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