borel -- make a Borel fixed submodule

borel -- make a Borel fixed submodule

borel m -- make a Borel fixed submodule

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 = | a2 ab b2 ac2 acd ad2 ace ade |



             1       8

o2 : Matrix R  <--- R

Ways to use borel :

borel Matrix

borel MonomialIdeal