I am doing some calculations and I was just check on some simplifications and came across a discrepancy. Logically, this does not make any sense to me, so I must assume this is something weird with sage that I am not aware of. I put the problem in a new worksheet to check that I didn't have some variable assigned to a different value elsewhere by accident.
[I apologize for the code and the formatting to follow, I can't upload an image since I am a new user]
in: l=arccosh(-8sqrt(2)(sqrt(2) - 2)/((2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2)^2(2sqrt(2)/(2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2) - 4/(2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2))(sqrt(2)/(2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2) - 2/(2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2))) + 1)
in: l
out:"arccosh(-4sqrt(2)(sqrt(2) - 2)/((2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2)^2(sqrt(2)/(2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2) - 2/(2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2))^2) + 1)
in: n=cosh(l)
in: n
out:"-4sqrt(2)(sqrt(2) - 2)/((2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2)^2(sqrt(2)/(2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2) - 2/(2^(3/4)sqrt(sqrt(2) + 2) + sqrt(2) + 2))^2) + 1
in: bool(n==5+4*sqrt(2))
out:"True"
in: bool(l==arccosh(n))
out:"True"
in: bool(l==arccosh(5+4*sqrt(2)))
out:"False"
So, what this says, I have some number l, which is arccosh of an ugly string, and I name the ugly string n. Turns out n simplifies to 5+4sqrt(2), which I check in the middle of the code with bool. And sage agrees, and I check that l is still arccosh of n, and sage agrees. BUT, then sage says that l is NOT arccosh of 5+4sqrt(2), which we see at the end of my code.
I don't understand how this could be giving me seemingly contradictory statements. Any help would be very appreciated.
