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
  • a polynomial ring, the ring in which the monomials are to live if $n$ is not specified
  • D, an integer, maximum degree
  • p, a real number, 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

See also

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