The eigenvectors associated with eigenvalue evals[i] can be computed as the Null Space of the Characteristic Matrix using at lambda = evals[i] .

Download eigenvects.mw

There are various ways to simplify your examples. Presumably you want approaches which are understandable and less ad hoc. (In the first examples in this attachment, the evala command does as well as radnormal.)

If the denominators (of the arguments of the ln calls) are factored after expanding, then one of the factors will cancel automatically with part of the corresponding numerator, for your examples. See the last two lines in this attachment, for insight on that as well as expansion without that factoring.

Download targeted.mw

The procedure Mutate acts in-place on the particleposition Array, so it seems like you want that Array to be a running state of the updated values.

But inside your procedure Mutate there is a statement y :=x .Perhaps you intended y:=copy(x), and to have the last line of that procedure be return y ?

If L2 is very large then you might want to ascertain a true result as soon as any element of L2 is found to be in the union of the L1 sets.

In other words, you may find it too costly to compute a full set intersection (or minus) involving examining all of L2, or a full seq of tests over all of L2.

In such a case you could try ormap , which will return true as soon as it finds its first true result. Ie.

   ormap(member,L2,`union`(L1[]));

There may, however, be some function-call overhead for calling member many times. (There are some kinds of calculation where it matters whether you want to focus on worst possible vs best average behavior, etc, in which case deciding what's best can entail figuring out what's likely as well as what you want.)
 

That do is our of place. That keyword is not part of an if..then..end if.

You likely don't want a loop here.

Are you trying to get something like this?

Here I use to frontend to suppress/freeze the derivatives, while using eliminate on the variable m, and then consider the remaining conditions (implied equations, the second part of what eliminate returns).

Download eliminate_examp.mw

You can substitute for m+F(xi) using freeze and algsubs, and then collect, and then resubstitute using thaw.

You have a variety of ways to simplify, or not, the coefficients (of the m+F(xi) powers). Below I show two ways, one with some simplification.

Download collect_freeze.mw

I don't know of a way to accomplish what you want using a legend per se, especially if the font size and dimensions have to be as you have them.

But what about a combination of shorter line segments alongside textplot, inlined into the plot? It's more effort to set up just right, but gives more flexibility to correct for the linestyles. legendwidth.mw

If the expression (dependinng on a, b, and c) has been assigned to the name `expr` then you can create an operator from that with,

f := unapply(expr, [a,b,c]);

The assumptions that modify your Int calls -- made using assuming -- don't carry over to the value calls.

Various simplifications can be made on the result of the value or int calls, using the same assumptions, say.

Another possibility is to convert the integrand to expln form prior to using value.

Download integrals_acc.mw

Try this in your Maple 2016, using the name `#msub(mi("n"),mi("r"))` wrapped in a typeset call.

mprime_ac.mw

If you are in (plaintext) 1D Maple Notation mode then you can do it as below.

If you are in 2D Input mode then you can use the Accent palette to insert a typeset c with a circumflex accent. See below for a result.

Download accent_label.mw

You can plot the four "roots" versus B (for a single value of V), or you can plot a single root versus B (for, say, multiple values of V).

You can use either solve or (a procedure that calls) fsolve, to evaluate the roots for the values of B.

Note the the individual formulas (any of the four returned by solve, whether explicit or as implicit RootOf) do not necessarily correspond to a (perceived) single one of the connected portions of solution curves in the plot of all roots. The same goes for picking off a particular place in the four roots returned by fsolve. Hopefully the colors illustrate this aspect. There are ways in which sometimes one can track one of the curves, say by picking the closest the previous value found, possibly also tracking yhe slope. Root crossing can be problematic. This is generally tricky on mathematical grounds, not just as a Maple issue.

Download rootplot.mw

restart;
A1:= [a1, a2, a3]:
A2:= [b1, b2]:

map[3](op@zip,`/`,A1,A2);
         
          a1    a2    a3    a1    a2    a3
        [----, ----, ----, ----, ----, ----]
          b1    b1    b1    b2    b2    b2

map[3](op@zip,f,A1,A2);

    [f(a1, b1), f(a2, b1), f(a3, b1), f(a1, b2), f(a2, b2), f(a3, b2)]

Here are three ways it may be accomplished, if I have understood the goal.

odeplots_in_an_Explore_command_ac.mw

(If you feel like some heavier reading you might glance at these two older posts, 1, 2 ).