## Working with 3D Plots (Product Balls)...

A colleague recently approached me with this problem: Given two sets S1 and S2 in R^3, define the "product ball" of S1 and S2 to be the set of all points in R^3 obtained as the componentwise product of a point in S1 and a point in S2. That is, PB(S1,S2) = { (a*x,b*y,c*z) : (a,b,c) in S1 and (x,y,z) in S2 }. Can Maple help me to visualize this set? For a concrete example, let S1 = { (x,y,z) : max( abs(z), abs(x)+abs(y) ) = 1 } and S2 = { (x,y,z) : max( abs(y), abs(x)+abs(z) ) = 1 } In this case it can be shown that PB(S1,S2) consists of the following eight parametric surfaces: (x,y,z) = ( s*t, 1-s, 1-t), s=0..1, t=0..1

## Obtaining all roots I.A.W. De Moivre's theorem...

Is there a command for obtaining "ALL" n roots of the nth root of a real or complex number in accordance with DeMoivre's theorem? For example there are three cube roots of unity, namely 1,-1/2+sqrt(3)/2*i, and -1/2-sqrt(3)/2*i

## separate subexpressions according to its variables...

Hello, suppose I have an expression that consists of a multiplication of subexpressions involving only one variable, for example a_m(z) = a(m) * f(z) How can I retrieve a(m) and f(z) resp. separately? That is, I would like to be able to identify only those subexpressions involving that one variable in which I am interested. For instance, how can I retrieve a(m) from a_m(z)? I have tried using select( depends, op(factor(a_m(z))), m ), but is this bullet proof and/or is there a better solution? Thanks in advance, Regards, Franky.

## Tip: Transpose a pair of indices of an Array

Maple
A note added: Although the coding below is correct, it has clearly been superseeded by the following two entries contributed by acer: Entry 1 and Entry 2. As in any fairytale (even though this blog of mine certainly is not) it takes three of something (at least according to the fairytales of my fellow-countryman H. C. Andersen). Todays entry is the third and last (at least for now) in a row of three consecutive ones dealing with manipulations of indices of Arrays. The other two entries are Tip: Index an Array and Tip: Permute the indices of an Array.

## Pls help me check this problem of "Kernel connecti... when i am using CodeGeneration for Matlab in this file, the Maple gives out this error of "Kernel connection has been lost". But when I tried other cased of CodeGeneration for Matlab, sometimes it is working well.

## Creating a caption that contains 2-D math

by: Maple
In Maple 11, we added the ability to put captions on a plot. To do this, just use the 'caption' option with any plotting command, in the same way you'd use the 'title' option. These options are described in the plot/options help page. One additional change we made in Maple 11 for these two options is to allow the right-hand-side of the option equation to be a list containing the title or caption, followed by a 'font' suboption. So now you can use title=["my title", font=[times, bold, 20]] instead of having to specify the font separately with the 'titlefont' option. You can also display 2-D math in captions, titles and other text elements in a 2-D plot. To do this, simply use the mathematical expression as the option value: e.g. caption=x^2/2. To combine math with plain text, wrap everything in a 'typeset' structure: caption=typeset("my plot of ", x^2/2). If you enter the plotting command in 2-D math, you can use the palettes to build the expression directly in the command.

## Trying to do an MISO...

Hello, I am doing some research with solar panels right now and I need to try and come up with equations for a multiple input single output system. What I am doing is taking numbers from a website and comparing to the actual numbers from solar panels I have set up in a field. But the head of the project is wanting to make some unique equations. I can easily do a single input single output by curve fitting or splining the information, but I have never tried a multiple input single output system. Is there a way to do this? Chris

## using maple to solve equations that have no algrai...

I'm completely new to maple, and I'm trying to solve some equations that have no algebraic solution but should be straightforward to solve with numerical methods. I'd be most grateful if anyone could offer some advice on how to do this. For example, I'd like to solve the following two equations for p: 2^(1-p)+(1-x)^(1-p)/(1-p) and x^(2-p)-y^(2-p))/(x-y) = (a^(2-p)-b^(2-p))/(a-b) The attached worksheet contains my unsuccessful attempts. View 4985_equations.mw on MapleNet

## Tip: Permute the indices of an Array

Maple
A note added: Although the coding below is correct, it has clearly been superseeded by the following two entries contributed by acer: Entry 1 and Entry 2 in the blog entry Tip: Transpose a pair of indices of an Array. Yesterday I wrote about a method to index an Array, using a procedure of the type `index/method`. Below, using the same sort of procedure, a method for permuting the indices of an Array is given (please feel free to suggest improvements; probably, the else-statement may be written more concisely):

## Solving Sparse Linear Systems in Maple

by: Maple

What is the largest linear system that Maple can solve? You might be surprised to find out. In this article we present strategies for solving sparse linear systems over the rationals. An example implementation is provided, but first we present a bit of background. Sparse linear systems arise naturally from problems in mathematics, science, and engineering. Typically many quantities are related, but because of an underlying structure only a small subset of the elements appear in most equations. Consider networks, finite element models, structural analysis problems, and linear programming problems.

## Tip: Index an Array

Maple
Sometimes it can be very useful to know the indices of entries (of an Array) which obey some conditions. The following procedure (which works for any Array) makes this possible:
````index/makeIndex` := proc(indices::list,array::Array,value::list)
# Retrieving from the Array
if nargs = 2 then return array[op(indices)]: end if:
# Storing in the Array
if nargs = 3 then array[op(indices)] := indices = op(value): end if:
end proc:
```
An example: For Array A find the set S of indices of entries being positive integers, using as an intermediate step the Array B with entries of the form "indices = value":

## How do I draw a cylinder with a curved top...

Hello I hope someone can help me with this. How do I draw a cylinder with a curved top? That is a cylinder whose height varies with radial angle The following doesn't work. plot3d(3,angle=0..2*Pi,height=0..cos(angle)+2, coords=cylindrical,axes=boxed); Thank you for any hints or tips Tyrian

## Accessing the values from the solve command

by: Maple
I am just getting started with Maple TA for Calc III. I am trying to solve LaGrange multipliers. When the solve command returns multiple sets of answers, how do I extract the specific values for the subs command? \$f=xyz; \$q=x^2+2y^2+3z^2-6; \$g=maple("f+mu*\$q"); \$exp1=maple("diff(\$g,x)"); \$exp2=maple("diff(\$g,y)"); \$exp3=maple("solve({\$q,\$exp1,\$exp2},[x,y,mu])"); \$ans1=maple("subs({x = ????,),y =???? )},\$f)"); \$ans2=maple("subs({x = ????,y = ????},\$f)"); The question marks are where I am lost.