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

## Synopsis

• Usage:
randomMonomialSets(ZZ,ZZ,RR,ZZ)
randomMonomialSets(PolynomialRing,ZZ,RR,ZZ)
randomMonomialSets(ZZ,ZZ,ZZ,ZZ)
randomMonomialSets(PolynomialRing,ZZ,ZZ,ZZ)
randomMonomialSets(ZZ,ZZ,List,ZZ)
randomMonomialSets(PolynomialRing,ZZ,List,ZZ)
• Inputs:
• n, an integer, number of variables, OR
• , the ring in which the monomials are to live if $n$ is not specified
• D, an integer, maximum degree
• p, , the probability of selecting a monomial, OR
• M, an integer, number of monomials in the set, up to the maximum number of monomials in $n$ variables of degree at most $D$ OR
• a list, of real numbers whose $i$-th entry is the probability of selecting a monomial of degree $i$, OR
• a list, of integers whose $i$-th entry is the number of monomials of degree $i$ in each set, up to the maximum number of monomials in $n$ variables of degree exactly $i$
• N, an integer, number of sets to be generated
• Optional inputs:
• Coefficients => ..., default value QQ, optional input to choose the coefficients of the ambient polynomial ring
• Strategy => ..., default value ER, optional input to choose the strategy for generating the random monomial set
• VariableName => ..., default value x, optional input to choose the indexed variable name for the polynomial ring
• Outputs:
• a list, random generating sets of monomials

## Description

This function creates $N$ random sets of monomials of degree $d$, $1\leq d\leq D$, in $n$ variables. It does so by calling randomMonomialSet $N$ times.

• randomMonomialSet -- randomly generates a list of monomials in fixed number of variables up to a given degree

## Ways to use randomMonomialSets :

• "randomMonomialSets(PolynomialRing,ZZ,List,ZZ)"
• "randomMonomialSets(PolynomialRing,ZZ,RR,ZZ)"
• "randomMonomialSets(PolynomialRing,ZZ,ZZ,ZZ)"
• "randomMonomialSets(ZZ,ZZ,List,ZZ)"
• "randomMonomialSets(ZZ,ZZ,RR,ZZ)"
• "randomMonomialSets(ZZ,ZZ,ZZ,ZZ)"

## For the programmer

The object randomMonomialSets is .