@Carl Love I have retyped it. I dont know what wrong button I pressed.

@mmcdara Thanks for this detailed response! I was not not aware of your sol trick and will give it a rey, but suspect that it will not completetly cure my problem, that I will now try to clarify,

I said that I had a complex cubic, by which I meant one who coefficients and roots are complex quantities. AFIK there is no mathematically meaningful ordering of the roots available in this case,  although there might be  certain paths through the cubic formula. Nevertheless, Maple solves the problem, and lists the roots as [[s[1],s[2],s[3]]. What I observe is that  if I rerun the problem with the same data, but intending to plot the results differently, the original ordering is not preserved, so I have to change the plotting instructions later on. This is because only one of the three roots actually solves the motivating problem, although the others are of some interest and deserve to be plotted in a distinguishing form (I dash them). There are actually two parameters. Ideally I would track the "physical" root, but imagine that may be inpossible. However, just having consistency from run to run would be a blessing. I observe the same issue with other kinds of "solve" instruction.

@Preben Alsholm 

Thanks for this! See my reply to mmcdara.