## 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.

## randpoly problem...

Hi all I am attempting to use the randpoly feature to generate a random polynomial of 1st degree with non-zero coeffs between -2 and 2.

I have tried the following:

factor1 := randpoly(x, dense, degree = 1, coeffs = rand(-2 .. 2))

unfortunately as you will find quite often this produces the polynomial "0".  Which it is very clear this is not wanted.

Any ideas would be appreciated.

Thanks,

Mark

## help with random numbers in sequence...

I am trying to construct a random set of angles measured in degrees with pairs that are the equivalent in radians.  for example [0,0],[90,Pi/2],[-30,-Pi/6],etc...  but completely random.

so far I have the following:

restart;
randomize();
a := rand(-90 .. 90);
seq([a(i), convert(a(i)*degrees, radians)], i = 1 .. 4);

the trouble is it appars it is randomizing a both times it is called in the sequence.  I would like to have it randomize for each iteration in the sequence.

## strange old rand() behavior in Maple...

http://www.maplesoft.com/applications/view.aspx?SID=1526&view=html

near the middle, it says

I just tried in Maple 2016 and that is not what it did. It says this was in Maple 8. It seems this was "fixed" in Maple 2015.

My question: How could Maple 8 have simplified rand()/rand() to 1 before evaluating rand()?  i.e. why was not rand() evaluated first, before the simplification was made? it seems to have worked as if one typed x/x , but rand() would have been a function, and it should be evaluated before?

Just wondering why Maple 8 did the above, that is all.

## 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

## Computing velocity and position with a random vari...

If a particle that moves in only one dimension is subject to a force Fi between the time

steps ti and ti+1, the velocity vi and position xi of the particle is:

v[i] := v[i − 1] +(1/m)*F[i]*Δt

x[i] := x[i − 1] + 0.5 (v[i − 1] + v[i])

Use the mean of v between ti and ti+1 when updating xi, since the value may change

a lot from step to step. In the subsequent, we set the mass m = 1 and the time steps

are Δt = 1, since we could absorb m and Δt in the expression for the force Fi anyway.

Write a procedure that computes xi and vi for a particle subject to random forces Fi,

uniformly distributed on the interval [-0.5..0.5].

I`ve written a procedure that generates random forces (F[i]) in the given interval. How can I write a for – procedure that computes xi and vi ?

## How do I generate random number between -x and +x?...

Hi

I need help to write a procedure that uses Maple`s built-in rand() - function to generate uniform random floating point numbers between -r and r, where r is an input parameter of the procedure.

>M:=600;

>R1:=rand(0..1):   R2:=() -> 2*R1()-1:
>for i from 1 to M do
f[i]:=R2()*rand()/10.^12:
end do:

With this procedure I get random floating point numbers (+/-), but I can`t figure out how to generate numbers between +/- a parameter (in this case r).

If anyone could help me understand how to get this to work I would be very gratefull.

## Random walk problem...

I have made an algorithm for producing random walks (only possible to walk one step to either direction except downwards(EDIT: It is possible to go downwards, but it has to be when making a turn to the right or left). The walks are determined by the rand function:

R3:=rand(1..3): (1: go straight on; 2: turn right; 3: turn left)
M:=15; N:=1500;

Randwalk3:=proc(R3)
local i,j,r,X,Y,L;
for j from 1 to M do
X[0,j]:=0;                                # Initialization
Y[0,j]:=0;
X[1,j]:=1;                                # The first step should still be taken to the point (1,0)
Y[1,j]:=0;
for i from 2 to N do
r:=R3();
if r=1 then X[i,j]:=2*X[i-1,j]-X[i-2,j]; Y[i,j]:=2*Y[i-1,j]-Y[i-2,j];                   # go straight on
elif r=2 then X[i,j]:=X[i-1,j]+Y[i-1,j]-Y[i-2,j]; Y[i,j]:=Y[i-1,j]-X[i-1,j]+X[i-2,j];    # turn right
else X[i,j]:=X[i-1,j]-Y[i-1,j]+Y[i-2,j]; Y[i,j]:=Y[i-1,j]+X[i-1,j]-X[i-2,j];             # turn left
end if;
if (X[i,j]=X[j,j] and Y[i,j]=Y[j,j]) then L[j]:=i; break; end if; (This is wrong)
end do;
end do:
return [X,Y,L];
end proc:

The question from is like this:
Modify the algorithm such that it stops at r[i] if r[i] = r[j] for any 0 <= j <= i-2. r=(xi,yi). M is the number of random walks and N is the number of steps. The length of the paths should be stored in L[m] (m=1..M). How do I implement the if-test correctly?

## Sampling from multivariate probability distributio...

Hi All,

I have a fucntion f(x,y,z) = exp(-x^2 -y^2 - z^4) and would like to plot the probabity density in real space. One method would be to randomly sample points in a grid based on f(x,y,z). The function f(x,y,z) is clearly peaked around x=y=z=0, so you would expect many points to lie around there. So the plot would look like a clump near (0,0,0) which gets less dense away from (0,0,0).

In the worksheet below, I sampled points from the Uniform distribution to file in the 3d-plot. I would like these points to be sampled from f instead, but am not sure how to do this.

Any help is appreciated,

 > restart;
 > with(Statistics):
 > R := 10; # x-axis size N := 100; # Number f points to sample
 (1)
 > # Unnormalized Probability distrubution f := (x,y,z) -> exp(-x^2 -y^2 - z^2);
 (2)
 > # Clearly f is peaked at (0,0,0) and decays. Therefore I want a plot a lot of points near (0,0,0), and fewer points away from (0,0,0) plot3d(f(x,y,0), x = -1..1, y = -1..1);
 > X := Sample(Uniform(-R, R), N):
 > Y := Sample(Uniform(-R, R), N): Z := Sample(Uniform(-R, R), N): XYZ := Matrix([[X], [Y], [Z]])^%T;
 (3)
 > ScatterPlot3D(XYZ, color = blue, symbolsize = 20);
 >
 >
 >
 >

## Random initial function for pdsolve...

Hi everybody,

I would like to define a function with random values to be used in pdsolve (numeric) as a initial condition.

Any help?

Thanks,

Javier

## List of random colors...

Dear Community,

How could I specify a list of random colors using some kind of an RGB function, which then could be used in another command for coloring? I think of something like this:

myColors := [ seq( RGB ( [rint(0,255) , rint(0,255) , rint(0,255)] ) , j = 1 .. 20 ) ] :

which does not work of course :-)  This should produce me a list of 20 random colors.  What would be the right RGB color function?

Tx for the kind help in advance

best regards

Andras

## Generation of a random array...

To gererate a random initail cofigration -1 or 1

spin = (-1).^(round(rand(N)));

for i=1:1000,

neighbours = circshift(spin, [ 0 1]) + ...

circshift(spin, [ 0 -1]) + ...

circshift(spin, [ 1 0]) + ...

circshift(spin, [-1 0]);

how to do this in maple?

## Is Ising a package?...

Hi all

Is Ising a package?

for i = 1:12000

%while (1),

% Choose a random value between 0 and 1 for the interaction strength

J = rand()+1e-10;

% Perform a simulation

[M, N, E] = ising2(n_grid, J);

% Records the results

Ms = [Ms M/(n_grid^2)];

Es = [Es E/(n_grid^2)];

Ns = [Ns N];

Js = [Js J];

i = i+1;

## 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.