For the past decade Doug Meade, at the University of South Carolina, has created and maintained a two-page document with essential Maple commands. The first version was created for Maple V, Release 4, in January 1998. n update has been created for each version of Maple (except Maple 10) as it was released. The document has become pretty stable - hence the omission for Maple 10. Here are links to the complete set of documents he has created
Comments, corrections, and suggestions for improvement are welcomed. Please contact the author by e-mail.
Inspired by the blog post
Find a point in every region defined by a system of linear equations, I have come up with the following method to find a point inside each bounded region. The assumptions are:
- No two lines are parallel.
- No three lines are coincident.
Due to numerical instability, it seems, using floats, the coefficients of the equations of the lines are taken to be integers (they could also have been taken to be fractions, of course). Then the method goes like follows:
I am coloring the xy plane, by using a procedure(x,y) to assign color.
The procedure returns a number and color is assigned according to that number.
It works fine but I really want some of the points to be colored BLACK.
What numerical value do I use for BLACK? WHITE?
I have written a module based Maple expressions to LaTeX converter which can handle the following nested (as given by ToInert) inert types:
_Inert_RATIONAL, _Inert_COMPLEX, _Inert_NAME, _Inert_SUM, _Inert_PROD, _Inert_POWER, _Inert_SET, _Inert_LIST, _Inert_FUNCTION, _Inert_MATRIX, _Inert_VECTOR_COLUMN, _Inert_VECTOR_ROW, _Inert_TABLEREF.
As a somewhat cruel test example consider
expr := Matrix(2,2,(i,j) ->
-(-x)^(-i/2+c)*sin(x)^(-j)*(a+I*b)^((i-j)/2)
+f({-i,j})/g([-i,j])
+m[i,j]
);
newLatex:-Latex(expr);
which yields
The recipe is quite simple to understand looking at an example (and it is understood best by having paper and pencil to follow it):
f:= x -> x^2 the parabola with its inverse g:= y -> sqrt(y).
Say you want the integral of g over 0 ... 2, which (here) is the area between the graph and its horizontal axis.
That is the same as the area of the rectangle minus the area between the graph of g and the vertical axis, where the rectangle has corners 0, 2 and g(0)= f^(-1)(0) and g(2)= f^(-1)(2).
Now recall the geometric interpretation of the compositional inverse of a function: it is reflection at the diagonal.
I've done a proc to produce a list of compound Poisson random variables as below, but it's not fast enough. I suspect there are better ways to do the same. Comments and solutions welcome!
with(Statistics):
FFFF := proc (g)
local i, x, y, S;
for i to g do x[i] := floor(convert(Sample(RandomVariable(Poisson(1)), 1), `+`));
if 0
Does anyone know how to get the
openmaple api to compile in the
presence of the package com.webobjects .foundation?
Just a friendly reminder,
Regards,
Introduction to Maple 11
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Have you ever plotted a function in Maple and then found that the range you plotted it on wasn't really what you wanted? You can always re-execute the command, of course, but that means working out exactly what the range is for that interesting feature you want to investigate, and if you've made changes to the plot those will be lost. However Maple has the ability to zoom in on a plot interactively, without re-executing the command.
The Axis Properties dialog lets you change the range numerically, but you can also do so using the mouse. Go to the plot toolbar and click on the Scale plot axes button (it looks like a red ball with an arrow). If you have an animation you will need to click on the word "plot" above the toolbar to switch from animation to plot toolbar. Now put the mouse in the middle of the plot and drag it. Dragging it down will zoom out, increasing the range; dragging it up will zoom in. The Translate plot axes button lets you 'pan' i.e. move the centre of the axis ranges without changing the range size.
This isn't specifically Maple-related; but mathematics-related;
related to Linear Algebra and Modern Algebra.
While reviewing Linear Algebra; I ran across the
concept of "Similar Matrices"; which are defined as:
if A,B are nxn matrices and
there exists invertible nxn matrix P such that
P^(-1)*A*P = B
then
A is similar to B
The payoff was:
if A, B are similar then
they "have the same eigenvalues"
(the characteristic equation is same for both A and B).
(Here we are talking about the group of invertible nxn matrices,
with operation matrix multiplication)
--
The command "latex(expression)" attempts to generate LaTeX commands that will recreate the expression in LaTeX. For example; latex(%) will try to generate LaTeX commands to recreate the last output from Maple.
Let's say I had just entered the Maple command to display an integral; for example:
Int(Int(Int(rho^2*sin(phi),rho=sec(phi)..5*sec(phi)),phi=Pi/6..Pi/3),theta=0..2*Pi);
If I would like to put that same integral in a LaTeX document; I could enter the
following command:
latex(%);
Which, in Maple 9, returned:
\int _{0}^{2\,\pi }\!\int _{1/6\,\pi }^{1/3\,\pi }\!\int _{\sec
There's an interesting set of posts on comp.soft-sys.math.maple about post-processing .eps plot output from Maple. Here's a
link via Google Groups.
The author's ideas revolve mostly about processing tickmarks and subtickmarks and replacing them with symbols. The claim is made that it's harder (or impossible) to do some things in Maple for .eps output that are possible in Mathematica or Matlab. I haven't yet tried or looked hard at the posted code, or verified the claim.
It seems to me that I found a tip
(I am a beginning user)
In running these three commands in
Maple 10, one gets:
> sum(1/(n^4+1), n = -infinity .. infinity)
sum(1/(n^4+1), n = -infinity .. infinity)
> sum(1/(n^4+1), n = 0 .. infinity)
1/4*(Sum(_alpha*Psi(-_alpha), _alpha = RootOf(_Z^4+1)))
> sum(1/(n^4+1), n = -infinity .. infinity)
0
The last answer is obviously wrong.
In other similar experiments,
Maple gives the answer -infinity
to the last expression, which
is also wrong.
Could somebody comment on this phenomenon?
Many thanks in advance.
Hello, I have a question concerning PDEs with initial / boundary conditions. Now, I am trying to solve this PDE.
The general solution to my PDE is achieved by:
governing equation : the homogeneous diffusion equation is
> PDE := diff(c(x,t),t)=diff(c(x,t),x,x);
the boundary condition are
> BC1 := c(0,t)=0;
> BC2 := c(0,L)=1;
the initial condition is
> IC := c(x,t)=1;
I want to solve above equation by using maple software(Currently I am using Maple 10). In this case I want to find the final expression. If you have any idea to lead this problem using this software, please help me help.
Usually exporting from classic interface as HTML works quite well (ok, not all the finer things, but with good (!) graphics and it is painless).
Now I want to hide input (for readers not used to Maple that might be better), but with M11.02 the input is exported anyway.
Any workaround (except using an editor for the HTML result) ?
