isAcyclic -- Determines if a DGAlgebra is acyclic.

Synopsis

• Usage:

  isAcyc = isAcyclic(A)

• Inputs:
  • A, an instance of the type DGAlgebra
• Optional inputs:
  • EndDegree => ..., default value -1, Option to specify the degree to finish checking acyclicity
• Outputs:
  • isAcyc, a Boolean value

Description

i1 : R = ZZ/101[a,b,c,d]/ideal{a^4+b^4+c^4+d^4}

o1 = R

o1 : QuotientRing

i2 : isAcyclic(koszulComplexDGA R)

o2 = false

i3 : Q = ZZ/101[a,b,c,d]

o3 = Q

o3 : PolynomialRing

i4 : I = ideal {a^4,b^4,c^4,d^4}

             4   4   4   4
o4 = ideal (a , b , c , d )

o4 : Ideal of Q

i5 : isAcyclic(koszulComplexDGA I)

o5 = true