# New to sage, but it seems wrong.

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(-8

sqrt(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(-4

sqrt(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:"-4

sqrt(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+4*sqrt(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+4*sqrt(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.

As it turns out,

`bool`

only returns`True`

when Sage knows the answer is true, and otherwise returns`False`

- even if it turns out it is true. So apparently whatever algorithm is checking the individual parts isn't able to check the last statement properly. I'm not sure if that happens in Pynac or Maxima, but hopefully someone will be able to give you more details; however, that is the essence.There is nothing wrong in being new to sage. (I have very often the same feeling.)

And Sage is so big that even those of us who are now superannuated in Sage terms feel new as soon as we step into an unfamiliar corner of it!