-17799961-(10941904462/121)*_X+(61823634144236824/14641)*_X^9-(31748793508955524/14641)*_X^8-(101389427707536/14641)*_X^7+(2187899683524768/14641)*_X^6+(660533278629392/14641)*_X^5-(35195970681077/1331)*_X^4+(4540912173250/1331)*_X^3-(226104907168/1331)*_X^2+_X^36+(562/11)*_X^35+(1306112/1331)*_X^34-(18882494/14641)*_X^33-(1885893201/14641)*_X^32-(8021957456/14641)*_X^31+(128807680096/14641)*_X^30+(601684442192/14641)*_X^29+(136952065956/14641)*_X^28-(7313279407608/14641)*_X^27-(20755313257248/14641)*_X^26-(72279502775080/14641)*_X^25-(235147325265588/14641)*_X^24+(407012808852624/14641)*_X^23-(2003920103008/1331)*_X^22-(2647129453154576/14641)*_X^21-(5329535956015778/14641)*_X^20-(11189597881735324/14641)*_X^19+(18014890583299168/14641)*_X^18-(25692630236542548/14641)*_X^17+(57603516516708946/14641)*_X^16-(875402744452912/121)*_X^15+(36990665431348512/14641)*_X^14+(67887070781490608/14641)*_X^13+(643327218250876/1331)*_X^12-(81888059180050616/14641)*_X^11+(306280599794336/14641)*_X^10}$

(2)

${14641*_X^36+748022*_X^35+14367232*_X^34-18882494*_X^33-1885893201*_X^32-8021957456*_X^31+128807680096*_X^30+601684442192*_X^29+136952065956*_X^28-7313279407608*_X^27-20755313257248*_X^26-72279502775080*_X^25-235147325265588*_X^24+407012808852624*_X^23-22043121133088*_X^22-2647129453154576*_X^21-5329535956015778*_X^20-11189597881735324*_X^19+18014890583299168*_X^18-25692630236542548*_X^17+57603516516708946*_X^16-105923732078802352*_X^15+36990665431348512*_X^14+67887070781490608*_X^13+7076599400759636*_X^12-81888059180050616*_X^11+306280599794336*_X^10+61823634144236824*_X^9-31748793508955524*_X^8-101389427707536*_X^7+2187899683524768*_X^6+660533278629392*_X^5-387155677491847*_X^4+49950033905750*_X^3-2487153978848*_X^2-1323970439902*_X-260609229001}$

(3)

$factor({{-260609229001-1323970439902*_X+407012808852624*_X^23-22043121133088*_X^22-2647129453154576*_X^21-5329535956015778*_X^20-11189597881735324*_X^19+18014890583299168*_X^18-25692630236542548*_X^17+57603516516708946*_X^16-105923732078802352*_X^15+36990665431348512*_X^14+67887070781490608*_X^13+7076599400759636*_X^12-81888059180050616*_X^11+306280599794336*_X^10+61823634144236824*_X^9-31748793508955524*_X^8-101389427707536*_X^7+2187899683524768*_X^6+660533278629392*_X^5-387155677491847*_X^4+49950033905750*_X^3-2487153978848*_X^2+14641*_X^36+748022*_X^35+14367232*_X^34-18882494*_X^33-1885893201*_X^32-8021957456*_X^31+128807680096*_X^30+601684442192*_X^29+136952065956*_X^28-7313279407608*_X^27-20755313257248*_X^26-72279502775080*_X^25-235147325265588*_X^24}[], {-17799961-(10941904462/121)*_X+(407012808852624/14641)*_X^23-(2003920103008/1331)*_X^22-(2647129453154576/14641)*_X^21-(5329535956015778/14641)*_X^20-(11189597881735324/14641)*_X^19+(18014890583299168/14641)*_X^18-(25692630236542548/14641)*_X^17+(57603516516708946/14641)*_X^16-(875402744452912/121)*_X^15+(36990665431348512/14641)*_X^14+(67887070781490608/14641)*_X^13+(643327218250876/1331)*_X^12-(81888059180050616/14641)*_X^11+(306280599794336/14641)*_X^10+(61823634144236824/14641)*_X^9-(31748793508955524/14641)*_X^8-(101389427707536/14641)*_X^7+(2187899683524768/14641)*_X^6+(660533278629392/14641)*_X^5-(35195970681077/1331)*_X^4+(4540912173250/1331)*_X^3-(226104907168/1331)*_X^2+_X^36+(562/11)*_X^35+(1306112/1331)*_X^34-(18882494/14641)*_X^33-(1885893201/14641)*_X^32-(8021957456/14641)*_X^31+(128807680096/14641)*_X^30+(601684442192/14641)*_X^29+(136952065956/14641)*_X^28-(7313279407608/14641)*_X^27-(20755313257248/14641)*_X^26-(72279502775080/14641)*_X^25-(235147325265588/14641)*_X^24}[]})$

