## How to obtain random decimal numbers...

Is there a simple command to generate decimal numbers in a given range?

For example, I wish to obtain a randomly generated number between, say ... -0.5 and 0.5.

## Command "Generate" produces the same objects each ...

I need to create randomly several {1,2,3}-sequences of length 15. I execute:

> with(RandomTools):

> w:=Generate(list(posint(range = 3), 15)):

The problem is that when I close the program and then open and run it again, it always produces the same sequences.

What should I do in order to make it work really randomly? That is, to start at a "random" sequence as well?

Thanks!

## Generate random NEGATIVE numbers...

How do I genereate random negative numbers?

when i put a minus sign in the rand-function i get an error.

I need to for example generate a random number between -r and r, where r is the input

## Generate suitable random integer ...

Coding in key generation of RSA Cryptosystem

message :=123456;

u := nextprime(RandomTools[Generate](integer(range = 10^100 .. 10^(110-1))));

v := nextprime(RandomTools[Generate](integer(range = 10^100 .. 10^(110-1))));

N := u*v;

phi := (u-1)*(v-1);

In RSA cryptosystem, the encryption or decryption of message only can be existed between range 1<=message<=N. This means that if the value of message bigger than N value then we can't get back the original value when performing decryption.Thus, wanna to ask that how can we create a coding so that the system will recognise the random integer u and v whether lie between range 1<=message<=N, means wanna crete a coding that if  N>=message then it will continue to the phi step whereas if message>=then the system need to regenerate the u and v until it satisfy the condition  1<=message<=N .Thus please help as i am a beginner in Maple.Thanks.

## User interface ...

Hi, all. I need to built a user interface for my program. First, I create two label and two text area for both the value of x and y. After that I assign a button to random generate the value for x and y within the range with x <y. I write the code below into click action of the button.

use DocumentTools in

Do(%x=RandomTools[Generate](integer(range=1..7);

Do(%y=RandomTools[Generate](integer(range=1..7);

while %x>= %y do

Do(%x=RandomTools[Generate](integer(range=1..7);

Do(%y=RandomTools[Generate](integer(range=1..7);

end do;

end use;

This code can generate two random number and insert inside the boxes created. When the button is clicked, two random number generated but the error dialog box shown on the screen with message : Error in component button with caption "generate" cannot determine if this expression is true or false: %y=%x. What I want is only the true value of x<y will be inserted to the text boxes.

Any suggestion? Any help will be highly appreciated. Thank you.

## How to generate random integers x < y?...

How to random generate 2 integer number with condition x must be less than y ?

I had tried the coding below. But the output shown not what i want.

x:=RandomTools[Generate](integer(range=1..7);

y:=RandomTools[Generate](integer(range=1..7);

if x>= y then x:=RandomTools[Generate](integer(range=1..7); y:=RandomTools[Generate](integer(range=1..7); end if;

Example:

I get x:= 5 , y:=1, then i need to regenerate the value of x and y using the last statemet above. but the problem is sometime i might still get the value of x>= y for example on second generate x:3, y=2. I need a code that x and y must be regerate until it get x<y. Can someone help ? Thank you in advance.

## How to find such a matrix? ...

hello everybody!

I want to create a random symmetric matrix which have det=2. I just made it like this, no better than those ones. Thanks!

Doixung := proc (n)

local A, i, j; A := Matrix(n);

n := LinearAlgebra[Dimension](A);

for i to n do A[i, i] := RandomTools[Generate](integer(range = 1 .. 20))

end do;

for i to n do

for j to n do

while j < i do A[i, j] := RandomTools[Generate](integer(range = 1 .. 20)) end do;

while i < j do A[i, j] := A[j, i] end do

end do

end do;

print(A) end proc

## Random numbers

by: Maple

Erik Postma from Maplesoft has recently posted a Maple application going through some of the ways how to produce random numbers in Maple: http://www.maplesoft.com/applications/view.aspx?SID=153662&P=TC-4444

Doing a fair bit of work involving random numbers (i.e. simulations) myself, I was naturally drawn to it. The document is a nice extension of the relevant help pages, making practical use of some of the procs in RandomTools easier and clearer.

One particular issue I recently ran into, however, is not covered. I needed a random generator for a particular custom pdf (not one of the already recognized pdfs) that happens to be 3-dimensional. And I needed to do this >twice<, with the second generation using the result of the first one as a parameter. the problem is not unlike the last example in the help page for Statistics:-Sample.

