## nonnegative integers in an identity...

In the example below, I find integers that solve the equation. That solution happens to be nonnegative. But in general, just plugging in zeros may not give me a nonnegative solution. What is a good way to find a *nonnegative* integer solution, if one exists?

> aa := x^(-4)*exp(-2*x);

> pmu:=product(muval[j]^a[j],j=1..kmax);

## Plotting a function which contains a (difficult) i...

Hello, This is related to my recent posts at http://www.mapleprimes.com/forum/integral-equations#comment-8339 I have a function of three variables one of which is inside a (difficult) integral. I want to calculate & store the array of points which satisfy the function, then use transform to change those points and then plot them. The function looks like this: P:=(x,m)->sqrt(x)/(sqrt((x+m)^2-1)*(x+m+sqrt((x+m)^2-1))); IntegralP:=(m)->Int(P(x,m),x=0..infinity); f4A:=(beta,Omega,m)->beta^2+(3*(beta*Omega)^(3/2)*evalf(IntegralP(m)))/(4*2^(3/4))-1; In my earlier case, m=1 (and there was another variable, but it wasn't under the integral) so the integral was not a problem. I tried the same method;

## chagne...

Hello, I hope someone can help me with this. 1) In Worksheet mode, if I type a:=b+c; and press Enter, Maple echoes a:=b+c 2) In Document mode, if I type a:=b+c; and press Enter, Maple echoes b+c I actually want Document mode to give me the same form of output as Worksheet mode (i.e. I want Document mode to give me a:=b+c as the output). Can this be done? Thank you for any assistance. Ty

## Change coordinate systems for substitutions...

Still being a newbie to Maple, I am stuck on this one. I am trying to create a general system of changing my equations in an [x,y] coordinate system to a [u,v] system. As a specific example: I have two substitution equations, u=2x-3y and v=-x+y. I have four equations: x=0, x=-3, y=x, y=x+1. I have tried MapToBasis with both static and procedure statements and I am not having any luck. The equations do not completely change to [u,v]. Here is one example: > proc (u, v) u = 2*x-3*y end proc; > proc (u, v) v = -x+y end proc; > with*VectorCalculus; > SetCoordinates('cartesian', [u, v]);

## Plotting functions of several variables...

I am trying to plot the equations shown in Figures 5 and 6, which are solutions to Equations (14), (15), and (16). These equations are developed in the Lo paper (attached). I am working through the symbolic solution by hand and would greatly appreciate any suggestions on how to set these equations and the graphs of the same in a worksheet. Thank you for the assistance anyone may offer. Wayne Bell Download 4865_Lo_p691.pdf
View file details

## Why it doesn't work?...

I'm having a problem to run this Maple. Thank you for your help. > solve({e1⊢e1=e1,e2⊢e2=e2, e1⊣e1=alpha1*e1+alpha2*e2,e1⊣e2=alpha3*e1+alpha4*e2,e2⊣e1=alpha5*e1+alpha6*e2,e2⊣e2=alpha7*e1+alpha8*e2, (e1⊣e1)⊣e1=e1⊣(e1⊣e1),(e1⊣e1)⊣e1=e1⊣(e1⊢e1),(e1⊢e1)⊣e1=e1⊢(e1⊣e1),(e1⊣e1)⊢e1=e1⊢(e1⊢e1),(e1⊢e1)⊢e1=e1⊢(e1⊢e1), (e1⊣e1)⊣e2=e1⊣(e1⊣e2),(e1⊣e1)⊣e2=e1⊣(e1⊢e2),(e1⊢e1)⊣e2=e1⊢(e1⊣e2),(e1⊣e1)⊢e2=e1⊢(e1⊢e2),(e1⊢e1)⊢e2=e1⊢(e1⊢e2), (e1⊣e2)⊣e1=e1⊣(e2⊣e1),(e1⊣e2)⊣e1=e1⊣(e2⊢e1),(e1⊢e2)⊣e1=e1⊢(e2⊣e1),(e1⊣e2)⊢e1=e1⊢(e2⊢e1),(e1⊢e2)⊢e1=e1⊢(e2⊢e1), (e1⊣e2)⊣e2=e1⊣(e2⊣e2),(e1⊣e2)⊣e2=e1⊣(e2⊢e2),(e1⊢e2)⊣e2=e1⊢(e2⊣e2),(e1⊣e2)⊢e2=e1⊢(e2⊢e2),(e1⊢e2)⊢e2=e1⊢(e2⊢e2), (e2⊣e1)⊣e1=e2⊣(e1⊣e1),(e2⊣e1)⊣e1=e2⊣(e1⊢e1),(e2⊢e1)⊣e1=e2⊢(e1⊣e1),(e2⊣e1)⊢e1=e2⊢(e1⊢e1),(e2⊢e1)⊢e1=e2⊢(e1⊢e1), (e2⊣e1)⊣e2=e2⊣(e1⊣e2),(e2⊣e1)⊣e2=e2⊣(e1⊢e2),(e2⊢e1)⊣e2=e2⊢(e1⊣e2),(e2⊣e1)⊢e2=e2⊢(e1⊢e2),(e2⊢e1)⊢e2=e2⊢(e1⊢e2), (e2⊣e2)⊣e1=e2⊣(e2⊣e1),(e2⊣e2)⊣e1=e2⊣(e2⊢e1),(e2⊢e2)⊣e1=e2⊢(e2⊣e1),(e2⊣e2)⊢e1=e2⊢(e2⊢e1),(e2⊢e2)⊢e1=e2⊢(e2⊢e1), (e2⊣e2)⊣e2=e2⊣(e2⊣e2),(e2⊣e2)⊣e2=e2⊣(e2⊢e2),(e2⊢e2)⊣e2=e2⊢(e2⊣e2),(e2⊣e2)⊢e2=e2⊢(e2⊢e2),(e2⊢e2)⊢e2=e2⊢(e2⊢e2)},{alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8});

