reset() RealNumber0 = RealNumber; RealNumber = lambda x : QQ(RealNumber0(x))
.3
3/10
.3333
3333/10000
n = matrix([ [-0.3, 0.2, 0.1],[0.2, -0.4, 0.4], [0.1, 0.2, -0.5] ])
n
[-3/10 1/5 1/10]
[ 1/5 -2/5 2/5]
[ 1/10 1/5 -1/2]
n.rank()
2
Their rational form is deceptive. In Octave: octave:1> format rat; octave:2> a = [-86/17,40/29,-68/43,-20/11;-24/17,-1/38,-2/25,49/17] a = -86/17 40/29 -68/43 -20/11 -24/17 -1/38 -2/25 49/17 octave:3> rref(a) ans = 1 0 155/2122 -725/384 0 1 -152/173 -6553/795 In Matlab: >> format rat; >> a = [-86/17,40/29,-68/43,-20/11;-24/17,-1/38,-2/25,49/17] a = -86/17 40/29 -68/43 -20/11 -24/17 -1/38 -2/25 49/17 >> rref(a) ans = 1 0 13/178 -725/384 0 1 -152/173 -1426/173 sage: F = matrix(2,[-86/17, 40/29, -68/43, -20/11, -24/17, -1/38, -2/25, 49/17]) sage: F.rref() [ 1 0 306034/4189705 -404710/214357] [ 0 1 -18405604/20948525 -30037214/3644069]