NetNews Usenet Archive 1992 #19/NN_1992_19.iso/spool/comp/theory/1827

Internet Message Format | 1992-08-26 | 1011 b

Path: sparky!uunet!cs.utexas.edu!sun-barr!ames!agate!ucbvax!MATH.ORST.EDU!pmontgom
From: [e-mail] (Peter Montgomery)
Newsgroups: comp.theory
Subject: Warning - Maple V lattice returns non-reduced basis
Message-ID: <[e-mail]>
Date: 26 Aug 92 15:45:42 GMT
Sender: [e-mail]
Reply-To: Peter Montgomery <[e-mail]>
Lines: 21

#       The lattice basis {v1, v2} where

#           v1 = [ 5,  7]      squared norm 74
#           v2 = [-3,  7]      squared norm 58

#       is not row-reduced, because
#       v1 - v2 = [8, 0] has squared norm 64 < 74.
#       However,  Maple V's lattice function
#       returns a basis with the two input vectors.

#       The problem seems to occur sometimes when

#       dot(v1, v1) > 2 |dot(v1, v2)| > dot(v2, v2)

readlib(lattice);
v1 := [ 5, 7];
v2 := [-3, 7];

outvecs1 := lattice(v1, v2);    # Fails to return reduced basis
outvecs2 := lattice(v2, v1);    # OK if smaller vector is input first
quit;