Python: Why does my 'less than' test fail? [closed]

Question

I have the following program:

def eigen(a, b, c, d, e, f):
    epsilon = 1E-9
    a = abs(float(a*e+b*f)/float(c*e+d*f) - float(e)/float(f))
    print a, epsilon
    print a < epsilon
    print abs((a*e+b*f)/float(c*e+d*f) - e/float(f)) < epsilon

Prints:

0.0 1e-09
True
False

when the values of a,b,c,...,f = 3, 1, 1, 3, 4, -4

I expected the last two lines to both print True as I thought they were equivelent statements. Will you kindly explain to me what is going on?

Thank you for your time.

Kind regards,

Marius

Answer 1

The problem is that

a = abs(float(a*e+b*f)/float(c*e+d*f) - float(e)/float(f))

assigns a different value to a, which messes up the calculation that follows:

print abs((a*e+b*f)/float(c*e+d*f) - e/float(f)) < epsilon
#          ^ This is no longer the original a