# ER(PolynomialRing,ZZ,List) -- Graded Erdos-Renyi type distribution on monomials over (R,D,L)

## Synopsis

• Function: ER
• Usage:
ER(PolynomialRing,ZZ,List)
• Inputs:
• R, , the ring in which monomials are chosen from
• D, an integer, maximum degree
• L, a list, of real numbers whose i-th entry is the probability of selecting a monomial of degree i, or of integers whose i-th entry is the number of monomials of degree i in each set
• Outputs:
• an instance of the type Model, Erdos-Renyi type model

## Description

Creates a graded ER-type model for sampling monomials of degree at most $D$ from the ring $R$.

 i1 : D1=4; L1={0.1,0.2,0.3,0.4}; i3 : D2=4; L2={1,2,2,1}; i5 : myModel1 = ER(ZZ/101[a..d],D1,L1) o5 = Model{Generate => -*Function[/usr/share/Macaulay2/RandomMonomialIdeals.m2:185:23-185:47]*-} Name => Erdos-Renyi ZZ Parameters => (---[a..d], 4, {.1, .2, .3, .4}) 101 o5 : Model i6 : myModel2 = ER(ZZ/101[a..d],D2,L2) o6 = Model{Generate => -*Function[/usr/share/Macaulay2/RandomMonomialIdeals.m2:185:23-185:47]*-} Name => Erdos-Renyi ZZ Parameters => (---[a..d], 4, {1, 2, 2, 1}) 101 o6 : Model