## Optimization...

Hello everybody, I have a question please. I would like to resolve an optimization program. The objective functions are not linear and the constraints are the inequality functions. Can somebody tell me if we can resolve this type of programs with maple. Thanks a lot, Sarah

## Local and global optimization

by: Maple

One issue that often confuses users is local versus global optimization in Maple. I'm just going to give an overview here and will explore specific optimization topics more deeply in future blog entries. Please note that I'm covering only the numeric optimization methods here. I'll leave discussion of the exact methods in Maple to others more knowledgeable about those areas.

The Optimization package is built into Maple and is available to all users. This is primarily...

## Plotting Large Sparse Matrices in Maple

by: Maple

When working with large sparse linear systems you often want to look at their non-zero structure, however Maple's existing tools are all designed for dense matrices. I wrote a little tool to produce images like this in reasonable time. You can download the code here, and the rest of this post is a quick tutorial on how to use the included command. Maple 11 is required.

## nonlinear identity / matching...

Do you have some suggestions on how to do this?

> restart;

> K := exp(-b*x+c*exp(x))*(log(x))^a-exp(-x);

> # for this identity, I want to get: {a=0, b=1, c=0} .

> solve(identity(K,x),{a,b,c}) assuming x>10;

## Plotting a graph...

I really seem to be having a lot of trouble with Maple that I don't have with Mathcad and I'm hoping you guys can show me what I"m doing wrong. the issue is that I'm trying to graph more than one curve on a grap which is very easy to do in Mathcad but not obviously so with Maple. My teacher told me to setup variables for each function and then use the display property to show the graphs and this works most of the time but then sometimes it does nothing at all but print the functions verbally. here is an example: restart; with(plots): g1 := implicitplot( 4-(x-2)^2): g2 := implicitplot( x/2 ):

## Reverse CDF...

The CDF function permits you to get a probability, given a random variable x. But how do I get the random variable x, given the probability? I have tried using the solver to do this: df := 29: chiSquare := RandomVariable(ChiSquare(df)): solve(CDF(chiSquare, x) = .95, x) But this code only returns the following warning: "Warning, solutions may have been lost" But even if the code did work, using a numerical solver for this kind of thing sucks. Surely Maple has a routine that does a revesre lookup? Can someone please give me some pointers on this? Jim Cicon

## displaying 2-D & 3-D plots together...

Hello, Does anybody know if there's any way to display a 2-D plot & a 3-D plot on the same axes? I tried using display and I got the message: Error, (in plots:-display) cannot display 2-D and 3-D plots together Regards, Drew

## 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

## Tickmarks in multiples of Pi

by: Maple
Question: How do I generate tickmarks in multiples of Pi? The answer has been posted before but this question comes up often enough that it is worth repeating. In Maple 10 and earlier versions, you had to build a custom list of tickmarks, and the only way you could get the Greek pi symbol was to use the Symbol font. In Maple 11, you can use the new 'spacing' structure with the 'tickmarks' option. To get tickmarks in multiples of Pi, use: > plot(sin(x), x=0..8*Pi, tickmarks=[spacing(Pi), default]); To get tickmarks spaced by 2*Pi, replace spacing(Pi) with spacing(2*Pi). To get the tickmarks occuring on the odd multiples of Pi, use spacing(2*Pi, Pi). The second argument is a fixed value from which the other tickmarks are determined.