Quote:b [3] k = b ^ k = y --> b = y /[3] k = k-srt y, k = b [3] \ y = b-slog y.I dont see this contrast, we have:
In other words, for rank 3 and > 3, we are in contrast with the traditional prefixed notation of the inverse operations.
\( y /[3] k=y^{1/k} \) and \( b [3]\backslash y = \log_b y \)
(And by this you can easily remember that / corresponds to the root type.)
I mean the side is anyway arbitrary, you also have \( {^n x} \) but you write x[4]n.
GFR Wrote:The advantage of this schematical notation is that we could admit an upside-down mirror inversion of the operation symbols, in their inverse
sequence, like (see the third line):
...
In general, for:
y = b [n] k, we might have:
b = k \n| y = y /n| k, the root-type left-inverse, and
k = b |n\ y = y |n/ b, the log-type left-inverse.
But Gianfranco thats confusing! \ and / for the same operation depending on which side. I dont want to first think a minute what is meant by the current symbol! There is also no mnemonics attached.
Neither is a both side variant really needed nor is it usual to have it. There is no opposite side variant for -, / or ^.
So if you really desperately need the both-side variants then keep the same operation symbol! E.g. /n| and |n/ as root-type inversion, but I dont see usage for them. And you have to burden your memory with another rule to decide on which side is the base/exponent, i.e. on the side which is not |.
However I see a bit a problem with /n|, as when you use it without spaces it can be confusing, for example
|a/n|x| = | a /n| x |
I placed some attention to this problem when I was deciding for /[n] because you can not misread the / as a division (because it is followed by an open bracket). This ruled out the other variant that I had in mind: /n/.
However your idea to put [n]\ instead of \[n] is a better one as you can better memorize the rule
b[n]k /[n] k = b and b [n]\ ( b[n] k ) = k
as "The thing to be reduced is on the (reducing) operation side (i.e. the side with the / or \ attached)"
PS: We can call this the BO-GFR simplified ASCII notation, however by such discussions there always comes up the image of a commitee designing conventions (by long and intense democratic discussions) which dont fit real needs of the using people. While really useful things are made without commitees! However I hope its not the case here.