isPrimary -- determine whether a submodule is primary

Synopsis

• Usage:

  isPrimary Q

  isPrimary(Q, P)

  isPrimary(M, Q)

• Inputs:
  • Q, an ideal or a module, the submodule or ideal to be checked for being primary
  • P, an ideal, the radical of Q
  • M, a module, the ambient module
• Optional inputs:
  • Strategy => a thing, default value null, See associatedPrimes(...,Strategy=>...) and isPrime(Ideal, Strategy => ...) (missing documentation)
• Outputs:
  • a Boolean value, true if Q is primary, false otherwise

Description

i1 : Q = ZZ/101[x,y,z]

o1 = Q

o1 : PolynomialRing

i2 : isPrimary ideal(y^6)

o2 = true

i3 : isPrimary(ideal(y^6), ideal(y))

o3 = true

i4 : isPrimary ideal(x^4, y^7)

o4 = true

i5 : isPrimary ideal(x*y, y^2)

o5 = false

See also

• primaryDecomposition(Ideal) -- irredundant primary decomposition of an ideal
• primaryDecomposition(Module) -- irredundant primary decomposition of a module
• associatedPrimes -- find associated primes