# maxMinors -- computes the ideal generated by the maximal non-vanishing minors of a given matrix

## Synopsis

• Usage:
maxMinors M
• Inputs:
• M, , with entries in a ring R.
• Outputs:
• an ideal, the ideal generated by maximal non-vanishing minors of the matrix M.

## Description

Let I_t(M) be the ideal in R generated by the t \times\ t minors of M. If there exists an r such that I_r(M) is non-zero and I_{r+1}(\phi) = 0, then maxMinors M gives I_r(M).

 i1 : R = QQ[x,y] o1 = R o1 : PolynomialRing i2 : M = matrix{{x,0},{-y,x},{0,-y}} o2 = | x 0 | | -y x | | 0 -y | 3 2 o2 : Matrix R <--- R i3 : maxMinors M 2 2 o3 = ideal (x , -x*y, y ) o3 : Ideal of R

This method returns the unit ideal as the ideal of maximal minors of the zero matrix.

 i4 : N = matrix{{0_R}} o4 = 0 1 1 o4 : Matrix R <--- R i5 : maxMinors N o5 = ideal 1 o5 : Ideal of R