# leadTerm(ZZ,Matrix) -- get the matrix of lead polynomials of each column

## Synopsis

• Usage:
leadTerm(n,f)
• Inputs:
• n, an integer
• f, , in a polynomial ring
• Outputs:
• , the lead term matrix of f using the first n parts of the monomial order

## Description

Returns the matrix whose i-th column is the lead term of the i-th column of f, using the first n parts of the monomial order.
 i1 : R = QQ[x,y,z,a..d,MonomialOrder=>ProductOrder{3,4}]; i2 : f = matrix{{0,x^2*(a+b)}, {a*x+2*b*y, y^2*(c+d)}} o2 = | 0 x2a+x2b | | xa+2yb y2c+y2d | 2 2 o2 : Matrix R <--- R i3 : leadTerm(1,f) o3 = | 0 x2a+x2b | | xa 0 | 2 2 o3 : Matrix R <--- R