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leadCoefficient -- the coefficient of the leading term

Usage:

leadCoefficient f
Inputs:
- f, a ring element, a polynomial
Outputs:
- a ring element, an element of the coefficientRing of the ring of f

Description

The leading term is with respect to the monomial ordering in the ring. See monomial orderings for details.

i1 : R = ZZ/5[a,b,c]; f = a*b^2 + 3*b*c^3 + 2;

i3 : leadCoefficient f

o3 = -2

     ZZ
o3 : --
      5

i4 : S = ZZ/5[a,b,c, MonomialOrder => Lex]; g = a*b^2 +3*b*c^3 + 2;

i6 : leadCoefficient g

o6 = 1

     ZZ
o6 : --
      5

See also

coefficients -- get the monomials and coefficients of a polynomial or matrix
coefficientRing -- get the coefficient ring
leadComponent -- the leading component(s) of a vector or matrix
leadMonomial -- the leading monomial of a ring element
leadTerm -- get the greatest term
someTerms -- select some terms of a polynomial
terms -- provide a list of terms of a polynomial

Ways to use leadCoefficient:

leadCoefficient(RingElement)

For the programmer

The object leadCoefficient is a method function.

The source of this document is in Macaulay2Doc/functions/leadCoefficient-doc.m2:36:0.