# leadTerm(ZZ,RingElement) -- get the lead polynomials using part of the monomial order

## Synopsis

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

## Description

Returns the sum of the terms of f which are greatest using the first n parts of the monomial order in the ring of f.

In the following example, the lead terms using the first part refers to all the monomials that have the lead monomial in the indeterminates a and b. This has a effect similar to selecting leadTerm in the ring QQ[c,d][a,b].

 i1 : R = QQ[a..d, MonomialOrder => ProductOrder{2,2}]; i2 : leadTerm(1, (c+d)*a^3 - c^100*a - 1) 3 3 o2 = a c + a d o2 : R