@Preben Alsholm Preben, these formal definitions should provide everything that you need to know for this question. I only post this because you said that you know next to nothing about graph theory. So, sorry if this is already familiar material.

Definition 1: A partition P of a set S is a set of nonempty pairwise-disjoint sets whose union is S. The members of P are called the blocks of the partition.

Definition 2: A coloring of a graph is a partition of its vertices such that no two vertices in the same block share an edge. If the coloring has k ​​​blocks, it's a k-coloring.

Definition 3: The chromatic number of a graph G is the minimal ​​​​​​k such that G has a k-coloring.

Definition 4: A k-clique of a graph is a k-subset of its vertices such that every pair of those vertices share an edge.

Definition 5: The clique number of a graph G is the maximal k such that G has a k-clique.

Obvious Theorem: For any graph G, CliqueNumber(G) <= ChromaticNumber(G).

@AHSAN Don't repost this same Question in other threads. And stop using the title "ODE solution".

@Carl Love Alas, specifying gridlines= false no longer works as a workaround for uploaded worksheets.

If you post some of those exercises, preferably with your solution attempts, people here will surely be able to respond.

@dantopa But note that you get the correct results with the 'col' option, as VV showed. When you examine 'col' after running the command, you'll get the color assignments, and you can easily verify that it's a valid coloring. What's more difficult to verify (indeed NP-complete difficult) is whether it's a minimal coloring. 

In Maple's 2D Input, you need to put a space after Pi. Without the space, there is no implied multiplication.

@Anthrazit Actually, using evalindets, it's trivial to generalize any procedure that acts on x of some particular (nonrecursive) type into a procedure that performs the same action on all x of that type contained in almost any superstructure, such as a Unit expression. Like this:

rnd2:= (x::realcons, n::integer)-> evalf[length(trunc(x))+n](round(x*10^n)/10^n): #Tom's original
Rnd2:= (super, n::integer)-> evalindets(super, float, x-> rnd2(x,n)): #massive generalization

I changed realcons to float because you'd probably not want to round exact constants (such as exponents) that may appear in some superstructures. Decimal exponents are nasty.

@Christopher2222 

I believe that Maple's first several generations were as an academic project. Now it's a corporate product. I believe that there were some generations where it was in an in-between state. So, the phrase "it's own product history" is ambiguous, and I think that that's the crux of the issue. It could be that the Maplesoft product history of Maple is complete as far as the versions of Maple that were produced by Maplesoft.

This is just to clarify both the Question and Kitonum's Answer regarding inverse. There is no command named inverse that applies in this situation. The inverse of Matrix S is S^(-1). For the uncommon cases where you need to use options with the inverse (e.g., for the pseudoinverse), you can use LinearAlgebra:-MatrixInverse(S, options). 

You may see a command inverse in some old code or old books. That command no longer applies, and it won't work on a Matrix.

@Joe Riel Thanks, Joe. You can find the most-recent code in the most-recent Reply to the most-recent Answer 

Now much faster and exports a procedure to check

below. All of the errors related compiled, multi-threaded, split-rank Iterators still occur. I also sent the code to you via email.

@Carl Love For your work today, please use this newest and fastest version: Symmetries.mw

@Tyttemus It's mathematically impossible to do what you want.

Looking through the help pages (in Maple 2020) whose names begin "updates," the oldest that I found was for Maple 4.0. At least that's something older than Maple 6.

@acer I failed to consider that in my definitions, although I was aware of that in the back of my mind! Thanks for pointing that out, and I'm glad to know that you're still reading this thread and monitoring the accuracy of what I say.

Fortunately, for the situation in this program, we are dealing only with sets of sets of lists of integers (type set(set(list(integer)))), and certainly all that I said applies to those. Agree? Would you be able to modify my definitions to encompass your example? Or is my whole thesis irreparably flawed?

@emendes 

1. Feasibility: Since evalf(7*binomial(60,7)) = 2.7*10^9, I'd guess that that's feasible, but near the upper limit of feasibility.

2. nterms: Yes, it totally makes sense. It's standard combinatorics.

7. Keep me updated on any need for new conditions. And be wary that I'm not sure that I've implemented the conditions correctly.

8. One problem at a time: Suppose that you wanted to use CondCheck with two (or more) different configurations of the index permutations and\or condition tables. Using a "basic" module (which is what we have), you need to re-call OrbitPartition every time that you want to change the configuration. With an object module, you can set different configurations and assign them to names, and those "objects" will exist simultaneously in memory, so that you can switch configurations for CondCheck just by using the different names.

9. I'd like to know the "parallel efficiency", which I define as  "cpu time" / ("real time" * "number of processors").