${(11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11)*(83746429305*_X-163433814*_X^23-1409885474*_X^22+7323055726*_X^21+92878340298*_X^20+291711433585*_X^19-28358008525*_X^18-1146850616945*_X^17+2003142623069*_X^16+7054039060380*_X^15+10860482240404*_X^14+4410674835220*_X^13-23715924119108*_X^12+39935154074341*_X^11-76564178781009*_X^10+246946329497683*_X^9-303627746551159*_X^8+41661161235738*_X^7+181533634595246*_X^6-146573328877410*_X^5+44279227597786*_X^4-3813039868649*_X^3+234521505317*_X^2+1331*_X^27+73689*_X^26+1609349*_X^25+4562111*_X^24+23691748091), (1/14641)*(11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11)*(83746429305*_X-163433814*_X^23-1409885474*_X^22+7323055726*_X^21+92878340298*_X^20+291711433585*_X^19-28358008525*_X^18-1146850616945*_X^17+2003142623069*_X^16+7054039060380*_X^15+10860482240404*_X^14+4410674835220*_X^13-23715924119108*_X^12+39935154074341*_X^11-76564178781009*_X^10+246946329497683*_X^9-303627746551159*_X^8+41661161235738*_X^7+181533634595246*_X^6-146573328877410*_X^5+44279227597786*_X^4-3813039868649*_X^3+234521505317*_X^2+1331*_X^27+73689*_X^26+1609349*_X^25+4562111*_X^24+23691748091)}$

(4)

Download minpoly.mw

Isn't the results incorrect?

Generally speaking, will eliminating the...

Asked: sursumCorda 1244 Product: Maple 2023

April 20 2023

1 4

Let us begin with the official descriptions of loops. The Maple^® documentation claims that:

Note that the examples above don't necessarily illustrate the best way to perform these operations. Often a functional form like seq, map, add, or mul is far more efficient.

Mma's tech tutorial also claims that:

If you have a big program full of If, Do, Return, etc., you're probably not doing things right.
Often, however, you can make more elegant and efficient programs using the functional programming constructs ….

Also, MatLab's Techniques to Improve Performance and Measure and Improve GPU Performance claims that:

You can achieve better performance by rewriting loops to make use of higher-dimensional operations. The performance of a wide variety of element-wise functions can be improved … instead of looping over the matrices.

Well, I'm confused. Why did the official help page say like this? Actually, I find that lots of users in this forum still (and usually) use traditional for-loops instead of something which fits in with the alleged functional programming ideas. Did I misconstrue those statements?
(For instance, as for the functional operations, it's unfortunate that Maple's built-in map cannot operate on arbitrary expression trees of any depth; so I have to use the loops to apply some procedure indirectly, which is not so convenient. In my opinion, owing to such limitation, people have to, and then gradually tend to, use the loops.)

Is there any bugs in GraphTheory['Transi...

Asked: sursumCorda 1244 Product: Maple 2023

April 16 2023

0 7

According to this help page,

the transitive reduction of graph G, is the graph with the fewest edges that still shares the same reachability as G (but might contain new edges not present in G).

However, in Maple 2023, things become strange; different branches return distinct numbers of edges:
(33 arcs or 40 arcs?)

restart;

>	with(GraphTheory):

GraphTheory:-TransitiveReduction := proc(G::GRAPHLN, $)
local D, V, T, i, j, k, A, M, n, flags, B;
       ...
   4   if _EnvDisableExt <> true then
           ...
       elif D <> (':-directed') then
           ...
       else
           ...
       end if;
       ...
end proc

$G__0 := Digraph({[2, 8], [3, 1], [4, 9], [5, 10], [6, 19], [7, 12], [8, 13], [9, 3], [10, 4], [10, 14], [11, 5], [11, 15], [12, 6], [12, 16], [13, 7], [13, 17], [14, 9], [15, 10], [15, 18], [16, 19], [17, 12], [17, 20], [18, 14], [19, 11], [19, 21], [20, 22], [21, 18], [22, 16], [22, 23], [23, 19]})$

(1)

(2)

(3)

(4)

Download TransReduction.mw

Any bugs?

