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

- Function: ER
- Usage:
    `ER(PolynomialRing,ZZ,List)`
- Inputs:
  - R, a polynomial ring, 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 => FunctionClosure[../RandomMonomialIdeals.m2:184:20-184:51]}
               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 => FunctionClosure[../RandomMonomialIdeals.m2:184:20-184:51]}
               Name => Erdos-Renyi
                               ZZ
               Parameters => (---[a..d], 4, {1, 2, 2, 1})
                              101

    o6 : Model

## See also

- randomMonomialSets -- randomly generates lists of monomials in fixed number of variables up to a given degree

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomMonomialIdeals.m2:2070:0.