randomMonomialSet(...,Strategy=>...) -- optional input to choose the strategy for generating the random monomial set

Description

Put Strategy => "ER" or Strategy => "Minimal" as an argument in the function randomMonomialSet, randomMonomialSets, or randomMonomialIdeals. "ER" draws random sets of monomials from the ER-type distribution $\mathcal B(n,D,p)$, while "Minimal" saves computation time by using quotient rings to exclude any non-minimal generators from the list. For randomMonomialSets with the number of generators of pre-specified degrees is the input, choosing Strategy => "Minimal" will result in larger minimal generating sets.

Further information

Default value: ER
Function: randomMonomialSet -- randomly generates a list of monomials in fixed number of variables up to a given degree
Option key: Strategy -- an optional argument

Functions with optional argument named Strategy:

addHook(...,Strategy=>...) -- see addHook -- add a hook function to an object for later processing
adjoint(...,Strategy=>...) (missing documentation)
annihilator(...,Strategy=>...) -- see annihilator -- the annihilator ideal
associatedPrimes(...,Strategy=>...) -- see associatedPrimes -- find associated primes
basis(...,Strategy=>...) -- see basis -- basis or generating set of all or part of a ring, ideal or module
canonicalBundle(...,Strategy=>...) (missing documentation)
mingens(...,Strategy=>...) -- see Complement -- a Strategy option value
trim(...,Strategy=>...) -- see Complement -- a Strategy option value
compose(Module,Module,Module,Strategy=>...) -- see compose -- composition as a pairing on Hom-modules
cotangentSheaf(...,Strategy=>...) (missing documentation)
determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
dual(ChainComplex,Strategy=>...) (missing documentation)
dual(Matrix,Strategy=>...) (missing documentation)
dual(MonomialIdeal,List,Strategy=>...) -- see dual(MonomialIdeal,Strategy=>...)
dual(MonomialIdeal,RingElement,Strategy=>...) -- see dual(MonomialIdeal,Strategy=>...)
dual(MonomialIdeal,Strategy=>...)
dual(SheafMap,Strategy=>...) (missing documentation)
End(...,Strategy=>...) -- see End -- module of endomorphisms
exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
gb(...,Strategy=>...) -- see gb -- compute a Gröbner basis
gcdLLL(...,Strategy=>...) (missing documentation)
GF(...,Strategy=>...) -- see GF -- make a finite field
groebnerBasis(...,Strategy=>...) -- see groebnerBasis -- Gröbner basis, as a matrix
hermite(...,Strategy=>...) (missing documentation)
Hom(...,Strategy=>...) -- see Hom -- module of homomorphisms
homomorphism'(...,Strategy=>...) -- see homomorphism' -- get the element of Hom from a homomorphism
hooks(...,Strategy=>...) -- see hooks -- list hooks attached to a key
idealizer(...,Strategy=>...) -- see idealizer -- compute Hom(I,I) as a quotient ring
integralClosure(...,Strategy=>...) -- control the algorithm used
intersect(Ideal,Ideal,Strategy=>...) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
intersect(Module,Module,Strategy=>...) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
intersectInP(...,Strategy=>...) -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
isPrimary(...,Strategy=>...) -- see isPrimary -- determine whether a submodule is primary
isPrime(Ideal,Strategy=>...) -- see isPrime(Ideal) -- whether an ideal is prime
LLL(...,Strategy=>...) -- choose among different algorithms
localize(...,Strategy=>...) -- see localize -- localize an ideal at a prime ideal
match(...,Strategy=>...) -- see match -- regular expression matching
decompose(Ideal,Strategy=>...) -- see minimalPrimes -- minimal primes of an ideal
minimalPrimes(...,Strategy=>...) -- see minimalPrimes -- minimal primes of an ideal
minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
parallelApply(...,Strategy=>...) -- see parallelApply -- apply a function to each element in parallel
primaryComponent(...,Strategy=>...) -- see primaryComponent -- find a primary component corresponding to an associated prime
pushForward(...,Strategy=>...) (missing documentation)
quotient(...,Strategy=>...)
radical(...,Strategy=>...) -- see radical -- the radical of an ideal
radicalContainment(...,Strategy=>...) -- see radicalContainment -- whether an element is contained in the radical of an ideal
randomMonomialIdeals(...,Strategy=>...)
randomMonomialSet(...,Strategy=>...) -- optional input to choose the strategy for generating the random monomial set
randomMonomialSets(...,Strategy=>...)
analyticSpread(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
associatedGradedRing(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
distinguished(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
isLinearType(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
isReduction(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
minimalReduction(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
multiplicity(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
normalCone(Ideal,RingElement,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
normalCone(Ideal,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
reesAlgebra(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
specialFiber(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
specialFiberIdeal(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
regSeqInIdeal(...,Strategy=>...) -- see regSeqInIdeal -- a regular sequence contained in an ideal
resolution(...,Strategy=>...)
saturate(...,Strategy=>...)
sheafHom(...,Strategy=>...) (missing documentation)
primaryDecomposition(...,Strategy=>...) -- see strategies for computing primary decomposition
syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix
tangentCone(...,Strategy=>...) -- see tangentCone(Ideal)
tangentSheaf(...,Strategy=>...) (missing documentation)