I wrote a procedure for drawing a 1d phase portrait of an equation

                        `x′`=f(x)

in Classic Maple,

phase:=proc(f,r)
local a,b,bn,bs,U;
a:=op([1,1],plot(args));
bn:=-`-`(op([2,1..2],r));
bs:=[a[1,1],seq(`if`(
(a[i-1,2]-0.0001*bn*signum(a[i-1,2]))*(a[i,2]-0.0001*bn*signum(a[i,2]))<0,
`if`(a[i-1,2]*a[i,2]<0, (a[i-1,1]*a[i,2]-a[i-1,2]*a[i,1])/(a[i,2]-a[i-1,2]),
fsolve(f,subsop([2,1]=a[i,2]-0.02*bn,[2,2]=a[i,2]+0.02*bn,r))),NULL),
i=2..nops(a)),a[-1,1]];
b:=bs/bn;
U:=remove(x->abs(x[2,1])<0.04,
[seq([[b[i]+0.01,0],[b[i+1]-b[i]-0.02,0]],i=`if`(a[1,2]<0,2,1)..nops(b)-1,2),
seq([[b[i+1]-0.01,0],[b[i]-b[i+1]+0.02,0]],i=`if`(a[1,2]<0,1,2)..nops(b)-1,2)]);
plots[display](plots[arrow](
U,width=0.02,head_length=0.04,view=[b[1]..b[-1],-1..1],color=blue),
plots[pointplot](map(x->[x,0],b[2..-2]),symbol=circle,symbolsize=19),
plots[textplot](map(x->[x/bn,-0.07,sprintf("%.2f",x)],bs[2..-2])),
axes=none)
end:

It works as in the following example for f(x)=sin(x),

phase(sin(x),x=-8..8);

One-dimensional Brownian motion can be simulated using the following (modified from the version posted here originally) procedure,

I find that when I'm working on something new I consistently end up reading the same set of help pages over and over. The "History" option in the help system has been very useful to me, but I would like to see a "Bookmarks" option added to Maple's help system as well.

Hi everyone, I am an undergraduate studying Stochastic Financial Modelling. I am currently writing up a simple brownian motion as shown on the attachment. I have difficulty in simulation a number of these paths and displaying 5 or so of them on the graph with the average path of all simulated paths. In this case, i would expect the average to be a straight line along the axis. Can anyone help me with this as i am only a novice in maple programming? Thanks, Steve

Well, I'm using Maple on a Mac with PowerPC. It's runing
wonderfully, but there is one problem. With Java 1.4.x it was running without problems, but after I upgraded my Java to version 5 there is a bug. Entering commands in a worksheet automatically inserts some whitespaces, but only in the view. That's looking really uggly, if the cursor is some whitespace further then the text I'm writing.
I hope it can be repaired in the future.

Matrix algebra over finite fields can be implemented using the following procedure,

Hi everyone! I posted the "multiple plot" question yesterday, unfortunately not worded all that clearly. But much thanks to the people who replied. Here is a better worded question, hopefully: Suppose I have created a series of plots {p[1], ..., p[n]}, how do I display them all on the same figure, EASILY! Suppose n = 100, it would be a chore to have to type out: with(plots): display(p[1],...,p[100]); Is there an easy way to display the n-plots? Perhaps something like display({p[i],i = 1..n}); ?? I did try this command, but it didn't work. I also tried p := array(1..n):

Hi everyone! I could display two plots named p[1], p[2] by with(plots): p[1] := ...: p[2] := ...: display(p[1],p[2]); How do I display n-plots name p[1], p[2], ..., p[n]? Thanks for your help! -Dan

In the following Maple code: Download 2636_Cartesian p-orbital.mws I just can't see how to clean it up properly. Can someone help? Thanks Carl David

Maple 10, when asked to evaluate int(sqrt(1/x^4+1), x = 1 .. 2) returns a complex value. (evalf gives 1.132 + (10^-9)I). Is there any way to get an accurate symbolic answer that is pure Real? Steven L Berntsen Montreal QC Canada

Nice implementation of Drupal. I like it!

Hi, I have a question about Gröbner bases and using the Rosenfeld_Grobner algorithm in diffalg. What is best to use? If the equations only contain time differentiated variables, is it better to differentiate the equations "by hand" first and let the Gröbner package deal with the problem or is it better to just plug the whole thing into diffalg from the start?

I am new to this forum and would appreciate any feedback. I do not use Maple myself but have users who report to me that when they use Maple 10 (both with and without the patch), if they go on to something else and come back to Maple, when they maximize it, the computer will randomly shut down. It only seems to happen with this application. Any one out there experience anything similar or know of any solutions. Thanks very much for any advice.

First time to this blog but I need help. I don't use Maple myself but I have many users that do and they are reporting to me that when using Maple 10 (with or without patch), if they go on to another application and then maximize the Maple again, it will cause the computer to re-boot. Has anyone out there run into this problem before? My users are using a 3.2 Ghz processor running WinXP SP2 with 1GB RAM and an 80 GB hard drive. They all say they have noticed this problem only with Maple! Help! Many thanks.

Hi again, Running Maple 10, WIN XP Pro, When I try and export worksheet as RTF Maple only exports a small portion. I have the "Disable Large RTF" checked as "Never" yet I still only get a small portion. Is this a bug? or am the one with a bug? TIA Larry Ciak aka malt_master@comcast.net