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sort(Matrix) -- sort the columns of a matrix



The default order is to sort the columns in ascending degree first, and within each degree, first compare ring elements in the highest non-zero component, breaking ties by going to the next lower component. Zero is considered earlier in the order than other elements
i1 : R = ZZ/32003[a..d,MonomialOrder=>Lex];
i2 : m = matrix{{a*d, b^2, b^100, b^50*d^50, c^2*d}}

o2 = | ad b2 b100 b50d50 c2d |

             1       5
o2 : Matrix R  <--- R
i3 : sort m

o3 = | c2d b2 b50d50 b100 ad |

             1       5
o3 : Matrix R  <--- R

The two optional arguments can modify this default order. The value of DegreeOrder is considered first (Ascending, Descending, or null), and after that the monomial (or ring) order is used to break ties, either ascending or descending, depending on the value of MonomialOrder.

To sort the columns of m in descending monomial order:
i4 : options sort

o4 = OptionTable{DegreeOrder => null       }
                 MonomialOrder => Ascending

o4 : OptionTable
i5 : sort(m, DegreeOrder=>null, MonomialOrder=>Descending)

o5 = | ad b100 b50d50 b2 c2d |

             1       5
o5 : Matrix R  <--- R

See also

Ways to use this method: