nbenj582's profile - activity

So from the documentation I found here: https://doc.sagemath.org/html/en/refe...

It looks like you can change the invariant form, but I tried this and Sage just yells at me saying that 'invariant_form" is an unexpected keyword argument, even if I copy and paste the exact code used there.

So I would love to utilize the unitary group feature in Sage; however, it does not seem like Sage defines this group in the standard way that I have seen, namely $n\times n$ matrices over the finite field $\mathbb F_{q^2}$ such that $U^* U = I$, where $U^*$ is the transpose of the matrix in which each entry of $U$ is raised to the $q$ power.

For some weird reason it appears as though sage uses the antitranspose instead of the traditional transpose operation to define unitary matrices, since the following matrix, for example, is included:

\begin{bmatrix} 0 & 1\\ 1 & 1 \end{bmatrix}

Does anyone know why this is and how I can easily rectify my computations so these matrices still preserve the Hermitian form $\langle x,x \rangle = x^*x$?

Here is my code:

def lam(n):
    m = 1
    while (n+1 - m >= 0):
        m = 2*m
    return m/2

def inter(n,l):
    return [(n+1-l)/l, (n+2 - l)/l]

def f(a,b,x):
    if x>=a and x<=b:
        return 1
    else:
        return 0

for n in range(1,15):
    I = inter(n,lam(n))
    lst = []
    for i in range(101):
        lst.append([i/100, f(I[0],I[1],i/100)])
    scatter_plot(lst,markersize=20,aspect_ratio=0.1)

I know that the plots are printing correctly, they are just out of order for some reason. Any ideas?

Also, I know this is a terrible way to plot this. I wanted to use:

plot(f(I[0],I[1],x),(x,0,1))

but that doesn't seem to be working (it just gives me the zero function), so if you have any suggestions for that as well, that would be great. Thank you.