How often a random real matrix has complex eigenvalues

dist.py

from random import uniform

def myvariate():
    return uniform(-2,2)

for i in range(1000000):
    a = myvariate()
    b = myvariate()
    c = myvariate()
    d = myvariate()
    print a**2 + 2*a*d + d**2 - 4*a*d - 4*b*c

makefile

all : dist.py
	python dist.py > variates.txt

plot.R

library(ggplot2)
library(e1071)

X = read.csv("../Desktop/variates.txt")
qplot(X[,1])
ggplot(X, aes(X[,1])) + geom_density()

moment(X[,1], order=1)
moment(X[,1], order=2, center=TRUE)
moment(X[,1], order=3, center=TRUE)
moment(X[,1], order=4, center=TRUE)