How can this assert() ever trigger?

[Peter Otten]

Albert van der Horst wrote:

> I have the following code for calculating the determinant of
> a matrix. It works inasfar that it gives the same result as an
> octave program on a same matrix.
> 
> / ----------------------------------------------------------------
> 
> def determinant( mat ):
>     ''' Return the determinant of the n by n matrix mat
>         i row j column
>         Destroys mat ! '''
>     #print "getting determinat of", mat
>     n=len(mat)
>     nom = 1.
>     if n == 1: return mat[0][0]
>     lastr = mat.pop()
>     jx=-1
>     for j in xrange(n):
>        if lastr[j]:
>            jx=j
>            break
>     if jx==-1: return 0.
>     result = lastr[jx]
>     assert(result<>0.)
>     # Make column jx zero by subtracting a multiple of the last row.
>     for i in xrange(n-1):
>         pivot = mat[i][jx]
>         if 0. == pivot: continue
>         assert(result<>0.)
>         nom *= result   # Compenstate for multiplying a row.
>         for j in xrange(n):
>             mat[i][j] *= result
>         for j in xrange(n):
>             mat[i][j] -= pivot*lastr[j]
>     # Remove colunm jx
>     for i in xrange(n-1):
>        x= mat[i].pop(jx)
>        assert( x==0 )
> 
>     if (n-1+jx)%2<>0: result = -result
>     det = determinant( mat )
>     assert(nom<>0.)
>     return result*det/nom
> 
> /-----------------------------------------
> 
> Now on some matrices the assert triggers, meaning that nom is zero.
> How can that ever happen? mon start out as 1. and gets multiplied
> with a number that is asserted to be not zero.
> 
> Any hints appreciated.

Floating point precision is limited:

>>> x = 1.0
>>> for i in itertools.count():
...     x *= .1
...     assert x
... 
Traceback (most recent call last):
  File "<stdin>", line 3, in <module>
AssertionError
>>> i
323