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# numerator -- numerator of a fraction

## Synopsis

• Usage:
numerator x
• Inputs:
• x, a fraction
• Outputs:
• the numerator of x

## Description

 i1 : numerator (4/6) o1 = 2

 i2 : R = frac(ZZ[x,y]); i3 : numerator((x+2*y-3)/(x-y)) o3 = x + 2y - 3 o3 : ZZ[x..y]

numerator also works with Hilbert series.
 i4 : R = QQ[a..d]/(a^2,b^2,c^3); i5 : hf = hilbertSeries R 2 3 4 5 7 1 - 2T - T + T + 2T - T o5 = ---------------------------- 4 (1 - T) o5 : Expression of class Divide i6 : numerator hf 2 3 4 5 7 o6 = 1 - 2T - T + T + 2T - T o6 : ZZ[T]

For a Laurent polynomial in a ring with inverses of variables, it gives the result after clearing all the denominators in each of the terms by multiplying by a suitable monomial.

 i7 : R = QQ[x,y,z,Inverses => true, MonomialOrder => Lex] o7 = R o7 : PolynomialRing i8 : numerator (x*y^-1+y*z^-2+1+y^-1*z^-1) 2 2 2 o8 = x*z + y + y*z + z o8 : R

## Ways to use numerator :

• numerator(Divide)

## For the programmer

The object numerator is .