multiplicity -- Compute the Hilbert-Samuel multiplicity of an ideal

Synopsis

• Usage:

  multiplicity I

  multiplicity(I,f)

• Inputs:
  • I, an ideal,
  • f, a ring element, optional argument, if given it should be a non-zero divisor in the ideal I
• Optional inputs:
  • BasisElementLimit => ..., default value infinity, Bound the number of Groebner basis elements to compute in the saturation step
  • DegreeLimit => ..., default value {}, Bound the degrees considered in the saturation step. Defaults to infinity
  • MinimalGenerators => ..., default value true, Whether the saturation step returns minimal generators
  • PairLimit => ..., default value infinity, Bound the number of s-pairs considered in the saturation step
  • Strategy => ..., default value null, Choose a strategy for the saturation step
  • Variable => ..., default value w, Option for intersectInP
• Outputs:
  • an integer, the normalized leading coefficient of the Hilbert-Samuel polynomial of $I$

Description

i1 : R=ZZ/101[x,y]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x^3, x^2*y, y^3)

             3   2    3
o2 = ideal (x , x y, y )

o2 : Ideal of R

i3 : multiplicity I

o3 = 9

i4 : degree I

o4 = 7

Caveat