randomSparseIdeal -- randomSparseIdeal made from a given set of monomials

Synopsis

• Usage:

  I = randomSparseIdeal(B,s,n)

• Inputs:
  • B, a matrix, 1xn matrix of monomials
  • s, an integer, positive integer, the number of terms in the generators of I
  • n, an integer, positive integer, the number of generators of I
• Outputs:
  • I, an ideal, generated by n polynomials, each a random linear combination of s monomials

Description

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing

i2 : S=kk[a..e]

o2 = S

o2 : PolynomialRing

i3 : L={3,3,4,6}

o3 = {3, 3, 4, 6}

o3 : List

i4 : B = matrix{{a^3,b^4,d^5,a*b*c,e}}

o4 = | a3 b4 d5 abc e |

             1       5
o4 : Matrix S  <--- S

i5 : I=randomSparseIdeal(B,3,2)

             3             4
o5 = ideal (a  + 35a*b*c, b  - 32a*b*c + 5e)

o5 : Ideal of S

See also

• randomIdeal -- randomIdeal made from a given set of monomials
• randomMonomialIdeal -- random monomial ideal with given degree generators
• randomSquareFreeMonomialIdeal -- random square-free monomial ideal with given degree generators
• randomMonomial -- Choose a random monomial of given degree in a given ring
• randomBinomialIdeal -- randomBinomialIdeal with binomials of given degrees
• randomPureBinomialIdeal -- randomPureBinomialIdeal with binomials of given degrees
• randomElementsFromIdeal -- Chooses random elements of given degrees in a given ideal.