I have a procedure, se, that takes 2 real numbers as arguments and returns a list of 3 real numbers,

so, for example,

se(1.2,2.7)=[-5.85,3.24,3.9].

(The exact nature of that procedure should not be important for plotting purposes.)

The command >plot3d(se(x,y),x=0..2,y=-2..3); returns a surface plot as hoped.

(I had some doubt because the help page suggests one needs 3 functions or procedures [f,g,h] to get a 3 d plot rather than one procedure that generates a list of 3 values but Maple 2017.3 came through).

I have another procedure , td,that takes 2 real numbers as arguments and returns a list of 3 real numbers, ;

so, for example,

td(2.7, 3.4)=[3.4, .594943507924521, -.111391393034295].

(Again, the exact nature of that procedure should not be important for plotting purposes.)

The command > plot3d(td(x,t),x=0..2,t=0..3); returns the error message:

Error, (in dsolve/numeric/process_parameters) parameter values must evaluate to numeric, got a = x

For some reason, plot3d is going back to the body of the procedure, td, rather than just accepting the values it provides.

Knowing that quotes can sometimes solve this sort of problem I then tried:

plot3d('td(x, t)', x = 0 .. 2, t = 0 .. 3);

only to get

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

I am not sure what plot3d is complaining about. The procedure I believe has all the information it needs in the form it needs it.

I then tried another workaround.

I set td1(x,t) :=td(x,t)[1], td2(x,t) :=td(x,t)[2], td3(x,t) :=td(x,t)[3] and tried :

plot3d([td1(x, t), td2(x, t), td3(x, t)], x = 0 .. 3, t = 0 .. 2);

to get

Error, (in dsolve/numeric/process_parameters) parameter values must evaluate to numeric, got a = x

Again, for some reason, plot3d is going back to the body of the procedure td.

Finally, I tried:

plot3d('[td1(x, t), td2(x, t), td3(x, t)]', x = 0 .. 3, t = 0 .. 2);

and I got the plot I wanted.

I am very happy to have a working file but I do not understand what worked and why. The nest time I have such a problem I will have to resort to the mysterious syntax manipulations again and hope that I hit on a combination that works.

For completeness I include the procedure bodies for se and td below but I think that is irrelevant information.

se := proc (x, y) [x^2-y^2, x*y, x+y] end proc;

td := proc (x, tt)

local des, ff, fpfp; global ans;

ans(parameters = [a = x]);

des := ans(tt); ff := rhs(des[2]); fpfp := rhs(des[3]); [tt, ff, fpfp]

end proc;

and

ans:=dsolve(ic,numeric,parameters=[a]): where ic is an ode (I used several with the same result) with initial condition involving a.;

Can anybody explain what is happening?