qtm-optimal corner-3-cycles

[Stefan]

It's not an applet. I hate Java.

He just said applet, not Java applet. On the other hand, you didn't say your Java comment refers to any of this, could just be a random remark.

The point was just that I could beat Lucas' ten characters because it's my site.

Bah, don't explain a joke, takes the fun out of it (also, I thought it was obvious even before you posted your two chars).

 

[mrCage]

I could do it in, let's say two characters, if I wanted.

Give me evidence.

#\

It's not hard to make it more compact than 10 chars, the problem would be to have it shown in that applet with that notation

It's not an applet. I hate Java.

Meh!! I have a sense of humour but that one was just silly. You just code that case into your "jslet". You can even make it 0 characters Less work for you also ...

On the serious side. Adding conjugate notation would be useful.
For instance F' R' D' R D F = F' [R',D'] F = [F':R',D'] or however you wanted the syntax to be:rolleyes:

-Per

 

[Johannes91]

It's not an applet. I hate Java.

He just said applet, not Java applet.

I stand corrected; I'm too used to using the word "applet" to refer exclusively to Java applets. According to the Wikipedia article, I had more or less misunderstood the meaning of the word.

On the serious side. Adding conjugate notation would be useful.
For instance F' R' D' R D F = F' [R',D'] F = [F':R',D'] or however you wanted the syntax to be:rolleyes:

I wrote it because I got tired of seeing algs like the following:

L z' (R U) [L' (U)] [(M') (U2)] (F) [R l] [U' l'2] U2
R'2 D'w - Rw R'- (f) R2 D'w D L'w (f') - L2

Understanding, memorizing, and finding my own way to execute them is much easier without all the sugar. For that purpose, adding some kind of conjugate notation wouldn't be useful unless people are actually using it.

And in any case, I'd rather start from scratch using a proper parser combinator library instead of trying to improve that script.

 

[cuBerBruce]

On the serious side. Adding conjugate notation would be useful.
For instance F' R' D' R D F = F' [R',D'] F = [F':R',D'] or however you wanted the syntax to be:rolleyes:

The standard way of denoting conjugation is with exponentiation or the ^ operator. For instance, GAP supports conjugation using the ^ operator. g^h means h'gh. So Per's example (F' [R',D'] F) could be written as [R',D']^F. It is not ambiguous with exponentiation for repetition, because for repetition, the exponent is a number (or represents a number).

I've been thinking of implementing conjugation in my CubeApp. I'm wondering how to treat relative precedence of implied multiplication vs. exponenentiation, so should I accept (R2 d' M d2 d' R2 ^ B L) to mean (R2 d' M d2 d' R2)^(B L) ?

I can see this syntax may be somewhat confusing for cubers who would think of the above sequence as:
setup: L' B'
alg: R2 d' M d2 d' R2
(undo setup)

That is, the standard mathematical notation uses the "undo setup" moves instead of the "setup" moves, and places them after the alg instead of before. Per's suggestion would probably correspond to the way cubers think, but as far as I know, it's not a standard notation.

 

[mrCage]

I've been thinking of implementing conjugation in my CubeApp. I'm wondering how to treat relative precedence of implied multiplication vs. exponenentiation, so should I accept (R2 d' M d2 d' R2 ^ B L) to mean (R2 d' M d2 d' R2)^(B L) ?

Well that seems correct, however ((sequence)^a)^b is different from (sequence)^(ab)

- Per

(edit)
My intuition told me that g^h should mean hgh' not h'gh. Oh well ...
(/edit)

 

[cuBerBruce]

My intuition told me that g^h should mean hgh' not h'gh. Oh well ...

You're not alone, Per.

In my previous post, my notation for conjugation was based upon David Joyner's book Adventures in Group Theory (see http://web.ew.usna.edu/~wdj/book/node180.html), as well as checking how GAP interprets the ^ operator with permutations. Apparently, there is not unanimous agreement in what the phrase "g conjugated by h" means or what g^h means. In fact, not even the commutator notation seems to have unanimous agreement as to what it means. See this Wikipedia page for comments about both (Group Theory section of the page):
http://en.wikipedia.org/wiki/Commutator

And the following web page by Joyner seems to give even a different meaning to g^h:

see http://web.usna.navy.mil/~wdj/sm485_5.txt

I'll have to research this some more before I implement something in my CubeApp.