maxColNum -- Returns a submatrix form by a maximal set of linear independent columns by random evaluation.

i1 : M = matrix {{1,2,3},{1,2,3},{4,5,6},{4,5,6}}

o1 = | 1 2 3 |
     | 1 2 3 |
     | 4 5 6 |
     | 4 5 6 |

              4        3
o1 : Matrix ZZ  <--- ZZ

i2 : maxColNum M

o2 = (| 1 2 |, {0, 1})
      | 1 2 |
      | 4 5 |
      | 4 5 |

o2 : Sequence

i3 : R=QQ[a..g]

o3 = R

o3 : PolynomialRing

i4 : M = matrix {{a,a,b},{c,c,d},{e,e,f},{g,g,g}}

o4 = | a a b |
     | c c d |
     | e e f |
     | g g g |

             4       3
o4 : Matrix R  <--- R

i5 : maxColNum M

o5 = (| a b |, {0, 2})
      | c d |
      | e f |
      | g g |

o5 : Sequence