@Pi If M is a matrix (such as I defined above), then the values that you want can be accessed as M[i,j].

Yes, I'd say that it's a bug. Your graph G__0 is acyclic (confirmed both by GraphTheory:-IsAcyclic and visually), so the edges of its transistive reduction should be a subset of the edges of G__0. Here's G__0:

The ability to express these things (referring to this and your previous Posts using implicitplot3d) as implicit equations is mathematically "interesting", but I don't think that it's particularly useful for plotting. Much better 3d plots can usually be obtained from parametric representations.

@lcz If G is a directed acyclic graph (DAG), then its transistive reduction

1. is unique,
2. is a subgraph of G,
3. can be computed in polynomial time.

But if G has a directed cycle, then none of those 3 things are necessarily true.

@acer Nesting elementwise operators by folding index (which is a kinder, gentler variation of `?[]`) is a great idea. Here's what I came up with:

`&~`:= (f, n::nonnegint)-> foldr(index, f, `~`$n):

Usage example:

(convert &~ 2)(fasteners, unit_free)

@acer I'm sorry if you mentioned this in your worksheet; I didn't read it because I'm posting from my phone. I see now that you mentioned nested elementwise operators in your posted text. Again, sorry for not reading closely.

@Oliver K Your suggestion only returns the 1st list element, not the left sides of the equations. 

@mmcdara I think a DataFrame combines the best features of a spreadsheet, a matrix, and a table. Its underlying data structure is identical to your matrix, but the indexing is overloaded so that it's indexed by the odds from 1 to 49.

@Michael Although prime factorization isn't the most efficient way to do this, you were well on your way to discovering the simplest code to do it: the degree command:

p_log:= (n::integer, p::prime)-> degree(ifactor(n), ``(p)):

The key is the `` function symbol. It doesn't show in prettyprinted output, so it serves as a way to display output with "just" parentheses. But you can see it with lprint (a command that shows a "raw form" of output):

lprint(ifactor(24));
``(2)^3*``(3)

All I see is that you've defined (implicitly) a sequence of polynomials. Rings have nothing to do with it.

@dharr I just came up with that formula off the cuff. Perhaps the mean would be better in general than the midrange.

@vs140580 A good choice of scale factor for each column (whether dependent or independent) is

10.^(-ilog10@((max+min)/2.)@abs~)(Data1[.., j])

where j is the column number. This formula gives the same scale factors that @dharr used, although I don't know whether he actually used a formula or just eyeballed it.

In plain words, the formula is "Divide by the power of 10 closest to (but not exceeding) the midrange of the absolute values of the data." 

Maple supports function composition via the operator @. But I don't understand your example. Please make a simpler example that uses no variables other than the function names and their parameters. And why is the parameter T of R not used at all?

@mmcdara As far as I know, Maple has no means of plotting any solids. We only plot the surfaces that are their boundaries and imagine that the interiors are filled. When the OP specified "intersection of two solid bodies", they were asking for a means to plot the surfaces that are the boundary of that intersection. 

@mmcdara A second range argument in a 2D plot command is allowed, and its effect is similar to using that range as the view of the vertical coordinate. If the additional range is given in the form name= range, then in addition the name is used as the vertical axis label.

If a keyword parameter that take truefalse values, such as gridlines, is given without a value, that's equivalent to setting the value to true.