borel

usage: borel m -- create a matrix of monomials

Yields the matrix with the same target as the matrix m, whose columns generate the smallest Borel fixed submodule containing the lead monomials of the columns of m.

For example, if R = ZZ/101[a..f], then

i1 : R = ZZ/101[a..e]

o1 = R

o1 : PolynomialRing
i2 : borel matrix {{a*d*e, b^2}}

o2 = {0} | a2 ab b2 ac2 acd ad2 ace ade |

             1       8
o2 : Matrix R  <--- R

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