Inspired by Jacques' blog entry Introduction to transseries, concerning a paper by Gerald A. Edgar, using Maple and published at arXiv, I here take the liberty to refer to a recent paper of mine which also uses Maple and is published at arXiv. The link is:

Linking electroweak and gravitational generators.

Most probably, this paper would not have existed without the possibility of performing lots of calculations in Maple, using for instance my own package COSVAM which deals with the octonions, the largest division algebra over the reals.

For instance, the pivotal Eq. (5) of the paper would probably not have been discovered by me using pen and paper. It was accidentally discovered while performing some Maple calculations with a different objective in mind.

Second note added: The issue below seems to have been resolved by clearing the cache of my Firefox browser, i.e., it seems to have been purely a local problem.

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:

Hi there. How are you? I feel sorry since I purchased Maple. Let see if you would agree. First of all, it is inferior to the Ti-89 in some aspects. I have tried to use Maple 11.02 to solve the problems: (sqrt(2)+1)^x+(sqrt(2)-1)^x = 3; And Maple 11.02 fail to solve, then I tried to solve numerically, it missed one solution. There must be 2 solutions for the problem above and Maple missed 1, the Ti-89 beats it hand down. The second problem I tried was: int(sqrt(sin(x))/(sqrt(sin(x))+sqrt(cos(x))), x = 0 .. (1/2)*Pi); and Maple even stuck... The Ti-89 return answer correctly within about 20 secs.

Inspired by the post Re: the physics package I decided to have a closer look at the function FeynmanDiagrams. As the Lagrangian I thought I might as well take the QED Lagrangian for a massless spinor field Q[i](X) coupled to an external electromagnetic field A[mu](X):

restart:
with(Physics):
Setup(advanced):
L_QED :=
   +Dagger(Q[i](X)) * Dgamma[4] * Dgamma[mu][i,j] * I * diff(Q[j](X),X[mu])
   +Dagger(Q[i](X)) * Dgamma[4] * Dgamma[mu][i,j] * e * A[mu](X) * (Q[j](X));

My previous blog entry was a real success. Even though my original idea about multi-part MIME has not gotten anywhere, I do now have a concise way to package a maplet with supplemental files in a single package that can be downloaded via the WWW and automatically extracted and executed. Most of the ideas were presented by acer. acer first suggested that I look at the interactive interface to the InstallerBuilder. The idea here was to embed the maplet in a worksheet saved in a help database (hdb). This did work, but was not suitable for actual use due to the overhead of the installer. In the attempt to reduce this overhead, acer then supplied some code that used march and LibraryTools. To test the product of this interaction, download the file at the URL http://www.math.sc.edu/~meade/TEST/SimpleTest.mla.

Note added: As correctly pointed out by Joe Riel in his post below, my function fromTree fails doing what it is supposed to do for expressions which contain lists and/or sets. For a version of fromTree which behaves properly (I believe) also for expressions containing lists and/or sets, see my post below. Consider the following two functions:

toTree   := x -> `if`(op(x) = x,x,[op(0,x),map(toTree,[op(x)])[]]):

I got an interesting question about integration yesterday. The question was about the integral of the rather innocuous looking function f := sqrt(1+sin(x)). The inside of the square root is always non-negative so the function is continuous (and bounded!) so it must have a continuous integral. The question I was asked, was if the following result was a bug in Maple: Int(sqrt(1+sin(x)),x) = (2*(sin(x)-1))*sqrt(1+sin(x))/cos(x) since the right-hand side is definitely not continuous at x=-Pi/2 + 2*n*Pi!

Below is a link to a file I uploaded showing an example of using assigning the value obtained from eval() to a variable and then using evalf() versus using eval() inside of evalf(). The fact that there is some difference is not surprising; it's the sheer amount of difference that amazes me--up to 100%! Do also note that the difference "settle down" over time, which is to be expected. View 413_odd_rounding_example.mw on MapleNet or

In my work developing Maplets for Calculus, there are many instances when I want to determine that a function is monotone (decreasing or increasing or non-decreasing or non-increasing) on an interval. If I can do one of these, I can do them all. So, let's focus on decreasing. I have no problem assuming f is continuous and differentiable on the interval. The interval could be unbounded, and I am not terribly concerned about endpoints (at least now). Given a function f, how would you use Maple to determine that f is decreasing on an interval (possibly unbounded)?

As a direct result of the tab indentation nuisance reported in the three threads

• Erratic formatting behaviour using tabbing
• Please give me some feedback
• Usability

today I have rolled back my system from Maple 11 to Maple 9.5: I have spend quite some time today manually going through all the Maple documents which have been contaminated by loads and loads of XML codes which Maple 11 produces.

find the small x series which approximates

(tan(x)log(1+x))/X

by plotting the function and the series approximations investigate how accurate this approximation is over the range 0<x< Pi/2 when different numbers are included in the series

i have no clue where to start can anyone help me please???

I present the following:

[> restart;
[> a1:= foo = bar;
                             a1 := foo = bar
[> a2:= blam = foo = bar;
Error, `=` unexpected
[> a3:= blam = a1;
                       a3 := blam = (foo = bar)

The fact that the definition of a2 (correctly) throws an error and the definition of a3 does not can lead to some odd errors down the way. I disagree with Maple's choice not to say that the assignment of a3 is in error.

The student is supposed to use the logistic differential equation given to them (with carrying capacity .52e12), dsolve() the differential equation with a specific initial condition, and then calculate the population at 3 different times. Notice what happens:

[> restart;
[> my_deq := (diff(P(t), t))/P(t) = .789*(1-P(t)/(.52*10^12));

                   d
                   -- P(t)
                   dt                               -11
         my_deq := ------- = 0.789 - 0.1517307692 10    P(t)
                    P(t)

[> dsolve({my_deq,P(2290)=.83*10^10});

In order to get better acquainted with the plotting facilities of Maple I thought I would try to plot the Möbius strip. In the proces I generalized the task so that I would be able to plot a ribbon twisted an arbitrary number of times. From these efforts the following code resulted:

with(plots):
radiusVector := (phi) -> Vector([cos(phi),sin(phi),0]):
ribbonVector := (phi) -> Vector([-sin(phi)*cos(phi),-sin(phi)*sin(phi),cos(phi)]):
p := (twist,theTitle,theOrientation) -> plot3d(
   radiusVector(phi) + t*ribbonVector(twist*phi),phi=0..2*Pi,t=-0.3..0.3,
   title=theTitle,orientation=theOrientation,grid=[100,10],scaling=constrained
):

Below follow two examples: 1. Ribbon with 1/2 twist: The Möbius strip:

display(p(1/2,"Ribbon with 1/2 twist: The Möbius strip",[200,70]));

 

2. Ribbon with 1/1 twist:

display(p(1/1,"Ribbon with 1/1 twist",[40,60]));

As a math phobic, I took a class this semester at UConn Math102Q. The instructor is pretty good but now at mid-semester there are a lot of "do more problems" answers. I hoped at the beginning this would help with my math phobia. The course is fairly new and uses the PSSSP model and the book is written by DeFranco and Vinsonhaler.