@acer My guess is that the CSV file contains instances of two consecutive commas with no intervening characters other than possibly white space.

@VaughanR Back ticks that enclose no characters denote a symbol, the empty symbol. It's not quite the same thing as NULL, but it works well in matrices because no characters are shown in its display. You could also do subs(0= NULL, A) or subs(0= (), A). These give true NULL values, but are ugly in matrices because they prettyprint as NULL.

The problem with any of these approaches: What if you have a datum that's legitimately 0?

@itsme Your points about Code Edit Regions (CERs) are well made. I never use them for codes less than 50 lines, so my experience has been different than yours. Yes, if I made every execution group in a typical worksheet into a CER, I would find them very difficult to work with.

You are slightly misusing the terms surface, level surface, and solid. An equation (not an algebraic expression) in 3 variables such as x^2 + y^2 + z^2 =1 defines a surface: an essentially 2-dimensional object that lives in 3-dimensional space, such as a sphere. A solid is an essentially 3-dimensional object, such as a ball: a sphere and the volume it encloses. An example of a relation defining a solid is the inequality x^2 + y^2 + z^2 <= 1. An expression (or function) of three variables such as f(x,y,z) = x^2 + y^2 + z^2 has level surfaces, which are the surfaces defined by f(x,y,z) = L for specific levels L.

@a_simsim It is possible to generate the numeric data without plotting, but why do you ask? I find Tom's method quite convenient, and the marginal effort required to produce the plots is insignificant. 

@Madhukesh J K There are two basic types of 3D plots, and they can be distinguished by the number of dimensions of independent variables (real values that you directly vary) and dependent variables (real values that are computed using the independent variables). So far, you have not given us a complete set with which to construct either type of plot. The two types are a space curve (1 independent variable, 3 dependent variables) and a surface (2 independent variables, 1 dependent variable).

Your Reply immediately above implies that you want 1 independent variable (phi2) and 2 dependent variables (skin friction and Nusselt). That's not one of the types of 3D plot that I discussed, although it's enough to make a 2D plot, a plane curve.

These are mathematical limitations, not limitations of Maple.

@Mac Dude I have the same problem. It has been there for years. I do not use a .bat file.

Currently, my := is lowercase d and my -> is numeral 1. One the problem infects one worksheet, it infects all open ones. The only solution I've found is to shut down and restart Maple entirely.

@Bohdan Like this:

MyA(1, 1, 2, 2, 2, 2, 2, gamma, beta, pi, alpha, epsilon):
diff(%, pi[1,2,1,2]);
 

@tomleslie The Question shows chi(eta) and its derivatives in eq4.

@9009134 You wrote:

• I think I need to plot the 2D gradient of V in-plane xz and xy, according to the relation between x,y,z, and tau and sigma.

I think that you need to plot in an alternate coordinate system. Maple knows many, or you can define your own.

@9009134 The problem was that you didn't remove the line V:= Gradient(V) like I said.

@Bohdan The problem is that you're using 2D input.

@a_simsim Your dsolve command should be

sol:= dsolve({odesys[], ics[]}, numeric, known= Q(t));

@Bohdan I only suggested Physics:-Library:-Add because it may be able to "pretty print" the summations with the inequalities at the bottom. Computing the formulas is straightforward with regular add, and shown below. If you do want to do that pretty printing, you should ask a separate Question. Here is your formula A:

MyA:= (
    i::posint, r::posint, j::posint, s::posint, F::posint,
    J::posint, S::posint,
    gamma::{name, table}, beta::{name, table}, pi::{name, table},
    alpha::{name, table}, epsilon::{name, table}
)->
local
    Jj:= {$1..J} minus {j},
    Omega:= zz->
        add(
            alpha[k,s]*pi[j,k,s,F]*
            `if`(nargs=0, add(pi[z,k,s,F], z= Jj), pi[zz,k,s,F])*
            add(gamma[k,u]*beta[k,u], u= 1..S)
            +
            add(
                gamma[k,s,u]*beta[k,u]*pi[j,k,s,u]*
                `if`(nargs=0, add(pi[z,k,s,u], z= Jj), pi[zz,k,s,u]),
                u= 1..S
            ),
            k= 1..J
       )
;
    epsilon[s]*gamma[i,r]/beta[j,s]*(
        Omega()*(pi[i,j,r,s]*gamma[j,r,s] + `if`(r=s, `if`(i=j, 1, -1), 0)) +
        add (pi[i,z,r,s]*gamma[z,r,s]*Omega(z), z= Jj)
    )
;     

Regarding the derivative of the formula: Do you mean when J, S, and the indices of the differentiation variable have specific integer values? If so, then plain diff will work.

Does that worksheet work for you? And, if so, what was the problem before?