@Carl Love 

Your composition operator  worked the way I wanted

Thank you very much

@Carl Love 

I need a procedure to calculate composition h = f "x" g of two permutations f and g of the same set A.

For example

I have two permutation as follow:

> f := LehmerInv(18606, 8);
                    [3, 5, 7, 0, 2, 1, 4, 6]

>g := LehmerInv(12294, 8);
                    [2, 4, 0, 5, 3, 1, 6, 7]

I need to calculate composition h = f "x" g (the result will be h=[5, 1, 7, 2, 0, 4, 3, 6]).

So

Input of procedure: f, g

Output: h = f "x" g

@Carl Love 

Thank you very much

@Carl Love 

Thank you very much

Your program worked the way I wanted. But with n=8 it is slow and there are many elements of equal value.

"x" operator in here is the composition h = f "x" g of two permutations f and g of the same set A, is the permutation mapping each y in A into h(y)=f (g(y)).

@Carl Love

Please help me to compute this expression based on Lehmer (I) and LehmerInv  (I^-1)

Let floor(y) denote a function which map a real number y to the largest integer less than
or equal to y; and let c= 4, x₀=5

a:= sin( (pi/2)*( (xi/(n!-1) ) + (c+1)/(n!+1) ) )*(n!-1))

x_i+1 = I( I^-1(x_i) "x" I^-1(floor(a)) ) for all i = 0... n!-1 where operation "x" is the combination of 2 permutations

Thank you very much

@Carl Love 

The procedure was running correctly

Thank you very much

@Carl Love 

There is error with LehmerInv on Maple15

> LehmerInv(2, 4);

Error, (in LehmerInv) invalid input: range expected for first argument of this form of seq, but received Array(0..3, {(1) = 0, (2) = 2, (3) = 1})

Thanks alot

@Carl Love 

How to call proc LehmerInv ???

@Carl Love 

Your procedures are very good

Thank you very much

@Carl Love 

I'm using Maple15

This is error:

> Lehmer([0, 2, 1, 3]);
Error, (in Lehmer) `Iterator` does not evaluate to a module
 

@Carl Love 

Thank you very much.

How to use your procedures?

I tried with Lehmer([0,2,1,3]), but no results! 

@Carl Love 

It is coding theory and effective implementation of linear transformations. K-th root (R) of matrix M can be a lightweight matrix (R^k = M). Meanwhile matrix M can be calculated through lightweight matrix R 

@Carl Love 

Program can successfully work in the general case?. It's mean that Degree of the characteristic polynomial is m (m = 2, 3, 4, ...), so the splitting field has degree 16, 24, 32, ...

Thank you very much

@Christian Wolinski  and @Carl Love 

How to combine GB with program Matrix_powers_finite_field.mw (this program at url http://www.mapleprimes.com/view.aspx?sf=215285_Answer/Matrix_powers_finite_field.mw)

Please help me!

Thank you very much

@Carl Love 

In this case, "don't run" mean that it doesn't stop running!

I think that because extension finite field is too large (degree of q is 3)!

How to solve this problem? Please help me! 

Thank you very much.