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.

What is the command which returns the length of a list? i.e. length of [1,2,3] is 3 ? More importantly, please tell me where in the help menu this command is listed. Thank you.

I've created a new blog entry concerning what I think might be an idea worth consideration:     slide rule

... I doubt that there has ever been a better way to learn the relationship between numbers - and even mathematics in general - than the slide-rule from days-gone-by, and the ability to plot functions using modern computer technology. For the young people here who may not have ever used a slide rule, below is a link to a virtual slide rule:     virtual slide rule

I wish, and think...

Here is the article. I wrote this as a blog entry, and felt it was better to leave it one place rather than duplicating it. Besides, I don't know how to delete a blog entry. A cheap way to earn five points; however, my next page addition—in the works—to this book will be recompense.

Occasionally it is necessary to temporarily assign a global flag to perform an action. Consider, for illustration, a procedure that returns the inert form of a procedure. We want it to be able to work with procedures that are local to modules. To do that, we need to temporarily assign the kernel flag opaquemodules to false.

GetInert1 := proc(p::uneval)
local opacity,inert;
    opacity := kernelopts('opaquemodules'=false);
    inert := ToInert(eval(p));
    kernelopts('opaquemodules'=opacity);
    inert;
end proc:

Here is a small module to test this on: