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Any way for simplification with WM functions

VolMike VolMike
Posted 2 years ago

Is there any way for simplification of

Log[3-2 Sqrt[2]]/Log[1+Sqrt[2]]

to -2 with some combinations of WM functions? FullSimplify, FunctionExpand and other functions in any combinations don't reduce expression to -2. Even WA can't simplify expression. P.S. WM 13.2 still contains this bug.
POSTED BY: VolMike VolMike
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Hans Milton
Hans Milton
Posted 2 years ago

But it's kind of strange to force Reals for simplifying expression, each part of which is clearly real itself.

Yes, it is strange. Its even more strange that FullSimplify will work as long as the second argument is present. Even when the argument itself is nonsensical.
POSTED BY: Hans Milton

That's really strange behaviour. Seems to be the WM bug.
POSTED BY: VolMike VolMike

I've sent the feedback about this bug to WM Support.
POSTED BY: VolMike VolMike
Rohit Namjoshi
Rohit Namjoshi
Posted 2 years ago

Restricting the domain to Reals works

FullSimplify[Log[3 - 2 Sqrt[2]]/Log[1 + Sqrt[2]], All \[Element] Reals]
(* -2 *)
POSTED BY: Rohit Namjoshi

Thanks in advance! Never used such kind of generalized restrictions (just for concrete variables only). FullSimplify[Log[3 - 2 Sqrt[2]]/Log[1 + Sqrt[2]], Reals] gives the same result. But it's kind of strange to force Reals for simplifying expression, each part of which is clearly real itself.
POSTED BY: VolMike VolMike
Eric Rimbey
Eric Rimbey
Posted 2 years ago

You could just apply N.

N[Log[3 - 2 Sqrt[2]]/Log[1 + Sqrt[2]]]
POSTED BY: Eric Rimbey

Well, this is not a simplification, but just a real approximation.

POSTED BY: VolMike VolMike
Eric Rimbey
Eric Rimbey
Posted 2 years ago

Right. I don't know your context. Just saying you can get a simpler representation by actually forcing finite precision computation. Sorry, I suppose it came off as flippant.
POSTED BY: Eric Rimbey
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