Cycle decomposition in Python

Is there an algorithmically better way of doing this?

import numpy as np
l=np.random.permutation(10)
p=list(range(10))
print(l,p)
i=0
k=0
prod=1
z=0
def gcd(a, b):

    while b:      
        a, b = b, a % b
    return a
def lcm(a, b):

    return a * b // gcd(a, b)

while z<10:
    """count how many times we have crossed (-1-ed) a number from p"""
    k=0
    while p[k]==-1 and k<9 :
        """find the first non -1 element in p (it's here that I feel that the code is especially clumsy) """

        k=k+1  
    i=k
    """k is the first element in the cycle """
    print(l[i])
    p[k]=-1
    z=z+1
    j=1
    while l[i]!=k:
        """go from i to l[i] until we get back to k, closing the cycle """
        p[l[i]]=-1
        z=z+1
        i=l[i]
        j+=1
        """g is just used to find the lcm """

        print(l[i])
    prod=lcm(prod,j)
    print('------')   
print(prod)

Use the built in gcd

In Python 3, you can just do:

from math import gcd

Consider keeping with the standard library

Instead of using np.random.permutation, consider just using random.shuffle to generate a random permutation. Removes the numpy dependency altogether.

Just use # instead of """

Comments such as:

"""count how many times we have crossed (-1-ed) a number from p"""

Are usually used for docstrings, you are using them to elaborate on certain steps in an algorithm, I would use # for this.

Place the cycle decomposition into a function

The while loop introduces a lot of global variables and makes it hard to use, I would put the contents into a function. Also explain that this function displays a permutation as disjoint cycles.

Please use better names.

I'm still not sure what every variable does. Like why is p=list(range(10))? I would think p is short for permutation, but l seems to be what the actual permutation is. This program is really hard to understand simply because of your name choice.

StackExchange Code Review Q#161704, answer score: 7