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# denominator -- denominator of a fraction

## Synopsis

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

## Description

 i1 : denominator (4/6) o1 = 3

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

denominator 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 : denominator hf 4 o6 = (1 - T) o6 : Expression of class Product

For a Laurent polynomial in a ring with inverses of variables, it gives the monomial needed to clear all the denominators in each of the terms.

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

## Ways to use denominator :

• "denominator(Divide)"

## For the programmer

The object denominator is .