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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[${prefix}/share/Macaulay2/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[${prefix}/share/Macaulay2/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 RandomMonomialIdeals.m2:2070:0.