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Macaulay2Doc :: borel(Matrix)

borel(Matrix) -- make a Borel fixed submodule

Synopsis

Description

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. If m is a monomial ideal, then the minimal Borel fixed monomial ideal containing it is returned.

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