## How to create random matrices with constraints?...

Hello Maple insiders, I'm still learning to get along with Maple (version 10.01). Currently, I would like to have a small procedure which creates a random matrix of arbitrary dimension with complex floats. However, the generated matix, say A, has to fulfill the following conditions (because it should be a valid physical density operator): 1.) A is hermitian 2.) A is positive semidefinite, together with 1.) this should mean that A has only real and nonnegative eigenvalues 3.) A should have trace equal 1 With the randomly generated matrices I would like to cover (reasonably uniformly) the set of all possible matrices with the above constraints.

## 3D polar contour surfaces with colour superimposit...

Hi, I would like to be able to plot a 3d surface of one variable, with another variable in colour on that surface. This plot should have a legend for the colour variable. At a stretch, I would also like to have all of this in polar co-ordinates, with polar axes and without having to write a transform myself. Is all this possible! cheers

## Global Optimization toolbox...

Hi, I am using the global optimization toolbox to minimize a matlab function as follows: restart; > (Matlab:-evalM)("cd 'C:/Documents and Settings/user/Maple'"); > mat2map1 := proc(a, b) local Res,res; Matlab:-setvar(\"a\",a); Matlab:-setvar(\"b\",b); Matlab:-evalM(\"result = mat2map1(a,b)\"); Res:=Matlab:-getvar(\"result\"); res:=convert(Res,float); return res; end proc; > with(GlobalOptimization): > infolevel[GlobalOptimization] := 3: > GlobalSolve(mat2map1, a = 0 .. 5, b = 0 .. 5); When I run this I get the following error message:

## Converting entire Maple worksheet into Fortran Cod...

Hi! I am trying to convert an entire Maple worksheet into Fortran code. At the moment, I have managed to convert a specific program using with(codegen): f:=proc(x) function end proc fortran(f) But this method can only convert one function at a time. Can someone please help me to convert an entire worksheet into Fortran or other languages? I have text and math in my worksheet, and I'm using 2D math in Maple 10. Thanks :)

Is there a way to track a thread without responding to it?

## How to get the index of some elements?...

I have two small questions: 1. Given a list L: L:=[false, false, true, true, FAIL,false]; and I want to get the positions of "FAIL" (in this case 5) and false (1,2,6). HOW could I get that? 2. Now, given another list Z with the same number of elements: Z:=[z1,z2,z3,z4,z5,z6]; I would like to replace the values of FAIL by 0 (zero). (in the way that Z became: Z:=[z1,z2,z3,z4,0,z6];) It is possible to do that without using "for do" commands? Thanks in advance, JJacques

## Prime Numbers...

Does anyone know if it's possible to discover the largest known prime number just using Maple 10 on a stand alone machine (PC)? Or does Maple 10 and or all of it's current additions / upgrades lack the computing power required to attempt this possible recreational task ? v/r, Dan

## 2 small questions.....

Hi dear Maple's gurus. I have the lists a and b: a:=[A, B, C] b:= [[K1,L1][K2,L2][K3,L3]] I want to add the each term of "a" in the intervals given in "b": sum(A from L1 to K1)+ ..+sum(C from L3 to K3). I tried with this procedure: > sums:= proc(a,b) local j,tot; tot:=0; for j from 1 to nops(a) do tot:=tot+sum(a[j], k=b[j,2]..b[j,1]); end do: end proc: >sums([a1,a2,a3],[[ku1,kl1],[ku2,kl2],[ku3,kl3]]); 1. Is there some more efficient way to do the same? 2. I would like also that the sums on a[j] under the following 2 join conditions: 2.1. assuming that a[j] is real and positive, and

## Numerator/ denominator......

Hi there! Assuming that I have the following fraction: fr1:= (x+1)/(x-1); I have the following 2 questions: 1. with which command could I take only the numerator "(x+1)"? (and for the denominator?) 2. Is it normal that whattype(fr1); returns a star * Thanks in advance for your answers, Jean Jacques

## Maplet - Slider - Negative Values?...

Simple question: I can't seem to use a negative number as a minimum value for a slider control (in Maplet Builder)... Is this not possible? Thanks! Bryan

## Symbolic characters in plot titles?...

Hello, I am relatively new to Maple and using version 9.5. Does anyone out there know of a way for symbolic characters such as Pi to appear in a plot title? This is the input I am working with. f:=x->piecewise(x < Pi/3,4*sin(x),Pi/3 <= x,x^3-x+1); plot (f(x),x=-Pi..Pi,discont=true,title="f(x) [-Pi, Pi]",titlefont=[TIMES,BOLD,16]); Any help would be greatly appreciated. Thanks

## how to use the solution of ODE system for explicit...

i got the solution of a ODE system (dsn), the results are time dependent variable theta[i](t),and its deriavtives diff(theta[i](t),t). and i have one set of expressions, which are explicit form of theta[i](t),and diff(theta[i](t),t), such as ss[1]:=fx[1]=sin(theta[1](t))*3+cos(theta[1](t))*diff(theta[2](t),t). I want to put the solution i got into the explicit expression of fx[i], and then polt them, how can I do it? i use eval(ss[1],dsn)but it does not work. here is the code: > restart: interface(warnlevel=0): with(SolveTools):with( plots ): with( plottools ): with( DEtools ): with( PDEtools ): g:=9.81: x[0][2]:=0: y[0][2]:=0: #initialization function of each beam,in this function, we should give 3 variables, n=the number of this #beam, la=the length of this beam, ma=the mass of this beam beams:=proc(n,la,ma) global l,m,x,y: l[n]:=la: #length of beam n m[n]:=ma: #mass of beam n #initialize the positions of each beam x[n][2]:=0: #the x position of the end point of each beam y[n][2]:=0: #the x position of the end point of each beam x[n][1]:=0: #the y position of the center point of each beam y[n][1]:=0: #the y position of the center point of each beam end proc; #define the forces that applied on the end of beam n Force:=proc(n,fm,fn) global fx,fy: fx[n]:=fm: fy[n]:=fn: end proc: