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]));

The Vim editor ships with a maple.vim file, which is a "maple mode". It was first created by Charles Campbell, and I provided some updates (up to Maple 9.5). I am about to rev that up to Maple 11, so I would like to know if there are any feature requests which I should consider rolling-in at the same time? If you have little bits of vim scripts which you yourself use, by all means, send them along! [You'll get full credit for that, I am fine with being just an aggregator...

I thought this might be of interest to anyone interested in seeing some simple ciphers broken with maple. Download 6039_huffaf_crack.mws
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Hi, I ran into this in my Modern Algebra class; and decided it might be of interest. We were given the problem to: "Find the least prime p s.t. 2^(p-1) congruent to 1 (mod p^2)" EVERY prime p > 2 has the property, 2^(p-1) congruent to 1 (mod p), by Fermat's Theorem (since 2 does not divide such prime p). But, mod p^2 is another story. This was given in a class where everything is done by hand calculation, based on theorems. I couldn't come up with any way to determine it other than brute force. Here is a tiny Maple snippet which finds it:

The fact that animate uses subs when replacing the animation parameter with a number in the animation range can cause problems when the expression to be animated is only evaluated when the animation parameter is replaced by a numeric value. This is shown in the simple example below My suggestion is that in the procedure `plots/animate` the three subs's are replaced by eval's. Is there any problem with that? Preben Alsholm The following does not work at all, apparently because animate uses subs instead of eval in 3 places, lines 29, 43, and 64 (using showstat(`plots/animate`).

I'm trying to do symbiolic manipulations to define new procedures but I have trouble figuring out how to achieve my goal. The context is as follows: We have a set of ODEs df/dt = R(f(t)) where f(0) = x. Here f and x are n-dimensional vectors with components f[i], x[i], and R is a vector valued function with components R[i]; t is time. Example: R[1] := proc (x::Vector) x[2] end proc; R[2] := proc (x::Vector) -x[1]*(1+x[3]^2) end proc; R[3] := proc (x::Vector) x[4] end proc; R[4] := proc (x::Vector) -x[3]*(1+x[1]^2) end proc; Now, the Liouville operator is defined as L := proc(F::algebraic,a::list(algebraic))

How do I get maple 11 to graph the surface and the horizontal tangent plane (same graph). The function I am working with is z=3x^2+2y^2-3x+4y-5 the point would be (1/2,-1,-31/4) I am a new user, so if you could take it step by step, that would be very helpful. Thank you, Jerry

Evaluate: lim [1/x * ( (a^x - 1) / (a-1) ) ] ^ 1/x x->infinity where a > 0 and a is not equal to 1

Can anyone explain how to write a 10 consecutive sequence of odd x^3 natural numbers?

Hi I wonder if anyone knows of any maple code to generate polynomials with algebraic constants. eg an order 1 poly would be: a+b*x, order 2: a+b*x+c*x^2, order 3: a+b*x+c*x^2+d*x^3, ...... etc what i'm looking for is a procedure where i input the order, eg 3, and it spits out a+b*x+c*x^2+d*x^3 thanks in advance

I need help. A homework problem superimposes a graph atop a DE. What am I doing wrong: _____________ plot1 := phaseportrait(eqn,y(x), x=-0.25..0.25, [[y(-1/2)=2],[y(3/2)=0]],titlefont=[TIMES,ROMAN,18],title=`Sec 2.1 #17`, color=grey, linecolor=[red,blue]): plot2 := (1/2)*x^2: display([plot1,plot2]); Error, (in DEtools/phaseportrait) the 'number' option must be specified before initial conditions Error, (in plots:-display) expecting plot structures but received: [plot1, (1/2)*x^2] _____________

I had the pleasure of visiting Oxford while on vacation in England. I regret that I did not get a chance to visit the NAG headquarters there, but that thought gave me the idea for this next blog entry. The Optimization package for local optimization uses as its underlying engine the NAG E04 optimization suite. It is possible to use the Optimization package without knowing the internal workings of the commands. However, for those of you who are interested in such details, it is possible to get more information. If you set infolevel[Optimization] to 2 or higher, the names of the NAG routines (e.g. E04UCA) are displayed. It is useful to set the infolevel value in any case, as the messages provide valuable information about how the computation is proceeding.

Maple can convert an ordinary (base 10) number into its constituents using the convert base command. eg 175 can be decomposed to its digits using: > convert(175,base,10) = [5,7,1] my question is "is there a maple command that turns [5,7,1] back to 175". obviously I could pluck out the numbers and multiply by 100,10 etc, but i'd rather have an inbuilt command. Mathematica has a command that does it: FromDigits. rgds

The Maple overload command provides a useful mechanism for splitting the implementation of a procedure that operates on different types of arguments into separate procedures. This article describes the mechanism that it uses to select the procedures, illustrates subtle issues, and shows how they can be resolved.