plummie

At the moment I'm trying to find the smallest difference between two things (of form E[i] i goes from 1 to n)  and input them in a list. To do this I need to use nested loops but I'm not sure of the best kind/way to do this. I have been experimenting with for and if loops so far

for instance, this is my most recent effort.
 

for i from 2 to n do;

a := abs(E[i]-E[1]);

for j from 2 to n do;

if i <> j then ;

b := abs(E[i]-E[j]);

end if;

if b < a then a := b end if;

end do;

I have been trying to do this for some while now but am not having much luck.

Basically what I need is a hermitian matrix, with real values on the diagonals X~N(0,1) and complex values on the off diagonals X~N(0,1/2)+i*N(0,1/2)

Obviously as its hermitian I need Xij = Xji*
 

I have tried a few things but can't get anything to work correctly, in my latest attempt I decided to try and construct the 2x2 case from scratch using if and for loops;

for i to n do

for j to n do

if i <> j then

I need to write a loop within a loop for something like this;

for i from 1 to n for j from i to n do;
A[i,j]:= rand();
A[j,i]:= A[i,j]

end do; end do;

(just random sample code, not what I need to do)

But I don't want the loop to carry this out for when i=j ie. A[i,i] for i = 1 to n. How can I do this?

I want to generate values which have a N(0,1) distribution (and also some which have a N(0,1/2)+I*N(0,1/2))

I have found the RandomVariable(Normal(0,1)) command but this just tells me things like _R44 and I need the numerical value.

Please can you help? (with both distribution cases)

I have only found rand() which gives me integer values and I need to generate (a lot of)  random rational numbers.

The boundary (0,2) doesn't really matter but I do need the numbers to at least go up to 2. Else any rational will do.

Thankyou.

For instance at the moment I need to write a for loop, with an 'if element' (I assume this can be done with maple)

if the elements satisfy it then I want to add the answer into an array X:=[a1,a2,a3.....] without changing or having to rewrite the data already in X.

Is there any way to do this, or would I have to write the array myself and put all of the elements in at one time?

Currently I have 500 values, I put them in an array x:= [a,b,c,d,.....] then using with(Statistics) plotted my histogram with Histogram(x) but this doesn't give me a very accurate histogram and there are only 10 or so bars. How can I make this better?

I have found eigenvalues of a  2x2 matrix A, these are displayed in a vector. eg.

a + sqrt(b)

a - sqrt(b)

Is there any way I can write code which will find the difference between them? At the moment I'm doing it manually and it is taking a lot of time as I have many matrices.

When i input something like sqrt(30) I just get back 30 with a square root symbol over it. How can I make maple evaluate it?

How do I generate a gaussian random matrix (2x2).

Is this the default setting already in maple or is there code I need to use?