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

## Synopsis

• Function: ER
• Usage:
ER(ZZ,ZZ,List)
• Inputs:
• n, an integer, number of variables
• 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 in $n$ variables of degree at most $D$.

 i1 : n1=3; D1=4; L1={0.1,0.2,0.3,0.4}; i4 : n2=3; D2=4; L2={1,2,2,1}; i7 : myModel1 = ER(n1,D1,L1) o7 = Model{Generate => -*Function[/usr/share/Macaulay2/RandomMonomialIdeals.m2:172:23-172:47]*-} Name => Erdos-Renyi Parameters => (3, 4, {.1, .2, .3, .4}) o7 : Model i8 : myModel2 = ER(n2,D2,L2) o8 = Model{Generate => -*Function[/usr/share/Macaulay2/RandomMonomialIdeals.m2:172:23-172:47]*-} Name => Erdos-Renyi Parameters => (3, 4, {1, 2, 2, 1}) o8 : Model