OLL algorithm (35/57)

#rubikscubeequation , #rubikscubemath , #rubikscubematrix , #rubikscube , #ollalgorithm , #oll
1
00:00
(RU2R2FRF'RU2R')^6=I
(L'U2L2F'L'FL'U2L)^6=I
2
02:00
(RUB'RBR2URU2R')^6=I
(L'U'BL'B'L2U'L'U2L)^6=I
3
04:00
(U'Y2F'U2FY'U2RUL'Y'R'L)^6=I
(UY2FU2F'Y'U2L'U'RY'LR')^6=I
4
06:31
(U'X2 LU2L'X'U2B'U'FX'F'B)^18=I
(UX2 R'U2RXU2BUF'XFB')^18=I
5
9:01
(R'U2RLY'U'R'UL'YU2R)^6=I
(LU2L'R'Y'ULU'RYU2L')^6=I
6
11:22
(R2DR'Y'URYD'R'Y'U'R'UY)^4=I
(L2D'LY'U'L'YDLY'ULU'Y)^4=I
7
14:04
(FXRUR'U'F'X'RUR'URU2R')^6=I
(F'X'L'U'LUFXL'U'LU'L'U2L)^6=I

Class (35/57) has 7 algorithms, the video demonstration is accurate, and the corresponding mirroring algorithm is given at the same time (the left hand mirrors the right hand, the right hand mirrors the left hand).The index of loop is given for each algorithm.
Hold the Rubik's Cube in your hand, start from its original state, and operate according to the listed operation sequence (algorithm). If it is operated repeatedly, the Rubik's Cube will return to its original state. This shows that the Rubik's Cube has completed a Loop (cycle), which can be expressed as ( )^n=I, where n is the Loop index, ( ) is the operation sequence, and I is the identity element (e) in group theory.
For example, (RU2R2FRF'RU2R')^6=I means that the operation sequence (RU2R2FRF'RU2R') is used to operate the Rubik's Cube. After repeating 6 times, the Rubik's Cube will return to its original state. If you stop after 5 operations, the Rubik's Cube will show the OLL (35/57) pattern. Use (RU2R2FRF'RU2R')^5 to generate the OLL (35/57) pattern, and (RU2R'FR'F'R2U2R') can also generate the OLL (35/57) pattern. Group theory says that (RU2R2FRF'RU2R') and (RU2R'FR'F'R2U2R') are inverses of each other, namely (RU2R2FRF'RU2R')(RU2R'FR'F'R2U2R') = I. Use (RU2R2FRF'RU2R') to operate the Rubik's Cube, and then return to its original state. The return operation is an inverse operation. Note down the inverse operation, which is (RU2R'FR'F'R2U2R'). There is no doubt that (RU2R2FRF'RU2R')^5=(RU2R'FR'F'R2U2R'). Other algorithms can be analyzed according to this method.