shadowslice e
Member
You do realize that RU and UR are in fact the same. If "U" were 3, and "R" were 2, then UR (3*2) would equal 6. Similarly, RU (2*3) would equal 6.
Also, g*b+g*a is the same as g*a+g*b as bedmas states to do multiplication first.
Not with matrix multiplication. With that you must have a specific order as AB does not equal BA unless B is the inverse of A or the identity matrix. And we have to use matricies to describe the transformations.
Thus, the cycle length may be the same for the example you provided because they are only length 2. If you try a longer one, you will find that something like R U R' U' does not have the same cycle length as R R' U U' despite bidmas/bodmas/bedmas saying that they would be the same as those acronyms only work for pure algebra with no matricies.
In fact, the only reason U R and R U have the same number is due to the symmetries that the two generators have (ie. Rotated 90 then reflected.)
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