@Stephen Forrest Compiling a symbolic piecewise produced by CurveFitting:-Spline is not a good approach in the case that there are many data points. The task of producing the piecewise scales badly with the number of points, and the compilation cost must be paid for each new set of data. That compiled-piecewise method is easy to set up, but its set up is very costly at large sizes. This is the kind of scenario for which ArrayInterpolation can be used for much more efficient set up. The addition of an even easier way to set up a proc that does lean scalar->scalar calls to ArrayInterpolation would improve Maple.

@Andriy I would concur with what Preben has said about `A` not being evaluated when say `A[1]` is called, and that is key.

If you are going to access elements of `A` many times then you would be better off assigning Q:=eval(A) after the assignment b:=a, and then working with `Q`. 

Note that if you had done all this inside a procedure with local `A` then numelems(A) would return 3 even after the assignment of `a` to `b`. That would be similar to calling numelems(eval(A,1)) at the top level which Preben described. In that procedure setting the extra statement like Q:=eval(A) might seem less unusual.

It might seem that another reasonable workaround for the top level is to use op(2,A) instead of A[2]. That should produce the results you were expecting, ie. op(1,A) returns `a` and op(2,A) returns `c`. But I suspect that for a large set `A` with many elements there could be large overhead with using `op` instead of square bracket indexing to handle this special situation that some entries change upon evaluation. I would worry that each new expression sequence of evaluated entries might get resorted during the uniquification process, upon each (higher than 1-level) evaluation of A.

@Markiyan Hirnyk I used the example about which the original poster had inquired. You're not contributing in a meaningful way here.

@sbh 

It worked for me in Maple 17.

restart:
main2 := X^Q = V^P*(V-1)^Q/(c^(P-Q)*(-c^2+V)^Q):
split := X^Q = V^P*(a[1]+a[2]*V+a[3]*V^2+O(V^3)):
one := (V-1)^Q/(c^(P-Q)*(-c^2+V)^Q):
N := 5:
two := simplify(series(one,V,N)) assuming real, V>c^2, c>1:
three := convert(two,polynom):
four := simplify(V^P*three,power):
ans1 := frontend(collect,[four,[seq(V^(P+i),i=1..N)]],[{`*`,`+`,list},{}]);
frontend(collect,[four,[seq(V^(P+i),i=1..N)],
                        u->factor(simplify(expand(u*c^(P+Q)))
                                           /c^(P+Q))],
         [{`*`,`+`,list},{}]):
ans2 := sort(eval(%));
simplify(ans1 - four);
simplify(ans1 - ans2);

I think that such a point plot which displays the ordered complex roots of a univariate polynomial (alongside each index value) would be a useful addition to the ?RootOf/indexed help-page. By that I mean useful for students.

@Markiyan Hirnyk Your plot misses the aspect of which red dot corresponds to which indexed RootOf, which to the new user may provide more insight.

I was trying to illustrate not just where the index=3 RootOf would appear (on the real line) but also how the complex roots get sorted altogether. Hence I made the extra effort in the plot and printing, going as far as writing extra code to ensure that a new user might get the whole concept more clearly (in particular, from the visual plot alone).

It's a true shame that this site (or its maplenet backend?) ruins inlined worksheets by automatically adding spurious gridlines on 2D plots.

@Thomas Richard Upon reading the Post it occured to me that perhaps the .bin installer file might not be set as executable.

@Markiyan Hirnyk Please tell us the point of your remark, because without any words of explanation it seems pointless. What were you hoping that your command would return, in terms of an explicit, exact symbolic result?

@Andriy Do you mean that you now want to unassign the names in `a`?

restart:

a:=[chris,jack,john,jason,fred,alex]:
seq(assign(i, 0), i = a);

map(unassign, eval(a,1))[];

a;
             [chris, jack, john, jason, fred, alex]

@J4James I only put the plottools:-transform in there to reflect the x- and y-axes. That command turns the data from Array into listlist. So either use some invocation involving nops (or numelems) instead of rtable_dims to pick off the dimensions of the two listlists, or don't transform the axes at that time.You don't necessarily need to transform and switch x-y axes, as it is easy to just change how the entries get printed.

F12 := -(1/2*(S+sqrt(S^2+4*alpha)))*alpha:
F22 := (1/2*(-S+sqrt(S^2+4*alpha)))*alpha:
p1 := plot3d({F12,F22}, alpha=max(-1,-S^2/4)..0, S=-20..20):
A:=op([1,1],p1):
m:= rhs(rtable_dims(A)[1]):
n:= rhs(rtable_dims(A)[2]):
for i from 1 to m do
for j from 1 to n do
X := A[i,j,1];
Y := A[i,j,2];
Z := A[i,j,3];
printf("%f %f %f\n",Y,X,Z);
end do:
end do:
B:=op([2,1],p1):
m:= rhs(rtable_dims(B)[1]):
n:= rhs(rtable_dims(B)[2]):
for i from 1 to m do
for j from 1 to n do
X := B[i,j,1];
Y := B[i,j,2];
Z := B[i,j,3];
printf("%f %f %f\n",Y,X,Z);
end do:
end do:

@J4James Yes.

op(p1) are all the operands of the PLOT3D structure assigned to `p1`. It has two MESH substructures, because the first argument to plot3d was a set of two expressions (lambda1 and lambda2).

op(1,p1) is the first MESH, and op(2,p1) is the second MESH.

