# leadTerm(RingElement) -- get the greatest term

## Synopsis

• Function: leadTerm
• Usage:
leadTerm f
• Inputs:
• f, , in a polynomial ring
• Outputs:
• , the lead term of f

## Description

Each polynomial ring comes equipped with a monomial ordering and this routine returns the lead (greatest) monomial and its coefficient. Recall that the default monomial order is the graded reverse lexicographic order.
 i1 : R = QQ[a..d]; i2 : leadTerm (3*b*c^2-d^3-1) 2 o2 = 3b*c o2 : R i3 : S = QQ[a..d, MonomialOrder => Lex] o3 = S o3 : PolynomialRing i4 : leadTerm (3*b*c^2-d^3-1) 2 o4 = 3b*c o4 : S
Coefficients are included in the result:
 i5 : R = ZZ[a..d][x,y,z]; i6 : leadTerm((a+b)*y^2 + (b+c)*x*z) 2 o6 = (a + b)y o6 : R