Wolfram alpha carries out cycle multiplication from left-to-right. If the context dictates a right-to-left (function composition) operation, there probably is a way (short of rearranging the order of the operands) to indicate the shift.
Although a command prompt would be greatly appreciated, the fact that I haven't found an answer to this questions in some posts on the topic outside MSE leads me to believe that there may not be one.
If this is the case, is there a way to get the right-to-left multiplication avoiding careless mistakes in reordering the factors?
For instance, in the case of 2 cycles in $S_5,$ it is pretty easy. Say, the cycle multiplication $(1 2 3 4) (3 4 5) $ entered into Wolfram Alpha as permutation (1 2 3 4) (3 4 5) results in:
But if what we want is right-to-left we only have to swap the cycles, i.e. $(3 4 5) (1 2 3 4) :$
However, when more cycles come into play the odds of making a mistake rearranging cycles and its tediousness negate the "double-checking" benefit of using a computer.
Here an example of how it can get clunky: Trying to check a slight oversight on an otherwise excellent series of lectures, where the right cosets of the subgroup $H=\{(),(12),(34),(12)(34)\}<S_4$ generated by $(13),$ with multiplication from right to left, i.e. $H(13)=\{()(13),(12)(13),(34)(13),(12)(34)(13)\}=\{(13),(132),(143),\color{red}{(1423)}\}$ entails swapping the order from $(12)(34)(13)$ to $(13)(34)(12):$
