The result from diff already had the completed square inside the radicals.

Download collect_denominator_ac.mw

Perhaps your would like to use the plots:-logplot command, or the axis options of the plot command.

I prefer kernel builtins over custom-procs, where reasonable.

remove(`=`, EQI__4, 0=0);

And I dislike using has (or hastype) for a targeted job. By this I mean that the stated goal was to remove entries that are 0=0 and not more generally all instances that might occur in subexpressions (even though the supplied example had none such).

Conversion to a set will, in general, remove duplicates as well as possibly reorder the entries. If that's ok (ie. neither of those happens for the given example) then one short syntax is,

[op({EQI__4[]} minus {0=0})]

It is important to note that there will not be a set of steps which will get "whatever form you expect" for all examples.

Download simpl_example.mw

R:=e->convert(expand(numer(e))/expand(denom(e)),sqrfree):
R(expr);
R(expr2);

You can use the plotsetup command to send the plotting results to a file.

You can generate the frames of each animation separately (if you aren't already). But rather than displaying them together, use plots:-display on them individually. Before each call to plots:-display, call plotsetup and make the filename (plotputput option) be a contenation of a base string and some counter (using the cat command). The counter could be your loop index, or the frame number.

If you uploaded a worksheet that demonstrated even one of your current animations then it would be possible to show you explicitly.

Your original eq contained t as the integration variable. Are any of the instances of t in your original eq procedure supposed to be the independent variable of the differential equation, or are they all just the integration variable? I am supposing the latter, in which case you might as easily have just used a parameter Z representing eq(z). (Fortunately evalf/int has a remember table.)

Your eq produces nonreal results. I don't know how you want to deal with that. I also don't understand your expected range for the independent variable of the differential equation, or what values of the parameter z you think are going to be useful.

I don't find your example, or your intention, clear.

Download eslam_acc.mw

Some of the expressions in list S contain the name u[10]. That is, they are polynomials with u[10] appearing a name and not a function call.

But you previously made the assignment

u[10]:=unapply(1,x):

Thus the call to fsolve does not make sense.

Did you intend to unassign the name 'u[10]' right before calling fsolve (which could result in a solution where u[10] were not 1, eg. u[10] = -.5220762901)?

Or did you intend on substituting the value of 1 for u[10] in S, and passing fsolve one less expression (eg, by removing, say, one of those containing u[10])?

It's not really clear what your general term is, from your description.

I have guessed a general term, where the summation can be done to produce an explicit closed form (last example below). But even when the terms have to be added individually I don't see it as taking "a long time".

Download evalfInt_example.mw

It is pretty fast also with Digits=15 (and reduced accuracy requested for plotting, since you cannot see the difference).

Perhaps you could provide an actual worksheet that illustrates the slow behavior.

evalfInt_example_15.mw

You incorrectly have square brackets around the first argument passed to NonlinearFit, which is not valid syntax. I got rid of them in the procedure k__plot .

Also, I suspect that the very large coefficient in the exp terms is unnecessary and serves only to make it harder for an optimizer (because the corresponding factor k is then needlessly small, with loss of working precision).

Download Nonlinear_Fit_Complex_Equation_acc.mw

restart;

f := (z, n) -> (1-z)^(n-1/2)/(z^(1/2)*Beta(0.5, 0.5+n)):

nJ := (p,c,hi) -> fsolve(n -> Int(unapply(f(z,n),z), 0..p) - c, 0..hi):

ans := nJ(10^(-5), 0.95, 10^6);

                                          5
                     ans := 1.920717307 10 

evalf(Int( unapply(f(z,ans),z), 0..10^(-5) ));

                          0.9499999999

Another way, using the symbolic integration result, and fsolve with a finite range as option.

Download fsolve_example.mw

And, slightly simpler and more robust,

Download RF_example.mw

Here are a few choices of format involving RealRange, if you don't just want to get the easy representation of {b<>2} by calling solve(det<>0) .

Download solve_example.mw

There is no such options as size for 3D plotting commands, and hence it is not accepted by the plots:-setoptions3d command.

However, the ROOT substructure which is used for 2D plots can in fact be inserted into a PLOT3D structure, and the GUI will repsect it.

Below is a command which will insert such a ROOT substructure into a PLOT3D structure, and resize it.

Since the Library commands don't expect to encounter such a substructure within a PLOT3D structure, you may need to ensure that this is the last operation done prior to displaying the plot. Eg, you may wish to apply it only after combining multiple plots using plots:-display, or applying plottools:-transform and friends to the original 3D plot.

You can always remove such a substructure with subsindets, since that substructure is a ROOT function call.

Note that the ROOT substructure modifies the plotting window's size, but does not rescale or zoom the plot. The routine I've provided allows width and height to be different, but in practice you'll find that only square dimensions (ie, m=n) produces something useful.

This functionality to specify the size of 3D plots has been on my wishlist for quite a while now. But I feel that a true solution would also consist of functionality to set the scaling factor (zoom) as well as custom aspect ratios for constrained 3D plots (which would need entirely new items allowed in the PLOT3D sustructure). For 2D plots all that is naturally obtained by just the dimensions, but for 3D plots all those features are related but distinct.

Download SetSize3D.mw

Sometimes it is convenient to pass multiple arguments via one or more Arrays (or Vectors), if you are going to be calling it several times, with manual typing.

This can make calling the procedure shorter to type, and less work if only a few entries get changed between calls. Eg,

Params[45] := newvalue:
Params[46] := anothervalue:
Func( Params );

Of course it's becomes necessary to document adequately the role of each Array entry. Stay organized, as that will pay off.

And you can use a few such Array parameters, separating them in various ways: by type (integers vs floats vs others), or by purpose. You can also have some additional parameters still be passed as scalar, or via positional or keyword options.

This approach can become awkward if you want to program a sequence of calls to the procedure, and one of the Array entries is varying.

You mentioned that your worksheet has 100 or more parameters. I would not be surprised if there would be benefits to doing the computations using several procedures, and those might not all require all the parameters to be passed. A reasonable amount of focus on an effective design of the computational flow usually pays off.

The background option for 2D plots was introduced in Maple 18.

So if really do have Maple 16 (and not Maple 2016, which later) then one way to get a curve plotted over an image involves first turning the image into a densityplot.

You didn't say whether you wanted to re-scale the sine curve, vertically, if the image was not in the same proportions as the x- and y-ranges. Or vice versa. So I chose the former. And it wasn't clear whether you wanted to display axes, whose tickmarks might match the sine values and x-y data.

Download background_maple16.mw

Look inside the Startup Code Region of this first attachment.  From the main menubar choose items Edit -> Startup Code (Ctrl-Shift-E).

MaplePlayerSlideShowTest_ac.mw

Alternatively, you could make the calls to DocumentTools:-SetProperty be full and explicit, in the action code of the Buttons. And you could also form their action strings with Plot1 explicitly replacing id. In this next attachment there is no need for Startup Code.

MaplePlayerSlideShowTest_ac_2.mw