## Plotting with a floor function...

I wonder if this is the right way to plot following function. > restart: > huur:=t->400*(1.01)^ceil(t); floor(t) huur := t -> 400 1.01 > plot(huur(t),t=0..50,discont=true); As you can see I have a the function huur(t) with t a positive integer. I can't find another way to plot this function except by making use of the floor function. Isn't there a better way? Asumming that t is a positive integer didn't worked.

## How do I assume Maple expression to be a constant?...

Hello, in a differential equation (in Maple 10) a variable should be replaced by a constant K so that all differentiations of this variable should evaluate to zero. This is my code: constants:= constants, K: myDG1:= u(t) + diff(u(t),t)^2 + v(t)=0: subs(u(t)=K,myDG1); K+(diff(K, t))^2+v(t) = 0 Although I have already assigned K to be constant, Maple doesn't replace d/dt K by 0. Any help would be appreciated.

## How to get this answer?...

Consider a sum: Sum((-1)^(i+1)*Sum(1/j,j=1..i)*x^i,i=1..infinity); value(%); The result given by Maple 11 is: sum((-1)^(i+1)*(Psi(i+1)+gamma)*x^i, i = 1 .. infinity) However, from an calculus book I know the answer is: log(1+x)/(1+x). How can I get this result from Maple? Whether should I give some assumptions? Best wishes.

## A question in plot command...

Here I difine a subfunction:

mandelbrot := proc(x, y)
local c, z, m;
c := evalf(x+y*I);
z := c;
for m to 30 while abs(z) < 2 do
z := z^2+c
od;
abs(z);
end:

Then I want to plot this function using densityplot command:

plots[densityplot](mandelbrot, -2 .. 0.7, -1.2 .. 1.2, grid=[50, 50], style=patchnogrid, scaling=constrained);#This command is right.

But...

plots[densityplot](mandelbrot(x,y), x=-2 .. 0.7, y=-1.2 .. 1.2, grid=[50, 50], style=patchnogrid, scaling=constrained);#Error, the proc I defined could not determine whether abs(x+1.*I*y) < 2.

## Maplet Plotter does not plot...

To Maplet enthusiast: I uploaded a functional shortened code from a 35-page code. See ShortVersion.mw under Recent Files. Although the file is compiled/interpreted successfully by Maple 11, the maplet plotter did not plot. I will appreciate it very much if someone can offer an explanation why the element failed and a possible suggestion on how to correct the problem. Many thanks Pat Velez

## Diff problem...

Here is a derivative that I'm trying to take that I get a different answer from Mathcad. This would normally be ok I guess except when trying to figure arclength in Maple I don't get an answer and in Mathcad it works fine. diff((3+4*y^4)/12*y,y); The original equation is: 12xy - 4y^4 = 3 Thanks, glenn