G__0 := GraphTheory:-Digraph({[3, 1], [9, 3], [4, 9], [14, 9], [10, 4], [5, 10], [15, 10], [11, 5], [19, 11], [12, 6], [7, 12], [17, 12], [13, 7], [8, 13], [2, 8], [10, 14], [18, 14], [11, 15], [6, 19], [16, 19], [23, 19], [13, 17], [15, 18], [21, 18], [12, 16], [22, 16], [22, 23], [20, 22], [19, 21], [17, 20]}):

How to use any number of expressions or ...

Asked: sursumCorda 1244 Product: Maple 2023

April 15 2023

1 2

For example, I'd like to do something like this (and then plot the graph):

 # display LaTeX markup
label__1 := '"\[\cfrac{\biguplus_\LaTeX}{{\color{red}\leadsto}^\unicode{2254}}\]"':
 # display non-executable notation
label__2 := '(Product(Int(i, j), Sum(k, l)) %assuming convert(log2(1 - 'x'), confrac, subdiagonal))':
 # display graphical object
label__3 := 'plots:-display(plottools:-stellate(plottools:-icosahedron()))':
 # note that the desired one is  instead of 
GraphTheory:-RelabelVertices(`some graph with 3 nodes`, [label__1, label__2, label__3]):

But unfortunately, the second argument of GraphTheory:-RelabelVertices must be of type list({indexed, integer, string, symbol}), and the GraphTheory:-SetVertexAttribute command doesn't work here. Is it possible to do so in Maple^® (rather than in other mathematical softwares)?

Why can't the Maple simplifier combine t...

Asked: sursumCorda 1244 Product: Maple 2023

April 14 2023

1 2

The result of is said to be the Catalan constant, but unfortunately, Maple^® only returns a lengthy output, so I have to apply the simplify command to get a shorter (and equivalent) form of it. However, I find that these do not work here:

restart;

((1/2)*I)*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+((1/2)*I)*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2+Catalan

(1)

simplify(expr__1, size = false)-Catalan; Physics:-Simplify(expr__1)-Catalan; simplify(expr__1-Catalan, size = false); Physics:-Simplify(expr__1-Catalan); verify(expr__1, Catalan, equal); is(expr__1 = Catalan); verify(expr__1-Catalan, 0, equal); is(expr__1-Catalan, 0)

((1/8)*I)*(-Pi^2+4*dilog(1-(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))+4*dilog(1-(1/2)*2^(1/2)-((1/2)*I)*2^(1/2))-4*dilog(1+(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-4*dilog(1+(1/2)*2^(1/2)-((1/2)*I)*2^(1/2)))

(2)

((1/2)*I)*polylog(2, (1/2)*2^(1/2)-((1/2)*I)*2^(1/2))+((1/2)*I)*polylog(2, (1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, -((1/2)*I)*2^(1/2)-(1/2)*2^(1/2))-((1/2)*I)*polylog(2, -(1/2)*2^(1/2)+((1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2+Catalan

(3)

simplify(expr__2, size = false)-Catalan; Physics:-Simplify(expr__2)-Catalan; simplify(expr__2-Catalan, size = false); Physics:-Simplify(expr__2-Catalan); verify(expr__2, Catalan, equal); is(expr__2 = Catalan); verify(expr__2-Catalan, 0, equal); is(expr__2-Catalan, 0)

((1/2)*I)*polylog(2, (1/2-(1/2)*I)*2^(1/2))+((1/2)*I)*polylog(2, (1/2+(1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, (-1/2-(1/2)*I)*2^(1/2))-((1/2)*I)*polylog(2, (-1/2+(1/2)*I)*2^(1/2))-((1/8)*I)*Pi^2

-((1/8)*I)*(Pi^2+4*polylog(2, (-1/2+(1/2)*I)*2^(1/2))+4*polylog(2, (-1/2-(1/2)*I)*2^(1/2))-4*polylog(2, (1/2+(1/2)*I)*2^(1/2))-4*polylog(2, (1/2-(1/2)*I)*2^(1/2)))