RE: Real vs. Integer paradox
- To: mathgroup at yoda.physics.unc.edu
- Subject: RE: Real vs. Integer paradox
- From: fulling at sarastro.math.tamu.edu (Stephen A. Fulling)
- Date: Fri, 5 Mar 93 17:15:33 CST
>In computing the NullSpace of a matrix with Mathematica, there seems
>to be a significantly different algorithm used depending on whether
>the matirx has real or symbolic (e.g. integer) entries. Here's an
>example: [condensed]
>In[3]:= NullSpace[A]
5 3
>Out[3]= {{-4, 1, 0, 1}, {-, -(-), 1, 0}}
2 2
>In[6]:= NullSpace[Ar]
>Out[6]= {{-0.943569, 0.211961, 0.0273498, 0.252986},
> {0., -0.59588, 0.681005, 0.425628}}
>why are they so different?
>Any help or explanation would be appreciated.
The answers are consistent: Both sets are bases for the same
two-dimensional space. Standard row reduction (quite pleasant to do
interactively within Mathematica) reduces both to the same set, within
roundoff error:
{1., 0, -0.285714, -0.428571}, {0, 1., -1.14286, -0.714286}
{1., 0., -0.285714, -0.428571}, {0., 1., -1.14286, -0.714285}
Presumably WRI chose the integer algorithm for algebraic simplicity
(speed) and the numerical algorithm to minimize roundoff error. It's
not surprising that these give different results to a question whose
answer is not unique.
S. A. Fulling