lcm(MonomialIdeal) -- least common multiple of all minimal generators

Synopsis

• Function: lcm

• Usage:

  m = lcm I

• Inputs:
  • I, a monomial ideal,
• Outputs:
  • m, a ring element,

Description

i1 : R = QQ[a..d];

i2 : I = monomialIdeal "a4,a3b6,a2b8c2,c4d5"

                     4   3 6   2 8 2   4 5
o2 = monomialIdeal (a , a b , a b c , c d )

o2 : MonomialIdeal of R

i3 : lcm I

      4 8 4 5
o3 = a b c d

o3 : R

i4 : first exponents lcm I

o4 = {4, 8, 4, 5}

o4 : List

See also

• dual(MonomialIdeal) -- the Alexander dual of a monomial ideal
• irreducibleDecomposition(MonomialIdeal) -- express a monomial ideal as an intersection of irreducible monomial ideals
• primaryDecomposition(Ideal) -- irredundant primary decomposition of an ideal