@Michael_Ormstrup I recommend making the parameters more like the plot command itself: The range being passed in the form a..b, and the functions in a list if there is more than one. So, the parameter declaration would be

integralplot2:= proc(
     F::{algebraic, [algebraic, algebraic]},
     R::range,
    {[color, colour]:= blue, transparency:= 0.5, numpoints:= 500}
),    

f1, f2, a, b would become local, and the first two lines of code would be

(a,b):= op(R);
(f1,f2):= `if`(F::list, F, [F,0])[];

@Michael_Ormstrup I recommend making the parameters more like the plot command itself: The range being passed in the form a..b, and the functions in a list if there is more than one. So, the parameter declaration would be

integralplot2:= proc(
     F::{algebraic, [algebraic, algebraic]},
     R::range,
    {[color, colour]:= blue, transparency:= 0.5, numpoints:= 500}
),    

f1, f2, a, b would become local, and the first two lines of code would be

(a,b):= op(R);
(f1,f2):= `if`(F::list, F, [F,0])[];

@spradlig If you click on your name, or anyone's name for that matter, you can see lists of their Questions, Posts, Answers, and Favorites. You do not need to be logged in to do this.

@spradlig If you click on your name, or anyone's name for that matter, you can see lists of their Questions, Posts, Answers, and Favorites. You do not need to be logged in to do this.

I think that the option should be added to the plotsetup command as a plotoptions for the default plot device. The reason is that all the commands that produce plots actually produce an algebraic structure that should be device independent; device specific parameters should not be stored in that structure.

@emma hassan Are you saying that you want the numbers themselves actually printed on the plot?

@emma hassan Are you saying that you want the numbers themselves actually printed on the plot?

@maxou Once you take the derivative with respect to a variable appearing in exponents (rho in this case), the expression becomes vastly complicated. I have no idea on how to approach it.

@maxou Once you take the derivative with respect to a variable appearing in exponents (rho in this case), the expression becomes vastly complicated. I have no idea on how to approach it.

@Michael_Ormstrup To expand on it, I need to know what a and b represent. I would've thought that they were the plot range, but you don't use them in the plot command in your procedure.

@Michael_Ormstrup To expand on it, I need to know what a and b represent. I would've thought that they were the plot range, but you don't use them in the plot command in your procedure.

@spradlig Can you show an example of a simple one-line function on which D doesn't work? The unapply solution will only work if the application of the function to a generic argument results in an algebraic expression. It's a somewhat specialized situation.

@spradlig Can you show an example of a simple one-line function on which D doesn't work? The unapply solution will only work if the application of the function to a generic argument results in an algebraic expression. It's a somewhat specialized situation.

How do you define the eigenvalues of a system of nonlinear equations?

@jschulzb You may be able to save memory by not using parameters (assign their values in the original dsolve), and using the output= Array form of output. With this form you specify the values of the independent value at which the system is to be evaluated and dsolve returns an Array with those evaluations. This should have an effect similar to interpolate= false. See ?dsolve,numeric .