And so op([1,1],p1) is the Array in the first MESH, and op([2,1],p1) is the Array in the second MESH.

@J4James It appears that you have some preconception of how the data that may represent a surface must be formatted or structured. There is no single way in which the data that represents a surface (to somebody or to some application) must be structured.

Are you saying that you need or expect a regular grid of data points -- evenly spaced in x and y directions say -- because you wish to use the data inside some other (plotting?) program which expects such a format? If so, then you could make that more clear, if that is what you mean by "extracting" the data.

What exactly do you consider to be wrong with the extracted data (triples) from your original posted code? Is it because some other application also renders one curved edge as very jagged? If that is so, then what format would you want instead? Using a very, very fine grid just to get rid of jaggedness that could otherise be far more easily handled by a different structure&interpretation seems like a resource expensive approach.

What is your target application for the exported data? What is the defintion of the format in which you want data to be exported?

The plottools:-getdata command is just an alternative (to `op`) for getting one's hands on the Arrays or data. It doesn't provide anything different about how that data is formatted. (All it really does is call `op` itself).

lambda1:=(S+sqrt(S^2+4*alpha))/(2):
lambda2:=(S-sqrt(S^2+4*alpha))/(2):
p1:= plot3d({lambda1,lambda2}, alpha=max(-1/4*S^2,-5)..5, S=-10..10, grid=[5,5]):
A:=op([1,1],p1):
B:=op([2,1],p1):
dd:=plottools:-getdata(p1);
dd[1,-1]; # A
dd[2,-1]; # B

The joy of the MESH structure for your example is that Maple's interfaces know how to render a surface from it that doesn't have the very jagged edge. There's no reason to expect that some other application should be able to do the same with it.

@J4James 

lambda1:=(S+sqrt(S^2+4*alpha))/(2):
lambda2:=(S-sqrt(S^2+4*alpha))/(2):
p1:= plot3d({lambda1,lambda2}, alpha=max(-1/4*S^2,-5)..5, S=-10..10, grid=[5,5]):
A:=op([1,1],p1):
m:= rhs(rtable_dims(A)[1]):
n:= rhs(rtable_dims(A)[2]):
for i from 1 to m do
for j from 1 to n do
X := A[i,j,1];
Y := A[i,j,2];
Z := A[i,j,3];
printf("%f %f %f\n",Y,X,Z);
end do:
end do:

Make sure that `A` is assigned a MESH Array. And repeat as necessary, for other MESH Arrays in the PLOT3D structure.

In modern Maple plottools:-getdata can be used instead of `op`, for getting at the rtables or listlists in the MESH or GRID. But that still leaves you the work of exporting it.

@J4James Your original plot3d call produces a GRID data substructure within the PLOT3D data structure itself.

On the other hand, when the plot3d call is modified to use a variable bound for the inner range then the result is a PLOT3D structure containing a MESH.

Ie, considering just one of the two surfaces from your example,

restart:
with(plots):
lambda1:=(S+sqrt(S^2+4*alpha))/(2):
P0:=plot3d(lambda1, alpha=-5..5, S=-10..10):
P1:=plot3d(lambda1, alpha=max(-1/4*S^2,-5)..5, S=-10..10):
op(P0);
op(P1);

It is the GRID vs MESH aspect which is making the difference to the nature of the resulting surface's own grid. Sorry, but I don't know of any source which discusses the rendering of these structures in great detail.

My call to `isolate` was just a way to get a parametrization of the joining spacecure between the two surface pieces. It was fortune, in a sense, that formulaically it worked out simply for this example. I wanted the (formulaic) variable end-point of the range just because I happened to recall how the patching/gridding of surfaces could get done, according to whether it is GRID or MESH.

Another example is below, (where I use some thought to figure out which result from `solve` might suffice, though perhaps the mimimum under assumptions of realness might simplify to what was wanted here). I flip the x- and y-axes, just to get the same exact view as the original.

F12 := -(1/2*(S+sqrt(S^2+4*alpha)))*alpha:
F22 := (1/2*(-S+sqrt(S^2+4*alpha)))*alpha:
solve(F12=F22,alpha);
plot3d({F12,F22}, S=-20..20, alpha=-1..0);
plottools:-transform((x,y,z)->[y,x,z])(
   plot3d({F12,F22}, alpha=max(-1,-S^2/4)..0, S=-20..20));

I'd be surprised if there wasn't an even easier way to force a suitable MESH in the plot3d result.

@Axel Vogt Yes, I was using 64bit Maple 17.02 on Windows 7.

I find it interesting that evalb returns true for the "equality" test of two procedures for which addressof returns two different results.