@Kitonum Numbers of the same general "type" are ordered the usual way within a set, but they get grouped by type. Observe:

{0, 1/2, 1};
                                         {0, 1, 1/2}

Regardless, one should not rely on the order because it may change in different versions.

@Kitonum It seems to me to be mere happenstance that each of the last three elements (as they're listed above) is greater than each of the first three elements.

@tomleslie Your randomize should be randomize().

@Ronan Your operation can be done by

13*~(1+~ListTools:-PartialSums(GRP5));

This produces a list rather than the set that you had. It's trivial to convert it to a set, but I can't imagine why you'd want to do that.

@tomleslie The mean (or expected) number of rolls (needed to achieve the desired outcome) is not necessarily the same as the median number of rolls. The OP's problem is essentially asking for that median (rounded up to the next integer).

You, on the other hand, have correctly computed the mean, which is exactly 147/10. This can be computed exactly by Maple from Kitonum's formula, which I'll call P(n): Take its first differences with respect to n, multiply by n, and sum from 6 to infinity:

sum(n*(P(n)-P(n-1)), n= 6..infinity);

The tell-tale sign that you have not computed the median is that nowhere (neither exactly nor via simulation) have you used the value 1/2. And you yourself said that you were computing the average number of rolls. Average is mean, not median.

@tomleslie I am sorry. You are correct that I misrepresented your Reply. I was misled by that Reply appearing after the OP's L^2 request. Indeed, upon a closer rereading of your Reply, I do see 

• that you didn't claim to compute the L^2 norm,
• that you had a good reason for squaring the function (to keep it differentiable), 
• that that wasn't a misguided attempt to compute the L^2 norm.

@acer No permission is needed. Posting the procedure is clearly covered under the Fair-Use Doctrine of copyright law. However, I'm not even asking for the procedure to be posted. All I want is its page number(s) in the thesis.

@Rim Given that your linked paper is 179 pages, you should specify the page number(s) on which "he used the command simplify".

@mmcdara Yes, thanks, that is precisely the thread that I was recalling.

@vv I was wrong about this. I was thinking about something related that you, I, mmcdara, and Tom Leslie were discussing at length a few months ago, but I don't remember the exact details. It was definitely about there being two ways to save, one of which mysteriously preserved significant environment details and one of which didn't. Do you recall it?

@vv For a generalized eigenvalue problem (which is the case considered in this Question), symmetry doesn't guarantee real eigenvalues. For example, consider this case, where the matrices are real symmetric and the computation is exact:

LinearAlgebra:-Eigenvalues( <1,0; 0,-1>, <0,1; 1,0>);

@tomleslie It looks like the MaplePrimes worksheet rendering ignores displayprecision. Actually, it's not even clear whether its value is stored in the worksheet..

@vv Why do you use shape= symmetric? Is the original matrix symmetric?

@Carl Love If the intent is to use the above procedure iteratively, using a list of vectors as the second argument, the overall efficiency can be substantially improved for that case.

Continuing Preben's line of thought, for any matrix that's small enough that I'd enter it manually, I do this (in 1D input (aka Maple Notation)):

M:= < 
   1,   1         ;
   1,   2/3.4
>;

For me, this spacing and visual result lets me totally see it as a mathematical matrix. In addition, the prettyprinted result of the above (explicitly typed without palettes) command is identical regardless of whether you use 1D or 2D Input.