The default monomial order is to sort the columns in ascending degree first, and within each degree, sort in ascending monomial order in the target free module.
i1 : R = ZZ/32003[a..d,MonomialOrder=>Lex];
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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
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i3 : sort m
o3 = | b2 ad c2d b50d50 b100 |
1 5
o3 : Matrix R <--- R
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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 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 => Ascending }
MonomialOrder => Ascending
o4 : OptionTable
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i5 : sort(m, DegreeOrder=>null, MonomialOrder=>Descending)
o5 = | ad b100 b50d50 b2 c2d |
1 5
o5 : Matrix R <--- R
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