At the present time I will not switch between conventions or between definitions. As long, as I am using Jamie Mulhollands book and sage math, I will use their conventions. Pros and cons of the different viewpoints are beyond the topic of this thread and I do not comment them here...

I like to see the permutations in 3d like this:
A simple sage script makes it possible:
cg=CubeGroup()
#movseq=cg.parse("F*R*U*R^-1*U^-1*F^-1") #works
movseq=cg.parse("U*R2*F*B*R*B2*R*U2*L*B2*R*U^-1*D^-1*R2*F*R^-1*L*B2*U2*F2")#works
print("Move sequence example\n",movseq)
f=cg.facets(movseq)...

Im interested, in what you have done so far. Comprehensible reports about your work could convince me.
Till now I have only seen declarations of intent.

A few lines in sage math result in a string, which can be copied and pasted to Kocembas Cube Explorer. The facets will be printed according to the permutation given in disjoint cycles notation.
# Singmaster Letters
SML=" UUUUUUUULLLLLLLLFFFFFFFFRRRRRRRRBBBBBBBBDDDDDDDD"
# Reid String Order...

Some seperate topics appeared in this thread.
Jamie Mulholland wrote in in his book:
Thats a fact and I do not judge it, when I use the book. I read the sequence of multiplying permutations in his book from left to right.
The next one is the behaviour of sage math.
cg=CubeGroup()...

Thanks a lot.
To my surprise, CE displays the facelet permutations perfetly. I can put them into the Maneuver field and the program recognizes them as different from the rotation sequences.
I think this is a big part of a solution to my software search.

I dont think so. Commonly "Singmaster notation" seems to refer to turn sequences. At least most of the time. When I played with CE, program reacted accordingly. The result showed, that the input of RU was interpreted as a cw turn of the right face (consisting of 9 cubies) followed by a cw turn...

Thank you.
Cube Explorer lets you paint the facelets by Mouseclick. The Maneuvers like FRUR'U'F' can be entered via keyboard or copy and paste. But Im no expert. I chose my nick without knowing the existence of a program with this name.
Currently Im working on the workflow of presenting turn...

Most likely it is so. So I will do it probably myself. There are simulators which can paint the facelets on demand, one by one. It would not be too extensive to let sage or something else generate a string, which controls the painting. I just have to decide which of my many tinkering sites have...

^---< This describes exactly what one can see watching a cube when applyin "RU" repeatedly.
6 Corners are moving. Corner URF is just rotated at its position by each "RU". This is mathematicly documented by the cycle "(8,25,19)".
The other 5 Corners make a round trip during 5 "RU" maneuvers...

So you seem to consider the following output of sage as wrong:
RU=R*U
RU = (1,3,38,43,11,35,27,32,30,17,9,33,48,24,6)(2,5,36,45,21,7,4)(8,25,19)(10,34,26,29,31,28,18)
Because thats not really the main topic of my thread, I do not comment or discuss it now.
EDIT: I just see the answer of Bruce...

I do not understand. What exactly does not represent what? Sorry for not being native speaker of english.
This image is sages representation of the said permutation.
Of which "it" are you talking there?
I related to the color scheme to be weird. Just look to the picture sage produces.
All...

What I mean is visualization of single permutations, one by one, given in disjoint cycle notation. Thats the topic I will stick to here in this thread.