Here is what I did:

The pdf looks graphically like this (and note that in this plot it is not normalized):

plot3d(Triangle63:-Trianglef(CrystalAngle,DeflectionAngle),\
CrystalAngle=-0.8..0.2,DeflectionAngle=-0.6..0.6,projection=0.7);

The first set of random numbers is generated by setting CrystalAngle to a fixed number (-0.1 in this case), normalizing the pdf to the integral over DeflectionAngle and then generating the random numbers. Note that evaluation of the integral is relatively time-consuming (seconds).

trianglepdf:=(CrystalAngle,DeflectionAngle) ->\
Triangle63:-Trianglef(CrystalAngle,DeflectionAngle)/\
'evalf(Int(Triangle63:-Trianglef(CrystalAngle,Da),Da=-0.6..0.6,method = _d01akc))':
triangle0pdf:=(t) -> trianglepdf(-0.1,t):
Cr1:=Distribution(PDF=triangle0pdf);
Y:=RandomVariable(Cr1);

samples:=Sample(Y,[1..600],method=[envelope,range=-0.6..0.6]);

This looks as it should; and the random number generation is reasonably fast once the initial setup has been done (i.e. the time used scales only relatively weakly with the count of random numbers generated.

The issue now is the second stage, where for each new random number, the number generated above is a new input parameter for CrystalAngle. So I can no longer define the pdf once since the pdf is different for each number generated.

The pedestrian way to do this is like the following:

samples2:=Vector(1..numelems(samples),datatype=float):
CrystalOffset:=0.3;

for ii from 1 to numelems(samples) do
triangleiipdf:=(t) -> (trianglepdf(samples[ii]-~CrystalOffset,t)); # subtract (VR peak -> 0)
Crii:=Distribution(PDF=triangleiipdf);
samples2[ii]:=evalf(Sample(RandomVariable(Crii),1,method=[envelope,range=-0.6..0.6])[1]+CrystalOffset);
end do:

This works, but only sort-of. First, it is very slow, since the whole sertup happens for each number generated (Sample()). Secondly, it tends to hang at a certain number of steps through the loop. The value of ii where it hangs is arbitrary and changes with the other parameters and CrystalOffset. It is however consistent for identical runs.

The last example in help for Statistics:-Sample would indicate that one needs to setup the pdf as a function of t as well as the parameter, call Distribution() only once and then assign the value to the parameter and call Sample() to get the random number(s) drawn from the pdf with the parameter being set to the wanted value. While this works in the example which uses a built-in pdf, I find that I cannot make it work with my pdf. Either the parameter gets ignored (i.e. stuck at the first value) or the thing runs just as slowly as my procedure above.

Ultimately I programmed my own random generator for an arbitrary pdf which, while not as efficient as Maple's built-in generator, does produce the expected set of random numbers for the 2nd path in a reasonable time. It is a simple-minded envelope-rejection method, that works fo reasonably well-behaved pdfs:

Rarbit:=proc(pdf,xmin,xmax,pdfmax)
local dx:=xmax-xmin;
local x1,x2;
x1:=RandomTools[MersenneTwister]:-GenerateFloat64()*dx+xmin; # pick location on x axis
x2:=RandomTools[MersenneTwister]:-GenerateFloat64()*pdfmax; # y axis, probability of returning x1

while (x2>evalf(pdf(x1))) do # if above pdf, reject
x1:=RandomTools[MersenneTwister]:-GenerateFloat64()*dx+xmin; # new x-axis value
x2:=RandomTools[MersenneTwister]:-GenerateFloat64()*pdfmax; # check value
end do; # eventually we'll succeed and return one.

x1;
end proc;

Using this routine I get my second and final set of randome:

for ii from 1 to numelems(samples) do
newpdf:=(DefAng) -> Triangle63:-Trianglef(samples[ii]-CrystalOffset,DefAng);
samples2[ii]:=Random:-Rarbit(newpdf,-0.6,0.6,28);
DocumentTools:-SetProperty(ProgressBar,'value',ii,refresh);
end do:
CrystalOffset := 0.3
Histogram(samples2+~samples,view=[-0.6..0.6,default]);

I would be interested in Erik's comment on this.

Mac Dude

## Looping of lobatto iiiA METHODS...

I try to loop this problem using if statement but i am getting wrong lobatooB.mwaswer,the works looks like this see the attached file

## Percolation theory and cylinder random packing...

Hi,

I'm working at the moment on percolation theory and, in order to get interesting images I use Maple to produce random spheres packing using the code below:

with(RandomTools):
with(plots):

x:=Generate(list(integer(range=0..20),100)): # random coordinate for x parameter
y:=Generate(list(integer(range=0..20),100)): # random coordinate for y parameter
z:=Generate(list(integer(range=0..20),100)): # random coordinate for z parameter
R:=Generate(list(float(range=1..3...

## RandomTools:-Generate Matrices and lists

by: Maple

I have found very little help about the Generate command of the RandomTools package.

I also have minor gripes about the syntax. And what better way to deal with these than to voice them?

This is how I was able to generate random lists and random Matrices.

A list of 10 random integers between 1 and 100:

L := RandomTools:-Generate(list(integer(range=1..100),10));

L := [47, 8, 46, 44, 9, 77, 59, 16, 1, 70]

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