sortColumns -- permutation giving sort order

Synopsis

Usage:

sortColumns m
Inputs:
- m, between free modules
Optional inputs:
- DegreeOrder => ..., default value null, specify Ascending, Descending, or null
- MonomialOrder => ..., default value Ascending, specify Ascending or Descending monomial order
Outputs:
- a list, of integers, representing the order which places the columns in order

See sort(Matrix) for the ordering used. The meanings of the optional parameters is also the same.

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 : p = sortColumns m

o3 = {4, 1, 3, 2, 0}

o3 : List

i4 : m_p

o4 = | c2d b2 b50d50 b100 ad |

             1       5
o4 : Matrix R  <--- R

i5 : p = sortColumns(m, DegreeOrder=>null, MonomialOrder=>Descending)

o5 = {0, 2, 3, 1, 4}

o5 : List

i6 : m_p

o6 = | ad b100 b50d50 b2 c2d |

             1       5
o6 : Matrix R  <--- R

i7 : R = ZZ/101[a..c];

i8 : f = matrix{{1,a,a^2,b^2,b,c,c^2,a*b,b*c,a*c}}

o8 = | 1 a a2 b2 b c c2 ab bc ac |

             1       10
o8 : Matrix R  <--- R

i9 : s = sortColumns f

o9 = {0, 5, 4, 1, 6, 8, 9, 3, 7, 2}

o9 : List

i10 : f_s

o10 = | 1 c b a c2 bc ac b2 ab a2 |

              1       10
o10 : Matrix R  <--- R

i11 : s = sortColumns(f,DegreeOrder => Descending)

o11 = {6, 8, 9, 3, 7, 2, 5, 4, 1, 0}

o11 : List

i12 : f_s

o12 = | c2 bc ac b2 ab a2 c b a 1 |

              1       10
o12 : Matrix R  <--- R